TSTP Solution File: GEO265+3 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO265+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n029.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 15:18:51 EDT 2022
% Result : Theorem 1.18s 0.57s
% Output : Proof 1.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO265+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n029.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 07:23:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.33 [DMT] DMT loaded with preskolemization
% 0.18/0.33 [EQ] equality loaded.
% 0.18/0.33 [0.000036s][1][MAIN] Problem : theBenchmark.p
% 0.18/0.34 Conjecture not found
% 0.18/0.34 Start search
% 0.18/0.34 nb_step : 1 - limit : 37
% 0.18/0.34 Launch Gotab with destructive = true
% 0.18/0.57 % SZS output start Proof for theBenchmark.p
% 1.18/0.57 [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, M90_90] : ((equally_directed_lines(L89_89, reverse_line(M90_90)) => equally_directed_opposite_lines(L89_89, M90_90))))
% 1.18/0.57 -> [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, M90_90] : ((equally_directed_lines(L89_89, reverse_line(M90_90)) => equally_directed_opposite_lines(L89_89, M90_90)))
% 1.18/0.57
% 1.18/0.57 [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)))))
% 1.18/0.57 -> [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))))
% 1.18/0.57
% 1.18/0.57 [2] DELTA_NOT_FORALL : ~! [L89_89, M90_90] : ((equally_directed_lines(L89_89, reverse_line(M90_90)) => equally_directed_opposite_lines(L89_89, M90_90)))
% 1.18/0.57 -> [3] ~(equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)) => equally_directed_opposite_lines(skolem_L8989, skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [3] ALPHA_NOT_IMPLY : ~(equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)) => equally_directed_opposite_lines(skolem_L8989, skolem_M9090))
% 1.18/0.57 -> [4] equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)), ~equally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57
% 1.18/0.57 [4] GAMMA_FORALL : ! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9))))
% 1.18/0.57 -> [5] (unequally_directed_opposite_lines(skolem_L8989, skolem_M9090) <=> unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)))
% 1.18/0.57
% 1.18/0.57 [5] BETA_EQUIV : (unequally_directed_opposite_lines(skolem_L8989, skolem_M9090) <=> unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)))
% 1.18/0.57 -> [6] ~unequally_directed_opposite_lines(skolem_L8989, skolem_M9090), ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57 -> [7] unequally_directed_opposite_lines(skolem_L8989, skolem_M9090), unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [7] GAMMA_FORALL : ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11))))
% 1.18/0.57 -> [9] (right_apart_point(X10_1_1, Y11_1_1) <=> left_apart_point(X10_1_1, reverse_line(Y11_1_1)))
% 1.18/0.57
% 1.18/0.57 [9] BETA_EQUIV : (right_apart_point(X10_1_1, Y11_1_1) <=> left_apart_point(X10_1_1, reverse_line(Y11_1_1)))
% 1.18/0.57 -> [12] ~right_apart_point(X10_1_1, Y11_1_1), ~left_apart_point(X10_1_1, reverse_line(Y11_1_1))
% 1.18/0.57 -> [13] right_apart_point(X10_1_1, Y11_1_1), left_apart_point(X10_1_1, reverse_line(Y11_1_1))
% 1.18/0.57
% 1.18/0.57 [13] GAMMA_FORALL : ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13))))
% 1.18/0.57 -> [21] (right_convergent_lines(X12_3_2, Y13_3_2) <=> left_convergent_lines(X12_3_2, reverse_line(Y13_3_2)))
% 1.18/0.57
% 1.18/0.57 [21] BETA_EQUIV : (right_convergent_lines(X12_3_2, Y13_3_2) <=> left_convergent_lines(X12_3_2, reverse_line(Y13_3_2)))
% 1.18/0.57 -> [24] ~right_convergent_lines(X12_3_2, Y13_3_2), ~left_convergent_lines(X12_3_2, reverse_line(Y13_3_2))
% 1.18/0.57 -> [25] right_convergent_lines(X12_3_2, Y13_3_2), left_convergent_lines(X12_3_2, reverse_line(Y13_3_2))
% 1.18/0.57
% 1.18/0.57 [25] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 1.18/0.57 -> [45] (equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)) <=> ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)))
% 1.18/0.57
% 1.18/0.57 [45] BETA_EQUIV : (equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)) <=> ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)))
% 1.18/0.57 -> [50] ~equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)), ~~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57 -> [51] equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)), ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [50] ALPHA_NOT_NOT : ~~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57 -> [64] unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [64] CLOSURE : ~~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [51] CLOSURE : ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [24] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 1.18/0.57 -> [40] (equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)) <=> ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)))
% 1.18/0.57
% 1.18/0.57 [40] BETA_EQUIV : (equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)) <=> ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)))
% 1.18/0.57 -> [46] ~equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)), ~~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57 -> [47] equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)), ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [46] ALPHA_NOT_NOT : ~~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57 -> [61] unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [61] CLOSURE : ~~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [47] CLOSURE : ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [12] GAMMA_FORALL : ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13))))
% 1.18/0.57 -> [18] (right_convergent_lines(X12_2_2, Y13_2_2) <=> left_convergent_lines(X12_2_2, reverse_line(Y13_2_2)))
% 1.18/0.57
% 1.18/0.57 [18] BETA_EQUIV : (right_convergent_lines(X12_2_2, Y13_2_2) <=> left_convergent_lines(X12_2_2, reverse_line(Y13_2_2)))
% 1.18/0.57 -> [22] ~right_convergent_lines(X12_2_2, Y13_2_2), ~left_convergent_lines(X12_2_2, reverse_line(Y13_2_2))
% 1.18/0.57 -> [23] right_convergent_lines(X12_2_2, Y13_2_2), left_convergent_lines(X12_2_2, reverse_line(Y13_2_2))
% 1.18/0.57
% 1.18/0.57 [23] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 1.18/0.57 -> [36] (equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)) <=> ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)))
% 1.18/0.57
% 1.18/0.57 [36] BETA_EQUIV : (equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)) <=> ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)))
% 1.18/0.57 -> [43] ~equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)), ~~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57 -> [44] equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)), ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [43] ALPHA_NOT_NOT : ~~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57 -> [63] unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [63] CLOSURE : ~~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [44] CLOSURE : ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [22] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 1.18/0.57 -> [37] (equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)) <=> ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)))
% 1.18/0.57
% 1.18/0.57 [37] BETA_EQUIV : (equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)) <=> ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)))
% 1.18/0.57 -> [48] ~equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)), ~~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57 -> [49] equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)), ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [48] ALPHA_NOT_NOT : ~~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57 -> [56] unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [56] CLOSURE : ~~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [49] CLOSURE : ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [6] GAMMA_FORALL : ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11))))
% 1.18/0.57 -> [8] (right_apart_point(X10_0_1, Y11_0_1) <=> left_apart_point(X10_0_1, reverse_line(Y11_0_1)))
% 1.18/0.57
% 1.18/0.57 [8] BETA_EQUIV : (right_apart_point(X10_0_1, Y11_0_1) <=> left_apart_point(X10_0_1, reverse_line(Y11_0_1)))
% 1.18/0.57 -> [10] ~right_apart_point(X10_0_1, Y11_0_1), ~left_apart_point(X10_0_1, reverse_line(Y11_0_1))
% 1.18/0.57 -> [11] right_apart_point(X10_0_1, Y11_0_1), left_apart_point(X10_0_1, reverse_line(Y11_0_1))
% 1.18/0.57
% 1.18/0.57 [10] GAMMA_FORALL : ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13))))
% 1.18/0.57 -> [14] (right_convergent_lines(X12_0_2, Y13_0_2) <=> left_convergent_lines(X12_0_2, reverse_line(Y13_0_2)))
% 1.18/0.57
% 1.18/0.57 [14] BETA_EQUIV : (right_convergent_lines(X12_0_2, Y13_0_2) <=> left_convergent_lines(X12_0_2, reverse_line(Y13_0_2)))
% 1.18/0.57 -> [15] ~right_convergent_lines(X12_0_2, Y13_0_2), ~left_convergent_lines(X12_0_2, reverse_line(Y13_0_2))
% 1.18/0.57 -> [16] right_convergent_lines(X12_0_2, Y13_0_2), left_convergent_lines(X12_0_2, reverse_line(Y13_0_2))
% 1.18/0.57
% 1.18/0.57 [15] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 1.18/0.57 -> [26] (equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)) <=> ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)))
% 1.18/0.57
% 1.18/0.57 [26] BETA_EQUIV : (equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)) <=> ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)))
% 1.18/0.57 -> [27] ~equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)), ~~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57 -> [28] equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)), ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [27] ALPHA_NOT_NOT : ~~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57 -> [32] unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [32] CLOSURE : unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [53] BETA_EQUIV : (equally_directed_opposite_lines(skolem_L8989, skolem_M9090) <=> ~unequally_directed_opposite_lines(skolem_L8989, skolem_M9090))
% 1.18/0.57 -> [74] ~equally_directed_opposite_lines(skolem_L8989, skolem_M9090), ~~unequally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57 -> [75] equally_directed_opposite_lines(skolem_L8989, skolem_M9090), ~unequally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57
% 1.18/0.57 [74] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57 -> [76] unequally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57
% 1.18/0.57 [76] CLOSURE : unequally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57
% 1.18/0.57 [75] CLOSURE : equally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57
% 1.18/0.57 [16] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 1.18/0.57 -> [29] (equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)) <=> ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)))
% 1.18/0.57
% 1.18/0.57 [29] BETA_EQUIV : (equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)) <=> ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)))
% 1.18/0.57 -> [30] ~equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)), ~~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57 -> [31] equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)), ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [30] ALPHA_NOT_NOT : ~~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57 -> [33] unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [33] CLOSURE : unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [52] BETA_EQUIV : (equally_directed_opposite_lines(skolem_L8989, skolem_M9090) <=> ~unequally_directed_opposite_lines(skolem_L8989, skolem_M9090))
% 1.18/0.57 -> [77] ~equally_directed_opposite_lines(skolem_L8989, skolem_M9090), ~~unequally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57 -> [78] equally_directed_opposite_lines(skolem_L8989, skolem_M9090), ~unequally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57
% 1.18/0.57 [77] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57 -> [81] unequally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57
% 1.18/0.57 [81] CLOSURE : unequally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57
% 1.18/0.57 [78] CLOSURE : equally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57
% 1.18/0.57 [11] GAMMA_FORALL : ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13))))
% 1.18/0.57 -> [17] (right_convergent_lines(X12_1_2, Y13_1_2) <=> left_convergent_lines(X12_1_2, reverse_line(Y13_1_2)))
% 1.18/0.57
% 1.18/0.57 [17] BETA_EQUIV : (right_convergent_lines(X12_1_2, Y13_1_2) <=> left_convergent_lines(X12_1_2, reverse_line(Y13_1_2)))
% 1.18/0.57 -> [19] ~right_convergent_lines(X12_1_2, Y13_1_2), ~left_convergent_lines(X12_1_2, reverse_line(Y13_1_2))
% 1.18/0.57 -> [20] right_convergent_lines(X12_1_2, Y13_1_2), left_convergent_lines(X12_1_2, reverse_line(Y13_1_2))
% 1.18/0.57
% 1.18/0.57 [20] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 1.18/0.57 -> [35] (equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)) <=> ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)))
% 1.18/0.57
% 1.18/0.57 [35] BETA_EQUIV : (equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)) <=> ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)))
% 1.18/0.57 -> [41] ~equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)), ~~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57 -> [42] equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)), ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [41] ALPHA_NOT_NOT : ~~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57 -> [60] unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [60] CLOSURE : unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [65] BETA_EQUIV : (equally_directed_opposite_lines(skolem_L8989, skolem_M9090) <=> ~unequally_directed_opposite_lines(skolem_L8989, skolem_M9090))
% 1.18/0.57 -> [79] ~equally_directed_opposite_lines(skolem_L8989, skolem_M9090), ~~unequally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57 -> [80] equally_directed_opposite_lines(skolem_L8989, skolem_M9090), ~unequally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57
% 1.18/0.57 [80] CLOSURE : equally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57
% 1.18/0.57 [84] CLOSURE : unequally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57
% 1.18/0.57 [19] GAMMA_FORALL : ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15)))
% 1.18/0.57 -> [34] (equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)) <=> ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)))
% 1.18/0.57
% 1.18/0.57 [34] BETA_EQUIV : (equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)) <=> ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)))
% 1.18/0.57 -> [38] ~equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)), ~~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57 -> [39] equally_directed_lines(skolem_L8989, reverse_line(skolem_M9090)), ~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [38] ALPHA_NOT_NOT : ~~unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57 -> [59] unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [59] CLOSURE : unequally_directed_lines(skolem_L8989, reverse_line(skolem_M9090))
% 1.18/0.57
% 1.18/0.57 [66] BETA_EQUIV : (equally_directed_opposite_lines(skolem_L8989, skolem_M9090) <=> ~unequally_directed_opposite_lines(skolem_L8989, skolem_M9090))
% 1.18/0.57 -> [82] ~equally_directed_opposite_lines(skolem_L8989, skolem_M9090), ~~unequally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57 -> [83] equally_directed_opposite_lines(skolem_L8989, skolem_M9090), ~unequally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57
% 1.18/0.57 [82] ALPHA_NOT_NOT : ~~unequally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57 -> [85] unequally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57
% 1.18/0.57 [85] CLOSURE : unequally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57
% 1.18/0.57 [83] CLOSURE : equally_directed_opposite_lines(skolem_L8989, skolem_M9090)
% 1.18/0.57
% 1.18/0.57 % SZS output end Proof for theBenchmark.p
% 1.18/0.57 [0.238867s][1][Res] 1507 goroutines created
% 1.18/0.57 ==== Result ====
% 1.18/0.57 [0.238890s][1][Res] VALID
% 1.18/0.57 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------