TSTP Solution File: GEO240+1 by Goeland---1.0.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO240+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n027.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 15:18:38 EDT 2022
% Result : Theorem 2.18s 0.86s
% Output : Proof 2.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GEO240+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.06/0.12 % Command : goeland -dmt -presko -proof %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 07:23:47 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 [DMT] DMT loaded with preskolemization
% 0.13/0.34 [EQ] equality loaded.
% 0.13/0.34 [0.000047s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.34 Conjecture not found
% 0.13/0.34 Start search
% 0.13/0.34 nb_step : 1 - limit : 32
% 0.13/0.34 Launch Gotab with destructive = true
% 2.18/0.85 % SZS output start Proof for theBenchmark.p
% 2.18/0.86 [0] ALPHA_AND : ((! [A20_20] : (~distinct_points(A20_20, A20_20)) & ! [A21_21, B22_22, C23_23] : ((distinct_points(A21_21, B22_22) => (distinct_points(A21_21, C23_23) | distinct_points(B22_22, C23_23)))) & ! [L24_24] : (~distinct_lines(L24_24, L24_24)) & ! [L25_25, M26_26, N27_27] : ((distinct_lines(L25_25, M26_26) => (distinct_lines(L25_25, N27_27) | distinct_lines(M26_26, N27_27)))) & ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28)) & ! [L29_29, M30_30, N31_31] : ((unequally_directed_lines(L29_29, M30_30) => (unequally_directed_lines(L29_29, N31_31) | unequally_directed_lines(M30_30, N31_31)))) & ! [L32_32, M33_33, N34_34] : (((unequally_directed_lines(L32_32, M33_33) & unequally_directed_lines(L32_32, reverse_line(M33_33))) => ((unequally_directed_lines(L32_32, N34_34) & unequally_directed_lines(L32_32, reverse_line(N34_34))) | (unequally_directed_lines(M33_33, N34_34) & unequally_directed_lines(M33_33, reverse_line(N34_34)))))) & ! [L35_35, M36_36] : (((line(L35_35) & line(M36_36)) => (unequally_directed_lines(L35_35, M36_36) | unequally_directed_lines(L35_35, reverse_line(M36_36))))) & ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38))))) & ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40)))) & ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42)))) & ! [A43_43, B44_44] : ((((point(A43_43) & point(B44_44)) & distinct_points(A43_43, B44_44)) => line(line_connecting(A43_43, B44_44)))) & ! [L45_45, M46_46] : (((((line(L45_45) & line(M46_46)) & unequally_directed_lines(L45_45, M46_46)) & unequally_directed_lines(L45_45, reverse_line(M46_46))) => point(intersection_point(L45_45, M46_46)))) & ! [L47_47, A48_48] : (((point(A48_48) & line(L47_47)) => line(parallel_through_point(L47_47, A48_48)))) & ! [L49_49] : ((line(L49_49) => line(reverse_line(L49_49)))) & ! [A50_50, B51_51] : ((distinct_points(A50_50, B51_51) => (~apart_point_and_line(A50_50, line_connecting(A50_50, B51_51)) & ~apart_point_and_line(B51_51, line_connecting(A50_50, B51_51))))) & ! [L52_52, M53_53] : (((unequally_directed_lines(L52_52, M53_53) & unequally_directed_lines(L52_52, reverse_line(M53_53))) => (~apart_point_and_line(intersection_point(L52_52, M53_53), L52_52) & ~apart_point_and_line(intersection_point(L52_52, M53_53), M53_53)))) & ! [A54_54, L55_55] : (~apart_point_and_line(A54_54, parallel_through_point(L55_55, A54_54))) & ! [L56_56] : (~distinct_lines(L56_56, reverse_line(L56_56))) & ! [A57_57, B58_58] : (~unequally_directed_lines(line_connecting(A57_57, B58_58), reverse_line(line_connecting(B58_58, A57_57)))) & ! [A59_59, L60_60] : (~unequally_directed_lines(parallel_through_point(L60_60, A59_59), L60_60)) & ! [A61_61, B62_62, L63_63, M64_64] : (((distinct_points(A61_61, B62_62) & distinct_lines(L63_63, M64_64)) => (((((((left_apart_point(A61_61, L63_63) | left_apart_point(B62_62, L63_63)) | left_apart_point(A61_61, M64_64)) | left_apart_point(B62_62, M64_64)) | left_apart_point(A61_61, reverse_line(L63_63))) | left_apart_point(B62_62, reverse_line(L63_63))) | left_apart_point(A61_61, reverse_line(M64_64))) | left_apart_point(B62_62, reverse_line(M64_64))))) & ! [A65_65, B66_66, L67_67] : (((distinct_points(A65_65, B66_66) & left_apart_point(A65_65, L67_67)) => (left_apart_point(B66_66, L67_67) | left_convergent_lines(line_connecting(A65_65, B66_66), L67_67)))) & ! [A68_68, B69_69, L70_70] : ((left_apart_point(A68_68, L70_70) => (distinct_points(A68_68, B69_69) | left_apart_point(B69_69, L70_70)))) & ! [A71_71, L72_72, M73_73] : (((left_apart_point(A71_71, L72_72) & unequally_directed_lines(L72_72, M73_73)) => (distinct_lines(L72_72, M73_73) | left_apart_point(A71_71, reverse_line(M73_73))))) & ! [L74_74, M75_75, N76_76] : ((left_convergent_lines(L74_74, M75_75) => (unequally_directed_lines(M75_75, N76_76) | left_convergent_lines(L74_74, N76_76))))) & ~! [A77_77, B78_78, L79_79] : (((~apart_point_and_line(A77_77, L79_79) & left_apart_point(B78_78, reverse_line(L79_79))) => left_convergent_lines(L79_79, reverse_line(line_connecting(A77_77, B78_78))))))
% 2.18/0.86 -> [1] (! [A20_20] : (~distinct_points(A20_20, A20_20)) & ! [A21_21, B22_22, C23_23] : ((distinct_points(A21_21, B22_22) => (distinct_points(A21_21, C23_23) | distinct_points(B22_22, C23_23)))) & ! [L24_24] : (~distinct_lines(L24_24, L24_24)) & ! [L25_25, M26_26, N27_27] : ((distinct_lines(L25_25, M26_26) => (distinct_lines(L25_25, N27_27) | distinct_lines(M26_26, N27_27)))) & ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28)) & ! [L29_29, M30_30, N31_31] : ((unequally_directed_lines(L29_29, M30_30) => (unequally_directed_lines(L29_29, N31_31) | unequally_directed_lines(M30_30, N31_31)))) & ! [L32_32, M33_33, N34_34] : (((unequally_directed_lines(L32_32, M33_33) & unequally_directed_lines(L32_32, reverse_line(M33_33))) => ((unequally_directed_lines(L32_32, N34_34) & unequally_directed_lines(L32_32, reverse_line(N34_34))) | (unequally_directed_lines(M33_33, N34_34) & unequally_directed_lines(M33_33, reverse_line(N34_34)))))) & ! [L35_35, M36_36] : (((line(L35_35) & line(M36_36)) => (unequally_directed_lines(L35_35, M36_36) | unequally_directed_lines(L35_35, reverse_line(M36_36))))) & ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38))))) & ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40)))) & ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42)))) & ! [A43_43, B44_44] : ((((point(A43_43) & point(B44_44)) & distinct_points(A43_43, B44_44)) => line(line_connecting(A43_43, B44_44)))) & ! [L45_45, M46_46] : (((((line(L45_45) & line(M46_46)) & unequally_directed_lines(L45_45, M46_46)) & unequally_directed_lines(L45_45, reverse_line(M46_46))) => point(intersection_point(L45_45, M46_46)))) & ! [L47_47, A48_48] : (((point(A48_48) & line(L47_47)) => line(parallel_through_point(L47_47, A48_48)))) & ! [L49_49] : ((line(L49_49) => line(reverse_line(L49_49)))) & ! [A50_50, B51_51] : ((distinct_points(A50_50, B51_51) => (~apart_point_and_line(A50_50, line_connecting(A50_50, B51_51)) & ~apart_point_and_line(B51_51, line_connecting(A50_50, B51_51))))) & ! [L52_52, M53_53] : (((unequally_directed_lines(L52_52, M53_53) & unequally_directed_lines(L52_52, reverse_line(M53_53))) => (~apart_point_and_line(intersection_point(L52_52, M53_53), L52_52) & ~apart_point_and_line(intersection_point(L52_52, M53_53), M53_53)))) & ! [A54_54, L55_55] : (~apart_point_and_line(A54_54, parallel_through_point(L55_55, A54_54))) & ! [L56_56] : (~distinct_lines(L56_56, reverse_line(L56_56))) & ! [A57_57, B58_58] : (~unequally_directed_lines(line_connecting(A57_57, B58_58), reverse_line(line_connecting(B58_58, A57_57)))) & ! [A59_59, L60_60] : (~unequally_directed_lines(parallel_through_point(L60_60, A59_59), L60_60)) & ! [A61_61, B62_62, L63_63, M64_64] : (((distinct_points(A61_61, B62_62) & distinct_lines(L63_63, M64_64)) => (((((((left_apart_point(A61_61, L63_63) | left_apart_point(B62_62, L63_63)) | left_apart_point(A61_61, M64_64)) | left_apart_point(B62_62, M64_64)) | left_apart_point(A61_61, reverse_line(L63_63))) | left_apart_point(B62_62, reverse_line(L63_63))) | left_apart_point(A61_61, reverse_line(M64_64))) | left_apart_point(B62_62, reverse_line(M64_64))))) & ! [A65_65, B66_66, L67_67] : (((distinct_points(A65_65, B66_66) & left_apart_point(A65_65, L67_67)) => (left_apart_point(B66_66, L67_67) | left_convergent_lines(line_connecting(A65_65, B66_66), L67_67)))) & ! [A68_68, B69_69, L70_70] : ((left_apart_point(A68_68, L70_70) => (distinct_points(A68_68, B69_69) | left_apart_point(B69_69, L70_70)))) & ! [A71_71, L72_72, M73_73] : (((left_apart_point(A71_71, L72_72) & unequally_directed_lines(L72_72, M73_73)) => (distinct_lines(L72_72, M73_73) | left_apart_point(A71_71, reverse_line(M73_73))))) & ! [L74_74, M75_75, N76_76] : ((left_convergent_lines(L74_74, M75_75) => (unequally_directed_lines(M75_75, N76_76) | left_convergent_lines(L74_74, N76_76))))), ~! [A77_77, B78_78, L79_79] : (((~apart_point_and_line(A77_77, L79_79) & left_apart_point(B78_78, reverse_line(L79_79))) => left_convergent_lines(L79_79, reverse_line(line_connecting(A77_77, B78_78)))))
% 2.18/0.86
% 2.18/0.86 [1] ALPHA_AND : (! [A20_20] : (~distinct_points(A20_20, A20_20)) & ! [A21_21, B22_22, C23_23] : ((distinct_points(A21_21, B22_22) => (distinct_points(A21_21, C23_23) | distinct_points(B22_22, C23_23)))) & ! [L24_24] : (~distinct_lines(L24_24, L24_24)) & ! [L25_25, M26_26, N27_27] : ((distinct_lines(L25_25, M26_26) => (distinct_lines(L25_25, N27_27) | distinct_lines(M26_26, N27_27)))) & ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28)) & ! [L29_29, M30_30, N31_31] : ((unequally_directed_lines(L29_29, M30_30) => (unequally_directed_lines(L29_29, N31_31) | unequally_directed_lines(M30_30, N31_31)))) & ! [L32_32, M33_33, N34_34] : (((unequally_directed_lines(L32_32, M33_33) & unequally_directed_lines(L32_32, reverse_line(M33_33))) => ((unequally_directed_lines(L32_32, N34_34) & unequally_directed_lines(L32_32, reverse_line(N34_34))) | (unequally_directed_lines(M33_33, N34_34) & unequally_directed_lines(M33_33, reverse_line(N34_34)))))) & ! [L35_35, M36_36] : (((line(L35_35) & line(M36_36)) => (unequally_directed_lines(L35_35, M36_36) | unequally_directed_lines(L35_35, reverse_line(M36_36))))) & ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38))))) & ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40)))) & ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42)))) & ! [A43_43, B44_44] : ((((point(A43_43) & point(B44_44)) & distinct_points(A43_43, B44_44)) => line(line_connecting(A43_43, B44_44)))) & ! [L45_45, M46_46] : (((((line(L45_45) & line(M46_46)) & unequally_directed_lines(L45_45, M46_46)) & unequally_directed_lines(L45_45, reverse_line(M46_46))) => point(intersection_point(L45_45, M46_46)))) & ! [L47_47, A48_48] : (((point(A48_48) & line(L47_47)) => line(parallel_through_point(L47_47, A48_48)))) & ! [L49_49] : ((line(L49_49) => line(reverse_line(L49_49)))) & ! [A50_50, B51_51] : ((distinct_points(A50_50, B51_51) => (~apart_point_and_line(A50_50, line_connecting(A50_50, B51_51)) & ~apart_point_and_line(B51_51, line_connecting(A50_50, B51_51))))) & ! [L52_52, M53_53] : (((unequally_directed_lines(L52_52, M53_53) & unequally_directed_lines(L52_52, reverse_line(M53_53))) => (~apart_point_and_line(intersection_point(L52_52, M53_53), L52_52) & ~apart_point_and_line(intersection_point(L52_52, M53_53), M53_53)))) & ! [A54_54, L55_55] : (~apart_point_and_line(A54_54, parallel_through_point(L55_55, A54_54))) & ! [L56_56] : (~distinct_lines(L56_56, reverse_line(L56_56))) & ! [A57_57, B58_58] : (~unequally_directed_lines(line_connecting(A57_57, B58_58), reverse_line(line_connecting(B58_58, A57_57)))) & ! [A59_59, L60_60] : (~unequally_directed_lines(parallel_through_point(L60_60, A59_59), L60_60)) & ! [A61_61, B62_62, L63_63, M64_64] : (((distinct_points(A61_61, B62_62) & distinct_lines(L63_63, M64_64)) => (((((((left_apart_point(A61_61, L63_63) | left_apart_point(B62_62, L63_63)) | left_apart_point(A61_61, M64_64)) | left_apart_point(B62_62, M64_64)) | left_apart_point(A61_61, reverse_line(L63_63))) | left_apart_point(B62_62, reverse_line(L63_63))) | left_apart_point(A61_61, reverse_line(M64_64))) | left_apart_point(B62_62, reverse_line(M64_64))))) & ! [A65_65, B66_66, L67_67] : (((distinct_points(A65_65, B66_66) & left_apart_point(A65_65, L67_67)) => (left_apart_point(B66_66, L67_67) | left_convergent_lines(line_connecting(A65_65, B66_66), L67_67)))) & ! [A68_68, B69_69, L70_70] : ((left_apart_point(A68_68, L70_70) => (distinct_points(A68_68, B69_69) | left_apart_point(B69_69, L70_70)))) & ! [A71_71, L72_72, M73_73] : (((left_apart_point(A71_71, L72_72) & unequally_directed_lines(L72_72, M73_73)) => (distinct_lines(L72_72, M73_73) | left_apart_point(A71_71, reverse_line(M73_73))))) & ! [L74_74, M75_75, N76_76] : ((left_convergent_lines(L74_74, M75_75) => (unequally_directed_lines(M75_75, N76_76) | left_convergent_lines(L74_74, N76_76)))))
% 2.18/0.86 -> [2] ! [A20_20] : (~distinct_points(A20_20, A20_20)), ! [A21_21, B22_22, C23_23] : ((distinct_points(A21_21, B22_22) => (distinct_points(A21_21, C23_23) | distinct_points(B22_22, C23_23)))), ! [L24_24] : (~distinct_lines(L24_24, L24_24)), ! [L25_25, M26_26, N27_27] : ((distinct_lines(L25_25, M26_26) => (distinct_lines(L25_25, N27_27) | distinct_lines(M26_26, N27_27)))), ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28)), ! [L29_29, M30_30, N31_31] : ((unequally_directed_lines(L29_29, M30_30) => (unequally_directed_lines(L29_29, N31_31) | unequally_directed_lines(M30_30, N31_31)))), ! [L32_32, M33_33, N34_34] : (((unequally_directed_lines(L32_32, M33_33) & unequally_directed_lines(L32_32, reverse_line(M33_33))) => ((unequally_directed_lines(L32_32, N34_34) & unequally_directed_lines(L32_32, reverse_line(N34_34))) | (unequally_directed_lines(M33_33, N34_34) & unequally_directed_lines(M33_33, reverse_line(N34_34)))))), ! [L35_35, M36_36] : (((line(L35_35) & line(M36_36)) => (unequally_directed_lines(L35_35, M36_36) | unequally_directed_lines(L35_35, reverse_line(M36_36))))), ! [L37_37, M38_38] : (((unequally_directed_lines(L37_37, M38_38) & unequally_directed_lines(L37_37, reverse_line(M38_38))) => (left_convergent_lines(L37_37, M38_38) | left_convergent_lines(L37_37, reverse_line(M38_38))))), ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40)))), ! [L41_41, M42_42] : (~(left_convergent_lines(L41_41, M42_42) | left_convergent_lines(L41_41, reverse_line(M42_42)))), ! [A43_43, B44_44] : ((((point(A43_43) & point(B44_44)) & distinct_points(A43_43, B44_44)) => line(line_connecting(A43_43, B44_44)))), ! [L45_45, M46_46] : (((((line(L45_45) & line(M46_46)) & unequally_directed_lines(L45_45, M46_46)) & unequally_directed_lines(L45_45, reverse_line(M46_46))) => point(intersection_point(L45_45, M46_46)))), ! [L47_47, A48_48] : (((point(A48_48) & line(L47_47)) => line(parallel_through_point(L47_47, A48_48)))), ! [L49_49] : ((line(L49_49) => line(reverse_line(L49_49)))), ! [A50_50, B51_51] : ((distinct_points(A50_50, B51_51) => (~apart_point_and_line(A50_50, line_connecting(A50_50, B51_51)) & ~apart_point_and_line(B51_51, line_connecting(A50_50, B51_51))))), ! [L52_52, M53_53] : (((unequally_directed_lines(L52_52, M53_53) & unequally_directed_lines(L52_52, reverse_line(M53_53))) => (~apart_point_and_line(intersection_point(L52_52, M53_53), L52_52) & ~apart_point_and_line(intersection_point(L52_52, M53_53), M53_53)))), ! [A54_54, L55_55] : (~apart_point_and_line(A54_54, parallel_through_point(L55_55, A54_54))), ! [L56_56] : (~distinct_lines(L56_56, reverse_line(L56_56))), ! [A57_57, B58_58] : (~unequally_directed_lines(line_connecting(A57_57, B58_58), reverse_line(line_connecting(B58_58, A57_57)))), ! [A59_59, L60_60] : (~unequally_directed_lines(parallel_through_point(L60_60, A59_59), L60_60)), ! [A61_61, B62_62, L63_63, M64_64] : (((distinct_points(A61_61, B62_62) & distinct_lines(L63_63, M64_64)) => (((((((left_apart_point(A61_61, L63_63) | left_apart_point(B62_62, L63_63)) | left_apart_point(A61_61, M64_64)) | left_apart_point(B62_62, M64_64)) | left_apart_point(A61_61, reverse_line(L63_63))) | left_apart_point(B62_62, reverse_line(L63_63))) | left_apart_point(A61_61, reverse_line(M64_64))) | left_apart_point(B62_62, reverse_line(M64_64))))), ! [A65_65, B66_66, L67_67] : (((distinct_points(A65_65, B66_66) & left_apart_point(A65_65, L67_67)) => (left_apart_point(B66_66, L67_67) | left_convergent_lines(line_connecting(A65_65, B66_66), L67_67)))), ! [A68_68, B69_69, L70_70] : ((left_apart_point(A68_68, L70_70) => (distinct_points(A68_68, B69_69) | left_apart_point(B69_69, L70_70)))), ! [A71_71, L72_72, M73_73] : (((left_apart_point(A71_71, L72_72) & unequally_directed_lines(L72_72, M73_73)) => (distinct_lines(L72_72, M73_73) | left_apart_point(A71_71, reverse_line(M73_73))))), ! [L74_74, M75_75, N76_76] : ((left_convergent_lines(L74_74, M75_75) => (unequally_directed_lines(M75_75, N76_76) | left_convergent_lines(L74_74, N76_76))))
% 2.18/0.86
% 2.18/0.86 [2] DELTA_NOT_FORALL : ~! [A77_77, B78_78, L79_79] : (((~apart_point_and_line(A77_77, L79_79) & left_apart_point(B78_78, reverse_line(L79_79))) => left_convergent_lines(L79_79, reverse_line(line_connecting(A77_77, B78_78)))))
% 2.18/0.86 -> [3] ~((~apart_point_and_line(skolem_A7777, skolem_L7979) & left_apart_point(skolem_B7878, reverse_line(skolem_L7979))) => left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.18/0.86
% 2.18/0.86 [3] ALPHA_NOT_IMPLY : ~((~apart_point_and_line(skolem_A7777, skolem_L7979) & left_apart_point(skolem_B7878, reverse_line(skolem_L7979))) => left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.18/0.86 -> [4] (~apart_point_and_line(skolem_A7777, skolem_L7979) & left_apart_point(skolem_B7878, reverse_line(skolem_L7979))), ~left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.18/0.86
% 2.18/0.86 [4] ALPHA_AND : (~apart_point_and_line(skolem_A7777, skolem_L7979) & left_apart_point(skolem_B7878, reverse_line(skolem_L7979)))
% 2.18/0.86 -> [5] ~apart_point_and_line(skolem_A7777, skolem_L7979), left_apart_point(skolem_B7878, reverse_line(skolem_L7979))
% 2.18/0.86
% 2.18/0.86 [5] Rewrite : ~apart_point_and_line(skolem_A7777, skolem_L7979)
% 2.18/0.86 -> [6] ~(left_apart_point(skolem_A7777, skolem_L7979) | left_apart_point(skolem_A7777, reverse_line(skolem_L7979)))
% 2.18/0.86
% 2.18/0.86 [6] ALPHA_NOT_OR : ~(left_apart_point(skolem_A7777, skolem_L7979) | left_apart_point(skolem_A7777, reverse_line(skolem_L7979)))
% 2.18/0.86 -> [7] ~left_apart_point(skolem_A7777, skolem_L7979), ~left_apart_point(skolem_A7777, reverse_line(skolem_L7979))
% 2.18/0.86
% 2.18/0.86 [7] GAMMA_FORALL : ! [A20_20] : (~distinct_points(A20_20, A20_20))
% 2.18/0.86 -> [8] ~distinct_points(C23_0_1, C23_0_1)
% 2.18/0.86
% 2.18/0.86 [8] 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))))
% 2.18/0.86 -> [9] (distinct_points(C23_0_1, C23_0_1) => (distinct_points(C23_0_1, C23_0_1) | distinct_points(C23_0_1, C23_0_1)))
% 2.18/0.86
% 2.18/0.86 [9] 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)))
% 2.18/0.86 -> [10] ~distinct_points(C23_0_1, C23_0_1)
% 2.18/0.86 -> [11] (distinct_points(C23_0_1, C23_0_1) | distinct_points(C23_0_1, C23_0_1))
% 2.18/0.86
% 2.18/0.86 [11] BETA_OR : (distinct_points(C23_0_1, C23_0_1) | distinct_points(C23_0_1, C23_0_1))
% 2.18/0.86 -> [12] distinct_points(C23_0_1, C23_0_1)
% 2.18/0.86 -> [13] distinct_points(C23_0_1, C23_0_1)
% 2.18/0.86
% 2.18/0.86 [13] CLOSURE : distinct_points(C23_0_1, C23_0_1)
% 2.18/0.86
% 2.18/0.86 [12] CLOSURE : distinct_points(C23_0_1, C23_0_1)
% 2.18/0.86
% 2.18/0.86 [10] GAMMA_FORALL : ! [L24_24] : (~distinct_lines(L24_24, L24_24))
% 2.18/0.86 -> [14] ~distinct_lines(N27_0_3, N27_0_3)
% 2.18/0.86
% 2.18/0.86 [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))))
% 2.18/0.86 -> [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)))
% 2.18/0.86
% 2.18/0.86 [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)))
% 2.18/0.86 -> [16] ~distinct_lines(N27_0_3, N27_0_3)
% 2.18/0.86 -> [17] (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3))
% 2.18/0.86
% 2.18/0.86 [17] BETA_OR : (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3))
% 2.18/0.86 -> [19] distinct_lines(N27_0_3, N27_0_3)
% 2.18/0.86 -> [20] distinct_lines(N27_0_3, N27_0_3)
% 2.18/0.86
% 2.18/0.86 [20] CLOSURE : distinct_lines(N27_0_3, N27_0_3)
% 2.18/0.86
% 2.18/0.86 [19] CLOSURE : distinct_lines(N27_0_3, N27_0_3)
% 2.18/0.86
% 2.18/0.86 [16] GAMMA_FORALL : ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28))
% 2.18/0.86 -> [18] ~unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6))
% 2.18/0.86
% 2.18/0.86 [18] GAMMA_FORALL : ! [L29_29, M30_30, N31_31] : ((unequally_directed_lines(L29_29, M30_30) => (unequally_directed_lines(L29_29, N31_31) | unequally_directed_lines(M30_30, N31_31))))
% 2.18/0.86 -> [21] (unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6)) => (unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6)) | unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6))))
% 2.18/0.86
% 2.18/0.86 [21] BETA_IMPLY : (unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6)) => (unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6)) | unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6))))
% 2.18/0.86 -> [22] ~unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6))
% 2.18/0.86 -> [23] (unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6)) | unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6)))
% 2.18/0.86
% 2.18/0.86 [23] BETA_OR : (unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6)) | unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6)))
% 2.18/0.86 -> [24] unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6))
% 2.18/0.86 -> [25] unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6))
% 2.18/0.86
% 2.18/0.86 [25] CLOSURE : unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6))
% 2.18/0.86
% 2.18/0.86 [24] CLOSURE : unequally_directed_lines(reverse_line(N34_0_6), reverse_line(N34_0_6))
% 2.18/0.86
% 2.18/0.86 [26] BETA_IMPLY : ((unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))) => ((unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))) | (unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))))
% 2.18/0.86 -> [201] ~(unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 2.18/0.86 -> [202] ((unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))) | (unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))))
% 2.18/0.86
% 2.18/0.86 [201] BETA_NOT_AND : ~(unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 2.18/0.86 -> [203] ~unequally_directed_lines(N34_0_6, N34_0_6)
% 2.18/0.86 -> [204] ~unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))
% 2.18/0.86
% 2.18/0.86 [204] 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)))))
% 2.18/0.86 -> [209] ((line(M36_4_7) & line(M36_4_7)) => (unequally_directed_lines(M36_4_7, M36_4_7) | unequally_directed_lines(M36_4_7, reverse_line(M36_4_7))))
% 2.18/0.86
% 2.18/0.86 [209] BETA_IMPLY : ((line(M36_4_7) & line(M36_4_7)) => (unequally_directed_lines(M36_4_7, M36_4_7) | unequally_directed_lines(M36_4_7, reverse_line(M36_4_7))))
% 2.18/0.86 -> [210] ~(line(M36_4_7) & line(M36_4_7))
% 2.18/0.86 -> [211] (unequally_directed_lines(M36_4_7, M36_4_7) | unequally_directed_lines(M36_4_7, reverse_line(M36_4_7)))
% 2.18/0.86
% 2.18/0.86 [211] BETA_OR : (unequally_directed_lines(M36_4_7, M36_4_7) | unequally_directed_lines(M36_4_7, reverse_line(M36_4_7)))
% 2.18/0.86 -> [219] unequally_directed_lines(M36_4_7, M36_4_7)
% 2.18/0.86 -> [220] unequally_directed_lines(M36_4_7, reverse_line(M36_4_7))
% 2.18/0.86
% 2.18/0.86 [220] CLOSURE : unequally_directed_lines(M36_4_7, reverse_line(M36_4_7))
% 2.18/0.86
% 2.18/0.86 [219] CLOSURE : unequally_directed_lines(M36_4_7, M36_4_7)
% 2.18/0.86
% 2.18/0.86 [210] BETA_NOT_AND : ~(line(M36_4_7) & line(M36_4_7))
% 2.18/0.86 -> [215] ~line(M36_4_7)
% 2.18/0.86 -> [216] ~line(M36_4_7)
% 2.18/0.86
% 2.18/0.86 [216] 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)))))
% 2.18/0.86 -> [223] ((unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) & unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))) => (left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) | left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))))
% 2.18/0.86
% 2.18/0.86 [223] BETA_IMPLY : ((unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) & unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))) => (left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) | left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))))
% 2.18/0.86 -> [225] ~(unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) & unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.18/0.86 -> [226] (left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) | left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.18/0.86
% 2.18/0.86 [225] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) & unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.18/0.86 -> [239] ~unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.18/0.86 -> [240] ~unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.18/0.86
% 2.18/0.86 [240] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.18/0.86 -> [255] ~(left_apart_point(A39_33_9, L40_33_9) | left_apart_point(A39_33_9, reverse_line(L40_33_9)))
% 2.18/0.86
% 2.18/0.86 [255] ALPHA_NOT_OR : ~(left_apart_point(A39_33_9, L40_33_9) | left_apart_point(A39_33_9, reverse_line(L40_33_9)))
% 2.18/0.86 -> [257] ~left_apart_point(A39_33_9, L40_33_9), ~left_apart_point(A39_33_9, reverse_line(L40_33_9))
% 2.18/0.86
% 2.18/0.86 [257] CLOSURE : ~left_apart_point(A39_33_9, L40_33_9)
% 2.18/0.86
% 2.18/0.86 [239] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.18/0.86 -> [251] ~(left_apart_point(A39_30_9, L40_30_9) | left_apart_point(A39_30_9, reverse_line(L40_30_9)))
% 2.18/0.86
% 2.18/0.86 [251] ALPHA_NOT_OR : ~(left_apart_point(A39_30_9, L40_30_9) | left_apart_point(A39_30_9, reverse_line(L40_30_9)))
% 2.18/0.86 -> [258] ~left_apart_point(A39_30_9, L40_30_9), ~left_apart_point(A39_30_9, reverse_line(L40_30_9))
% 2.18/0.86
% 2.18/0.86 [258] CLOSURE : ~left_apart_point(A39_30_9, L40_30_9)
% 2.18/0.86
% 2.18/0.86 [226] BETA_OR : (left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) | left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.18/0.86 -> [235] left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.18/0.86 -> [236] left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.18/0.86
% 2.18/0.86 [236] CLOSURE : left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.18/0.86
% 2.18/0.86 [235] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.18/0.86 -> [265] ~(left_apart_point(A39_37_9, L40_37_9) | left_apart_point(A39_37_9, reverse_line(L40_37_9)))
% 2.18/0.86
% 2.18/0.86 [265] ALPHA_NOT_OR : ~(left_apart_point(A39_37_9, L40_37_9) | left_apart_point(A39_37_9, reverse_line(L40_37_9)))
% 2.18/0.86 -> [267] ~left_apart_point(A39_37_9, L40_37_9), ~left_apart_point(A39_37_9, reverse_line(L40_37_9))
% 2.18/0.86
% 2.18/0.86 [267] CLOSURE : ~left_apart_point(A39_37_9, L40_37_9)
% 2.18/0.86
% 2.18/0.86 [215] 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)))))
% 2.18/0.86 -> [224] ((unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) & unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))) => (left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) | left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))))
% 2.18/0.86
% 2.18/0.86 [224] BETA_IMPLY : ((unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) & unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))) => (left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) | left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))))
% 2.18/0.86 -> [227] ~(unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) & unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.18/0.86 -> [228] (left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) | left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.18/0.86
% 2.18/0.86 [227] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) & unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.18/0.86 -> [241] ~unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.18/0.86 -> [242] ~unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.18/0.86
% 2.18/0.86 [241] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.18/0.86 -> [253] ~(left_apart_point(A39_32_9, L40_32_9) | left_apart_point(A39_32_9, reverse_line(L40_32_9)))
% 2.18/0.86
% 2.18/0.86 [253] ALPHA_NOT_OR : ~(left_apart_point(A39_32_9, L40_32_9) | left_apart_point(A39_32_9, reverse_line(L40_32_9)))
% 2.18/0.86 -> [256] ~left_apart_point(A39_32_9, L40_32_9), ~left_apart_point(A39_32_9, reverse_line(L40_32_9))
% 2.18/0.86
% 2.18/0.86 [256] CLOSURE : ~left_apart_point(A39_32_9, L40_32_9)
% 2.18/0.86
% 2.18/0.86 [242] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.18/0.86 -> [262] ~(left_apart_point(A39_36_9, L40_36_9) | left_apart_point(A39_36_9, reverse_line(L40_36_9)))
% 2.18/0.86
% 2.18/0.86 [262] ALPHA_NOT_OR : ~(left_apart_point(A39_36_9, L40_36_9) | left_apart_point(A39_36_9, reverse_line(L40_36_9)))
% 2.18/0.86 -> [264] ~left_apart_point(A39_36_9, L40_36_9), ~left_apart_point(A39_36_9, reverse_line(L40_36_9))
% 2.18/0.86
% 2.18/0.86 [264] CLOSURE : ~left_apart_point(A39_36_9, L40_36_9)
% 2.18/0.86
% 2.18/0.86 [228] BETA_OR : (left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) | left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.18/0.86 -> [237] left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.18/0.86 -> [238] left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.18/0.86
% 2.18/0.86 [238] CLOSURE : left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.18/0.86
% 2.18/0.86 [237] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.18/0.86 -> [269] ~(left_apart_point(A39_39_9, L40_39_9) | left_apart_point(A39_39_9, reverse_line(L40_39_9)))
% 2.18/0.86
% 2.18/0.86 [269] ALPHA_NOT_OR : ~(left_apart_point(A39_39_9, L40_39_9) | left_apart_point(A39_39_9, reverse_line(L40_39_9)))
% 2.18/0.86 -> [270] ~left_apart_point(A39_39_9, L40_39_9), ~left_apart_point(A39_39_9, reverse_line(L40_39_9))
% 2.18/0.86
% 2.18/0.86 [270] CLOSURE : ~left_apart_point(A39_39_9, L40_39_9)
% 2.18/0.86
% 2.18/0.86 [212] BETA_IMPLY : ((line(M36_5_7) & line(M36_5_7)) => (unequally_directed_lines(M36_5_7, M36_5_7) | unequally_directed_lines(M36_5_7, reverse_line(M36_5_7))))
% 2.18/0.86 -> [275] ~(line(M36_5_7) & line(M36_5_7))
% 2.18/0.86 -> [276] (unequally_directed_lines(M36_5_7, M36_5_7) | unequally_directed_lines(M36_5_7, reverse_line(M36_5_7)))
% 2.18/0.86
% 2.18/0.86 [275] BETA_NOT_AND : ~(line(M36_5_7) & line(M36_5_7))
% 2.18/0.86 -> [277] ~line(M36_5_7)
% 2.18/0.86 -> [278] ~line(M36_5_7)
% 2.18/0.86
% 2.18/0.86 [277] 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)))))
% 2.18/0.86 -> [281] ((unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) & unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))) => (left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) | left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))))
% 2.18/0.86
% 2.18/0.86 [281] BETA_IMPLY : ((unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) & unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))) => (left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) | left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))))
% 2.18/0.86 -> [283] ~(unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) & unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.18/0.86 -> [284] (left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) | left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.18/0.86
% 2.18/0.86 [283] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) & unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.18/0.86 -> [287] ~unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.18/0.86 -> [288] ~unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.18/0.86
% 2.18/0.86 [288] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.18/0.86 -> [297] ~(left_apart_point(A39_43_9, L40_43_9) | left_apart_point(A39_43_9, reverse_line(L40_43_9)))
% 2.18/0.86
% 2.18/0.86 [297] ALPHA_NOT_OR : ~(left_apart_point(A39_43_9, L40_43_9) | left_apart_point(A39_43_9, reverse_line(L40_43_9)))
% 2.18/0.86 -> [303] ~left_apart_point(A39_43_9, L40_43_9), ~left_apart_point(A39_43_9, reverse_line(L40_43_9))
% 2.18/0.86
% 2.18/0.86 [303] CLOSURE : ~left_apart_point(A39_43_9, L40_43_9)
% 2.18/0.86
% 2.18/0.86 [287] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.18/0.86 -> [300] ~(left_apart_point(A39_44_9, L40_44_9) | left_apart_point(A39_44_9, reverse_line(L40_44_9)))
% 2.18/0.86
% 2.18/0.86 [300] ALPHA_NOT_OR : ~(left_apart_point(A39_44_9, L40_44_9) | left_apart_point(A39_44_9, reverse_line(L40_44_9)))
% 2.18/0.86 -> [304] ~left_apart_point(A39_44_9, L40_44_9), ~left_apart_point(A39_44_9, reverse_line(L40_44_9))
% 2.18/0.86
% 2.18/0.86 [304] CLOSURE : ~left_apart_point(A39_44_9, L40_44_9)
% 2.18/0.86
% 2.18/0.86 [284] BETA_OR : (left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) | left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.18/0.86 -> [293] left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.18/0.86 -> [294] left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.18/0.86
% 2.18/0.86 [294] CLOSURE : left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.18/0.86
% 2.18/0.86 [293] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.18/0.86 -> [310] ~(left_apart_point(A39_46_9, L40_46_9) | left_apart_point(A39_46_9, reverse_line(L40_46_9)))
% 2.18/0.86
% 2.18/0.86 [310] ALPHA_NOT_OR : ~(left_apart_point(A39_46_9, L40_46_9) | left_apart_point(A39_46_9, reverse_line(L40_46_9)))
% 2.18/0.86 -> [312] ~left_apart_point(A39_46_9, L40_46_9), ~left_apart_point(A39_46_9, reverse_line(L40_46_9))
% 2.18/0.86
% 2.18/0.86 [312] CLOSURE : ~left_apart_point(A39_46_9, L40_46_9)
% 2.18/0.86
% 2.18/0.86 [278] 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)))))
% 2.18/0.86 -> [282] ((unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))) & unequally_directed_lines(skolem_L7979, reverse_line(reverse_line(line_connecting(skolem_A7777, skolem_B7878))))) => (left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))) | left_convergent_lines(skolem_L7979, reverse_line(reverse_line(line_connecting(skolem_A7777, skolem_B7878))))))
% 2.18/0.86
% 2.18/0.86 [282] BETA_IMPLY : ((unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))) & unequally_directed_lines(skolem_L7979, reverse_line(reverse_line(line_connecting(skolem_A7777, skolem_B7878))))) => (left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))) | left_convergent_lines(skolem_L7979, reverse_line(reverse_line(line_connecting(skolem_A7777, skolem_B7878))))))
% 2.18/0.86 -> [285] ~(unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))) & unequally_directed_lines(skolem_L7979, reverse_line(reverse_line(line_connecting(skolem_A7777, skolem_B7878)))))
% 2.18/0.86 -> [286] (left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))) | left_convergent_lines(skolem_L7979, reverse_line(reverse_line(line_connecting(skolem_A7777, skolem_B7878)))))
% 2.18/0.86
% 2.18/0.86 [285] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))) & unequally_directed_lines(skolem_L7979, reverse_line(reverse_line(line_connecting(skolem_A7777, skolem_B7878)))))
% 2.18/0.86 -> [289] ~unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.18/0.86 -> [290] ~unequally_directed_lines(skolem_L7979, reverse_line(reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.18/0.86
% 2.18/0.86 [289] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.18/0.86 -> [296] ~(left_apart_point(A39_42_9, L40_42_9) | left_apart_point(A39_42_9, reverse_line(L40_42_9)))
% 2.18/0.86
% 2.18/0.86 [296] ALPHA_NOT_OR : ~(left_apart_point(A39_42_9, L40_42_9) | left_apart_point(A39_42_9, reverse_line(L40_42_9)))
% 2.18/0.86 -> [302] ~left_apart_point(A39_42_9, L40_42_9), ~left_apart_point(A39_42_9, reverse_line(L40_42_9))
% 2.18/0.86
% 2.18/0.86 [302] CLOSURE : ~left_apart_point(A39_42_9, L40_42_9)
% 2.18/0.86
% 2.18/0.86 [290] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.18/0.86 -> [301] ~(left_apart_point(A39_45_9, L40_45_9) | left_apart_point(A39_45_9, reverse_line(L40_45_9)))
% 2.18/0.86
% 2.18/0.86 [301] ALPHA_NOT_OR : ~(left_apart_point(A39_45_9, L40_45_9) | left_apart_point(A39_45_9, reverse_line(L40_45_9)))
% 2.18/0.86 -> [305] ~left_apart_point(A39_45_9, L40_45_9), ~left_apart_point(A39_45_9, reverse_line(L40_45_9))
% 2.18/0.86
% 2.18/0.86 [305] CLOSURE : ~left_apart_point(A39_45_9, L40_45_9)
% 2.18/0.86
% 2.18/0.86 [286] BETA_OR : (left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))) | left_convergent_lines(skolem_L7979, reverse_line(reverse_line(line_connecting(skolem_A7777, skolem_B7878)))))
% 2.18/0.86 -> [291] left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.18/0.86 -> [292] left_convergent_lines(skolem_L7979, reverse_line(reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.18/0.86
% 2.18/0.86 [291] CLOSURE : left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.18/0.86
% 2.18/0.86 [292] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.18/0.86 -> [311] ~(left_apart_point(A39_47_9, L40_47_9) | left_apart_point(A39_47_9, reverse_line(L40_47_9)))
% 2.18/0.86
% 2.18/0.86 [311] ALPHA_NOT_OR : ~(left_apart_point(A39_47_9, L40_47_9) | left_apart_point(A39_47_9, reverse_line(L40_47_9)))
% 2.18/0.86 -> [313] ~left_apart_point(A39_47_9, L40_47_9), ~left_apart_point(A39_47_9, reverse_line(L40_47_9))
% 2.18/0.86
% 2.18/0.86 [313] CLOSURE : ~left_apart_point(A39_47_9, L40_47_9)
% 2.18/0.86
% 2.18/0.86 [276] BETA_OR : (unequally_directed_lines(M36_5_7, M36_5_7) | unequally_directed_lines(M36_5_7, reverse_line(M36_5_7)))
% 2.18/0.86 -> [279] unequally_directed_lines(M36_5_7, M36_5_7)
% 2.18/0.86 -> [280] unequally_directed_lines(M36_5_7, reverse_line(M36_5_7))
% 2.18/0.86
% 2.18/0.86 [279] CLOSURE : unequally_directed_lines(M36_5_7, M36_5_7)
% 2.18/0.86
% 2.18/0.86 [280] 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)))))
% 2.18/0.86 -> [295] ((unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) & unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))) => (left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) | left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))))
% 2.18/0.86
% 2.18/0.86 [295] BETA_IMPLY : ((unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) & unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))) => (left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) | left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))))
% 2.18/0.86 -> [298] ~(unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) & unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.18/0.86 -> [299] (left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) | left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.18/0.86
% 2.18/0.86 [299] BETA_OR : (left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) | left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.18/0.86 -> [306] left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.18/0.86 -> [307] left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.18/0.86
% 2.18/0.86 [307] CLOSURE : left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.18/0.86
% 2.18/0.86 [306] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.18/0.86 -> [316] ~(left_apart_point(A39_49_9, L40_49_9) | left_apart_point(A39_49_9, reverse_line(L40_49_9)))
% 2.18/0.86
% 2.18/0.86 [316] ALPHA_NOT_OR : ~(left_apart_point(A39_49_9, L40_49_9) | left_apart_point(A39_49_9, reverse_line(L40_49_9)))
% 2.18/0.86 -> [317] ~left_apart_point(A39_49_9, L40_49_9), ~left_apart_point(A39_49_9, reverse_line(L40_49_9))
% 2.18/0.86
% 2.18/0.86 [317] CLOSURE : ~left_apart_point(A39_49_9, L40_49_9)
% 2.18/0.86
% 2.18/0.86 [298] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) & unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.18/0.86 -> [318] ~unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.18/0.86 -> [319] ~unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.18/0.86
% 2.18/0.86 [318] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.18/0.86 -> [320] ~(left_apart_point(A39_50_9, L40_50_9) | left_apart_point(A39_50_9, reverse_line(L40_50_9)))
% 2.18/0.86
% 2.18/0.86 [320] ALPHA_NOT_OR : ~(left_apart_point(A39_50_9, L40_50_9) | left_apart_point(A39_50_9, reverse_line(L40_50_9)))
% 2.18/0.86 -> [322] ~left_apart_point(A39_50_9, L40_50_9), ~left_apart_point(A39_50_9, reverse_line(L40_50_9))
% 2.18/0.86
% 2.18/0.86 [322] CLOSURE : ~left_apart_point(A39_50_9, L40_50_9)
% 2.18/0.86
% 2.18/0.86 [319] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.18/0.86 -> [321] ~(left_apart_point(A39_51_9, L40_51_9) | left_apart_point(A39_51_9, reverse_line(L40_51_9)))
% 2.18/0.86
% 2.18/0.86 [321] ALPHA_NOT_OR : ~(left_apart_point(A39_51_9, L40_51_9) | left_apart_point(A39_51_9, reverse_line(L40_51_9)))
% 2.18/0.86 -> [323] ~left_apart_point(A39_51_9, L40_51_9), ~left_apart_point(A39_51_9, reverse_line(L40_51_9))
% 2.18/0.86
% 2.18/0.86 [323] CLOSURE : ~left_apart_point(A39_51_9, L40_51_9)
% 2.18/0.86
% 2.18/0.86 [202] BETA_OR : ((unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))) | (unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))))
% 2.18/0.86 -> [324] (unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 2.18/0.86 -> [325] (unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 2.18/0.86
% 2.18/0.86 [324] ALPHA_AND : (unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 2.18/0.86 -> [326] unequally_directed_lines(N34_0_6, N34_0_6), unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))
% 2.18/0.86
% 2.18/0.86 [326] CLOSURE : unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))
% 2.18/0.86
% 2.18/0.86 [325] ALPHA_AND : (unequally_directed_lines(N34_0_6, N34_0_6) & unequally_directed_lines(N34_0_6, reverse_line(N34_0_6)))
% 2.18/0.86 -> [327] unequally_directed_lines(N34_0_6, N34_0_6), unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))
% 2.18/0.86
% 2.18/0.86 [327] CLOSURE : unequally_directed_lines(N34_0_6, reverse_line(N34_0_6))
% 2.18/0.86
% 2.18/0.86 % SZS output end Proof for theBenchmark.p
% 2.18/0.86 [0.523937s][1][Res] 1794 goroutines created
% 2.18/0.86 ==== Result ====
% 2.18/0.86 [0.523971s][1][Res] VALID
% 2.18/0.86 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------