TSTP Solution File: GEO227+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO227+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n011.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 15:18:34 EDT 2022
% Result : Theorem 0.11s 0.39s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : GEO227+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.00/0.07 % Command : goeland -dmt -presko -proof %s
% 0.06/0.26 % Computer : n011.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Wed Aug 31 07:02:10 EDT 2022
% 0.06/0.26 % CPUTime :
% 0.06/0.27 [DMT] DMT loaded with preskolemization
% 0.06/0.27 [EQ] equality loaded.
% 0.06/0.27 [0.000023s][1][MAIN] Problem : theBenchmark.p
% 0.06/0.27 Conjecture not found
% 0.06/0.27 Start search
% 0.06/0.27 nb_step : 1 - limit : 32
% 0.06/0.27 Launch Gotab with destructive = true
% 0.11/0.39 % SZS output start Proof for theBenchmark.p
% 0.11/0.39 [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))))) & ~! [L77_77, M78_78] : (((line(L77_77) & line(M78_78)) => ~(~unequally_directed_lines(L77_77, M78_78) & ~unequally_directed_lines(L77_77, reverse_line(M78_78))))))
% 0.11/0.39 -> [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))))), ~! [L77_77, M78_78] : (((line(L77_77) & line(M78_78)) => ~(~unequally_directed_lines(L77_77, M78_78) & ~unequally_directed_lines(L77_77, reverse_line(M78_78)))))
% 0.11/0.39
% 0.11/0.39 [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)))))
% 0.11/0.39 -> [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))))
% 0.11/0.39
% 0.11/0.39 [2] DELTA_NOT_FORALL : ~! [L77_77, M78_78] : (((line(L77_77) & line(M78_78)) => ~(~unequally_directed_lines(L77_77, M78_78) & ~unequally_directed_lines(L77_77, reverse_line(M78_78)))))
% 0.11/0.39 -> [3] ~((line(skolem_L7777) & line(skolem_M7878)) => ~(~unequally_directed_lines(skolem_L7777, skolem_M7878) & ~unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878))))
% 0.11/0.39
% 0.11/0.39 [3] ALPHA_NOT_IMPLY : ~((line(skolem_L7777) & line(skolem_M7878)) => ~(~unequally_directed_lines(skolem_L7777, skolem_M7878) & ~unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878))))
% 0.11/0.39 -> [4] (line(skolem_L7777) & line(skolem_M7878)), ~~(~unequally_directed_lines(skolem_L7777, skolem_M7878) & ~unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878)))
% 0.11/0.39
% 0.11/0.39 [4] ALPHA_AND : (line(skolem_L7777) & line(skolem_M7878))
% 0.11/0.39 -> [5] line(skolem_L7777), line(skolem_M7878)
% 0.11/0.39
% 0.11/0.39 [5] ALPHA_NOT_NOT : ~~(~unequally_directed_lines(skolem_L7777, skolem_M7878) & ~unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878)))
% 0.11/0.39 -> [6] (~unequally_directed_lines(skolem_L7777, skolem_M7878) & ~unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878)))
% 0.11/0.39
% 0.11/0.39 [6] ALPHA_AND : (~unequally_directed_lines(skolem_L7777, skolem_M7878) & ~unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878)))
% 0.11/0.39 -> [7] ~unequally_directed_lines(skolem_L7777, skolem_M7878), ~unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878))
% 0.11/0.39
% 0.11/0.39 [7] GAMMA_FORALL : ! [A20_20] : (~distinct_points(A20_20, A20_20))
% 0.11/0.39 -> [8] ~distinct_points(C23_0_1, C23_0_1)
% 0.11/0.39
% 0.11/0.39 [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))))
% 0.11/0.39 -> [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)))
% 0.11/0.39
% 0.11/0.39 [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)))
% 0.11/0.39 -> [10] ~distinct_points(C23_0_1, C23_0_1)
% 0.11/0.39 -> [11] (distinct_points(C23_0_1, C23_0_1) | distinct_points(C23_0_1, C23_0_1))
% 0.11/0.39
% 0.11/0.39 [11] BETA_OR : (distinct_points(C23_0_1, C23_0_1) | distinct_points(C23_0_1, C23_0_1))
% 0.11/0.39 -> [12] distinct_points(C23_0_1, C23_0_1)
% 0.11/0.39 -> [13] distinct_points(C23_0_1, C23_0_1)
% 0.11/0.39
% 0.11/0.39 [13] CLOSURE : distinct_points(C23_0_1, C23_0_1)
% 0.11/0.39
% 0.11/0.39 [12] CLOSURE : distinct_points(C23_0_1, C23_0_1)
% 0.11/0.39
% 0.11/0.39 [10] GAMMA_FORALL : ! [L24_24] : (~distinct_lines(L24_24, L24_24))
% 0.11/0.39 -> [14] ~distinct_lines(N27_0_3, N27_0_3)
% 0.11/0.39
% 0.11/0.39 [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))))
% 0.11/0.39 -> [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)))
% 0.11/0.39
% 0.11/0.39 [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)))
% 0.11/0.39 -> [16] ~distinct_lines(N27_0_3, N27_0_3)
% 0.11/0.39 -> [17] (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3))
% 0.11/0.39
% 0.11/0.39 [17] BETA_OR : (distinct_lines(N27_0_3, N27_0_3) | distinct_lines(N27_0_3, N27_0_3))
% 0.11/0.39 -> [18] distinct_lines(N27_0_3, N27_0_3)
% 0.11/0.39 -> [19] distinct_lines(N27_0_3, N27_0_3)
% 0.11/0.39
% 0.11/0.39 [18] CLOSURE : distinct_lines(N27_0_3, N27_0_3)
% 0.11/0.39
% 0.11/0.39 [19] CLOSURE : distinct_lines(N27_0_3, N27_0_3)
% 0.11/0.39
% 0.11/0.39 [16] GAMMA_FORALL : ! [L28_28] : (~unequally_directed_lines(L28_28, L28_28))
% 0.11/0.39 -> [20] ~unequally_directed_lines(skolem_M7878, skolem_M7878)
% 0.11/0.39
% 0.11/0.39 [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))))
% 0.11/0.39 -> [21] (unequally_directed_lines(skolem_M7878, skolem_L7777) => (unequally_directed_lines(skolem_M7878, skolem_M7878) | unequally_directed_lines(skolem_L7777, skolem_M7878)))
% 0.11/0.39
% 0.11/0.39 [21] BETA_IMPLY : (unequally_directed_lines(skolem_M7878, skolem_L7777) => (unequally_directed_lines(skolem_M7878, skolem_M7878) | unequally_directed_lines(skolem_L7777, skolem_M7878)))
% 0.11/0.39 -> [22] ~unequally_directed_lines(skolem_M7878, skolem_L7777)
% 0.11/0.39 -> [23] (unequally_directed_lines(skolem_M7878, skolem_M7878) | unequally_directed_lines(skolem_L7777, skolem_M7878))
% 0.11/0.39
% 0.11/0.39 [23] BETA_OR : (unequally_directed_lines(skolem_M7878, skolem_M7878) | unequally_directed_lines(skolem_L7777, skolem_M7878))
% 0.11/0.39 -> [24] unequally_directed_lines(skolem_M7878, skolem_M7878)
% 0.11/0.39 -> [25] unequally_directed_lines(skolem_L7777, skolem_M7878)
% 0.11/0.39
% 0.11/0.39 [25] CLOSURE : unequally_directed_lines(skolem_L7777, skolem_M7878)
% 0.11/0.39
% 0.11/0.39 [24] CLOSURE : unequally_directed_lines(skolem_M7878, skolem_M7878)
% 0.11/0.39
% 0.11/0.39 [26] BETA_IMPLY : ((unequally_directed_lines(skolem_L7777, skolem_L7777) & unequally_directed_lines(skolem_L7777, reverse_line(skolem_L7777))) => ((unequally_directed_lines(skolem_L7777, skolem_M7878) & unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878))) | (unequally_directed_lines(skolem_L7777, skolem_M7878) & unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878)))))
% 0.11/0.39 -> [51] ~(unequally_directed_lines(skolem_L7777, skolem_L7777) & unequally_directed_lines(skolem_L7777, reverse_line(skolem_L7777)))
% 0.11/0.39 -> [52] ((unequally_directed_lines(skolem_L7777, skolem_M7878) & unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878))) | (unequally_directed_lines(skolem_L7777, skolem_M7878) & unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878))))
% 0.11/0.39
% 0.11/0.39 [52] BETA_OR : ((unequally_directed_lines(skolem_L7777, skolem_M7878) & unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878))) | (unequally_directed_lines(skolem_L7777, skolem_M7878) & unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878))))
% 0.11/0.39 -> [55] (unequally_directed_lines(skolem_L7777, skolem_M7878) & unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878)))
% 0.11/0.39 -> [56] (unequally_directed_lines(skolem_L7777, skolem_M7878) & unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878)))
% 0.11/0.39
% 0.11/0.39 [55] ALPHA_AND : (unequally_directed_lines(skolem_L7777, skolem_M7878) & unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878)))
% 0.11/0.39 -> [57] unequally_directed_lines(skolem_L7777, skolem_M7878), unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878))
% 0.11/0.39
% 0.11/0.39 [57] CLOSURE : unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878))
% 0.11/0.39
% 0.11/0.39 [58] CLOSURE : unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878))
% 0.11/0.39
% 0.11/0.39 [51] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L7777, skolem_L7777) & unequally_directed_lines(skolem_L7777, reverse_line(skolem_L7777)))
% 0.11/0.39 -> [53] ~unequally_directed_lines(skolem_L7777, skolem_L7777)
% 0.11/0.39 -> [54] ~unequally_directed_lines(skolem_L7777, reverse_line(skolem_L7777))
% 0.11/0.39
% 0.11/0.39 [53] 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)))))
% 0.11/0.39 -> [59] ((line(skolem_L7777) & line(skolem_M7878)) => (unequally_directed_lines(skolem_L7777, skolem_M7878) | unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878))))
% 0.11/0.39
% 0.11/0.39 [59] BETA_IMPLY : ((line(skolem_L7777) & line(skolem_M7878)) => (unequally_directed_lines(skolem_L7777, skolem_M7878) | unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878))))
% 0.11/0.39 -> [61] ~(line(skolem_L7777) & line(skolem_M7878))
% 0.11/0.39 -> [62] (unequally_directed_lines(skolem_L7777, skolem_M7878) | unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878)))
% 0.11/0.39
% 0.11/0.39 [62] BETA_OR : (unequally_directed_lines(skolem_L7777, skolem_M7878) | unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878)))
% 0.11/0.39 -> [69] unequally_directed_lines(skolem_L7777, skolem_M7878)
% 0.11/0.39 -> [70] unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878))
% 0.11/0.39
% 0.11/0.39 [70] CLOSURE : unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878))
% 0.11/0.39
% 0.11/0.39 [69] CLOSURE : unequally_directed_lines(skolem_L7777, skolem_M7878)
% 0.11/0.39
% 0.11/0.39 [61] BETA_NOT_AND : ~(line(skolem_L7777) & line(skolem_M7878))
% 0.11/0.39 -> [73] ~line(skolem_L7777)
% 0.11/0.39 -> [74] ~line(skolem_M7878)
% 0.11/0.39
% 0.11/0.39 [73] CLOSURE : ~line(skolem_L7777)
% 0.11/0.39
% 0.11/0.39 [74] CLOSURE : ~line(skolem_M7878)
% 0.11/0.39
% 0.11/0.39 [54] 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)))))
% 0.11/0.39 -> [60] ((line(skolem_L7777) & line(skolem_M7878)) => (unequally_directed_lines(skolem_L7777, skolem_M7878) | unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878))))
% 0.11/0.39
% 0.11/0.39 [60] BETA_IMPLY : ((line(skolem_L7777) & line(skolem_M7878)) => (unequally_directed_lines(skolem_L7777, skolem_M7878) | unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878))))
% 0.11/0.39 -> [63] ~(line(skolem_L7777) & line(skolem_M7878))
% 0.11/0.39 -> [64] (unequally_directed_lines(skolem_L7777, skolem_M7878) | unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878)))
% 0.11/0.39
% 0.11/0.39 [64] BETA_OR : (unequally_directed_lines(skolem_L7777, skolem_M7878) | unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878)))
% 0.11/0.39 -> [71] unequally_directed_lines(skolem_L7777, skolem_M7878)
% 0.11/0.39 -> [72] unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878))
% 0.11/0.39
% 0.11/0.39 [71] CLOSURE : unequally_directed_lines(skolem_L7777, skolem_M7878)
% 0.11/0.39
% 0.11/0.39 [72] CLOSURE : unequally_directed_lines(skolem_L7777, reverse_line(skolem_M7878))
% 0.11/0.39
% 0.11/0.39 [63] BETA_NOT_AND : ~(line(skolem_L7777) & line(skolem_M7878))
% 0.11/0.39 -> [75] ~line(skolem_L7777)
% 0.11/0.39 -> [76] ~line(skolem_M7878)
% 0.11/0.39
% 0.11/0.39 [75] CLOSURE : ~line(skolem_L7777)
% 0.11/0.39
% 0.11/0.39 [76] CLOSURE : ~line(skolem_M7878)
% 0.11/0.39
% 0.11/0.39 % SZS output end Proof for theBenchmark.p
% 0.11/0.39 [0.128604s][1][Res] 524 goroutines created
% 0.11/0.39 ==== Result ====
% 0.11/0.39 [0.128625s][1][Res] VALID
% 0.11/0.39 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------