TSTP Solution File: GEO239+1 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO239+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n005.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 2.29s 0.93s
% Output : Proof 2.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO239+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.07/0.13 % Command : goeland -dmt -presko -proof %s
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 31 07:08:18 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 [DMT] DMT loaded with preskolemization
% 0.14/0.35 [EQ] equality loaded.
% 0.14/0.35 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.14/0.35 Conjecture not found
% 0.14/0.35 Start search
% 0.14/0.35 nb_step : 1 - limit : 32
% 0.14/0.35 Launch Gotab with destructive = true
% 2.29/0.92 % SZS output start Proof for theBenchmark.p
% 2.29/0.93 [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, L79_79)) => left_convergent_lines(L79_79, line_connecting(A77_77, B78_78)))))
% 2.29/0.93 -> [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, L79_79)) => left_convergent_lines(L79_79, line_connecting(A77_77, B78_78))))
% 2.29/0.93
% 2.29/0.93 [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)))))
% 2.29/0.93 -> [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))))
% 2.29/0.93
% 2.29/0.93 [2] DELTA_NOT_FORALL : ~! [A77_77, B78_78, L79_79] : (((~apart_point_and_line(A77_77, L79_79) & left_apart_point(B78_78, L79_79)) => left_convergent_lines(L79_79, line_connecting(A77_77, B78_78))))
% 2.29/0.93 -> [3] ~((~apart_point_and_line(skolem_A7777, skolem_L7979) & left_apart_point(skolem_B7878, skolem_L7979)) => left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)))
% 2.29/0.93
% 2.29/0.93 [3] ALPHA_NOT_IMPLY : ~((~apart_point_and_line(skolem_A7777, skolem_L7979) & left_apart_point(skolem_B7878, skolem_L7979)) => left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)))
% 2.29/0.93 -> [4] (~apart_point_and_line(skolem_A7777, skolem_L7979) & left_apart_point(skolem_B7878, skolem_L7979)), ~left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.29/0.93
% 2.29/0.93 [4] ALPHA_AND : (~apart_point_and_line(skolem_A7777, skolem_L7979) & left_apart_point(skolem_B7878, skolem_L7979))
% 2.29/0.93 -> [5] ~apart_point_and_line(skolem_A7777, skolem_L7979), left_apart_point(skolem_B7878, skolem_L7979)
% 2.29/0.93
% 2.29/0.93 [5] Rewrite : ~apart_point_and_line(skolem_A7777, skolem_L7979)
% 2.29/0.93 -> [6] ~(left_apart_point(skolem_A7777, skolem_L7979) | left_apart_point(skolem_A7777, reverse_line(skolem_L7979)))
% 2.29/0.93
% 2.29/0.93 [6] ALPHA_NOT_OR : ~(left_apart_point(skolem_A7777, skolem_L7979) | left_apart_point(skolem_A7777, reverse_line(skolem_L7979)))
% 2.29/0.93 -> [7] ~left_apart_point(skolem_A7777, skolem_L7979), ~left_apart_point(skolem_A7777, reverse_line(skolem_L7979))
% 2.29/0.93
% 2.29/0.93 [7] GAMMA_FORALL : ! [A20_20] : (~distinct_points(A20_20, A20_20))
% 2.29/0.93 -> [8] ~distinct_points(C23_0_1, C23_0_1)
% 2.29/0.93
% 2.29/0.93 [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))))
% 2.29/0.93 -> [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)))
% 2.29/0.93
% 2.29/0.93 [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)))
% 2.29/0.93 -> [10] ~distinct_points(C23_0_1, C23_0_1)
% 2.29/0.93 -> [11] (distinct_points(C23_0_1, C23_0_1) | distinct_points(C23_0_1, C23_0_1))
% 2.29/0.93
% 2.29/0.93 [11] BETA_OR : (distinct_points(C23_0_1, C23_0_1) | distinct_points(C23_0_1, C23_0_1))
% 2.29/0.93 -> [12] distinct_points(C23_0_1, C23_0_1)
% 2.29/0.93 -> [13] distinct_points(C23_0_1, C23_0_1)
% 2.29/0.93
% 2.29/0.93 [13] CLOSURE : distinct_points(C23_0_1, C23_0_1)
% 2.29/0.93
% 2.29/0.93 [12] CLOSURE : distinct_points(C23_0_1, C23_0_1)
% 2.29/0.93
% 2.29/0.93 [10] GAMMA_FORALL : ! [L24_24] : (~distinct_lines(L24_24, L24_24))
% 2.29/0.93 -> [14] ~distinct_lines(N27_0_3, N27_0_3)
% 2.29/0.93
% 2.29/0.93 [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))))
% 2.29/0.93 -> [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)))
% 2.29/0.93
% 2.29/0.93 [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)))
% 2.29/0.93 -> [16] ~distinct_lines(N27_0_3, N27_0_3)
% 2.29/0.93 -> [17] (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3))
% 2.29/0.93
% 2.29/0.93 [17] BETA_OR : (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3))
% 2.29/0.93 -> [18] distinct_lines(N27_0_3, N27_0_3)
% 2.29/0.93 -> [19] distinct_lines(N27_0_3, N27_0_3)
% 2.29/0.93
% 2.29/0.93 [18] CLOSURE : distinct_lines(N27_0_3, N27_0_3)
% 2.29/0.93
% 2.29/0.93 [19] CLOSURE : distinct_lines(N27_0_3, N27_0_3)
% 2.29/0.93
% 2.29/0.93 [16] GAMMA_FORALL : ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28))
% 2.29/0.93 -> [20] ~unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))
% 2.29/0.93
% 2.29/0.93 [20] GAMMA_FORALL : ! [L29_29, M30_30, N31_31] : ((unequally_directed_lines(L29_29, M30_30) => (unequally_directed_lines(L29_29, N31_31) | unequally_directed_lines(M30_30, N31_31))))
% 2.29/0.93 -> [21] (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) => (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))))
% 2.29/0.93
% 2.29/0.93 [21] BETA_IMPLY : (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) => (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))))
% 2.29/0.93 -> [22] ~unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))
% 2.29/0.93 -> [23] (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)))
% 2.29/0.93
% 2.29/0.93 [23] BETA_OR : (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)))
% 2.29/0.93 -> [24] unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))
% 2.29/0.93 -> [25] unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))
% 2.29/0.93
% 2.29/0.93 [25] CLOSURE : unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))
% 2.29/0.93
% 2.29/0.93 [24] CLOSURE : unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))
% 2.29/0.93
% 2.29/0.93 [26] BETA_IMPLY : ((unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7)))) => ((unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7)))) | (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))))))
% 2.29/0.93 -> [201] ~(unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))))
% 2.29/0.93 -> [202] ((unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7)))) | (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7)))))
% 2.29/0.93
% 2.29/0.93 [202] BETA_OR : ((unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7)))) | (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7)))))
% 2.29/0.93 -> [205] (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))))
% 2.29/0.93 -> [206] (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))))
% 2.29/0.93
% 2.29/0.93 [205] ALPHA_AND : (unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))))
% 2.29/0.93 -> [207] unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)), unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7)))
% 2.29/0.93
% 2.29/0.93 [207] CLOSURE : unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7)))
% 2.29/0.93
% 2.29/0.93 [209] CLOSURE : unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))
% 2.29/0.93
% 2.29/0.93 [201] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)) & unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7))))
% 2.29/0.93 -> [324] ~unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))
% 2.29/0.93 -> [325] ~unequally_directed_lines(reverse_line(M36_6_7), reverse_line(reverse_line(M36_6_7)))
% 2.29/0.93
% 2.29/0.93 [325] 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)))))
% 2.29/0.93 -> [327] ((line(M36_7_7) & line(M36_7_7)) => (unequally_directed_lines(M36_7_7, M36_7_7) | unequally_directed_lines(M36_7_7, reverse_line(M36_7_7))))
% 2.29/0.93
% 2.29/0.93 [327] BETA_IMPLY : ((line(M36_7_7) & line(M36_7_7)) => (unequally_directed_lines(M36_7_7, M36_7_7) | unequally_directed_lines(M36_7_7, reverse_line(M36_7_7))))
% 2.29/0.93 -> [330] ~(line(M36_7_7) & line(M36_7_7))
% 2.29/0.93 -> [331] (unequally_directed_lines(M36_7_7, M36_7_7) | unequally_directed_lines(M36_7_7, reverse_line(M36_7_7)))
% 2.29/0.93
% 2.29/0.93 [331] BETA_OR : (unequally_directed_lines(M36_7_7, M36_7_7) | unequally_directed_lines(M36_7_7, reverse_line(M36_7_7)))
% 2.29/0.93 -> [338] unequally_directed_lines(M36_7_7, M36_7_7)
% 2.29/0.93 -> [339] unequally_directed_lines(M36_7_7, reverse_line(M36_7_7))
% 2.29/0.93
% 2.29/0.93 [339] CLOSURE : unequally_directed_lines(M36_7_7, reverse_line(M36_7_7))
% 2.29/0.93
% 2.29/0.93 [338] CLOSURE : unequally_directed_lines(M36_7_7, M36_7_7)
% 2.29/0.93
% 2.29/0.93 [330] BETA_NOT_AND : ~(line(M36_7_7) & line(M36_7_7))
% 2.29/0.93 -> [336] ~line(M36_7_7)
% 2.29/0.93 -> [337] ~line(M36_7_7)
% 2.29/0.93
% 2.29/0.93 [336] 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)))))
% 2.29/0.93 -> [341] ((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)))))
% 2.29/0.93
% 2.29/0.93 [341] 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)))))
% 2.29/0.93 -> [348] ~(unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) & unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.29/0.93 -> [349] (left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) | left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.29/0.93
% 2.29/0.93 [348] 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))))
% 2.29/0.93 -> [354] ~unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.29/0.93 -> [355] ~unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.29/0.93
% 2.29/0.93 [355] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.29/0.93 -> [366] ~(left_apart_point(A39_52_9, L40_52_9) | left_apart_point(A39_52_9, reverse_line(L40_52_9)))
% 2.29/0.93
% 2.29/0.93 [366] ALPHA_NOT_OR : ~(left_apart_point(A39_52_9, L40_52_9) | left_apart_point(A39_52_9, reverse_line(L40_52_9)))
% 2.29/0.93 -> [369] ~left_apart_point(A39_52_9, L40_52_9), ~left_apart_point(A39_52_9, reverse_line(L40_52_9))
% 2.29/0.93
% 2.29/0.93 [369] CLOSURE : ~left_apart_point(A39_52_9, L40_52_9)
% 2.29/0.93
% 2.29/0.93 [354] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.29/0.93 -> [379] ~(left_apart_point(A39_58_9, L40_58_9) | left_apart_point(A39_58_9, reverse_line(L40_58_9)))
% 2.29/0.93
% 2.29/0.93 [379] ALPHA_NOT_OR : ~(left_apart_point(A39_58_9, L40_58_9) | left_apart_point(A39_58_9, reverse_line(L40_58_9)))
% 2.29/0.93 -> [383] ~left_apart_point(A39_58_9, L40_58_9), ~left_apart_point(A39_58_9, reverse_line(L40_58_9))
% 2.29/0.93
% 2.29/0.93 [383] CLOSURE : ~left_apart_point(A39_58_9, L40_58_9)
% 2.29/0.93
% 2.29/0.93 [349] 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))))
% 2.29/0.93 -> [360] left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.29/0.93 -> [361] left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.29/0.93
% 2.29/0.93 [360] CLOSURE : left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.29/0.93
% 2.29/0.93 [361] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.29/0.93 -> [384] ~(left_apart_point(A39_61_9, L40_61_9) | left_apart_point(A39_61_9, reverse_line(L40_61_9)))
% 2.29/0.93
% 2.29/0.93 [384] ALPHA_NOT_OR : ~(left_apart_point(A39_61_9, L40_61_9) | left_apart_point(A39_61_9, reverse_line(L40_61_9)))
% 2.29/0.93 -> [386] ~left_apart_point(A39_61_9, L40_61_9), ~left_apart_point(A39_61_9, reverse_line(L40_61_9))
% 2.29/0.93
% 2.29/0.93 [386] CLOSURE : ~left_apart_point(A39_61_9, L40_61_9)
% 2.29/0.93
% 2.29/0.93 [337] 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)))))
% 2.29/0.93 -> [345] ((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)))))
% 2.29/0.93
% 2.29/0.93 [345] 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)))))
% 2.29/0.93 -> [350] ~(unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) & unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.29/0.93 -> [351] (left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) | left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.29/0.93
% 2.29/0.93 [350] 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))))
% 2.29/0.93 -> [362] ~unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.29/0.93 -> [363] ~unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.29/0.93
% 2.29/0.93 [363] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.29/0.93 -> [368] ~(left_apart_point(A39_54_9, L40_54_9) | left_apart_point(A39_54_9, reverse_line(L40_54_9)))
% 2.29/0.93
% 2.29/0.93 [368] ALPHA_NOT_OR : ~(left_apart_point(A39_54_9, L40_54_9) | left_apart_point(A39_54_9, reverse_line(L40_54_9)))
% 2.29/0.93 -> [373] ~left_apart_point(A39_54_9, L40_54_9), ~left_apart_point(A39_54_9, reverse_line(L40_54_9))
% 2.29/0.93
% 2.29/0.93 [373] CLOSURE : ~left_apart_point(A39_54_9, L40_54_9)
% 2.29/0.93
% 2.29/0.93 [362] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.29/0.93 -> [378] ~(left_apart_point(A39_57_9, L40_57_9) | left_apart_point(A39_57_9, reverse_line(L40_57_9)))
% 2.29/0.93
% 2.29/0.93 [378] ALPHA_NOT_OR : ~(left_apart_point(A39_57_9, L40_57_9) | left_apart_point(A39_57_9, reverse_line(L40_57_9)))
% 2.29/0.93 -> [381] ~left_apart_point(A39_57_9, L40_57_9), ~left_apart_point(A39_57_9, reverse_line(L40_57_9))
% 2.29/0.93
% 2.29/0.93 [381] CLOSURE : ~left_apart_point(A39_57_9, L40_57_9)
% 2.29/0.93
% 2.29/0.93 [351] 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))))
% 2.29/0.93 -> [375] left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.29/0.93 -> [376] left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.29/0.93
% 2.29/0.93 [375] CLOSURE : left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.29/0.93
% 2.29/0.93 [376] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.29/0.93 -> [390] ~(left_apart_point(A39_62_9, L40_62_9) | left_apart_point(A39_62_9, reverse_line(L40_62_9)))
% 2.29/0.93
% 2.29/0.93 [390] ALPHA_NOT_OR : ~(left_apart_point(A39_62_9, L40_62_9) | left_apart_point(A39_62_9, reverse_line(L40_62_9)))
% 2.29/0.93 -> [393] ~left_apart_point(A39_62_9, L40_62_9), ~left_apart_point(A39_62_9, reverse_line(L40_62_9))
% 2.29/0.93
% 2.29/0.93 [393] CLOSURE : ~left_apart_point(A39_62_9, L40_62_9)
% 2.29/0.93
% 2.29/0.93 [324] 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)))))
% 2.29/0.93 -> [326] ((line(reverse_line(M36_6_7)) & line(M36_6_7)) => (unequally_directed_lines(reverse_line(M36_6_7), M36_6_7) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))))
% 2.29/0.93
% 2.29/0.93 [326] BETA_IMPLY : ((line(reverse_line(M36_6_7)) & line(M36_6_7)) => (unequally_directed_lines(reverse_line(M36_6_7), M36_6_7) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))))
% 2.29/0.93 -> [328] ~(line(reverse_line(M36_6_7)) & line(M36_6_7))
% 2.29/0.93 -> [329] (unequally_directed_lines(reverse_line(M36_6_7), M36_6_7) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)))
% 2.29/0.93
% 2.29/0.93 [328] BETA_NOT_AND : ~(line(reverse_line(M36_6_7)) & line(M36_6_7))
% 2.29/0.93 -> [332] ~line(reverse_line(M36_6_7))
% 2.29/0.93 -> [333] ~line(M36_6_7)
% 2.29/0.93
% 2.29/0.93 [332] 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)))))
% 2.29/0.93 -> [342] ((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)))))
% 2.29/0.93
% 2.29/0.93 [342] 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)))))
% 2.29/0.93 -> [346] ~(unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) & unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.29/0.93 -> [347] (left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) | left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.29/0.93
% 2.29/0.93 [346] 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))))
% 2.29/0.93 -> [356] ~unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.29/0.93 -> [357] ~unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.29/0.93
% 2.29/0.93 [356] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.29/0.93 -> [367] ~(left_apart_point(A39_53_9, L40_53_9) | left_apart_point(A39_53_9, reverse_line(L40_53_9)))
% 2.29/0.93
% 2.29/0.93 [367] ALPHA_NOT_OR : ~(left_apart_point(A39_53_9, L40_53_9) | left_apart_point(A39_53_9, reverse_line(L40_53_9)))
% 2.29/0.93 -> [370] ~left_apart_point(A39_53_9, L40_53_9), ~left_apart_point(A39_53_9, reverse_line(L40_53_9))
% 2.29/0.93
% 2.29/0.93 [370] CLOSURE : ~left_apart_point(A39_53_9, L40_53_9)
% 2.29/0.93
% 2.29/0.93 [357] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.29/0.93 -> [382] ~(left_apart_point(A39_60_9, L40_60_9) | left_apart_point(A39_60_9, reverse_line(L40_60_9)))
% 2.29/0.93
% 2.29/0.93 [382] ALPHA_NOT_OR : ~(left_apart_point(A39_60_9, L40_60_9) | left_apart_point(A39_60_9, reverse_line(L40_60_9)))
% 2.29/0.93 -> [387] ~left_apart_point(A39_60_9, L40_60_9), ~left_apart_point(A39_60_9, reverse_line(L40_60_9))
% 2.29/0.93
% 2.29/0.93 [387] CLOSURE : ~left_apart_point(A39_60_9, L40_60_9)
% 2.29/0.93
% 2.29/0.93 [347] 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))))
% 2.29/0.93 -> [364] left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.29/0.93 -> [365] left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.29/0.93
% 2.29/0.93 [364] CLOSURE : left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.29/0.93
% 2.29/0.93 [365] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.29/0.93 -> [380] ~(left_apart_point(A39_59_9, L40_59_9) | left_apart_point(A39_59_9, reverse_line(L40_59_9)))
% 2.29/0.93
% 2.29/0.93 [380] ALPHA_NOT_OR : ~(left_apart_point(A39_59_9, L40_59_9) | left_apart_point(A39_59_9, reverse_line(L40_59_9)))
% 2.29/0.93 -> [391] ~left_apart_point(A39_59_9, L40_59_9), ~left_apart_point(A39_59_9, reverse_line(L40_59_9))
% 2.29/0.93
% 2.29/0.93 [391] CLOSURE : ~left_apart_point(A39_59_9, L40_59_9)
% 2.29/0.93
% 2.29/0.93 [333] 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)))))
% 2.29/0.93 -> [340] ((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)))))
% 2.29/0.93
% 2.29/0.93 [340] 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)))))
% 2.29/0.93 -> [343] ~(unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) & unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.29/0.93 -> [344] (left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) | left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.29/0.93
% 2.29/0.93 [343] 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))))
% 2.29/0.93 -> [352] ~unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.29/0.93 -> [353] ~unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.29/0.93
% 2.29/0.93 [352] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.29/0.93 -> [371] ~(left_apart_point(A39_55_9, L40_55_9) | left_apart_point(A39_55_9, reverse_line(L40_55_9)))
% 2.29/0.93
% 2.29/0.93 [371] ALPHA_NOT_OR : ~(left_apart_point(A39_55_9, L40_55_9) | left_apart_point(A39_55_9, reverse_line(L40_55_9)))
% 2.29/0.93 -> [372] ~left_apart_point(A39_55_9, L40_55_9), ~left_apart_point(A39_55_9, reverse_line(L40_55_9))
% 2.29/0.93
% 2.29/0.93 [372] CLOSURE : ~left_apart_point(A39_55_9, L40_55_9)
% 2.29/0.93
% 2.29/0.93 [353] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.29/0.93 -> [374] ~(left_apart_point(A39_56_9, L40_56_9) | left_apart_point(A39_56_9, reverse_line(L40_56_9)))
% 2.29/0.93
% 2.29/0.93 [374] ALPHA_NOT_OR : ~(left_apart_point(A39_56_9, L40_56_9) | left_apart_point(A39_56_9, reverse_line(L40_56_9)))
% 2.29/0.93 -> [377] ~left_apart_point(A39_56_9, L40_56_9), ~left_apart_point(A39_56_9, reverse_line(L40_56_9))
% 2.29/0.93
% 2.29/0.93 [377] CLOSURE : ~left_apart_point(A39_56_9, L40_56_9)
% 2.29/0.93
% 2.29/0.93 [344] 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))))
% 2.29/0.93 -> [358] left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.29/0.93 -> [359] left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.29/0.93
% 2.29/0.93 [358] CLOSURE : left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.29/0.93
% 2.29/0.93 [359] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.29/0.93 -> [392] ~(left_apart_point(A39_63_9, L40_63_9) | left_apart_point(A39_63_9, reverse_line(L40_63_9)))
% 2.29/0.93
% 2.29/0.93 [392] ALPHA_NOT_OR : ~(left_apart_point(A39_63_9, L40_63_9) | left_apart_point(A39_63_9, reverse_line(L40_63_9)))
% 2.29/0.93 -> [396] ~left_apart_point(A39_63_9, L40_63_9), ~left_apart_point(A39_63_9, reverse_line(L40_63_9))
% 2.29/0.93
% 2.29/0.93 [396] CLOSURE : ~left_apart_point(A39_63_9, L40_63_9)
% 2.29/0.93
% 2.29/0.93 [329] BETA_OR : (unequally_directed_lines(reverse_line(M36_6_7), M36_6_7) | unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7)))
% 2.29/0.93 -> [334] unequally_directed_lines(reverse_line(M36_6_7), M36_6_7)
% 2.29/0.93 -> [335] unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))
% 2.29/0.93
% 2.29/0.93 [335] CLOSURE : unequally_directed_lines(reverse_line(M36_6_7), reverse_line(M36_6_7))
% 2.29/0.93
% 2.29/0.93 [334] 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)))))
% 2.29/0.93 -> [385] ((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)))))
% 2.29/0.93
% 2.29/0.93 [385] 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)))))
% 2.29/0.93 -> [388] ~(unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) & unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.29/0.93 -> [389] (left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878)) | left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878))))
% 2.29/0.93
% 2.29/0.93 [389] 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))))
% 2.29/0.93 -> [397] left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.29/0.93 -> [398] left_convergent_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.29/0.93
% 2.29/0.93 [397] CLOSURE : left_convergent_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.29/0.93
% 2.29/0.93 [398] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.29/0.93 -> [399] ~(left_apart_point(A39_64_9, L40_64_9) | left_apart_point(A39_64_9, reverse_line(L40_64_9)))
% 2.29/0.93
% 2.29/0.93 [399] ALPHA_NOT_OR : ~(left_apart_point(A39_64_9, L40_64_9) | left_apart_point(A39_64_9, reverse_line(L40_64_9)))
% 2.29/0.93 -> [400] ~left_apart_point(A39_64_9, L40_64_9), ~left_apart_point(A39_64_9, reverse_line(L40_64_9))
% 2.29/0.93
% 2.29/0.93 [400] CLOSURE : ~left_apart_point(A39_64_9, L40_64_9)
% 2.29/0.93
% 2.29/0.93 [388] 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))))
% 2.29/0.93 -> [403] ~unequally_directed_lines(skolem_L7979, line_connecting(skolem_A7777, skolem_B7878))
% 2.29/0.93 -> [404] ~unequally_directed_lines(skolem_L7979, reverse_line(line_connecting(skolem_A7777, skolem_B7878)))
% 2.29/0.93
% 2.29/0.93 [404] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.29/0.93 -> [406] ~(left_apart_point(A39_67_9, L40_67_9) | left_apart_point(A39_67_9, reverse_line(L40_67_9)))
% 2.29/0.93
% 2.29/0.93 [406] ALPHA_NOT_OR : ~(left_apart_point(A39_67_9, L40_67_9) | left_apart_point(A39_67_9, reverse_line(L40_67_9)))
% 2.29/0.93 -> [408] ~left_apart_point(A39_67_9, L40_67_9), ~left_apart_point(A39_67_9, reverse_line(L40_67_9))
% 2.29/0.93
% 2.29/0.93 [408] CLOSURE : ~left_apart_point(A39_67_9, L40_67_9)
% 2.29/0.93
% 2.29/0.93 [403] GAMMA_FORALL : ! [A39_39, L40_40] : (~(left_apart_point(A39_39, L40_40) | left_apart_point(A39_39, reverse_line(L40_40))))
% 2.29/0.93 -> [405] ~(left_apart_point(A39_66_9, L40_66_9) | left_apart_point(A39_66_9, reverse_line(L40_66_9)))
% 2.29/0.93
% 2.29/0.93 [405] ALPHA_NOT_OR : ~(left_apart_point(A39_66_9, L40_66_9) | left_apart_point(A39_66_9, reverse_line(L40_66_9)))
% 2.29/0.93 -> [407] ~left_apart_point(A39_66_9, L40_66_9), ~left_apart_point(A39_66_9, reverse_line(L40_66_9))
% 2.29/0.93
% 2.29/0.93 [407] CLOSURE : ~left_apart_point(A39_66_9, L40_66_9)
% 2.29/0.93
% 2.29/0.93 % SZS output end Proof for theBenchmark.p
% 2.29/0.93 [0.579455s][1][Res] 1871 goroutines created
% 2.29/0.93 ==== Result ====
% 2.29/0.93 [0.579491s][1][Res] VALID
% 2.29/0.93 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------