TSTP Solution File: GEO235+1 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO235+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n013.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 15:18:36 EDT 2022
% Result : Theorem 2.03s 0.86s
% Output : Proof 2.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GEO235+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.03/0.14 % Command : goeland -dmt -presko -proof %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 07:04:02 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 [DMT] DMT loaded with preskolemization
% 0.13/0.36 [EQ] equality loaded.
% 0.13/0.36 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.20/0.36 Conjecture not found
% 0.20/0.36 Start search
% 0.20/0.37 nb_step : 1 - limit : 32
% 0.20/0.37 Launch Gotab with destructive = true
% 2.03/0.86 % SZS output start Proof for theBenchmark.p
% 2.03/0.86 [0] ALPHA_AND : ((! [A20_20] : (~distinct_points(A20_20, A20_20)) & ! [A21_21, B22_22, C23_23] : ((distinct_points(A21_21, B22_22) => (distinct_points(A21_21, C23_23) | distinct_points(B22_22, C23_23)))) & ! [L24_24] : (~distinct_lines(L24_24, L24_24)) & ! [L25_25, M26_26, N27_27] : ((distinct_lines(L25_25, M26_26) => (distinct_lines(L25_25, N27_27) | distinct_lines(M26_26, N27_27)))) & ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28)) & ! [L29_29, M30_30, N31_31] : ((unequally_directed_lines(L29_29, M30_30) => (unequally_directed_lines(L29_29, N31_31) | unequally_directed_lines(M30_30, N31_31)))) & ! [L32_32, M33_33, N34_34] : (((unequally_directed_lines(L32_32, M33_33) & unequally_directed_lines(L32_32, reverse_line(M33_33))) => ((unequally_directed_lines(L32_32, N34_34) & unequally_directed_lines(L32_32, reverse_line(N34_34))) | (unequally_directed_lines(M33_33, N34_34) & unequally_directed_lines(M33_33, reverse_line(N34_34)))))) & ! [L35_35, M36_36] : (((line(L35_35) & line(M36_36)) => (unequally_directed_lines(L35_35, M36_36) | unequally_directed_lines(L35_35, reverse_line(M36_36))))) & ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38))))) & ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40)))) & ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42)))) & ! [A43_43, B44_44] : ((((point(A43_43) & point(B44_44)) & distinct_points(A43_43, B44_44)) => line(line_connecting(A43_43, B44_44)))) & ! [L45_45, M46_46] : (((((line(L45_45) & line(M46_46)) & unequally_directed_lines(L45_45, M46_46)) & unequally_directed_lines(L45_45, reverse_line(M46_46))) => point(intersection_point(L45_45, M46_46)))) & ! [L47_47, A48_48] : (((point(A48_48) & line(L47_47)) => line(parallel_through_point(L47_47, A48_48)))) & ! [L49_49] : ((line(L49_49) => line(reverse_line(L49_49)))) & ! [A50_50, B51_51] : ((distinct_points(A50_50, B51_51) => (~apart_point_and_line(A50_50, line_connecting(A50_50, B51_51)) & ~apart_point_and_line(B51_51, line_connecting(A50_50, B51_51))))) & ! [L52_52, M53_53] : (((unequally_directed_lines(L52_52, M53_53) & unequally_directed_lines(L52_52, reverse_line(M53_53))) => (~apart_point_and_line(intersection_point(L52_52, M53_53), L52_52) & ~apart_point_and_line(intersection_point(L52_52, M53_53), M53_53)))) & ! [A54_54, L55_55] : (~apart_point_and_line(A54_54, parallel_through_point(L55_55, A54_54))) & ! [L56_56] : (~distinct_lines(L56_56, reverse_line(L56_56))) & ! [A57_57, B58_58] : (~unequally_directed_lines(line_connecting(A57_57, B58_58), reverse_line(line_connecting(B58_58, A57_57)))) & ! [A59_59, L60_60] : (~unequally_directed_lines(parallel_through_point(L60_60, A59_59), L60_60)) & ! [A61_61, B62_62, L63_63, M64_64] : (((distinct_points(A61_61, B62_62) & distinct_lines(L63_63, M64_64)) => (((((((left_apart_point(A61_61, L63_63) | left_apart_point(B62_62, L63_63)) | left_apart_point(A61_61, M64_64)) | left_apart_point(B62_62, M64_64)) | left_apart_point(A61_61, reverse_line(L63_63))) | left_apart_point(B62_62, reverse_line(L63_63))) | left_apart_point(A61_61, reverse_line(M64_64))) | left_apart_point(B62_62, reverse_line(M64_64))))) & ! [A65_65, B66_66, L67_67] : (((distinct_points(A65_65, B66_66) & left_apart_point(A65_65, L67_67)) => (left_apart_point(B66_66, L67_67) | left_convergent_lines(line_connecting(A65_65, B66_66), L67_67)))) & ! [A68_68, B69_69, L70_70] : ((left_apart_point(A68_68, L70_70) => (distinct_points(A68_68, B69_69) | left_apart_point(B69_69, L70_70)))) & ! [A71_71, L72_72, M73_73] : (((left_apart_point(A71_71, L72_72) & unequally_directed_lines(L72_72, M73_73)) => (distinct_lines(L72_72, M73_73) | left_apart_point(A71_71, reverse_line(M73_73))))) & ! [L74_74, M75_75, N76_76] : ((left_convergent_lines(L74_74, M75_75) => (unequally_directed_lines(M75_75, N76_76) | left_convergent_lines(L74_74, N76_76))))) & ~! [A77_77, B78_78, L79_79] : (((left_apart_point(A77_77, L79_79) & left_apart_point(B78_78, reverse_line(L79_79))) => distinct_points(A77_77, B78_78))))
% 2.03/0.86 -> [1] (! [A20_20] : (~distinct_points(A20_20, A20_20)) & ! [A21_21, B22_22, C23_23] : ((distinct_points(A21_21, B22_22) => (distinct_points(A21_21, C23_23) | distinct_points(B22_22, C23_23)))) & ! [L24_24] : (~distinct_lines(L24_24, L24_24)) & ! [L25_25, M26_26, N27_27] : ((distinct_lines(L25_25, M26_26) => (distinct_lines(L25_25, N27_27) | distinct_lines(M26_26, N27_27)))) & ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28)) & ! [L29_29, M30_30, N31_31] : ((unequally_directed_lines(L29_29, M30_30) => (unequally_directed_lines(L29_29, N31_31) | unequally_directed_lines(M30_30, N31_31)))) & ! [L32_32, M33_33, N34_34] : (((unequally_directed_lines(L32_32, M33_33) & unequally_directed_lines(L32_32, reverse_line(M33_33))) => ((unequally_directed_lines(L32_32, N34_34) & unequally_directed_lines(L32_32, reverse_line(N34_34))) | (unequally_directed_lines(M33_33, N34_34) & unequally_directed_lines(M33_33, reverse_line(N34_34)))))) & ! [L35_35, M36_36] : (((line(L35_35) & line(M36_36)) => (unequally_directed_lines(L35_35, M36_36) | unequally_directed_lines(L35_35, reverse_line(M36_36))))) & ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38))))) & ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40)))) & ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42)))) & ! [A43_43, B44_44] : ((((point(A43_43) & point(B44_44)) & distinct_points(A43_43, B44_44)) => line(line_connecting(A43_43, B44_44)))) & ! [L45_45, M46_46] : (((((line(L45_45) & line(M46_46)) & unequally_directed_lines(L45_45, M46_46)) & unequally_directed_lines(L45_45, reverse_line(M46_46))) => point(intersection_point(L45_45, M46_46)))) & ! [L47_47, A48_48] : (((point(A48_48) & line(L47_47)) => line(parallel_through_point(L47_47, A48_48)))) & ! [L49_49] : ((line(L49_49) => line(reverse_line(L49_49)))) & ! [A50_50, B51_51] : ((distinct_points(A50_50, B51_51) => (~apart_point_and_line(A50_50, line_connecting(A50_50, B51_51)) & ~apart_point_and_line(B51_51, line_connecting(A50_50, B51_51))))) & ! [L52_52, M53_53] : (((unequally_directed_lines(L52_52, M53_53) & unequally_directed_lines(L52_52, reverse_line(M53_53))) => (~apart_point_and_line(intersection_point(L52_52, M53_53), L52_52) & ~apart_point_and_line(intersection_point(L52_52, M53_53), M53_53)))) & ! [A54_54, L55_55] : (~apart_point_and_line(A54_54, parallel_through_point(L55_55, A54_54))) & ! [L56_56] : (~distinct_lines(L56_56, reverse_line(L56_56))) & ! [A57_57, B58_58] : (~unequally_directed_lines(line_connecting(A57_57, B58_58), reverse_line(line_connecting(B58_58, A57_57)))) & ! [A59_59, L60_60] : (~unequally_directed_lines(parallel_through_point(L60_60, A59_59), L60_60)) & ! [A61_61, B62_62, L63_63, M64_64] : (((distinct_points(A61_61, B62_62) & distinct_lines(L63_63, M64_64)) => (((((((left_apart_point(A61_61, L63_63) | left_apart_point(B62_62, L63_63)) | left_apart_point(A61_61, M64_64)) | left_apart_point(B62_62, M64_64)) | left_apart_point(A61_61, reverse_line(L63_63))) | left_apart_point(B62_62, reverse_line(L63_63))) | left_apart_point(A61_61, reverse_line(M64_64))) | left_apart_point(B62_62, reverse_line(M64_64))))) & ! [A65_65, B66_66, L67_67] : (((distinct_points(A65_65, B66_66) & left_apart_point(A65_65, L67_67)) => (left_apart_point(B66_66, L67_67) | left_convergent_lines(line_connecting(A65_65, B66_66), L67_67)))) & ! [A68_68, B69_69, L70_70] : ((left_apart_point(A68_68, L70_70) => (distinct_points(A68_68, B69_69) | left_apart_point(B69_69, L70_70)))) & ! [A71_71, L72_72, M73_73] : (((left_apart_point(A71_71, L72_72) & unequally_directed_lines(L72_72, M73_73)) => (distinct_lines(L72_72, M73_73) | left_apart_point(A71_71, reverse_line(M73_73))))) & ! [L74_74, M75_75, N76_76] : ((left_convergent_lines(L74_74, M75_75) => (unequally_directed_lines(M75_75, N76_76) | left_convergent_lines(L74_74, N76_76))))), ~! [A77_77, B78_78, L79_79] : (((left_apart_point(A77_77, L79_79) & left_apart_point(B78_78, reverse_line(L79_79))) => distinct_points(A77_77, B78_78)))
% 2.03/0.86
% 2.03/0.86 [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)))))
% 2.03/0.86 -> [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))))
% 2.03/0.86
% 2.03/0.86 [2] DELTA_NOT_FORALL : ~! [A77_77, B78_78, L79_79] : (((left_apart_point(A77_77, L79_79) & left_apart_point(B78_78, reverse_line(L79_79))) => distinct_points(A77_77, B78_78)))
% 2.03/0.86 -> [3] ~((left_apart_point(skolem_A7777, skolem_L7979) & left_apart_point(skolem_B7878, reverse_line(skolem_L7979))) => distinct_points(skolem_A7777, skolem_B7878))
% 2.03/0.86
% 2.03/0.86 [3] ALPHA_NOT_IMPLY : ~((left_apart_point(skolem_A7777, skolem_L7979) & left_apart_point(skolem_B7878, reverse_line(skolem_L7979))) => distinct_points(skolem_A7777, skolem_B7878))
% 2.03/0.86 -> [4] (left_apart_point(skolem_A7777, skolem_L7979) & left_apart_point(skolem_B7878, reverse_line(skolem_L7979))), ~distinct_points(skolem_A7777, skolem_B7878)
% 2.03/0.86
% 2.03/0.86 [4] ALPHA_AND : (left_apart_point(skolem_A7777, skolem_L7979) & left_apart_point(skolem_B7878, reverse_line(skolem_L7979)))
% 2.03/0.86 -> [5] left_apart_point(skolem_A7777, skolem_L7979), left_apart_point(skolem_B7878, reverse_line(skolem_L7979))
% 2.03/0.86
% 2.03/0.86 [5] GAMMA_FORALL : ! [A20_20] : (~distinct_points(A20_20, A20_20))
% 2.03/0.86 -> [6] ~distinct_points(A20_0_0, A20_0_0)
% 2.03/0.86
% 2.03/0.86 [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))))
% 2.03/0.86 -> [7] (distinct_points(skolem_A7777, skolem_A7777) => (distinct_points(skolem_A7777, skolem_B7878) | distinct_points(skolem_A7777, skolem_B7878)))
% 2.03/0.86
% 2.03/0.86 [7] BETA_IMPLY : (distinct_points(skolem_A7777, skolem_A7777) => (distinct_points(skolem_A7777, skolem_B7878) | distinct_points(skolem_A7777, skolem_B7878)))
% 2.03/0.86 -> [8] ~distinct_points(skolem_A7777, skolem_A7777)
% 2.03/0.86 -> [9] (distinct_points(skolem_A7777, skolem_B7878) | distinct_points(skolem_A7777, skolem_B7878))
% 2.03/0.86
% 2.03/0.86 [9] BETA_OR : (distinct_points(skolem_A7777, skolem_B7878) | distinct_points(skolem_A7777, skolem_B7878))
% 2.03/0.86 -> [10] distinct_points(skolem_A7777, skolem_B7878)
% 2.03/0.86 -> [11] distinct_points(skolem_A7777, skolem_B7878)
% 2.03/0.86
% 2.03/0.86 [10] CLOSURE : distinct_points(skolem_A7777, skolem_B7878)
% 2.03/0.86
% 2.03/0.86 [11] CLOSURE : distinct_points(skolem_A7777, skolem_B7878)
% 2.03/0.86
% 2.03/0.86 [8] GAMMA_FORALL : ! [L24_24] : (~distinct_lines(L24_24, L24_24))
% 2.03/0.86 -> [12] ~distinct_lines(L25_0_3, L25_0_3)
% 2.03/0.86
% 2.03/0.86 [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))))
% 2.03/0.86 -> [13] (distinct_lines(L25_0_3, L25_0_3) => (distinct_lines(L25_0_3, L25_0_3) | distinct_lines(L25_0_3, L25_0_3)))
% 2.03/0.86
% 2.03/0.86 [13] BETA_IMPLY : (distinct_lines(L25_0_3, L25_0_3) => (distinct_lines(L25_0_3, L25_0_3) | distinct_lines(L25_0_3, L25_0_3)))
% 2.03/0.86 -> [14] ~distinct_lines(L25_0_3, L25_0_3)
% 2.03/0.86 -> [15] (distinct_lines(L25_0_3, L25_0_3) | distinct_lines(L25_0_3, L25_0_3))
% 2.03/0.86
% 2.03/0.86 [15] BETA_OR : (distinct_lines(L25_0_3, L25_0_3) | distinct_lines(L25_0_3, L25_0_3))
% 2.03/0.86 -> [16] distinct_lines(L25_0_3, L25_0_3)
% 2.03/0.86 -> [17] distinct_lines(L25_0_3, L25_0_3)
% 2.03/0.86
% 2.03/0.86 [17] CLOSURE : distinct_lines(L25_0_3, L25_0_3)
% 2.03/0.86
% 2.03/0.86 [16] CLOSURE : distinct_lines(L25_0_3, L25_0_3)
% 2.03/0.86
% 2.03/0.86 [14] GAMMA_FORALL : ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28))
% 2.03/0.86 -> [18] ~unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6))
% 2.03/0.86
% 2.03/0.86 [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))))
% 2.03/0.86 -> [19] (unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6)) => (unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6)) | unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6))))
% 2.03/0.86
% 2.03/0.86 [19] BETA_IMPLY : (unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6)) => (unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6)) | unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6))))
% 2.03/0.86 -> [20] ~unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6))
% 2.03/0.86 -> [21] (unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6)) | unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6)))
% 2.03/0.86
% 2.03/0.86 [21] BETA_OR : (unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6)) | unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6)))
% 2.03/0.86 -> [22] unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6))
% 2.03/0.86 -> [23] unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6))
% 2.03/0.86
% 2.03/0.86 [23] CLOSURE : unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6))
% 2.03/0.86
% 2.03/0.86 [22] CLOSURE : unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6))
% 2.03/0.86
% 2.03/0.86 [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)))))
% 2.03/0.86 -> [219] ~(unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 2.03/0.86 -> [220] ((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))))
% 2.03/0.86
% 2.03/0.86 [219] BETA_NOT_AND : ~(unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 2.03/0.86 -> [221] ~unequally_directed_lines(N34_0_6, N34_0_6)
% 2.03/0.86 -> [222] ~unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))
% 2.03/0.86
% 2.03/0.86 [222] 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)))))
% 2.03/0.86 -> [227] ((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))))
% 2.03/0.86
% 2.03/0.86 [227] 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))))
% 2.03/0.86 -> [231] ~(line(M36_5_7) & line(M36_5_7))
% 2.03/0.86 -> [232] (unequally_directed_lines(M36_5_7, M36_5_7) | unequally_directed_lines(M36_5_7, reverse_line(M36_5_7)))
% 2.03/0.86
% 2.03/0.86 [232] BETA_OR : (unequally_directed_lines(M36_5_7, M36_5_7) | unequally_directed_lines(M36_5_7, reverse_line(M36_5_7)))
% 2.03/0.86 -> [239] unequally_directed_lines(M36_5_7, M36_5_7)
% 2.03/0.86 -> [240] unequally_directed_lines(M36_5_7, reverse_line(M36_5_7))
% 2.03/0.86
% 2.03/0.86 [240] CLOSURE : unequally_directed_lines(M36_5_7, reverse_line(M36_5_7))
% 2.03/0.86
% 2.03/0.86 [239] CLOSURE : unequally_directed_lines(M36_5_7, M36_5_7)
% 2.03/0.86
% 2.03/0.86 [231] BETA_NOT_AND : ~(line(M36_5_7) & line(M36_5_7))
% 2.03/0.86 -> [233] ~line(M36_5_7)
% 2.03/0.86 -> [234] ~line(M36_5_7)
% 2.03/0.86
% 2.03/0.86 [234] GAMMA_FORALL : ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38)))))
% 2.03/0.86 -> [242] ((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))))
% 2.03/0.86
% 2.03/0.86 [242] 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))))
% 2.03/0.86 -> [245] ~(unequally_directed_lines(L37_11_8, M38_11_8) & unequally_directed_lines(L37_11_8, reverse_line(M38_11_8)))
% 2.03/0.86 -> [246] (left_convergent_lines(L37_11_8, M38_11_8) | left_convergent_lines(L37_11_8, reverse_line(M38_11_8)))
% 2.03/0.86
% 2.03/0.86 [245] BETA_NOT_AND : ~(unequally_directed_lines(L37_11_8, M38_11_8) & unequally_directed_lines(L37_11_8, reverse_line(M38_11_8)))
% 2.03/0.86 -> [259] ~unequally_directed_lines(L37_11_8, M38_11_8)
% 2.03/0.86 -> [260] ~unequally_directed_lines(L37_11_8, reverse_line(M38_11_8))
% 2.03/0.86
% 2.03/0.86 [260] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.03/0.86 -> [274] ~(left_apart_point(A39_43_9, L40_43_9) | left_apart_point(A39_43_9, reverse_line(L40_43_9)))
% 2.03/0.86
% 2.03/0.86 [274] ALPHA_NOT_OR : ~(left_apart_point(A39_43_9, L40_43_9) | left_apart_point(A39_43_9, reverse_line(L40_43_9)))
% 2.03/0.86 -> [279] ~left_apart_point(A39_43_9, L40_43_9), ~left_apart_point(A39_43_9, reverse_line(L40_43_9))
% 2.03/0.86
% 2.03/0.86 [279] CLOSURE : ~left_apart_point(A39_43_9, L40_43_9)
% 2.03/0.86
% 2.03/0.86 [259] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.03/0.86 -> [281] ~(left_apart_point(A39_47_9, L40_47_9) | left_apart_point(A39_47_9, reverse_line(L40_47_9)))
% 2.03/0.86
% 2.03/0.86 [281] ALPHA_NOT_OR : ~(left_apart_point(A39_47_9, L40_47_9) | left_apart_point(A39_47_9, reverse_line(L40_47_9)))
% 2.03/0.86 -> [282] ~left_apart_point(A39_47_9, L40_47_9), ~left_apart_point(A39_47_9, reverse_line(L40_47_9))
% 2.03/0.86
% 2.03/0.86 [282] CLOSURE : ~left_apart_point(A39_47_9, L40_47_9)
% 2.03/0.86
% 2.03/0.86 [246] BETA_OR : (left_convergent_lines(L37_11_8, M38_11_8) | left_convergent_lines(L37_11_8, reverse_line(M38_11_8)))
% 2.03/0.86 -> [266] left_convergent_lines(L37_11_8, M38_11_8)
% 2.03/0.86 -> [267] left_convergent_lines(L37_11_8, reverse_line(M38_11_8))
% 2.03/0.86
% 2.03/0.86 [267] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.03/0.86 -> [277] ~(left_apart_point(A39_45_9, L40_45_9) | left_apart_point(A39_45_9, reverse_line(L40_45_9)))
% 2.03/0.86
% 2.03/0.86 [277] ALPHA_NOT_OR : ~(left_apart_point(A39_45_9, L40_45_9) | left_apart_point(A39_45_9, reverse_line(L40_45_9)))
% 2.03/0.86 -> [292] ~left_apart_point(A39_45_9, L40_45_9), ~left_apart_point(A39_45_9, reverse_line(L40_45_9))
% 2.03/0.86
% 2.03/0.86 [292] CLOSURE : ~left_apart_point(A39_45_9, L40_45_9)
% 2.03/0.86
% 2.03/0.86 [266] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.03/0.86 -> [293] ~(left_apart_point(A39_52_9, L40_52_9) | left_apart_point(A39_52_9, reverse_line(L40_52_9)))
% 2.03/0.86
% 2.03/0.86 [293] ALPHA_NOT_OR : ~(left_apart_point(A39_52_9, L40_52_9) | left_apart_point(A39_52_9, reverse_line(L40_52_9)))
% 2.03/0.86 -> [294] ~left_apart_point(A39_52_9, L40_52_9), ~left_apart_point(A39_52_9, reverse_line(L40_52_9))
% 2.03/0.86
% 2.03/0.86 [294] CLOSURE : ~left_apart_point(A39_52_9, L40_52_9)
% 2.03/0.86
% 2.03/0.86 [233] 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)))))
% 2.03/0.86 -> [248] ((unequally_directed_lines(L37_13_8, M38_13_8) & unequally_directed_lines(L37_13_8, reverse_line(M38_13_8))) => (left_convergent_lines(L37_13_8, M38_13_8) | left_convergent_lines(L37_13_8, reverse_line(M38_13_8))))
% 2.03/0.86
% 2.03/0.86 [248] BETA_IMPLY : ((unequally_directed_lines(L37_13_8, M38_13_8) & unequally_directed_lines(L37_13_8, reverse_line(M38_13_8))) => (left_convergent_lines(L37_13_8, M38_13_8) | left_convergent_lines(L37_13_8, reverse_line(M38_13_8))))
% 2.03/0.86 -> [253] ~(unequally_directed_lines(L37_13_8, M38_13_8) & unequally_directed_lines(L37_13_8, reverse_line(M38_13_8)))
% 2.03/0.86 -> [254] (left_convergent_lines(L37_13_8, M38_13_8) | left_convergent_lines(L37_13_8, reverse_line(M38_13_8)))
% 2.03/0.86
% 2.03/0.86 [253] BETA_NOT_AND : ~(unequally_directed_lines(L37_13_8, M38_13_8) & unequally_directed_lines(L37_13_8, reverse_line(M38_13_8)))
% 2.03/0.86 -> [261] ~unequally_directed_lines(L37_13_8, M38_13_8)
% 2.03/0.86 -> [262] ~unequally_directed_lines(L37_13_8, reverse_line(M38_13_8))
% 2.03/0.86
% 2.03/0.86 [262] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.03/0.86 -> [271] ~(left_apart_point(A39_41_9, L40_41_9) | left_apart_point(A39_41_9, reverse_line(L40_41_9)))
% 2.03/0.86
% 2.03/0.86 [271] ALPHA_NOT_OR : ~(left_apart_point(A39_41_9, L40_41_9) | left_apart_point(A39_41_9, reverse_line(L40_41_9)))
% 2.03/0.86 -> [273] ~left_apart_point(A39_41_9, L40_41_9), ~left_apart_point(A39_41_9, reverse_line(L40_41_9))
% 2.03/0.86
% 2.03/0.86 [273] CLOSURE : ~left_apart_point(A39_41_9, L40_41_9)
% 2.03/0.86
% 2.03/0.86 [261] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.03/0.86 -> [295] ~(left_apart_point(A39_53_9, L40_53_9) | left_apart_point(A39_53_9, reverse_line(L40_53_9)))
% 2.03/0.86
% 2.03/0.86 [295] ALPHA_NOT_OR : ~(left_apart_point(A39_53_9, L40_53_9) | left_apart_point(A39_53_9, reverse_line(L40_53_9)))
% 2.03/0.86 -> [296] ~left_apart_point(A39_53_9, L40_53_9), ~left_apart_point(A39_53_9, reverse_line(L40_53_9))
% 2.03/0.86
% 2.03/0.86 [296] CLOSURE : ~left_apart_point(A39_53_9, L40_53_9)
% 2.03/0.86
% 2.03/0.86 [254] BETA_OR : (left_convergent_lines(L37_13_8, M38_13_8) | left_convergent_lines(L37_13_8, reverse_line(M38_13_8)))
% 2.03/0.86 -> [264] left_convergent_lines(L37_13_8, M38_13_8)
% 2.03/0.86 -> [265] left_convergent_lines(L37_13_8, reverse_line(M38_13_8))
% 2.03/0.86
% 2.03/0.86 [264] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.03/0.86 -> [297] ~(left_apart_point(A39_54_9, L40_54_9) | left_apart_point(A39_54_9, reverse_line(L40_54_9)))
% 2.03/0.86
% 2.03/0.86 [297] ALPHA_NOT_OR : ~(left_apart_point(A39_54_9, L40_54_9) | left_apart_point(A39_54_9, reverse_line(L40_54_9)))
% 2.03/0.86 -> [299] ~left_apart_point(A39_54_9, L40_54_9), ~left_apart_point(A39_54_9, reverse_line(L40_54_9))
% 2.03/0.86
% 2.03/0.86 [299] CLOSURE : ~left_apart_point(A39_54_9, L40_54_9)
% 2.03/0.86
% 2.03/0.86 [265] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.03/0.86 -> [298] ~(left_apart_point(A39_55_9, L40_55_9) | left_apart_point(A39_55_9, reverse_line(L40_55_9)))
% 2.03/0.86
% 2.03/0.86 [298] ALPHA_NOT_OR : ~(left_apart_point(A39_55_9, L40_55_9) | left_apart_point(A39_55_9, reverse_line(L40_55_9)))
% 2.03/0.86 -> [300] ~left_apart_point(A39_55_9, L40_55_9), ~left_apart_point(A39_55_9, reverse_line(L40_55_9))
% 2.03/0.86
% 2.03/0.86 [300] CLOSURE : ~left_apart_point(A39_55_9, L40_55_9)
% 2.03/0.86
% 2.03/0.86 [226] 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))))
% 2.03/0.86 -> [301] ~(line(N34_0_6) & line(N34_0_6))
% 2.03/0.86 -> [302] (unequally_directed_lines(N34_0_6, N34_0_6) | unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 2.03/0.86
% 2.03/0.86 [301] BETA_NOT_AND : ~(line(N34_0_6) & line(N34_0_6))
% 2.03/0.86 -> [305] ~line(N34_0_6)
% 2.03/0.86 -> [306] ~line(N34_0_6)
% 2.03/0.86
% 2.03/0.86 [306] 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)))))
% 2.03/0.86 -> [307] ((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))))
% 2.03/0.86
% 2.03/0.86 [307] 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))))
% 2.03/0.86 -> [309] ~(unequally_directed_lines(L37_14_8, M38_14_8) & unequally_directed_lines(L37_14_8, reverse_line(M38_14_8)))
% 2.03/0.86 -> [310] (left_convergent_lines(L37_14_8, M38_14_8) | left_convergent_lines(L37_14_8, reverse_line(M38_14_8)))
% 2.03/0.86
% 2.03/0.86 [310] BETA_OR : (left_convergent_lines(L37_14_8, M38_14_8) | left_convergent_lines(L37_14_8, reverse_line(M38_14_8)))
% 2.03/0.86 -> [315] left_convergent_lines(L37_14_8, M38_14_8)
% 2.03/0.86 -> [316] left_convergent_lines(L37_14_8, reverse_line(M38_14_8))
% 2.03/0.86
% 2.03/0.86 [316] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.03/0.86 -> [329] ~(left_apart_point(A39_60_9, L40_60_9) | left_apart_point(A39_60_9, reverse_line(L40_60_9)))
% 2.03/0.86
% 2.03/0.86 [329] ALPHA_NOT_OR : ~(left_apart_point(A39_60_9, L40_60_9) | left_apart_point(A39_60_9, reverse_line(L40_60_9)))
% 2.03/0.86 -> [336] ~left_apart_point(A39_60_9, L40_60_9), ~left_apart_point(A39_60_9, reverse_line(L40_60_9))
% 2.03/0.86
% 2.03/0.86 [336] CLOSURE : ~left_apart_point(A39_60_9, L40_60_9)
% 2.03/0.86
% 2.03/0.86 [315] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.03/0.86 -> [328] ~(left_apart_point(A39_59_9, L40_59_9) | left_apart_point(A39_59_9, reverse_line(L40_59_9)))
% 2.03/0.86
% 2.03/0.86 [328] ALPHA_NOT_OR : ~(left_apart_point(A39_59_9, L40_59_9) | left_apart_point(A39_59_9, reverse_line(L40_59_9)))
% 2.03/0.86 -> [335] ~left_apart_point(A39_59_9, L40_59_9), ~left_apart_point(A39_59_9, reverse_line(L40_59_9))
% 2.03/0.86
% 2.03/0.86 [335] CLOSURE : ~left_apart_point(A39_59_9, L40_59_9)
% 2.03/0.86
% 2.03/0.86 [309] BETA_NOT_AND : ~(unequally_directed_lines(L37_14_8, M38_14_8) & unequally_directed_lines(L37_14_8, reverse_line(M38_14_8)))
% 2.03/0.86 -> [313] ~unequally_directed_lines(L37_14_8, M38_14_8)
% 2.03/0.86 -> [314] ~unequally_directed_lines(L37_14_8, reverse_line(M38_14_8))
% 2.03/0.86
% 2.03/0.86 [314] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.03/0.86 -> [324] ~(left_apart_point(A39_56_9, L40_56_9) | left_apart_point(A39_56_9, reverse_line(L40_56_9)))
% 2.03/0.86
% 2.03/0.86 [324] ALPHA_NOT_OR : ~(left_apart_point(A39_56_9, L40_56_9) | left_apart_point(A39_56_9, reverse_line(L40_56_9)))
% 2.03/0.86 -> [325] ~left_apart_point(A39_56_9, L40_56_9), ~left_apart_point(A39_56_9, reverse_line(L40_56_9))
% 2.03/0.86
% 2.03/0.86 [325] CLOSURE : ~left_apart_point(A39_56_9, L40_56_9)
% 2.03/0.86
% 2.03/0.86 [313] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.03/0.86 -> [327] ~(left_apart_point(A39_58_9, L40_58_9) | left_apart_point(A39_58_9, reverse_line(L40_58_9)))
% 2.03/0.86
% 2.03/0.86 [327] ALPHA_NOT_OR : ~(left_apart_point(A39_58_9, L40_58_9) | left_apart_point(A39_58_9, reverse_line(L40_58_9)))
% 2.03/0.86 -> [339] ~left_apart_point(A39_58_9, L40_58_9), ~left_apart_point(A39_58_9, reverse_line(L40_58_9))
% 2.03/0.86
% 2.03/0.86 [339] CLOSURE : ~left_apart_point(A39_58_9, L40_58_9)
% 2.03/0.86
% 2.03/0.86 [305] 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)))))
% 2.03/0.86 -> [308] ((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))))
% 2.03/0.86
% 2.03/0.86 [308] 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))))
% 2.03/0.86 -> [311] ~(unequally_directed_lines(L37_15_8, M38_15_8) & unequally_directed_lines(L37_15_8, reverse_line(M38_15_8)))
% 2.03/0.86 -> [312] (left_convergent_lines(L37_15_8, M38_15_8) | left_convergent_lines(L37_15_8, reverse_line(M38_15_8)))
% 2.03/0.86
% 2.03/0.86 [312] BETA_OR : (left_convergent_lines(L37_15_8, M38_15_8) | left_convergent_lines(L37_15_8, reverse_line(M38_15_8)))
% 2.03/0.86 -> [319] left_convergent_lines(L37_15_8, M38_15_8)
% 2.03/0.86 -> [320] left_convergent_lines(L37_15_8, reverse_line(M38_15_8))
% 2.03/0.86
% 2.03/0.86 [320] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.03/0.86 -> [332] ~(left_apart_point(A39_61_9, L40_61_9) | left_apart_point(A39_61_9, reverse_line(L40_61_9)))
% 2.03/0.86
% 2.03/0.86 [332] ALPHA_NOT_OR : ~(left_apart_point(A39_61_9, L40_61_9) | left_apart_point(A39_61_9, reverse_line(L40_61_9)))
% 2.03/0.86 -> [340] ~left_apart_point(A39_61_9, L40_61_9), ~left_apart_point(A39_61_9, reverse_line(L40_61_9))
% 2.03/0.86
% 2.03/0.86 [340] CLOSURE : ~left_apart_point(A39_61_9, L40_61_9)
% 2.03/0.86
% 2.03/0.86 [319] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.03/0.86 -> [337] ~(left_apart_point(A39_63_9, L40_63_9) | left_apart_point(A39_63_9, reverse_line(L40_63_9)))
% 2.03/0.86
% 2.03/0.86 [337] ALPHA_NOT_OR : ~(left_apart_point(A39_63_9, L40_63_9) | left_apart_point(A39_63_9, reverse_line(L40_63_9)))
% 2.03/0.86 -> [338] ~left_apart_point(A39_63_9, L40_63_9), ~left_apart_point(A39_63_9, reverse_line(L40_63_9))
% 2.03/0.86
% 2.03/0.86 [338] CLOSURE : ~left_apart_point(A39_63_9, L40_63_9)
% 2.03/0.86
% 2.03/0.86 [311] BETA_NOT_AND : ~(unequally_directed_lines(L37_15_8, M38_15_8) & unequally_directed_lines(L37_15_8, reverse_line(M38_15_8)))
% 2.03/0.86 -> [317] ~unequally_directed_lines(L37_15_8, M38_15_8)
% 2.03/0.86 -> [318] ~unequally_directed_lines(L37_15_8, reverse_line(M38_15_8))
% 2.03/0.86
% 2.03/0.86 [318] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.03/0.86 -> [326] ~(left_apart_point(A39_57_9, L40_57_9) | left_apart_point(A39_57_9, reverse_line(L40_57_9)))
% 2.03/0.86
% 2.03/0.86 [326] ALPHA_NOT_OR : ~(left_apart_point(A39_57_9, L40_57_9) | left_apart_point(A39_57_9, reverse_line(L40_57_9)))
% 2.03/0.86 -> [334] ~left_apart_point(A39_57_9, L40_57_9), ~left_apart_point(A39_57_9, reverse_line(L40_57_9))
% 2.03/0.86
% 2.03/0.86 [334] CLOSURE : ~left_apart_point(A39_57_9, L40_57_9)
% 2.03/0.86
% 2.03/0.86 [317] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.03/0.86 -> [333] ~(left_apart_point(A39_62_9, L40_62_9) | left_apart_point(A39_62_9, reverse_line(L40_62_9)))
% 2.03/0.86
% 2.03/0.86 [333] ALPHA_NOT_OR : ~(left_apart_point(A39_62_9, L40_62_9) | left_apart_point(A39_62_9, reverse_line(L40_62_9)))
% 2.03/0.86 -> [343] ~left_apart_point(A39_62_9, L40_62_9), ~left_apart_point(A39_62_9, reverse_line(L40_62_9))
% 2.03/0.86
% 2.03/0.86 [343] CLOSURE : ~left_apart_point(A39_62_9, L40_62_9)
% 2.03/0.86
% 2.03/0.86 [302] BETA_OR : (unequally_directed_lines(N34_0_6, N34_0_6) | unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 2.03/0.86 -> [303] unequally_directed_lines(N34_0_6, N34_0_6)
% 2.03/0.86 -> [304] unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))
% 2.03/0.86
% 2.03/0.86 [303] CLOSURE : unequally_directed_lines(N34_0_6, N34_0_6)
% 2.03/0.86
% 2.03/0.86 [304] GAMMA_FORALL : ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38)))))
% 2.03/0.86 -> [321] ((unequally_directed_lines(M38_16_8, M38_16_8) & unequally_directed_lines(M38_16_8, reverse_line(M38_16_8))) => (left_convergent_lines(M38_16_8, M38_16_8) | left_convergent_lines(M38_16_8, reverse_line(M38_16_8))))
% 2.03/0.86
% 2.03/0.86 [321] BETA_IMPLY : ((unequally_directed_lines(M38_16_8, M38_16_8) & unequally_directed_lines(M38_16_8, reverse_line(M38_16_8))) => (left_convergent_lines(M38_16_8, M38_16_8) | left_convergent_lines(M38_16_8, reverse_line(M38_16_8))))
% 2.03/0.86 -> [322] ~(unequally_directed_lines(M38_16_8, M38_16_8) & unequally_directed_lines(M38_16_8, reverse_line(M38_16_8)))
% 2.03/0.86 -> [323] (left_convergent_lines(M38_16_8, M38_16_8) | left_convergent_lines(M38_16_8, reverse_line(M38_16_8)))
% 2.03/0.86
% 2.03/0.86 [323] BETA_OR : (left_convergent_lines(M38_16_8, M38_16_8) | left_convergent_lines(M38_16_8, reverse_line(M38_16_8)))
% 2.03/0.86 -> [341] left_convergent_lines(M38_16_8, M38_16_8)
% 2.03/0.86 -> [342] left_convergent_lines(M38_16_8, reverse_line(M38_16_8))
% 2.03/0.86
% 2.03/0.86 [342] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.03/0.86 -> [344] ~(left_apart_point(A39_64_9, L40_64_9) | left_apart_point(A39_64_9, reverse_line(L40_64_9)))
% 2.03/0.86
% 2.03/0.86 [344] ALPHA_NOT_OR : ~(left_apart_point(A39_64_9, L40_64_9) | left_apart_point(A39_64_9, reverse_line(L40_64_9)))
% 2.03/0.86 -> [345] ~left_apart_point(A39_64_9, L40_64_9), ~left_apart_point(A39_64_9, reverse_line(L40_64_9))
% 2.03/0.86
% 2.03/0.86 [345] CLOSURE : ~left_apart_point(A39_64_9, L40_64_9)
% 2.03/0.86
% 2.03/0.86 [341] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.03/0.86 -> [346] ~(left_apart_point(A39_65_9, L40_65_9) | left_apart_point(A39_65_9, reverse_line(L40_65_9)))
% 2.03/0.86
% 2.03/0.86 [346] ALPHA_NOT_OR : ~(left_apart_point(A39_65_9, L40_65_9) | left_apart_point(A39_65_9, reverse_line(L40_65_9)))
% 2.03/0.86 -> [348] ~left_apart_point(A39_65_9, L40_65_9), ~left_apart_point(A39_65_9, reverse_line(L40_65_9))
% 2.03/0.86
% 2.03/0.86 [348] CLOSURE : ~left_apart_point(A39_65_9, L40_65_9)
% 2.03/0.86
% 2.03/0.86 [322] BETA_NOT_AND : ~(unequally_directed_lines(M38_16_8, M38_16_8) & unequally_directed_lines(M38_16_8, reverse_line(M38_16_8)))
% 2.03/0.86 -> [330] ~unequally_directed_lines(M38_16_8, M38_16_8)
% 2.03/0.86 -> [331] ~unequally_directed_lines(M38_16_8, reverse_line(M38_16_8))
% 2.03/0.86
% 2.03/0.86 [331] CLOSURE : ~unequally_directed_lines(M38_16_8, reverse_line(M38_16_8))
% 2.03/0.86
% 2.03/0.86 [330] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.03/0.86 -> [347] ~(left_apart_point(A39_66_9, L40_66_9) | left_apart_point(A39_66_9, reverse_line(L40_66_9)))
% 2.03/0.86
% 2.03/0.86 [347] ALPHA_NOT_OR : ~(left_apart_point(A39_66_9, L40_66_9) | left_apart_point(A39_66_9, reverse_line(L40_66_9)))
% 2.03/0.86 -> [349] ~left_apart_point(A39_66_9, L40_66_9), ~left_apart_point(A39_66_9, reverse_line(L40_66_9))
% 2.03/0.86
% 2.03/0.86 [349] CLOSURE : ~left_apart_point(A39_66_9, L40_66_9)
% 2.03/0.86
% 2.03/0.86 [220] 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))))
% 2.03/0.86 -> [350] (unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 2.03/0.86 -> [351] (unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 2.03/0.86
% 2.03/0.86 [350] ALPHA_AND : (unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 2.03/0.86 -> [353] unequally_directed_lines(N34_0_6, N34_0_6), unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))
% 2.03/0.86
% 2.03/0.86 [353] CLOSURE : unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))
% 2.03/0.86
% 2.03/0.86 [351] ALPHA_AND : (unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 2.03/0.86 -> [352] unequally_directed_lines(N34_0_6, N34_0_6), unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))
% 2.03/0.86
% 2.03/0.86 [352] CLOSURE : unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))
% 2.03/0.86
% 2.03/0.86 % SZS output end Proof for theBenchmark.p
% 2.03/0.86 [0.505942s][1][Res] 1584 goroutines created
% 2.03/0.86 ==== Result ====
% 2.03/0.86 [0.505993s][1][Res] VALID
% 2.03/0.86 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------