TSTP Solution File: GEO250+1 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO250+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n020.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 15:18:43 EDT 2022
% Result : Theorem 2.34s 0.92s
% Output : Proof 2.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO250+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.07/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n020.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 07:13:30 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 [DMT] DMT loaded with preskolemization
% 0.13/0.35 [EQ] equality loaded.
% 0.13/0.35 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.36 Conjecture not found
% 0.13/0.36 Start search
% 0.13/0.36 nb_step : 1 - limit : 32
% 0.13/0.36 Launch Gotab with destructive = true
% 2.34/0.91 % SZS output start Proof for theBenchmark.p
% 2.34/0.92 [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, parallel_through_point(L79_79, A77_77)) => left_apart_point(A77_77, reverse_line(parallel_through_point(L79_79, B78_78))))))
% 2.34/0.92 -> [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, parallel_through_point(L79_79, A77_77)) => left_apart_point(A77_77, reverse_line(parallel_through_point(L79_79, B78_78)))))
% 2.34/0.92
% 2.34/0.92 [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)))))
% 2.34/0.92 -> [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))))
% 2.34/0.92
% 2.34/0.92 [2] DELTA_NOT_FORALL : ~! [A77_77, B78_78, L79_79] : ((left_apart_point(B78_78, parallel_through_point(L79_79, A77_77)) => left_apart_point(A77_77, reverse_line(parallel_through_point(L79_79, B78_78)))))
% 2.34/0.92 -> [3] ~(left_apart_point(skolem_B7878, parallel_through_point(skolem_L7979, skolem_A7777)) => left_apart_point(skolem_A7777, reverse_line(parallel_through_point(skolem_L7979, skolem_B7878))))
% 2.34/0.92
% 2.34/0.92 [3] ALPHA_NOT_IMPLY : ~(left_apart_point(skolem_B7878, parallel_through_point(skolem_L7979, skolem_A7777)) => left_apart_point(skolem_A7777, reverse_line(parallel_through_point(skolem_L7979, skolem_B7878))))
% 2.34/0.92 -> [4] left_apart_point(skolem_B7878, parallel_through_point(skolem_L7979, skolem_A7777)), ~left_apart_point(skolem_A7777, reverse_line(parallel_through_point(skolem_L7979, skolem_B7878)))
% 2.34/0.92
% 2.34/0.92 [4] GAMMA_FORALL : ! [A20_20] : (~distinct_points(A20_20, A20_20))
% 2.34/0.92 -> [5] ~distinct_points(C23_0_1, C23_0_1)
% 2.34/0.92
% 2.34/0.92 [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))))
% 2.34/0.92 -> [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)))
% 2.34/0.92
% 2.34/0.92 [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)))
% 2.34/0.92 -> [7] ~distinct_points(C23_0_1, C23_0_1)
% 2.34/0.92 -> [8] (distinct_points(C23_0_1, C23_0_1) | distinct_points(C23_0_1, C23_0_1))
% 2.34/0.92
% 2.34/0.92 [8] BETA_OR : (distinct_points(C23_0_1, C23_0_1) | distinct_points(C23_0_1, C23_0_1))
% 2.34/0.92 -> [9] distinct_points(C23_0_1, C23_0_1)
% 2.34/0.92 -> [10] distinct_points(C23_0_1, C23_0_1)
% 2.34/0.92
% 2.34/0.92 [10] CLOSURE : distinct_points(C23_0_1, C23_0_1)
% 2.34/0.92
% 2.34/0.92 [9] CLOSURE : distinct_points(C23_0_1, C23_0_1)
% 2.34/0.92
% 2.34/0.92 [7] GAMMA_FORALL : ! [L24_24] : (~distinct_lines(L24_24, L24_24))
% 2.34/0.92 -> [11] ~distinct_lines(N27_0_3, N27_0_3)
% 2.34/0.92
% 2.34/0.92 [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))))
% 2.34/0.92 -> [12] (distinct_lines(N27_0_3, N27_0_3) => (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3)))
% 2.34/0.92
% 2.34/0.92 [12] BETA_IMPLY : (distinct_lines(N27_0_3, N27_0_3) => (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3)))
% 2.34/0.92 -> [13] ~distinct_lines(N27_0_3, N27_0_3)
% 2.34/0.92 -> [14] (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3))
% 2.34/0.92
% 2.34/0.92 [14] BETA_OR : (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3))
% 2.34/0.92 -> [15] distinct_lines(N27_0_3, N27_0_3)
% 2.34/0.92 -> [16] distinct_lines(N27_0_3, N27_0_3)
% 2.34/0.92
% 2.34/0.92 [16] CLOSURE : distinct_lines(N27_0_3, N27_0_3)
% 2.34/0.92
% 2.34/0.92 [15] CLOSURE : distinct_lines(N27_0_3, N27_0_3)
% 2.34/0.92
% 2.34/0.92 [13] GAMMA_FORALL : ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28))
% 2.34/0.92 -> [17] ~unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8)))
% 2.34/0.92
% 2.34/0.92 [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))))
% 2.34/0.92 -> [18] (unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))) => (unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))) | unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8)))))
% 2.34/0.92
% 2.34/0.92 [18] BETA_IMPLY : (unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))) => (unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))) | unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8)))))
% 2.34/0.92 -> [19] ~unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8)))
% 2.34/0.92 -> [20] (unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))) | unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))))
% 2.34/0.92
% 2.34/0.92 [20] BETA_OR : (unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))) | unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))))
% 2.34/0.92 -> [21] unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8)))
% 2.34/0.92 -> [22] unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8)))
% 2.34/0.92
% 2.34/0.92 [22] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8)))
% 2.34/0.92
% 2.34/0.92 [21] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8)))
% 2.34/0.92
% 2.34/0.92 [23] BETA_IMPLY : ((unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(reverse_line(M38_19_8))))) => ((unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(reverse_line(M38_19_8))))) | (unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(reverse_line(M38_19_8)))))))
% 2.34/0.92 -> [267] ~(unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(reverse_line(M38_19_8)))))
% 2.34/0.92 -> [268] ((unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(reverse_line(M38_19_8))))) | (unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(reverse_line(M38_19_8))))))
% 2.34/0.92
% 2.34/0.92 [267] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(reverse_line(M38_19_8)))))
% 2.34/0.92 -> [271] ~unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8)))
% 2.34/0.92 -> [272] ~unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(reverse_line(M38_19_8))))
% 2.34/0.92
% 2.34/0.92 [272] 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)))))
% 2.34/0.92 -> [276] ((line(M36_5_7) & line(M36_5_7)) => (unequally_directed_lines(M36_5_7, M36_5_7) | unequally_directed_lines(M36_5_7, reverse_line(M36_5_7))))
% 2.34/0.92
% 2.34/0.92 [276] BETA_IMPLY : ((line(M36_5_7) & line(M36_5_7)) => (unequally_directed_lines(M36_5_7, M36_5_7) | unequally_directed_lines(M36_5_7, reverse_line(M36_5_7))))
% 2.34/0.92 -> [279] ~(line(M36_5_7) & line(M36_5_7))
% 2.34/0.92 -> [280] (unequally_directed_lines(M36_5_7, M36_5_7) | unequally_directed_lines(M36_5_7, reverse_line(M36_5_7)))
% 2.34/0.92
% 2.34/0.92 [280] BETA_OR : (unequally_directed_lines(M36_5_7, M36_5_7) | unequally_directed_lines(M36_5_7, reverse_line(M36_5_7)))
% 2.34/0.92 -> [287] unequally_directed_lines(M36_5_7, M36_5_7)
% 2.34/0.92 -> [288] unequally_directed_lines(M36_5_7, reverse_line(M36_5_7))
% 2.34/0.92
% 2.34/0.92 [288] CLOSURE : unequally_directed_lines(M36_5_7, reverse_line(M36_5_7))
% 2.34/0.92
% 2.34/0.92 [287] CLOSURE : unequally_directed_lines(M36_5_7, M36_5_7)
% 2.34/0.92
% 2.34/0.92 [279] BETA_NOT_AND : ~(line(M36_5_7) & line(M36_5_7))
% 2.34/0.92 -> [283] ~line(M36_5_7)
% 2.34/0.92 -> [284] ~line(M36_5_7)
% 2.34/0.92
% 2.34/0.92 [284] 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)))))
% 2.34/0.92 -> [290] ((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))))
% 2.34/0.92
% 2.34/0.92 [290] 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))))
% 2.34/0.92 -> [295] ~(unequally_directed_lines(L37_14_8, M38_14_8) & unequally_directed_lines(L37_14_8, reverse_line(M38_14_8)))
% 2.34/0.92 -> [296] (left_convergent_lines(L37_14_8, M38_14_8) | left_convergent_lines(L37_14_8, reverse_line(M38_14_8)))
% 2.34/0.92
% 2.34/0.92 [296] BETA_OR : (left_convergent_lines(L37_14_8, M38_14_8) | left_convergent_lines(L37_14_8, reverse_line(M38_14_8)))
% 2.34/0.92 -> [305] left_convergent_lines(L37_14_8, M38_14_8)
% 2.34/0.92 -> [306] left_convergent_lines(L37_14_8, reverse_line(M38_14_8))
% 2.34/0.92
% 2.34/0.92 [305] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.34/0.92 -> [329] ~(left_apart_point(A39_58_9, L40_58_9) | left_apart_point(A39_58_9, reverse_line(L40_58_9)))
% 2.34/0.92
% 2.34/0.92 [329] ALPHA_NOT_OR : ~(left_apart_point(A39_58_9, L40_58_9) | left_apart_point(A39_58_9, reverse_line(L40_58_9)))
% 2.34/0.92 -> [332] ~left_apart_point(A39_58_9, L40_58_9), ~left_apart_point(A39_58_9, reverse_line(L40_58_9))
% 2.34/0.92
% 2.34/0.92 [332] CLOSURE : ~left_apart_point(A39_58_9, L40_58_9)
% 2.34/0.92
% 2.34/0.92 [306] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.34/0.92 -> [337] ~(left_apart_point(A39_61_9, L40_61_9) | left_apart_point(A39_61_9, reverse_line(L40_61_9)))
% 2.34/0.92
% 2.34/0.92 [337] ALPHA_NOT_OR : ~(left_apart_point(A39_61_9, L40_61_9) | left_apart_point(A39_61_9, reverse_line(L40_61_9)))
% 2.34/0.92 -> [338] ~left_apart_point(A39_61_9, L40_61_9), ~left_apart_point(A39_61_9, reverse_line(L40_61_9))
% 2.34/0.92
% 2.34/0.92 [338] CLOSURE : ~left_apart_point(A39_61_9, L40_61_9)
% 2.34/0.92
% 2.34/0.92 [295] BETA_NOT_AND : ~(unequally_directed_lines(L37_14_8, M38_14_8) & unequally_directed_lines(L37_14_8, reverse_line(M38_14_8)))
% 2.34/0.92 -> [309] ~unequally_directed_lines(L37_14_8, M38_14_8)
% 2.34/0.92 -> [310] ~unequally_directed_lines(L37_14_8, reverse_line(M38_14_8))
% 2.34/0.92
% 2.34/0.92 [310] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.34/0.92 -> [326] ~(left_apart_point(A39_56_9, L40_56_9) | left_apart_point(A39_56_9, reverse_line(L40_56_9)))
% 2.34/0.92
% 2.34/0.92 [326] ALPHA_NOT_OR : ~(left_apart_point(A39_56_9, L40_56_9) | left_apart_point(A39_56_9, reverse_line(L40_56_9)))
% 2.34/0.92 -> [335] ~left_apart_point(A39_56_9, L40_56_9), ~left_apart_point(A39_56_9, reverse_line(L40_56_9))
% 2.34/0.92
% 2.34/0.92 [335] CLOSURE : ~left_apart_point(A39_56_9, L40_56_9)
% 2.34/0.92
% 2.34/0.92 [309] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.34/0.92 -> [340] ~(left_apart_point(A39_63_9, L40_63_9) | left_apart_point(A39_63_9, reverse_line(L40_63_9)))
% 2.34/0.92
% 2.34/0.92 [340] ALPHA_NOT_OR : ~(left_apart_point(A39_63_9, L40_63_9) | left_apart_point(A39_63_9, reverse_line(L40_63_9)))
% 2.34/0.92 -> [343] ~left_apart_point(A39_63_9, L40_63_9), ~left_apart_point(A39_63_9, reverse_line(L40_63_9))
% 2.34/0.92
% 2.34/0.92 [343] CLOSURE : ~left_apart_point(A39_63_9, L40_63_9)
% 2.34/0.92
% 2.34/0.92 [283] 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)))))
% 2.34/0.92 -> [294] ((unequally_directed_lines(L37_16_8, M38_16_8) & unequally_directed_lines(L37_16_8, reverse_line(M38_16_8))) => (left_convergent_lines(L37_16_8, M38_16_8) | left_convergent_lines(L37_16_8, reverse_line(M38_16_8))))
% 2.34/0.92
% 2.34/0.92 [294] BETA_IMPLY : ((unequally_directed_lines(L37_16_8, M38_16_8) & unequally_directed_lines(L37_16_8, reverse_line(M38_16_8))) => (left_convergent_lines(L37_16_8, M38_16_8) | left_convergent_lines(L37_16_8, reverse_line(M38_16_8))))
% 2.34/0.92 -> [303] ~(unequally_directed_lines(L37_16_8, M38_16_8) & unequally_directed_lines(L37_16_8, reverse_line(M38_16_8)))
% 2.34/0.92 -> [304] (left_convergent_lines(L37_16_8, M38_16_8) | left_convergent_lines(L37_16_8, reverse_line(M38_16_8)))
% 2.34/0.92
% 2.34/0.92 [303] BETA_NOT_AND : ~(unequally_directed_lines(L37_16_8, M38_16_8) & unequally_directed_lines(L37_16_8, reverse_line(M38_16_8)))
% 2.34/0.92 -> [313] ~unequally_directed_lines(L37_16_8, M38_16_8)
% 2.34/0.92 -> [314] ~unequally_directed_lines(L37_16_8, reverse_line(M38_16_8))
% 2.34/0.92
% 2.34/0.92 [314] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.34/0.92 -> [322] ~(left_apart_point(A39_54_9, L40_54_9) | left_apart_point(A39_54_9, reverse_line(L40_54_9)))
% 2.34/0.92
% 2.34/0.92 [322] ALPHA_NOT_OR : ~(left_apart_point(A39_54_9, L40_54_9) | left_apart_point(A39_54_9, reverse_line(L40_54_9)))
% 2.34/0.92 -> [325] ~left_apart_point(A39_54_9, L40_54_9), ~left_apart_point(A39_54_9, reverse_line(L40_54_9))
% 2.34/0.92
% 2.34/0.92 [325] CLOSURE : ~left_apart_point(A39_54_9, L40_54_9)
% 2.34/0.92
% 2.34/0.92 [313] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.34/0.92 -> [345] ~(left_apart_point(A39_65_9, L40_65_9) | left_apart_point(A39_65_9, reverse_line(L40_65_9)))
% 2.34/0.92
% 2.34/0.92 [345] ALPHA_NOT_OR : ~(left_apart_point(A39_65_9, L40_65_9) | left_apart_point(A39_65_9, reverse_line(L40_65_9)))
% 2.34/0.92 -> [347] ~left_apart_point(A39_65_9, L40_65_9), ~left_apart_point(A39_65_9, reverse_line(L40_65_9))
% 2.34/0.92
% 2.34/0.92 [347] CLOSURE : ~left_apart_point(A39_65_9, L40_65_9)
% 2.34/0.92
% 2.34/0.92 [304] BETA_OR : (left_convergent_lines(L37_16_8, M38_16_8) | left_convergent_lines(L37_16_8, reverse_line(M38_16_8)))
% 2.34/0.92 -> [311] left_convergent_lines(L37_16_8, M38_16_8)
% 2.34/0.92 -> [312] left_convergent_lines(L37_16_8, reverse_line(M38_16_8))
% 2.34/0.92
% 2.34/0.92 [311] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.34/0.92 -> [342] ~(left_apart_point(A39_64_9, L40_64_9) | left_apart_point(A39_64_9, reverse_line(L40_64_9)))
% 2.34/0.92
% 2.34/0.92 [342] ALPHA_NOT_OR : ~(left_apart_point(A39_64_9, L40_64_9) | left_apart_point(A39_64_9, reverse_line(L40_64_9)))
% 2.34/0.92 -> [344] ~left_apart_point(A39_64_9, L40_64_9), ~left_apart_point(A39_64_9, reverse_line(L40_64_9))
% 2.34/0.92
% 2.34/0.92 [344] CLOSURE : ~left_apart_point(A39_64_9, L40_64_9)
% 2.34/0.92
% 2.34/0.92 [312] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.34/0.92 -> [346] ~(left_apart_point(A39_66_9, L40_66_9) | left_apart_point(A39_66_9, reverse_line(L40_66_9)))
% 2.34/0.92
% 2.34/0.92 [346] ALPHA_NOT_OR : ~(left_apart_point(A39_66_9, L40_66_9) | left_apart_point(A39_66_9, reverse_line(L40_66_9)))
% 2.34/0.92 -> [348] ~left_apart_point(A39_66_9, L40_66_9), ~left_apart_point(A39_66_9, reverse_line(L40_66_9))
% 2.34/0.92
% 2.34/0.92 [348] CLOSURE : ~left_apart_point(A39_66_9, L40_66_9)
% 2.34/0.92
% 2.34/0.92 [275] BETA_IMPLY : ((line(reverse_line(reverse_line(M38_19_8))) & line(reverse_line(M38_19_8))) => (unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(M38_19_8)) | unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8)))))
% 2.34/0.92 -> [349] ~(line(reverse_line(reverse_line(M38_19_8))) & line(reverse_line(M38_19_8)))
% 2.34/0.92 -> [350] (unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(M38_19_8)) | unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))))
% 2.34/0.92
% 2.34/0.92 [349] BETA_NOT_AND : ~(line(reverse_line(reverse_line(M38_19_8))) & line(reverse_line(M38_19_8)))
% 2.34/0.92 -> [351] ~line(reverse_line(reverse_line(M38_19_8)))
% 2.34/0.92 -> [352] ~line(reverse_line(M38_19_8))
% 2.34/0.92
% 2.34/0.92 [352] 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)))))
% 2.34/0.92 -> [356] ((unequally_directed_lines(L37_18_8, M38_18_8) & unequally_directed_lines(L37_18_8, reverse_line(M38_18_8))) => (left_convergent_lines(L37_18_8, M38_18_8) | left_convergent_lines(L37_18_8, reverse_line(M38_18_8))))
% 2.34/0.92
% 2.34/0.92 [356] BETA_IMPLY : ((unequally_directed_lines(L37_18_8, M38_18_8) & unequally_directed_lines(L37_18_8, reverse_line(M38_18_8))) => (left_convergent_lines(L37_18_8, M38_18_8) | left_convergent_lines(L37_18_8, reverse_line(M38_18_8))))
% 2.34/0.92 -> [359] ~(unequally_directed_lines(L37_18_8, M38_18_8) & unequally_directed_lines(L37_18_8, reverse_line(M38_18_8)))
% 2.34/0.92 -> [360] (left_convergent_lines(L37_18_8, M38_18_8) | left_convergent_lines(L37_18_8, reverse_line(M38_18_8)))
% 2.34/0.92
% 2.34/0.92 [359] BETA_NOT_AND : ~(unequally_directed_lines(L37_18_8, M38_18_8) & unequally_directed_lines(L37_18_8, reverse_line(M38_18_8)))
% 2.34/0.92 -> [365] ~unequally_directed_lines(L37_18_8, M38_18_8)
% 2.34/0.92 -> [366] ~unequally_directed_lines(L37_18_8, reverse_line(M38_18_8))
% 2.34/0.92
% 2.34/0.92 [366] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.34/0.92 -> [371] ~(left_apart_point(A39_68_9, L40_68_9) | left_apart_point(A39_68_9, reverse_line(L40_68_9)))
% 2.34/0.92
% 2.34/0.92 [371] ALPHA_NOT_OR : ~(left_apart_point(A39_68_9, L40_68_9) | left_apart_point(A39_68_9, reverse_line(L40_68_9)))
% 2.34/0.92 -> [377] ~left_apart_point(A39_68_9, L40_68_9), ~left_apart_point(A39_68_9, reverse_line(L40_68_9))
% 2.34/0.92
% 2.34/0.92 [377] CLOSURE : ~left_apart_point(A39_68_9, L40_68_9)
% 2.34/0.92
% 2.34/0.92 [365] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.34/0.92 -> [379] ~(left_apart_point(A39_71_9, L40_71_9) | left_apart_point(A39_71_9, reverse_line(L40_71_9)))
% 2.34/0.92
% 2.34/0.92 [379] ALPHA_NOT_OR : ~(left_apart_point(A39_71_9, L40_71_9) | left_apart_point(A39_71_9, reverse_line(L40_71_9)))
% 2.34/0.92 -> [388] ~left_apart_point(A39_71_9, L40_71_9), ~left_apart_point(A39_71_9, reverse_line(L40_71_9))
% 2.34/0.92
% 2.34/0.92 [388] CLOSURE : ~left_apart_point(A39_71_9, L40_71_9)
% 2.34/0.92
% 2.34/0.92 [360] BETA_OR : (left_convergent_lines(L37_18_8, M38_18_8) | left_convergent_lines(L37_18_8, reverse_line(M38_18_8)))
% 2.34/0.92 -> [367] left_convergent_lines(L37_18_8, M38_18_8)
% 2.34/0.92 -> [368] left_convergent_lines(L37_18_8, reverse_line(M38_18_8))
% 2.34/0.92
% 2.34/0.92 [368] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.34/0.92 -> [386] ~(left_apart_point(A39_73_9, L40_73_9) | left_apart_point(A39_73_9, reverse_line(L40_73_9)))
% 2.34/0.92
% 2.34/0.92 [386] ALPHA_NOT_OR : ~(left_apart_point(A39_73_9, L40_73_9) | left_apart_point(A39_73_9, reverse_line(L40_73_9)))
% 2.34/0.92 -> [389] ~left_apart_point(A39_73_9, L40_73_9), ~left_apart_point(A39_73_9, reverse_line(L40_73_9))
% 2.34/0.92
% 2.34/0.92 [389] CLOSURE : ~left_apart_point(A39_73_9, L40_73_9)
% 2.34/0.92
% 2.34/0.92 [367] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.34/0.92 -> [387] ~(left_apart_point(A39_74_9, L40_74_9) | left_apart_point(A39_74_9, reverse_line(L40_74_9)))
% 2.34/0.92
% 2.34/0.92 [387] ALPHA_NOT_OR : ~(left_apart_point(A39_74_9, L40_74_9) | left_apart_point(A39_74_9, reverse_line(L40_74_9)))
% 2.34/0.92 -> [390] ~left_apart_point(A39_74_9, L40_74_9), ~left_apart_point(A39_74_9, reverse_line(L40_74_9))
% 2.34/0.92
% 2.34/0.92 [390] CLOSURE : ~left_apart_point(A39_74_9, L40_74_9)
% 2.34/0.92
% 2.34/0.92 [351] 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)))))
% 2.34/0.92 -> [355] ((unequally_directed_lines(L37_17_8, M38_17_8) & unequally_directed_lines(L37_17_8, reverse_line(M38_17_8))) => (left_convergent_lines(L37_17_8, M38_17_8) | left_convergent_lines(L37_17_8, reverse_line(M38_17_8))))
% 2.34/0.92
% 2.34/0.92 [355] BETA_IMPLY : ((unequally_directed_lines(L37_17_8, M38_17_8) & unequally_directed_lines(L37_17_8, reverse_line(M38_17_8))) => (left_convergent_lines(L37_17_8, M38_17_8) | left_convergent_lines(L37_17_8, reverse_line(M38_17_8))))
% 2.34/0.92 -> [357] ~(unequally_directed_lines(L37_17_8, M38_17_8) & unequally_directed_lines(L37_17_8, reverse_line(M38_17_8)))
% 2.34/0.92 -> [358] (left_convergent_lines(L37_17_8, M38_17_8) | left_convergent_lines(L37_17_8, reverse_line(M38_17_8)))
% 2.34/0.92
% 2.34/0.92 [357] BETA_NOT_AND : ~(unequally_directed_lines(L37_17_8, M38_17_8) & unequally_directed_lines(L37_17_8, reverse_line(M38_17_8)))
% 2.34/0.92 -> [361] ~unequally_directed_lines(L37_17_8, M38_17_8)
% 2.34/0.92 -> [362] ~unequally_directed_lines(L37_17_8, reverse_line(M38_17_8))
% 2.34/0.92
% 2.34/0.92 [362] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.34/0.92 -> [370] ~(left_apart_point(A39_67_9, L40_67_9) | left_apart_point(A39_67_9, reverse_line(L40_67_9)))
% 2.34/0.92
% 2.34/0.92 [370] ALPHA_NOT_OR : ~(left_apart_point(A39_67_9, L40_67_9) | left_apart_point(A39_67_9, reverse_line(L40_67_9)))
% 2.34/0.92 -> [376] ~left_apart_point(A39_67_9, L40_67_9), ~left_apart_point(A39_67_9, reverse_line(L40_67_9))
% 2.34/0.92
% 2.34/0.92 [376] CLOSURE : ~left_apart_point(A39_67_9, L40_67_9)
% 2.34/0.92
% 2.34/0.92 [361] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.34/0.92 -> [372] ~(left_apart_point(A39_69_9, L40_69_9) | left_apart_point(A39_69_9, reverse_line(L40_69_9)))
% 2.34/0.92
% 2.34/0.92 [372] ALPHA_NOT_OR : ~(left_apart_point(A39_69_9, L40_69_9) | left_apart_point(A39_69_9, reverse_line(L40_69_9)))
% 2.34/0.92 -> [378] ~left_apart_point(A39_69_9, L40_69_9), ~left_apart_point(A39_69_9, reverse_line(L40_69_9))
% 2.34/0.92
% 2.34/0.92 [378] CLOSURE : ~left_apart_point(A39_69_9, L40_69_9)
% 2.34/0.92
% 2.34/0.92 [358] BETA_OR : (left_convergent_lines(L37_17_8, M38_17_8) | left_convergent_lines(L37_17_8, reverse_line(M38_17_8)))
% 2.34/0.92 -> [363] left_convergent_lines(L37_17_8, M38_17_8)
% 2.34/0.92 -> [364] left_convergent_lines(L37_17_8, reverse_line(M38_17_8))
% 2.34/0.92
% 2.34/0.92 [363] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.34/0.92 -> [375] ~(left_apart_point(A39_70_9, L40_70_9) | left_apart_point(A39_70_9, reverse_line(L40_70_9)))
% 2.34/0.92
% 2.34/0.92 [375] ALPHA_NOT_OR : ~(left_apart_point(A39_70_9, L40_70_9) | left_apart_point(A39_70_9, reverse_line(L40_70_9)))
% 2.34/0.92 -> [380] ~left_apart_point(A39_70_9, L40_70_9), ~left_apart_point(A39_70_9, reverse_line(L40_70_9))
% 2.34/0.92
% 2.34/0.92 [380] CLOSURE : ~left_apart_point(A39_70_9, L40_70_9)
% 2.34/0.92
% 2.34/0.92 [364] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.34/0.92 -> [385] ~(left_apart_point(A39_72_9, L40_72_9) | left_apart_point(A39_72_9, reverse_line(L40_72_9)))
% 2.34/0.92
% 2.34/0.92 [385] ALPHA_NOT_OR : ~(left_apart_point(A39_72_9, L40_72_9) | left_apart_point(A39_72_9, reverse_line(L40_72_9)))
% 2.34/0.92 -> [391] ~left_apart_point(A39_72_9, L40_72_9), ~left_apart_point(A39_72_9, reverse_line(L40_72_9))
% 2.34/0.92
% 2.34/0.92 [391] CLOSURE : ~left_apart_point(A39_72_9, L40_72_9)
% 2.34/0.92
% 2.34/0.92 [350] BETA_OR : (unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(M38_19_8)) | unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))))
% 2.34/0.92 -> [353] unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(M38_19_8))
% 2.34/0.92 -> [354] unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8)))
% 2.34/0.92
% 2.34/0.92 [354] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8)))
% 2.34/0.92
% 2.34/0.92 [353] 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)))))
% 2.34/0.92 -> [369] ((unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), M38_19_8) & unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(M38_19_8))) => (left_convergent_lines(reverse_line(reverse_line(M38_19_8)), M38_19_8) | left_convergent_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(M38_19_8))))
% 2.34/0.92
% 2.34/0.92 [369] BETA_IMPLY : ((unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), M38_19_8) & unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(M38_19_8))) => (left_convergent_lines(reverse_line(reverse_line(M38_19_8)), M38_19_8) | left_convergent_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(M38_19_8))))
% 2.34/0.92 -> [373] ~(unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), M38_19_8) & unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(M38_19_8)))
% 2.34/0.92 -> [374] (left_convergent_lines(reverse_line(reverse_line(M38_19_8)), M38_19_8) | left_convergent_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(M38_19_8)))
% 2.34/0.92
% 2.34/0.92 [374] BETA_OR : (left_convergent_lines(reverse_line(reverse_line(M38_19_8)), M38_19_8) | left_convergent_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(M38_19_8)))
% 2.34/0.92 -> [381] left_convergent_lines(reverse_line(reverse_line(M38_19_8)), M38_19_8)
% 2.34/0.92 -> [382] left_convergent_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(M38_19_8))
% 2.34/0.92
% 2.34/0.92 [381] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.34/0.92 -> [392] ~(left_apart_point(A39_75_9, L40_75_9) | left_apart_point(A39_75_9, reverse_line(L40_75_9)))
% 2.34/0.92
% 2.34/0.92 [392] ALPHA_NOT_OR : ~(left_apart_point(A39_75_9, L40_75_9) | left_apart_point(A39_75_9, reverse_line(L40_75_9)))
% 2.34/0.92 -> [394] ~left_apart_point(A39_75_9, L40_75_9), ~left_apart_point(A39_75_9, reverse_line(L40_75_9))
% 2.34/0.92
% 2.34/0.92 [394] CLOSURE : ~left_apart_point(A39_75_9, L40_75_9)
% 2.34/0.92
% 2.34/0.92 [382] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.34/0.92 -> [393] ~(left_apart_point(A39_76_9, L40_76_9) | left_apart_point(A39_76_9, reverse_line(L40_76_9)))
% 2.34/0.92
% 2.34/0.92 [393] ALPHA_NOT_OR : ~(left_apart_point(A39_76_9, L40_76_9) | left_apart_point(A39_76_9, reverse_line(L40_76_9)))
% 2.34/0.92 -> [395] ~left_apart_point(A39_76_9, L40_76_9), ~left_apart_point(A39_76_9, reverse_line(L40_76_9))
% 2.34/0.92
% 2.34/0.92 [395] CLOSURE : ~left_apart_point(A39_76_9, L40_76_9)
% 2.34/0.92
% 2.34/0.92 [373] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), M38_19_8) & unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(M38_19_8)))
% 2.34/0.92 -> [383] ~unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), M38_19_8)
% 2.34/0.92 -> [384] ~unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(M38_19_8))
% 2.34/0.92
% 2.34/0.92 [384] CLOSURE : ~unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(M38_19_8))
% 2.34/0.92
% 2.34/0.92 [383] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.34/0.92 -> [396] ~(left_apart_point(A39_77_9, L40_77_9) | left_apart_point(A39_77_9, reverse_line(L40_77_9)))
% 2.34/0.92
% 2.34/0.92 [396] ALPHA_NOT_OR : ~(left_apart_point(A39_77_9, L40_77_9) | left_apart_point(A39_77_9, reverse_line(L40_77_9)))
% 2.34/0.92 -> [397] ~left_apart_point(A39_77_9, L40_77_9), ~left_apart_point(A39_77_9, reverse_line(L40_77_9))
% 2.34/0.92
% 2.34/0.92 [397] CLOSURE : ~left_apart_point(A39_77_9, L40_77_9)
% 2.34/0.92
% 2.34/0.92 [268] BETA_OR : ((unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(reverse_line(M38_19_8))))) | (unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(reverse_line(M38_19_8))))))
% 2.34/0.92 -> [398] (unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(reverse_line(M38_19_8)))))
% 2.34/0.92 -> [399] (unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(reverse_line(M38_19_8)))))
% 2.34/0.92
% 2.34/0.92 [398] ALPHA_AND : (unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(reverse_line(M38_19_8)))))
% 2.34/0.92 -> [400] unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))), unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(reverse_line(M38_19_8))))
% 2.34/0.92
% 2.34/0.92 [400] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(reverse_line(M38_19_8))))
% 2.34/0.92
% 2.34/0.92 [399] ALPHA_AND : (unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(reverse_line(M38_19_8)))))
% 2.34/0.92 -> [401] unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(M38_19_8))), unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(reverse_line(M38_19_8))))
% 2.34/0.92
% 2.34/0.92 [401] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M38_19_8)), reverse_line(reverse_line(reverse_line(M38_19_8))))
% 2.34/0.92
% 2.34/0.92 % SZS output end Proof for theBenchmark.p
% 2.34/0.92 [0.563755s][1][Res] 1758 goroutines created
% 2.34/0.92 ==== Result ====
% 2.34/0.92 [0.563800s][1][Res] VALID
% 2.34/0.92 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------