TSTP Solution File: GEO242+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO242+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 15:18:39 EDT 2022
% Result : Theorem 5.61s 1.39s
% Output : Proof 5.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO242+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.03/0.13 % Command : goeland -dmt -presko -proof %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 07:18:15 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 [DMT] DMT loaded with preskolemization
% 0.12/0.35 [EQ] equality loaded.
% 0.12/0.35 [0.000048s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.35 Conjecture not found
% 0.12/0.35 Start search
% 0.12/0.36 nb_step : 1 - limit : 32
% 0.12/0.36 Launch Gotab with destructive = true
% 5.61/1.39 % SZS output start Proof for theBenchmark.p
% 5.61/1.39 [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] : ((((~apart_point_and_line(A77_77, L79_79) & distinct_points(A77_77, B78_78)) & left_convergent_lines(L79_79, reverse_line(line_connecting(A77_77, B78_78)))) => left_apart_point(B78_78, reverse_line(L79_79)))))
% 5.61/1.39 -> [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] : ((((~apart_point_and_line(A77_77, L79_79) & distinct_points(A77_77, B78_78)) & left_convergent_lines(L79_79, reverse_line(line_connecting(A77_77, B78_78)))) => left_apart_point(B78_78, reverse_line(L79_79))))
% 5.61/1.39
% 5.61/1.39 [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)))))
% 5.61/1.39 -> [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))))
% 5.61/1.39
% 5.61/1.39 [2] DELTA_NOT_FORALL : ~! [A77_77, B78_78, L79_79] : ((((~apart_point_and_line(A77_77, L79_79) & distinct_points(A77_77, B78_78)) & left_convergent_lines(L79_79, reverse_line(line_connecting(A77_77, B78_78)))) => left_apart_point(B78_78, reverse_line(L79_79))))
% 5.61/1.39 -> [3] ~(((~apart_point_and_line(skolem_A7777, skolem_L7979) & distinct_points(skolem_A7777, skolem_B7878)) & left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))) => left_apart_point(skolem_B7878, reverse_line(skolem_L7979)))
% 5.61/1.39
% 5.61/1.39 [3] ALPHA_NOT_IMPLY : ~(((~apart_point_and_line(skolem_A7777, skolem_L7979) & distinct_points(skolem_A7777, skolem_B7878)) & left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))) => left_apart_point(skolem_B7878, reverse_line(skolem_L7979)))
% 5.61/1.39 -> [4] ((~apart_point_and_line(skolem_A7777, skolem_L7979) & distinct_points(skolem_A7777, skolem_B7878)) & left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))), ~left_apart_point(skolem_B7878, reverse_line(skolem_L7979))
% 5.61/1.39
% 5.61/1.39 [4] ALPHA_AND : ((~apart_point_and_line(skolem_A7777, skolem_L7979) & distinct_points(skolem_A7777, skolem_B7878)) & left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 5.61/1.39 -> [5] (~apart_point_and_line(skolem_A7777, skolem_L7979) & distinct_points(skolem_A7777, skolem_B7878)), left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 5.61/1.39
% 5.61/1.39 [5] ALPHA_AND : (~apart_point_and_line(skolem_A7777, skolem_L7979) & distinct_points(skolem_A7777, skolem_B7878))
% 5.61/1.39 -> [6] ~apart_point_and_line(skolem_A7777, skolem_L7979), distinct_points(skolem_A7777, skolem_B7878)
% 5.61/1.39
% 5.61/1.39 [6] Rewrite : ~apart_point_and_line(skolem_A7777, skolem_L7979)
% 5.61/1.39 -> [7] ~(left_apart_point(skolem_A7777, skolem_L7979) | left_apart_point(skolem_A7777, reverse_line(skolem_L7979)))
% 5.61/1.39
% 5.61/1.39 [7] ALPHA_NOT_OR : ~(left_apart_point(skolem_A7777, skolem_L7979) | left_apart_point(skolem_A7777, reverse_line(skolem_L7979)))
% 5.61/1.39 -> [8] ~left_apart_point(skolem_A7777, skolem_L7979), ~left_apart_point(skolem_A7777, reverse_line(skolem_L7979))
% 5.61/1.39
% 5.61/1.39 [8] GAMMA_FORALL : ! [A20_20] : (~distinct_points(A20_20, A20_20))
% 5.61/1.39 -> [9] ~distinct_points(skolem_B7878, skolem_B7878)
% 5.61/1.39
% 5.61/1.39 [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))))
% 5.61/1.39 -> [10] (distinct_points(skolem_A7777, skolem_B7878) => (distinct_points(skolem_A7777, skolem_B7878) | distinct_points(skolem_B7878, skolem_B7878)))
% 5.61/1.39
% 5.61/1.39 [10] BETA_IMPLY : (distinct_points(skolem_A7777, skolem_B7878) => (distinct_points(skolem_A7777, skolem_B7878) | distinct_points(skolem_B7878, skolem_B7878)))
% 5.61/1.39 -> [11] ~distinct_points(skolem_A7777, skolem_B7878)
% 5.61/1.39 -> [12] (distinct_points(skolem_A7777, skolem_B7878) | distinct_points(skolem_B7878, skolem_B7878))
% 5.61/1.39
% 5.61/1.39 [11] CLOSURE : ~distinct_points(skolem_A7777, skolem_B7878)
% 5.61/1.39
% 5.61/1.39 [12] BETA_OR : (distinct_points(skolem_A7777, skolem_B7878) | distinct_points(skolem_B7878, skolem_B7878))
% 5.61/1.39 -> [15] distinct_points(skolem_A7777, skolem_B7878)
% 5.61/1.39 -> [16] distinct_points(skolem_B7878, skolem_B7878)
% 5.61/1.39
% 5.61/1.39 [16] CLOSURE : distinct_points(skolem_B7878, skolem_B7878)
% 5.61/1.39
% 5.61/1.39 [15] GAMMA_FORALL : ! [L24_24] : (~distinct_lines(L24_24, L24_24))
% 5.61/1.39 -> [17] ~distinct_lines(N27_0_3, N27_0_3)
% 5.61/1.39
% 5.61/1.39 [17] 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))))
% 5.61/1.39 -> [18] (distinct_lines(N27_0_3, N27_0_3) => (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3)))
% 5.61/1.39
% 5.61/1.39 [18] 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)))
% 5.61/1.39 -> [19] ~distinct_lines(N27_0_3, N27_0_3)
% 5.61/1.39 -> [20] (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3))
% 5.61/1.39
% 5.61/1.39 [20] BETA_OR : (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3))
% 5.61/1.39 -> [21] distinct_lines(N27_0_3, N27_0_3)
% 5.61/1.39 -> [22] distinct_lines(N27_0_3, N27_0_3)
% 5.61/1.39
% 5.61/1.39 [22] CLOSURE : distinct_lines(N27_0_3, N27_0_3)
% 5.61/1.39
% 5.61/1.39 [21] CLOSURE : distinct_lines(N27_0_3, N27_0_3)
% 5.61/1.39
% 5.61/1.39 [19] GAMMA_FORALL : ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28))
% 5.61/1.39 -> [23] ~unequally_directed_lines(L29_0_5, L29_0_5)
% 5.61/1.39
% 5.61/1.39 [23] 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))))
% 5.61/1.39 -> [24] (unequally_directed_lines(L29_0_5, L29_0_5) => (unequally_directed_lines(L29_0_5, L29_0_5) | unequally_directed_lines(L29_0_5, L29_0_5)))
% 5.61/1.39
% 5.61/1.39 [24] BETA_IMPLY : (unequally_directed_lines(L29_0_5, L29_0_5) => (unequally_directed_lines(L29_0_5, L29_0_5) | unequally_directed_lines(L29_0_5, L29_0_5)))
% 5.61/1.39 -> [25] ~unequally_directed_lines(L29_0_5, L29_0_5)
% 5.61/1.39 -> [26] (unequally_directed_lines(L29_0_5, L29_0_5) | unequally_directed_lines(L29_0_5, L29_0_5))
% 5.61/1.39
% 5.61/1.39 [26] BETA_OR : (unequally_directed_lines(L29_0_5, L29_0_5) | unequally_directed_lines(L29_0_5, L29_0_5))
% 5.61/1.39 -> [27] unequally_directed_lines(L29_0_5, L29_0_5)
% 5.61/1.39 -> [28] unequally_directed_lines(L29_0_5, L29_0_5)
% 5.61/1.39
% 5.61/1.39 [28] CLOSURE : unequally_directed_lines(L29_0_5, L29_0_5)
% 5.61/1.39
% 5.61/1.39 [27] CLOSURE : unequally_directed_lines(L29_0_5, L29_0_5)
% 5.61/1.39
% 5.61/1.39 [29] BETA_IMPLY : ((unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))) => ((unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))) | (unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))))
% 5.61/1.39 -> [375] ~(unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 5.61/1.39 -> [376] ((unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))) | (unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))))
% 5.61/1.39
% 5.61/1.39 [376] BETA_OR : ((unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))) | (unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))))
% 5.61/1.39 -> [379] (unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 5.61/1.39 -> [380] (unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 5.61/1.39
% 5.61/1.39 [380] ALPHA_AND : (unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 5.61/1.39 -> [382] unequally_directed_lines(N34_0_6, N34_0_6), unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))
% 5.61/1.39
% 5.61/1.39 [382] CLOSURE : unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))
% 5.61/1.39
% 5.61/1.39 [381] CLOSURE : unequally_directed_lines(N34_0_6, N34_0_6)
% 5.61/1.39
% 5.61/1.39 [375] BETA_NOT_AND : ~(unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 5.61/1.39 -> [560] ~unequally_directed_lines(N34_0_6, N34_0_6)
% 5.61/1.39 -> [561] ~unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))
% 5.61/1.39
% 5.61/1.39 [561] 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)))))
% 5.61/1.39 -> [563] ((line(M36_7_7) & line(M36_7_7)) => (unequally_directed_lines(M36_7_7, M36_7_7) | unequally_directed_lines(M36_7_7, reverse_line(M36_7_7))))
% 5.61/1.39
% 5.61/1.39 [563] BETA_IMPLY : ((line(M36_7_7) & line(M36_7_7)) => (unequally_directed_lines(M36_7_7, M36_7_7) | unequally_directed_lines(M36_7_7, reverse_line(M36_7_7))))
% 5.61/1.39 -> [566] ~(line(M36_7_7) & line(M36_7_7))
% 5.61/1.39 -> [567] (unequally_directed_lines(M36_7_7, M36_7_7) | unequally_directed_lines(M36_7_7, reverse_line(M36_7_7)))
% 5.61/1.39
% 5.61/1.39 [567] BETA_OR : (unequally_directed_lines(M36_7_7, M36_7_7) | unequally_directed_lines(M36_7_7, reverse_line(M36_7_7)))
% 5.61/1.39 -> [574] unequally_directed_lines(M36_7_7, M36_7_7)
% 5.61/1.39 -> [575] unequally_directed_lines(M36_7_7, reverse_line(M36_7_7))
% 5.61/1.39
% 5.61/1.39 [574] CLOSURE : unequally_directed_lines(M36_7_7, M36_7_7)
% 5.61/1.39
% 5.61/1.39 [575] CLOSURE : unequally_directed_lines(M36_7_7, reverse_line(M36_7_7))
% 5.61/1.39
% 5.61/1.39 [566] BETA_NOT_AND : ~(line(M36_7_7) & line(M36_7_7))
% 5.61/1.39 -> [570] ~line(M36_7_7)
% 5.61/1.39 -> [571] ~line(M36_7_7)
% 5.61/1.39
% 5.61/1.39 [571] 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)))))
% 5.61/1.39 -> [577] ((unequally_directed_lines(L37_21_8, M38_21_8) & unequally_directed_lines(L37_21_8, reverse_line(M38_21_8))) => (left_convergent_lines(L37_21_8, M38_21_8) | left_convergent_lines(L37_21_8, reverse_line(M38_21_8))))
% 5.61/1.39
% 5.61/1.39 [577] BETA_IMPLY : ((unequally_directed_lines(L37_21_8, M38_21_8) & unequally_directed_lines(L37_21_8, reverse_line(M38_21_8))) => (left_convergent_lines(L37_21_8, M38_21_8) | left_convergent_lines(L37_21_8, reverse_line(M38_21_8))))
% 5.61/1.39 -> [582] ~(unequally_directed_lines(L37_21_8, M38_21_8) & unequally_directed_lines(L37_21_8, reverse_line(M38_21_8)))
% 5.61/1.39 -> [583] (left_convergent_lines(L37_21_8, M38_21_8) | left_convergent_lines(L37_21_8, reverse_line(M38_21_8)))
% 5.61/1.39
% 5.61/1.39 [583] BETA_OR : (left_convergent_lines(L37_21_8, M38_21_8) | left_convergent_lines(L37_21_8, reverse_line(M38_21_8)))
% 5.61/1.39 -> [596] left_convergent_lines(L37_21_8, M38_21_8)
% 5.61/1.39 -> [597] left_convergent_lines(L37_21_8, reverse_line(M38_21_8))
% 5.61/1.39
% 5.61/1.39 [597] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 5.61/1.39 -> [612] ~(left_apart_point(A39_84_9, L40_84_9) | left_apart_point(A39_84_9, reverse_line(L40_84_9)))
% 5.61/1.39
% 5.61/1.39 [612] ALPHA_NOT_OR : ~(left_apart_point(A39_84_9, L40_84_9) | left_apart_point(A39_84_9, reverse_line(L40_84_9)))
% 5.61/1.39 -> [614] ~left_apart_point(A39_84_9, L40_84_9), ~left_apart_point(A39_84_9, reverse_line(L40_84_9))
% 5.61/1.39
% 5.61/1.39 [614] GAMMA_FORALL : ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42))))
% 5.61/1.39 -> [656] ~(left_convergent_lines(L41_86_10, M42_86_10) | left_convergent_lines(L41_86_10, reverse_line(M42_86_10)))
% 5.61/1.39
% 5.61/1.39 [656] ALPHA_NOT_OR : ~(left_convergent_lines(L41_86_10, M42_86_10) | left_convergent_lines(L41_86_10, reverse_line(M42_86_10)))
% 5.61/1.39 -> [659] ~left_convergent_lines(L41_86_10, M42_86_10), ~left_convergent_lines(L41_86_10, reverse_line(M42_86_10))
% 5.61/1.39
% 5.61/1.39 [659] CLOSURE : ~left_convergent_lines(L41_86_10, M42_86_10)
% 5.61/1.39
% 5.61/1.39 [596] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 5.61/1.39 -> [618] ~(left_apart_point(A39_86_9, L40_86_9) | left_apart_point(A39_86_9, reverse_line(L40_86_9)))
% 5.61/1.39
% 5.61/1.39 [618] ALPHA_NOT_OR : ~(left_apart_point(A39_86_9, L40_86_9) | left_apart_point(A39_86_9, reverse_line(L40_86_9)))
% 5.61/1.39 -> [622] ~left_apart_point(A39_86_9, L40_86_9), ~left_apart_point(A39_86_9, reverse_line(L40_86_9))
% 5.61/1.39
% 5.61/1.39 [622] GAMMA_FORALL : ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42))))
% 5.61/1.39 -> [657] ~(left_convergent_lines(L41_87_10, M42_87_10) | left_convergent_lines(L41_87_10, reverse_line(M42_87_10)))
% 5.61/1.39
% 5.61/1.39 [657] ALPHA_NOT_OR : ~(left_convergent_lines(L41_87_10, M42_87_10) | left_convergent_lines(L41_87_10, reverse_line(M42_87_10)))
% 5.61/1.39 -> [660] ~left_convergent_lines(L41_87_10, M42_87_10), ~left_convergent_lines(L41_87_10, reverse_line(M42_87_10))
% 5.61/1.39
% 5.61/1.39 [660] CLOSURE : ~left_convergent_lines(L41_87_10, M42_87_10)
% 5.61/1.39
% 5.61/1.39 [582] BETA_NOT_AND : ~(unequally_directed_lines(L37_21_8, M38_21_8) & unequally_directed_lines(L37_21_8, reverse_line(M38_21_8)))
% 5.61/1.39 -> [592] ~unequally_directed_lines(L37_21_8, M38_21_8)
% 5.61/1.39 -> [593] ~unequally_directed_lines(L37_21_8, reverse_line(M38_21_8))
% 5.61/1.39
% 5.61/1.39 [592] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 5.61/1.39 -> [607] ~(left_apart_point(A39_82_9, L40_82_9) | left_apart_point(A39_82_9, reverse_line(L40_82_9)))
% 5.61/1.39
% 5.61/1.39 [607] ALPHA_NOT_OR : ~(left_apart_point(A39_82_9, L40_82_9) | left_apart_point(A39_82_9, reverse_line(L40_82_9)))
% 5.61/1.39 -> [610] ~left_apart_point(A39_82_9, L40_82_9), ~left_apart_point(A39_82_9, reverse_line(L40_82_9))
% 5.61/1.39
% 5.61/1.39 [610] GAMMA_FORALL : ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42))))
% 5.61/1.39 -> [646] ~(left_convergent_lines(L41_81_10, M42_81_10) | left_convergent_lines(L41_81_10, reverse_line(M42_81_10)))
% 5.61/1.39
% 5.61/1.39 [646] ALPHA_NOT_OR : ~(left_convergent_lines(L41_81_10, M42_81_10) | left_convergent_lines(L41_81_10, reverse_line(M42_81_10)))
% 5.61/1.39 -> [647] ~left_convergent_lines(L41_81_10, M42_81_10), ~left_convergent_lines(L41_81_10, reverse_line(M42_81_10))
% 5.61/1.39
% 5.61/1.39 [647] CLOSURE : ~left_convergent_lines(L41_81_10, M42_81_10)
% 5.61/1.39
% 5.61/1.39 [593] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 5.61/1.39 -> [629] ~(left_apart_point(A39_91_9, L40_91_9) | left_apart_point(A39_91_9, reverse_line(L40_91_9)))
% 5.61/1.39
% 5.61/1.39 [629] ALPHA_NOT_OR : ~(left_apart_point(A39_91_9, L40_91_9) | left_apart_point(A39_91_9, reverse_line(L40_91_9)))
% 5.61/1.39 -> [631] ~left_apart_point(A39_91_9, L40_91_9), ~left_apart_point(A39_91_9, reverse_line(L40_91_9))
% 5.61/1.39
% 5.61/1.39 [631] GAMMA_FORALL : ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42))))
% 5.61/1.39 -> [663] ~(left_convergent_lines(L41_89_10, M42_89_10) | left_convergent_lines(L41_89_10, reverse_line(M42_89_10)))
% 5.61/1.39
% 5.61/1.39 [663] ALPHA_NOT_OR : ~(left_convergent_lines(L41_89_10, M42_89_10) | left_convergent_lines(L41_89_10, reverse_line(M42_89_10)))
% 5.61/1.39 -> [665] ~left_convergent_lines(L41_89_10, M42_89_10), ~left_convergent_lines(L41_89_10, reverse_line(M42_89_10))
% 5.61/1.39
% 5.61/1.39 [665] CLOSURE : ~left_convergent_lines(L41_89_10, M42_89_10)
% 5.61/1.39
% 5.61/1.39 [570] 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)))))
% 5.61/1.39 -> [578] ((unequally_directed_lines(L37_22_8, M38_22_8) & unequally_directed_lines(L37_22_8, reverse_line(M38_22_8))) => (left_convergent_lines(L37_22_8, M38_22_8) | left_convergent_lines(L37_22_8, reverse_line(M38_22_8))))
% 5.61/1.39
% 5.61/1.39 [578] BETA_IMPLY : ((unequally_directed_lines(L37_22_8, M38_22_8) & unequally_directed_lines(L37_22_8, reverse_line(M38_22_8))) => (left_convergent_lines(L37_22_8, M38_22_8) | left_convergent_lines(L37_22_8, reverse_line(M38_22_8))))
% 5.61/1.39 -> [584] ~(unequally_directed_lines(L37_22_8, M38_22_8) & unequally_directed_lines(L37_22_8, reverse_line(M38_22_8)))
% 5.61/1.39 -> [585] (left_convergent_lines(L37_22_8, M38_22_8) | left_convergent_lines(L37_22_8, reverse_line(M38_22_8)))
% 5.61/1.39
% 5.61/1.39 [584] BETA_NOT_AND : ~(unequally_directed_lines(L37_22_8, M38_22_8) & unequally_directed_lines(L37_22_8, reverse_line(M38_22_8)))
% 5.61/1.39 -> [594] ~unequally_directed_lines(L37_22_8, M38_22_8)
% 5.61/1.39 -> [595] ~unequally_directed_lines(L37_22_8, reverse_line(M38_22_8))
% 5.61/1.39
% 5.61/1.39 [594] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 5.61/1.39 -> [602] ~(left_apart_point(A39_78_9, L40_78_9) | left_apart_point(A39_78_9, reverse_line(L40_78_9)))
% 5.61/1.39
% 5.61/1.39 [602] ALPHA_NOT_OR : ~(left_apart_point(A39_78_9, L40_78_9) | left_apart_point(A39_78_9, reverse_line(L40_78_9)))
% 5.61/1.39 -> [606] ~left_apart_point(A39_78_9, L40_78_9), ~left_apart_point(A39_78_9, reverse_line(L40_78_9))
% 5.61/1.39
% 5.61/1.39 [606] GAMMA_FORALL : ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42))))
% 5.61/1.39 -> [632] ~(left_convergent_lines(L41_78_10, M42_78_10) | left_convergent_lines(L41_78_10, reverse_line(M42_78_10)))
% 5.61/1.39
% 5.61/1.39 [632] ALPHA_NOT_OR : ~(left_convergent_lines(L41_78_10, M42_78_10) | left_convergent_lines(L41_78_10, reverse_line(M42_78_10)))
% 5.61/1.39 -> [633] ~left_convergent_lines(L41_78_10, M42_78_10), ~left_convergent_lines(L41_78_10, reverse_line(M42_78_10))
% 5.61/1.39
% 5.61/1.39 [633] CLOSURE : ~left_convergent_lines(L41_78_10, M42_78_10)
% 5.61/1.39
% 5.61/1.39 [595] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 5.61/1.39 -> [621] ~(left_apart_point(A39_88_9, L40_88_9) | left_apart_point(A39_88_9, reverse_line(L40_88_9)))
% 5.61/1.39
% 5.61/1.39 [621] ALPHA_NOT_OR : ~(left_apart_point(A39_88_9, L40_88_9) | left_apart_point(A39_88_9, reverse_line(L40_88_9)))
% 5.61/1.39 -> [623] ~left_apart_point(A39_88_9, L40_88_9), ~left_apart_point(A39_88_9, reverse_line(L40_88_9))
% 5.61/1.39
% 5.61/1.39 [623] GAMMA_FORALL : ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42))))
% 5.61/1.39 -> [651] ~(left_convergent_lines(L41_84_10, M42_84_10) | left_convergent_lines(L41_84_10, reverse_line(M42_84_10)))
% 5.61/1.39
% 5.61/1.39 [651] ALPHA_NOT_OR : ~(left_convergent_lines(L41_84_10, M42_84_10) | left_convergent_lines(L41_84_10, reverse_line(M42_84_10)))
% 5.61/1.39 -> [652] ~left_convergent_lines(L41_84_10, M42_84_10), ~left_convergent_lines(L41_84_10, reverse_line(M42_84_10))
% 5.61/1.39
% 5.61/1.39 [652] CLOSURE : ~left_convergent_lines(L41_84_10, M42_84_10)
% 5.61/1.39
% 5.61/1.39 [585] BETA_OR : (left_convergent_lines(L37_22_8, M38_22_8) | left_convergent_lines(L37_22_8, reverse_line(M38_22_8)))
% 5.61/1.39 -> [598] left_convergent_lines(L37_22_8, M38_22_8)
% 5.61/1.39 -> [599] left_convergent_lines(L37_22_8, reverse_line(M38_22_8))
% 5.61/1.39
% 5.61/1.39 [599] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 5.61/1.39 -> [604] ~(left_apart_point(A39_80_9, L40_80_9) | left_apart_point(A39_80_9, reverse_line(L40_80_9)))
% 5.61/1.39
% 5.61/1.39 [604] ALPHA_NOT_OR : ~(left_apart_point(A39_80_9, L40_80_9) | left_apart_point(A39_80_9, reverse_line(L40_80_9)))
% 5.61/1.39 -> [608] ~left_apart_point(A39_80_9, L40_80_9), ~left_apart_point(A39_80_9, reverse_line(L40_80_9))
% 5.61/1.39
% 5.61/1.39 [608] GAMMA_FORALL : ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42))))
% 5.61/1.39 -> [650] ~(left_convergent_lines(L41_83_10, M42_83_10) | left_convergent_lines(L41_83_10, reverse_line(M42_83_10)))
% 5.61/1.39
% 5.61/1.39 [650] ALPHA_NOT_OR : ~(left_convergent_lines(L41_83_10, M42_83_10) | left_convergent_lines(L41_83_10, reverse_line(M42_83_10)))
% 5.61/1.39 -> [654] ~left_convergent_lines(L41_83_10, M42_83_10), ~left_convergent_lines(L41_83_10, reverse_line(M42_83_10))
% 5.61/1.39
% 5.61/1.39 [654] CLOSURE : ~left_convergent_lines(L41_83_10, M42_83_10)
% 5.61/1.39
% 5.61/1.39 [598] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 5.61/1.39 -> [619] ~(left_apart_point(A39_87_9, L40_87_9) | left_apart_point(A39_87_9, reverse_line(L40_87_9)))
% 5.61/1.39
% 5.61/1.39 [619] ALPHA_NOT_OR : ~(left_apart_point(A39_87_9, L40_87_9) | left_apart_point(A39_87_9, reverse_line(L40_87_9)))
% 5.61/1.39 -> [620] ~left_apart_point(A39_87_9, L40_87_9), ~left_apart_point(A39_87_9, reverse_line(L40_87_9))
% 5.61/1.39
% 5.61/1.39 [620] GAMMA_FORALL : ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42))))
% 5.61/1.39 -> [669] ~(left_convergent_lines(L41_91_10, M42_91_10) | left_convergent_lines(L41_91_10, reverse_line(M42_91_10)))
% 5.61/1.39
% 5.61/1.39 [669] ALPHA_NOT_OR : ~(left_convergent_lines(L41_91_10, M42_91_10) | left_convergent_lines(L41_91_10, reverse_line(M42_91_10)))
% 5.61/1.39 -> [670] ~left_convergent_lines(L41_91_10, M42_91_10), ~left_convergent_lines(L41_91_10, reverse_line(M42_91_10))
% 5.61/1.39
% 5.61/1.39 [670] CLOSURE : ~left_convergent_lines(L41_91_10, M42_91_10)
% 5.61/1.39
% 5.61/1.39 [560] 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)))))
% 5.61/1.39 -> [562] ((line(L35_6_7) & line(L35_6_7)) => (unequally_directed_lines(L35_6_7, L35_6_7) | unequally_directed_lines(L35_6_7, reverse_line(L35_6_7))))
% 5.61/1.39
% 5.61/1.39 [562] BETA_IMPLY : ((line(L35_6_7) & line(L35_6_7)) => (unequally_directed_lines(L35_6_7, L35_6_7) | unequally_directed_lines(L35_6_7, reverse_line(L35_6_7))))
% 5.61/1.39 -> [564] ~(line(L35_6_7) & line(L35_6_7))
% 5.61/1.39 -> [565] (unequally_directed_lines(L35_6_7, L35_6_7) | unequally_directed_lines(L35_6_7, reverse_line(L35_6_7)))
% 5.61/1.39
% 5.61/1.39 [564] BETA_NOT_AND : ~(line(L35_6_7) & line(L35_6_7))
% 5.61/1.39 -> [568] ~line(L35_6_7)
% 5.61/1.39 -> [569] ~line(L35_6_7)
% 5.61/1.39
% 5.61/1.39 [568] 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)))))
% 5.61/1.39 -> [576] ((unequally_directed_lines(L37_20_8, M38_20_8) & unequally_directed_lines(L37_20_8, reverse_line(M38_20_8))) => (left_convergent_lines(L37_20_8, M38_20_8) | left_convergent_lines(L37_20_8, reverse_line(M38_20_8))))
% 5.61/1.39
% 5.61/1.39 [576] BETA_IMPLY : ((unequally_directed_lines(L37_20_8, M38_20_8) & unequally_directed_lines(L37_20_8, reverse_line(M38_20_8))) => (left_convergent_lines(L37_20_8, M38_20_8) | left_convergent_lines(L37_20_8, reverse_line(M38_20_8))))
% 5.61/1.39 -> [579] ~(unequally_directed_lines(L37_20_8, M38_20_8) & unequally_directed_lines(L37_20_8, reverse_line(M38_20_8)))
% 5.61/1.39 -> [580] (left_convergent_lines(L37_20_8, M38_20_8) | left_convergent_lines(L37_20_8, reverse_line(M38_20_8)))
% 5.61/1.39
% 5.61/1.39 [579] BETA_NOT_AND : ~(unequally_directed_lines(L37_20_8, M38_20_8) & unequally_directed_lines(L37_20_8, reverse_line(M38_20_8)))
% 5.61/1.39 -> [588] ~unequally_directed_lines(L37_20_8, M38_20_8)
% 5.61/1.39 -> [589] ~unequally_directed_lines(L37_20_8, reverse_line(M38_20_8))
% 5.61/1.39
% 5.61/1.39 [588] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 5.61/1.39 -> [603] ~(left_apart_point(A39_79_9, L40_79_9) | left_apart_point(A39_79_9, reverse_line(L40_79_9)))
% 5.61/1.39
% 5.61/1.39 [603] ALPHA_NOT_OR : ~(left_apart_point(A39_79_9, L40_79_9) | left_apart_point(A39_79_9, reverse_line(L40_79_9)))
% 5.61/1.39 -> [615] ~left_apart_point(A39_79_9, L40_79_9), ~left_apart_point(A39_79_9, reverse_line(L40_79_9))
% 5.61/1.39
% 5.61/1.39 [615] GAMMA_FORALL : ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42))))
% 5.61/1.39 -> [648] ~(left_convergent_lines(L41_82_10, M42_82_10) | left_convergent_lines(L41_82_10, reverse_line(M42_82_10)))
% 5.61/1.39
% 5.61/1.39 [648] ALPHA_NOT_OR : ~(left_convergent_lines(L41_82_10, M42_82_10) | left_convergent_lines(L41_82_10, reverse_line(M42_82_10)))
% 5.61/1.39 -> [649] ~left_convergent_lines(L41_82_10, M42_82_10), ~left_convergent_lines(L41_82_10, reverse_line(M42_82_10))
% 5.61/1.39
% 5.61/1.39 [649] CLOSURE : ~left_convergent_lines(L41_82_10, M42_82_10)
% 5.61/1.39
% 5.61/1.39 [589] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 5.61/1.39 -> [626] ~(left_apart_point(A39_89_9, L40_89_9) | left_apart_point(A39_89_9, reverse_line(L40_89_9)))
% 5.61/1.39
% 5.61/1.39 [626] ALPHA_NOT_OR : ~(left_apart_point(A39_89_9, L40_89_9) | left_apart_point(A39_89_9, reverse_line(L40_89_9)))
% 5.61/1.39 -> [627] ~left_apart_point(A39_89_9, L40_89_9), ~left_apart_point(A39_89_9, reverse_line(L40_89_9))
% 5.61/1.39
% 5.61/1.39 [627] GAMMA_FORALL : ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42))))
% 5.61/1.39 -> [664] ~(left_convergent_lines(L41_90_10, M42_90_10) | left_convergent_lines(L41_90_10, reverse_line(M42_90_10)))
% 5.61/1.39
% 5.61/1.39 [664] ALPHA_NOT_OR : ~(left_convergent_lines(L41_90_10, M42_90_10) | left_convergent_lines(L41_90_10, reverse_line(M42_90_10)))
% 5.61/1.39 -> [666] ~left_convergent_lines(L41_90_10, M42_90_10), ~left_convergent_lines(L41_90_10, reverse_line(M42_90_10))
% 5.61/1.39
% 5.61/1.39 [666] CLOSURE : ~left_convergent_lines(L41_90_10, M42_90_10)
% 5.61/1.39
% 5.61/1.39 [580] BETA_OR : (left_convergent_lines(L37_20_8, M38_20_8) | left_convergent_lines(L37_20_8, reverse_line(M38_20_8)))
% 5.61/1.39 -> [590] left_convergent_lines(L37_20_8, M38_20_8)
% 5.61/1.39 -> [591] left_convergent_lines(L37_20_8, reverse_line(M38_20_8))
% 5.61/1.39
% 5.61/1.39 [590] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 5.61/1.39 -> [605] ~(left_apart_point(A39_81_9, L40_81_9) | left_apart_point(A39_81_9, reverse_line(L40_81_9)))
% 5.61/1.39
% 5.61/1.39 [605] ALPHA_NOT_OR : ~(left_apart_point(A39_81_9, L40_81_9) | left_apart_point(A39_81_9, reverse_line(L40_81_9)))
% 5.61/1.39 -> [609] ~left_apart_point(A39_81_9, L40_81_9), ~left_apart_point(A39_81_9, reverse_line(L40_81_9))
% 5.61/1.39
% 5.61/1.39 [609] GAMMA_FORALL : ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42))))
% 5.61/1.39 -> [634] ~(left_convergent_lines(L41_79_10, M42_79_10) | left_convergent_lines(L41_79_10, reverse_line(M42_79_10)))
% 5.61/1.39
% 5.61/1.39 [634] ALPHA_NOT_OR : ~(left_convergent_lines(L41_79_10, M42_79_10) | left_convergent_lines(L41_79_10, reverse_line(M42_79_10)))
% 5.61/1.39 -> [635] ~left_convergent_lines(L41_79_10, M42_79_10), ~left_convergent_lines(L41_79_10, reverse_line(M42_79_10))
% 5.61/1.39
% 5.61/1.39 [635] CLOSURE : ~left_convergent_lines(L41_79_10, M42_79_10)
% 5.61/1.39
% 5.61/1.39 [591] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 5.61/1.39 -> [628] ~(left_apart_point(A39_90_9, L40_90_9) | left_apart_point(A39_90_9, reverse_line(L40_90_9)))
% 5.61/1.39
% 5.61/1.39 [628] ALPHA_NOT_OR : ~(left_apart_point(A39_90_9, L40_90_9) | left_apart_point(A39_90_9, reverse_line(L40_90_9)))
% 5.61/1.39 -> [630] ~left_apart_point(A39_90_9, L40_90_9), ~left_apart_point(A39_90_9, reverse_line(L40_90_9))
% 5.61/1.39
% 5.61/1.39 [630] GAMMA_FORALL : ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42))))
% 5.61/1.39 -> [671] ~(left_convergent_lines(L41_92_10, M42_92_10) | left_convergent_lines(L41_92_10, reverse_line(M42_92_10)))
% 5.61/1.39
% 5.61/1.39 [671] ALPHA_NOT_OR : ~(left_convergent_lines(L41_92_10, M42_92_10) | left_convergent_lines(L41_92_10, reverse_line(M42_92_10)))
% 5.61/1.39 -> [673] ~left_convergent_lines(L41_92_10, M42_92_10), ~left_convergent_lines(L41_92_10, reverse_line(M42_92_10))
% 5.61/1.39
% 5.61/1.39 [673] CLOSURE : ~left_convergent_lines(L41_92_10, M42_92_10)
% 5.61/1.39
% 5.61/1.39 [569] 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)))))
% 5.61/1.39 -> [581] ((unequally_directed_lines(L37_23_8, M38_23_8) & unequally_directed_lines(L37_23_8, reverse_line(M38_23_8))) => (left_convergent_lines(L37_23_8, M38_23_8) | left_convergent_lines(L37_23_8, reverse_line(M38_23_8))))
% 5.61/1.39
% 5.61/1.39 [581] BETA_IMPLY : ((unequally_directed_lines(L37_23_8, M38_23_8) & unequally_directed_lines(L37_23_8, reverse_line(M38_23_8))) => (left_convergent_lines(L37_23_8, M38_23_8) | left_convergent_lines(L37_23_8, reverse_line(M38_23_8))))
% 5.61/1.39 -> [586] ~(unequally_directed_lines(L37_23_8, M38_23_8) & unequally_directed_lines(L37_23_8, reverse_line(M38_23_8)))
% 5.61/1.39 -> [587] (left_convergent_lines(L37_23_8, M38_23_8) | left_convergent_lines(L37_23_8, reverse_line(M38_23_8)))
% 5.61/1.39
% 5.61/1.39 [586] BETA_NOT_AND : ~(unequally_directed_lines(L37_23_8, M38_23_8) & unequally_directed_lines(L37_23_8, reverse_line(M38_23_8)))
% 5.61/1.39 -> [600] ~unequally_directed_lines(L37_23_8, M38_23_8)
% 5.61/1.39 -> [601] ~unequally_directed_lines(L37_23_8, reverse_line(M38_23_8))
% 5.61/1.39
% 5.61/1.39 [601] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 5.61/1.39 -> [611] ~(left_apart_point(A39_83_9, L40_83_9) | left_apart_point(A39_83_9, reverse_line(L40_83_9)))
% 5.61/1.39
% 5.61/1.39 [611] ALPHA_NOT_OR : ~(left_apart_point(A39_83_9, L40_83_9) | left_apart_point(A39_83_9, reverse_line(L40_83_9)))
% 5.61/1.39 -> [613] ~left_apart_point(A39_83_9, L40_83_9), ~left_apart_point(A39_83_9, reverse_line(L40_83_9))
% 5.61/1.39
% 5.61/1.39 [613] GAMMA_FORALL : ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42))))
% 5.61/1.39 -> [641] ~(left_convergent_lines(L41_80_10, M42_80_10) | left_convergent_lines(L41_80_10, reverse_line(M42_80_10)))
% 5.61/1.39
% 5.61/1.39 [641] ALPHA_NOT_OR : ~(left_convergent_lines(L41_80_10, M42_80_10) | left_convergent_lines(L41_80_10, reverse_line(M42_80_10)))
% 5.61/1.39 -> [642] ~left_convergent_lines(L41_80_10, M42_80_10), ~left_convergent_lines(L41_80_10, reverse_line(M42_80_10))
% 5.61/1.39
% 5.61/1.39 [642] CLOSURE : ~left_convergent_lines(L41_80_10, M42_80_10)
% 5.61/1.39
% 5.61/1.39 [600] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 5.61/1.39 -> [616] ~(left_apart_point(A39_85_9, L40_85_9) | left_apart_point(A39_85_9, reverse_line(L40_85_9)))
% 5.61/1.39
% 5.61/1.39 [616] ALPHA_NOT_OR : ~(left_apart_point(A39_85_9, L40_85_9) | left_apart_point(A39_85_9, reverse_line(L40_85_9)))
% 5.61/1.39 -> [617] ~left_apart_point(A39_85_9, L40_85_9), ~left_apart_point(A39_85_9, reverse_line(L40_85_9))
% 5.61/1.39
% 5.61/1.39 [617] GAMMA_FORALL : ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42))))
% 5.61/1.39 -> [653] ~(left_convergent_lines(L41_85_10, M42_85_10) | left_convergent_lines(L41_85_10, reverse_line(M42_85_10)))
% 5.61/1.39
% 5.61/1.39 [653] ALPHA_NOT_OR : ~(left_convergent_lines(L41_85_10, M42_85_10) | left_convergent_lines(L41_85_10, reverse_line(M42_85_10)))
% 5.61/1.39 -> [655] ~left_convergent_lines(L41_85_10, M42_85_10), ~left_convergent_lines(L41_85_10, reverse_line(M42_85_10))
% 5.61/1.39
% 5.61/1.39 [655] CLOSURE : ~left_convergent_lines(L41_85_10, M42_85_10)
% 5.61/1.39
% 5.61/1.39 [587] BETA_OR : (left_convergent_lines(L37_23_8, M38_23_8) | left_convergent_lines(L37_23_8, reverse_line(M38_23_8)))
% 5.61/1.39 -> [624] left_convergent_lines(L37_23_8, M38_23_8)
% 5.61/1.39 -> [625] left_convergent_lines(L37_23_8, reverse_line(M38_23_8))
% 5.61/1.39
% 5.61/1.39 [624] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 5.61/1.39 -> [639] ~(left_apart_point(A39_92_9, L40_92_9) | left_apart_point(A39_92_9, reverse_line(L40_92_9)))
% 5.61/1.39
% 5.61/1.39 [639] ALPHA_NOT_OR : ~(left_apart_point(A39_92_9, L40_92_9) | left_apart_point(A39_92_9, reverse_line(L40_92_9)))
% 5.61/1.39 -> [640] ~left_apart_point(A39_92_9, L40_92_9), ~left_apart_point(A39_92_9, reverse_line(L40_92_9))
% 5.61/1.39
% 5.61/1.39 [640] GAMMA_FORALL : ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42))))
% 5.61/1.39 -> [658] ~(left_convergent_lines(L41_88_10, M42_88_10) | left_convergent_lines(L41_88_10, reverse_line(M42_88_10)))
% 5.61/1.39
% 5.61/1.39 [658] ALPHA_NOT_OR : ~(left_convergent_lines(L41_88_10, M42_88_10) | left_convergent_lines(L41_88_10, reverse_line(M42_88_10)))
% 5.61/1.39 -> [662] ~left_convergent_lines(L41_88_10, M42_88_10), ~left_convergent_lines(L41_88_10, reverse_line(M42_88_10))
% 5.61/1.39
% 5.61/1.39 [662] CLOSURE : ~left_convergent_lines(L41_88_10, M42_88_10)
% 5.61/1.39
% 5.61/1.39 [625] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 5.61/1.39 -> [645] ~(left_apart_point(A39_93_9, L40_93_9) | left_apart_point(A39_93_9, reverse_line(L40_93_9)))
% 5.61/1.39
% 5.61/1.39 [645] ALPHA_NOT_OR : ~(left_apart_point(A39_93_9, L40_93_9) | left_apart_point(A39_93_9, reverse_line(L40_93_9)))
% 5.61/1.39 -> [661] ~left_apart_point(A39_93_9, L40_93_9), ~left_apart_point(A39_93_9, reverse_line(L40_93_9))
% 5.61/1.39
% 5.61/1.39 [661] GAMMA_FORALL : ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42))))
% 5.61/1.39 -> [677] ~(left_convergent_lines(L41_93_10, M42_93_10) | left_convergent_lines(L41_93_10, reverse_line(M42_93_10)))
% 5.61/1.39
% 5.61/1.39 [677] ALPHA_NOT_OR : ~(left_convergent_lines(L41_93_10, M42_93_10) | left_convergent_lines(L41_93_10, reverse_line(M42_93_10)))
% 5.61/1.39 -> [678] ~left_convergent_lines(L41_93_10, M42_93_10), ~left_convergent_lines(L41_93_10, reverse_line(M42_93_10))
% 5.61/1.39
% 5.61/1.39 [678] CLOSURE : ~left_convergent_lines(L41_93_10, M42_93_10)
% 5.61/1.39
% 5.61/1.39 [565] BETA_OR : (unequally_directed_lines(L35_6_7, L35_6_7) | unequally_directed_lines(L35_6_7, reverse_line(L35_6_7)))
% 5.61/1.39 -> [572] unequally_directed_lines(L35_6_7, L35_6_7)
% 5.61/1.39 -> [573] unequally_directed_lines(L35_6_7, reverse_line(L35_6_7))
% 5.61/1.39
% 5.61/1.39 [572] CLOSURE : unequally_directed_lines(L35_6_7, L35_6_7)
% 5.61/1.39
% 5.61/1.39 [573] 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)))))
% 5.61/1.39 -> [636] ((unequally_directed_lines(L37_24_8, reverse_line(L37_24_8)) & unequally_directed_lines(L37_24_8, reverse_line(reverse_line(L37_24_8)))) => (left_convergent_lines(L37_24_8, reverse_line(L37_24_8)) | left_convergent_lines(L37_24_8, reverse_line(reverse_line(L37_24_8)))))
% 5.61/1.39
% 5.61/1.39 [636] BETA_IMPLY : ((unequally_directed_lines(L37_24_8, reverse_line(L37_24_8)) & unequally_directed_lines(L37_24_8, reverse_line(reverse_line(L37_24_8)))) => (left_convergent_lines(L37_24_8, reverse_line(L37_24_8)) | left_convergent_lines(L37_24_8, reverse_line(reverse_line(L37_24_8)))))
% 5.61/1.39 -> [637] ~(unequally_directed_lines(L37_24_8, reverse_line(L37_24_8)) & unequally_directed_lines(L37_24_8, reverse_line(reverse_line(L37_24_8))))
% 5.61/1.39 -> [638] (left_convergent_lines(L37_24_8, reverse_line(L37_24_8)) | left_convergent_lines(L37_24_8, reverse_line(reverse_line(L37_24_8))))
% 5.61/1.39
% 5.61/1.39 [638] BETA_OR : (left_convergent_lines(L37_24_8, reverse_line(L37_24_8)) | left_convergent_lines(L37_24_8, reverse_line(reverse_line(L37_24_8))))
% 5.61/1.39 -> [643] left_convergent_lines(L37_24_8, reverse_line(L37_24_8))
% 5.61/1.39 -> [644] left_convergent_lines(L37_24_8, reverse_line(reverse_line(L37_24_8)))
% 5.61/1.39
% 5.61/1.39 [643] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 5.61/1.39 -> [675] ~(left_apart_point(A39_95_9, L40_95_9) | left_apart_point(A39_95_9, reverse_line(L40_95_9)))
% 5.61/1.39
% 5.61/1.39 [675] ALPHA_NOT_OR : ~(left_apart_point(A39_95_9, L40_95_9) | left_apart_point(A39_95_9, reverse_line(L40_95_9)))
% 5.61/1.39 -> [676] ~left_apart_point(A39_95_9, L40_95_9), ~left_apart_point(A39_95_9, reverse_line(L40_95_9))
% 5.61/1.39
% 5.61/1.39 [676] GAMMA_FORALL : ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42))))
% 5.61/1.39 -> [681] ~(left_convergent_lines(L41_95_10, M42_95_10) | left_convergent_lines(L41_95_10, reverse_line(M42_95_10)))
% 5.61/1.39
% 5.61/1.39 [681] ALPHA_NOT_OR : ~(left_convergent_lines(L41_95_10, M42_95_10) | left_convergent_lines(L41_95_10, reverse_line(M42_95_10)))
% 5.61/1.39 -> [684] ~left_convergent_lines(L41_95_10, M42_95_10), ~left_convergent_lines(L41_95_10, reverse_line(M42_95_10))
% 5.61/1.39
% 5.61/1.39 [684] CLOSURE : ~left_convergent_lines(L41_95_10, M42_95_10)
% 5.61/1.39
% 5.61/1.39 [644] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 5.61/1.39 -> [672] ~(left_apart_point(A39_94_9, L40_94_9) | left_apart_point(A39_94_9, reverse_line(L40_94_9)))
% 5.61/1.39
% 5.61/1.39 [672] ALPHA_NOT_OR : ~(left_apart_point(A39_94_9, L40_94_9) | left_apart_point(A39_94_9, reverse_line(L40_94_9)))
% 5.61/1.39 -> [674] ~left_apart_point(A39_94_9, L40_94_9), ~left_apart_point(A39_94_9, reverse_line(L40_94_9))
% 5.61/1.39
% 5.61/1.39 [674] GAMMA_FORALL : ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42))))
% 5.61/1.39 -> [680] ~(left_convergent_lines(L41_94_10, M42_94_10) | left_convergent_lines(L41_94_10, reverse_line(M42_94_10)))
% 5.61/1.39
% 5.61/1.39 [680] ALPHA_NOT_OR : ~(left_convergent_lines(L41_94_10, M42_94_10) | left_convergent_lines(L41_94_10, reverse_line(M42_94_10)))
% 5.61/1.39 -> [683] ~left_convergent_lines(L41_94_10, M42_94_10), ~left_convergent_lines(L41_94_10, reverse_line(M42_94_10))
% 5.61/1.39
% 5.61/1.39 [683] CLOSURE : ~left_convergent_lines(L41_94_10, M42_94_10)
% 5.61/1.39
% 5.61/1.39 [637] BETA_NOT_AND : ~(unequally_directed_lines(L37_24_8, reverse_line(L37_24_8)) & unequally_directed_lines(L37_24_8, reverse_line(reverse_line(L37_24_8))))
% 5.61/1.39 -> [667] ~unequally_directed_lines(L37_24_8, reverse_line(L37_24_8))
% 5.61/1.39 -> [668] ~unequally_directed_lines(L37_24_8, reverse_line(reverse_line(L37_24_8)))
% 5.61/1.39
% 5.61/1.39 [667] CLOSURE : ~unequally_directed_lines(L37_24_8, reverse_line(L37_24_8))
% 5.61/1.39
% 5.61/1.39 [668] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 5.61/1.39 -> [679] ~(left_apart_point(A39_96_9, L40_96_9) | left_apart_point(A39_96_9, reverse_line(L40_96_9)))
% 5.61/1.39
% 5.61/1.39 [679] ALPHA_NOT_OR : ~(left_apart_point(A39_96_9, L40_96_9) | left_apart_point(A39_96_9, reverse_line(L40_96_9)))
% 5.61/1.39 -> [682] ~left_apart_point(A39_96_9, L40_96_9), ~left_apart_point(A39_96_9, reverse_line(L40_96_9))
% 5.61/1.39
% 5.61/1.39 [682] GAMMA_FORALL : ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42))))
% 5.61/1.39 -> [685] ~(left_convergent_lines(L41_96_10, M42_96_10) | left_convergent_lines(L41_96_10, reverse_line(M42_96_10)))
% 5.61/1.39
% 5.61/1.39 [685] ALPHA_NOT_OR : ~(left_convergent_lines(L41_96_10, M42_96_10) | left_convergent_lines(L41_96_10, reverse_line(M42_96_10)))
% 5.61/1.39 -> [686] ~left_convergent_lines(L41_96_10, M42_96_10), ~left_convergent_lines(L41_96_10, reverse_line(M42_96_10))
% 5.61/1.39
% 5.61/1.39 [686] CLOSURE : ~left_convergent_lines(L41_96_10, M42_96_10)
% 5.61/1.39
% 5.61/1.39 % SZS output end Proof for theBenchmark.p
% 5.61/1.39 [1.042526s][1][Res] 5127 goroutines created
% 5.61/1.39 ==== Result ====
% 5.61/1.39 [1.042542s][1][Res] VALID
% 5.61/1.39 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------