TSTP Solution File: GEO251+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO251+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n016.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 2.39s 0.97s
% Output : Proof 2.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO251+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.07/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n016.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 07:34:17 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 [DMT] DMT loaded with preskolemization
% 0.13/0.34 [EQ] equality loaded.
% 0.13/0.34 [0.000037s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.35 Conjecture not found
% 0.13/0.35 Start search
% 0.13/0.35 nb_step : 1 - limit : 32
% 0.13/0.35 Launch Gotab with destructive = true
% 2.39/0.96 % SZS output start Proof for theBenchmark.p
% 2.39/0.96 [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(B78_78, reverse_line(parallel_through_point(L79_79, A77_77))) => left_apart_point(A77_77, parallel_through_point(L79_79, B78_78)))))
% 2.39/0.96 -> [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(B78_78, reverse_line(parallel_through_point(L79_79, A77_77))) => left_apart_point(A77_77, parallel_through_point(L79_79, B78_78))))
% 2.39/0.96
% 2.39/0.96 [1] ALPHA_AND : (! [A20_20] : (~distinct_points(A20_20, A20_20)) & ! [A21_21, B22_22, C23_23] : ((distinct_points(A21_21, B22_22) => (distinct_points(A21_21, C23_23) | distinct_points(B22_22, C23_23)))) & ! [L24_24] : (~distinct_lines(L24_24, L24_24)) & ! [L25_25, M26_26, N27_27] : ((distinct_lines(L25_25, M26_26) => (distinct_lines(L25_25, N27_27) | distinct_lines(M26_26, N27_27)))) & ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28)) & ! [L29_29, M30_30, N31_31] : ((unequally_directed_lines(L29_29, M30_30) => (unequally_directed_lines(L29_29, N31_31) | unequally_directed_lines(M30_30, N31_31)))) & ! [L32_32, M33_33, N34_34] : (((unequally_directed_lines(L32_32, M33_33) & unequally_directed_lines(L32_32, reverse_line(M33_33))) => ((unequally_directed_lines(L32_32, N34_34) & unequally_directed_lines(L32_32, reverse_line(N34_34))) | (unequally_directed_lines(M33_33, N34_34) & unequally_directed_lines(M33_33, reverse_line(N34_34)))))) & ! [L35_35, M36_36] : (((line(L35_35) & line(M36_36)) => (unequally_directed_lines(L35_35, M36_36) | unequally_directed_lines(L35_35, reverse_line(M36_36))))) & ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38))))) & ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40)))) & ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42)))) & ! [A43_43, B44_44] : ((((point(A43_43) & point(B44_44)) & distinct_points(A43_43, B44_44)) => line(line_connecting(A43_43, B44_44)))) & ! [L45_45, M46_46] : (((((line(L45_45) & line(M46_46)) & unequally_directed_lines(L45_45, M46_46)) & unequally_directed_lines(L45_45, reverse_line(M46_46))) => point(intersection_point(L45_45, M46_46)))) & ! [L47_47, A48_48] : (((point(A48_48) & line(L47_47)) => line(parallel_through_point(L47_47, A48_48)))) & ! [L49_49] : ((line(L49_49) => line(reverse_line(L49_49)))) & ! [A50_50, B51_51] : ((distinct_points(A50_50, B51_51) => (~apart_point_and_line(A50_50, line_connecting(A50_50, B51_51)) & ~apart_point_and_line(B51_51, line_connecting(A50_50, B51_51))))) & ! [L52_52, M53_53] : (((unequally_directed_lines(L52_52, M53_53) & unequally_directed_lines(L52_52, reverse_line(M53_53))) => (~apart_point_and_line(intersection_point(L52_52, M53_53), L52_52) & ~apart_point_and_line(intersection_point(L52_52, M53_53), M53_53)))) & ! [A54_54, L55_55] : (~apart_point_and_line(A54_54, parallel_through_point(L55_55, A54_54))) & ! [L56_56] : (~distinct_lines(L56_56, reverse_line(L56_56))) & ! [A57_57, B58_58] : (~unequally_directed_lines(line_connecting(A57_57, B58_58), reverse_line(line_connecting(B58_58, A57_57)))) & ! [A59_59, L60_60] : (~unequally_directed_lines(parallel_through_point(L60_60, A59_59), L60_60)) & ! [A61_61, B62_62, L63_63, M64_64] : (((distinct_points(A61_61, B62_62) & distinct_lines(L63_63, M64_64)) => (((((((left_apart_point(A61_61, L63_63) | left_apart_point(B62_62, L63_63)) | left_apart_point(A61_61, M64_64)) | left_apart_point(B62_62, M64_64)) | left_apart_point(A61_61, reverse_line(L63_63))) | left_apart_point(B62_62, reverse_line(L63_63))) | left_apart_point(A61_61, reverse_line(M64_64))) | left_apart_point(B62_62, reverse_line(M64_64))))) & ! [A65_65, B66_66, L67_67] : (((distinct_points(A65_65, B66_66) & left_apart_point(A65_65, L67_67)) => (left_apart_point(B66_66, L67_67) | left_convergent_lines(line_connecting(A65_65, B66_66), L67_67)))) & ! [A68_68, B69_69, L70_70] : ((left_apart_point(A68_68, L70_70) => (distinct_points(A68_68, B69_69) | left_apart_point(B69_69, L70_70)))) & ! [A71_71, L72_72, M73_73] : (((left_apart_point(A71_71, L72_72) & unequally_directed_lines(L72_72, M73_73)) => (distinct_lines(L72_72, M73_73) | left_apart_point(A71_71, reverse_line(M73_73))))) & ! [L74_74, M75_75, N76_76] : ((left_convergent_lines(L74_74, M75_75) => (unequally_directed_lines(M75_75, N76_76) | left_convergent_lines(L74_74, N76_76)))))
% 2.39/0.96 -> [2] ! [A20_20] : (~distinct_points(A20_20, A20_20)), ! [A21_21, B22_22, C23_23] : ((distinct_points(A21_21, B22_22) => (distinct_points(A21_21, C23_23) | distinct_points(B22_22, C23_23)))), ! [L24_24] : (~distinct_lines(L24_24, L24_24)), ! [L25_25, M26_26, N27_27] : ((distinct_lines(L25_25, M26_26) => (distinct_lines(L25_25, N27_27) | distinct_lines(M26_26, N27_27)))), ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28)), ! [L29_29, M30_30, N31_31] : ((unequally_directed_lines(L29_29, M30_30) => (unequally_directed_lines(L29_29, N31_31) | unequally_directed_lines(M30_30, N31_31)))), ! [L32_32, M33_33, N34_34] : (((unequally_directed_lines(L32_32, M33_33) & unequally_directed_lines(L32_32, reverse_line(M33_33))) => ((unequally_directed_lines(L32_32, N34_34) & unequally_directed_lines(L32_32, reverse_line(N34_34))) | (unequally_directed_lines(M33_33, N34_34) & unequally_directed_lines(M33_33, reverse_line(N34_34)))))), ! [L35_35, M36_36] : (((line(L35_35) & line(M36_36)) => (unequally_directed_lines(L35_35, M36_36) | unequally_directed_lines(L35_35, reverse_line(M36_36))))), ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38))))), ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40)))), ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42)))), ! [A43_43, B44_44] : ((((point(A43_43) & point(B44_44)) & distinct_points(A43_43, B44_44)) => line(line_connecting(A43_43, B44_44)))), ! [L45_45, M46_46] : (((((line(L45_45) & line(M46_46)) & unequally_directed_lines(L45_45, M46_46)) & unequally_directed_lines(L45_45, reverse_line(M46_46))) => point(intersection_point(L45_45, M46_46)))), ! [L47_47, A48_48] : (((point(A48_48) & line(L47_47)) => line(parallel_through_point(L47_47, A48_48)))), ! [L49_49] : ((line(L49_49) => line(reverse_line(L49_49)))), ! [A50_50, B51_51] : ((distinct_points(A50_50, B51_51) => (~apart_point_and_line(A50_50, line_connecting(A50_50, B51_51)) & ~apart_point_and_line(B51_51, line_connecting(A50_50, B51_51))))), ! [L52_52, M53_53] : (((unequally_directed_lines(L52_52, M53_53) & unequally_directed_lines(L52_52, reverse_line(M53_53))) => (~apart_point_and_line(intersection_point(L52_52, M53_53), L52_52) & ~apart_point_and_line(intersection_point(L52_52, M53_53), M53_53)))), ! [A54_54, L55_55] : (~apart_point_and_line(A54_54, parallel_through_point(L55_55, A54_54))), ! [L56_56] : (~distinct_lines(L56_56, reverse_line(L56_56))), ! [A57_57, B58_58] : (~unequally_directed_lines(line_connecting(A57_57, B58_58), reverse_line(line_connecting(B58_58, A57_57)))), ! [A59_59, L60_60] : (~unequally_directed_lines(parallel_through_point(L60_60, A59_59), L60_60)), ! [A61_61, B62_62, L63_63, M64_64] : (((distinct_points(A61_61, B62_62) & distinct_lines(L63_63, M64_64)) => (((((((left_apart_point(A61_61, L63_63) | left_apart_point(B62_62, L63_63)) | left_apart_point(A61_61, M64_64)) | left_apart_point(B62_62, M64_64)) | left_apart_point(A61_61, reverse_line(L63_63))) | left_apart_point(B62_62, reverse_line(L63_63))) | left_apart_point(A61_61, reverse_line(M64_64))) | left_apart_point(B62_62, reverse_line(M64_64))))), ! [A65_65, B66_66, L67_67] : (((distinct_points(A65_65, B66_66) & left_apart_point(A65_65, L67_67)) => (left_apart_point(B66_66, L67_67) | left_convergent_lines(line_connecting(A65_65, B66_66), L67_67)))), ! [A68_68, B69_69, L70_70] : ((left_apart_point(A68_68, L70_70) => (distinct_points(A68_68, B69_69) | left_apart_point(B69_69, L70_70)))), ! [A71_71, L72_72, M73_73] : (((left_apart_point(A71_71, L72_72) & unequally_directed_lines(L72_72, M73_73)) => (distinct_lines(L72_72, M73_73) | left_apart_point(A71_71, reverse_line(M73_73))))), ! [L74_74, M75_75, N76_76] : ((left_convergent_lines(L74_74, M75_75) => (unequally_directed_lines(M75_75, N76_76) | left_convergent_lines(L74_74, N76_76))))
% 2.39/0.96
% 2.39/0.96 [2] DELTA_NOT_FORALL : ~! [A77_77, B78_78, L79_79] : ((left_apart_point(B78_78, reverse_line(parallel_through_point(L79_79, A77_77))) => left_apart_point(A77_77, parallel_through_point(L79_79, B78_78))))
% 2.39/0.96 -> [3] ~(left_apart_point(skolem_B7878, reverse_line(parallel_through_point(skolem_L7979, skolem_A7777))) => left_apart_point(skolem_A7777, parallel_through_point(skolem_L7979, skolem_B7878)))
% 2.39/0.96
% 2.39/0.96 [3] ALPHA_NOT_IMPLY : ~(left_apart_point(skolem_B7878, reverse_line(parallel_through_point(skolem_L7979, skolem_A7777))) => left_apart_point(skolem_A7777, parallel_through_point(skolem_L7979, skolem_B7878)))
% 2.39/0.96 -> [4] left_apart_point(skolem_B7878, reverse_line(parallel_through_point(skolem_L7979, skolem_A7777))), ~left_apart_point(skolem_A7777, parallel_through_point(skolem_L7979, skolem_B7878))
% 2.39/0.96
% 2.39/0.96 [4] GAMMA_FORALL : ! [A20_20] : (~distinct_points(A20_20, A20_20))
% 2.39/0.96 -> [5] ~distinct_points(C23_0_1, C23_0_1)
% 2.39/0.96
% 2.39/0.96 [5] GAMMA_FORALL : ! [A21_21, B22_22, C23_23] : ((distinct_points(A21_21, B22_22) => (distinct_points(A21_21, C23_23) | distinct_points(B22_22, C23_23))))
% 2.39/0.96 -> [6] (distinct_points(C23_0_1, C23_0_1) => (distinct_points(C23_0_1, C23_0_1) | distinct_points(C23_0_1, C23_0_1)))
% 2.39/0.96
% 2.39/0.96 [6] BETA_IMPLY : (distinct_points(C23_0_1, C23_0_1) => (distinct_points(C23_0_1, C23_0_1) | distinct_points(C23_0_1, C23_0_1)))
% 2.39/0.96 -> [7] ~distinct_points(C23_0_1, C23_0_1)
% 2.39/0.96 -> [8] (distinct_points(C23_0_1, C23_0_1) | distinct_points(C23_0_1, C23_0_1))
% 2.39/0.96
% 2.39/0.96 [8] BETA_OR : (distinct_points(C23_0_1, C23_0_1) | distinct_points(C23_0_1, C23_0_1))
% 2.39/0.96 -> [9] distinct_points(C23_0_1, C23_0_1)
% 2.39/0.96 -> [10] distinct_points(C23_0_1, C23_0_1)
% 2.39/0.96
% 2.39/0.96 [10] CLOSURE : distinct_points(C23_0_1, C23_0_1)
% 2.39/0.97
% 2.39/0.97 [9] CLOSURE : distinct_points(C23_0_1, C23_0_1)
% 2.39/0.97
% 2.39/0.97 [7] GAMMA_FORALL : ! [L24_24] : (~distinct_lines(L24_24, L24_24))
% 2.39/0.97 -> [11] ~distinct_lines(L25_0_3, L25_0_3)
% 2.39/0.97
% 2.39/0.97 [11] GAMMA_FORALL : ! [L25_25, M26_26, N27_27] : ((distinct_lines(L25_25, M26_26) => (distinct_lines(L25_25, N27_27) | distinct_lines(M26_26, N27_27))))
% 2.39/0.97 -> [12] (distinct_lines(L25_0_3, L25_0_3) => (distinct_lines(L25_0_3, L25_0_3) | distinct_lines(L25_0_3, L25_0_3)))
% 2.39/0.97
% 2.39/0.97 [12] BETA_IMPLY : (distinct_lines(L25_0_3, L25_0_3) => (distinct_lines(L25_0_3, L25_0_3) | distinct_lines(L25_0_3, L25_0_3)))
% 2.39/0.97 -> [13] ~distinct_lines(L25_0_3, L25_0_3)
% 2.39/0.97 -> [14] (distinct_lines(L25_0_3, L25_0_3) | distinct_lines(L25_0_3, L25_0_3))
% 2.39/0.97
% 2.39/0.97 [14] BETA_OR : (distinct_lines(L25_0_3, L25_0_3) | distinct_lines(L25_0_3, L25_0_3))
% 2.39/0.97 -> [15] distinct_lines(L25_0_3, L25_0_3)
% 2.39/0.97 -> [16] distinct_lines(L25_0_3, L25_0_3)
% 2.39/0.97
% 2.39/0.97 [16] CLOSURE : distinct_lines(L25_0_3, L25_0_3)
% 2.39/0.97
% 2.39/0.97 [15] CLOSURE : distinct_lines(L25_0_3, L25_0_3)
% 2.39/0.97
% 2.39/0.97 [13] GAMMA_FORALL : ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28))
% 2.39/0.97 -> [17] ~unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))
% 2.39/0.97
% 2.39/0.97 [17] GAMMA_FORALL : ! [L29_29, M30_30, N31_31] : ((unequally_directed_lines(L29_29, M30_30) => (unequally_directed_lines(L29_29, N31_31) | unequally_directed_lines(M30_30, N31_31))))
% 2.39/0.97 -> [18] (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) => (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))))
% 2.39/0.97
% 2.39/0.97 [18] BETA_IMPLY : (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) => (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))))
% 2.39/0.97 -> [19] ~unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))
% 2.39/0.97 -> [20] (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)))
% 2.39/0.97
% 2.39/0.97 [20] BETA_OR : (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)))
% 2.39/0.97 -> [21] unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))
% 2.39/0.97 -> [22] unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))
% 2.39/0.97
% 2.39/0.97 [22] CLOSURE : unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))
% 2.39/0.97
% 2.39/0.97 [21] CLOSURE : unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))
% 2.39/0.97
% 2.39/0.97 [23] BETA_IMPLY : ((unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(reverse_line(M36_6_7))))) => ((unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7)))) | (unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M36_6_7)) & unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(reverse_line(M36_6_7))))))
% 2.39/0.97 -> [218] ~(unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(reverse_line(M36_6_7)))))
% 2.39/0.97 -> [219] ((unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7)))) | (unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M36_6_7)) & unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(reverse_line(M36_6_7)))))
% 2.39/0.97
% 2.39/0.97 [218] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(reverse_line(M36_6_7)))))
% 2.39/0.97 -> [220] ~unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7)))
% 2.39/0.97 -> [221] ~unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(reverse_line(M36_6_7))))
% 2.39/0.97
% 2.39/0.97 [220] GAMMA_FORALL : ! [L35_35, M36_36] : (((line(L35_35) & line(M36_36)) => (unequally_directed_lines(L35_35, M36_36) | unequally_directed_lines(L35_35, reverse_line(M36_36)))))
% 2.39/0.97 -> [227] ((line(reverse_line(M36_6_7)) & line(reverse_line(M36_6_7))) => (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7)))))
% 2.39/0.97
% 2.39/0.97 [227] BETA_IMPLY : ((line(reverse_line(M36_6_7)) & line(reverse_line(M36_6_7))) => (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7)))))
% 2.39/0.97 -> [230] ~(line(reverse_line(M36_6_7)) & line(reverse_line(M36_6_7)))
% 2.39/0.97 -> [231] (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))))
% 2.39/0.97
% 2.39/0.97 [231] BETA_OR : (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))))
% 2.39/0.97 -> [238] unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))
% 2.39/0.97 -> [239] unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7)))
% 2.39/0.97
% 2.39/0.97 [238] CLOSURE : unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))
% 2.39/0.97
% 2.39/0.97 [239] CLOSURE : unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7)))
% 2.39/0.97
% 2.39/0.97 [230] BETA_NOT_AND : ~(line(reverse_line(M36_6_7)) & line(reverse_line(M36_6_7)))
% 2.39/0.97 -> [234] ~line(reverse_line(M36_6_7))
% 2.39/0.97 -> [235] ~line(reverse_line(M36_6_7))
% 2.39/0.97
% 2.39/0.97 [235] GAMMA_FORALL : ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38)))))
% 2.39/0.97 -> [243] ((unequally_directed_lines(L37_11_8, M38_11_8) & unequally_directed_lines(L37_11_8, reverse_line(M38_11_8))) => (left_convergent_lines(L37_11_8, M38_11_8) | left_convergent_lines(L37_11_8, reverse_line(M38_11_8))))
% 2.39/0.97
% 2.39/0.97 [243] BETA_IMPLY : ((unequally_directed_lines(L37_11_8, M38_11_8) & unequally_directed_lines(L37_11_8, reverse_line(M38_11_8))) => (left_convergent_lines(L37_11_8, M38_11_8) | left_convergent_lines(L37_11_8, reverse_line(M38_11_8))))
% 2.39/0.97 -> [246] ~(unequally_directed_lines(L37_11_8, M38_11_8) & unequally_directed_lines(L37_11_8, reverse_line(M38_11_8)))
% 2.39/0.97 -> [247] (left_convergent_lines(L37_11_8, M38_11_8) | left_convergent_lines(L37_11_8, reverse_line(M38_11_8)))
% 2.39/0.97
% 2.39/0.97 [246] BETA_NOT_AND : ~(unequally_directed_lines(L37_11_8, M38_11_8) & unequally_directed_lines(L37_11_8, reverse_line(M38_11_8)))
% 2.39/0.97 -> [256] ~unequally_directed_lines(L37_11_8, M38_11_8)
% 2.39/0.97 -> [257] ~unequally_directed_lines(L37_11_8, reverse_line(M38_11_8))
% 2.39/0.97
% 2.39/0.97 [256] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [264] ~(left_apart_point(A39_41_9, L40_41_9) | left_apart_point(A39_41_9, reverse_line(L40_41_9)))
% 2.39/0.97
% 2.39/0.97 [264] ALPHA_NOT_OR : ~(left_apart_point(A39_41_9, L40_41_9) | left_apart_point(A39_41_9, reverse_line(L40_41_9)))
% 2.39/0.97 -> [268] ~left_apart_point(A39_41_9, L40_41_9), ~left_apart_point(A39_41_9, reverse_line(L40_41_9))
% 2.39/0.97
% 2.39/0.97 [268] CLOSURE : ~left_apart_point(A39_41_9, L40_41_9)
% 2.39/0.97
% 2.39/0.97 [257] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [277] ~(left_apart_point(A39_45_9, L40_45_9) | left_apart_point(A39_45_9, reverse_line(L40_45_9)))
% 2.39/0.97
% 2.39/0.97 [277] ALPHA_NOT_OR : ~(left_apart_point(A39_45_9, L40_45_9) | left_apart_point(A39_45_9, reverse_line(L40_45_9)))
% 2.39/0.97 -> [284] ~left_apart_point(A39_45_9, L40_45_9), ~left_apart_point(A39_45_9, reverse_line(L40_45_9))
% 2.39/0.97
% 2.39/0.97 [284] CLOSURE : ~left_apart_point(A39_45_9, L40_45_9)
% 2.39/0.97
% 2.39/0.97 [247] BETA_OR : (left_convergent_lines(L37_11_8, M38_11_8) | left_convergent_lines(L37_11_8, reverse_line(M38_11_8)))
% 2.39/0.97 -> [258] left_convergent_lines(L37_11_8, M38_11_8)
% 2.39/0.97 -> [259] left_convergent_lines(L37_11_8, reverse_line(M38_11_8))
% 2.39/0.97
% 2.39/0.97 [259] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [269] ~(left_apart_point(A39_43_9, L40_43_9) | left_apart_point(A39_43_9, reverse_line(L40_43_9)))
% 2.39/0.97
% 2.39/0.97 [269] ALPHA_NOT_OR : ~(left_apart_point(A39_43_9, L40_43_9) | left_apart_point(A39_43_9, reverse_line(L40_43_9)))
% 2.39/0.97 -> [272] ~left_apart_point(A39_43_9, L40_43_9), ~left_apart_point(A39_43_9, reverse_line(L40_43_9))
% 2.39/0.97
% 2.39/0.97 [272] CLOSURE : ~left_apart_point(A39_43_9, L40_43_9)
% 2.39/0.97
% 2.39/0.97 [258] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [267] ~(left_apart_point(A39_42_9, L40_42_9) | left_apart_point(A39_42_9, reverse_line(L40_42_9)))
% 2.39/0.97
% 2.39/0.97 [267] ALPHA_NOT_OR : ~(left_apart_point(A39_42_9, L40_42_9) | left_apart_point(A39_42_9, reverse_line(L40_42_9)))
% 2.39/0.97 -> [282] ~left_apart_point(A39_42_9, L40_42_9), ~left_apart_point(A39_42_9, reverse_line(L40_42_9))
% 2.39/0.97
% 2.39/0.97 [282] CLOSURE : ~left_apart_point(A39_42_9, L40_42_9)
% 2.39/0.97
% 2.39/0.97 [234] GAMMA_FORALL : ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38)))))
% 2.39/0.97 -> [244] ((unequally_directed_lines(L37_12_8, M38_12_8) & unequally_directed_lines(L37_12_8, reverse_line(M38_12_8))) => (left_convergent_lines(L37_12_8, M38_12_8) | left_convergent_lines(L37_12_8, reverse_line(M38_12_8))))
% 2.39/0.97
% 2.39/0.97 [244] BETA_IMPLY : ((unequally_directed_lines(L37_12_8, M38_12_8) & unequally_directed_lines(L37_12_8, reverse_line(M38_12_8))) => (left_convergent_lines(L37_12_8, M38_12_8) | left_convergent_lines(L37_12_8, reverse_line(M38_12_8))))
% 2.39/0.97 -> [252] ~(unequally_directed_lines(L37_12_8, M38_12_8) & unequally_directed_lines(L37_12_8, reverse_line(M38_12_8)))
% 2.39/0.97 -> [253] (left_convergent_lines(L37_12_8, M38_12_8) | left_convergent_lines(L37_12_8, reverse_line(M38_12_8)))
% 2.39/0.97
% 2.39/0.97 [252] BETA_NOT_AND : ~(unequally_directed_lines(L37_12_8, M38_12_8) & unequally_directed_lines(L37_12_8, reverse_line(M38_12_8)))
% 2.39/0.97 -> [270] ~unequally_directed_lines(L37_12_8, M38_12_8)
% 2.39/0.97 -> [271] ~unequally_directed_lines(L37_12_8, reverse_line(M38_12_8))
% 2.39/0.97
% 2.39/0.97 [271] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [286] ~(left_apart_point(A39_50_9, L40_50_9) | left_apart_point(A39_50_9, reverse_line(L40_50_9)))
% 2.39/0.97
% 2.39/0.97 [286] ALPHA_NOT_OR : ~(left_apart_point(A39_50_9, L40_50_9) | left_apart_point(A39_50_9, reverse_line(L40_50_9)))
% 2.39/0.97 -> [288] ~left_apart_point(A39_50_9, L40_50_9), ~left_apart_point(A39_50_9, reverse_line(L40_50_9))
% 2.39/0.97
% 2.39/0.97 [288] CLOSURE : ~left_apart_point(A39_50_9, L40_50_9)
% 2.39/0.97
% 2.39/0.97 [270] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [281] ~(left_apart_point(A39_48_9, L40_48_9) | left_apart_point(A39_48_9, reverse_line(L40_48_9)))
% 2.39/0.97
% 2.39/0.97 [281] ALPHA_NOT_OR : ~(left_apart_point(A39_48_9, L40_48_9) | left_apart_point(A39_48_9, reverse_line(L40_48_9)))
% 2.39/0.97 -> [290] ~left_apart_point(A39_48_9, L40_48_9), ~left_apart_point(A39_48_9, reverse_line(L40_48_9))
% 2.39/0.97
% 2.39/0.97 [290] CLOSURE : ~left_apart_point(A39_48_9, L40_48_9)
% 2.39/0.97
% 2.39/0.97 [253] BETA_OR : (left_convergent_lines(L37_12_8, M38_12_8) | left_convergent_lines(L37_12_8, reverse_line(M38_12_8)))
% 2.39/0.97 -> [273] left_convergent_lines(L37_12_8, M38_12_8)
% 2.39/0.97 -> [274] left_convergent_lines(L37_12_8, reverse_line(M38_12_8))
% 2.39/0.97
% 2.39/0.97 [274] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [292] ~(left_apart_point(A39_52_9, L40_52_9) | left_apart_point(A39_52_9, reverse_line(L40_52_9)))
% 2.39/0.97
% 2.39/0.97 [292] ALPHA_NOT_OR : ~(left_apart_point(A39_52_9, L40_52_9) | left_apart_point(A39_52_9, reverse_line(L40_52_9)))
% 2.39/0.97 -> [294] ~left_apart_point(A39_52_9, L40_52_9), ~left_apart_point(A39_52_9, reverse_line(L40_52_9))
% 2.39/0.97
% 2.39/0.97 [294] CLOSURE : ~left_apart_point(A39_52_9, L40_52_9)
% 2.39/0.97
% 2.39/0.97 [273] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [298] ~(left_apart_point(A39_55_9, L40_55_9) | left_apart_point(A39_55_9, reverse_line(L40_55_9)))
% 2.39/0.97
% 2.39/0.97 [298] ALPHA_NOT_OR : ~(left_apart_point(A39_55_9, L40_55_9) | left_apart_point(A39_55_9, reverse_line(L40_55_9)))
% 2.39/0.97 -> [299] ~left_apart_point(A39_55_9, L40_55_9), ~left_apart_point(A39_55_9, reverse_line(L40_55_9))
% 2.39/0.97
% 2.39/0.97 [299] CLOSURE : ~left_apart_point(A39_55_9, L40_55_9)
% 2.39/0.97
% 2.39/0.97 [226] BETA_IMPLY : ((line(reverse_line(M36_6_7)) & line(reverse_line(reverse_line(M36_6_7)))) => (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(reverse_line(M36_6_7))))))
% 2.39/0.97 -> [300] ~(line(reverse_line(M36_6_7)) & line(reverse_line(reverse_line(M36_6_7))))
% 2.39/0.97 -> [301] (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(reverse_line(M36_6_7)))))
% 2.39/0.97
% 2.39/0.97 [300] BETA_NOT_AND : ~(line(reverse_line(M36_6_7)) & line(reverse_line(reverse_line(M36_6_7))))
% 2.39/0.97 -> [302] ~line(reverse_line(M36_6_7))
% 2.39/0.97 -> [303] ~line(reverse_line(reverse_line(M36_6_7)))
% 2.39/0.97
% 2.39/0.97 [302] GAMMA_FORALL : ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38)))))
% 2.39/0.97 -> [306] ((unequally_directed_lines(L37_14_8, M38_14_8) & unequally_directed_lines(L37_14_8, reverse_line(M38_14_8))) => (left_convergent_lines(L37_14_8, M38_14_8) | left_convergent_lines(L37_14_8, reverse_line(M38_14_8))))
% 2.39/0.97
% 2.39/0.97 [306] BETA_IMPLY : ((unequally_directed_lines(L37_14_8, M38_14_8) & unequally_directed_lines(L37_14_8, reverse_line(M38_14_8))) => (left_convergent_lines(L37_14_8, M38_14_8) | left_convergent_lines(L37_14_8, reverse_line(M38_14_8))))
% 2.39/0.97 -> [308] ~(unequally_directed_lines(L37_14_8, M38_14_8) & unequally_directed_lines(L37_14_8, reverse_line(M38_14_8)))
% 2.39/0.97 -> [309] (left_convergent_lines(L37_14_8, M38_14_8) | left_convergent_lines(L37_14_8, reverse_line(M38_14_8)))
% 2.39/0.97
% 2.39/0.97 [308] BETA_NOT_AND : ~(unequally_directed_lines(L37_14_8, M38_14_8) & unequally_directed_lines(L37_14_8, reverse_line(M38_14_8)))
% 2.39/0.97 -> [310] ~unequally_directed_lines(L37_14_8, M38_14_8)
% 2.39/0.97 -> [311] ~unequally_directed_lines(L37_14_8, reverse_line(M38_14_8))
% 2.39/0.97
% 2.39/0.97 [311] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [321] ~(left_apart_point(A39_56_9, L40_56_9) | left_apart_point(A39_56_9, reverse_line(L40_56_9)))
% 2.39/0.97
% 2.39/0.97 [321] ALPHA_NOT_OR : ~(left_apart_point(A39_56_9, L40_56_9) | left_apart_point(A39_56_9, reverse_line(L40_56_9)))
% 2.39/0.97 -> [322] ~left_apart_point(A39_56_9, L40_56_9), ~left_apart_point(A39_56_9, reverse_line(L40_56_9))
% 2.39/0.97
% 2.39/0.97 [322] CLOSURE : ~left_apart_point(A39_56_9, L40_56_9)
% 2.39/0.97
% 2.39/0.97 [310] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [324] ~(left_apart_point(A39_58_9, L40_58_9) | left_apart_point(A39_58_9, reverse_line(L40_58_9)))
% 2.39/0.97
% 2.39/0.97 [324] ALPHA_NOT_OR : ~(left_apart_point(A39_58_9, L40_58_9) | left_apart_point(A39_58_9, reverse_line(L40_58_9)))
% 2.39/0.97 -> [327] ~left_apart_point(A39_58_9, L40_58_9), ~left_apart_point(A39_58_9, reverse_line(L40_58_9))
% 2.39/0.97
% 2.39/0.97 [327] CLOSURE : ~left_apart_point(A39_58_9, L40_58_9)
% 2.39/0.97
% 2.39/0.97 [309] BETA_OR : (left_convergent_lines(L37_14_8, M38_14_8) | left_convergent_lines(L37_14_8, reverse_line(M38_14_8)))
% 2.39/0.97 -> [314] left_convergent_lines(L37_14_8, M38_14_8)
% 2.39/0.97 -> [315] left_convergent_lines(L37_14_8, reverse_line(M38_14_8))
% 2.39/0.97
% 2.39/0.97 [314] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [323] ~(left_apart_point(A39_57_9, L40_57_9) | left_apart_point(A39_57_9, reverse_line(L40_57_9)))
% 2.39/0.97
% 2.39/0.97 [323] ALPHA_NOT_OR : ~(left_apart_point(A39_57_9, L40_57_9) | left_apart_point(A39_57_9, reverse_line(L40_57_9)))
% 2.39/0.97 -> [326] ~left_apart_point(A39_57_9, L40_57_9), ~left_apart_point(A39_57_9, reverse_line(L40_57_9))
% 2.39/0.97
% 2.39/0.97 [326] CLOSURE : ~left_apart_point(A39_57_9, L40_57_9)
% 2.39/0.97
% 2.39/0.97 [315] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [337] ~(left_apart_point(A39_62_9, L40_62_9) | left_apart_point(A39_62_9, reverse_line(L40_62_9)))
% 2.39/0.97
% 2.39/0.97 [337] ALPHA_NOT_OR : ~(left_apart_point(A39_62_9, L40_62_9) | left_apart_point(A39_62_9, reverse_line(L40_62_9)))
% 2.39/0.97 -> [339] ~left_apart_point(A39_62_9, L40_62_9), ~left_apart_point(A39_62_9, reverse_line(L40_62_9))
% 2.39/0.97
% 2.39/0.97 [339] CLOSURE : ~left_apart_point(A39_62_9, L40_62_9)
% 2.39/0.97
% 2.39/0.97 [303] GAMMA_FORALL : ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38)))))
% 2.39/0.97 -> [307] ((unequally_directed_lines(L37_15_8, M38_15_8) & unequally_directed_lines(L37_15_8, reverse_line(M38_15_8))) => (left_convergent_lines(L37_15_8, M38_15_8) | left_convergent_lines(L37_15_8, reverse_line(M38_15_8))))
% 2.39/0.97
% 2.39/0.97 [307] BETA_IMPLY : ((unequally_directed_lines(L37_15_8, M38_15_8) & unequally_directed_lines(L37_15_8, reverse_line(M38_15_8))) => (left_convergent_lines(L37_15_8, M38_15_8) | left_convergent_lines(L37_15_8, reverse_line(M38_15_8))))
% 2.39/0.97 -> [312] ~(unequally_directed_lines(L37_15_8, M38_15_8) & unequally_directed_lines(L37_15_8, reverse_line(M38_15_8)))
% 2.39/0.97 -> [313] (left_convergent_lines(L37_15_8, M38_15_8) | left_convergent_lines(L37_15_8, reverse_line(M38_15_8)))
% 2.39/0.97
% 2.39/0.97 [312] BETA_NOT_AND : ~(unequally_directed_lines(L37_15_8, M38_15_8) & unequally_directed_lines(L37_15_8, reverse_line(M38_15_8)))
% 2.39/0.97 -> [316] ~unequally_directed_lines(L37_15_8, M38_15_8)
% 2.39/0.97 -> [317] ~unequally_directed_lines(L37_15_8, reverse_line(M38_15_8))
% 2.39/0.97
% 2.39/0.97 [316] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [325] ~(left_apart_point(A39_59_9, L40_59_9) | left_apart_point(A39_59_9, reverse_line(L40_59_9)))
% 2.39/0.97
% 2.39/0.97 [325] ALPHA_NOT_OR : ~(left_apart_point(A39_59_9, L40_59_9) | left_apart_point(A39_59_9, reverse_line(L40_59_9)))
% 2.39/0.97 -> [331] ~left_apart_point(A39_59_9, L40_59_9), ~left_apart_point(A39_59_9, reverse_line(L40_59_9))
% 2.39/0.97
% 2.39/0.97 [331] CLOSURE : ~left_apart_point(A39_59_9, L40_59_9)
% 2.39/0.97
% 2.39/0.97 [317] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [328] ~(left_apart_point(A39_60_9, L40_60_9) | left_apart_point(A39_60_9, reverse_line(L40_60_9)))
% 2.39/0.97
% 2.39/0.97 [328] ALPHA_NOT_OR : ~(left_apart_point(A39_60_9, L40_60_9) | left_apart_point(A39_60_9, reverse_line(L40_60_9)))
% 2.39/0.97 -> [333] ~left_apart_point(A39_60_9, L40_60_9), ~left_apart_point(A39_60_9, reverse_line(L40_60_9))
% 2.39/0.97
% 2.39/0.97 [333] CLOSURE : ~left_apart_point(A39_60_9, L40_60_9)
% 2.39/0.97
% 2.39/0.97 [313] BETA_OR : (left_convergent_lines(L37_15_8, M38_15_8) | left_convergent_lines(L37_15_8, reverse_line(M38_15_8)))
% 2.39/0.97 -> [318] left_convergent_lines(L37_15_8, M38_15_8)
% 2.39/0.97 -> [319] left_convergent_lines(L37_15_8, reverse_line(M38_15_8))
% 2.39/0.97
% 2.39/0.97 [318] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [332] ~(left_apart_point(A39_61_9, L40_61_9) | left_apart_point(A39_61_9, reverse_line(L40_61_9)))
% 2.39/0.97
% 2.39/0.97 [332] ALPHA_NOT_OR : ~(left_apart_point(A39_61_9, L40_61_9) | left_apart_point(A39_61_9, reverse_line(L40_61_9)))
% 2.39/0.97 -> [334] ~left_apart_point(A39_61_9, L40_61_9), ~left_apart_point(A39_61_9, reverse_line(L40_61_9))
% 2.39/0.97
% 2.39/0.97 [334] CLOSURE : ~left_apart_point(A39_61_9, L40_61_9)
% 2.39/0.97
% 2.39/0.97 [319] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [338] ~(left_apart_point(A39_63_9, L40_63_9) | left_apart_point(A39_63_9, reverse_line(L40_63_9)))
% 2.39/0.97
% 2.39/0.97 [338] ALPHA_NOT_OR : ~(left_apart_point(A39_63_9, L40_63_9) | left_apart_point(A39_63_9, reverse_line(L40_63_9)))
% 2.39/0.97 -> [342] ~left_apart_point(A39_63_9, L40_63_9), ~left_apart_point(A39_63_9, reverse_line(L40_63_9))
% 2.39/0.97
% 2.39/0.97 [342] CLOSURE : ~left_apart_point(A39_63_9, L40_63_9)
% 2.39/0.97
% 2.39/0.97 [301] BETA_OR : (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(reverse_line(M36_6_7)))))
% 2.39/0.97 -> [304] unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7)))
% 2.39/0.97 -> [305] unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(reverse_line(M36_6_7))))
% 2.39/0.97
% 2.39/0.97 [305] CLOSURE : unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(reverse_line(M36_6_7))))
% 2.39/0.97
% 2.39/0.97 [304] GAMMA_FORALL : ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38)))))
% 2.39/0.97 -> [320] ((unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(reverse_line(M36_6_7))))) => (left_convergent_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))) | left_convergent_lines(reverse_line(M36_6_7), reverse_line(reverse_line(reverse_line(M36_6_7))))))
% 2.39/0.97
% 2.39/0.97 [320] BETA_IMPLY : ((unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(reverse_line(M36_6_7))))) => (left_convergent_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))) | left_convergent_lines(reverse_line(M36_6_7), reverse_line(reverse_line(reverse_line(M36_6_7))))))
% 2.39/0.97 -> [329] ~(unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(reverse_line(M36_6_7)))))
% 2.39/0.97 -> [330] (left_convergent_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))) | left_convergent_lines(reverse_line(M36_6_7), reverse_line(reverse_line(reverse_line(M36_6_7)))))
% 2.39/0.97
% 2.39/0.97 [330] BETA_OR : (left_convergent_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))) | left_convergent_lines(reverse_line(M36_6_7), reverse_line(reverse_line(reverse_line(M36_6_7)))))
% 2.39/0.97 -> [340] left_convergent_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7)))
% 2.39/0.97 -> [341] left_convergent_lines(reverse_line(M36_6_7), reverse_line(reverse_line(reverse_line(M36_6_7))))
% 2.39/0.97
% 2.39/0.97 [341] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [344] ~(left_apart_point(A39_65_9, L40_65_9) | left_apart_point(A39_65_9, reverse_line(L40_65_9)))
% 2.39/0.97
% 2.39/0.97 [344] ALPHA_NOT_OR : ~(left_apart_point(A39_65_9, L40_65_9) | left_apart_point(A39_65_9, reverse_line(L40_65_9)))
% 2.39/0.97 -> [346] ~left_apart_point(A39_65_9, L40_65_9), ~left_apart_point(A39_65_9, reverse_line(L40_65_9))
% 2.39/0.97
% 2.39/0.97 [346] CLOSURE : ~left_apart_point(A39_65_9, L40_65_9)
% 2.39/0.97
% 2.39/0.97 [340] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [343] ~(left_apart_point(A39_64_9, L40_64_9) | left_apart_point(A39_64_9, reverse_line(L40_64_9)))
% 2.39/0.97
% 2.39/0.97 [343] ALPHA_NOT_OR : ~(left_apart_point(A39_64_9, L40_64_9) | left_apart_point(A39_64_9, reverse_line(L40_64_9)))
% 2.39/0.97 -> [345] ~left_apart_point(A39_64_9, L40_64_9), ~left_apart_point(A39_64_9, reverse_line(L40_64_9))
% 2.39/0.97
% 2.39/0.97 [345] CLOSURE : ~left_apart_point(A39_64_9, L40_64_9)
% 2.39/0.97
% 2.39/0.97 [329] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(reverse_line(M36_6_7)))))
% 2.39/0.97 -> [335] ~unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7)))
% 2.39/0.97 -> [336] ~unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(reverse_line(M36_6_7))))
% 2.39/0.97
% 2.39/0.97 [335] CLOSURE : ~unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7)))
% 2.39/0.97
% 2.39/0.97 [336] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [347] ~(left_apart_point(A39_66_9, L40_66_9) | left_apart_point(A39_66_9, reverse_line(L40_66_9)))
% 2.39/0.97
% 2.39/0.97 [347] ALPHA_NOT_OR : ~(left_apart_point(A39_66_9, L40_66_9) | left_apart_point(A39_66_9, reverse_line(L40_66_9)))
% 2.39/0.97 -> [348] ~left_apart_point(A39_66_9, L40_66_9), ~left_apart_point(A39_66_9, reverse_line(L40_66_9))
% 2.39/0.97
% 2.39/0.97 [348] CLOSURE : ~left_apart_point(A39_66_9, L40_66_9)
% 2.39/0.97
% 2.39/0.97 [219] BETA_OR : ((unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7)))) | (unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M36_6_7)) & unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(reverse_line(M36_6_7)))))
% 2.39/0.97 -> [349] (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))))
% 2.39/0.97 -> [350] (unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M36_6_7)) & unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(reverse_line(M36_6_7))))
% 2.39/0.97
% 2.39/0.97 [350] ALPHA_AND : (unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M36_6_7)) & unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(reverse_line(M36_6_7))))
% 2.39/0.97 -> [352] unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M36_6_7)), unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(reverse_line(M36_6_7)))
% 2.39/0.97
% 2.39/0.97 [352] GAMMA_FORALL : ! [L35_35, M36_36] : (((line(L35_35) & line(M36_36)) => (unequally_directed_lines(L35_35, M36_36) | unequally_directed_lines(L35_35, reverse_line(M36_36)))))
% 2.39/0.97 -> [353] ((line(reverse_line(M36_6_7)) & line(M36_6_7)) => (unequally_directed_lines(reverse_line(M36_6_7), M36_6_7) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))))
% 2.39/0.97
% 2.39/0.97 [353] BETA_IMPLY : ((line(reverse_line(M36_6_7)) & line(M36_6_7)) => (unequally_directed_lines(reverse_line(M36_6_7), M36_6_7) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))))
% 2.39/0.97 -> [354] ~(line(reverse_line(M36_6_7)) & line(M36_6_7))
% 2.39/0.97 -> [355] (unequally_directed_lines(reverse_line(M36_6_7), M36_6_7) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)))
% 2.39/0.97
% 2.39/0.97 [354] BETA_NOT_AND : ~(line(reverse_line(M36_6_7)) & line(M36_6_7))
% 2.39/0.97 -> [356] ~line(reverse_line(M36_6_7))
% 2.39/0.97 -> [357] ~line(M36_6_7)
% 2.39/0.97
% 2.39/0.97 [357] GAMMA_FORALL : ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38)))))
% 2.39/0.97 -> [363] ((unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), M38_18_8) & unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_18_8))) => (left_convergent_lines(reverse_line(reverse_line(M36_6_7)), M38_18_8) | left_convergent_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_18_8))))
% 2.39/0.97
% 2.39/0.97 [363] BETA_IMPLY : ((unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), M38_18_8) & unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_18_8))) => (left_convergent_lines(reverse_line(reverse_line(M36_6_7)), M38_18_8) | left_convergent_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_18_8))))
% 2.39/0.97 -> [366] ~(unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), M38_18_8) & unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_18_8)))
% 2.39/0.97 -> [367] (left_convergent_lines(reverse_line(reverse_line(M36_6_7)), M38_18_8) | left_convergent_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_18_8)))
% 2.39/0.97
% 2.39/0.97 [366] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), M38_18_8) & unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_18_8)))
% 2.39/0.97 -> [370] ~unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), M38_18_8)
% 2.39/0.97 -> [371] ~unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_18_8))
% 2.39/0.97
% 2.39/0.97 [371] CLOSURE : ~unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_18_8))
% 2.39/0.97
% 2.39/0.97 [370] CLOSURE : ~unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), M38_18_8)
% 2.39/0.97
% 2.39/0.97 [367] BETA_OR : (left_convergent_lines(reverse_line(reverse_line(M36_6_7)), M38_18_8) | left_convergent_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_18_8)))
% 2.39/0.97 -> [372] left_convergent_lines(reverse_line(reverse_line(M36_6_7)), M38_18_8)
% 2.39/0.97 -> [373] left_convergent_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_18_8))
% 2.39/0.97
% 2.39/0.97 [372] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [383] ~(left_apart_point(A39_68_9, L40_68_9) | left_apart_point(A39_68_9, reverse_line(L40_68_9)))
% 2.39/0.97
% 2.39/0.97 [383] ALPHA_NOT_OR : ~(left_apart_point(A39_68_9, L40_68_9) | left_apart_point(A39_68_9, reverse_line(L40_68_9)))
% 2.39/0.97 -> [385] ~left_apart_point(A39_68_9, L40_68_9), ~left_apart_point(A39_68_9, reverse_line(L40_68_9))
% 2.39/0.97
% 2.39/0.97 [385] CLOSURE : ~left_apart_point(A39_68_9, L40_68_9)
% 2.39/0.97
% 2.39/0.97 [373] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [384] ~(left_apart_point(A39_69_9, L40_69_9) | left_apart_point(A39_69_9, reverse_line(L40_69_9)))
% 2.39/0.97
% 2.39/0.97 [384] ALPHA_NOT_OR : ~(left_apart_point(A39_69_9, L40_69_9) | left_apart_point(A39_69_9, reverse_line(L40_69_9)))
% 2.39/0.97 -> [386] ~left_apart_point(A39_69_9, L40_69_9), ~left_apart_point(A39_69_9, reverse_line(L40_69_9))
% 2.39/0.97
% 2.39/0.97 [386] CLOSURE : ~left_apart_point(A39_69_9, L40_69_9)
% 2.39/0.97
% 2.39/0.97 [356] GAMMA_FORALL : ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38)))))
% 2.39/0.97 -> [360] ((unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), M38_17_8) & unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_17_8))) => (left_convergent_lines(reverse_line(reverse_line(M36_6_7)), M38_17_8) | left_convergent_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_17_8))))
% 2.39/0.97
% 2.39/0.97 [360] BETA_IMPLY : ((unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), M38_17_8) & unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_17_8))) => (left_convergent_lines(reverse_line(reverse_line(M36_6_7)), M38_17_8) | left_convergent_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_17_8))))
% 2.39/0.97 -> [361] ~(unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), M38_17_8) & unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_17_8)))
% 2.39/0.97 -> [362] (left_convergent_lines(reverse_line(reverse_line(M36_6_7)), M38_17_8) | left_convergent_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_17_8)))
% 2.39/0.97
% 2.39/0.97 [361] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), M38_17_8) & unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_17_8)))
% 2.39/0.97 -> [364] ~unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), M38_17_8)
% 2.39/0.97 -> [365] ~unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_17_8))
% 2.39/0.97
% 2.39/0.97 [365] CLOSURE : ~unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_17_8))
% 2.39/0.97
% 2.39/0.97 [364] CLOSURE : ~unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), M38_17_8)
% 2.39/0.97
% 2.39/0.97 [362] BETA_OR : (left_convergent_lines(reverse_line(reverse_line(M36_6_7)), M38_17_8) | left_convergent_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_17_8)))
% 2.39/0.97 -> [368] left_convergent_lines(reverse_line(reverse_line(M36_6_7)), M38_17_8)
% 2.39/0.97 -> [369] left_convergent_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_17_8))
% 2.39/0.97
% 2.39/0.97 [369] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [377] ~(left_apart_point(A39_67_9, L40_67_9) | left_apart_point(A39_67_9, reverse_line(L40_67_9)))
% 2.39/0.97
% 2.39/0.97 [377] ALPHA_NOT_OR : ~(left_apart_point(A39_67_9, L40_67_9) | left_apart_point(A39_67_9, reverse_line(L40_67_9)))
% 2.39/0.97 -> [382] ~left_apart_point(A39_67_9, L40_67_9), ~left_apart_point(A39_67_9, reverse_line(L40_67_9))
% 2.39/0.97
% 2.39/0.97 [382] CLOSURE : ~left_apart_point(A39_67_9, L40_67_9)
% 2.39/0.97
% 2.39/0.97 [368] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [387] ~(left_apart_point(A39_70_9, L40_70_9) | left_apart_point(A39_70_9, reverse_line(L40_70_9)))
% 2.39/0.97
% 2.39/0.97 [387] ALPHA_NOT_OR : ~(left_apart_point(A39_70_9, L40_70_9) | left_apart_point(A39_70_9, reverse_line(L40_70_9)))
% 2.39/0.97 -> [388] ~left_apart_point(A39_70_9, L40_70_9), ~left_apart_point(A39_70_9, reverse_line(L40_70_9))
% 2.39/0.97
% 2.39/0.97 [388] CLOSURE : ~left_apart_point(A39_70_9, L40_70_9)
% 2.39/0.97
% 2.39/0.97 [355] BETA_OR : (unequally_directed_lines(reverse_line(M36_6_7), M36_6_7) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)))
% 2.39/0.97 -> [358] unequally_directed_lines(reverse_line(M36_6_7), M36_6_7)
% 2.39/0.97 -> [359] unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))
% 2.39/0.97
% 2.39/0.97 [359] CLOSURE : unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))
% 2.39/0.97
% 2.39/0.97 [358] GAMMA_FORALL : ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38)))))
% 2.39/0.97 -> [374] ((unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), M38_19_8) & unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_19_8))) => (left_convergent_lines(reverse_line(reverse_line(M36_6_7)), M38_19_8) | left_convergent_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_19_8))))
% 2.39/0.97
% 2.39/0.97 [374] BETA_IMPLY : ((unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), M38_19_8) & unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_19_8))) => (left_convergent_lines(reverse_line(reverse_line(M36_6_7)), M38_19_8) | left_convergent_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_19_8))))
% 2.39/0.97 -> [375] ~(unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), M38_19_8) & unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_19_8)))
% 2.39/0.97 -> [376] (left_convergent_lines(reverse_line(reverse_line(M36_6_7)), M38_19_8) | left_convergent_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_19_8)))
% 2.39/0.97
% 2.39/0.97 [375] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), M38_19_8) & unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_19_8)))
% 2.39/0.97 -> [378] ~unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), M38_19_8)
% 2.39/0.97 -> [379] ~unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_19_8))
% 2.39/0.97
% 2.39/0.97 [378] CLOSURE : ~unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), M38_19_8)
% 2.39/0.97
% 2.39/0.97 [379] CLOSURE : ~unequally_directed_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_19_8))
% 2.39/0.97
% 2.39/0.97 [376] BETA_OR : (left_convergent_lines(reverse_line(reverse_line(M36_6_7)), M38_19_8) | left_convergent_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_19_8)))
% 2.39/0.97 -> [380] left_convergent_lines(reverse_line(reverse_line(M36_6_7)), M38_19_8)
% 2.39/0.97 -> [381] left_convergent_lines(reverse_line(reverse_line(M36_6_7)), reverse_line(M38_19_8))
% 2.39/0.97
% 2.39/0.97 [381] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [389] ~(left_apart_point(A39_71_9, L40_71_9) | left_apart_point(A39_71_9, reverse_line(L40_71_9)))
% 2.39/0.97
% 2.39/0.97 [389] ALPHA_NOT_OR : ~(left_apart_point(A39_71_9, L40_71_9) | left_apart_point(A39_71_9, reverse_line(L40_71_9)))
% 2.39/0.97 -> [391] ~left_apart_point(A39_71_9, L40_71_9), ~left_apart_point(A39_71_9, reverse_line(L40_71_9))
% 2.39/0.97
% 2.39/0.97 [391] CLOSURE : ~left_apart_point(A39_71_9, L40_71_9)
% 2.39/0.97
% 2.39/0.97 [380] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.39/0.97 -> [390] ~(left_apart_point(A39_72_9, L40_72_9) | left_apart_point(A39_72_9, reverse_line(L40_72_9)))
% 2.39/0.97
% 2.39/0.97 [390] ALPHA_NOT_OR : ~(left_apart_point(A39_72_9, L40_72_9) | left_apart_point(A39_72_9, reverse_line(L40_72_9)))
% 2.39/0.97 -> [392] ~left_apart_point(A39_72_9, L40_72_9), ~left_apart_point(A39_72_9, reverse_line(L40_72_9))
% 2.39/0.97
% 2.39/0.97 [392] CLOSURE : ~left_apart_point(A39_72_9, L40_72_9)
% 2.39/0.97
% 2.39/0.97 [351] CLOSURE : unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7)))
% 2.39/0.97
% 2.39/0.97 % SZS output end Proof for theBenchmark.p
% 2.39/0.97 [0.620426s][1][Res] 1768 goroutines created
% 2.39/0.97 ==== Result ====
% 2.39/0.97 [0.620448s][1][Res] VALID
% 2.39/0.97 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------