TSTP Solution File: GEO236+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO236+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n029.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 15:18:37 EDT 2022
% Result : Theorem 2.19s 0.84s
% Output : Proof 2.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO236+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.07/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 07:17:42 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 [DMT] DMT loaded with preskolemization
% 0.13/0.35 [EQ] equality loaded.
% 0.13/0.35 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.35 Conjecture not found
% 0.13/0.35 Start search
% 0.13/0.35 nb_step : 1 - limit : 32
% 0.13/0.35 Launch Gotab with destructive = true
% 2.19/0.83 % SZS output start Proof for theBenchmark.p
% 2.19/0.83 [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, L78_78, M79_79] : (((left_apart_point(A77_77, L78_78) & left_apart_point(A77_77, reverse_line(M79_79))) => (unequally_directed_lines(L78_78, M79_79) | distinct_lines(L78_78, M79_79)))))
% 2.19/0.83 -> [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, L78_78, M79_79] : (((left_apart_point(A77_77, L78_78) & left_apart_point(A77_77, reverse_line(M79_79))) => (unequally_directed_lines(L78_78, M79_79) | distinct_lines(L78_78, M79_79))))
% 2.19/0.83
% 2.19/0.83 [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)))))
% 2.19/0.83 -> [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))))
% 2.19/0.83
% 2.19/0.83 [2] DELTA_NOT_FORALL : ~! [A77_77, L78_78, M79_79] : (((left_apart_point(A77_77, L78_78) & left_apart_point(A77_77, reverse_line(M79_79))) => (unequally_directed_lines(L78_78, M79_79) | distinct_lines(L78_78, M79_79))))
% 2.19/0.83 -> [3] ~((left_apart_point(skolem_A7777, skolem_L7878) & left_apart_point(skolem_A7777, reverse_line(skolem_M7979))) => (unequally_directed_lines(skolem_L7878, skolem_M7979) | distinct_lines(skolem_L7878, skolem_M7979)))
% 2.19/0.83
% 2.19/0.83 [3] ALPHA_NOT_IMPLY : ~((left_apart_point(skolem_A7777, skolem_L7878) & left_apart_point(skolem_A7777, reverse_line(skolem_M7979))) => (unequally_directed_lines(skolem_L7878, skolem_M7979) | distinct_lines(skolem_L7878, skolem_M7979)))
% 2.19/0.83 -> [4] (left_apart_point(skolem_A7777, skolem_L7878) & left_apart_point(skolem_A7777, reverse_line(skolem_M7979))), ~(unequally_directed_lines(skolem_L7878, skolem_M7979) | distinct_lines(skolem_L7878, skolem_M7979))
% 2.19/0.83
% 2.19/0.83 [4] ALPHA_AND : (left_apart_point(skolem_A7777, skolem_L7878) & left_apart_point(skolem_A7777, reverse_line(skolem_M7979)))
% 2.19/0.83 -> [5] left_apart_point(skolem_A7777, skolem_L7878), left_apart_point(skolem_A7777, reverse_line(skolem_M7979))
% 2.19/0.83
% 2.19/0.83 [5] ALPHA_NOT_OR : ~(unequally_directed_lines(skolem_L7878, skolem_M7979) | distinct_lines(skolem_L7878, skolem_M7979))
% 2.19/0.83 -> [6] ~unequally_directed_lines(skolem_L7878, skolem_M7979), ~distinct_lines(skolem_L7878, skolem_M7979)
% 2.19/0.83
% 2.19/0.83 [6] GAMMA_FORALL : ! [A20_20] : (~distinct_points(A20_20, A20_20))
% 2.19/0.83 -> [7] ~distinct_points(C23_0_1, C23_0_1)
% 2.19/0.83
% 2.19/0.83 [7] 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))))
% 2.19/0.83 -> [8] (distinct_points(C23_0_1, C23_0_1) => (distinct_points(C23_0_1, C23_0_1) | distinct_points(C23_0_1, C23_0_1)))
% 2.19/0.83
% 2.19/0.83 [8] BETA_IMPLY : (distinct_points(C23_0_1, C23_0_1) => (distinct_points(C23_0_1, C23_0_1) | distinct_points(C23_0_1, C23_0_1)))
% 2.19/0.83 -> [9] ~distinct_points(C23_0_1, C23_0_1)
% 2.19/0.83 -> [10] (distinct_points(C23_0_1, C23_0_1) | distinct_points(C23_0_1, C23_0_1))
% 2.19/0.83
% 2.19/0.83 [10] BETA_OR : (distinct_points(C23_0_1, C23_0_1) | distinct_points(C23_0_1, C23_0_1))
% 2.19/0.83 -> [11] distinct_points(C23_0_1, C23_0_1)
% 2.19/0.83 -> [12] distinct_points(C23_0_1, C23_0_1)
% 2.19/0.83
% 2.19/0.83 [11] CLOSURE : distinct_points(C23_0_1, C23_0_1)
% 2.19/0.83
% 2.19/0.83 [12] CLOSURE : distinct_points(C23_0_1, C23_0_1)
% 2.19/0.83
% 2.19/0.83 [9] GAMMA_FORALL : ! [L24_24] : (~distinct_lines(L24_24, L24_24))
% 2.19/0.83 -> [13] ~distinct_lines(N27_0_3, N27_0_3)
% 2.19/0.83
% 2.19/0.83 [13] 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))))
% 2.19/0.83 -> [14] (distinct_lines(N27_0_3, N27_0_3) => (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3)))
% 2.19/0.83
% 2.19/0.83 [14] BETA_IMPLY : (distinct_lines(N27_0_3, N27_0_3) => (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3)))
% 2.19/0.83 -> [15] ~distinct_lines(N27_0_3, N27_0_3)
% 2.19/0.83 -> [16] (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3))
% 2.19/0.83
% 2.19/0.83 [16] BETA_OR : (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3))
% 2.19/0.83 -> [17] distinct_lines(N27_0_3, N27_0_3)
% 2.19/0.83 -> [18] distinct_lines(N27_0_3, N27_0_3)
% 2.19/0.83
% 2.19/0.83 [18] CLOSURE : distinct_lines(N27_0_3, N27_0_3)
% 2.19/0.83
% 2.19/0.83 [17] CLOSURE : distinct_lines(N27_0_3, N27_0_3)
% 2.19/0.83
% 2.19/0.83 [15] GAMMA_FORALL : ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28))
% 2.19/0.83 -> [19] ~unequally_directed_lines(skolem_M7979, skolem_M7979)
% 2.19/0.83
% 2.19/0.83 [19] 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))))
% 2.19/0.83 -> [20] (unequally_directed_lines(skolem_M7979, skolem_L7878) => (unequally_directed_lines(skolem_M7979, skolem_M7979) | unequally_directed_lines(skolem_L7878, skolem_M7979)))
% 2.19/0.83
% 2.19/0.83 [20] BETA_IMPLY : (unequally_directed_lines(skolem_M7979, skolem_L7878) => (unequally_directed_lines(skolem_M7979, skolem_M7979) | unequally_directed_lines(skolem_L7878, skolem_M7979)))
% 2.19/0.83 -> [21] ~unequally_directed_lines(skolem_M7979, skolem_L7878)
% 2.19/0.83 -> [22] (unequally_directed_lines(skolem_M7979, skolem_M7979) | unequally_directed_lines(skolem_L7878, skolem_M7979))
% 2.19/0.83
% 2.19/0.83 [22] BETA_OR : (unequally_directed_lines(skolem_M7979, skolem_M7979) | unequally_directed_lines(skolem_L7878, skolem_M7979))
% 2.19/0.83 -> [23] unequally_directed_lines(skolem_M7979, skolem_M7979)
% 2.19/0.83 -> [24] unequally_directed_lines(skolem_L7878, skolem_M7979)
% 2.19/0.83
% 2.19/0.83 [23] CLOSURE : unequally_directed_lines(skolem_M7979, skolem_M7979)
% 2.19/0.83
% 2.19/0.83 [24] CLOSURE : unequally_directed_lines(skolem_L7878, skolem_M7979)
% 2.19/0.83
% 2.19/0.83 [25] BETA_IMPLY : ((unequally_directed_lines(skolem_L7878, skolem_M7979) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_M7979))) => ((unequally_directed_lines(skolem_L7878, skolem_M7979) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_M7979))) | (unequally_directed_lines(skolem_M7979, skolem_M7979) & unequally_directed_lines(skolem_M7979, reverse_line(skolem_M7979)))))
% 2.19/0.83 -> [233] ~(unequally_directed_lines(skolem_L7878, skolem_M7979) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_M7979)))
% 2.19/0.83 -> [234] ((unequally_directed_lines(skolem_L7878, skolem_M7979) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_M7979))) | (unequally_directed_lines(skolem_M7979, skolem_M7979) & unequally_directed_lines(skolem_M7979, reverse_line(skolem_M7979))))
% 2.19/0.83
% 2.19/0.83 [233] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L7878, skolem_M7979) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_M7979)))
% 2.19/0.83 -> [235] ~unequally_directed_lines(skolem_L7878, skolem_M7979)
% 2.19/0.83 -> [236] ~unequally_directed_lines(skolem_L7878, reverse_line(skolem_M7979))
% 2.19/0.83
% 2.19/0.83 [236] 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)))))
% 2.19/0.83 -> [242] ((line(skolem_L7878) & line(skolem_M7979)) => (unequally_directed_lines(skolem_L7878, skolem_M7979) | unequally_directed_lines(skolem_L7878, reverse_line(skolem_M7979))))
% 2.19/0.83
% 2.19/0.83 [242] BETA_IMPLY : ((line(skolem_L7878) & line(skolem_M7979)) => (unequally_directed_lines(skolem_L7878, skolem_M7979) | unequally_directed_lines(skolem_L7878, reverse_line(skolem_M7979))))
% 2.19/0.83 -> [245] ~(line(skolem_L7878) & line(skolem_M7979))
% 2.19/0.83 -> [246] (unequally_directed_lines(skolem_L7878, skolem_M7979) | unequally_directed_lines(skolem_L7878, reverse_line(skolem_M7979)))
% 2.19/0.83
% 2.19/0.83 [246] BETA_OR : (unequally_directed_lines(skolem_L7878, skolem_M7979) | unequally_directed_lines(skolem_L7878, reverse_line(skolem_M7979)))
% 2.19/0.83 -> [253] unequally_directed_lines(skolem_L7878, skolem_M7979)
% 2.19/0.83 -> [254] unequally_directed_lines(skolem_L7878, reverse_line(skolem_M7979))
% 2.19/0.83
% 2.19/0.83 [253] CLOSURE : unequally_directed_lines(skolem_L7878, skolem_M7979)
% 2.19/0.83
% 2.19/0.83 [254] CLOSURE : unequally_directed_lines(skolem_L7878, reverse_line(skolem_M7979))
% 2.19/0.83
% 2.19/0.83 [245] BETA_NOT_AND : ~(line(skolem_L7878) & line(skolem_M7979))
% 2.19/0.83 -> [249] ~line(skolem_L7878)
% 2.19/0.83 -> [250] ~line(skolem_M7979)
% 2.19/0.83
% 2.19/0.83 [250] 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)))))
% 2.19/0.83 -> [257] ((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))))
% 2.19/0.83
% 2.19/0.83 [257] 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))))
% 2.19/0.83 -> [263] ~(unequally_directed_lines(L37_13_8, M38_13_8) & unequally_directed_lines(L37_13_8, reverse_line(M38_13_8)))
% 2.19/0.83 -> [264] (left_convergent_lines(L37_13_8, M38_13_8) | left_convergent_lines(L37_13_8, reverse_line(M38_13_8)))
% 2.19/0.83
% 2.19/0.83 [264] BETA_OR : (left_convergent_lines(L37_13_8, M38_13_8) | left_convergent_lines(L37_13_8, reverse_line(M38_13_8)))
% 2.19/0.83 -> [275] left_convergent_lines(L37_13_8, M38_13_8)
% 2.19/0.83 -> [276] left_convergent_lines(L37_13_8, reverse_line(M38_13_8))
% 2.19/0.83
% 2.19/0.83 [276] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.19/0.83 -> [292] ~(left_apart_point(A39_48_9, L40_48_9) | left_apart_point(A39_48_9, reverse_line(L40_48_9)))
% 2.19/0.83
% 2.19/0.83 [292] ALPHA_NOT_OR : ~(left_apart_point(A39_48_9, L40_48_9) | left_apart_point(A39_48_9, reverse_line(L40_48_9)))
% 2.19/0.83 -> [297] ~left_apart_point(A39_48_9, L40_48_9), ~left_apart_point(A39_48_9, reverse_line(L40_48_9))
% 2.19/0.83
% 2.19/0.83 [297] CLOSURE : ~left_apart_point(A39_48_9, L40_48_9)
% 2.19/0.83
% 2.19/0.83 [275] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.19/0.83 -> [293] ~(left_apart_point(A39_49_9, L40_49_9) | left_apart_point(A39_49_9, reverse_line(L40_49_9)))
% 2.19/0.83
% 2.19/0.83 [293] ALPHA_NOT_OR : ~(left_apart_point(A39_49_9, L40_49_9) | left_apart_point(A39_49_9, reverse_line(L40_49_9)))
% 2.19/0.84 -> [298] ~left_apart_point(A39_49_9, L40_49_9), ~left_apart_point(A39_49_9, reverse_line(L40_49_9))
% 2.19/0.84
% 2.19/0.84 [298] CLOSURE : ~left_apart_point(A39_49_9, L40_49_9)
% 2.19/0.84
% 2.19/0.84 [263] BETA_NOT_AND : ~(unequally_directed_lines(L37_13_8, M38_13_8) & unequally_directed_lines(L37_13_8, reverse_line(M38_13_8)))
% 2.19/0.84 -> [285] ~unequally_directed_lines(L37_13_8, M38_13_8)
% 2.19/0.84 -> [286] ~unequally_directed_lines(L37_13_8, reverse_line(M38_13_8))
% 2.19/0.84
% 2.19/0.84 [286] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.19/0.84 -> [296] ~(left_apart_point(A39_52_9, L40_52_9) | left_apart_point(A39_52_9, reverse_line(L40_52_9)))
% 2.19/0.84
% 2.19/0.84 [296] ALPHA_NOT_OR : ~(left_apart_point(A39_52_9, L40_52_9) | left_apart_point(A39_52_9, reverse_line(L40_52_9)))
% 2.19/0.84 -> [304] ~left_apart_point(A39_52_9, L40_52_9), ~left_apart_point(A39_52_9, reverse_line(L40_52_9))
% 2.19/0.84
% 2.19/0.84 [304] CLOSURE : ~left_apart_point(A39_52_9, L40_52_9)
% 2.19/0.84
% 2.19/0.84 [285] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.19/0.84 -> [302] ~(left_apart_point(A39_54_9, L40_54_9) | left_apart_point(A39_54_9, reverse_line(L40_54_9)))
% 2.19/0.84
% 2.19/0.84 [302] ALPHA_NOT_OR : ~(left_apart_point(A39_54_9, L40_54_9) | left_apart_point(A39_54_9, reverse_line(L40_54_9)))
% 2.19/0.84 -> [306] ~left_apart_point(A39_54_9, L40_54_9), ~left_apart_point(A39_54_9, reverse_line(L40_54_9))
% 2.19/0.84
% 2.19/0.84 [306] CLOSURE : ~left_apart_point(A39_54_9, L40_54_9)
% 2.19/0.84
% 2.19/0.84 [249] 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)))))
% 2.19/0.84 -> [262] ((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))))
% 2.19/0.84
% 2.19/0.84 [262] 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))))
% 2.19/0.84 -> [267] ~(unequally_directed_lines(L37_14_8, M38_14_8) & unequally_directed_lines(L37_14_8, reverse_line(M38_14_8)))
% 2.19/0.84 -> [268] (left_convergent_lines(L37_14_8, M38_14_8) | left_convergent_lines(L37_14_8, reverse_line(M38_14_8)))
% 2.19/0.84
% 2.19/0.84 [267] BETA_NOT_AND : ~(unequally_directed_lines(L37_14_8, M38_14_8) & unequally_directed_lines(L37_14_8, reverse_line(M38_14_8)))
% 2.19/0.84 -> [279] ~unequally_directed_lines(L37_14_8, M38_14_8)
% 2.19/0.84 -> [280] ~unequally_directed_lines(L37_14_8, reverse_line(M38_14_8))
% 2.19/0.84
% 2.19/0.84 [279] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.19/0.84 -> [284] ~(left_apart_point(A39_45_9, L40_45_9) | left_apart_point(A39_45_9, reverse_line(L40_45_9)))
% 2.19/0.84
% 2.19/0.84 [284] ALPHA_NOT_OR : ~(left_apart_point(A39_45_9, L40_45_9) | left_apart_point(A39_45_9, reverse_line(L40_45_9)))
% 2.19/0.84 -> [287] ~left_apart_point(A39_45_9, L40_45_9), ~left_apart_point(A39_45_9, reverse_line(L40_45_9))
% 2.19/0.84
% 2.19/0.84 [287] CLOSURE : ~left_apart_point(A39_45_9, L40_45_9)
% 2.19/0.84
% 2.19/0.84 [280] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.19/0.84 -> [307] ~(left_apart_point(A39_55_9, L40_55_9) | left_apart_point(A39_55_9, reverse_line(L40_55_9)))
% 2.19/0.84
% 2.19/0.84 [307] ALPHA_NOT_OR : ~(left_apart_point(A39_55_9, L40_55_9) | left_apart_point(A39_55_9, reverse_line(L40_55_9)))
% 2.19/0.84 -> [309] ~left_apart_point(A39_55_9, L40_55_9), ~left_apart_point(A39_55_9, reverse_line(L40_55_9))
% 2.19/0.84
% 2.19/0.84 [309] CLOSURE : ~left_apart_point(A39_55_9, L40_55_9)
% 2.19/0.84
% 2.19/0.84 [268] BETA_OR : (left_convergent_lines(L37_14_8, M38_14_8) | left_convergent_lines(L37_14_8, reverse_line(M38_14_8)))
% 2.19/0.84 -> [277] left_convergent_lines(L37_14_8, M38_14_8)
% 2.19/0.84 -> [278] left_convergent_lines(L37_14_8, reverse_line(M38_14_8))
% 2.19/0.84
% 2.19/0.84 [278] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.19/0.84 -> [294] ~(left_apart_point(A39_50_9, L40_50_9) | left_apart_point(A39_50_9, reverse_line(L40_50_9)))
% 2.19/0.84
% 2.19/0.84 [294] ALPHA_NOT_OR : ~(left_apart_point(A39_50_9, L40_50_9) | left_apart_point(A39_50_9, reverse_line(L40_50_9)))
% 2.19/0.84 -> [303] ~left_apart_point(A39_50_9, L40_50_9), ~left_apart_point(A39_50_9, reverse_line(L40_50_9))
% 2.19/0.84
% 2.19/0.84 [303] CLOSURE : ~left_apart_point(A39_50_9, L40_50_9)
% 2.19/0.84
% 2.19/0.84 [277] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.19/0.84 -> [311] ~(left_apart_point(A39_58_9, L40_58_9) | left_apart_point(A39_58_9, reverse_line(L40_58_9)))
% 2.19/0.84
% 2.19/0.84 [311] ALPHA_NOT_OR : ~(left_apart_point(A39_58_9, L40_58_9) | left_apart_point(A39_58_9, reverse_line(L40_58_9)))
% 2.19/0.84 -> [314] ~left_apart_point(A39_58_9, L40_58_9), ~left_apart_point(A39_58_9, reverse_line(L40_58_9))
% 2.19/0.84
% 2.19/0.84 [314] CLOSURE : ~left_apart_point(A39_58_9, L40_58_9)
% 2.19/0.84
% 2.19/0.84 [241] BETA_IMPLY : ((line(skolem_L7878) & line(skolem_M7979)) => (unequally_directed_lines(skolem_L7878, skolem_M7979) | unequally_directed_lines(skolem_L7878, reverse_line(skolem_M7979))))
% 2.19/0.84 -> [315] ~(line(skolem_L7878) & line(skolem_M7979))
% 2.19/0.84 -> [316] (unequally_directed_lines(skolem_L7878, skolem_M7979) | unequally_directed_lines(skolem_L7878, reverse_line(skolem_M7979)))
% 2.19/0.84
% 2.19/0.84 [315] BETA_NOT_AND : ~(line(skolem_L7878) & line(skolem_M7979))
% 2.19/0.84 -> [317] ~line(skolem_L7878)
% 2.19/0.84 -> [318] ~line(skolem_M7979)
% 2.19/0.84
% 2.19/0.84 [318] 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)))))
% 2.19/0.84 -> [322] ((unequally_directed_lines(L37_16_8, M38_16_8) & unequally_directed_lines(L37_16_8, reverse_line(M38_16_8))) => (left_convergent_lines(L37_16_8, M38_16_8) | left_convergent_lines(L37_16_8, reverse_line(M38_16_8))))
% 2.19/0.84
% 2.19/0.84 [322] BETA_IMPLY : ((unequally_directed_lines(L37_16_8, M38_16_8) & unequally_directed_lines(L37_16_8, reverse_line(M38_16_8))) => (left_convergent_lines(L37_16_8, M38_16_8) | left_convergent_lines(L37_16_8, reverse_line(M38_16_8))))
% 2.19/0.84 -> [326] ~(unequally_directed_lines(L37_16_8, M38_16_8) & unequally_directed_lines(L37_16_8, reverse_line(M38_16_8)))
% 2.19/0.84 -> [327] (left_convergent_lines(L37_16_8, M38_16_8) | left_convergent_lines(L37_16_8, reverse_line(M38_16_8)))
% 2.19/0.84
% 2.19/0.84 [327] BETA_OR : (left_convergent_lines(L37_16_8, M38_16_8) | left_convergent_lines(L37_16_8, reverse_line(M38_16_8)))
% 2.19/0.84 -> [338] left_convergent_lines(L37_16_8, M38_16_8)
% 2.19/0.84 -> [339] left_convergent_lines(L37_16_8, reverse_line(M38_16_8))
% 2.19/0.84
% 2.19/0.84 [339] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.19/0.84 -> [349] ~(left_apart_point(A39_63_9, L40_63_9) | left_apart_point(A39_63_9, reverse_line(L40_63_9)))
% 2.19/0.84
% 2.19/0.84 [349] ALPHA_NOT_OR : ~(left_apart_point(A39_63_9, L40_63_9) | left_apart_point(A39_63_9, reverse_line(L40_63_9)))
% 2.19/0.84 -> [353] ~left_apart_point(A39_63_9, L40_63_9), ~left_apart_point(A39_63_9, reverse_line(L40_63_9))
% 2.19/0.84
% 2.19/0.84 [353] CLOSURE : ~left_apart_point(A39_63_9, L40_63_9)
% 2.19/0.84
% 2.19/0.84 [338] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.19/0.84 -> [352] ~(left_apart_point(A39_65_9, L40_65_9) | left_apart_point(A39_65_9, reverse_line(L40_65_9)))
% 2.19/0.84
% 2.19/0.84 [352] ALPHA_NOT_OR : ~(left_apart_point(A39_65_9, L40_65_9) | left_apart_point(A39_65_9, reverse_line(L40_65_9)))
% 2.19/0.84 -> [356] ~left_apart_point(A39_65_9, L40_65_9), ~left_apart_point(A39_65_9, reverse_line(L40_65_9))
% 2.19/0.84
% 2.19/0.84 [356] CLOSURE : ~left_apart_point(A39_65_9, L40_65_9)
% 2.19/0.84
% 2.19/0.84 [326] BETA_NOT_AND : ~(unequally_directed_lines(L37_16_8, M38_16_8) & unequally_directed_lines(L37_16_8, reverse_line(M38_16_8)))
% 2.19/0.84 -> [334] ~unequally_directed_lines(L37_16_8, M38_16_8)
% 2.19/0.84 -> [335] ~unequally_directed_lines(L37_16_8, reverse_line(M38_16_8))
% 2.19/0.84
% 2.19/0.84 [335] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.19/0.84 -> [344] ~(left_apart_point(A39_60_9, L40_60_9) | left_apart_point(A39_60_9, reverse_line(L40_60_9)))
% 2.19/0.84
% 2.19/0.84 [344] ALPHA_NOT_OR : ~(left_apart_point(A39_60_9, L40_60_9) | left_apart_point(A39_60_9, reverse_line(L40_60_9)))
% 2.19/0.84 -> [346] ~left_apart_point(A39_60_9, L40_60_9), ~left_apart_point(A39_60_9, reverse_line(L40_60_9))
% 2.19/0.84
% 2.19/0.84 [346] CLOSURE : ~left_apart_point(A39_60_9, L40_60_9)
% 2.19/0.84
% 2.19/0.84 [334] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.19/0.84 -> [354] ~(left_apart_point(A39_66_9, L40_66_9) | left_apart_point(A39_66_9, reverse_line(L40_66_9)))
% 2.19/0.84
% 2.19/0.84 [354] ALPHA_NOT_OR : ~(left_apart_point(A39_66_9, L40_66_9) | left_apart_point(A39_66_9, reverse_line(L40_66_9)))
% 2.19/0.84 -> [357] ~left_apart_point(A39_66_9, L40_66_9), ~left_apart_point(A39_66_9, reverse_line(L40_66_9))
% 2.19/0.84
% 2.19/0.84 [357] CLOSURE : ~left_apart_point(A39_66_9, L40_66_9)
% 2.19/0.84
% 2.19/0.84 [317] GAMMA_FORALL : ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38)))))
% 2.19/0.84 -> [321] ((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))))
% 2.19/0.84
% 2.19/0.84 [321] 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))))
% 2.19/0.84 -> [324] ~(unequally_directed_lines(L37_15_8, M38_15_8) & unequally_directed_lines(L37_15_8, reverse_line(M38_15_8)))
% 2.19/0.84 -> [325] (left_convergent_lines(L37_15_8, M38_15_8) | left_convergent_lines(L37_15_8, reverse_line(M38_15_8)))
% 2.19/0.84
% 2.19/0.84 [324] BETA_NOT_AND : ~(unequally_directed_lines(L37_15_8, M38_15_8) & unequally_directed_lines(L37_15_8, reverse_line(M38_15_8)))
% 2.19/0.84 -> [330] ~unequally_directed_lines(L37_15_8, M38_15_8)
% 2.19/0.84 -> [331] ~unequally_directed_lines(L37_15_8, reverse_line(M38_15_8))
% 2.19/0.84
% 2.19/0.84 [330] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.19/0.84 -> [342] ~(left_apart_point(A39_59_9, L40_59_9) | left_apart_point(A39_59_9, reverse_line(L40_59_9)))
% 2.19/0.84
% 2.19/0.84 [342] ALPHA_NOT_OR : ~(left_apart_point(A39_59_9, L40_59_9) | left_apart_point(A39_59_9, reverse_line(L40_59_9)))
% 2.19/0.84 -> [343] ~left_apart_point(A39_59_9, L40_59_9), ~left_apart_point(A39_59_9, reverse_line(L40_59_9))
% 2.19/0.84
% 2.19/0.84 [343] CLOSURE : ~left_apart_point(A39_59_9, L40_59_9)
% 2.19/0.84
% 2.19/0.84 [331] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.19/0.84 -> [347] ~(left_apart_point(A39_62_9, L40_62_9) | left_apart_point(A39_62_9, reverse_line(L40_62_9)))
% 2.19/0.84
% 2.19/0.84 [347] ALPHA_NOT_OR : ~(left_apart_point(A39_62_9, L40_62_9) | left_apart_point(A39_62_9, reverse_line(L40_62_9)))
% 2.19/0.84 -> [351] ~left_apart_point(A39_62_9, L40_62_9), ~left_apart_point(A39_62_9, reverse_line(L40_62_9))
% 2.19/0.84
% 2.19/0.84 [351] CLOSURE : ~left_apart_point(A39_62_9, L40_62_9)
% 2.19/0.84
% 2.19/0.84 [325] BETA_OR : (left_convergent_lines(L37_15_8, M38_15_8) | left_convergent_lines(L37_15_8, reverse_line(M38_15_8)))
% 2.19/0.84 -> [332] left_convergent_lines(L37_15_8, M38_15_8)
% 2.19/0.84 -> [333] left_convergent_lines(L37_15_8, reverse_line(M38_15_8))
% 2.19/0.84
% 2.19/0.84 [333] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.19/0.84 -> [345] ~(left_apart_point(A39_61_9, L40_61_9) | left_apart_point(A39_61_9, reverse_line(L40_61_9)))
% 2.19/0.84
% 2.19/0.84 [345] ALPHA_NOT_OR : ~(left_apart_point(A39_61_9, L40_61_9) | left_apart_point(A39_61_9, reverse_line(L40_61_9)))
% 2.19/0.84 -> [348] ~left_apart_point(A39_61_9, L40_61_9), ~left_apart_point(A39_61_9, reverse_line(L40_61_9))
% 2.19/0.84
% 2.19/0.84 [348] CLOSURE : ~left_apart_point(A39_61_9, L40_61_9)
% 2.19/0.84
% 2.19/0.84 [332] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.19/0.84 -> [358] ~(left_apart_point(A39_67_9, L40_67_9) | left_apart_point(A39_67_9, reverse_line(L40_67_9)))
% 2.19/0.84
% 2.19/0.84 [358] ALPHA_NOT_OR : ~(left_apart_point(A39_67_9, L40_67_9) | left_apart_point(A39_67_9, reverse_line(L40_67_9)))
% 2.19/0.84 -> [360] ~left_apart_point(A39_67_9, L40_67_9), ~left_apart_point(A39_67_9, reverse_line(L40_67_9))
% 2.19/0.84
% 2.19/0.84 [360] CLOSURE : ~left_apart_point(A39_67_9, L40_67_9)
% 2.19/0.84
% 2.19/0.84 [316] BETA_OR : (unequally_directed_lines(skolem_L7878, skolem_M7979) | unequally_directed_lines(skolem_L7878, reverse_line(skolem_M7979)))
% 2.19/0.84 -> [319] unequally_directed_lines(skolem_L7878, skolem_M7979)
% 2.19/0.84 -> [320] unequally_directed_lines(skolem_L7878, reverse_line(skolem_M7979))
% 2.19/0.84
% 2.19/0.84 [319] CLOSURE : unequally_directed_lines(skolem_L7878, skolem_M7979)
% 2.19/0.84
% 2.19/0.84 [320] 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)))))
% 2.19/0.84 -> [323] ((unequally_directed_lines(L37_17_8, M38_17_8) & unequally_directed_lines(L37_17_8, reverse_line(M38_17_8))) => (left_convergent_lines(L37_17_8, M38_17_8) | left_convergent_lines(L37_17_8, reverse_line(M38_17_8))))
% 2.19/0.84
% 2.19/0.84 [323] BETA_IMPLY : ((unequally_directed_lines(L37_17_8, M38_17_8) & unequally_directed_lines(L37_17_8, reverse_line(M38_17_8))) => (left_convergent_lines(L37_17_8, M38_17_8) | left_convergent_lines(L37_17_8, reverse_line(M38_17_8))))
% 2.19/0.84 -> [328] ~(unequally_directed_lines(L37_17_8, M38_17_8) & unequally_directed_lines(L37_17_8, reverse_line(M38_17_8)))
% 2.19/0.84 -> [329] (left_convergent_lines(L37_17_8, M38_17_8) | left_convergent_lines(L37_17_8, reverse_line(M38_17_8)))
% 2.19/0.84
% 2.19/0.84 [329] BETA_OR : (left_convergent_lines(L37_17_8, M38_17_8) | left_convergent_lines(L37_17_8, reverse_line(M38_17_8)))
% 2.19/0.84 -> [340] left_convergent_lines(L37_17_8, M38_17_8)
% 2.19/0.84 -> [341] left_convergent_lines(L37_17_8, reverse_line(M38_17_8))
% 2.19/0.84
% 2.19/0.84 [340] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.19/0.84 -> [350] ~(left_apart_point(A39_64_9, L40_64_9) | left_apart_point(A39_64_9, reverse_line(L40_64_9)))
% 2.19/0.84
% 2.19/0.84 [350] ALPHA_NOT_OR : ~(left_apart_point(A39_64_9, L40_64_9) | left_apart_point(A39_64_9, reverse_line(L40_64_9)))
% 2.19/0.84 -> [355] ~left_apart_point(A39_64_9, L40_64_9), ~left_apart_point(A39_64_9, reverse_line(L40_64_9))
% 2.19/0.84
% 2.19/0.84 [355] CLOSURE : ~left_apart_point(A39_64_9, L40_64_9)
% 2.19/0.84
% 2.19/0.84 [341] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.19/0.84 -> [359] ~(left_apart_point(A39_68_9, L40_68_9) | left_apart_point(A39_68_9, reverse_line(L40_68_9)))
% 2.19/0.84
% 2.19/0.84 [359] ALPHA_NOT_OR : ~(left_apart_point(A39_68_9, L40_68_9) | left_apart_point(A39_68_9, reverse_line(L40_68_9)))
% 2.19/0.84 -> [361] ~left_apart_point(A39_68_9, L40_68_9), ~left_apart_point(A39_68_9, reverse_line(L40_68_9))
% 2.19/0.84
% 2.19/0.84 [361] CLOSURE : ~left_apart_point(A39_68_9, L40_68_9)
% 2.19/0.84
% 2.19/0.84 [328] BETA_NOT_AND : ~(unequally_directed_lines(L37_17_8, M38_17_8) & unequally_directed_lines(L37_17_8, reverse_line(M38_17_8)))
% 2.19/0.84 -> [336] ~unequally_directed_lines(L37_17_8, M38_17_8)
% 2.19/0.84 -> [337] ~unequally_directed_lines(L37_17_8, reverse_line(M38_17_8))
% 2.19/0.84
% 2.19/0.84 [337] CLOSURE : ~unequally_directed_lines(L37_17_8, reverse_line(M38_17_8))
% 2.19/0.84
% 2.19/0.84 [336] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.19/0.84 -> [362] ~(left_apart_point(A39_69_9, L40_69_9) | left_apart_point(A39_69_9, reverse_line(L40_69_9)))
% 2.19/0.84
% 2.19/0.84 [362] ALPHA_NOT_OR : ~(left_apart_point(A39_69_9, L40_69_9) | left_apart_point(A39_69_9, reverse_line(L40_69_9)))
% 2.19/0.84 -> [363] ~left_apart_point(A39_69_9, L40_69_9), ~left_apart_point(A39_69_9, reverse_line(L40_69_9))
% 2.19/0.84
% 2.19/0.84 [363] CLOSURE : ~left_apart_point(A39_69_9, L40_69_9)
% 2.19/0.84
% 2.19/0.84 [234] BETA_OR : ((unequally_directed_lines(skolem_L7878, skolem_M7979) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_M7979))) | (unequally_directed_lines(skolem_M7979, skolem_M7979) & unequally_directed_lines(skolem_M7979, reverse_line(skolem_M7979))))
% 2.19/0.84 -> [364] (unequally_directed_lines(skolem_L7878, skolem_M7979) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_M7979)))
% 2.19/0.84 -> [365] (unequally_directed_lines(skolem_M7979, skolem_M7979) & unequally_directed_lines(skolem_M7979, reverse_line(skolem_M7979)))
% 2.19/0.84
% 2.19/0.84 [364] ALPHA_AND : (unequally_directed_lines(skolem_L7878, skolem_M7979) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_M7979)))
% 2.19/0.84 -> [366] unequally_directed_lines(skolem_L7878, skolem_M7979), unequally_directed_lines(skolem_L7878, reverse_line(skolem_M7979))
% 2.19/0.84
% 2.19/0.84 [366] CLOSURE : unequally_directed_lines(skolem_L7878, skolem_M7979)
% 2.19/0.84
% 2.19/0.84 [365] ALPHA_AND : (unequally_directed_lines(skolem_M7979, skolem_M7979) & unequally_directed_lines(skolem_M7979, reverse_line(skolem_M7979)))
% 2.19/0.84 -> [367] unequally_directed_lines(skolem_M7979, skolem_M7979), unequally_directed_lines(skolem_M7979, reverse_line(skolem_M7979))
% 2.19/0.84
% 2.19/0.84 [367] CLOSURE : unequally_directed_lines(skolem_M7979, skolem_M7979)
% 2.19/0.84
% 2.19/0.84 % SZS output end Proof for theBenchmark.p
% 2.19/0.84 [0.488020s][1][Res] 1816 goroutines created
% 2.19/0.84 ==== Result ====
% 2.19/0.84 [0.488045s][1][Res] VALID
% 2.19/0.84 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------