TSTP Solution File: GEO246+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO246+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 15:18:41 EDT 2022
% Result : Theorem 3.26s 1.09s
% Output : Proof 3.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GEO246+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.07/0.12 % Command : goeland -dmt -presko -proof %s
% 0.11/0.33 % Computer : n023.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Aug 31 07:31:34 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.34 [DMT] DMT loaded with preskolemization
% 0.11/0.34 [EQ] equality loaded.
% 0.11/0.34 [0.000037s][1][MAIN] Problem : theBenchmark.p
% 0.11/0.34 Conjecture not found
% 0.11/0.34 Start search
% 0.11/0.34 nb_step : 1 - limit : 32
% 0.11/0.34 Launch Gotab with destructive = true
% 3.26/1.08 % SZS output start Proof for theBenchmark.p
% 3.26/1.09 [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, C79_79] : ((distinct_points(A77_77, B78_78) => (left_apart_point(C79_79, reverse_line(line_connecting(A77_77, B78_78))) => left_apart_point(B78_78, line_connecting(A77_77, C79_79))))))
% 3.26/1.09 -> [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, C79_79] : ((distinct_points(A77_77, B78_78) => (left_apart_point(C79_79, reverse_line(line_connecting(A77_77, B78_78))) => left_apart_point(B78_78, line_connecting(A77_77, C79_79)))))
% 3.26/1.09
% 3.26/1.09 [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)))))
% 3.26/1.09 -> [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))))
% 3.26/1.09
% 3.26/1.09 [2] DELTA_NOT_FORALL : ~! [A77_77, B78_78, C79_79] : ((distinct_points(A77_77, B78_78) => (left_apart_point(C79_79, reverse_line(line_connecting(A77_77, B78_78))) => left_apart_point(B78_78, line_connecting(A77_77, C79_79)))))
% 3.26/1.09 -> [3] ~(distinct_points(skolem_A7777, skolem_B7878) => (left_apart_point(skolem_C7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))) => left_apart_point(skolem_B7878, line_connecting(skolem_A7777, skolem_C7979))))
% 3.26/1.09
% 3.26/1.09 [3] ALPHA_NOT_IMPLY : ~(distinct_points(skolem_A7777, skolem_B7878) => (left_apart_point(skolem_C7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))) => left_apart_point(skolem_B7878, line_connecting(skolem_A7777, skolem_C7979))))
% 3.26/1.09 -> [4] distinct_points(skolem_A7777, skolem_B7878), ~(left_apart_point(skolem_C7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))) => left_apart_point(skolem_B7878, line_connecting(skolem_A7777, skolem_C7979)))
% 3.26/1.09
% 3.26/1.09 [4] ALPHA_NOT_IMPLY : ~(left_apart_point(skolem_C7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))) => left_apart_point(skolem_B7878, line_connecting(skolem_A7777, skolem_C7979)))
% 3.26/1.09 -> [5] left_apart_point(skolem_C7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))), ~left_apart_point(skolem_B7878, line_connecting(skolem_A7777, skolem_C7979))
% 3.26/1.09
% 3.26/1.09 [5] GAMMA_FORALL : ! [A20_20] : (~distinct_points(A20_20, A20_20))
% 3.26/1.09 -> [6] ~distinct_points(skolem_B7878, skolem_B7878)
% 3.26/1.09
% 3.26/1.09 [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))))
% 3.26/1.09 -> [7] (distinct_points(skolem_A7777, skolem_B7878) => (distinct_points(skolem_A7777, skolem_B7878) | distinct_points(skolem_B7878, skolem_B7878)))
% 3.26/1.09
% 3.26/1.09 [7] BETA_IMPLY : (distinct_points(skolem_A7777, skolem_B7878) => (distinct_points(skolem_A7777, skolem_B7878) | distinct_points(skolem_B7878, skolem_B7878)))
% 3.26/1.09 -> [8] ~distinct_points(skolem_A7777, skolem_B7878)
% 3.26/1.09 -> [9] (distinct_points(skolem_A7777, skolem_B7878) | distinct_points(skolem_B7878, skolem_B7878))
% 3.26/1.09
% 3.26/1.09 [8] CLOSURE : ~distinct_points(skolem_A7777, skolem_B7878)
% 3.26/1.09
% 3.26/1.09 [9] BETA_OR : (distinct_points(skolem_A7777, skolem_B7878) | distinct_points(skolem_B7878, skolem_B7878))
% 3.26/1.09 -> [12] distinct_points(skolem_A7777, skolem_B7878)
% 3.26/1.09 -> [13] distinct_points(skolem_B7878, skolem_B7878)
% 3.26/1.09
% 3.26/1.09 [13] CLOSURE : distinct_points(skolem_B7878, skolem_B7878)
% 3.26/1.09
% 3.26/1.09 [12] GAMMA_FORALL : ! [L24_24] : (~distinct_lines(L24_24, L24_24))
% 3.26/1.09 -> [14] ~distinct_lines(N27_0_3, N27_0_3)
% 3.26/1.09
% 3.26/1.09 [14] 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))))
% 3.26/1.09 -> [15] (distinct_lines(N27_0_3, N27_0_3) => (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3)))
% 3.26/1.09
% 3.26/1.09 [15] 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)))
% 3.26/1.09 -> [16] ~distinct_lines(N27_0_3, N27_0_3)
% 3.26/1.09 -> [17] (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3))
% 3.26/1.09
% 3.26/1.09 [17] BETA_OR : (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3))
% 3.26/1.09 -> [18] distinct_lines(N27_0_3, N27_0_3)
% 3.26/1.09 -> [19] distinct_lines(N27_0_3, N27_0_3)
% 3.26/1.09
% 3.26/1.09 [19] CLOSURE : distinct_lines(N27_0_3, N27_0_3)
% 3.26/1.09
% 3.26/1.09 [18] CLOSURE : distinct_lines(N27_0_3, N27_0_3)
% 3.26/1.09
% 3.26/1.09 [16] GAMMA_FORALL : ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28))
% 3.26/1.09 -> [20] ~unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8)))
% 3.26/1.09
% 3.26/1.09 [20] 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))))
% 3.26/1.09 -> [21] (unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))) => (unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))) | unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8)))))
% 3.26/1.09
% 3.26/1.09 [21] BETA_IMPLY : (unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))) => (unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))) | unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8)))))
% 3.26/1.09 -> [22] ~unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8)))
% 3.26/1.09 -> [23] (unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))) | unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))))
% 3.26/1.09
% 3.26/1.09 [23] BETA_OR : (unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))) | unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))))
% 3.26/1.09 -> [24] unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8)))
% 3.26/1.09 -> [25] unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8)))
% 3.26/1.09
% 3.26/1.09 [25] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8)))
% 3.26/1.09
% 3.26/1.09 [24] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8)))
% 3.26/1.09
% 3.26/1.09 [26] BETA_IMPLY : ((unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(reverse_line(M38_24_8))))) => ((unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(reverse_line(M38_24_8))))) | (unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(reverse_line(M38_24_8)))))))
% 3.26/1.09 -> [270] ~(unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(reverse_line(M38_24_8)))))
% 3.26/1.09 -> [271] ((unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(reverse_line(M38_24_8))))) | (unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(reverse_line(M38_24_8))))))
% 3.26/1.09
% 3.26/1.09 [271] BETA_OR : ((unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(reverse_line(M38_24_8))))) | (unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(reverse_line(M38_24_8))))))
% 3.26/1.09 -> [274] (unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(reverse_line(M38_24_8)))))
% 3.26/1.09 -> [275] (unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(reverse_line(M38_24_8)))))
% 3.26/1.09
% 3.26/1.09 [275] ALPHA_AND : (unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(reverse_line(M38_24_8)))))
% 3.26/1.09 -> [277] unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))), unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(reverse_line(M38_24_8))))
% 3.26/1.09
% 3.26/1.09 [277] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(reverse_line(M38_24_8))))
% 3.26/1.09
% 3.26/1.09 [276] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8)))
% 3.26/1.09
% 3.26/1.09 [270] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))) & unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(reverse_line(M38_24_8)))))
% 3.26/1.09 -> [401] ~unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8)))
% 3.26/1.09 -> [402] ~unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(reverse_line(M38_24_8))))
% 3.26/1.09
% 3.26/1.09 [402] 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)))))
% 3.26/1.09 -> [404] ((line(M36_7_7) & line(M36_7_7)) => (unequally_directed_lines(M36_7_7, M36_7_7) | unequally_directed_lines(M36_7_7, reverse_line(M36_7_7))))
% 3.26/1.09
% 3.26/1.09 [404] BETA_IMPLY : ((line(M36_7_7) & line(M36_7_7)) => (unequally_directed_lines(M36_7_7, M36_7_7) | unequally_directed_lines(M36_7_7, reverse_line(M36_7_7))))
% 3.26/1.09 -> [407] ~(line(M36_7_7) & line(M36_7_7))
% 3.26/1.09 -> [408] (unequally_directed_lines(M36_7_7, M36_7_7) | unequally_directed_lines(M36_7_7, reverse_line(M36_7_7)))
% 3.26/1.09
% 3.26/1.09 [408] BETA_OR : (unequally_directed_lines(M36_7_7, M36_7_7) | unequally_directed_lines(M36_7_7, reverse_line(M36_7_7)))
% 3.26/1.09 -> [415] unequally_directed_lines(M36_7_7, M36_7_7)
% 3.26/1.09 -> [416] unequally_directed_lines(M36_7_7, reverse_line(M36_7_7))
% 3.26/1.09
% 3.26/1.09 [415] CLOSURE : unequally_directed_lines(M36_7_7, M36_7_7)
% 3.26/1.09
% 3.26/1.09 [416] CLOSURE : unequally_directed_lines(M36_7_7, reverse_line(M36_7_7))
% 3.26/1.09
% 3.26/1.09 [407] BETA_NOT_AND : ~(line(M36_7_7) & line(M36_7_7))
% 3.26/1.09 -> [411] ~line(M36_7_7)
% 3.26/1.09 -> [412] ~line(M36_7_7)
% 3.26/1.09
% 3.26/1.09 [411] 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)))))
% 3.26/1.09 -> [418] ((unequally_directed_lines(L37_21_8, M38_21_8) & unequally_directed_lines(L37_21_8, reverse_line(M38_21_8))) => (left_convergent_lines(L37_21_8, M38_21_8) | left_convergent_lines(L37_21_8, reverse_line(M38_21_8))))
% 3.26/1.09
% 3.26/1.09 [418] BETA_IMPLY : ((unequally_directed_lines(L37_21_8, M38_21_8) & unequally_directed_lines(L37_21_8, reverse_line(M38_21_8))) => (left_convergent_lines(L37_21_8, M38_21_8) | left_convergent_lines(L37_21_8, reverse_line(M38_21_8))))
% 3.26/1.09 -> [421] ~(unequally_directed_lines(L37_21_8, M38_21_8) & unequally_directed_lines(L37_21_8, reverse_line(M38_21_8)))
% 3.26/1.09 -> [422] (left_convergent_lines(L37_21_8, M38_21_8) | left_convergent_lines(L37_21_8, reverse_line(M38_21_8)))
% 3.26/1.09
% 3.26/1.09 [421] BETA_NOT_AND : ~(unequally_directed_lines(L37_21_8, M38_21_8) & unequally_directed_lines(L37_21_8, reverse_line(M38_21_8)))
% 3.26/1.09 -> [431] ~unequally_directed_lines(L37_21_8, M38_21_8)
% 3.26/1.09 -> [432] ~unequally_directed_lines(L37_21_8, reverse_line(M38_21_8))
% 3.26/1.09
% 3.26/1.09 [432] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 3.26/1.09 -> [447] ~(left_apart_point(A39_79_9, L40_79_9) | left_apart_point(A39_79_9, reverse_line(L40_79_9)))
% 3.26/1.09
% 3.26/1.09 [447] ALPHA_NOT_OR : ~(left_apart_point(A39_79_9, L40_79_9) | left_apart_point(A39_79_9, reverse_line(L40_79_9)))
% 3.26/1.09 -> [448] ~left_apart_point(A39_79_9, L40_79_9), ~left_apart_point(A39_79_9, reverse_line(L40_79_9))
% 3.26/1.09
% 3.26/1.09 [448] CLOSURE : ~left_apart_point(A39_79_9, L40_79_9)
% 3.26/1.09
% 3.26/1.09 [431] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 3.26/1.09 -> [468] ~(left_apart_point(A39_87_9, L40_87_9) | left_apart_point(A39_87_9, reverse_line(L40_87_9)))
% 3.26/1.09
% 3.26/1.09 [468] ALPHA_NOT_OR : ~(left_apart_point(A39_87_9, L40_87_9) | left_apart_point(A39_87_9, reverse_line(L40_87_9)))
% 3.26/1.09 -> [472] ~left_apart_point(A39_87_9, L40_87_9), ~left_apart_point(A39_87_9, reverse_line(L40_87_9))
% 3.26/1.09
% 3.26/1.09 [472] CLOSURE : ~left_apart_point(A39_87_9, L40_87_9)
% 3.26/1.09
% 3.26/1.09 [422] BETA_OR : (left_convergent_lines(L37_21_8, M38_21_8) | left_convergent_lines(L37_21_8, reverse_line(M38_21_8)))
% 3.26/1.09 -> [437] left_convergent_lines(L37_21_8, M38_21_8)
% 3.26/1.09 -> [438] left_convergent_lines(L37_21_8, reverse_line(M38_21_8))
% 3.26/1.09
% 3.26/1.09 [437] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 3.26/1.09 -> [470] ~(left_apart_point(A39_88_9, L40_88_9) | left_apart_point(A39_88_9, reverse_line(L40_88_9)))
% 3.26/1.09
% 3.26/1.09 [470] ALPHA_NOT_OR : ~(left_apart_point(A39_88_9, L40_88_9) | left_apart_point(A39_88_9, reverse_line(L40_88_9)))
% 3.26/1.09 -> [474] ~left_apart_point(A39_88_9, L40_88_9), ~left_apart_point(A39_88_9, reverse_line(L40_88_9))
% 3.26/1.09
% 3.26/1.09 [474] CLOSURE : ~left_apart_point(A39_88_9, L40_88_9)
% 3.26/1.09
% 3.26/1.09 [438] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 3.26/1.09 -> [480] ~(left_apart_point(A39_92_9, L40_92_9) | left_apart_point(A39_92_9, reverse_line(L40_92_9)))
% 3.26/1.09
% 3.26/1.09 [480] ALPHA_NOT_OR : ~(left_apart_point(A39_92_9, L40_92_9) | left_apart_point(A39_92_9, reverse_line(L40_92_9)))
% 3.26/1.09 -> [484] ~left_apart_point(A39_92_9, L40_92_9), ~left_apart_point(A39_92_9, reverse_line(L40_92_9))
% 3.26/1.09
% 3.26/1.09 [484] CLOSURE : ~left_apart_point(A39_92_9, L40_92_9)
% 3.26/1.09
% 3.26/1.09 [412] 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)))))
% 3.26/1.09 -> [424] ((unequally_directed_lines(L37_23_8, M38_23_8) & unequally_directed_lines(L37_23_8, reverse_line(M38_23_8))) => (left_convergent_lines(L37_23_8, M38_23_8) | left_convergent_lines(L37_23_8, reverse_line(M38_23_8))))
% 3.26/1.09
% 3.26/1.09 [424] BETA_IMPLY : ((unequally_directed_lines(L37_23_8, M38_23_8) & unequally_directed_lines(L37_23_8, reverse_line(M38_23_8))) => (left_convergent_lines(L37_23_8, M38_23_8) | left_convergent_lines(L37_23_8, reverse_line(M38_23_8))))
% 3.26/1.09 -> [429] ~(unequally_directed_lines(L37_23_8, M38_23_8) & unequally_directed_lines(L37_23_8, reverse_line(M38_23_8)))
% 3.26/1.09 -> [430] (left_convergent_lines(L37_23_8, M38_23_8) | left_convergent_lines(L37_23_8, reverse_line(M38_23_8)))
% 3.26/1.09
% 3.26/1.09 [429] BETA_NOT_AND : ~(unequally_directed_lines(L37_23_8, M38_23_8) & unequally_directed_lines(L37_23_8, reverse_line(M38_23_8)))
% 3.26/1.09 -> [435] ~unequally_directed_lines(L37_23_8, M38_23_8)
% 3.26/1.09 -> [436] ~unequally_directed_lines(L37_23_8, reverse_line(M38_23_8))
% 3.26/1.09
% 3.26/1.09 [435] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 3.26/1.09 -> [450] ~(left_apart_point(A39_81_9, L40_81_9) | left_apart_point(A39_81_9, reverse_line(L40_81_9)))
% 3.26/1.09
% 3.26/1.09 [450] ALPHA_NOT_OR : ~(left_apart_point(A39_81_9, L40_81_9) | left_apart_point(A39_81_9, reverse_line(L40_81_9)))
% 3.26/1.09 -> [453] ~left_apart_point(A39_81_9, L40_81_9), ~left_apart_point(A39_81_9, reverse_line(L40_81_9))
% 3.26/1.09
% 3.26/1.09 [453] CLOSURE : ~left_apart_point(A39_81_9, L40_81_9)
% 3.26/1.09
% 3.26/1.09 [436] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 3.26/1.09 -> [458] ~(left_apart_point(A39_84_9, L40_84_9) | left_apart_point(A39_84_9, reverse_line(L40_84_9)))
% 3.26/1.09
% 3.26/1.09 [458] ALPHA_NOT_OR : ~(left_apart_point(A39_84_9, L40_84_9) | left_apart_point(A39_84_9, reverse_line(L40_84_9)))
% 3.26/1.09 -> [461] ~left_apart_point(A39_84_9, L40_84_9), ~left_apart_point(A39_84_9, reverse_line(L40_84_9))
% 3.26/1.09
% 3.26/1.09 [461] CLOSURE : ~left_apart_point(A39_84_9, L40_84_9)
% 3.26/1.09
% 3.26/1.09 [430] BETA_OR : (left_convergent_lines(L37_23_8, M38_23_8) | left_convergent_lines(L37_23_8, reverse_line(M38_23_8)))
% 3.26/1.09 -> [445] left_convergent_lines(L37_23_8, M38_23_8)
% 3.26/1.09 -> [446] left_convergent_lines(L37_23_8, reverse_line(M38_23_8))
% 3.26/1.09
% 3.26/1.09 [445] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 3.26/1.09 -> [462] ~(left_apart_point(A39_85_9, L40_85_9) | left_apart_point(A39_85_9, reverse_line(L40_85_9)))
% 3.26/1.09
% 3.26/1.09 [462] ALPHA_NOT_OR : ~(left_apart_point(A39_85_9, L40_85_9) | left_apart_point(A39_85_9, reverse_line(L40_85_9)))
% 3.26/1.09 -> [469] ~left_apart_point(A39_85_9, L40_85_9), ~left_apart_point(A39_85_9, reverse_line(L40_85_9))
% 3.26/1.09
% 3.26/1.09 [469] CLOSURE : ~left_apart_point(A39_85_9, L40_85_9)
% 3.26/1.09
% 3.26/1.09 [446] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 3.26/1.09 -> [482] ~(left_apart_point(A39_94_9, L40_94_9) | left_apart_point(A39_94_9, reverse_line(L40_94_9)))
% 3.26/1.09
% 3.26/1.09 [482] ALPHA_NOT_OR : ~(left_apart_point(A39_94_9, L40_94_9) | left_apart_point(A39_94_9, reverse_line(L40_94_9)))
% 3.26/1.09 -> [486] ~left_apart_point(A39_94_9, L40_94_9), ~left_apart_point(A39_94_9, reverse_line(L40_94_9))
% 3.26/1.09
% 3.26/1.09 [486] CLOSURE : ~left_apart_point(A39_94_9, L40_94_9)
% 3.26/1.09
% 3.26/1.09 [401] 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)))))
% 3.26/1.09 -> [403] ((line(reverse_line(reverse_line(M38_24_8))) & line(reverse_line(M38_24_8))) => (unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(M38_24_8)) | unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8)))))
% 3.26/1.09
% 3.26/1.09 [403] BETA_IMPLY : ((line(reverse_line(reverse_line(M38_24_8))) & line(reverse_line(M38_24_8))) => (unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(M38_24_8)) | unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8)))))
% 3.26/1.09 -> [405] ~(line(reverse_line(reverse_line(M38_24_8))) & line(reverse_line(M38_24_8)))
% 3.26/1.09 -> [406] (unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(M38_24_8)) | unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))))
% 3.26/1.09
% 3.26/1.09 [405] BETA_NOT_AND : ~(line(reverse_line(reverse_line(M38_24_8))) & line(reverse_line(M38_24_8)))
% 3.26/1.09 -> [409] ~line(reverse_line(reverse_line(M38_24_8)))
% 3.26/1.09 -> [410] ~line(reverse_line(M38_24_8))
% 3.26/1.09
% 3.26/1.09 [410] 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)))))
% 3.26/1.09 -> [417] ((unequally_directed_lines(L37_20_8, M38_20_8) & unequally_directed_lines(L37_20_8, reverse_line(M38_20_8))) => (left_convergent_lines(L37_20_8, M38_20_8) | left_convergent_lines(L37_20_8, reverse_line(M38_20_8))))
% 3.26/1.09
% 3.26/1.09 [417] BETA_IMPLY : ((unequally_directed_lines(L37_20_8, M38_20_8) & unequally_directed_lines(L37_20_8, reverse_line(M38_20_8))) => (left_convergent_lines(L37_20_8, M38_20_8) | left_convergent_lines(L37_20_8, reverse_line(M38_20_8))))
% 3.26/1.09 -> [419] ~(unequally_directed_lines(L37_20_8, M38_20_8) & unequally_directed_lines(L37_20_8, reverse_line(M38_20_8)))
% 3.26/1.09 -> [420] (left_convergent_lines(L37_20_8, M38_20_8) | left_convergent_lines(L37_20_8, reverse_line(M38_20_8)))
% 3.26/1.09
% 3.26/1.09 [419] BETA_NOT_AND : ~(unequally_directed_lines(L37_20_8, M38_20_8) & unequally_directed_lines(L37_20_8, reverse_line(M38_20_8)))
% 3.26/1.09 -> [425] ~unequally_directed_lines(L37_20_8, M38_20_8)
% 3.26/1.09 -> [426] ~unequally_directed_lines(L37_20_8, reverse_line(M38_20_8))
% 3.26/1.09
% 3.26/1.09 [425] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 3.26/1.09 -> [443] ~(left_apart_point(A39_78_9, L40_78_9) | left_apart_point(A39_78_9, reverse_line(L40_78_9)))
% 3.26/1.09
% 3.26/1.09 [443] ALPHA_NOT_OR : ~(left_apart_point(A39_78_9, L40_78_9) | left_apart_point(A39_78_9, reverse_line(L40_78_9)))
% 3.26/1.09 -> [444] ~left_apart_point(A39_78_9, L40_78_9), ~left_apart_point(A39_78_9, reverse_line(L40_78_9))
% 3.26/1.09
% 3.26/1.09 [444] CLOSURE : ~left_apart_point(A39_78_9, L40_78_9)
% 3.26/1.09
% 3.26/1.09 [426] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 3.26/1.09 -> [454] ~(left_apart_point(A39_82_9, L40_82_9) | left_apart_point(A39_82_9, reverse_line(L40_82_9)))
% 3.26/1.09
% 3.26/1.09 [454] ALPHA_NOT_OR : ~(left_apart_point(A39_82_9, L40_82_9) | left_apart_point(A39_82_9, reverse_line(L40_82_9)))
% 3.26/1.09 -> [459] ~left_apart_point(A39_82_9, L40_82_9), ~left_apart_point(A39_82_9, reverse_line(L40_82_9))
% 3.26/1.09
% 3.26/1.09 [459] CLOSURE : ~left_apart_point(A39_82_9, L40_82_9)
% 3.26/1.09
% 3.26/1.09 [420] BETA_OR : (left_convergent_lines(L37_20_8, M38_20_8) | left_convergent_lines(L37_20_8, reverse_line(M38_20_8)))
% 3.26/1.09 -> [433] left_convergent_lines(L37_20_8, M38_20_8)
% 3.26/1.09 -> [434] left_convergent_lines(L37_20_8, reverse_line(M38_20_8))
% 3.26/1.09
% 3.26/1.09 [434] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 3.26/1.09 -> [457] ~(left_apart_point(A39_83_9, L40_83_9) | left_apart_point(A39_83_9, reverse_line(L40_83_9)))
% 3.26/1.09
% 3.26/1.09 [457] ALPHA_NOT_OR : ~(left_apart_point(A39_83_9, L40_83_9) | left_apart_point(A39_83_9, reverse_line(L40_83_9)))
% 3.26/1.09 -> [460] ~left_apart_point(A39_83_9, L40_83_9), ~left_apart_point(A39_83_9, reverse_line(L40_83_9))
% 3.26/1.09
% 3.26/1.09 [460] CLOSURE : ~left_apart_point(A39_83_9, L40_83_9)
% 3.26/1.09
% 3.26/1.09 [433] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 3.26/1.09 -> [476] ~(left_apart_point(A39_90_9, L40_90_9) | left_apart_point(A39_90_9, reverse_line(L40_90_9)))
% 3.26/1.09
% 3.26/1.09 [476] ALPHA_NOT_OR : ~(left_apart_point(A39_90_9, L40_90_9) | left_apart_point(A39_90_9, reverse_line(L40_90_9)))
% 3.26/1.09 -> [477] ~left_apart_point(A39_90_9, L40_90_9), ~left_apart_point(A39_90_9, reverse_line(L40_90_9))
% 3.26/1.09
% 3.26/1.09 [477] CLOSURE : ~left_apart_point(A39_90_9, L40_90_9)
% 3.26/1.09
% 3.26/1.09 [409] 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)))))
% 3.26/1.09 -> [423] ((unequally_directed_lines(L37_22_8, M38_22_8) & unequally_directed_lines(L37_22_8, reverse_line(M38_22_8))) => (left_convergent_lines(L37_22_8, M38_22_8) | left_convergent_lines(L37_22_8, reverse_line(M38_22_8))))
% 3.26/1.09
% 3.26/1.09 [423] BETA_IMPLY : ((unequally_directed_lines(L37_22_8, M38_22_8) & unequally_directed_lines(L37_22_8, reverse_line(M38_22_8))) => (left_convergent_lines(L37_22_8, M38_22_8) | left_convergent_lines(L37_22_8, reverse_line(M38_22_8))))
% 3.26/1.09 -> [427] ~(unequally_directed_lines(L37_22_8, M38_22_8) & unequally_directed_lines(L37_22_8, reverse_line(M38_22_8)))
% 3.26/1.09 -> [428] (left_convergent_lines(L37_22_8, M38_22_8) | left_convergent_lines(L37_22_8, reverse_line(M38_22_8)))
% 3.26/1.09
% 3.26/1.09 [428] BETA_OR : (left_convergent_lines(L37_22_8, M38_22_8) | left_convergent_lines(L37_22_8, reverse_line(M38_22_8)))
% 3.26/1.09 -> [439] left_convergent_lines(L37_22_8, M38_22_8)
% 3.26/1.09 -> [440] left_convergent_lines(L37_22_8, reverse_line(M38_22_8))
% 3.26/1.09
% 3.26/1.09 [439] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 3.26/1.09 -> [473] ~(left_apart_point(A39_89_9, L40_89_9) | left_apart_point(A39_89_9, reverse_line(L40_89_9)))
% 3.26/1.09
% 3.26/1.09 [473] ALPHA_NOT_OR : ~(left_apart_point(A39_89_9, L40_89_9) | left_apart_point(A39_89_9, reverse_line(L40_89_9)))
% 3.26/1.09 -> [475] ~left_apart_point(A39_89_9, L40_89_9), ~left_apart_point(A39_89_9, reverse_line(L40_89_9))
% 3.26/1.09
% 3.26/1.09 [475] CLOSURE : ~left_apart_point(A39_89_9, L40_89_9)
% 3.26/1.09
% 3.26/1.09 [440] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 3.26/1.09 -> [465] ~(left_apart_point(A39_86_9, L40_86_9) | left_apart_point(A39_86_9, reverse_line(L40_86_9)))
% 3.26/1.09
% 3.26/1.09 [465] ALPHA_NOT_OR : ~(left_apart_point(A39_86_9, L40_86_9) | left_apart_point(A39_86_9, reverse_line(L40_86_9)))
% 3.26/1.09 -> [471] ~left_apart_point(A39_86_9, L40_86_9), ~left_apart_point(A39_86_9, reverse_line(L40_86_9))
% 3.26/1.09
% 3.26/1.09 [471] CLOSURE : ~left_apart_point(A39_86_9, L40_86_9)
% 3.26/1.09
% 3.26/1.09 [427] BETA_NOT_AND : ~(unequally_directed_lines(L37_22_8, M38_22_8) & unequally_directed_lines(L37_22_8, reverse_line(M38_22_8)))
% 3.26/1.09 -> [441] ~unequally_directed_lines(L37_22_8, M38_22_8)
% 3.26/1.09 -> [442] ~unequally_directed_lines(L37_22_8, reverse_line(M38_22_8))
% 3.26/1.09
% 3.26/1.09 [442] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 3.26/1.09 -> [449] ~(left_apart_point(A39_80_9, L40_80_9) | left_apart_point(A39_80_9, reverse_line(L40_80_9)))
% 3.26/1.09
% 3.26/1.09 [449] ALPHA_NOT_OR : ~(left_apart_point(A39_80_9, L40_80_9) | left_apart_point(A39_80_9, reverse_line(L40_80_9)))
% 3.26/1.09 -> [452] ~left_apart_point(A39_80_9, L40_80_9), ~left_apart_point(A39_80_9, reverse_line(L40_80_9))
% 3.26/1.09
% 3.26/1.09 [452] CLOSURE : ~left_apart_point(A39_80_9, L40_80_9)
% 3.26/1.09
% 3.26/1.09 [441] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 3.26/1.09 -> [478] ~(left_apart_point(A39_91_9, L40_91_9) | left_apart_point(A39_91_9, reverse_line(L40_91_9)))
% 3.26/1.09
% 3.26/1.09 [478] ALPHA_NOT_OR : ~(left_apart_point(A39_91_9, L40_91_9) | left_apart_point(A39_91_9, reverse_line(L40_91_9)))
% 3.26/1.09 -> [479] ~left_apart_point(A39_91_9, L40_91_9), ~left_apart_point(A39_91_9, reverse_line(L40_91_9))
% 3.26/1.09
% 3.26/1.09 [479] CLOSURE : ~left_apart_point(A39_91_9, L40_91_9)
% 3.26/1.09
% 3.26/1.09 [406] BETA_OR : (unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(M38_24_8)) | unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8))))
% 3.26/1.09 -> [413] unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(M38_24_8))
% 3.26/1.09 -> [414] unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8)))
% 3.26/1.09
% 3.26/1.09 [414] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(reverse_line(M38_24_8)))
% 3.26/1.09
% 3.26/1.09 [413] 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)))))
% 3.26/1.09 -> [451] ((unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), M38_24_8) & unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(M38_24_8))) => (left_convergent_lines(reverse_line(reverse_line(M38_24_8)), M38_24_8) | left_convergent_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(M38_24_8))))
% 3.26/1.09
% 3.26/1.09 [451] BETA_IMPLY : ((unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), M38_24_8) & unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(M38_24_8))) => (left_convergent_lines(reverse_line(reverse_line(M38_24_8)), M38_24_8) | left_convergent_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(M38_24_8))))
% 3.26/1.09 -> [455] ~(unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), M38_24_8) & unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(M38_24_8)))
% 3.26/1.09 -> [456] (left_convergent_lines(reverse_line(reverse_line(M38_24_8)), M38_24_8) | left_convergent_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(M38_24_8)))
% 3.26/1.09
% 3.26/1.09 [456] BETA_OR : (left_convergent_lines(reverse_line(reverse_line(M38_24_8)), M38_24_8) | left_convergent_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(M38_24_8)))
% 3.26/1.09 -> [463] left_convergent_lines(reverse_line(reverse_line(M38_24_8)), M38_24_8)
% 3.26/1.09 -> [464] left_convergent_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(M38_24_8))
% 3.26/1.09
% 3.26/1.09 [464] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 3.26/1.09 -> [481] ~(left_apart_point(A39_93_9, L40_93_9) | left_apart_point(A39_93_9, reverse_line(L40_93_9)))
% 3.26/1.09
% 3.26/1.09 [481] ALPHA_NOT_OR : ~(left_apart_point(A39_93_9, L40_93_9) | left_apart_point(A39_93_9, reverse_line(L40_93_9)))
% 3.26/1.09 -> [485] ~left_apart_point(A39_93_9, L40_93_9), ~left_apart_point(A39_93_9, reverse_line(L40_93_9))
% 3.26/1.09
% 3.26/1.09 [485] CLOSURE : ~left_apart_point(A39_93_9, L40_93_9)
% 3.26/1.09
% 3.26/1.09 [463] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 3.26/1.09 -> [483] ~(left_apart_point(A39_95_9, L40_95_9) | left_apart_point(A39_95_9, reverse_line(L40_95_9)))
% 3.26/1.09
% 3.26/1.09 [483] ALPHA_NOT_OR : ~(left_apart_point(A39_95_9, L40_95_9) | left_apart_point(A39_95_9, reverse_line(L40_95_9)))
% 3.26/1.09 -> [487] ~left_apart_point(A39_95_9, L40_95_9), ~left_apart_point(A39_95_9, reverse_line(L40_95_9))
% 3.26/1.09
% 3.26/1.09 [487] CLOSURE : ~left_apart_point(A39_95_9, L40_95_9)
% 3.26/1.09
% 3.26/1.09 [455] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), M38_24_8) & unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(M38_24_8)))
% 3.26/1.09 -> [466] ~unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), M38_24_8)
% 3.26/1.09 -> [467] ~unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(M38_24_8))
% 3.26/1.09
% 3.26/1.09 [467] CLOSURE : ~unequally_directed_lines(reverse_line(reverse_line(M38_24_8)), reverse_line(M38_24_8))
% 3.26/1.09
% 3.26/1.09 [466] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 3.26/1.09 -> [488] ~(left_apart_point(A39_96_9, L40_96_9) | left_apart_point(A39_96_9, reverse_line(L40_96_9)))
% 3.26/1.09
% 3.26/1.09 [488] ALPHA_NOT_OR : ~(left_apart_point(A39_96_9, L40_96_9) | left_apart_point(A39_96_9, reverse_line(L40_96_9)))
% 3.26/1.09 -> [489] ~left_apart_point(A39_96_9, L40_96_9), ~left_apart_point(A39_96_9, reverse_line(L40_96_9))
% 3.26/1.09
% 3.26/1.09 [489] CLOSURE : ~left_apart_point(A39_96_9, L40_96_9)
% 3.26/1.09
% 3.26/1.09 % SZS output end Proof for theBenchmark.p
% 3.26/1.09 [0.750425s][1][Res] 3282 goroutines created
% 3.26/1.09 ==== Result ====
% 3.26/1.09 [0.750449s][1][Res] VALID
% 3.26/1.09 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------