TSTP Solution File: GEO243+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO243+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n026.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 15:18:40 EDT 2022
% Result : Theorem 2.73s 1.04s
% Output : Proof 2.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GEO243+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.10/0.12 % Command : goeland -dmt -presko -proof %s
% 0.13/0.31 % Computer : n026.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Wed Aug 31 07:23:36 EDT 2022
% 0.13/0.31 % CPUTime :
% 0.17/0.32 [DMT] DMT loaded with preskolemization
% 0.17/0.32 [EQ] equality loaded.
% 0.17/0.32 [0.000051s][1][MAIN] Problem : theBenchmark.p
% 0.17/0.33 Conjecture not found
% 0.17/0.33 Start search
% 0.17/0.33 nb_step : 1 - limit : 32
% 0.17/0.33 Launch Gotab with destructive = true
% 2.73/1.03 % SZS output start Proof for theBenchmark.p
% 2.73/1.04 [0] ALPHA_AND : ((! [A20_20] : (~distinct_points(A20_20, A20_20)) & ! [A21_21, B22_22, C23_23] : ((distinct_points(A21_21, B22_22) => (distinct_points(A21_21, C23_23) | distinct_points(B22_22, C23_23)))) & ! [L24_24] : (~distinct_lines(L24_24, L24_24)) & ! [L25_25, M26_26, N27_27] : ((distinct_lines(L25_25, M26_26) => (distinct_lines(L25_25, N27_27) | distinct_lines(M26_26, N27_27)))) & ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28)) & ! [L29_29, M30_30, N31_31] : ((unequally_directed_lines(L29_29, M30_30) => (unequally_directed_lines(L29_29, N31_31) | unequally_directed_lines(M30_30, N31_31)))) & ! [L32_32, M33_33, N34_34] : (((unequally_directed_lines(L32_32, M33_33) & unequally_directed_lines(L32_32, reverse_line(M33_33))) => ((unequally_directed_lines(L32_32, N34_34) & unequally_directed_lines(L32_32, reverse_line(N34_34))) | (unequally_directed_lines(M33_33, N34_34) & unequally_directed_lines(M33_33, reverse_line(N34_34)))))) & ! [L35_35, M36_36] : (((line(L35_35) & line(M36_36)) => (unequally_directed_lines(L35_35, M36_36) | unequally_directed_lines(L35_35, reverse_line(M36_36))))) & ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38))))) & ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40)))) & ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42)))) & ! [A43_43, B44_44] : ((((point(A43_43) & point(B44_44)) & distinct_points(A43_43, B44_44)) => line(line_connecting(A43_43, B44_44)))) & ! [L45_45, M46_46] : (((((line(L45_45) & line(M46_46)) & unequally_directed_lines(L45_45, M46_46)) & unequally_directed_lines(L45_45, reverse_line(M46_46))) => point(intersection_point(L45_45, M46_46)))) & ! [L47_47, A48_48] : (((point(A48_48) & line(L47_47)) => line(parallel_through_point(L47_47, A48_48)))) & ! [L49_49] : ((line(L49_49) => line(reverse_line(L49_49)))) & ! [A50_50, B51_51] : ((distinct_points(A50_50, B51_51) => (~apart_point_and_line(A50_50, line_connecting(A50_50, B51_51)) & ~apart_point_and_line(B51_51, line_connecting(A50_50, B51_51))))) & ! [L52_52, M53_53] : (((unequally_directed_lines(L52_52, M53_53) & unequally_directed_lines(L52_52, reverse_line(M53_53))) => (~apart_point_and_line(intersection_point(L52_52, M53_53), L52_52) & ~apart_point_and_line(intersection_point(L52_52, M53_53), M53_53)))) & ! [A54_54, L55_55] : (~apart_point_and_line(A54_54, parallel_through_point(L55_55, A54_54))) & ! [L56_56] : (~distinct_lines(L56_56, reverse_line(L56_56))) & ! [A57_57, B58_58] : (~unequally_directed_lines(line_connecting(A57_57, B58_58), reverse_line(line_connecting(B58_58, A57_57)))) & ! [A59_59, L60_60] : (~unequally_directed_lines(parallel_through_point(L60_60, A59_59), L60_60)) & ! [A61_61, B62_62, L63_63, M64_64] : (((distinct_points(A61_61, B62_62) & distinct_lines(L63_63, M64_64)) => (((((((left_apart_point(A61_61, L63_63) | left_apart_point(B62_62, L63_63)) | left_apart_point(A61_61, M64_64)) | left_apart_point(B62_62, M64_64)) | left_apart_point(A61_61, reverse_line(L63_63))) | left_apart_point(B62_62, reverse_line(L63_63))) | left_apart_point(A61_61, reverse_line(M64_64))) | left_apart_point(B62_62, reverse_line(M64_64))))) & ! [A65_65, B66_66, L67_67] : (((distinct_points(A65_65, B66_66) & left_apart_point(A65_65, L67_67)) => (left_apart_point(B66_66, L67_67) | left_convergent_lines(line_connecting(A65_65, B66_66), L67_67)))) & ! [A68_68, B69_69, L70_70] : ((left_apart_point(A68_68, L70_70) => (distinct_points(A68_68, B69_69) | left_apart_point(B69_69, L70_70)))) & ! [A71_71, L72_72, M73_73] : (((left_apart_point(A71_71, L72_72) & unequally_directed_lines(L72_72, M73_73)) => (distinct_lines(L72_72, M73_73) | left_apart_point(A71_71, reverse_line(M73_73))))) & ! [L74_74, M75_75, N76_76] : ((left_convergent_lines(L74_74, M75_75) => (unequally_directed_lines(M75_75, N76_76) | left_convergent_lines(L74_74, N76_76))))) & ~! [A77_77, B78_78, C79_79] : ((distinct_points(A77_77, B78_78) => (left_apart_point(C79_79, line_connecting(A77_77, B78_78)) => left_apart_point(C79_79, reverse_line(line_connecting(B78_78, A77_77)))))))
% 2.73/1.04 -> [1] (! [A20_20] : (~distinct_points(A20_20, A20_20)) & ! [A21_21, B22_22, C23_23] : ((distinct_points(A21_21, B22_22) => (distinct_points(A21_21, C23_23) | distinct_points(B22_22, C23_23)))) & ! [L24_24] : (~distinct_lines(L24_24, L24_24)) & ! [L25_25, M26_26, N27_27] : ((distinct_lines(L25_25, M26_26) => (distinct_lines(L25_25, N27_27) | distinct_lines(M26_26, N27_27)))) & ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28)) & ! [L29_29, M30_30, N31_31] : ((unequally_directed_lines(L29_29, M30_30) => (unequally_directed_lines(L29_29, N31_31) | unequally_directed_lines(M30_30, N31_31)))) & ! [L32_32, M33_33, N34_34] : (((unequally_directed_lines(L32_32, M33_33) & unequally_directed_lines(L32_32, reverse_line(M33_33))) => ((unequally_directed_lines(L32_32, N34_34) & unequally_directed_lines(L32_32, reverse_line(N34_34))) | (unequally_directed_lines(M33_33, N34_34) & unequally_directed_lines(M33_33, reverse_line(N34_34)))))) & ! [L35_35, M36_36] : (((line(L35_35) & line(M36_36)) => (unequally_directed_lines(L35_35, M36_36) | unequally_directed_lines(L35_35, reverse_line(M36_36))))) & ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38))))) & ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40)))) & ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42)))) & ! [A43_43, B44_44] : ((((point(A43_43) & point(B44_44)) & distinct_points(A43_43, B44_44)) => line(line_connecting(A43_43, B44_44)))) & ! [L45_45, M46_46] : (((((line(L45_45) & line(M46_46)) & unequally_directed_lines(L45_45, M46_46)) & unequally_directed_lines(L45_45, reverse_line(M46_46))) => point(intersection_point(L45_45, M46_46)))) & ! [L47_47, A48_48] : (((point(A48_48) & line(L47_47)) => line(parallel_through_point(L47_47, A48_48)))) & ! [L49_49] : ((line(L49_49) => line(reverse_line(L49_49)))) & ! [A50_50, B51_51] : ((distinct_points(A50_50, B51_51) => (~apart_point_and_line(A50_50, line_connecting(A50_50, B51_51)) & ~apart_point_and_line(B51_51, line_connecting(A50_50, B51_51))))) & ! [L52_52, M53_53] : (((unequally_directed_lines(L52_52, M53_53) & unequally_directed_lines(L52_52, reverse_line(M53_53))) => (~apart_point_and_line(intersection_point(L52_52, M53_53), L52_52) & ~apart_point_and_line(intersection_point(L52_52, M53_53), M53_53)))) & ! [A54_54, L55_55] : (~apart_point_and_line(A54_54, parallel_through_point(L55_55, A54_54))) & ! [L56_56] : (~distinct_lines(L56_56, reverse_line(L56_56))) & ! [A57_57, B58_58] : (~unequally_directed_lines(line_connecting(A57_57, B58_58), reverse_line(line_connecting(B58_58, A57_57)))) & ! [A59_59, L60_60] : (~unequally_directed_lines(parallel_through_point(L60_60, A59_59), L60_60)) & ! [A61_61, B62_62, L63_63, M64_64] : (((distinct_points(A61_61, B62_62) & distinct_lines(L63_63, M64_64)) => (((((((left_apart_point(A61_61, L63_63) | left_apart_point(B62_62, L63_63)) | left_apart_point(A61_61, M64_64)) | left_apart_point(B62_62, M64_64)) | left_apart_point(A61_61, reverse_line(L63_63))) | left_apart_point(B62_62, reverse_line(L63_63))) | left_apart_point(A61_61, reverse_line(M64_64))) | left_apart_point(B62_62, reverse_line(M64_64))))) & ! [A65_65, B66_66, L67_67] : (((distinct_points(A65_65, B66_66) & left_apart_point(A65_65, L67_67)) => (left_apart_point(B66_66, L67_67) | left_convergent_lines(line_connecting(A65_65, B66_66), L67_67)))) & ! [A68_68, B69_69, L70_70] : ((left_apart_point(A68_68, L70_70) => (distinct_points(A68_68, B69_69) | left_apart_point(B69_69, L70_70)))) & ! [A71_71, L72_72, M73_73] : (((left_apart_point(A71_71, L72_72) & unequally_directed_lines(L72_72, M73_73)) => (distinct_lines(L72_72, M73_73) | left_apart_point(A71_71, reverse_line(M73_73))))) & ! [L74_74, M75_75, N76_76] : ((left_convergent_lines(L74_74, M75_75) => (unequally_directed_lines(M75_75, N76_76) | left_convergent_lines(L74_74, N76_76))))), ~! [A77_77, B78_78, C79_79] : ((distinct_points(A77_77, B78_78) => (left_apart_point(C79_79, line_connecting(A77_77, B78_78)) => left_apart_point(C79_79, reverse_line(line_connecting(B78_78, A77_77))))))
% 2.73/1.04
% 2.73/1.04 [1] ALPHA_AND : (! [A20_20] : (~distinct_points(A20_20, A20_20)) & ! [A21_21, B22_22, C23_23] : ((distinct_points(A21_21, B22_22) => (distinct_points(A21_21, C23_23) | distinct_points(B22_22, C23_23)))) & ! [L24_24] : (~distinct_lines(L24_24, L24_24)) & ! [L25_25, M26_26, N27_27] : ((distinct_lines(L25_25, M26_26) => (distinct_lines(L25_25, N27_27) | distinct_lines(M26_26, N27_27)))) & ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28)) & ! [L29_29, M30_30, N31_31] : ((unequally_directed_lines(L29_29, M30_30) => (unequally_directed_lines(L29_29, N31_31) | unequally_directed_lines(M30_30, N31_31)))) & ! [L32_32, M33_33, N34_34] : (((unequally_directed_lines(L32_32, M33_33) & unequally_directed_lines(L32_32, reverse_line(M33_33))) => ((unequally_directed_lines(L32_32, N34_34) & unequally_directed_lines(L32_32, reverse_line(N34_34))) | (unequally_directed_lines(M33_33, N34_34) & unequally_directed_lines(M33_33, reverse_line(N34_34)))))) & ! [L35_35, M36_36] : (((line(L35_35) & line(M36_36)) => (unequally_directed_lines(L35_35, M36_36) | unequally_directed_lines(L35_35, reverse_line(M36_36))))) & ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38))))) & ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40)))) & ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42)))) & ! [A43_43, B44_44] : ((((point(A43_43) & point(B44_44)) & distinct_points(A43_43, B44_44)) => line(line_connecting(A43_43, B44_44)))) & ! [L45_45, M46_46] : (((((line(L45_45) & line(M46_46)) & unequally_directed_lines(L45_45, M46_46)) & unequally_directed_lines(L45_45, reverse_line(M46_46))) => point(intersection_point(L45_45, M46_46)))) & ! [L47_47, A48_48] : (((point(A48_48) & line(L47_47)) => line(parallel_through_point(L47_47, A48_48)))) & ! [L49_49] : ((line(L49_49) => line(reverse_line(L49_49)))) & ! [A50_50, B51_51] : ((distinct_points(A50_50, B51_51) => (~apart_point_and_line(A50_50, line_connecting(A50_50, B51_51)) & ~apart_point_and_line(B51_51, line_connecting(A50_50, B51_51))))) & ! [L52_52, M53_53] : (((unequally_directed_lines(L52_52, M53_53) & unequally_directed_lines(L52_52, reverse_line(M53_53))) => (~apart_point_and_line(intersection_point(L52_52, M53_53), L52_52) & ~apart_point_and_line(intersection_point(L52_52, M53_53), M53_53)))) & ! [A54_54, L55_55] : (~apart_point_and_line(A54_54, parallel_through_point(L55_55, A54_54))) & ! [L56_56] : (~distinct_lines(L56_56, reverse_line(L56_56))) & ! [A57_57, B58_58] : (~unequally_directed_lines(line_connecting(A57_57, B58_58), reverse_line(line_connecting(B58_58, A57_57)))) & ! [A59_59, L60_60] : (~unequally_directed_lines(parallel_through_point(L60_60, A59_59), L60_60)) & ! [A61_61, B62_62, L63_63, M64_64] : (((distinct_points(A61_61, B62_62) & distinct_lines(L63_63, M64_64)) => (((((((left_apart_point(A61_61, L63_63) | left_apart_point(B62_62, L63_63)) | left_apart_point(A61_61, M64_64)) | left_apart_point(B62_62, M64_64)) | left_apart_point(A61_61, reverse_line(L63_63))) | left_apart_point(B62_62, reverse_line(L63_63))) | left_apart_point(A61_61, reverse_line(M64_64))) | left_apart_point(B62_62, reverse_line(M64_64))))) & ! [A65_65, B66_66, L67_67] : (((distinct_points(A65_65, B66_66) & left_apart_point(A65_65, L67_67)) => (left_apart_point(B66_66, L67_67) | left_convergent_lines(line_connecting(A65_65, B66_66), L67_67)))) & ! [A68_68, B69_69, L70_70] : ((left_apart_point(A68_68, L70_70) => (distinct_points(A68_68, B69_69) | left_apart_point(B69_69, L70_70)))) & ! [A71_71, L72_72, M73_73] : (((left_apart_point(A71_71, L72_72) & unequally_directed_lines(L72_72, M73_73)) => (distinct_lines(L72_72, M73_73) | left_apart_point(A71_71, reverse_line(M73_73))))) & ! [L74_74, M75_75, N76_76] : ((left_convergent_lines(L74_74, M75_75) => (unequally_directed_lines(M75_75, N76_76) | left_convergent_lines(L74_74, N76_76)))))
% 2.73/1.04 -> [2] ! [A20_20] : (~distinct_points(A20_20, A20_20)), ! [A21_21, B22_22, C23_23] : ((distinct_points(A21_21, B22_22) => (distinct_points(A21_21, C23_23) | distinct_points(B22_22, C23_23)))), ! [L24_24] : (~distinct_lines(L24_24, L24_24)), ! [L25_25, M26_26, N27_27] : ((distinct_lines(L25_25, M26_26) => (distinct_lines(L25_25, N27_27) | distinct_lines(M26_26, N27_27)))), ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28)), ! [L29_29, M30_30, N31_31] : ((unequally_directed_lines(L29_29, M30_30) => (unequally_directed_lines(L29_29, N31_31) | unequally_directed_lines(M30_30, N31_31)))), ! [L32_32, M33_33, N34_34] : (((unequally_directed_lines(L32_32, M33_33) & unequally_directed_lines(L32_32, reverse_line(M33_33))) => ((unequally_directed_lines(L32_32, N34_34) & unequally_directed_lines(L32_32, reverse_line(N34_34))) | (unequally_directed_lines(M33_33, N34_34) & unequally_directed_lines(M33_33, reverse_line(N34_34)))))), ! [L35_35, M36_36] : (((line(L35_35) & line(M36_36)) => (unequally_directed_lines(L35_35, M36_36) | unequally_directed_lines(L35_35, reverse_line(M36_36))))), ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38))))), ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40)))), ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42)))), ! [A43_43, B44_44] : ((((point(A43_43) & point(B44_44)) & distinct_points(A43_43, B44_44)) => line(line_connecting(A43_43, B44_44)))), ! [L45_45, M46_46] : (((((line(L45_45) & line(M46_46)) & unequally_directed_lines(L45_45, M46_46)) & unequally_directed_lines(L45_45, reverse_line(M46_46))) => point(intersection_point(L45_45, M46_46)))), ! [L47_47, A48_48] : (((point(A48_48) & line(L47_47)) => line(parallel_through_point(L47_47, A48_48)))), ! [L49_49] : ((line(L49_49) => line(reverse_line(L49_49)))), ! [A50_50, B51_51] : ((distinct_points(A50_50, B51_51) => (~apart_point_and_line(A50_50, line_connecting(A50_50, B51_51)) & ~apart_point_and_line(B51_51, line_connecting(A50_50, B51_51))))), ! [L52_52, M53_53] : (((unequally_directed_lines(L52_52, M53_53) & unequally_directed_lines(L52_52, reverse_line(M53_53))) => (~apart_point_and_line(intersection_point(L52_52, M53_53), L52_52) & ~apart_point_and_line(intersection_point(L52_52, M53_53), M53_53)))), ! [A54_54, L55_55] : (~apart_point_and_line(A54_54, parallel_through_point(L55_55, A54_54))), ! [L56_56] : (~distinct_lines(L56_56, reverse_line(L56_56))), ! [A57_57, B58_58] : (~unequally_directed_lines(line_connecting(A57_57, B58_58), reverse_line(line_connecting(B58_58, A57_57)))), ! [A59_59, L60_60] : (~unequally_directed_lines(parallel_through_point(L60_60, A59_59), L60_60)), ! [A61_61, B62_62, L63_63, M64_64] : (((distinct_points(A61_61, B62_62) & distinct_lines(L63_63, M64_64)) => (((((((left_apart_point(A61_61, L63_63) | left_apart_point(B62_62, L63_63)) | left_apart_point(A61_61, M64_64)) | left_apart_point(B62_62, M64_64)) | left_apart_point(A61_61, reverse_line(L63_63))) | left_apart_point(B62_62, reverse_line(L63_63))) | left_apart_point(A61_61, reverse_line(M64_64))) | left_apart_point(B62_62, reverse_line(M64_64))))), ! [A65_65, B66_66, L67_67] : (((distinct_points(A65_65, B66_66) & left_apart_point(A65_65, L67_67)) => (left_apart_point(B66_66, L67_67) | left_convergent_lines(line_connecting(A65_65, B66_66), L67_67)))), ! [A68_68, B69_69, L70_70] : ((left_apart_point(A68_68, L70_70) => (distinct_points(A68_68, B69_69) | left_apart_point(B69_69, L70_70)))), ! [A71_71, L72_72, M73_73] : (((left_apart_point(A71_71, L72_72) & unequally_directed_lines(L72_72, M73_73)) => (distinct_lines(L72_72, M73_73) | left_apart_point(A71_71, reverse_line(M73_73))))), ! [L74_74, M75_75, N76_76] : ((left_convergent_lines(L74_74, M75_75) => (unequally_directed_lines(M75_75, N76_76) | left_convergent_lines(L74_74, N76_76))))
% 2.73/1.04
% 2.73/1.04 [2] DELTA_NOT_FORALL : ~! [A77_77, B78_78, C79_79] : ((distinct_points(A77_77, B78_78) => (left_apart_point(C79_79, line_connecting(A77_77, B78_78)) => left_apart_point(C79_79, reverse_line(line_connecting(B78_78, A77_77))))))
% 2.73/1.04 -> [3] ~(distinct_points(skolem_A7777, skolem_B7878) => (left_apart_point(skolem_C7979, line_connecting(skolem_A7777, skolem_B7878)) => left_apart_point(skolem_C7979, reverse_line(line_connecting(skolem_B7878, skolem_A7777)))))
% 2.73/1.04
% 2.73/1.04 [3] ALPHA_NOT_IMPLY : ~(distinct_points(skolem_A7777, skolem_B7878) => (left_apart_point(skolem_C7979, line_connecting(skolem_A7777, skolem_B7878)) => left_apart_point(skolem_C7979, reverse_line(line_connecting(skolem_B7878, skolem_A7777)))))
% 2.73/1.04 -> [4] distinct_points(skolem_A7777, skolem_B7878), ~(left_apart_point(skolem_C7979, line_connecting(skolem_A7777, skolem_B7878)) => left_apart_point(skolem_C7979, reverse_line(line_connecting(skolem_B7878, skolem_A7777))))
% 2.73/1.04
% 2.73/1.04 [4] ALPHA_NOT_IMPLY : ~(left_apart_point(skolem_C7979, line_connecting(skolem_A7777, skolem_B7878)) => left_apart_point(skolem_C7979, reverse_line(line_connecting(skolem_B7878, skolem_A7777))))
% 2.73/1.04 -> [5] left_apart_point(skolem_C7979, line_connecting(skolem_A7777, skolem_B7878)), ~left_apart_point(skolem_C7979, reverse_line(line_connecting(skolem_B7878, skolem_A7777)))
% 2.73/1.04
% 2.73/1.04 [5] GAMMA_FORALL : ! [A20_20] : (~distinct_points(A20_20, A20_20))
% 2.73/1.04 -> [6] ~distinct_points(skolem_B7878, skolem_B7878)
% 2.73/1.04
% 2.73/1.04 [6] GAMMA_FORALL : ! [A21_21, B22_22, C23_23] : ((distinct_points(A21_21, B22_22) => (distinct_points(A21_21, C23_23) | distinct_points(B22_22, C23_23))))
% 2.73/1.04 -> [7] (distinct_points(skolem_A7777, skolem_B7878) => (distinct_points(skolem_A7777, skolem_B7878) | distinct_points(skolem_B7878, skolem_B7878)))
% 2.73/1.04
% 2.73/1.04 [7] BETA_IMPLY : (distinct_points(skolem_A7777, skolem_B7878) => (distinct_points(skolem_A7777, skolem_B7878) | distinct_points(skolem_B7878, skolem_B7878)))
% 2.73/1.04 -> [8] ~distinct_points(skolem_A7777, skolem_B7878)
% 2.73/1.04 -> [9] (distinct_points(skolem_A7777, skolem_B7878) | distinct_points(skolem_B7878, skolem_B7878))
% 2.73/1.04
% 2.73/1.04 [8] CLOSURE : ~distinct_points(skolem_A7777, skolem_B7878)
% 2.73/1.04
% 2.73/1.04 [9] BETA_OR : (distinct_points(skolem_A7777, skolem_B7878) | distinct_points(skolem_B7878, skolem_B7878))
% 2.73/1.04 -> [12] distinct_points(skolem_A7777, skolem_B7878)
% 2.73/1.04 -> [13] distinct_points(skolem_B7878, skolem_B7878)
% 2.73/1.04
% 2.73/1.04 [13] CLOSURE : distinct_points(skolem_B7878, skolem_B7878)
% 2.73/1.04
% 2.73/1.04 [12] GAMMA_FORALL : ! [L24_24] : (~distinct_lines(L24_24, L24_24))
% 2.73/1.04 -> [14] ~distinct_lines(N27_0_3, N27_0_3)
% 2.73/1.04
% 2.73/1.04 [14] GAMMA_FORALL : ! [L25_25, M26_26, N27_27] : ((distinct_lines(L25_25, M26_26) => (distinct_lines(L25_25, N27_27) | distinct_lines(M26_26, N27_27))))
% 2.73/1.04 -> [15] (distinct_lines(N27_0_3, N27_0_3) => (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3)))
% 2.73/1.04
% 2.73/1.04 [15] BETA_IMPLY : (distinct_lines(N27_0_3, N27_0_3) => (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3)))
% 2.73/1.04 -> [16] ~distinct_lines(N27_0_3, N27_0_3)
% 2.73/1.04 -> [17] (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3))
% 2.73/1.04
% 2.73/1.04 [17] BETA_OR : (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3))
% 2.73/1.04 -> [18] distinct_lines(N27_0_3, N27_0_3)
% 2.73/1.04 -> [19] distinct_lines(N27_0_3, N27_0_3)
% 2.73/1.04
% 2.73/1.04 [19] CLOSURE : distinct_lines(N27_0_3, N27_0_3)
% 2.73/1.04
% 2.73/1.04 [18] CLOSURE : distinct_lines(N27_0_3, N27_0_3)
% 2.73/1.04
% 2.73/1.04 [16] GAMMA_FORALL : ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28))
% 2.73/1.04 -> [20] ~unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8)))
% 2.73/1.04
% 2.73/1.04 [20] GAMMA_FORALL : ! [L29_29, M30_30, N31_31] : ((unequally_directed_lines(L29_29, M30_30) => (unequally_directed_lines(L29_29, N31_31) | unequally_directed_lines(M30_30, N31_31))))
% 2.73/1.04 -> [21] (unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8))) => (unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8))) | unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8)))))
% 2.73/1.04
% 2.73/1.04 [21] BETA_IMPLY : (unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8))) => (unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8))) | unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8)))))
% 2.73/1.04 -> [22] ~unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8)))
% 2.73/1.04 -> [23] (unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8))) | unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8))))
% 2.73/1.04
% 2.73/1.04 [23] BETA_OR : (unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8))) | unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8))))
% 2.73/1.04 -> [24] unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8)))
% 2.73/1.04 -> [25] unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8)))
% 2.73/1.04
% 2.73/1.04 [25] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8)))
% 2.73/1.04
% 2.73/1.04 [24] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8)))
% 2.73/1.04
% 2.73/1.04 [26] BETA_IMPLY : ((unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8)) & unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8)))) => ((unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(reverse_line(M38_16_8))))) | (unequally_directed_lines(reverse_line(M38_16_8), reverse_line(reverse_line(M38_16_8))) & unequally_directed_lines(reverse_line(M38_16_8), reverse_line(reverse_line(reverse_line(M38_16_8)))))))
% 2.73/1.04 -> [221] ~(unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8)) & unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8))))
% 2.73/1.04 -> [222] ((unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(reverse_line(M38_16_8))))) | (unequally_directed_lines(reverse_line(M38_16_8), reverse_line(reverse_line(M38_16_8))) & unequally_directed_lines(reverse_line(M38_16_8), reverse_line(reverse_line(reverse_line(M38_16_8))))))
% 2.73/1.04
% 2.73/1.04 [221] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8)) & unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8))))
% 2.73/1.04 -> [223] ~unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8))
% 2.73/1.04 -> [224] ~unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8)))
% 2.73/1.04
% 2.73/1.04 [223] GAMMA_FORALL : ! [L35_35, M36_36] : (((line(L35_35) & line(M36_36)) => (unequally_directed_lines(L35_35, M36_36) | unequally_directed_lines(L35_35, reverse_line(M36_36)))))
% 2.73/1.04 -> [229] ((line(reverse_line(reverse_line(M38_16_8))) & line(reverse_line(M38_16_8))) => (unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8)) | unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8)))))
% 2.73/1.04
% 2.73/1.04 [229] BETA_IMPLY : ((line(reverse_line(reverse_line(M38_16_8))) & line(reverse_line(M38_16_8))) => (unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8)) | unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8)))))
% 2.73/1.04 -> [231] ~(line(reverse_line(reverse_line(M38_16_8))) & line(reverse_line(M38_16_8)))
% 2.73/1.04 -> [232] (unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8)) | unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8))))
% 2.73/1.04
% 2.73/1.04 [232] BETA_OR : (unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8)) | unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8))))
% 2.73/1.04 -> [239] unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8))
% 2.73/1.04 -> [240] unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8)))
% 2.73/1.04
% 2.73/1.04 [240] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8)))
% 2.73/1.04
% 2.73/1.04 [239] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8))
% 2.73/1.04
% 2.73/1.04 [231] BETA_NOT_AND : ~(line(reverse_line(reverse_line(M38_16_8))) & line(reverse_line(M38_16_8)))
% 2.73/1.04 -> [235] ~line(reverse_line(reverse_line(M38_16_8)))
% 2.73/1.04 -> [236] ~line(reverse_line(M38_16_8))
% 2.73/1.04
% 2.73/1.04 [235] GAMMA_FORALL : ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38)))))
% 2.73/1.04 -> [244] ((unequally_directed_lines(L37_11_8, M38_11_8) & unequally_directed_lines(L37_11_8, reverse_line(M38_11_8))) => (left_convergent_lines(L37_11_8, M38_11_8) | left_convergent_lines(L37_11_8, reverse_line(M38_11_8))))
% 2.73/1.04
% 2.73/1.04 [244] BETA_IMPLY : ((unequally_directed_lines(L37_11_8, M38_11_8) & unequally_directed_lines(L37_11_8, reverse_line(M38_11_8))) => (left_convergent_lines(L37_11_8, M38_11_8) | left_convergent_lines(L37_11_8, reverse_line(M38_11_8))))
% 2.73/1.04 -> [248] ~(unequally_directed_lines(L37_11_8, M38_11_8) & unequally_directed_lines(L37_11_8, reverse_line(M38_11_8)))
% 2.73/1.04 -> [249] (left_convergent_lines(L37_11_8, M38_11_8) | left_convergent_lines(L37_11_8, reverse_line(M38_11_8)))
% 2.73/1.04
% 2.73/1.04 [248] BETA_NOT_AND : ~(unequally_directed_lines(L37_11_8, M38_11_8) & unequally_directed_lines(L37_11_8, reverse_line(M38_11_8)))
% 2.73/1.04 -> [261] ~unequally_directed_lines(L37_11_8, M38_11_8)
% 2.73/1.04 -> [262] ~unequally_directed_lines(L37_11_8, reverse_line(M38_11_8))
% 2.73/1.04
% 2.73/1.04 [262] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [269] ~(left_apart_point(A39_40_9, L40_40_9) | left_apart_point(A39_40_9, reverse_line(L40_40_9)))
% 2.73/1.04
% 2.73/1.04 [269] ALPHA_NOT_OR : ~(left_apart_point(A39_40_9, L40_40_9) | left_apart_point(A39_40_9, reverse_line(L40_40_9)))
% 2.73/1.04 -> [270] ~left_apart_point(A39_40_9, L40_40_9), ~left_apart_point(A39_40_9, reverse_line(L40_40_9))
% 2.73/1.04
% 2.73/1.04 [270] CLOSURE : ~left_apart_point(A39_40_9, L40_40_9)
% 2.73/1.04
% 2.73/1.04 [261] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [274] ~(left_apart_point(A39_44_9, L40_44_9) | left_apart_point(A39_44_9, reverse_line(L40_44_9)))
% 2.73/1.04
% 2.73/1.04 [274] ALPHA_NOT_OR : ~(left_apart_point(A39_44_9, L40_44_9) | left_apart_point(A39_44_9, reverse_line(L40_44_9)))
% 2.73/1.04 -> [279] ~left_apart_point(A39_44_9, L40_44_9), ~left_apart_point(A39_44_9, reverse_line(L40_44_9))
% 2.73/1.04
% 2.73/1.04 [279] CLOSURE : ~left_apart_point(A39_44_9, L40_44_9)
% 2.73/1.04
% 2.73/1.04 [249] BETA_OR : (left_convergent_lines(L37_11_8, M38_11_8) | left_convergent_lines(L37_11_8, reverse_line(M38_11_8)))
% 2.73/1.04 -> [259] left_convergent_lines(L37_11_8, M38_11_8)
% 2.73/1.04 -> [260] left_convergent_lines(L37_11_8, reverse_line(M38_11_8))
% 2.73/1.04
% 2.73/1.04 [259] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [281] ~(left_apart_point(A39_46_9, L40_46_9) | left_apart_point(A39_46_9, reverse_line(L40_46_9)))
% 2.73/1.04
% 2.73/1.04 [281] ALPHA_NOT_OR : ~(left_apart_point(A39_46_9, L40_46_9) | left_apart_point(A39_46_9, reverse_line(L40_46_9)))
% 2.73/1.04 -> [282] ~left_apart_point(A39_46_9, L40_46_9), ~left_apart_point(A39_46_9, reverse_line(L40_46_9))
% 2.73/1.04
% 2.73/1.04 [282] CLOSURE : ~left_apart_point(A39_46_9, L40_46_9)
% 2.73/1.04
% 2.73/1.04 [260] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [284] ~(left_apart_point(A39_48_9, L40_48_9) | left_apart_point(A39_48_9, reverse_line(L40_48_9)))
% 2.73/1.04
% 2.73/1.04 [284] ALPHA_NOT_OR : ~(left_apart_point(A39_48_9, L40_48_9) | left_apart_point(A39_48_9, reverse_line(L40_48_9)))
% 2.73/1.04 -> [291] ~left_apart_point(A39_48_9, L40_48_9), ~left_apart_point(A39_48_9, reverse_line(L40_48_9))
% 2.73/1.04
% 2.73/1.04 [291] CLOSURE : ~left_apart_point(A39_48_9, L40_48_9)
% 2.73/1.04
% 2.73/1.04 [236] GAMMA_FORALL : ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38)))))
% 2.73/1.04 -> [245] ((unequally_directed_lines(L37_12_8, M38_12_8) & unequally_directed_lines(L37_12_8, reverse_line(M38_12_8))) => (left_convergent_lines(L37_12_8, M38_12_8) | left_convergent_lines(L37_12_8, reverse_line(M38_12_8))))
% 2.73/1.04
% 2.73/1.04 [245] BETA_IMPLY : ((unequally_directed_lines(L37_12_8, M38_12_8) & unequally_directed_lines(L37_12_8, reverse_line(M38_12_8))) => (left_convergent_lines(L37_12_8, M38_12_8) | left_convergent_lines(L37_12_8, reverse_line(M38_12_8))))
% 2.73/1.04 -> [251] ~(unequally_directed_lines(L37_12_8, M38_12_8) & unequally_directed_lines(L37_12_8, reverse_line(M38_12_8)))
% 2.73/1.04 -> [252] (left_convergent_lines(L37_12_8, M38_12_8) | left_convergent_lines(L37_12_8, reverse_line(M38_12_8)))
% 2.73/1.04
% 2.73/1.04 [252] BETA_OR : (left_convergent_lines(L37_12_8, M38_12_8) | left_convergent_lines(L37_12_8, reverse_line(M38_12_8)))
% 2.73/1.04 -> [267] left_convergent_lines(L37_12_8, M38_12_8)
% 2.73/1.04 -> [268] left_convergent_lines(L37_12_8, reverse_line(M38_12_8))
% 2.73/1.04
% 2.73/1.04 [268] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [275] ~(left_apart_point(A39_45_9, L40_45_9) | left_apart_point(A39_45_9, reverse_line(L40_45_9)))
% 2.73/1.04
% 2.73/1.04 [275] ALPHA_NOT_OR : ~(left_apart_point(A39_45_9, L40_45_9) | left_apart_point(A39_45_9, reverse_line(L40_45_9)))
% 2.73/1.04 -> [280] ~left_apart_point(A39_45_9, L40_45_9), ~left_apart_point(A39_45_9, reverse_line(L40_45_9))
% 2.73/1.04
% 2.73/1.04 [280] CLOSURE : ~left_apart_point(A39_45_9, L40_45_9)
% 2.73/1.04
% 2.73/1.04 [267] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [290] ~(left_apart_point(A39_51_9, L40_51_9) | left_apart_point(A39_51_9, reverse_line(L40_51_9)))
% 2.73/1.04
% 2.73/1.04 [290] ALPHA_NOT_OR : ~(left_apart_point(A39_51_9, L40_51_9) | left_apart_point(A39_51_9, reverse_line(L40_51_9)))
% 2.73/1.04 -> [295] ~left_apart_point(A39_51_9, L40_51_9), ~left_apart_point(A39_51_9, reverse_line(L40_51_9))
% 2.73/1.04
% 2.73/1.04 [295] CLOSURE : ~left_apart_point(A39_51_9, L40_51_9)
% 2.73/1.04
% 2.73/1.04 [251] BETA_NOT_AND : ~(unequally_directed_lines(L37_12_8, M38_12_8) & unequally_directed_lines(L37_12_8, reverse_line(M38_12_8)))
% 2.73/1.04 -> [263] ~unequally_directed_lines(L37_12_8, M38_12_8)
% 2.73/1.04 -> [264] ~unequally_directed_lines(L37_12_8, reverse_line(M38_12_8))
% 2.73/1.04
% 2.73/1.04 [264] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [272] ~(left_apart_point(A39_42_9, L40_42_9) | left_apart_point(A39_42_9, reverse_line(L40_42_9)))
% 2.73/1.04
% 2.73/1.04 [272] ALPHA_NOT_OR : ~(left_apart_point(A39_42_9, L40_42_9) | left_apart_point(A39_42_9, reverse_line(L40_42_9)))
% 2.73/1.04 -> [277] ~left_apart_point(A39_42_9, L40_42_9), ~left_apart_point(A39_42_9, reverse_line(L40_42_9))
% 2.73/1.04
% 2.73/1.04 [277] CLOSURE : ~left_apart_point(A39_42_9, L40_42_9)
% 2.73/1.04
% 2.73/1.04 [263] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [297] ~(left_apart_point(A39_53_9, L40_53_9) | left_apart_point(A39_53_9, reverse_line(L40_53_9)))
% 2.73/1.04
% 2.73/1.04 [297] ALPHA_NOT_OR : ~(left_apart_point(A39_53_9, L40_53_9) | left_apart_point(A39_53_9, reverse_line(L40_53_9)))
% 2.73/1.04 -> [298] ~left_apart_point(A39_53_9, L40_53_9), ~left_apart_point(A39_53_9, reverse_line(L40_53_9))
% 2.73/1.04
% 2.73/1.04 [298] CLOSURE : ~left_apart_point(A39_53_9, L40_53_9)
% 2.73/1.04
% 2.73/1.04 [230] BETA_IMPLY : ((line(reverse_line(reverse_line(M38_16_8))) & line(reverse_line(M38_16_8))) => (unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8)) | unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8)))))
% 2.73/1.04 -> [303] ~(line(reverse_line(reverse_line(M38_16_8))) & line(reverse_line(M38_16_8)))
% 2.73/1.04 -> [304] (unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8)) | unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8))))
% 2.73/1.04
% 2.73/1.04 [303] BETA_NOT_AND : ~(line(reverse_line(reverse_line(M38_16_8))) & line(reverse_line(M38_16_8)))
% 2.73/1.04 -> [305] ~line(reverse_line(reverse_line(M38_16_8)))
% 2.73/1.04 -> [306] ~line(reverse_line(M38_16_8))
% 2.73/1.04
% 2.73/1.04 [305] GAMMA_FORALL : ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38)))))
% 2.73/1.04 -> [309] ((unequally_directed_lines(L37_14_8, M38_14_8) & unequally_directed_lines(L37_14_8, reverse_line(M38_14_8))) => (left_convergent_lines(L37_14_8, M38_14_8) | left_convergent_lines(L37_14_8, reverse_line(M38_14_8))))
% 2.73/1.04
% 2.73/1.04 [309] BETA_IMPLY : ((unequally_directed_lines(L37_14_8, M38_14_8) & unequally_directed_lines(L37_14_8, reverse_line(M38_14_8))) => (left_convergent_lines(L37_14_8, M38_14_8) | left_convergent_lines(L37_14_8, reverse_line(M38_14_8))))
% 2.73/1.04 -> [311] ~(unequally_directed_lines(L37_14_8, M38_14_8) & unequally_directed_lines(L37_14_8, reverse_line(M38_14_8)))
% 2.73/1.04 -> [312] (left_convergent_lines(L37_14_8, M38_14_8) | left_convergent_lines(L37_14_8, reverse_line(M38_14_8)))
% 2.73/1.04
% 2.73/1.04 [311] BETA_NOT_AND : ~(unequally_directed_lines(L37_14_8, M38_14_8) & unequally_directed_lines(L37_14_8, reverse_line(M38_14_8)))
% 2.73/1.04 -> [315] ~unequally_directed_lines(L37_14_8, M38_14_8)
% 2.73/1.04 -> [316] ~unequally_directed_lines(L37_14_8, reverse_line(M38_14_8))
% 2.73/1.04
% 2.73/1.04 [315] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [323] ~(left_apart_point(A39_56_9, L40_56_9) | left_apart_point(A39_56_9, reverse_line(L40_56_9)))
% 2.73/1.04
% 2.73/1.04 [323] ALPHA_NOT_OR : ~(left_apart_point(A39_56_9, L40_56_9) | left_apart_point(A39_56_9, reverse_line(L40_56_9)))
% 2.73/1.04 -> [324] ~left_apart_point(A39_56_9, L40_56_9), ~left_apart_point(A39_56_9, reverse_line(L40_56_9))
% 2.73/1.04
% 2.73/1.04 [324] CLOSURE : ~left_apart_point(A39_56_9, L40_56_9)
% 2.73/1.04
% 2.73/1.04 [316] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [326] ~(left_apart_point(A39_58_9, L40_58_9) | left_apart_point(A39_58_9, reverse_line(L40_58_9)))
% 2.73/1.04
% 2.73/1.04 [326] ALPHA_NOT_OR : ~(left_apart_point(A39_58_9, L40_58_9) | left_apart_point(A39_58_9, reverse_line(L40_58_9)))
% 2.73/1.04 -> [329] ~left_apart_point(A39_58_9, L40_58_9), ~left_apart_point(A39_58_9, reverse_line(L40_58_9))
% 2.73/1.04
% 2.73/1.04 [329] CLOSURE : ~left_apart_point(A39_58_9, L40_58_9)
% 2.73/1.04
% 2.73/1.04 [312] BETA_OR : (left_convergent_lines(L37_14_8, M38_14_8) | left_convergent_lines(L37_14_8, reverse_line(M38_14_8)))
% 2.73/1.04 -> [317] left_convergent_lines(L37_14_8, M38_14_8)
% 2.73/1.04 -> [318] left_convergent_lines(L37_14_8, reverse_line(M38_14_8))
% 2.73/1.04
% 2.73/1.04 [317] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [327] ~(left_apart_point(A39_59_9, L40_59_9) | left_apart_point(A39_59_9, reverse_line(L40_59_9)))
% 2.73/1.04
% 2.73/1.04 [327] ALPHA_NOT_OR : ~(left_apart_point(A39_59_9, L40_59_9) | left_apart_point(A39_59_9, reverse_line(L40_59_9)))
% 2.73/1.04 -> [332] ~left_apart_point(A39_59_9, L40_59_9), ~left_apart_point(A39_59_9, reverse_line(L40_59_9))
% 2.73/1.04
% 2.73/1.04 [332] CLOSURE : ~left_apart_point(A39_59_9, L40_59_9)
% 2.73/1.04
% 2.73/1.04 [318] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [330] ~(left_apart_point(A39_60_9, L40_60_9) | left_apart_point(A39_60_9, reverse_line(L40_60_9)))
% 2.73/1.04
% 2.73/1.04 [330] ALPHA_NOT_OR : ~(left_apart_point(A39_60_9, L40_60_9) | left_apart_point(A39_60_9, reverse_line(L40_60_9)))
% 2.73/1.04 -> [333] ~left_apart_point(A39_60_9, L40_60_9), ~left_apart_point(A39_60_9, reverse_line(L40_60_9))
% 2.73/1.04
% 2.73/1.04 [333] CLOSURE : ~left_apart_point(A39_60_9, L40_60_9)
% 2.73/1.04
% 2.73/1.04 [306] GAMMA_FORALL : ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38)))))
% 2.73/1.04 -> [310] ((unequally_directed_lines(L37_15_8, M38_15_8) & unequally_directed_lines(L37_15_8, reverse_line(M38_15_8))) => (left_convergent_lines(L37_15_8, M38_15_8) | left_convergent_lines(L37_15_8, reverse_line(M38_15_8))))
% 2.73/1.04
% 2.73/1.04 [310] BETA_IMPLY : ((unequally_directed_lines(L37_15_8, M38_15_8) & unequally_directed_lines(L37_15_8, reverse_line(M38_15_8))) => (left_convergent_lines(L37_15_8, M38_15_8) | left_convergent_lines(L37_15_8, reverse_line(M38_15_8))))
% 2.73/1.04 -> [313] ~(unequally_directed_lines(L37_15_8, M38_15_8) & unequally_directed_lines(L37_15_8, reverse_line(M38_15_8)))
% 2.73/1.04 -> [314] (left_convergent_lines(L37_15_8, M38_15_8) | left_convergent_lines(L37_15_8, reverse_line(M38_15_8)))
% 2.73/1.04
% 2.73/1.04 [313] BETA_NOT_AND : ~(unequally_directed_lines(L37_15_8, M38_15_8) & unequally_directed_lines(L37_15_8, reverse_line(M38_15_8)))
% 2.73/1.04 -> [319] ~unequally_directed_lines(L37_15_8, M38_15_8)
% 2.73/1.04 -> [320] ~unequally_directed_lines(L37_15_8, reverse_line(M38_15_8))
% 2.73/1.04
% 2.73/1.04 [319] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [325] ~(left_apart_point(A39_57_9, L40_57_9) | left_apart_point(A39_57_9, reverse_line(L40_57_9)))
% 2.73/1.04
% 2.73/1.04 [325] ALPHA_NOT_OR : ~(left_apart_point(A39_57_9, L40_57_9) | left_apart_point(A39_57_9, reverse_line(L40_57_9)))
% 2.73/1.04 -> [328] ~left_apart_point(A39_57_9, L40_57_9), ~left_apart_point(A39_57_9, reverse_line(L40_57_9))
% 2.73/1.04
% 2.73/1.04 [328] CLOSURE : ~left_apart_point(A39_57_9, L40_57_9)
% 2.73/1.04
% 2.73/1.04 [320] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [336] ~(left_apart_point(A39_61_9, L40_61_9) | left_apart_point(A39_61_9, reverse_line(L40_61_9)))
% 2.73/1.04
% 2.73/1.04 [336] ALPHA_NOT_OR : ~(left_apart_point(A39_61_9, L40_61_9) | left_apart_point(A39_61_9, reverse_line(L40_61_9)))
% 2.73/1.04 -> [338] ~left_apart_point(A39_61_9, L40_61_9), ~left_apart_point(A39_61_9, reverse_line(L40_61_9))
% 2.73/1.04
% 2.73/1.04 [338] CLOSURE : ~left_apart_point(A39_61_9, L40_61_9)
% 2.73/1.04
% 2.73/1.04 [314] BETA_OR : (left_convergent_lines(L37_15_8, M38_15_8) | left_convergent_lines(L37_15_8, reverse_line(M38_15_8)))
% 2.73/1.04 -> [321] left_convergent_lines(L37_15_8, M38_15_8)
% 2.73/1.04 -> [322] left_convergent_lines(L37_15_8, reverse_line(M38_15_8))
% 2.73/1.04
% 2.73/1.04 [322] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [337] ~(left_apart_point(A39_62_9, L40_62_9) | left_apart_point(A39_62_9, reverse_line(L40_62_9)))
% 2.73/1.04
% 2.73/1.04 [337] ALPHA_NOT_OR : ~(left_apart_point(A39_62_9, L40_62_9) | left_apart_point(A39_62_9, reverse_line(L40_62_9)))
% 2.73/1.04 -> [339] ~left_apart_point(A39_62_9, L40_62_9), ~left_apart_point(A39_62_9, reverse_line(L40_62_9))
% 2.73/1.04
% 2.73/1.04 [339] CLOSURE : ~left_apart_point(A39_62_9, L40_62_9)
% 2.73/1.04
% 2.73/1.04 [321] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [344] ~(left_apart_point(A39_63_9, L40_63_9) | left_apart_point(A39_63_9, reverse_line(L40_63_9)))
% 2.73/1.04
% 2.73/1.04 [344] ALPHA_NOT_OR : ~(left_apart_point(A39_63_9, L40_63_9) | left_apart_point(A39_63_9, reverse_line(L40_63_9)))
% 2.73/1.04 -> [345] ~left_apart_point(A39_63_9, L40_63_9), ~left_apart_point(A39_63_9, reverse_line(L40_63_9))
% 2.73/1.04
% 2.73/1.04 [345] CLOSURE : ~left_apart_point(A39_63_9, L40_63_9)
% 2.73/1.04
% 2.73/1.04 [304] BETA_OR : (unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8)) | unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8))))
% 2.73/1.04 -> [307] unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8))
% 2.73/1.04 -> [308] unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8)))
% 2.73/1.04
% 2.73/1.04 [308] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8)))
% 2.73/1.04
% 2.73/1.04 [307] GAMMA_FORALL : ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38)))))
% 2.73/1.04 -> [331] ((unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), M38_16_8) & unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8))) => (left_convergent_lines(reverse_line(reverse_line(M38_16_8)), M38_16_8) | left_convergent_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8))))
% 2.73/1.04
% 2.73/1.04 [331] BETA_IMPLY : ((unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), M38_16_8) & unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8))) => (left_convergent_lines(reverse_line(reverse_line(M38_16_8)), M38_16_8) | left_convergent_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8))))
% 2.73/1.04 -> [334] ~(unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), M38_16_8) & unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8)))
% 2.73/1.04 -> [335] (left_convergent_lines(reverse_line(reverse_line(M38_16_8)), M38_16_8) | left_convergent_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8)))
% 2.73/1.04
% 2.73/1.04 [335] BETA_OR : (left_convergent_lines(reverse_line(reverse_line(M38_16_8)), M38_16_8) | left_convergent_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8)))
% 2.73/1.04 -> [340] left_convergent_lines(reverse_line(reverse_line(M38_16_8)), M38_16_8)
% 2.73/1.04 -> [341] left_convergent_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8))
% 2.73/1.04
% 2.73/1.04 [340] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [346] ~(left_apart_point(A39_64_9, L40_64_9) | left_apart_point(A39_64_9, reverse_line(L40_64_9)))
% 2.73/1.04
% 2.73/1.04 [346] ALPHA_NOT_OR : ~(left_apart_point(A39_64_9, L40_64_9) | left_apart_point(A39_64_9, reverse_line(L40_64_9)))
% 2.73/1.04 -> [348] ~left_apart_point(A39_64_9, L40_64_9), ~left_apart_point(A39_64_9, reverse_line(L40_64_9))
% 2.73/1.04
% 2.73/1.04 [348] CLOSURE : ~left_apart_point(A39_64_9, L40_64_9)
% 2.73/1.04
% 2.73/1.04 [341] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [347] ~(left_apart_point(A39_65_9, L40_65_9) | left_apart_point(A39_65_9, reverse_line(L40_65_9)))
% 2.73/1.04
% 2.73/1.04 [347] ALPHA_NOT_OR : ~(left_apart_point(A39_65_9, L40_65_9) | left_apart_point(A39_65_9, reverse_line(L40_65_9)))
% 2.73/1.04 -> [349] ~left_apart_point(A39_65_9, L40_65_9), ~left_apart_point(A39_65_9, reverse_line(L40_65_9))
% 2.73/1.04
% 2.73/1.04 [349] CLOSURE : ~left_apart_point(A39_65_9, L40_65_9)
% 2.73/1.04
% 2.73/1.04 [334] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), M38_16_8) & unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8)))
% 2.73/1.04 -> [342] ~unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), M38_16_8)
% 2.73/1.04 -> [343] ~unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8))
% 2.73/1.04
% 2.73/1.04 [343] CLOSURE : ~unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8))
% 2.73/1.04
% 2.73/1.04 [342] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [350] ~(left_apart_point(A39_66_9, L40_66_9) | left_apart_point(A39_66_9, reverse_line(L40_66_9)))
% 2.73/1.04
% 2.73/1.04 [350] ALPHA_NOT_OR : ~(left_apart_point(A39_66_9, L40_66_9) | left_apart_point(A39_66_9, reverse_line(L40_66_9)))
% 2.73/1.04 -> [351] ~left_apart_point(A39_66_9, L40_66_9), ~left_apart_point(A39_66_9, reverse_line(L40_66_9))
% 2.73/1.04
% 2.73/1.04 [351] CLOSURE : ~left_apart_point(A39_66_9, L40_66_9)
% 2.73/1.04
% 2.73/1.04 [222] BETA_OR : ((unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(reverse_line(M38_16_8))))) | (unequally_directed_lines(reverse_line(M38_16_8), reverse_line(reverse_line(M38_16_8))) & unequally_directed_lines(reverse_line(M38_16_8), reverse_line(reverse_line(reverse_line(M38_16_8))))))
% 2.73/1.04 -> [352] (unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(reverse_line(M38_16_8)))))
% 2.73/1.04 -> [353] (unequally_directed_lines(reverse_line(M38_16_8), reverse_line(reverse_line(M38_16_8))) & unequally_directed_lines(reverse_line(M38_16_8), reverse_line(reverse_line(reverse_line(M38_16_8)))))
% 2.73/1.04
% 2.73/1.04 [352] ALPHA_AND : (unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(reverse_line(M38_16_8)))))
% 2.73/1.04 -> [354] unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8))), unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(reverse_line(M38_16_8))))
% 2.73/1.04
% 2.73/1.04 [354] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(reverse_line(M38_16_8))))
% 2.73/1.04
% 2.73/1.04 [353] ALPHA_AND : (unequally_directed_lines(reverse_line(M38_16_8), reverse_line(reverse_line(M38_16_8))) & unequally_directed_lines(reverse_line(M38_16_8), reverse_line(reverse_line(reverse_line(M38_16_8)))))
% 2.73/1.04 -> [355] unequally_directed_lines(reverse_line(M38_16_8), reverse_line(reverse_line(M38_16_8))), unequally_directed_lines(reverse_line(M38_16_8), reverse_line(reverse_line(reverse_line(M38_16_8))))
% 2.73/1.04
% 2.73/1.04 [355] GAMMA_FORALL : ! [L35_35, M36_36] : (((line(L35_35) & line(M36_36)) => (unequally_directed_lines(L35_35, M36_36) | unequally_directed_lines(L35_35, reverse_line(M36_36)))))
% 2.73/1.04 -> [356] ((line(reverse_line(reverse_line(M38_16_8))) & line(reverse_line(M38_16_8))) => (unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8)) | unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8)))))
% 2.73/1.04
% 2.73/1.04 [356] BETA_IMPLY : ((line(reverse_line(reverse_line(M38_16_8))) & line(reverse_line(M38_16_8))) => (unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8)) | unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8)))))
% 2.73/1.04 -> [357] ~(line(reverse_line(reverse_line(M38_16_8))) & line(reverse_line(M38_16_8)))
% 2.73/1.04 -> [358] (unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8)) | unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8))))
% 2.73/1.04
% 2.73/1.04 [357] BETA_NOT_AND : ~(line(reverse_line(reverse_line(M38_16_8))) & line(reverse_line(M38_16_8)))
% 2.73/1.04 -> [359] ~line(reverse_line(reverse_line(M38_16_8)))
% 2.73/1.04 -> [360] ~line(reverse_line(M38_16_8))
% 2.73/1.04
% 2.73/1.04 [359] GAMMA_FORALL : ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38)))))
% 2.73/1.04 -> [363] ((unequally_directed_lines(reverse_line(M38_16_8), M38_17_8) & unequally_directed_lines(reverse_line(M38_16_8), reverse_line(M38_17_8))) => (left_convergent_lines(reverse_line(M38_16_8), M38_17_8) | left_convergent_lines(reverse_line(M38_16_8), reverse_line(M38_17_8))))
% 2.73/1.04
% 2.73/1.04 [363] BETA_IMPLY : ((unequally_directed_lines(reverse_line(M38_16_8), M38_17_8) & unequally_directed_lines(reverse_line(M38_16_8), reverse_line(M38_17_8))) => (left_convergent_lines(reverse_line(M38_16_8), M38_17_8) | left_convergent_lines(reverse_line(M38_16_8), reverse_line(M38_17_8))))
% 2.73/1.04 -> [365] ~(unequally_directed_lines(reverse_line(M38_16_8), M38_17_8) & unequally_directed_lines(reverse_line(M38_16_8), reverse_line(M38_17_8)))
% 2.73/1.04 -> [366] (left_convergent_lines(reverse_line(M38_16_8), M38_17_8) | left_convergent_lines(reverse_line(M38_16_8), reverse_line(M38_17_8)))
% 2.73/1.04
% 2.73/1.04 [365] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(M38_16_8), M38_17_8) & unequally_directed_lines(reverse_line(M38_16_8), reverse_line(M38_17_8)))
% 2.73/1.04 -> [369] ~unequally_directed_lines(reverse_line(M38_16_8), M38_17_8)
% 2.73/1.04 -> [370] ~unequally_directed_lines(reverse_line(M38_16_8), reverse_line(M38_17_8))
% 2.73/1.04
% 2.73/1.04 [369] CLOSURE : ~unequally_directed_lines(reverse_line(M38_16_8), M38_17_8)
% 2.73/1.04
% 2.73/1.04 [370] CLOSURE : ~unequally_directed_lines(reverse_line(M38_16_8), reverse_line(M38_17_8))
% 2.73/1.04
% 2.73/1.04 [366] BETA_OR : (left_convergent_lines(reverse_line(M38_16_8), M38_17_8) | left_convergent_lines(reverse_line(M38_16_8), reverse_line(M38_17_8)))
% 2.73/1.04 -> [371] left_convergent_lines(reverse_line(M38_16_8), M38_17_8)
% 2.73/1.04 -> [372] left_convergent_lines(reverse_line(M38_16_8), reverse_line(M38_17_8))
% 2.73/1.04
% 2.73/1.04 [372] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [377] ~(left_apart_point(A39_67_9, L40_67_9) | left_apart_point(A39_67_9, reverse_line(L40_67_9)))
% 2.73/1.04
% 2.73/1.04 [377] ALPHA_NOT_OR : ~(left_apart_point(A39_67_9, L40_67_9) | left_apart_point(A39_67_9, reverse_line(L40_67_9)))
% 2.73/1.04 -> [379] ~left_apart_point(A39_67_9, L40_67_9), ~left_apart_point(A39_67_9, reverse_line(L40_67_9))
% 2.73/1.04
% 2.73/1.04 [379] CLOSURE : ~left_apart_point(A39_67_9, L40_67_9)
% 2.73/1.04
% 2.73/1.04 [371] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [378] ~(left_apart_point(A39_68_9, L40_68_9) | left_apart_point(A39_68_9, reverse_line(L40_68_9)))
% 2.73/1.04
% 2.73/1.04 [378] ALPHA_NOT_OR : ~(left_apart_point(A39_68_9, L40_68_9) | left_apart_point(A39_68_9, reverse_line(L40_68_9)))
% 2.73/1.04 -> [381] ~left_apart_point(A39_68_9, L40_68_9), ~left_apart_point(A39_68_9, reverse_line(L40_68_9))
% 2.73/1.04
% 2.73/1.04 [381] CLOSURE : ~left_apart_point(A39_68_9, L40_68_9)
% 2.73/1.04
% 2.73/1.04 [360] GAMMA_FORALL : ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38)))))
% 2.73/1.04 -> [364] ((unequally_directed_lines(reverse_line(M38_16_8), M38_18_8) & unequally_directed_lines(reverse_line(M38_16_8), reverse_line(M38_18_8))) => (left_convergent_lines(reverse_line(M38_16_8), M38_18_8) | left_convergent_lines(reverse_line(M38_16_8), reverse_line(M38_18_8))))
% 2.73/1.04
% 2.73/1.04 [364] BETA_IMPLY : ((unequally_directed_lines(reverse_line(M38_16_8), M38_18_8) & unequally_directed_lines(reverse_line(M38_16_8), reverse_line(M38_18_8))) => (left_convergent_lines(reverse_line(M38_16_8), M38_18_8) | left_convergent_lines(reverse_line(M38_16_8), reverse_line(M38_18_8))))
% 2.73/1.04 -> [367] ~(unequally_directed_lines(reverse_line(M38_16_8), M38_18_8) & unequally_directed_lines(reverse_line(M38_16_8), reverse_line(M38_18_8)))
% 2.73/1.04 -> [368] (left_convergent_lines(reverse_line(M38_16_8), M38_18_8) | left_convergent_lines(reverse_line(M38_16_8), reverse_line(M38_18_8)))
% 2.73/1.04
% 2.73/1.04 [367] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(M38_16_8), M38_18_8) & unequally_directed_lines(reverse_line(M38_16_8), reverse_line(M38_18_8)))
% 2.73/1.04 -> [373] ~unequally_directed_lines(reverse_line(M38_16_8), M38_18_8)
% 2.73/1.04 -> [374] ~unequally_directed_lines(reverse_line(M38_16_8), reverse_line(M38_18_8))
% 2.73/1.04
% 2.73/1.04 [373] CLOSURE : ~unequally_directed_lines(reverse_line(M38_16_8), M38_18_8)
% 2.73/1.04
% 2.73/1.04 [374] CLOSURE : ~unequally_directed_lines(reverse_line(M38_16_8), reverse_line(M38_18_8))
% 2.73/1.04
% 2.73/1.04 [368] BETA_OR : (left_convergent_lines(reverse_line(M38_16_8), M38_18_8) | left_convergent_lines(reverse_line(M38_16_8), reverse_line(M38_18_8)))
% 2.73/1.04 -> [375] left_convergent_lines(reverse_line(M38_16_8), M38_18_8)
% 2.73/1.04 -> [376] left_convergent_lines(reverse_line(M38_16_8), reverse_line(M38_18_8))
% 2.73/1.04
% 2.73/1.04 [375] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [380] ~(left_apart_point(A39_69_9, L40_69_9) | left_apart_point(A39_69_9, reverse_line(L40_69_9)))
% 2.73/1.04
% 2.73/1.04 [380] ALPHA_NOT_OR : ~(left_apart_point(A39_69_9, L40_69_9) | left_apart_point(A39_69_9, reverse_line(L40_69_9)))
% 2.73/1.04 -> [384] ~left_apart_point(A39_69_9, L40_69_9), ~left_apart_point(A39_69_9, reverse_line(L40_69_9))
% 2.73/1.04
% 2.73/1.04 [384] CLOSURE : ~left_apart_point(A39_69_9, L40_69_9)
% 2.73/1.04
% 2.73/1.04 [376] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [382] ~(left_apart_point(A39_70_9, L40_70_9) | left_apart_point(A39_70_9, reverse_line(L40_70_9)))
% 2.73/1.04
% 2.73/1.04 [382] ALPHA_NOT_OR : ~(left_apart_point(A39_70_9, L40_70_9) | left_apart_point(A39_70_9, reverse_line(L40_70_9)))
% 2.73/1.04 -> [385] ~left_apart_point(A39_70_9, L40_70_9), ~left_apart_point(A39_70_9, reverse_line(L40_70_9))
% 2.73/1.04
% 2.73/1.04 [385] CLOSURE : ~left_apart_point(A39_70_9, L40_70_9)
% 2.73/1.04
% 2.73/1.04 [358] BETA_OR : (unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8)) | unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8))))
% 2.73/1.04 -> [361] unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(M38_16_8))
% 2.73/1.04 -> [362] unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8)))
% 2.73/1.04
% 2.73/1.04 [362] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M38_16_8)), reverse_line(reverse_line(M38_16_8)))
% 2.73/1.04
% 2.73/1.04 [361] GAMMA_FORALL : ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38)))))
% 2.73/1.04 -> [383] ((unequally_directed_lines(reverse_line(M38_16_8), M38_19_8) & unequally_directed_lines(reverse_line(M38_16_8), reverse_line(M38_19_8))) => (left_convergent_lines(reverse_line(M38_16_8), M38_19_8) | left_convergent_lines(reverse_line(M38_16_8), reverse_line(M38_19_8))))
% 2.73/1.04
% 2.73/1.04 [383] BETA_IMPLY : ((unequally_directed_lines(reverse_line(M38_16_8), M38_19_8) & unequally_directed_lines(reverse_line(M38_16_8), reverse_line(M38_19_8))) => (left_convergent_lines(reverse_line(M38_16_8), M38_19_8) | left_convergent_lines(reverse_line(M38_16_8), reverse_line(M38_19_8))))
% 2.73/1.04 -> [386] ~(unequally_directed_lines(reverse_line(M38_16_8), M38_19_8) & unequally_directed_lines(reverse_line(M38_16_8), reverse_line(M38_19_8)))
% 2.73/1.04 -> [387] (left_convergent_lines(reverse_line(M38_16_8), M38_19_8) | left_convergent_lines(reverse_line(M38_16_8), reverse_line(M38_19_8)))
% 2.73/1.04
% 2.73/1.04 [386] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(M38_16_8), M38_19_8) & unequally_directed_lines(reverse_line(M38_16_8), reverse_line(M38_19_8)))
% 2.73/1.04 -> [388] ~unequally_directed_lines(reverse_line(M38_16_8), M38_19_8)
% 2.73/1.04 -> [389] ~unequally_directed_lines(reverse_line(M38_16_8), reverse_line(M38_19_8))
% 2.73/1.04
% 2.73/1.04 [388] CLOSURE : ~unequally_directed_lines(reverse_line(M38_16_8), M38_19_8)
% 2.73/1.04
% 2.73/1.04 [389] CLOSURE : ~unequally_directed_lines(reverse_line(M38_16_8), reverse_line(M38_19_8))
% 2.73/1.04
% 2.73/1.04 [387] BETA_OR : (left_convergent_lines(reverse_line(M38_16_8), M38_19_8) | left_convergent_lines(reverse_line(M38_16_8), reverse_line(M38_19_8)))
% 2.73/1.04 -> [390] left_convergent_lines(reverse_line(M38_16_8), M38_19_8)
% 2.73/1.04 -> [391] left_convergent_lines(reverse_line(M38_16_8), reverse_line(M38_19_8))
% 2.73/1.04
% 2.73/1.04 [390] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [392] ~(left_apart_point(A39_71_9, L40_71_9) | left_apart_point(A39_71_9, reverse_line(L40_71_9)))
% 2.73/1.04
% 2.73/1.04 [392] ALPHA_NOT_OR : ~(left_apart_point(A39_71_9, L40_71_9) | left_apart_point(A39_71_9, reverse_line(L40_71_9)))
% 2.73/1.04 -> [394] ~left_apart_point(A39_71_9, L40_71_9), ~left_apart_point(A39_71_9, reverse_line(L40_71_9))
% 2.73/1.04
% 2.73/1.04 [394] CLOSURE : ~left_apart_point(A39_71_9, L40_71_9)
% 2.73/1.04
% 2.73/1.04 [391] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.73/1.04 -> [393] ~(left_apart_point(A39_72_9, L40_72_9) | left_apart_point(A39_72_9, reverse_line(L40_72_9)))
% 2.73/1.04
% 2.73/1.04 [393] ALPHA_NOT_OR : ~(left_apart_point(A39_72_9, L40_72_9) | left_apart_point(A39_72_9, reverse_line(L40_72_9)))
% 2.73/1.04 -> [395] ~left_apart_point(A39_72_9, L40_72_9), ~left_apart_point(A39_72_9, reverse_line(L40_72_9))
% 2.73/1.04
% 2.73/1.04 [395] CLOSURE : ~left_apart_point(A39_72_9, L40_72_9)
% 2.73/1.04
% 2.73/1.04 % SZS output end Proof for theBenchmark.p
% 2.73/1.04 [0.720519s][1][Res] 2662 goroutines created
% 2.73/1.04 ==== Result ====
% 2.73/1.04 [0.720566s][1][Res] VALID
% 2.73/1.04 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------