TSTP Solution File: GEO252+1 by Goeland---1.0.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO252+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n007.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 15:18:44 EDT 2022
% Result : Theorem 4.44s 1.13s
% Output : Proof 4.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO252+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.12/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 06:56:01 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 [DMT] DMT loaded with preskolemization
% 0.13/0.35 [EQ] equality loaded.
% 0.13/0.35 [0.000043s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.36 Conjecture not found
% 0.13/0.36 Start search
% 0.13/0.36 nb_step : 1 - limit : 32
% 0.13/0.36 Launch Gotab with destructive = true
% 4.44/1.12 % SZS output start Proof for theBenchmark.p
% 4.44/1.13 [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, L79_79] : (((left_apart_point(A77_77, L79_79) & left_apart_point(B78_78, reverse_line(L79_79))) => (distinct_points(A77_77, B78_78) & left_convergent_lines(line_connecting(A77_77, B78_78), L79_79)))))
% 4.44/1.13 -> [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, L79_79] : (((left_apart_point(A77_77, L79_79) & left_apart_point(B78_78, reverse_line(L79_79))) => (distinct_points(A77_77, B78_78) & left_convergent_lines(line_connecting(A77_77, B78_78), L79_79))))
% 4.44/1.13
% 4.44/1.13 [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)))))
% 4.44/1.13 -> [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))))
% 4.44/1.13
% 4.44/1.13 [2] DELTA_NOT_FORALL : ~! [A77_77, B78_78, L79_79] : (((left_apart_point(A77_77, L79_79) & left_apart_point(B78_78, reverse_line(L79_79))) => (distinct_points(A77_77, B78_78) & left_convergent_lines(line_connecting(A77_77, B78_78), L79_79))))
% 4.44/1.13 -> [3] ~((left_apart_point(skolem_A7777, skolem_L7979) & left_apart_point(skolem_B7878, reverse_line(skolem_L7979))) => (distinct_points(skolem_A7777, skolem_B7878) & left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979)))
% 4.44/1.13
% 4.44/1.13 [3] ALPHA_NOT_IMPLY : ~((left_apart_point(skolem_A7777, skolem_L7979) & left_apart_point(skolem_B7878, reverse_line(skolem_L7979))) => (distinct_points(skolem_A7777, skolem_B7878) & left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979)))
% 4.44/1.13 -> [4] (left_apart_point(skolem_A7777, skolem_L7979) & left_apart_point(skolem_B7878, reverse_line(skolem_L7979))), ~(distinct_points(skolem_A7777, skolem_B7878) & left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979))
% 4.44/1.13
% 4.44/1.13 [4] ALPHA_AND : (left_apart_point(skolem_A7777, skolem_L7979) & left_apart_point(skolem_B7878, reverse_line(skolem_L7979)))
% 4.44/1.13 -> [5] left_apart_point(skolem_A7777, skolem_L7979), left_apart_point(skolem_B7878, reverse_line(skolem_L7979))
% 4.44/1.13
% 4.44/1.13 [5] BETA_NOT_AND : ~(distinct_points(skolem_A7777, skolem_B7878) & left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979))
% 4.44/1.13 -> [6] ~distinct_points(skolem_A7777, skolem_B7878)
% 4.44/1.13 -> [7] ~left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979)
% 4.44/1.13
% 4.44/1.13 [6] GAMMA_FORALL : ! [A20_20] : (~distinct_points(A20_20, A20_20))
% 4.44/1.13 -> [8] ~distinct_points(A20_0_0, A20_0_0)
% 4.44/1.13
% 4.44/1.13 [8] 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))))
% 4.44/1.13 -> [10] (distinct_points(skolem_A7777, skolem_A7777) => (distinct_points(skolem_A7777, skolem_B7878) | distinct_points(skolem_A7777, skolem_B7878)))
% 4.44/1.13
% 4.44/1.13 [10] BETA_IMPLY : (distinct_points(skolem_A7777, skolem_A7777) => (distinct_points(skolem_A7777, skolem_B7878) | distinct_points(skolem_A7777, skolem_B7878)))
% 4.44/1.13 -> [12] ~distinct_points(skolem_A7777, skolem_A7777)
% 4.44/1.13 -> [13] (distinct_points(skolem_A7777, skolem_B7878) | distinct_points(skolem_A7777, skolem_B7878))
% 4.44/1.13
% 4.44/1.13 [13] BETA_OR : (distinct_points(skolem_A7777, skolem_B7878) | distinct_points(skolem_A7777, skolem_B7878))
% 4.44/1.13 -> [16] distinct_points(skolem_A7777, skolem_B7878)
% 4.44/1.13 -> [17] distinct_points(skolem_A7777, skolem_B7878)
% 4.44/1.13
% 4.44/1.13 [16] CLOSURE : distinct_points(skolem_A7777, skolem_B7878)
% 4.44/1.13
% 4.44/1.13 [17] CLOSURE : distinct_points(skolem_A7777, skolem_B7878)
% 4.44/1.13
% 4.44/1.13 [12] GAMMA_FORALL : ! [L24_24] : (~distinct_lines(L24_24, L24_24))
% 4.44/1.13 -> [20] ~distinct_lines(N27_1_3, N27_1_3)
% 4.44/1.13
% 4.44/1.13 [20] 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))))
% 4.44/1.13 -> [23] (distinct_lines(N27_1_3, N27_1_3) => (distinct_lines(N27_1_3, N27_1_3) | distinct_lines(N27_1_3, N27_1_3)))
% 4.44/1.13
% 4.44/1.13 [23] BETA_IMPLY : (distinct_lines(N27_1_3, N27_1_3) => (distinct_lines(N27_1_3, N27_1_3) | distinct_lines(N27_1_3, N27_1_3)))
% 4.44/1.13 -> [26] ~distinct_lines(N27_1_3, N27_1_3)
% 4.44/1.13 -> [27] (distinct_lines(N27_1_3, N27_1_3) | distinct_lines(N27_1_3, N27_1_3))
% 4.44/1.13
% 4.44/1.13 [27] BETA_OR : (distinct_lines(N27_1_3, N27_1_3) | distinct_lines(N27_1_3, N27_1_3))
% 4.44/1.13 -> [30] distinct_lines(N27_1_3, N27_1_3)
% 4.44/1.13 -> [31] distinct_lines(N27_1_3, N27_1_3)
% 4.44/1.13
% 4.44/1.13 [31] CLOSURE : distinct_lines(N27_1_3, N27_1_3)
% 4.44/1.13
% 4.44/1.13 [30] CLOSURE : distinct_lines(N27_1_3, N27_1_3)
% 4.44/1.13
% 4.44/1.13 [26] GAMMA_FORALL : ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28))
% 4.44/1.13 -> [32] ~unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))
% 4.44/1.13
% 4.44/1.13 [32] 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))))
% 4.44/1.13 -> [34] (unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)) => (unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)) | unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))))
% 4.44/1.13
% 4.44/1.13 [34] BETA_IMPLY : (unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)) => (unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)) | unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))))
% 4.44/1.13 -> [36] ~unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))
% 4.44/1.13 -> [37] (unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)) | unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)))
% 4.44/1.13
% 4.44/1.13 [37] BETA_OR : (unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)) | unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)))
% 4.44/1.13 -> [40] unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))
% 4.44/1.13 -> [41] unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))
% 4.44/1.13
% 4.44/1.13 [41] CLOSURE : unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))
% 4.44/1.13
% 4.44/1.13 [40] CLOSURE : unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))
% 4.44/1.13
% 4.44/1.13 [44] BETA_IMPLY : ((unequally_directed_lines(reverse_line(M38_32_8), M38_32_8) & unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))) => ((unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)) & unequally_directed_lines(reverse_line(M38_32_8), reverse_line(reverse_line(M38_32_8)))) | (unequally_directed_lines(M38_32_8, reverse_line(M38_32_8)) & unequally_directed_lines(M38_32_8, reverse_line(reverse_line(M38_32_8))))))
% 4.44/1.13 -> [514] ~(unequally_directed_lines(reverse_line(M38_32_8), M38_32_8) & unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)))
% 4.44/1.13 -> [515] ((unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)) & unequally_directed_lines(reverse_line(M38_32_8), reverse_line(reverse_line(M38_32_8)))) | (unequally_directed_lines(M38_32_8, reverse_line(M38_32_8)) & unequally_directed_lines(M38_32_8, reverse_line(reverse_line(M38_32_8)))))
% 4.44/1.13
% 4.44/1.13 [514] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(M38_32_8), M38_32_8) & unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)))
% 4.44/1.13 -> [516] ~unequally_directed_lines(reverse_line(M38_32_8), M38_32_8)
% 4.44/1.13 -> [517] ~unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))
% 4.44/1.13
% 4.44/1.13 [516] 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)))))
% 4.44/1.13 -> [524] ((line(reverse_line(M38_32_8)) & line(M38_32_8)) => (unequally_directed_lines(reverse_line(M38_32_8), M38_32_8) | unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))))
% 4.44/1.13
% 4.44/1.13 [524] BETA_IMPLY : ((line(reverse_line(M38_32_8)) & line(M38_32_8)) => (unequally_directed_lines(reverse_line(M38_32_8), M38_32_8) | unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))))
% 4.44/1.13 -> [528] ~(line(reverse_line(M38_32_8)) & line(M38_32_8))
% 4.44/1.13 -> [529] (unequally_directed_lines(reverse_line(M38_32_8), M38_32_8) | unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)))
% 4.44/1.13
% 4.44/1.13 [529] BETA_OR : (unequally_directed_lines(reverse_line(M38_32_8), M38_32_8) | unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)))
% 4.44/1.13 -> [536] unequally_directed_lines(reverse_line(M38_32_8), M38_32_8)
% 4.44/1.13 -> [537] unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))
% 4.44/1.13
% 4.44/1.13 [536] CLOSURE : unequally_directed_lines(reverse_line(M38_32_8), M38_32_8)
% 4.44/1.13
% 4.44/1.13 [537] CLOSURE : unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))
% 4.44/1.13
% 4.44/1.13 [528] BETA_NOT_AND : ~(line(reverse_line(M38_32_8)) & line(M38_32_8))
% 4.44/1.13 -> [532] ~line(reverse_line(M38_32_8))
% 4.44/1.13 -> [533] ~line(M38_32_8)
% 4.44/1.13
% 4.44/1.13 [533] 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)))))
% 4.44/1.13 -> [555] ((unequally_directed_lines(L37_29_8, M38_29_8) & unequally_directed_lines(L37_29_8, reverse_line(M38_29_8))) => (left_convergent_lines(L37_29_8, M38_29_8) | left_convergent_lines(L37_29_8, reverse_line(M38_29_8))))
% 4.44/1.13
% 4.44/1.13 [555] BETA_IMPLY : ((unequally_directed_lines(L37_29_8, M38_29_8) & unequally_directed_lines(L37_29_8, reverse_line(M38_29_8))) => (left_convergent_lines(L37_29_8, M38_29_8) | left_convergent_lines(L37_29_8, reverse_line(M38_29_8))))
% 4.44/1.13 -> [556] ~(unequally_directed_lines(L37_29_8, M38_29_8) & unequally_directed_lines(L37_29_8, reverse_line(M38_29_8)))
% 4.44/1.13 -> [557] (left_convergent_lines(L37_29_8, M38_29_8) | left_convergent_lines(L37_29_8, reverse_line(M38_29_8)))
% 4.44/1.13
% 4.44/1.13 [556] BETA_NOT_AND : ~(unequally_directed_lines(L37_29_8, M38_29_8) & unequally_directed_lines(L37_29_8, reverse_line(M38_29_8)))
% 4.44/1.13 -> [561] ~unequally_directed_lines(L37_29_8, M38_29_8)
% 4.44/1.13 -> [562] ~unequally_directed_lines(L37_29_8, reverse_line(M38_29_8))
% 4.44/1.13
% 4.44/1.13 [561] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [576] ~(left_apart_point(A39_94_9, L40_94_9) | left_apart_point(A39_94_9, reverse_line(L40_94_9)))
% 4.44/1.13
% 4.44/1.13 [576] ALPHA_NOT_OR : ~(left_apart_point(A39_94_9, L40_94_9) | left_apart_point(A39_94_9, reverse_line(L40_94_9)))
% 4.44/1.13 -> [577] ~left_apart_point(A39_94_9, L40_94_9), ~left_apart_point(A39_94_9, reverse_line(L40_94_9))
% 4.44/1.13
% 4.44/1.13 [577] CLOSURE : ~left_apart_point(A39_94_9, L40_94_9)
% 4.44/1.13
% 4.44/1.13 [562] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [585] ~(left_apart_point(A39_100_9, L40_100_9) | left_apart_point(A39_100_9, reverse_line(L40_100_9)))
% 4.44/1.13
% 4.44/1.13 [585] ALPHA_NOT_OR : ~(left_apart_point(A39_100_9, L40_100_9) | left_apart_point(A39_100_9, reverse_line(L40_100_9)))
% 4.44/1.13 -> [588] ~left_apart_point(A39_100_9, L40_100_9), ~left_apart_point(A39_100_9, reverse_line(L40_100_9))
% 4.44/1.13
% 4.44/1.13 [588] CLOSURE : ~left_apart_point(A39_100_9, L40_100_9)
% 4.44/1.13
% 4.44/1.13 [557] BETA_OR : (left_convergent_lines(L37_29_8, M38_29_8) | left_convergent_lines(L37_29_8, reverse_line(M38_29_8)))
% 4.44/1.13 -> [558] left_convergent_lines(L37_29_8, M38_29_8)
% 4.44/1.13 -> [559] left_convergent_lines(L37_29_8, reverse_line(M38_29_8))
% 4.44/1.13
% 4.44/1.13 [559] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [578] ~(left_apart_point(A39_95_9, L40_95_9) | left_apart_point(A39_95_9, reverse_line(L40_95_9)))
% 4.44/1.13
% 4.44/1.13 [578] ALPHA_NOT_OR : ~(left_apart_point(A39_95_9, L40_95_9) | left_apart_point(A39_95_9, reverse_line(L40_95_9)))
% 4.44/1.13 -> [587] ~left_apart_point(A39_95_9, L40_95_9), ~left_apart_point(A39_95_9, reverse_line(L40_95_9))
% 4.44/1.13
% 4.44/1.13 [587] CLOSURE : ~left_apart_point(A39_95_9, L40_95_9)
% 4.44/1.13
% 4.44/1.13 [558] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [580] ~(left_apart_point(A39_97_9, L40_97_9) | left_apart_point(A39_97_9, reverse_line(L40_97_9)))
% 4.44/1.13
% 4.44/1.13 [580] ALPHA_NOT_OR : ~(left_apart_point(A39_97_9, L40_97_9) | left_apart_point(A39_97_9, reverse_line(L40_97_9)))
% 4.44/1.13 -> [596] ~left_apart_point(A39_97_9, L40_97_9), ~left_apart_point(A39_97_9, reverse_line(L40_97_9))
% 4.44/1.13
% 4.44/1.13 [596] CLOSURE : ~left_apart_point(A39_97_9, L40_97_9)
% 4.44/1.13
% 4.44/1.13 [532] 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)))))
% 4.44/1.13 -> [544] ((unequally_directed_lines(L37_28_8, M38_28_8) & unequally_directed_lines(L37_28_8, reverse_line(M38_28_8))) => (left_convergent_lines(L37_28_8, M38_28_8) | left_convergent_lines(L37_28_8, reverse_line(M38_28_8))))
% 4.44/1.13
% 4.44/1.13 [544] BETA_IMPLY : ((unequally_directed_lines(L37_28_8, M38_28_8) & unequally_directed_lines(L37_28_8, reverse_line(M38_28_8))) => (left_convergent_lines(L37_28_8, M38_28_8) | left_convergent_lines(L37_28_8, reverse_line(M38_28_8))))
% 4.44/1.13 -> [563] ~(unequally_directed_lines(L37_28_8, M38_28_8) & unequally_directed_lines(L37_28_8, reverse_line(M38_28_8)))
% 4.44/1.13 -> [564] (left_convergent_lines(L37_28_8, M38_28_8) | left_convergent_lines(L37_28_8, reverse_line(M38_28_8)))
% 4.44/1.13
% 4.44/1.13 [564] BETA_OR : (left_convergent_lines(L37_28_8, M38_28_8) | left_convergent_lines(L37_28_8, reverse_line(M38_28_8)))
% 4.44/1.13 -> [572] left_convergent_lines(L37_28_8, M38_28_8)
% 4.44/1.13 -> [573] left_convergent_lines(L37_28_8, reverse_line(M38_28_8))
% 4.44/1.13
% 4.44/1.13 [573] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [591] ~(left_apart_point(A39_102_9, L40_102_9) | left_apart_point(A39_102_9, reverse_line(L40_102_9)))
% 4.44/1.13
% 4.44/1.13 [591] ALPHA_NOT_OR : ~(left_apart_point(A39_102_9, L40_102_9) | left_apart_point(A39_102_9, reverse_line(L40_102_9)))
% 4.44/1.13 -> [592] ~left_apart_point(A39_102_9, L40_102_9), ~left_apart_point(A39_102_9, reverse_line(L40_102_9))
% 4.44/1.13
% 4.44/1.13 [592] CLOSURE : ~left_apart_point(A39_102_9, L40_102_9)
% 4.44/1.13
% 4.44/1.13 [572] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [598] ~(left_apart_point(A39_104_9, L40_104_9) | left_apart_point(A39_104_9, reverse_line(L40_104_9)))
% 4.44/1.13
% 4.44/1.13 [598] ALPHA_NOT_OR : ~(left_apart_point(A39_104_9, L40_104_9) | left_apart_point(A39_104_9, reverse_line(L40_104_9)))
% 4.44/1.13 -> [599] ~left_apart_point(A39_104_9, L40_104_9), ~left_apart_point(A39_104_9, reverse_line(L40_104_9))
% 4.44/1.13
% 4.44/1.13 [599] CLOSURE : ~left_apart_point(A39_104_9, L40_104_9)
% 4.44/1.13
% 4.44/1.13 [563] BETA_NOT_AND : ~(unequally_directed_lines(L37_28_8, M38_28_8) & unequally_directed_lines(L37_28_8, reverse_line(M38_28_8)))
% 4.44/1.13 -> [594] ~unequally_directed_lines(L37_28_8, M38_28_8)
% 4.44/1.13 -> [595] ~unequally_directed_lines(L37_28_8, reverse_line(M38_28_8))
% 4.44/1.13
% 4.44/1.13 [594] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [600] ~(left_apart_point(A39_105_9, L40_105_9) | left_apart_point(A39_105_9, reverse_line(L40_105_9)))
% 4.44/1.13
% 4.44/1.13 [600] ALPHA_NOT_OR : ~(left_apart_point(A39_105_9, L40_105_9) | left_apart_point(A39_105_9, reverse_line(L40_105_9)))
% 4.44/1.13 -> [602] ~left_apart_point(A39_105_9, L40_105_9), ~left_apart_point(A39_105_9, reverse_line(L40_105_9))
% 4.44/1.13
% 4.44/1.13 [602] CLOSURE : ~left_apart_point(A39_105_9, L40_105_9)
% 4.44/1.13
% 4.44/1.13 [595] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [601] ~(left_apart_point(A39_106_9, L40_106_9) | left_apart_point(A39_106_9, reverse_line(L40_106_9)))
% 4.44/1.13
% 4.44/1.13 [601] ALPHA_NOT_OR : ~(left_apart_point(A39_106_9, L40_106_9) | left_apart_point(A39_106_9, reverse_line(L40_106_9)))
% 4.44/1.13 -> [603] ~left_apart_point(A39_106_9, L40_106_9), ~left_apart_point(A39_106_9, reverse_line(L40_106_9))
% 4.44/1.13
% 4.44/1.13 [603] CLOSURE : ~left_apart_point(A39_106_9, L40_106_9)
% 4.44/1.13
% 4.44/1.13 [525] BETA_IMPLY : ((line(reverse_line(M38_32_8)) & line(M38_32_8)) => (unequally_directed_lines(reverse_line(M38_32_8), M38_32_8) | unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))))
% 4.44/1.13 -> [604] ~(line(reverse_line(M38_32_8)) & line(M38_32_8))
% 4.44/1.13 -> [605] (unequally_directed_lines(reverse_line(M38_32_8), M38_32_8) | unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)))
% 4.44/1.13
% 4.44/1.13 [604] BETA_NOT_AND : ~(line(reverse_line(M38_32_8)) & line(M38_32_8))
% 4.44/1.13 -> [606] ~line(reverse_line(M38_32_8))
% 4.44/1.13 -> [607] ~line(M38_32_8)
% 4.44/1.13
% 4.44/1.13 [606] 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)))))
% 4.44/1.13 -> [610] ((unequally_directed_lines(L37_30_8, M38_30_8) & unequally_directed_lines(L37_30_8, reverse_line(M38_30_8))) => (left_convergent_lines(L37_30_8, M38_30_8) | left_convergent_lines(L37_30_8, reverse_line(M38_30_8))))
% 4.44/1.13
% 4.44/1.13 [610] BETA_IMPLY : ((unequally_directed_lines(L37_30_8, M38_30_8) & unequally_directed_lines(L37_30_8, reverse_line(M38_30_8))) => (left_convergent_lines(L37_30_8, M38_30_8) | left_convergent_lines(L37_30_8, reverse_line(M38_30_8))))
% 4.44/1.13 -> [612] ~(unequally_directed_lines(L37_30_8, M38_30_8) & unequally_directed_lines(L37_30_8, reverse_line(M38_30_8)))
% 4.44/1.13 -> [613] (left_convergent_lines(L37_30_8, M38_30_8) | left_convergent_lines(L37_30_8, reverse_line(M38_30_8)))
% 4.44/1.13
% 4.44/1.13 [612] BETA_NOT_AND : ~(unequally_directed_lines(L37_30_8, M38_30_8) & unequally_directed_lines(L37_30_8, reverse_line(M38_30_8)))
% 4.44/1.13 -> [618] ~unequally_directed_lines(L37_30_8, M38_30_8)
% 4.44/1.13 -> [619] ~unequally_directed_lines(L37_30_8, reverse_line(M38_30_8))
% 4.44/1.13
% 4.44/1.13 [618] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [628] ~(left_apart_point(A39_107_9, L40_107_9) | left_apart_point(A39_107_9, reverse_line(L40_107_9)))
% 4.44/1.13
% 4.44/1.13 [628] ALPHA_NOT_OR : ~(left_apart_point(A39_107_9, L40_107_9) | left_apart_point(A39_107_9, reverse_line(L40_107_9)))
% 4.44/1.13 -> [629] ~left_apart_point(A39_107_9, L40_107_9), ~left_apart_point(A39_107_9, reverse_line(L40_107_9))
% 4.44/1.13
% 4.44/1.13 [629] CLOSURE : ~left_apart_point(A39_107_9, L40_107_9)
% 4.44/1.13
% 4.44/1.13 [619] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [633] ~(left_apart_point(A39_108_9, L40_108_9) | left_apart_point(A39_108_9, reverse_line(L40_108_9)))
% 4.44/1.13
% 4.44/1.13 [633] ALPHA_NOT_OR : ~(left_apart_point(A39_108_9, L40_108_9) | left_apart_point(A39_108_9, reverse_line(L40_108_9)))
% 4.44/1.13 -> [634] ~left_apart_point(A39_108_9, L40_108_9), ~left_apart_point(A39_108_9, reverse_line(L40_108_9))
% 4.44/1.13
% 4.44/1.13 [634] CLOSURE : ~left_apart_point(A39_108_9, L40_108_9)
% 4.44/1.13
% 4.44/1.13 [613] BETA_OR : (left_convergent_lines(L37_30_8, M38_30_8) | left_convergent_lines(L37_30_8, reverse_line(M38_30_8)))
% 4.44/1.13 -> [624] left_convergent_lines(L37_30_8, M38_30_8)
% 4.44/1.13 -> [625] left_convergent_lines(L37_30_8, reverse_line(M38_30_8))
% 4.44/1.13
% 4.44/1.13 [625] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [648] ~(left_apart_point(A39_112_9, L40_112_9) | left_apart_point(A39_112_9, reverse_line(L40_112_9)))
% 4.44/1.13
% 4.44/1.13 [648] ALPHA_NOT_OR : ~(left_apart_point(A39_112_9, L40_112_9) | left_apart_point(A39_112_9, reverse_line(L40_112_9)))
% 4.44/1.13 -> [651] ~left_apart_point(A39_112_9, L40_112_9), ~left_apart_point(A39_112_9, reverse_line(L40_112_9))
% 4.44/1.13
% 4.44/1.13 [651] CLOSURE : ~left_apart_point(A39_112_9, L40_112_9)
% 4.44/1.13
% 4.44/1.13 [624] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [649] ~(left_apart_point(A39_113_9, L40_113_9) | left_apart_point(A39_113_9, reverse_line(L40_113_9)))
% 4.44/1.13
% 4.44/1.13 [649] ALPHA_NOT_OR : ~(left_apart_point(A39_113_9, L40_113_9) | left_apart_point(A39_113_9, reverse_line(L40_113_9)))
% 4.44/1.13 -> [650] ~left_apart_point(A39_113_9, L40_113_9), ~left_apart_point(A39_113_9, reverse_line(L40_113_9))
% 4.44/1.13
% 4.44/1.13 [650] CLOSURE : ~left_apart_point(A39_113_9, L40_113_9)
% 4.44/1.13
% 4.44/1.13 [607] 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)))))
% 4.44/1.13 -> [611] ((unequally_directed_lines(L37_31_8, M38_31_8) & unequally_directed_lines(L37_31_8, reverse_line(M38_31_8))) => (left_convergent_lines(L37_31_8, M38_31_8) | left_convergent_lines(L37_31_8, reverse_line(M38_31_8))))
% 4.44/1.13
% 4.44/1.13 [611] BETA_IMPLY : ((unequally_directed_lines(L37_31_8, M38_31_8) & unequally_directed_lines(L37_31_8, reverse_line(M38_31_8))) => (left_convergent_lines(L37_31_8, M38_31_8) | left_convergent_lines(L37_31_8, reverse_line(M38_31_8))))
% 4.44/1.13 -> [614] ~(unequally_directed_lines(L37_31_8, M38_31_8) & unequally_directed_lines(L37_31_8, reverse_line(M38_31_8)))
% 4.44/1.13 -> [615] (left_convergent_lines(L37_31_8, M38_31_8) | left_convergent_lines(L37_31_8, reverse_line(M38_31_8)))
% 4.44/1.13
% 4.44/1.13 [614] BETA_NOT_AND : ~(unequally_directed_lines(L37_31_8, M38_31_8) & unequally_directed_lines(L37_31_8, reverse_line(M38_31_8)))
% 4.44/1.13 -> [620] ~unequally_directed_lines(L37_31_8, M38_31_8)
% 4.44/1.13 -> [621] ~unequally_directed_lines(L37_31_8, reverse_line(M38_31_8))
% 4.44/1.13
% 4.44/1.13 [620] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [638] ~(left_apart_point(A39_110_9, L40_110_9) | left_apart_point(A39_110_9, reverse_line(L40_110_9)))
% 4.44/1.13
% 4.44/1.13 [638] ALPHA_NOT_OR : ~(left_apart_point(A39_110_9, L40_110_9) | left_apart_point(A39_110_9, reverse_line(L40_110_9)))
% 4.44/1.13 -> [639] ~left_apart_point(A39_110_9, L40_110_9), ~left_apart_point(A39_110_9, reverse_line(L40_110_9))
% 4.44/1.13
% 4.44/1.13 [639] CLOSURE : ~left_apart_point(A39_110_9, L40_110_9)
% 4.44/1.13
% 4.44/1.13 [621] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [644] ~(left_apart_point(A39_111_9, L40_111_9) | left_apart_point(A39_111_9, reverse_line(L40_111_9)))
% 4.44/1.13
% 4.44/1.13 [644] ALPHA_NOT_OR : ~(left_apart_point(A39_111_9, L40_111_9) | left_apart_point(A39_111_9, reverse_line(L40_111_9)))
% 4.44/1.13 -> [647] ~left_apart_point(A39_111_9, L40_111_9), ~left_apart_point(A39_111_9, reverse_line(L40_111_9))
% 4.44/1.13
% 4.44/1.13 [647] CLOSURE : ~left_apart_point(A39_111_9, L40_111_9)
% 4.44/1.13
% 4.44/1.13 [615] BETA_OR : (left_convergent_lines(L37_31_8, M38_31_8) | left_convergent_lines(L37_31_8, reverse_line(M38_31_8)))
% 4.44/1.13 -> [622] left_convergent_lines(L37_31_8, M38_31_8)
% 4.44/1.13 -> [623] left_convergent_lines(L37_31_8, reverse_line(M38_31_8))
% 4.44/1.13
% 4.44/1.13 [623] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [635] ~(left_apart_point(A39_109_9, L40_109_9) | left_apart_point(A39_109_9, reverse_line(L40_109_9)))
% 4.44/1.13
% 4.44/1.13 [635] ALPHA_NOT_OR : ~(left_apart_point(A39_109_9, L40_109_9) | left_apart_point(A39_109_9, reverse_line(L40_109_9)))
% 4.44/1.13 -> [640] ~left_apart_point(A39_109_9, L40_109_9), ~left_apart_point(A39_109_9, reverse_line(L40_109_9))
% 4.44/1.13
% 4.44/1.13 [640] CLOSURE : ~left_apart_point(A39_109_9, L40_109_9)
% 4.44/1.13
% 4.44/1.13 [622] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [654] ~(left_apart_point(A39_114_9, L40_114_9) | left_apart_point(A39_114_9, reverse_line(L40_114_9)))
% 4.44/1.13
% 4.44/1.13 [654] ALPHA_NOT_OR : ~(left_apart_point(A39_114_9, L40_114_9) | left_apart_point(A39_114_9, reverse_line(L40_114_9)))
% 4.44/1.13 -> [658] ~left_apart_point(A39_114_9, L40_114_9), ~left_apart_point(A39_114_9, reverse_line(L40_114_9))
% 4.44/1.13
% 4.44/1.13 [658] CLOSURE : ~left_apart_point(A39_114_9, L40_114_9)
% 4.44/1.13
% 4.44/1.13 [605] BETA_OR : (unequally_directed_lines(reverse_line(M38_32_8), M38_32_8) | unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)))
% 4.44/1.13 -> [608] unequally_directed_lines(reverse_line(M38_32_8), M38_32_8)
% 4.44/1.13 -> [609] unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))
% 4.44/1.13
% 4.44/1.13 [609] CLOSURE : unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))
% 4.44/1.13
% 4.44/1.13 [608] 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)))))
% 4.44/1.13 -> [630] ((unequally_directed_lines(reverse_line(M38_32_8), M38_32_8) & unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))) => (left_convergent_lines(reverse_line(M38_32_8), M38_32_8) | left_convergent_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))))
% 4.44/1.13
% 4.44/1.13 [630] BETA_IMPLY : ((unequally_directed_lines(reverse_line(M38_32_8), M38_32_8) & unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))) => (left_convergent_lines(reverse_line(M38_32_8), M38_32_8) | left_convergent_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))))
% 4.44/1.13 -> [631] ~(unequally_directed_lines(reverse_line(M38_32_8), M38_32_8) & unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)))
% 4.44/1.13 -> [632] (left_convergent_lines(reverse_line(M38_32_8), M38_32_8) | left_convergent_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)))
% 4.44/1.13
% 4.44/1.13 [632] BETA_OR : (left_convergent_lines(reverse_line(M38_32_8), M38_32_8) | left_convergent_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)))
% 4.44/1.13 -> [636] left_convergent_lines(reverse_line(M38_32_8), M38_32_8)
% 4.44/1.13 -> [637] left_convergent_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))
% 4.44/1.13
% 4.44/1.13 [637] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [657] ~(left_apart_point(A39_115_9, L40_115_9) | left_apart_point(A39_115_9, reverse_line(L40_115_9)))
% 4.44/1.13
% 4.44/1.13 [657] ALPHA_NOT_OR : ~(left_apart_point(A39_115_9, L40_115_9) | left_apart_point(A39_115_9, reverse_line(L40_115_9)))
% 4.44/1.13 -> [659] ~left_apart_point(A39_115_9, L40_115_9), ~left_apart_point(A39_115_9, reverse_line(L40_115_9))
% 4.44/1.13
% 4.44/1.13 [659] CLOSURE : ~left_apart_point(A39_115_9, L40_115_9)
% 4.44/1.13
% 4.44/1.13 [636] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [660] ~(left_apart_point(A39_116_9, L40_116_9) | left_apart_point(A39_116_9, reverse_line(L40_116_9)))
% 4.44/1.13
% 4.44/1.13 [660] ALPHA_NOT_OR : ~(left_apart_point(A39_116_9, L40_116_9) | left_apart_point(A39_116_9, reverse_line(L40_116_9)))
% 4.44/1.13 -> [661] ~left_apart_point(A39_116_9, L40_116_9), ~left_apart_point(A39_116_9, reverse_line(L40_116_9))
% 4.44/1.13
% 4.44/1.13 [661] CLOSURE : ~left_apart_point(A39_116_9, L40_116_9)
% 4.44/1.13
% 4.44/1.13 [631] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(M38_32_8), M38_32_8) & unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)))
% 4.44/1.13 -> [641] ~unequally_directed_lines(reverse_line(M38_32_8), M38_32_8)
% 4.44/1.13 -> [642] ~unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8))
% 4.44/1.13
% 4.44/1.13 [641] CLOSURE : ~unequally_directed_lines(reverse_line(M38_32_8), M38_32_8)
% 4.44/1.13
% 4.44/1.13 [642] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [672] ~(left_apart_point(A39_117_9, L40_117_9) | left_apart_point(A39_117_9, reverse_line(L40_117_9)))
% 4.44/1.13
% 4.44/1.13 [672] ALPHA_NOT_OR : ~(left_apart_point(A39_117_9, L40_117_9) | left_apart_point(A39_117_9, reverse_line(L40_117_9)))
% 4.44/1.13 -> [677] ~left_apart_point(A39_117_9, L40_117_9), ~left_apart_point(A39_117_9, reverse_line(L40_117_9))
% 4.44/1.13
% 4.44/1.13 [677] CLOSURE : ~left_apart_point(A39_117_9, L40_117_9)
% 4.44/1.13
% 4.44/1.13 [515] BETA_OR : ((unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)) & unequally_directed_lines(reverse_line(M38_32_8), reverse_line(reverse_line(M38_32_8)))) | (unequally_directed_lines(M38_32_8, reverse_line(M38_32_8)) & unequally_directed_lines(M38_32_8, reverse_line(reverse_line(M38_32_8)))))
% 4.44/1.13 -> [697] (unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)) & unequally_directed_lines(reverse_line(M38_32_8), reverse_line(reverse_line(M38_32_8))))
% 4.44/1.13 -> [698] (unequally_directed_lines(M38_32_8, reverse_line(M38_32_8)) & unequally_directed_lines(M38_32_8, reverse_line(reverse_line(M38_32_8))))
% 4.44/1.13
% 4.44/1.13 [697] ALPHA_AND : (unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)) & unequally_directed_lines(reverse_line(M38_32_8), reverse_line(reverse_line(M38_32_8))))
% 4.44/1.13 -> [700] unequally_directed_lines(reverse_line(M38_32_8), reverse_line(M38_32_8)), unequally_directed_lines(reverse_line(M38_32_8), reverse_line(reverse_line(M38_32_8)))
% 4.44/1.13
% 4.44/1.13 [700] CLOSURE : unequally_directed_lines(reverse_line(M38_32_8), reverse_line(reverse_line(M38_32_8)))
% 4.44/1.13
% 4.44/1.13 [698] ALPHA_AND : (unequally_directed_lines(L37_38_8, reverse_line(M38_32_8)) & unequally_directed_lines(L37_38_8, reverse_line(reverse_line(M38_32_8))))
% 4.44/1.13 -> [702] unequally_directed_lines(L37_38_8, reverse_line(M38_32_8)), unequally_directed_lines(L37_38_8, reverse_line(reverse_line(M38_32_8)))
% 4.44/1.13
% 4.44/1.13 [702] 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)))))
% 4.44/1.13 -> [703] ((line(reverse_line(L37_38_8)) & line(reverse_line(L37_38_8))) => (unequally_directed_lines(reverse_line(L37_38_8), reverse_line(L37_38_8)) | unequally_directed_lines(reverse_line(L37_38_8), reverse_line(reverse_line(L37_38_8)))))
% 4.44/1.13
% 4.44/1.13 [703] BETA_IMPLY : ((line(reverse_line(L37_38_8)) & line(reverse_line(L37_38_8))) => (unequally_directed_lines(reverse_line(L37_38_8), reverse_line(L37_38_8)) | unequally_directed_lines(reverse_line(L37_38_8), reverse_line(reverse_line(L37_38_8)))))
% 4.44/1.13 -> [704] ~(line(reverse_line(L37_38_8)) & line(reverse_line(L37_38_8)))
% 4.44/1.13 -> [705] (unequally_directed_lines(reverse_line(L37_38_8), reverse_line(L37_38_8)) | unequally_directed_lines(reverse_line(L37_38_8), reverse_line(reverse_line(L37_38_8))))
% 4.44/1.13
% 4.44/1.13 [704] BETA_NOT_AND : ~(line(reverse_line(L37_38_8)) & line(reverse_line(L37_38_8)))
% 4.44/1.13 -> [706] ~line(reverse_line(L37_38_8))
% 4.44/1.13 -> [707] ~line(reverse_line(L37_38_8))
% 4.44/1.13
% 4.44/1.13 [707] 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)))))
% 4.44/1.13 -> [710] ((unequally_directed_lines(L37_36_8, M38_36_8) & unequally_directed_lines(L37_36_8, reverse_line(M38_36_8))) => (left_convergent_lines(L37_36_8, M38_36_8) | left_convergent_lines(L37_36_8, reverse_line(M38_36_8))))
% 4.44/1.13
% 4.44/1.13 [710] BETA_IMPLY : ((unequally_directed_lines(L37_36_8, M38_36_8) & unequally_directed_lines(L37_36_8, reverse_line(M38_36_8))) => (left_convergent_lines(L37_36_8, M38_36_8) | left_convergent_lines(L37_36_8, reverse_line(M38_36_8))))
% 4.44/1.13 -> [712] ~(unequally_directed_lines(L37_36_8, M38_36_8) & unequally_directed_lines(L37_36_8, reverse_line(M38_36_8)))
% 4.44/1.13 -> [713] (left_convergent_lines(L37_36_8, M38_36_8) | left_convergent_lines(L37_36_8, reverse_line(M38_36_8)))
% 4.44/1.13
% 4.44/1.13 [712] BETA_NOT_AND : ~(unequally_directed_lines(L37_36_8, M38_36_8) & unequally_directed_lines(L37_36_8, reverse_line(M38_36_8)))
% 4.44/1.13 -> [716] ~unequally_directed_lines(L37_36_8, M38_36_8)
% 4.44/1.13 -> [717] ~unequally_directed_lines(L37_36_8, reverse_line(M38_36_8))
% 4.44/1.13
% 4.44/1.13 [716] CLOSURE : ~unequally_directed_lines(L37_36_8, M38_36_8)
% 4.44/1.13
% 4.44/1.13 [717] CLOSURE : ~unequally_directed_lines(L37_36_8, reverse_line(M38_36_8))
% 4.44/1.13
% 4.44/1.13 [713] BETA_OR : (left_convergent_lines(L37_36_8, M38_36_8) | left_convergent_lines(L37_36_8, reverse_line(M38_36_8)))
% 4.44/1.13 -> [720] left_convergent_lines(L37_36_8, M38_36_8)
% 4.44/1.13 -> [721] left_convergent_lines(L37_36_8, reverse_line(M38_36_8))
% 4.44/1.13
% 4.44/1.13 [720] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [727] ~(left_apart_point(A39_124_9, L40_124_9) | left_apart_point(A39_124_9, reverse_line(L40_124_9)))
% 4.44/1.13
% 4.44/1.13 [727] ALPHA_NOT_OR : ~(left_apart_point(A39_124_9, L40_124_9) | left_apart_point(A39_124_9, reverse_line(L40_124_9)))
% 4.44/1.13 -> [733] ~left_apart_point(A39_124_9, L40_124_9), ~left_apart_point(A39_124_9, reverse_line(L40_124_9))
% 4.44/1.13
% 4.44/1.13 [733] CLOSURE : ~left_apart_point(A39_124_9, L40_124_9)
% 4.44/1.13
% 4.44/1.13 [721] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [725] ~(left_apart_point(A39_123_9, L40_123_9) | left_apart_point(A39_123_9, reverse_line(L40_123_9)))
% 4.44/1.13
% 4.44/1.13 [725] ALPHA_NOT_OR : ~(left_apart_point(A39_123_9, L40_123_9) | left_apart_point(A39_123_9, reverse_line(L40_123_9)))
% 4.44/1.13 -> [730] ~left_apart_point(A39_123_9, L40_123_9), ~left_apart_point(A39_123_9, reverse_line(L40_123_9))
% 4.44/1.13
% 4.44/1.13 [730] CLOSURE : ~left_apart_point(A39_123_9, L40_123_9)
% 4.44/1.13
% 4.44/1.13 [706] 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)))))
% 4.44/1.13 -> [711] ((unequally_directed_lines(L37_37_8, M38_37_8) & unequally_directed_lines(L37_37_8, reverse_line(M38_37_8))) => (left_convergent_lines(L37_37_8, M38_37_8) | left_convergent_lines(L37_37_8, reverse_line(M38_37_8))))
% 4.44/1.13
% 4.44/1.13 [711] BETA_IMPLY : ((unequally_directed_lines(L37_37_8, M38_37_8) & unequally_directed_lines(L37_37_8, reverse_line(M38_37_8))) => (left_convergent_lines(L37_37_8, M38_37_8) | left_convergent_lines(L37_37_8, reverse_line(M38_37_8))))
% 4.44/1.13 -> [714] ~(unequally_directed_lines(L37_37_8, M38_37_8) & unequally_directed_lines(L37_37_8, reverse_line(M38_37_8)))
% 4.44/1.13 -> [715] (left_convergent_lines(L37_37_8, M38_37_8) | left_convergent_lines(L37_37_8, reverse_line(M38_37_8)))
% 4.44/1.13
% 4.44/1.13 [714] BETA_NOT_AND : ~(unequally_directed_lines(L37_37_8, M38_37_8) & unequally_directed_lines(L37_37_8, reverse_line(M38_37_8)))
% 4.44/1.13 -> [718] ~unequally_directed_lines(L37_37_8, M38_37_8)
% 4.44/1.13 -> [719] ~unequally_directed_lines(L37_37_8, reverse_line(M38_37_8))
% 4.44/1.13
% 4.44/1.13 [718] CLOSURE : ~unequally_directed_lines(L37_37_8, M38_37_8)
% 4.44/1.13
% 4.44/1.13 [719] CLOSURE : ~unequally_directed_lines(L37_37_8, reverse_line(M38_37_8))
% 4.44/1.13
% 4.44/1.13 [715] BETA_OR : (left_convergent_lines(L37_37_8, M38_37_8) | left_convergent_lines(L37_37_8, reverse_line(M38_37_8)))
% 4.44/1.13 -> [722] left_convergent_lines(L37_37_8, M38_37_8)
% 4.44/1.13 -> [723] left_convergent_lines(L37_37_8, reverse_line(M38_37_8))
% 4.44/1.13
% 4.44/1.13 [723] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [724] ~(left_apart_point(A39_122_9, L40_122_9) | left_apart_point(A39_122_9, reverse_line(L40_122_9)))
% 4.44/1.13
% 4.44/1.13 [724] ALPHA_NOT_OR : ~(left_apart_point(A39_122_9, L40_122_9) | left_apart_point(A39_122_9, reverse_line(L40_122_9)))
% 4.44/1.13 -> [729] ~left_apart_point(A39_122_9, L40_122_9), ~left_apart_point(A39_122_9, reverse_line(L40_122_9))
% 4.44/1.13
% 4.44/1.13 [729] CLOSURE : ~left_apart_point(A39_122_9, L40_122_9)
% 4.44/1.13
% 4.44/1.13 [722] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [728] ~(left_apart_point(A39_125_9, L40_125_9) | left_apart_point(A39_125_9, reverse_line(L40_125_9)))
% 4.44/1.13
% 4.44/1.13 [728] ALPHA_NOT_OR : ~(left_apart_point(A39_125_9, L40_125_9) | left_apart_point(A39_125_9, reverse_line(L40_125_9)))
% 4.44/1.13 -> [734] ~left_apart_point(A39_125_9, L40_125_9), ~left_apart_point(A39_125_9, reverse_line(L40_125_9))
% 4.44/1.13
% 4.44/1.13 [734] CLOSURE : ~left_apart_point(A39_125_9, L40_125_9)
% 4.44/1.13
% 4.44/1.13 [705] BETA_OR : (unequally_directed_lines(reverse_line(L37_38_8), reverse_line(L37_38_8)) | unequally_directed_lines(reverse_line(L37_38_8), reverse_line(reverse_line(L37_38_8))))
% 4.44/1.13 -> [708] unequally_directed_lines(reverse_line(L37_38_8), reverse_line(L37_38_8))
% 4.44/1.13 -> [709] unequally_directed_lines(reverse_line(L37_38_8), reverse_line(reverse_line(L37_38_8)))
% 4.44/1.13
% 4.44/1.13 [708] CLOSURE : unequally_directed_lines(reverse_line(L37_38_8), reverse_line(L37_38_8))
% 4.44/1.13
% 4.44/1.13 [709] 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)))))
% 4.44/1.13 -> [726] ((unequally_directed_lines(L37_38_8, M38_38_8) & unequally_directed_lines(L37_38_8, reverse_line(M38_38_8))) => (left_convergent_lines(L37_38_8, M38_38_8) | left_convergent_lines(L37_38_8, reverse_line(M38_38_8))))
% 4.44/1.13
% 4.44/1.13 [726] BETA_IMPLY : ((unequally_directed_lines(L37_38_8, M38_38_8) & unequally_directed_lines(L37_38_8, reverse_line(M38_38_8))) => (left_convergent_lines(L37_38_8, M38_38_8) | left_convergent_lines(L37_38_8, reverse_line(M38_38_8))))
% 4.44/1.13 -> [731] ~(unequally_directed_lines(L37_38_8, M38_38_8) & unequally_directed_lines(L37_38_8, reverse_line(M38_38_8)))
% 4.44/1.13 -> [732] (left_convergent_lines(L37_38_8, M38_38_8) | left_convergent_lines(L37_38_8, reverse_line(M38_38_8)))
% 4.44/1.13
% 4.44/1.13 [731] BETA_NOT_AND : ~(unequally_directed_lines(L37_38_8, M38_38_8) & unequally_directed_lines(L37_38_8, reverse_line(M38_38_8)))
% 4.44/1.13 -> [737] ~unequally_directed_lines(L37_38_8, M38_38_8)
% 4.44/1.13 -> [738] ~unequally_directed_lines(L37_38_8, reverse_line(M38_38_8))
% 4.44/1.13
% 4.44/1.13 [737] CLOSURE : ~unequally_directed_lines(L37_38_8, M38_38_8)
% 4.44/1.13
% 4.44/1.13 [738] CLOSURE : ~unequally_directed_lines(L37_38_8, reverse_line(M38_38_8))
% 4.44/1.13
% 4.44/1.13 [732] BETA_OR : (left_convergent_lines(L37_38_8, M38_38_8) | left_convergent_lines(L37_38_8, reverse_line(M38_38_8)))
% 4.44/1.13 -> [739] left_convergent_lines(L37_38_8, M38_38_8)
% 4.44/1.13 -> [740] left_convergent_lines(L37_38_8, reverse_line(M38_38_8))
% 4.44/1.13
% 4.44/1.13 [739] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [742] ~(left_apart_point(A39_127_9, L40_127_9) | left_apart_point(A39_127_9, reverse_line(L40_127_9)))
% 4.44/1.13
% 4.44/1.13 [742] ALPHA_NOT_OR : ~(left_apart_point(A39_127_9, L40_127_9) | left_apart_point(A39_127_9, reverse_line(L40_127_9)))
% 4.44/1.13 -> [744] ~left_apart_point(A39_127_9, L40_127_9), ~left_apart_point(A39_127_9, reverse_line(L40_127_9))
% 4.44/1.13
% 4.44/1.13 [744] CLOSURE : ~left_apart_point(A39_127_9, L40_127_9)
% 4.44/1.13
% 4.44/1.13 [740] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [741] ~(left_apart_point(A39_126_9, L40_126_9) | left_apart_point(A39_126_9, reverse_line(L40_126_9)))
% 4.44/1.13
% 4.44/1.13 [741] ALPHA_NOT_OR : ~(left_apart_point(A39_126_9, L40_126_9) | left_apart_point(A39_126_9, reverse_line(L40_126_9)))
% 4.44/1.13 -> [743] ~left_apart_point(A39_126_9, L40_126_9), ~left_apart_point(A39_126_9, reverse_line(L40_126_9))
% 4.44/1.13
% 4.44/1.13 [743] CLOSURE : ~left_apart_point(A39_126_9, L40_126_9)
% 4.44/1.13
% 4.44/1.13 [7] GAMMA_FORALL : ! [A20_20] : (~distinct_points(A20_20, A20_20))
% 4.44/1.13 -> [9] ~distinct_points(C23_1_1, C23_1_1)
% 4.44/1.13
% 4.44/1.13 [9] 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))))
% 4.44/1.13 -> [11] (distinct_points(C23_1_1, C23_1_1) => (distinct_points(C23_1_1, C23_1_1) | distinct_points(C23_1_1, C23_1_1)))
% 4.44/1.13
% 4.44/1.13 [11] BETA_IMPLY : (distinct_points(C23_1_1, C23_1_1) => (distinct_points(C23_1_1, C23_1_1) | distinct_points(C23_1_1, C23_1_1)))
% 4.44/1.13 -> [14] ~distinct_points(C23_1_1, C23_1_1)
% 4.44/1.13 -> [15] (distinct_points(C23_1_1, C23_1_1) | distinct_points(C23_1_1, C23_1_1))
% 4.44/1.13
% 4.44/1.13 [15] BETA_OR : (distinct_points(C23_1_1, C23_1_1) | distinct_points(C23_1_1, C23_1_1))
% 4.44/1.13 -> [18] distinct_points(C23_1_1, C23_1_1)
% 4.44/1.13 -> [19] distinct_points(C23_1_1, C23_1_1)
% 4.44/1.13
% 4.44/1.13 [19] CLOSURE : distinct_points(C23_1_1, C23_1_1)
% 4.44/1.13
% 4.44/1.13 [18] CLOSURE : distinct_points(C23_1_1, C23_1_1)
% 4.44/1.13
% 4.44/1.13 [14] GAMMA_FORALL : ! [L24_24] : (~distinct_lines(L24_24, L24_24))
% 4.44/1.13 -> [21] ~distinct_lines(N27_0_3, N27_0_3)
% 4.44/1.13
% 4.44/1.13 [21] 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))))
% 4.44/1.13 -> [22] (distinct_lines(N27_0_3, N27_0_3) => (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3)))
% 4.44/1.13
% 4.44/1.13 [22] 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)))
% 4.44/1.13 -> [24] ~distinct_lines(N27_0_3, N27_0_3)
% 4.44/1.13 -> [25] (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3))
% 4.44/1.13
% 4.44/1.13 [25] BETA_OR : (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3))
% 4.44/1.13 -> [28] distinct_lines(N27_0_3, N27_0_3)
% 4.44/1.13 -> [29] distinct_lines(N27_0_3, N27_0_3)
% 4.44/1.13
% 4.44/1.13 [28] CLOSURE : distinct_lines(N27_0_3, N27_0_3)
% 4.44/1.13
% 4.44/1.13 [29] CLOSURE : distinct_lines(N27_0_3, N27_0_3)
% 4.44/1.13
% 4.44/1.13 [24] GAMMA_FORALL : ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28))
% 4.44/1.13 -> [33] ~unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6)))
% 4.44/1.13
% 4.44/1.13 [33] 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))))
% 4.44/1.13 -> [35] (unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6))) => (unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6))) | unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6)))))
% 4.44/1.13
% 4.44/1.13 [35] BETA_IMPLY : (unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6))) => (unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6))) | unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6)))))
% 4.44/1.13 -> [38] ~unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6)))
% 4.44/1.13 -> [39] (unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6))) | unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6))))
% 4.44/1.13
% 4.44/1.13 [39] BETA_OR : (unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6))) | unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6))))
% 4.44/1.13 -> [42] unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6)))
% 4.44/1.13 -> [43] unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6)))
% 4.44/1.13
% 4.44/1.13 [42] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6)))
% 4.44/1.13
% 4.44/1.13 [43] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6)))
% 4.44/1.13
% 4.44/1.13 [45] BETA_IMPLY : ((unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), M33_1_6) & unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(M33_1_6))) => ((unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(M33_1_6)) & unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6)))) | (unequally_directed_lines(M33_1_6, reverse_line(M33_1_6)) & unequally_directed_lines(M33_1_6, reverse_line(reverse_line(M33_1_6))))))
% 4.44/1.13 -> [381] ~(unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), M33_1_6) & unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(M33_1_6)))
% 4.44/1.13 -> [382] ((unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(M33_1_6)) & unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6)))) | (unequally_directed_lines(M33_1_6, reverse_line(M33_1_6)) & unequally_directed_lines(M33_1_6, reverse_line(reverse_line(M33_1_6)))))
% 4.44/1.13
% 4.44/1.13 [381] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), M33_1_6) & unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(M33_1_6)))
% 4.44/1.13 -> [399] ~unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), M33_1_6)
% 4.44/1.13 -> [400] ~unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(M33_1_6))
% 4.44/1.13
% 4.44/1.13 [400] 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)))))
% 4.44/1.13 -> [405] ((line(reverse_line(reverse_line(M33_1_6))) & line(reverse_line(M33_1_6))) => (unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(M33_1_6)) | unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6)))))
% 4.44/1.13
% 4.44/1.13 [405] BETA_IMPLY : ((line(reverse_line(reverse_line(M33_1_6))) & line(reverse_line(M33_1_6))) => (unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(M33_1_6)) | unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6)))))
% 4.44/1.13 -> [406] ~(line(reverse_line(reverse_line(M33_1_6))) & line(reverse_line(M33_1_6)))
% 4.44/1.13 -> [407] (unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(M33_1_6)) | unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6))))
% 4.44/1.13
% 4.44/1.13 [407] BETA_OR : (unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(M33_1_6)) | unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6))))
% 4.44/1.13 -> [413] unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(M33_1_6))
% 4.44/1.13 -> [414] unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6)))
% 4.44/1.13
% 4.44/1.13 [414] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6)))
% 4.44/1.13
% 4.44/1.13 [413] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(M33_1_6))
% 4.44/1.13
% 4.44/1.13 [406] BETA_NOT_AND : ~(line(reverse_line(reverse_line(M33_1_6))) & line(reverse_line(M33_1_6)))
% 4.44/1.13 -> [411] ~line(reverse_line(reverse_line(M33_1_6)))
% 4.44/1.13 -> [412] ~line(reverse_line(M33_1_6))
% 4.44/1.13
% 4.44/1.13 [412] 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)))))
% 4.44/1.13 -> [421] ((unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))) => (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))))
% 4.44/1.13
% 4.44/1.13 [421] BETA_IMPLY : ((unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))) => (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))))
% 4.44/1.13 -> [424] ~(unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13 -> [425] (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13
% 4.44/1.13 [425] BETA_OR : (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13 -> [433] left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979)
% 4.44/1.13 -> [434] left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))
% 4.44/1.13
% 4.44/1.13 [433] CLOSURE : left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979)
% 4.44/1.13
% 4.44/1.13 [434] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [456] ~(left_apart_point(A39_73_9, L40_73_9) | left_apart_point(A39_73_9, reverse_line(L40_73_9)))
% 4.44/1.13
% 4.44/1.13 [456] ALPHA_NOT_OR : ~(left_apart_point(A39_73_9, L40_73_9) | left_apart_point(A39_73_9, reverse_line(L40_73_9)))
% 4.44/1.13 -> [457] ~left_apart_point(A39_73_9, L40_73_9), ~left_apart_point(A39_73_9, reverse_line(L40_73_9))
% 4.44/1.13
% 4.44/1.13 [457] CLOSURE : ~left_apart_point(A39_73_9, L40_73_9)
% 4.44/1.13
% 4.44/1.13 [424] BETA_NOT_AND : ~(unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13 -> [439] ~unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979)
% 4.44/1.13 -> [440] ~unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))
% 4.44/1.13
% 4.44/1.13 [440] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [447] ~(left_apart_point(A39_69_9, L40_69_9) | left_apart_point(A39_69_9, reverse_line(L40_69_9)))
% 4.44/1.13
% 4.44/1.13 [447] ALPHA_NOT_OR : ~(left_apart_point(A39_69_9, L40_69_9) | left_apart_point(A39_69_9, reverse_line(L40_69_9)))
% 4.44/1.13 -> [460] ~left_apart_point(A39_69_9, L40_69_9), ~left_apart_point(A39_69_9, reverse_line(L40_69_9))
% 4.44/1.13
% 4.44/1.13 [460] CLOSURE : ~left_apart_point(A39_69_9, L40_69_9)
% 4.44/1.13
% 4.44/1.13 [439] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [459] ~(left_apart_point(A39_75_9, L40_75_9) | left_apart_point(A39_75_9, reverse_line(L40_75_9)))
% 4.44/1.13
% 4.44/1.13 [459] ALPHA_NOT_OR : ~(left_apart_point(A39_75_9, L40_75_9) | left_apart_point(A39_75_9, reverse_line(L40_75_9)))
% 4.44/1.13 -> [464] ~left_apart_point(A39_75_9, L40_75_9), ~left_apart_point(A39_75_9, reverse_line(L40_75_9))
% 4.44/1.13
% 4.44/1.13 [464] CLOSURE : ~left_apart_point(A39_75_9, L40_75_9)
% 4.44/1.13
% 4.44/1.13 [411] 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)))))
% 4.44/1.13 -> [422] ((unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))) => (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))))
% 4.44/1.13
% 4.44/1.13 [422] BETA_IMPLY : ((unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))) => (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))))
% 4.44/1.13 -> [426] ~(unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13 -> [427] (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13
% 4.44/1.13 [426] BETA_NOT_AND : ~(unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13 -> [437] ~unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979)
% 4.44/1.13 -> [438] ~unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))
% 4.44/1.13
% 4.44/1.13 [437] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [451] ~(left_apart_point(A39_71_9, L40_71_9) | left_apart_point(A39_71_9, reverse_line(L40_71_9)))
% 4.44/1.13
% 4.44/1.13 [451] ALPHA_NOT_OR : ~(left_apart_point(A39_71_9, L40_71_9) | left_apart_point(A39_71_9, reverse_line(L40_71_9)))
% 4.44/1.13 -> [454] ~left_apart_point(A39_71_9, L40_71_9), ~left_apart_point(A39_71_9, reverse_line(L40_71_9))
% 4.44/1.13
% 4.44/1.13 [454] CLOSURE : ~left_apart_point(A39_71_9, L40_71_9)
% 4.44/1.13
% 4.44/1.13 [438] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [458] ~(left_apart_point(A39_74_9, L40_74_9) | left_apart_point(A39_74_9, reverse_line(L40_74_9)))
% 4.44/1.13
% 4.44/1.13 [458] ALPHA_NOT_OR : ~(left_apart_point(A39_74_9, L40_74_9) | left_apart_point(A39_74_9, reverse_line(L40_74_9)))
% 4.44/1.13 -> [461] ~left_apart_point(A39_74_9, L40_74_9), ~left_apart_point(A39_74_9, reverse_line(L40_74_9))
% 4.44/1.13
% 4.44/1.13 [461] CLOSURE : ~left_apart_point(A39_74_9, L40_74_9)
% 4.44/1.13
% 4.44/1.13 [427] BETA_OR : (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13 -> [431] left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979)
% 4.44/1.13 -> [432] left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))
% 4.44/1.13
% 4.44/1.13 [431] CLOSURE : left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979)
% 4.44/1.13
% 4.44/1.13 [432] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [470] ~(left_apart_point(A39_80_9, L40_80_9) | left_apart_point(A39_80_9, reverse_line(L40_80_9)))
% 4.44/1.13
% 4.44/1.13 [470] ALPHA_NOT_OR : ~(left_apart_point(A39_80_9, L40_80_9) | left_apart_point(A39_80_9, reverse_line(L40_80_9)))
% 4.44/1.13 -> [472] ~left_apart_point(A39_80_9, L40_80_9), ~left_apart_point(A39_80_9, reverse_line(L40_80_9))
% 4.44/1.13
% 4.44/1.13 [472] CLOSURE : ~left_apart_point(A39_80_9, L40_80_9)
% 4.44/1.13
% 4.44/1.13 [408] BETA_IMPLY : ((line(reverse_line(reverse_line(M33_1_6))) & line(reverse_line(reverse_line(M33_1_6)))) => (unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6))) | unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(reverse_line(M33_1_6))))))
% 4.44/1.13 -> [473] ~(line(reverse_line(reverse_line(M33_1_6))) & line(reverse_line(reverse_line(M33_1_6))))
% 4.44/1.13 -> [474] (unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6))) | unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(reverse_line(M33_1_6)))))
% 4.44/1.13
% 4.44/1.13 [473] BETA_NOT_AND : ~(line(reverse_line(reverse_line(M33_1_6))) & line(reverse_line(reverse_line(M33_1_6))))
% 4.44/1.13 -> [475] ~line(reverse_line(reverse_line(M33_1_6)))
% 4.44/1.13 -> [476] ~line(reverse_line(reverse_line(M33_1_6)))
% 4.44/1.13
% 4.44/1.13 [475] 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)))))
% 4.44/1.13 -> [479] ((unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))) => (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))))
% 4.44/1.13
% 4.44/1.13 [479] BETA_IMPLY : ((unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))) => (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))))
% 4.44/1.13 -> [483] ~(unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13 -> [484] (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13
% 4.44/1.13 [483] BETA_NOT_AND : ~(unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13 -> [487] ~unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979)
% 4.44/1.13 -> [488] ~unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))
% 4.44/1.13
% 4.44/1.13 [487] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [497] ~(left_apart_point(A39_82_9, L40_82_9) | left_apart_point(A39_82_9, reverse_line(L40_82_9)))
% 4.44/1.13
% 4.44/1.13 [497] ALPHA_NOT_OR : ~(left_apart_point(A39_82_9, L40_82_9) | left_apart_point(A39_82_9, reverse_line(L40_82_9)))
% 4.44/1.13 -> [502] ~left_apart_point(A39_82_9, L40_82_9), ~left_apart_point(A39_82_9, reverse_line(L40_82_9))
% 4.44/1.13
% 4.44/1.13 [502] CLOSURE : ~left_apart_point(A39_82_9, L40_82_9)
% 4.44/1.13
% 4.44/1.13 [488] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [498] ~(left_apart_point(A39_83_9, L40_83_9) | left_apart_point(A39_83_9, reverse_line(L40_83_9)))
% 4.44/1.13
% 4.44/1.13 [498] ALPHA_NOT_OR : ~(left_apart_point(A39_83_9, L40_83_9) | left_apart_point(A39_83_9, reverse_line(L40_83_9)))
% 4.44/1.13 -> [501] ~left_apart_point(A39_83_9, L40_83_9), ~left_apart_point(A39_83_9, reverse_line(L40_83_9))
% 4.44/1.13
% 4.44/1.13 [501] CLOSURE : ~left_apart_point(A39_83_9, L40_83_9)
% 4.44/1.13
% 4.44/1.13 [484] BETA_OR : (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13 -> [491] left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979)
% 4.44/1.13 -> [492] left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))
% 4.44/1.13
% 4.44/1.13 [491] CLOSURE : left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979)
% 4.44/1.13
% 4.44/1.13 [492] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [500] ~(left_apart_point(A39_84_9, L40_84_9) | left_apart_point(A39_84_9, reverse_line(L40_84_9)))
% 4.44/1.13
% 4.44/1.13 [500] ALPHA_NOT_OR : ~(left_apart_point(A39_84_9, L40_84_9) | left_apart_point(A39_84_9, reverse_line(L40_84_9)))
% 4.44/1.13 -> [504] ~left_apart_point(A39_84_9, L40_84_9), ~left_apart_point(A39_84_9, reverse_line(L40_84_9))
% 4.44/1.13
% 4.44/1.13 [504] CLOSURE : ~left_apart_point(A39_84_9, L40_84_9)
% 4.44/1.13
% 4.44/1.13 [476] 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)))))
% 4.44/1.13 -> [480] ((unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))) => (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))))
% 4.44/1.13
% 4.44/1.13 [480] BETA_IMPLY : ((unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))) => (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))))
% 4.44/1.13 -> [481] ~(unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13 -> [482] (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13
% 4.44/1.13 [481] BETA_NOT_AND : ~(unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13 -> [485] ~unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979)
% 4.44/1.13 -> [486] ~unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))
% 4.44/1.13
% 4.44/1.13 [485] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [496] ~(left_apart_point(A39_81_9, L40_81_9) | left_apart_point(A39_81_9, reverse_line(L40_81_9)))
% 4.44/1.13
% 4.44/1.13 [496] ALPHA_NOT_OR : ~(left_apart_point(A39_81_9, L40_81_9) | left_apart_point(A39_81_9, reverse_line(L40_81_9)))
% 4.44/1.13 -> [499] ~left_apart_point(A39_81_9, L40_81_9), ~left_apart_point(A39_81_9, reverse_line(L40_81_9))
% 4.44/1.13
% 4.44/1.13 [499] CLOSURE : ~left_apart_point(A39_81_9, L40_81_9)
% 4.44/1.13
% 4.44/1.13 [486] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [505] ~(left_apart_point(A39_86_9, L40_86_9) | left_apart_point(A39_86_9, reverse_line(L40_86_9)))
% 4.44/1.13
% 4.44/1.13 [505] ALPHA_NOT_OR : ~(left_apart_point(A39_86_9, L40_86_9) | left_apart_point(A39_86_9, reverse_line(L40_86_9)))
% 4.44/1.13 -> [511] ~left_apart_point(A39_86_9, L40_86_9), ~left_apart_point(A39_86_9, reverse_line(L40_86_9))
% 4.44/1.13
% 4.44/1.13 [511] CLOSURE : ~left_apart_point(A39_86_9, L40_86_9)
% 4.44/1.13
% 4.44/1.13 [482] BETA_OR : (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13 -> [489] left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979)
% 4.44/1.13 -> [490] left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))
% 4.44/1.13
% 4.44/1.13 [489] CLOSURE : left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979)
% 4.44/1.13
% 4.44/1.13 [490] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [503] ~(left_apart_point(A39_85_9, L40_85_9) | left_apart_point(A39_85_9, reverse_line(L40_85_9)))
% 4.44/1.13
% 4.44/1.13 [503] ALPHA_NOT_OR : ~(left_apart_point(A39_85_9, L40_85_9) | left_apart_point(A39_85_9, reverse_line(L40_85_9)))
% 4.44/1.13 -> [506] ~left_apart_point(A39_85_9, L40_85_9), ~left_apart_point(A39_85_9, reverse_line(L40_85_9))
% 4.44/1.13
% 4.44/1.13 [506] CLOSURE : ~left_apart_point(A39_85_9, L40_85_9)
% 4.44/1.13
% 4.44/1.13 [474] BETA_OR : (unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6))) | unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(reverse_line(M33_1_6)))))
% 4.44/1.13 -> [477] unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6)))
% 4.44/1.13 -> [478] unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(reverse_line(M33_1_6))))
% 4.44/1.13
% 4.44/1.13 [477] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6)))
% 4.44/1.13
% 4.44/1.13 [478] 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)))))
% 4.44/1.13 -> [493] ((unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))) => (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))))
% 4.44/1.13
% 4.44/1.13 [493] BETA_IMPLY : ((unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))) => (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))))
% 4.44/1.13 -> [494] ~(unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13 -> [495] (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13
% 4.44/1.13 [495] BETA_OR : (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13 -> [509] left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979)
% 4.44/1.13 -> [510] left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))
% 4.44/1.13
% 4.44/1.13 [509] CLOSURE : left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979)
% 4.44/1.13
% 4.44/1.13 [510] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [512] ~(left_apart_point(A39_87_9, L40_87_9) | left_apart_point(A39_87_9, reverse_line(L40_87_9)))
% 4.44/1.13
% 4.44/1.13 [512] ALPHA_NOT_OR : ~(left_apart_point(A39_87_9, L40_87_9) | left_apart_point(A39_87_9, reverse_line(L40_87_9)))
% 4.44/1.13 -> [513] ~left_apart_point(A39_87_9, L40_87_9), ~left_apart_point(A39_87_9, reverse_line(L40_87_9))
% 4.44/1.13
% 4.44/1.13 [513] CLOSURE : ~left_apart_point(A39_87_9, L40_87_9)
% 4.44/1.13
% 4.44/1.13 [494] BETA_NOT_AND : ~(unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13 -> [545] ~unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979)
% 4.44/1.13 -> [546] ~unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))
% 4.44/1.13
% 4.44/1.13 [546] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [579] ~(left_apart_point(A39_96_9, L40_96_9) | left_apart_point(A39_96_9, reverse_line(L40_96_9)))
% 4.44/1.13
% 4.44/1.13 [579] ALPHA_NOT_OR : ~(left_apart_point(A39_96_9, L40_96_9) | left_apart_point(A39_96_9, reverse_line(L40_96_9)))
% 4.44/1.13 -> [581] ~left_apart_point(A39_96_9, L40_96_9), ~left_apart_point(A39_96_9, reverse_line(L40_96_9))
% 4.44/1.13
% 4.44/1.13 [581] CLOSURE : ~left_apart_point(A39_96_9, L40_96_9)
% 4.44/1.13
% 4.44/1.13 [545] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [586] ~(left_apart_point(A39_101_9, L40_101_9) | left_apart_point(A39_101_9, reverse_line(L40_101_9)))
% 4.44/1.13
% 4.44/1.13 [586] ALPHA_NOT_OR : ~(left_apart_point(A39_101_9, L40_101_9) | left_apart_point(A39_101_9, reverse_line(L40_101_9)))
% 4.44/1.13 -> [590] ~left_apart_point(A39_101_9, L40_101_9), ~left_apart_point(A39_101_9, reverse_line(L40_101_9))
% 4.44/1.13
% 4.44/1.13 [590] CLOSURE : ~left_apart_point(A39_101_9, L40_101_9)
% 4.44/1.13
% 4.44/1.13 [382] BETA_OR : ((unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(M33_1_6)) & unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6)))) | (unequally_directed_lines(M33_1_6, reverse_line(M33_1_6)) & unequally_directed_lines(M33_1_6, reverse_line(reverse_line(M33_1_6)))))
% 4.44/1.13 -> [616] (unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(M33_1_6)) & unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6))))
% 4.44/1.13 -> [617] (unequally_directed_lines(M33_1_6, reverse_line(M33_1_6)) & unequally_directed_lines(M33_1_6, reverse_line(reverse_line(M33_1_6))))
% 4.44/1.13
% 4.44/1.13 [616] ALPHA_AND : (unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(M33_1_6)) & unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6))))
% 4.44/1.13 -> [626] unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(M33_1_6)), unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6)))
% 4.44/1.13
% 4.44/1.13 [626] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6)))
% 4.44/1.13
% 4.44/1.13 [643] BETA_IMPLY : ((line(reverse_line(reverse_line(M33_1_6))) & line(reverse_line(M33_1_6))) => (unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(M33_1_6)) | unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6)))))
% 4.44/1.13 -> [754] ~(line(reverse_line(reverse_line(M33_1_6))) & line(reverse_line(M33_1_6)))
% 4.44/1.13 -> [755] (unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(M33_1_6)) | unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6))))
% 4.44/1.13
% 4.44/1.13 [754] BETA_NOT_AND : ~(line(reverse_line(reverse_line(M33_1_6))) & line(reverse_line(M33_1_6)))
% 4.44/1.13 -> [756] ~line(reverse_line(reverse_line(M33_1_6)))
% 4.44/1.13 -> [757] ~line(reverse_line(M33_1_6))
% 4.44/1.13
% 4.44/1.13 [756] 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)))))
% 4.44/1.13 -> [760] ((unequally_directed_lines(L37_40_8, reverse_line(L37_40_8)) & unequally_directed_lines(L37_40_8, reverse_line(reverse_line(L37_40_8)))) => (left_convergent_lines(L37_40_8, reverse_line(L37_40_8)) | left_convergent_lines(L37_40_8, reverse_line(reverse_line(L37_40_8)))))
% 4.44/1.13
% 4.44/1.13 [760] BETA_IMPLY : ((unequally_directed_lines(L37_40_8, reverse_line(L37_40_8)) & unequally_directed_lines(L37_40_8, reverse_line(reverse_line(L37_40_8)))) => (left_convergent_lines(L37_40_8, reverse_line(L37_40_8)) | left_convergent_lines(L37_40_8, reverse_line(reverse_line(L37_40_8)))))
% 4.44/1.13 -> [762] ~(unequally_directed_lines(L37_40_8, reverse_line(L37_40_8)) & unequally_directed_lines(L37_40_8, reverse_line(reverse_line(L37_40_8))))
% 4.44/1.13 -> [763] (left_convergent_lines(L37_40_8, reverse_line(L37_40_8)) | left_convergent_lines(L37_40_8, reverse_line(reverse_line(L37_40_8))))
% 4.44/1.13
% 4.44/1.13 [762] BETA_NOT_AND : ~(unequally_directed_lines(L37_40_8, reverse_line(L37_40_8)) & unequally_directed_lines(L37_40_8, reverse_line(reverse_line(L37_40_8))))
% 4.44/1.13 -> [766] ~unequally_directed_lines(L37_40_8, reverse_line(L37_40_8))
% 4.44/1.13 -> [767] ~unequally_directed_lines(L37_40_8, reverse_line(reverse_line(L37_40_8)))
% 4.44/1.13
% 4.44/1.13 [766] CLOSURE : ~unequally_directed_lines(L37_40_8, reverse_line(L37_40_8))
% 4.44/1.13
% 4.44/1.13 [767] CLOSURE : ~unequally_directed_lines(L37_40_8, reverse_line(reverse_line(L37_40_8)))
% 4.44/1.13
% 4.44/1.13 [763] BETA_OR : (left_convergent_lines(L37_40_8, reverse_line(L37_40_8)) | left_convergent_lines(L37_40_8, reverse_line(reverse_line(L37_40_8))))
% 4.44/1.13 -> [786] left_convergent_lines(L37_40_8, reverse_line(L37_40_8))
% 4.44/1.13 -> [787] left_convergent_lines(L37_40_8, reverse_line(reverse_line(L37_40_8)))
% 4.44/1.13
% 4.44/1.13 [786] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [791] ~(left_apart_point(A39_132_9, L40_132_9) | left_apart_point(A39_132_9, reverse_line(L40_132_9)))
% 4.44/1.13
% 4.44/1.13 [791] ALPHA_NOT_OR : ~(left_apart_point(A39_132_9, L40_132_9) | left_apart_point(A39_132_9, reverse_line(L40_132_9)))
% 4.44/1.13 -> [795] ~left_apart_point(A39_132_9, L40_132_9), ~left_apart_point(A39_132_9, reverse_line(L40_132_9))
% 4.44/1.13
% 4.44/1.13 [795] CLOSURE : ~left_apart_point(A39_132_9, L40_132_9)
% 4.44/1.13
% 4.44/1.13 [787] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [793] ~(left_apart_point(A39_134_9, L40_134_9) | left_apart_point(A39_134_9, reverse_line(L40_134_9)))
% 4.44/1.13
% 4.44/1.13 [793] ALPHA_NOT_OR : ~(left_apart_point(A39_134_9, L40_134_9) | left_apart_point(A39_134_9, reverse_line(L40_134_9)))
% 4.44/1.13 -> [798] ~left_apart_point(A39_134_9, L40_134_9), ~left_apart_point(A39_134_9, reverse_line(L40_134_9))
% 4.44/1.13
% 4.44/1.13 [798] CLOSURE : ~left_apart_point(A39_134_9, L40_134_9)
% 4.44/1.13
% 4.44/1.13 [757] 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)))))
% 4.44/1.13 -> [761] ((unequally_directed_lines(L37_41_8, reverse_line(L37_41_8)) & unequally_directed_lines(L37_41_8, reverse_line(reverse_line(L37_41_8)))) => (left_convergent_lines(L37_41_8, reverse_line(L37_41_8)) | left_convergent_lines(L37_41_8, reverse_line(reverse_line(L37_41_8)))))
% 4.44/1.13
% 4.44/1.13 [761] BETA_IMPLY : ((unequally_directed_lines(L37_41_8, reverse_line(L37_41_8)) & unequally_directed_lines(L37_41_8, reverse_line(reverse_line(L37_41_8)))) => (left_convergent_lines(L37_41_8, reverse_line(L37_41_8)) | left_convergent_lines(L37_41_8, reverse_line(reverse_line(L37_41_8)))))
% 4.44/1.13 -> [764] ~(unequally_directed_lines(L37_41_8, reverse_line(L37_41_8)) & unequally_directed_lines(L37_41_8, reverse_line(reverse_line(L37_41_8))))
% 4.44/1.13 -> [765] (left_convergent_lines(L37_41_8, reverse_line(L37_41_8)) | left_convergent_lines(L37_41_8, reverse_line(reverse_line(L37_41_8))))
% 4.44/1.13
% 4.44/1.13 [764] BETA_NOT_AND : ~(unequally_directed_lines(L37_41_8, reverse_line(L37_41_8)) & unequally_directed_lines(L37_41_8, reverse_line(reverse_line(L37_41_8))))
% 4.44/1.13 -> [770] ~unequally_directed_lines(L37_41_8, reverse_line(L37_41_8))
% 4.44/1.13 -> [771] ~unequally_directed_lines(L37_41_8, reverse_line(reverse_line(L37_41_8)))
% 4.44/1.13
% 4.44/1.13 [771] CLOSURE : ~unequally_directed_lines(L37_41_8, reverse_line(reverse_line(L37_41_8)))
% 4.44/1.13
% 4.44/1.13 [770] CLOSURE : ~unequally_directed_lines(L37_41_8, reverse_line(L37_41_8))
% 4.44/1.13
% 4.44/1.13 [765] BETA_OR : (left_convergent_lines(L37_41_8, reverse_line(L37_41_8)) | left_convergent_lines(L37_41_8, reverse_line(reverse_line(L37_41_8))))
% 4.44/1.13 -> [789] left_convergent_lines(L37_41_8, reverse_line(L37_41_8))
% 4.44/1.13 -> [790] left_convergent_lines(L37_41_8, reverse_line(reverse_line(L37_41_8)))
% 4.44/1.13
% 4.44/1.13 [789] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [792] ~(left_apart_point(A39_133_9, L40_133_9) | left_apart_point(A39_133_9, reverse_line(L40_133_9)))
% 4.44/1.13
% 4.44/1.13 [792] ALPHA_NOT_OR : ~(left_apart_point(A39_133_9, L40_133_9) | left_apart_point(A39_133_9, reverse_line(L40_133_9)))
% 4.44/1.13 -> [796] ~left_apart_point(A39_133_9, L40_133_9), ~left_apart_point(A39_133_9, reverse_line(L40_133_9))
% 4.44/1.13
% 4.44/1.13 [796] CLOSURE : ~left_apart_point(A39_133_9, L40_133_9)
% 4.44/1.13
% 4.44/1.13 [790] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [794] ~(left_apart_point(A39_135_9, L40_135_9) | left_apart_point(A39_135_9, reverse_line(L40_135_9)))
% 4.44/1.13
% 4.44/1.13 [794] ALPHA_NOT_OR : ~(left_apart_point(A39_135_9, L40_135_9) | left_apart_point(A39_135_9, reverse_line(L40_135_9)))
% 4.44/1.13 -> [797] ~left_apart_point(A39_135_9, L40_135_9), ~left_apart_point(A39_135_9, reverse_line(L40_135_9))
% 4.44/1.13
% 4.44/1.13 [797] CLOSURE : ~left_apart_point(A39_135_9, L40_135_9)
% 4.44/1.13
% 4.44/1.13 [755] BETA_OR : (unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(M33_1_6)) | unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6))))
% 4.44/1.13 -> [758] unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(M33_1_6))
% 4.44/1.13 -> [759] unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6)))
% 4.44/1.13
% 4.44/1.13 [759] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M33_1_6)), reverse_line(reverse_line(M33_1_6)))
% 4.44/1.13
% 4.44/1.13 [758] 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)))))
% 4.44/1.13 -> [776] ((unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))) => (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))))
% 4.44/1.13
% 4.44/1.13 [776] BETA_IMPLY : ((unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))) => (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))))
% 4.44/1.13 -> [778] ~(unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13 -> [779] (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13
% 4.44/1.13 [779] BETA_OR : (left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) | left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13 -> [783] left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979)
% 4.44/1.13 -> [784] left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))
% 4.44/1.13
% 4.44/1.13 [783] CLOSURE : left_convergent_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979)
% 4.44/1.13
% 4.44/1.13 [784] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [785] ~(left_apart_point(A39_131_9, L40_131_9) | left_apart_point(A39_131_9, reverse_line(L40_131_9)))
% 4.44/1.13
% 4.44/1.13 [785] ALPHA_NOT_OR : ~(left_apart_point(A39_131_9, L40_131_9) | left_apart_point(A39_131_9, reverse_line(L40_131_9)))
% 4.44/1.13 -> [788] ~left_apart_point(A39_131_9, L40_131_9), ~left_apart_point(A39_131_9, reverse_line(L40_131_9))
% 4.44/1.13
% 4.44/1.13 [788] CLOSURE : ~left_apart_point(A39_131_9, L40_131_9)
% 4.44/1.13
% 4.44/1.13 [778] BETA_NOT_AND : ~(unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979) & unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979)))
% 4.44/1.13 -> [799] ~unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), skolem_L7979)
% 4.44/1.13 -> [800] ~unequally_directed_lines(line_connecting(skolem_A7777, skolem_B7878), reverse_line(skolem_L7979))
% 4.44/1.13
% 4.44/1.13 [799] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [801] ~(left_apart_point(A39_136_9, L40_136_9) | left_apart_point(A39_136_9, reverse_line(L40_136_9)))
% 4.44/1.13
% 4.44/1.13 [801] ALPHA_NOT_OR : ~(left_apart_point(A39_136_9, L40_136_9) | left_apart_point(A39_136_9, reverse_line(L40_136_9)))
% 4.44/1.13 -> [803] ~left_apart_point(A39_136_9, L40_136_9), ~left_apart_point(A39_136_9, reverse_line(L40_136_9))
% 4.44/1.13
% 4.44/1.13 [803] CLOSURE : ~left_apart_point(A39_136_9, L40_136_9)
% 4.44/1.13
% 4.44/1.13 [800] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 4.44/1.13 -> [802] ~(left_apart_point(A39_137_9, L40_137_9) | left_apart_point(A39_137_9, reverse_line(L40_137_9)))
% 4.44/1.13
% 4.44/1.13 [802] ALPHA_NOT_OR : ~(left_apart_point(A39_137_9, L40_137_9) | left_apart_point(A39_137_9, reverse_line(L40_137_9)))
% 4.44/1.13 -> [804] ~left_apart_point(A39_137_9, L40_137_9), ~left_apart_point(A39_137_9, reverse_line(L40_137_9))
% 4.44/1.13
% 4.44/1.13 [804] CLOSURE : ~left_apart_point(A39_137_9, L40_137_9)
% 4.44/1.13
% 4.44/1.13 % SZS output end Proof for theBenchmark.p
% 4.44/1.13 [0.777001s][1][Res] 4502 goroutines created
% 4.44/1.13 ==== Result ====
% 4.44/1.13 [0.777019s][1][Res] VALID
% 4.44/1.13 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------