TSTP Solution File: GEO248+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO248+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n023.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 15:18:42 EDT 2022
% Result : Theorem 2.33s 0.89s
% Output : Proof 2.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO248+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.07/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n023.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 07:31:04 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 [0.000041s][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
% 2.33/0.89 % SZS output start Proof for theBenchmark.p
% 2.33/0.89 [0] ALPHA_AND : ((! [A20_20] : (~distinct_points(A20_20, A20_20)) & ! [A21_21, B22_22, C23_23] : ((distinct_points(A21_21, B22_22) => (distinct_points(A21_21, C23_23) | distinct_points(B22_22, C23_23)))) & ! [L24_24] : (~distinct_lines(L24_24, L24_24)) & ! [L25_25, M26_26, N27_27] : ((distinct_lines(L25_25, M26_26) => (distinct_lines(L25_25, N27_27) | distinct_lines(M26_26, N27_27)))) & ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28)) & ! [L29_29, M30_30, N31_31] : ((unequally_directed_lines(L29_29, M30_30) => (unequally_directed_lines(L29_29, N31_31) | unequally_directed_lines(M30_30, N31_31)))) & ! [L32_32, M33_33, N34_34] : (((unequally_directed_lines(L32_32, M33_33) & unequally_directed_lines(L32_32, reverse_line(M33_33))) => ((unequally_directed_lines(L32_32, N34_34) & unequally_directed_lines(L32_32, reverse_line(N34_34))) | (unequally_directed_lines(M33_33, N34_34) & unequally_directed_lines(M33_33, reverse_line(N34_34)))))) & ! [L35_35, M36_36] : (((line(L35_35) & line(M36_36)) => (unequally_directed_lines(L35_35, M36_36) | unequally_directed_lines(L35_35, reverse_line(M36_36))))) & ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38))))) & ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40)))) & ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42)))) & ! [A43_43, B44_44] : ((((point(A43_43) & point(B44_44)) & distinct_points(A43_43, B44_44)) => line(line_connecting(A43_43, B44_44)))) & ! [L45_45, M46_46] : (((((line(L45_45) & line(M46_46)) & unequally_directed_lines(L45_45, M46_46)) & unequally_directed_lines(L45_45, reverse_line(M46_46))) => point(intersection_point(L45_45, M46_46)))) & ! [L47_47, A48_48] : (((point(A48_48) & line(L47_47)) => line(parallel_through_point(L47_47, A48_48)))) & ! [L49_49] : ((line(L49_49) => line(reverse_line(L49_49)))) & ! [A50_50, B51_51] : ((distinct_points(A50_50, B51_51) => (~apart_point_and_line(A50_50, line_connecting(A50_50, B51_51)) & ~apart_point_and_line(B51_51, line_connecting(A50_50, B51_51))))) & ! [L52_52, M53_53] : (((unequally_directed_lines(L52_52, M53_53) & unequally_directed_lines(L52_52, reverse_line(M53_53))) => (~apart_point_and_line(intersection_point(L52_52, M53_53), L52_52) & ~apart_point_and_line(intersection_point(L52_52, M53_53), M53_53)))) & ! [A54_54, L55_55] : (~apart_point_and_line(A54_54, parallel_through_point(L55_55, A54_54))) & ! [L56_56] : (~distinct_lines(L56_56, reverse_line(L56_56))) & ! [A57_57, B58_58] : (~unequally_directed_lines(line_connecting(A57_57, B58_58), reverse_line(line_connecting(B58_58, A57_57)))) & ! [A59_59, L60_60] : (~unequally_directed_lines(parallel_through_point(L60_60, A59_59), L60_60)) & ! [A61_61, B62_62, L63_63, M64_64] : (((distinct_points(A61_61, B62_62) & distinct_lines(L63_63, M64_64)) => (((((((left_apart_point(A61_61, L63_63) | left_apart_point(B62_62, L63_63)) | left_apart_point(A61_61, M64_64)) | left_apart_point(B62_62, M64_64)) | left_apart_point(A61_61, reverse_line(L63_63))) | left_apart_point(B62_62, reverse_line(L63_63))) | left_apart_point(A61_61, reverse_line(M64_64))) | left_apart_point(B62_62, reverse_line(M64_64))))) & ! [A65_65, B66_66, L67_67] : (((distinct_points(A65_65, B66_66) & left_apart_point(A65_65, L67_67)) => (left_apart_point(B66_66, L67_67) | left_convergent_lines(line_connecting(A65_65, B66_66), L67_67)))) & ! [A68_68, B69_69, L70_70] : ((left_apart_point(A68_68, L70_70) => (distinct_points(A68_68, B69_69) | left_apart_point(B69_69, L70_70)))) & ! [A71_71, L72_72, M73_73] : (((left_apart_point(A71_71, L72_72) & unequally_directed_lines(L72_72, M73_73)) => (distinct_lines(L72_72, M73_73) | left_apart_point(A71_71, reverse_line(M73_73))))) & ! [L74_74, M75_75, N76_76] : ((left_convergent_lines(L74_74, M75_75) => (unequally_directed_lines(M75_75, N76_76) | left_convergent_lines(L74_74, N76_76))))) & ~! [A77_77, B78_78, L79_79] : (((left_apart_point(A77_77, L79_79) & left_apart_point(B78_78, parallel_through_point(L79_79, A77_77))) => left_apart_point(B78_78, L79_79))))
% 2.33/0.89 -> [1] (! [A20_20] : (~distinct_points(A20_20, A20_20)) & ! [A21_21, B22_22, C23_23] : ((distinct_points(A21_21, B22_22) => (distinct_points(A21_21, C23_23) | distinct_points(B22_22, C23_23)))) & ! [L24_24] : (~distinct_lines(L24_24, L24_24)) & ! [L25_25, M26_26, N27_27] : ((distinct_lines(L25_25, M26_26) => (distinct_lines(L25_25, N27_27) | distinct_lines(M26_26, N27_27)))) & ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28)) & ! [L29_29, M30_30, N31_31] : ((unequally_directed_lines(L29_29, M30_30) => (unequally_directed_lines(L29_29, N31_31) | unequally_directed_lines(M30_30, N31_31)))) & ! [L32_32, M33_33, N34_34] : (((unequally_directed_lines(L32_32, M33_33) & unequally_directed_lines(L32_32, reverse_line(M33_33))) => ((unequally_directed_lines(L32_32, N34_34) & unequally_directed_lines(L32_32, reverse_line(N34_34))) | (unequally_directed_lines(M33_33, N34_34) & unequally_directed_lines(M33_33, reverse_line(N34_34)))))) & ! [L35_35, M36_36] : (((line(L35_35) & line(M36_36)) => (unequally_directed_lines(L35_35, M36_36) | unequally_directed_lines(L35_35, reverse_line(M36_36))))) & ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38))))) & ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40)))) & ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42)))) & ! [A43_43, B44_44] : ((((point(A43_43) & point(B44_44)) & distinct_points(A43_43, B44_44)) => line(line_connecting(A43_43, B44_44)))) & ! [L45_45, M46_46] : (((((line(L45_45) & line(M46_46)) & unequally_directed_lines(L45_45, M46_46)) & unequally_directed_lines(L45_45, reverse_line(M46_46))) => point(intersection_point(L45_45, M46_46)))) & ! [L47_47, A48_48] : (((point(A48_48) & line(L47_47)) => line(parallel_through_point(L47_47, A48_48)))) & ! [L49_49] : ((line(L49_49) => line(reverse_line(L49_49)))) & ! [A50_50, B51_51] : ((distinct_points(A50_50, B51_51) => (~apart_point_and_line(A50_50, line_connecting(A50_50, B51_51)) & ~apart_point_and_line(B51_51, line_connecting(A50_50, B51_51))))) & ! [L52_52, M53_53] : (((unequally_directed_lines(L52_52, M53_53) & unequally_directed_lines(L52_52, reverse_line(M53_53))) => (~apart_point_and_line(intersection_point(L52_52, M53_53), L52_52) & ~apart_point_and_line(intersection_point(L52_52, M53_53), M53_53)))) & ! [A54_54, L55_55] : (~apart_point_and_line(A54_54, parallel_through_point(L55_55, A54_54))) & ! [L56_56] : (~distinct_lines(L56_56, reverse_line(L56_56))) & ! [A57_57, B58_58] : (~unequally_directed_lines(line_connecting(A57_57, B58_58), reverse_line(line_connecting(B58_58, A57_57)))) & ! [A59_59, L60_60] : (~unequally_directed_lines(parallel_through_point(L60_60, A59_59), L60_60)) & ! [A61_61, B62_62, L63_63, M64_64] : (((distinct_points(A61_61, B62_62) & distinct_lines(L63_63, M64_64)) => (((((((left_apart_point(A61_61, L63_63) | left_apart_point(B62_62, L63_63)) | left_apart_point(A61_61, M64_64)) | left_apart_point(B62_62, M64_64)) | left_apart_point(A61_61, reverse_line(L63_63))) | left_apart_point(B62_62, reverse_line(L63_63))) | left_apart_point(A61_61, reverse_line(M64_64))) | left_apart_point(B62_62, reverse_line(M64_64))))) & ! [A65_65, B66_66, L67_67] : (((distinct_points(A65_65, B66_66) & left_apart_point(A65_65, L67_67)) => (left_apart_point(B66_66, L67_67) | left_convergent_lines(line_connecting(A65_65, B66_66), L67_67)))) & ! [A68_68, B69_69, L70_70] : ((left_apart_point(A68_68, L70_70) => (distinct_points(A68_68, B69_69) | left_apart_point(B69_69, L70_70)))) & ! [A71_71, L72_72, M73_73] : (((left_apart_point(A71_71, L72_72) & unequally_directed_lines(L72_72, M73_73)) => (distinct_lines(L72_72, M73_73) | left_apart_point(A71_71, reverse_line(M73_73))))) & ! [L74_74, M75_75, N76_76] : ((left_convergent_lines(L74_74, M75_75) => (unequally_directed_lines(M75_75, N76_76) | left_convergent_lines(L74_74, N76_76))))), ~! [A77_77, B78_78, L79_79] : (((left_apart_point(A77_77, L79_79) & left_apart_point(B78_78, parallel_through_point(L79_79, A77_77))) => left_apart_point(B78_78, L79_79)))
% 2.33/0.89
% 2.33/0.89 [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)))))
% 2.33/0.89 -> [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))))
% 2.33/0.89
% 2.33/0.89 [2] DELTA_NOT_FORALL : ~! [A77_77, B78_78, L79_79] : (((left_apart_point(A77_77, L79_79) & left_apart_point(B78_78, parallel_through_point(L79_79, A77_77))) => left_apart_point(B78_78, L79_79)))
% 2.33/0.89 -> [3] ~((left_apart_point(skolem_A7777, skolem_L7979) & left_apart_point(skolem_B7878, parallel_through_point(skolem_L7979, skolem_A7777))) => left_apart_point(skolem_B7878, skolem_L7979))
% 2.33/0.89
% 2.33/0.89 [3] ALPHA_NOT_IMPLY : ~((left_apart_point(skolem_A7777, skolem_L7979) & left_apart_point(skolem_B7878, parallel_through_point(skolem_L7979, skolem_A7777))) => left_apart_point(skolem_B7878, skolem_L7979))
% 2.33/0.89 -> [4] (left_apart_point(skolem_A7777, skolem_L7979) & left_apart_point(skolem_B7878, parallel_through_point(skolem_L7979, skolem_A7777))), ~left_apart_point(skolem_B7878, skolem_L7979)
% 2.33/0.89
% 2.33/0.89 [4] ALPHA_AND : (left_apart_point(skolem_A7777, skolem_L7979) & left_apart_point(skolem_B7878, parallel_through_point(skolem_L7979, skolem_A7777)))
% 2.33/0.89 -> [5] left_apart_point(skolem_A7777, skolem_L7979), left_apart_point(skolem_B7878, parallel_through_point(skolem_L7979, skolem_A7777))
% 2.33/0.89
% 2.33/0.89 [5] GAMMA_FORALL : ! [A20_20] : (~distinct_points(A20_20, A20_20))
% 2.33/0.89 -> [6] ~distinct_points(C23_0_1, C23_0_1)
% 2.33/0.89
% 2.33/0.89 [6] GAMMA_FORALL : ! [A21_21, B22_22, C23_23] : ((distinct_points(A21_21, B22_22) => (distinct_points(A21_21, C23_23) | distinct_points(B22_22, C23_23))))
% 2.33/0.89 -> [7] (distinct_points(C23_0_1, C23_0_1) => (distinct_points(C23_0_1, C23_0_1) | distinct_points(C23_0_1, C23_0_1)))
% 2.33/0.89
% 2.33/0.89 [7] 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)))
% 2.33/0.89 -> [8] ~distinct_points(C23_0_1, C23_0_1)
% 2.33/0.89 -> [9] (distinct_points(C23_0_1, C23_0_1) | distinct_points(C23_0_1, C23_0_1))
% 2.33/0.89
% 2.33/0.89 [9] BETA_OR : (distinct_points(C23_0_1, C23_0_1) | distinct_points(C23_0_1, C23_0_1))
% 2.33/0.89 -> [10] distinct_points(C23_0_1, C23_0_1)
% 2.33/0.89 -> [11] distinct_points(C23_0_1, C23_0_1)
% 2.33/0.89
% 2.33/0.89 [11] CLOSURE : distinct_points(C23_0_1, C23_0_1)
% 2.33/0.89
% 2.33/0.89 [10] CLOSURE : distinct_points(C23_0_1, C23_0_1)
% 2.33/0.89
% 2.33/0.89 [8] GAMMA_FORALL : ! [L24_24] : (~distinct_lines(L24_24, L24_24))
% 2.33/0.89 -> [12] ~distinct_lines(N27_0_3, N27_0_3)
% 2.33/0.89
% 2.33/0.89 [12] 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))))
% 2.33/0.89 -> [13] (distinct_lines(N27_0_3, N27_0_3) => (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3)))
% 2.33/0.89
% 2.33/0.89 [13] 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)))
% 2.33/0.89 -> [14] ~distinct_lines(N27_0_3, N27_0_3)
% 2.33/0.89 -> [15] (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3))
% 2.33/0.89
% 2.33/0.89 [15] BETA_OR : (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3))
% 2.33/0.89 -> [16] distinct_lines(N27_0_3, N27_0_3)
% 2.33/0.89 -> [17] distinct_lines(N27_0_3, N27_0_3)
% 2.33/0.89
% 2.33/0.89 [17] CLOSURE : distinct_lines(N27_0_3, N27_0_3)
% 2.33/0.89
% 2.33/0.89 [16] CLOSURE : distinct_lines(N27_0_3, N27_0_3)
% 2.33/0.89
% 2.33/0.89 [14] GAMMA_FORALL : ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28))
% 2.33/0.89 -> [18] ~unequally_directed_lines(L29_0_5, L29_0_5)
% 2.33/0.89
% 2.33/0.89 [18] 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))))
% 2.33/0.89 -> [19] (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)))
% 2.33/0.89
% 2.33/0.89 [19] 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)))
% 2.33/0.89 -> [20] ~unequally_directed_lines(L29_0_5, L29_0_5)
% 2.33/0.89 -> [21] (unequally_directed_lines(L29_0_5, L29_0_5) | unequally_directed_lines(L29_0_5, L29_0_5))
% 2.33/0.89
% 2.33/0.89 [21] BETA_OR : (unequally_directed_lines(L29_0_5, L29_0_5) | unequally_directed_lines(L29_0_5, L29_0_5))
% 2.33/0.89 -> [22] unequally_directed_lines(L29_0_5, L29_0_5)
% 2.33/0.89 -> [23] unequally_directed_lines(L29_0_5, L29_0_5)
% 2.33/0.89
% 2.33/0.89 [23] CLOSURE : unequally_directed_lines(L29_0_5, L29_0_5)
% 2.33/0.89
% 2.33/0.89 [22] CLOSURE : unequally_directed_lines(L29_0_5, L29_0_5)
% 2.33/0.89
% 2.33/0.89 [24] 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)))))
% 2.33/0.89 -> [232] ~(unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 2.33/0.89 -> [233] ((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))))
% 2.33/0.89
% 2.33/0.89 [232] BETA_NOT_AND : ~(unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 2.33/0.89 -> [234] ~unequally_directed_lines(N34_0_6, N34_0_6)
% 2.33/0.89 -> [235] ~unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))
% 2.33/0.89
% 2.33/0.89 [235] 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)))))
% 2.33/0.89 -> [240] ((line(M36_4_7) & line(M36_4_7)) => (unequally_directed_lines(M36_4_7, M36_4_7) | unequally_directed_lines(M36_4_7, reverse_line(M36_4_7))))
% 2.33/0.89
% 2.33/0.89 [240] BETA_IMPLY : ((line(M36_4_7) & line(M36_4_7)) => (unequally_directed_lines(M36_4_7, M36_4_7) | unequally_directed_lines(M36_4_7, reverse_line(M36_4_7))))
% 2.33/0.89 -> [242] ~(line(M36_4_7) & line(M36_4_7))
% 2.33/0.89 -> [243] (unequally_directed_lines(M36_4_7, M36_4_7) | unequally_directed_lines(M36_4_7, reverse_line(M36_4_7)))
% 2.33/0.89
% 2.33/0.89 [243] BETA_OR : (unequally_directed_lines(M36_4_7, M36_4_7) | unequally_directed_lines(M36_4_7, reverse_line(M36_4_7)))
% 2.33/0.89 -> [248] unequally_directed_lines(M36_4_7, M36_4_7)
% 2.33/0.89 -> [249] unequally_directed_lines(M36_4_7, reverse_line(M36_4_7))
% 2.33/0.89
% 2.33/0.89 [249] CLOSURE : unequally_directed_lines(M36_4_7, reverse_line(M36_4_7))
% 2.33/0.89
% 2.33/0.89 [248] CLOSURE : unequally_directed_lines(M36_4_7, M36_4_7)
% 2.33/0.89
% 2.33/0.89 [242] BETA_NOT_AND : ~(line(M36_4_7) & line(M36_4_7))
% 2.33/0.89 -> [246] ~line(M36_4_7)
% 2.33/0.89 -> [247] ~line(M36_4_7)
% 2.33/0.89
% 2.33/0.89 [247] 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)))))
% 2.33/0.89 -> [254] ((unequally_directed_lines(L37_11_8, M38_11_8) & unequally_directed_lines(L37_11_8, reverse_line(M38_11_8))) => (left_convergent_lines(L37_11_8, M38_11_8) | left_convergent_lines(L37_11_8, reverse_line(M38_11_8))))
% 2.33/0.89
% 2.33/0.89 [254] BETA_IMPLY : ((unequally_directed_lines(L37_11_8, M38_11_8) & unequally_directed_lines(L37_11_8, reverse_line(M38_11_8))) => (left_convergent_lines(L37_11_8, M38_11_8) | left_convergent_lines(L37_11_8, reverse_line(M38_11_8))))
% 2.33/0.89 -> [256] ~(unequally_directed_lines(L37_11_8, M38_11_8) & unequally_directed_lines(L37_11_8, reverse_line(M38_11_8)))
% 2.33/0.89 -> [257] (left_convergent_lines(L37_11_8, M38_11_8) | left_convergent_lines(L37_11_8, reverse_line(M38_11_8)))
% 2.33/0.89
% 2.33/0.89 [256] BETA_NOT_AND : ~(unequally_directed_lines(L37_11_8, M38_11_8) & unequally_directed_lines(L37_11_8, reverse_line(M38_11_8)))
% 2.33/0.89 -> [263] ~unequally_directed_lines(L37_11_8, M38_11_8)
% 2.33/0.89 -> [264] ~unequally_directed_lines(L37_11_8, reverse_line(M38_11_8))
% 2.33/0.89
% 2.33/0.89 [264] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.33/0.89 -> [276] ~(left_apart_point(A39_43_9, L40_43_9) | left_apart_point(A39_43_9, reverse_line(L40_43_9)))
% 2.33/0.89
% 2.33/0.89 [276] ALPHA_NOT_OR : ~(left_apart_point(A39_43_9, L40_43_9) | left_apart_point(A39_43_9, reverse_line(L40_43_9)))
% 2.33/0.89 -> [277] ~left_apart_point(A39_43_9, L40_43_9), ~left_apart_point(A39_43_9, reverse_line(L40_43_9))
% 2.33/0.89
% 2.33/0.89 [277] CLOSURE : ~left_apart_point(A39_43_9, L40_43_9)
% 2.33/0.89
% 2.33/0.89 [263] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.33/0.89 -> [278] ~(left_apart_point(A39_44_9, L40_44_9) | left_apart_point(A39_44_9, reverse_line(L40_44_9)))
% 2.33/0.89
% 2.33/0.89 [278] ALPHA_NOT_OR : ~(left_apart_point(A39_44_9, L40_44_9) | left_apart_point(A39_44_9, reverse_line(L40_44_9)))
% 2.33/0.89 -> [285] ~left_apart_point(A39_44_9, L40_44_9), ~left_apart_point(A39_44_9, reverse_line(L40_44_9))
% 2.33/0.89
% 2.33/0.89 [285] CLOSURE : ~left_apart_point(A39_44_9, L40_44_9)
% 2.33/0.89
% 2.33/0.89 [257] BETA_OR : (left_convergent_lines(L37_11_8, M38_11_8) | left_convergent_lines(L37_11_8, reverse_line(M38_11_8)))
% 2.33/0.89 -> [265] left_convergent_lines(L37_11_8, M38_11_8)
% 2.33/0.89 -> [266] left_convergent_lines(L37_11_8, reverse_line(M38_11_8))
% 2.33/0.89
% 2.33/0.89 [266] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.33/0.89 -> [284] ~(left_apart_point(A39_46_9, L40_46_9) | left_apart_point(A39_46_9, reverse_line(L40_46_9)))
% 2.33/0.89
% 2.33/0.89 [284] ALPHA_NOT_OR : ~(left_apart_point(A39_46_9, L40_46_9) | left_apart_point(A39_46_9, reverse_line(L40_46_9)))
% 2.33/0.89 -> [287] ~left_apart_point(A39_46_9, L40_46_9), ~left_apart_point(A39_46_9, reverse_line(L40_46_9))
% 2.33/0.89
% 2.33/0.89 [287] CLOSURE : ~left_apart_point(A39_46_9, L40_46_9)
% 2.33/0.89
% 2.33/0.89 [265] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.33/0.89 -> [283] ~(left_apart_point(A39_45_9, L40_45_9) | left_apart_point(A39_45_9, reverse_line(L40_45_9)))
% 2.33/0.89
% 2.33/0.89 [283] ALPHA_NOT_OR : ~(left_apart_point(A39_45_9, L40_45_9) | left_apart_point(A39_45_9, reverse_line(L40_45_9)))
% 2.33/0.89 -> [288] ~left_apart_point(A39_45_9, L40_45_9), ~left_apart_point(A39_45_9, reverse_line(L40_45_9))
% 2.33/0.89
% 2.33/0.89 [288] CLOSURE : ~left_apart_point(A39_45_9, L40_45_9)
% 2.33/0.89
% 2.33/0.89 [246] 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)))))
% 2.33/0.89 -> [255] ((unequally_directed_lines(L37_12_8, M38_12_8) & unequally_directed_lines(L37_12_8, reverse_line(M38_12_8))) => (left_convergent_lines(L37_12_8, M38_12_8) | left_convergent_lines(L37_12_8, reverse_line(M38_12_8))))
% 2.33/0.89
% 2.33/0.89 [255] BETA_IMPLY : ((unequally_directed_lines(L37_12_8, M38_12_8) & unequally_directed_lines(L37_12_8, reverse_line(M38_12_8))) => (left_convergent_lines(L37_12_8, M38_12_8) | left_convergent_lines(L37_12_8, reverse_line(M38_12_8))))
% 2.33/0.89 -> [261] ~(unequally_directed_lines(L37_12_8, M38_12_8) & unequally_directed_lines(L37_12_8, reverse_line(M38_12_8)))
% 2.33/0.89 -> [262] (left_convergent_lines(L37_12_8, M38_12_8) | left_convergent_lines(L37_12_8, reverse_line(M38_12_8)))
% 2.33/0.89
% 2.33/0.89 [261] BETA_NOT_AND : ~(unequally_directed_lines(L37_12_8, M38_12_8) & unequally_directed_lines(L37_12_8, reverse_line(M38_12_8)))
% 2.33/0.89 -> [272] ~unequally_directed_lines(L37_12_8, M38_12_8)
% 2.33/0.89 -> [273] ~unequally_directed_lines(L37_12_8, reverse_line(M38_12_8))
% 2.33/0.89
% 2.33/0.89 [273] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.33/0.89 -> [289] ~(left_apart_point(A39_49_9, L40_49_9) | left_apart_point(A39_49_9, reverse_line(L40_49_9)))
% 2.33/0.89
% 2.33/0.89 [289] ALPHA_NOT_OR : ~(left_apart_point(A39_49_9, L40_49_9) | left_apart_point(A39_49_9, reverse_line(L40_49_9)))
% 2.33/0.89 -> [293] ~left_apart_point(A39_49_9, L40_49_9), ~left_apart_point(A39_49_9, reverse_line(L40_49_9))
% 2.33/0.89
% 2.33/0.89 [293] CLOSURE : ~left_apart_point(A39_49_9, L40_49_9)
% 2.33/0.89
% 2.33/0.89 [272] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.33/0.89 -> [290] ~(left_apart_point(A39_50_9, L40_50_9) | left_apart_point(A39_50_9, reverse_line(L40_50_9)))
% 2.33/0.89
% 2.33/0.89 [290] ALPHA_NOT_OR : ~(left_apart_point(A39_50_9, L40_50_9) | left_apart_point(A39_50_9, reverse_line(L40_50_9)))
% 2.33/0.89 -> [292] ~left_apart_point(A39_50_9, L40_50_9), ~left_apart_point(A39_50_9, reverse_line(L40_50_9))
% 2.33/0.89
% 2.33/0.89 [292] CLOSURE : ~left_apart_point(A39_50_9, L40_50_9)
% 2.33/0.89
% 2.33/0.89 [262] BETA_OR : (left_convergent_lines(L37_12_8, M38_12_8) | left_convergent_lines(L37_12_8, reverse_line(M38_12_8)))
% 2.33/0.89 -> [270] left_convergent_lines(L37_12_8, M38_12_8)
% 2.33/0.89 -> [271] left_convergent_lines(L37_12_8, reverse_line(M38_12_8))
% 2.33/0.89
% 2.33/0.89 [270] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.33/0.89 -> [291] ~(left_apart_point(A39_48_9, L40_48_9) | left_apart_point(A39_48_9, reverse_line(L40_48_9)))
% 2.33/0.89
% 2.33/0.89 [291] ALPHA_NOT_OR : ~(left_apart_point(A39_48_9, L40_48_9) | left_apart_point(A39_48_9, reverse_line(L40_48_9)))
% 2.33/0.89 -> [294] ~left_apart_point(A39_48_9, L40_48_9), ~left_apart_point(A39_48_9, reverse_line(L40_48_9))
% 2.33/0.89
% 2.33/0.89 [294] CLOSURE : ~left_apart_point(A39_48_9, L40_48_9)
% 2.33/0.89
% 2.33/0.89 [271] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.33/0.89 -> [306] ~(left_apart_point(A39_56_9, L40_56_9) | left_apart_point(A39_56_9, reverse_line(L40_56_9)))
% 2.33/0.89
% 2.33/0.89 [306] ALPHA_NOT_OR : ~(left_apart_point(A39_56_9, L40_56_9) | left_apart_point(A39_56_9, reverse_line(L40_56_9)))
% 2.33/0.89 -> [308] ~left_apart_point(A39_56_9, L40_56_9), ~left_apart_point(A39_56_9, reverse_line(L40_56_9))
% 2.33/0.89
% 2.33/0.89 [308] CLOSURE : ~left_apart_point(A39_56_9, L40_56_9)
% 2.33/0.89
% 2.33/0.89 [241] BETA_IMPLY : ((line(N34_0_6) & line(N34_0_6)) => (unequally_directed_lines(N34_0_6, N34_0_6) | unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))))
% 2.33/0.89 -> [314] ~(line(N34_0_6) & line(N34_0_6))
% 2.33/0.89 -> [315] (unequally_directed_lines(N34_0_6, N34_0_6) | unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 2.33/0.89
% 2.33/0.89 [314] BETA_NOT_AND : ~(line(N34_0_6) & line(N34_0_6))
% 2.33/0.89 -> [316] ~line(N34_0_6)
% 2.33/0.89 -> [317] ~line(N34_0_6)
% 2.33/0.89
% 2.33/0.89 [316] 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)))))
% 2.33/0.89 -> [320] ((unequally_directed_lines(L37_15_8, M38_15_8) & unequally_directed_lines(L37_15_8, reverse_line(M38_15_8))) => (left_convergent_lines(L37_15_8, M38_15_8) | left_convergent_lines(L37_15_8, reverse_line(M38_15_8))))
% 2.33/0.89
% 2.33/0.89 [320] BETA_IMPLY : ((unequally_directed_lines(L37_15_8, M38_15_8) & unequally_directed_lines(L37_15_8, reverse_line(M38_15_8))) => (left_convergent_lines(L37_15_8, M38_15_8) | left_convergent_lines(L37_15_8, reverse_line(M38_15_8))))
% 2.33/0.89 -> [322] ~(unequally_directed_lines(L37_15_8, M38_15_8) & unequally_directed_lines(L37_15_8, reverse_line(M38_15_8)))
% 2.33/0.89 -> [323] (left_convergent_lines(L37_15_8, M38_15_8) | left_convergent_lines(L37_15_8, reverse_line(M38_15_8)))
% 2.33/0.89
% 2.33/0.89 [322] BETA_NOT_AND : ~(unequally_directed_lines(L37_15_8, M38_15_8) & unequally_directed_lines(L37_15_8, reverse_line(M38_15_8)))
% 2.33/0.89 -> [330] ~unequally_directed_lines(L37_15_8, M38_15_8)
% 2.33/0.89 -> [331] ~unequally_directed_lines(L37_15_8, reverse_line(M38_15_8))
% 2.33/0.89
% 2.33/0.89 [330] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.33/0.89 -> [338] ~(left_apart_point(A39_61_9, L40_61_9) | left_apart_point(A39_61_9, reverse_line(L40_61_9)))
% 2.33/0.89
% 2.33/0.89 [338] ALPHA_NOT_OR : ~(left_apart_point(A39_61_9, L40_61_9) | left_apart_point(A39_61_9, reverse_line(L40_61_9)))
% 2.33/0.89 -> [342] ~left_apart_point(A39_61_9, L40_61_9), ~left_apart_point(A39_61_9, reverse_line(L40_61_9))
% 2.33/0.89
% 2.33/0.89 [342] CLOSURE : ~left_apart_point(A39_61_9, L40_61_9)
% 2.33/0.89
% 2.33/0.89 [331] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.33/0.89 -> [343] ~(left_apart_point(A39_62_9, L40_62_9) | left_apart_point(A39_62_9, reverse_line(L40_62_9)))
% 2.33/0.89
% 2.33/0.89 [343] ALPHA_NOT_OR : ~(left_apart_point(A39_62_9, L40_62_9) | left_apart_point(A39_62_9, reverse_line(L40_62_9)))
% 2.33/0.89 -> [344] ~left_apart_point(A39_62_9, L40_62_9), ~left_apart_point(A39_62_9, reverse_line(L40_62_9))
% 2.33/0.89
% 2.33/0.89 [344] CLOSURE : ~left_apart_point(A39_62_9, L40_62_9)
% 2.33/0.89
% 2.33/0.89 [323] BETA_OR : (left_convergent_lines(L37_15_8, M38_15_8) | left_convergent_lines(L37_15_8, reverse_line(M38_15_8)))
% 2.33/0.89 -> [328] left_convergent_lines(L37_15_8, M38_15_8)
% 2.33/0.89 -> [329] left_convergent_lines(L37_15_8, reverse_line(M38_15_8))
% 2.33/0.89
% 2.33/0.89 [328] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.33/0.89 -> [345] ~(left_apart_point(A39_64_9, L40_64_9) | left_apart_point(A39_64_9, reverse_line(L40_64_9)))
% 2.33/0.89
% 2.33/0.89 [345] ALPHA_NOT_OR : ~(left_apart_point(A39_64_9, L40_64_9) | left_apart_point(A39_64_9, reverse_line(L40_64_9)))
% 2.33/0.89 -> [353] ~left_apart_point(A39_64_9, L40_64_9), ~left_apart_point(A39_64_9, reverse_line(L40_64_9))
% 2.33/0.89
% 2.33/0.89 [353] CLOSURE : ~left_apart_point(A39_64_9, L40_64_9)
% 2.33/0.89
% 2.33/0.89 [329] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.33/0.89 -> [352] ~(left_apart_point(A39_66_9, L40_66_9) | left_apart_point(A39_66_9, reverse_line(L40_66_9)))
% 2.33/0.89
% 2.33/0.89 [352] ALPHA_NOT_OR : ~(left_apart_point(A39_66_9, L40_66_9) | left_apart_point(A39_66_9, reverse_line(L40_66_9)))
% 2.33/0.89 -> [356] ~left_apart_point(A39_66_9, L40_66_9), ~left_apart_point(A39_66_9, reverse_line(L40_66_9))
% 2.33/0.89
% 2.33/0.89 [356] CLOSURE : ~left_apart_point(A39_66_9, L40_66_9)
% 2.33/0.89
% 2.33/0.89 [317] 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)))))
% 2.33/0.89 -> [321] ((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))))
% 2.33/0.89
% 2.33/0.89 [321] 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))))
% 2.33/0.89 -> [324] ~(unequally_directed_lines(L37_16_8, M38_16_8) & unequally_directed_lines(L37_16_8, reverse_line(M38_16_8)))
% 2.33/0.89 -> [325] (left_convergent_lines(L37_16_8, M38_16_8) | left_convergent_lines(L37_16_8, reverse_line(M38_16_8)))
% 2.33/0.89
% 2.33/0.89 [324] BETA_NOT_AND : ~(unequally_directed_lines(L37_16_8, M38_16_8) & unequally_directed_lines(L37_16_8, reverse_line(M38_16_8)))
% 2.33/0.89 -> [326] ~unequally_directed_lines(L37_16_8, M38_16_8)
% 2.33/0.89 -> [327] ~unequally_directed_lines(L37_16_8, reverse_line(M38_16_8))
% 2.33/0.89
% 2.33/0.89 [327] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.33/0.89 -> [334] ~(left_apart_point(A39_59_9, L40_59_9) | left_apart_point(A39_59_9, reverse_line(L40_59_9)))
% 2.33/0.89
% 2.33/0.89 [334] ALPHA_NOT_OR : ~(left_apart_point(A39_59_9, L40_59_9) | left_apart_point(A39_59_9, reverse_line(L40_59_9)))
% 2.33/0.89 -> [335] ~left_apart_point(A39_59_9, L40_59_9), ~left_apart_point(A39_59_9, reverse_line(L40_59_9))
% 2.33/0.89
% 2.33/0.89 [335] CLOSURE : ~left_apart_point(A39_59_9, L40_59_9)
% 2.33/0.89
% 2.33/0.89 [326] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.33/0.89 -> [337] ~(left_apart_point(A39_60_9, L40_60_9) | left_apart_point(A39_60_9, reverse_line(L40_60_9)))
% 2.33/0.89
% 2.33/0.89 [337] ALPHA_NOT_OR : ~(left_apart_point(A39_60_9, L40_60_9) | left_apart_point(A39_60_9, reverse_line(L40_60_9)))
% 2.33/0.89 -> [341] ~left_apart_point(A39_60_9, L40_60_9), ~left_apart_point(A39_60_9, reverse_line(L40_60_9))
% 2.33/0.89
% 2.33/0.89 [341] CLOSURE : ~left_apart_point(A39_60_9, L40_60_9)
% 2.33/0.89
% 2.33/0.89 [325] BETA_OR : (left_convergent_lines(L37_16_8, M38_16_8) | left_convergent_lines(L37_16_8, reverse_line(M38_16_8)))
% 2.33/0.89 -> [332] left_convergent_lines(L37_16_8, M38_16_8)
% 2.33/0.89 -> [333] left_convergent_lines(L37_16_8, reverse_line(M38_16_8))
% 2.33/0.89
% 2.33/0.89 [333] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.33/0.89 -> [346] ~(left_apart_point(A39_63_9, L40_63_9) | left_apart_point(A39_63_9, reverse_line(L40_63_9)))
% 2.33/0.89
% 2.33/0.89 [346] ALPHA_NOT_OR : ~(left_apart_point(A39_63_9, L40_63_9) | left_apart_point(A39_63_9, reverse_line(L40_63_9)))
% 2.33/0.89 -> [354] ~left_apart_point(A39_63_9, L40_63_9), ~left_apart_point(A39_63_9, reverse_line(L40_63_9))
% 2.33/0.89
% 2.33/0.89 [354] CLOSURE : ~left_apart_point(A39_63_9, L40_63_9)
% 2.33/0.89
% 2.33/0.89 [332] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.33/0.89 -> [349] ~(left_apart_point(A39_65_9, L40_65_9) | left_apart_point(A39_65_9, reverse_line(L40_65_9)))
% 2.33/0.89
% 2.33/0.89 [349] ALPHA_NOT_OR : ~(left_apart_point(A39_65_9, L40_65_9) | left_apart_point(A39_65_9, reverse_line(L40_65_9)))
% 2.33/0.89 -> [355] ~left_apart_point(A39_65_9, L40_65_9), ~left_apart_point(A39_65_9, reverse_line(L40_65_9))
% 2.33/0.89
% 2.33/0.89 [355] CLOSURE : ~left_apart_point(A39_65_9, L40_65_9)
% 2.33/0.89
% 2.33/0.89 [315] BETA_OR : (unequally_directed_lines(N34_0_6, N34_0_6) | unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 2.33/0.89 -> [318] unequally_directed_lines(N34_0_6, N34_0_6)
% 2.33/0.89 -> [319] unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))
% 2.33/0.89
% 2.33/0.89 [318] CLOSURE : unequally_directed_lines(N34_0_6, N34_0_6)
% 2.33/0.89
% 2.33/0.89 [319] 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)))))
% 2.33/0.89 -> [336] ((unequally_directed_lines(M38_17_8, M38_17_8) & unequally_directed_lines(M38_17_8, reverse_line(M38_17_8))) => (left_convergent_lines(M38_17_8, M38_17_8) | left_convergent_lines(M38_17_8, reverse_line(M38_17_8))))
% 2.33/0.89
% 2.33/0.89 [336] BETA_IMPLY : ((unequally_directed_lines(M38_17_8, M38_17_8) & unequally_directed_lines(M38_17_8, reverse_line(M38_17_8))) => (left_convergent_lines(M38_17_8, M38_17_8) | left_convergent_lines(M38_17_8, reverse_line(M38_17_8))))
% 2.33/0.89 -> [339] ~(unequally_directed_lines(M38_17_8, M38_17_8) & unequally_directed_lines(M38_17_8, reverse_line(M38_17_8)))
% 2.33/0.89 -> [340] (left_convergent_lines(M38_17_8, M38_17_8) | left_convergent_lines(M38_17_8, reverse_line(M38_17_8)))
% 2.33/0.89
% 2.33/0.89 [340] BETA_OR : (left_convergent_lines(M38_17_8, M38_17_8) | left_convergent_lines(M38_17_8, reverse_line(M38_17_8)))
% 2.33/0.89 -> [347] left_convergent_lines(M38_17_8, M38_17_8)
% 2.33/0.89 -> [348] left_convergent_lines(M38_17_8, reverse_line(M38_17_8))
% 2.33/0.89
% 2.33/0.89 [348] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.33/0.89 -> [357] ~(left_apart_point(A39_67_9, L40_67_9) | left_apart_point(A39_67_9, reverse_line(L40_67_9)))
% 2.33/0.89
% 2.33/0.89 [357] ALPHA_NOT_OR : ~(left_apart_point(A39_67_9, L40_67_9) | left_apart_point(A39_67_9, reverse_line(L40_67_9)))
% 2.33/0.89 -> [359] ~left_apart_point(A39_67_9, L40_67_9), ~left_apart_point(A39_67_9, reverse_line(L40_67_9))
% 2.33/0.89
% 2.33/0.89 [359] CLOSURE : ~left_apart_point(A39_67_9, L40_67_9)
% 2.33/0.89
% 2.33/0.89 [347] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.33/0.89 -> [358] ~(left_apart_point(A39_68_9, L40_68_9) | left_apart_point(A39_68_9, reverse_line(L40_68_9)))
% 2.33/0.89
% 2.33/0.89 [358] ALPHA_NOT_OR : ~(left_apart_point(A39_68_9, L40_68_9) | left_apart_point(A39_68_9, reverse_line(L40_68_9)))
% 2.33/0.89 -> [360] ~left_apart_point(A39_68_9, L40_68_9), ~left_apart_point(A39_68_9, reverse_line(L40_68_9))
% 2.33/0.89
% 2.33/0.89 [360] CLOSURE : ~left_apart_point(A39_68_9, L40_68_9)
% 2.33/0.89
% 2.33/0.89 [339] BETA_NOT_AND : ~(unequally_directed_lines(M38_17_8, M38_17_8) & unequally_directed_lines(M38_17_8, reverse_line(M38_17_8)))
% 2.33/0.89 -> [350] ~unequally_directed_lines(M38_17_8, M38_17_8)
% 2.33/0.89 -> [351] ~unequally_directed_lines(M38_17_8, reverse_line(M38_17_8))
% 2.33/0.89
% 2.33/0.89 [351] CLOSURE : ~unequally_directed_lines(M38_17_8, reverse_line(M38_17_8))
% 2.33/0.89
% 2.33/0.89 [350] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.33/0.89 -> [361] ~(left_apart_point(A39_69_9, L40_69_9) | left_apart_point(A39_69_9, reverse_line(L40_69_9)))
% 2.33/0.89
% 2.33/0.89 [361] ALPHA_NOT_OR : ~(left_apart_point(A39_69_9, L40_69_9) | left_apart_point(A39_69_9, reverse_line(L40_69_9)))
% 2.33/0.89 -> [362] ~left_apart_point(A39_69_9, L40_69_9), ~left_apart_point(A39_69_9, reverse_line(L40_69_9))
% 2.33/0.89
% 2.33/0.89 [362] CLOSURE : ~left_apart_point(A39_69_9, L40_69_9)
% 2.33/0.89
% 2.33/0.89 [233] 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))))
% 2.33/0.89 -> [363] (unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 2.33/0.89 -> [364] (unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 2.33/0.89
% 2.33/0.89 [363] ALPHA_AND : (unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 2.33/0.89 -> [365] unequally_directed_lines(N34_0_6, N34_0_6), unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))
% 2.33/0.89
% 2.33/0.89 [365] CLOSURE : unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))
% 2.33/0.89
% 2.33/0.89 [364] ALPHA_AND : (unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 2.33/0.89 -> [366] unequally_directed_lines(N34_0_6, N34_0_6), unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))
% 2.33/0.89
% 2.33/0.89 [366] CLOSURE : unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))
% 2.33/0.89
% 2.33/0.89 % SZS output end Proof for theBenchmark.p
% 2.33/0.89 [0.538909s][1][Res] 1835 goroutines created
% 2.33/0.89 ==== Result ====
% 2.33/0.89 [0.538936s][1][Res] VALID
% 2.33/0.89 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------