TSTP Solution File: GEO264+1 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO264+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n008.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 15:18:51 EDT 2022
% Result : Theorem 2.70s 0.94s
% Output : Proof 2.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GEO264+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.03/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 07:16:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.35 [DMT] DMT loaded with preskolemization
% 0.20/0.35 [EQ] equality loaded.
% 0.20/0.35 [0.000039s][1][MAIN] Problem : theBenchmark.p
% 0.20/0.36 Conjecture not found
% 0.20/0.36 Start search
% 0.20/0.36 nb_step : 1 - limit : 32
% 0.20/0.36 Launch Gotab with destructive = true
% 2.70/0.93 % SZS output start Proof for theBenchmark.p
% 2.70/0.94 [0] ALPHA_AND : ((! [A21_21] : (~distinct_points(A21_21, A21_21)) & ! [A22_22, B23_23, C24_24] : ((distinct_points(A22_22, B23_23) => (distinct_points(A22_22, C24_24) | distinct_points(B23_23, C24_24)))) & ! [L25_25] : (~distinct_lines(L25_25, L25_25)) & ! [L26_26, M27_27, N28_28] : ((distinct_lines(L26_26, M27_27) => (distinct_lines(L26_26, N28_28) | distinct_lines(M27_27, N28_28)))) & ! [L29_29] : (~unequally_directed_lines(L29_29, L29_29)) & ! [L30_30, M31_31, N32_32] : ((unequally_directed_lines(L30_30, M31_31) => (unequally_directed_lines(L30_30, N32_32) | unequally_directed_lines(M31_31, N32_32)))) & ! [L33_33, M34_34, N35_35] : (((unequally_directed_lines(L33_33, M34_34) & unequally_directed_lines(L33_33, reverse_line(M34_34))) => ((unequally_directed_lines(L33_33, N35_35) & unequally_directed_lines(L33_33, reverse_line(N35_35))) | (unequally_directed_lines(M34_34, N35_35) & unequally_directed_lines(M34_34, reverse_line(N35_35)))))) & ! [L36_36, M37_37] : (((line(L36_36) & line(M37_37)) => (unequally_directed_lines(L36_36, M37_37) | unequally_directed_lines(L36_36, reverse_line(M37_37))))) & ! [L38_38, M39_39] : (((unequally_directed_lines(L38_38, M39_39) & unequally_directed_lines(L38_38, reverse_line(M39_39))) => (left_convergent_lines(L38_38, M39_39) | left_convergent_lines(L38_38, reverse_line(M39_39))))) & ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41)))) & ! [L42_42, M43_43] : (~(left_convergent_lines(L42_42, M43_43) | left_convergent_lines(L42_42, reverse_line(M43_43)))) & ! [A44_44, B45_45] : ((((point(A44_44) & point(B45_45)) & distinct_points(A44_44, B45_45)) => line(line_connecting(A44_44, B45_45)))) & ! [L46_46, M47_47] : (((((line(L46_46) & line(M47_47)) & unequally_directed_lines(L46_46, M47_47)) & unequally_directed_lines(L46_46, reverse_line(M47_47))) => point(intersection_point(L46_46, M47_47)))) & ! [L48_48, A49_49] : (((point(A49_49) & line(L48_48)) => line(parallel_through_point(L48_48, A49_49)))) & ! [L50_50] : ((line(L50_50) => line(reverse_line(L50_50)))) & ! [A51_51, B52_52] : ((distinct_points(A51_51, B52_52) => (~apart_point_and_line(A51_51, line_connecting(A51_51, B52_52)) & ~apart_point_and_line(B52_52, line_connecting(A51_51, B52_52))))) & ! [L53_53, M54_54] : (((unequally_directed_lines(L53_53, M54_54) & unequally_directed_lines(L53_53, reverse_line(M54_54))) => (~apart_point_and_line(intersection_point(L53_53, M54_54), L53_53) & ~apart_point_and_line(intersection_point(L53_53, M54_54), M54_54)))) & ! [A55_55, L56_56] : (~apart_point_and_line(A55_55, parallel_through_point(L56_56, A55_55))) & ! [L57_57] : (~distinct_lines(L57_57, reverse_line(L57_57))) & ! [A58_58, B59_59] : (~unequally_directed_lines(line_connecting(A58_58, B59_59), reverse_line(line_connecting(B59_59, A58_58)))) & ! [A60_60, L61_61] : (~unequally_directed_lines(parallel_through_point(L61_61, A60_60), L61_61)) & ! [A62_62, B63_63, L64_64, M65_65] : (((distinct_points(A62_62, B63_63) & distinct_lines(L64_64, M65_65)) => (((((((left_apart_point(A62_62, L64_64) | left_apart_point(B63_63, L64_64)) | left_apart_point(A62_62, M65_65)) | left_apart_point(B63_63, M65_65)) | left_apart_point(A62_62, reverse_line(L64_64))) | left_apart_point(B63_63, reverse_line(L64_64))) | left_apart_point(A62_62, reverse_line(M65_65))) | left_apart_point(B63_63, reverse_line(M65_65))))) & ! [A66_66, B67_67, L68_68] : (((distinct_points(A66_66, B67_67) & left_apart_point(A66_66, L68_68)) => (left_apart_point(B67_67, L68_68) | left_convergent_lines(line_connecting(A66_66, B67_67), L68_68)))) & ! [A69_69, B70_70, L71_71] : ((left_apart_point(A69_69, L71_71) => (distinct_points(A69_69, B70_70) | left_apart_point(B70_70, L71_71)))) & ! [A72_72, L73_73, M74_74] : (((left_apart_point(A72_72, L73_73) & unequally_directed_lines(L73_73, M74_74)) => (distinct_lines(L73_73, M74_74) | left_apart_point(A72_72, reverse_line(M74_74))))) & ! [L75_75, M76_76, N77_77] : ((left_convergent_lines(L75_75, M76_76) => (unequally_directed_lines(M76_76, N77_77) | left_convergent_lines(L75_75, N77_77))))) & ~! [A78_78, B79_79, C80_80, D81_81] : ((left_apart_point(C80_80, line_connecting(A78_78, B79_79)) => ((left_apart_point(D81_81, reverse_line(line_connecting(B79_79, C80_80))) & left_apart_point(D81_81, reverse_line(line_connecting(C80_80, A78_78)))) => left_apart_point(D81_81, line_connecting(A78_78, B79_79))))))
% 2.70/0.94 -> [1] (! [A21_21] : (~distinct_points(A21_21, A21_21)) & ! [A22_22, B23_23, C24_24] : ((distinct_points(A22_22, B23_23) => (distinct_points(A22_22, C24_24) | distinct_points(B23_23, C24_24)))) & ! [L25_25] : (~distinct_lines(L25_25, L25_25)) & ! [L26_26, M27_27, N28_28] : ((distinct_lines(L26_26, M27_27) => (distinct_lines(L26_26, N28_28) | distinct_lines(M27_27, N28_28)))) & ! [L29_29] : (~unequally_directed_lines(L29_29, L29_29)) & ! [L30_30, M31_31, N32_32] : ((unequally_directed_lines(L30_30, M31_31) => (unequally_directed_lines(L30_30, N32_32) | unequally_directed_lines(M31_31, N32_32)))) & ! [L33_33, M34_34, N35_35] : (((unequally_directed_lines(L33_33, M34_34) & unequally_directed_lines(L33_33, reverse_line(M34_34))) => ((unequally_directed_lines(L33_33, N35_35) & unequally_directed_lines(L33_33, reverse_line(N35_35))) | (unequally_directed_lines(M34_34, N35_35) & unequally_directed_lines(M34_34, reverse_line(N35_35)))))) & ! [L36_36, M37_37] : (((line(L36_36) & line(M37_37)) => (unequally_directed_lines(L36_36, M37_37) | unequally_directed_lines(L36_36, reverse_line(M37_37))))) & ! [L38_38, M39_39] : (((unequally_directed_lines(L38_38, M39_39) & unequally_directed_lines(L38_38, reverse_line(M39_39))) => (left_convergent_lines(L38_38, M39_39) | left_convergent_lines(L38_38, reverse_line(M39_39))))) & ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41)))) & ! [L42_42, M43_43] : (~(left_convergent_lines(L42_42, M43_43) | left_convergent_lines(L42_42, reverse_line(M43_43)))) & ! [A44_44, B45_45] : ((((point(A44_44) & point(B45_45)) & distinct_points(A44_44, B45_45)) => line(line_connecting(A44_44, B45_45)))) & ! [L46_46, M47_47] : (((((line(L46_46) & line(M47_47)) & unequally_directed_lines(L46_46, M47_47)) & unequally_directed_lines(L46_46, reverse_line(M47_47))) => point(intersection_point(L46_46, M47_47)))) & ! [L48_48, A49_49] : (((point(A49_49) & line(L48_48)) => line(parallel_through_point(L48_48, A49_49)))) & ! [L50_50] : ((line(L50_50) => line(reverse_line(L50_50)))) & ! [A51_51, B52_52] : ((distinct_points(A51_51, B52_52) => (~apart_point_and_line(A51_51, line_connecting(A51_51, B52_52)) & ~apart_point_and_line(B52_52, line_connecting(A51_51, B52_52))))) & ! [L53_53, M54_54] : (((unequally_directed_lines(L53_53, M54_54) & unequally_directed_lines(L53_53, reverse_line(M54_54))) => (~apart_point_and_line(intersection_point(L53_53, M54_54), L53_53) & ~apart_point_and_line(intersection_point(L53_53, M54_54), M54_54)))) & ! [A55_55, L56_56] : (~apart_point_and_line(A55_55, parallel_through_point(L56_56, A55_55))) & ! [L57_57] : (~distinct_lines(L57_57, reverse_line(L57_57))) & ! [A58_58, B59_59] : (~unequally_directed_lines(line_connecting(A58_58, B59_59), reverse_line(line_connecting(B59_59, A58_58)))) & ! [A60_60, L61_61] : (~unequally_directed_lines(parallel_through_point(L61_61, A60_60), L61_61)) & ! [A62_62, B63_63, L64_64, M65_65] : (((distinct_points(A62_62, B63_63) & distinct_lines(L64_64, M65_65)) => (((((((left_apart_point(A62_62, L64_64) | left_apart_point(B63_63, L64_64)) | left_apart_point(A62_62, M65_65)) | left_apart_point(B63_63, M65_65)) | left_apart_point(A62_62, reverse_line(L64_64))) | left_apart_point(B63_63, reverse_line(L64_64))) | left_apart_point(A62_62, reverse_line(M65_65))) | left_apart_point(B63_63, reverse_line(M65_65))))) & ! [A66_66, B67_67, L68_68] : (((distinct_points(A66_66, B67_67) & left_apart_point(A66_66, L68_68)) => (left_apart_point(B67_67, L68_68) | left_convergent_lines(line_connecting(A66_66, B67_67), L68_68)))) & ! [A69_69, B70_70, L71_71] : ((left_apart_point(A69_69, L71_71) => (distinct_points(A69_69, B70_70) | left_apart_point(B70_70, L71_71)))) & ! [A72_72, L73_73, M74_74] : (((left_apart_point(A72_72, L73_73) & unequally_directed_lines(L73_73, M74_74)) => (distinct_lines(L73_73, M74_74) | left_apart_point(A72_72, reverse_line(M74_74))))) & ! [L75_75, M76_76, N77_77] : ((left_convergent_lines(L75_75, M76_76) => (unequally_directed_lines(M76_76, N77_77) | left_convergent_lines(L75_75, N77_77))))), ~! [A78_78, B79_79, C80_80, D81_81] : ((left_apart_point(C80_80, line_connecting(A78_78, B79_79)) => ((left_apart_point(D81_81, reverse_line(line_connecting(B79_79, C80_80))) & left_apart_point(D81_81, reverse_line(line_connecting(C80_80, A78_78)))) => left_apart_point(D81_81, line_connecting(A78_78, B79_79)))))
% 2.70/0.94
% 2.70/0.94 [1] ALPHA_AND : (! [A21_21] : (~distinct_points(A21_21, A21_21)) & ! [A22_22, B23_23, C24_24] : ((distinct_points(A22_22, B23_23) => (distinct_points(A22_22, C24_24) | distinct_points(B23_23, C24_24)))) & ! [L25_25] : (~distinct_lines(L25_25, L25_25)) & ! [L26_26, M27_27, N28_28] : ((distinct_lines(L26_26, M27_27) => (distinct_lines(L26_26, N28_28) | distinct_lines(M27_27, N28_28)))) & ! [L29_29] : (~unequally_directed_lines(L29_29, L29_29)) & ! [L30_30, M31_31, N32_32] : ((unequally_directed_lines(L30_30, M31_31) => (unequally_directed_lines(L30_30, N32_32) | unequally_directed_lines(M31_31, N32_32)))) & ! [L33_33, M34_34, N35_35] : (((unequally_directed_lines(L33_33, M34_34) & unequally_directed_lines(L33_33, reverse_line(M34_34))) => ((unequally_directed_lines(L33_33, N35_35) & unequally_directed_lines(L33_33, reverse_line(N35_35))) | (unequally_directed_lines(M34_34, N35_35) & unequally_directed_lines(M34_34, reverse_line(N35_35)))))) & ! [L36_36, M37_37] : (((line(L36_36) & line(M37_37)) => (unequally_directed_lines(L36_36, M37_37) | unequally_directed_lines(L36_36, reverse_line(M37_37))))) & ! [L38_38, M39_39] : (((unequally_directed_lines(L38_38, M39_39) & unequally_directed_lines(L38_38, reverse_line(M39_39))) => (left_convergent_lines(L38_38, M39_39) | left_convergent_lines(L38_38, reverse_line(M39_39))))) & ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41)))) & ! [L42_42, M43_43] : (~(left_convergent_lines(L42_42, M43_43) | left_convergent_lines(L42_42, reverse_line(M43_43)))) & ! [A44_44, B45_45] : ((((point(A44_44) & point(B45_45)) & distinct_points(A44_44, B45_45)) => line(line_connecting(A44_44, B45_45)))) & ! [L46_46, M47_47] : (((((line(L46_46) & line(M47_47)) & unequally_directed_lines(L46_46, M47_47)) & unequally_directed_lines(L46_46, reverse_line(M47_47))) => point(intersection_point(L46_46, M47_47)))) & ! [L48_48, A49_49] : (((point(A49_49) & line(L48_48)) => line(parallel_through_point(L48_48, A49_49)))) & ! [L50_50] : ((line(L50_50) => line(reverse_line(L50_50)))) & ! [A51_51, B52_52] : ((distinct_points(A51_51, B52_52) => (~apart_point_and_line(A51_51, line_connecting(A51_51, B52_52)) & ~apart_point_and_line(B52_52, line_connecting(A51_51, B52_52))))) & ! [L53_53, M54_54] : (((unequally_directed_lines(L53_53, M54_54) & unequally_directed_lines(L53_53, reverse_line(M54_54))) => (~apart_point_and_line(intersection_point(L53_53, M54_54), L53_53) & ~apart_point_and_line(intersection_point(L53_53, M54_54), M54_54)))) & ! [A55_55, L56_56] : (~apart_point_and_line(A55_55, parallel_through_point(L56_56, A55_55))) & ! [L57_57] : (~distinct_lines(L57_57, reverse_line(L57_57))) & ! [A58_58, B59_59] : (~unequally_directed_lines(line_connecting(A58_58, B59_59), reverse_line(line_connecting(B59_59, A58_58)))) & ! [A60_60, L61_61] : (~unequally_directed_lines(parallel_through_point(L61_61, A60_60), L61_61)) & ! [A62_62, B63_63, L64_64, M65_65] : (((distinct_points(A62_62, B63_63) & distinct_lines(L64_64, M65_65)) => (((((((left_apart_point(A62_62, L64_64) | left_apart_point(B63_63, L64_64)) | left_apart_point(A62_62, M65_65)) | left_apart_point(B63_63, M65_65)) | left_apart_point(A62_62, reverse_line(L64_64))) | left_apart_point(B63_63, reverse_line(L64_64))) | left_apart_point(A62_62, reverse_line(M65_65))) | left_apart_point(B63_63, reverse_line(M65_65))))) & ! [A66_66, B67_67, L68_68] : (((distinct_points(A66_66, B67_67) & left_apart_point(A66_66, L68_68)) => (left_apart_point(B67_67, L68_68) | left_convergent_lines(line_connecting(A66_66, B67_67), L68_68)))) & ! [A69_69, B70_70, L71_71] : ((left_apart_point(A69_69, L71_71) => (distinct_points(A69_69, B70_70) | left_apart_point(B70_70, L71_71)))) & ! [A72_72, L73_73, M74_74] : (((left_apart_point(A72_72, L73_73) & unequally_directed_lines(L73_73, M74_74)) => (distinct_lines(L73_73, M74_74) | left_apart_point(A72_72, reverse_line(M74_74))))) & ! [L75_75, M76_76, N77_77] : ((left_convergent_lines(L75_75, M76_76) => (unequally_directed_lines(M76_76, N77_77) | left_convergent_lines(L75_75, N77_77)))))
% 2.70/0.94 -> [2] ! [A21_21] : (~distinct_points(A21_21, A21_21)), ! [A22_22, B23_23, C24_24] : ((distinct_points(A22_22, B23_23) => (distinct_points(A22_22, C24_24) | distinct_points(B23_23, C24_24)))), ! [L25_25] : (~distinct_lines(L25_25, L25_25)), ! [L26_26, M27_27, N28_28] : ((distinct_lines(L26_26, M27_27) => (distinct_lines(L26_26, N28_28) | distinct_lines(M27_27, N28_28)))), ! [L29_29] : (~unequally_directed_lines(L29_29, L29_29)), ! [L30_30, M31_31, N32_32] : ((unequally_directed_lines(L30_30, M31_31) => (unequally_directed_lines(L30_30, N32_32) | unequally_directed_lines(M31_31, N32_32)))), ! [L33_33, M34_34, N35_35] : (((unequally_directed_lines(L33_33, M34_34) & unequally_directed_lines(L33_33, reverse_line(M34_34))) => ((unequally_directed_lines(L33_33, N35_35) & unequally_directed_lines(L33_33, reverse_line(N35_35))) | (unequally_directed_lines(M34_34, N35_35) & unequally_directed_lines(M34_34, reverse_line(N35_35)))))), ! [L36_36, M37_37] : (((line(L36_36) & line(M37_37)) => (unequally_directed_lines(L36_36, M37_37) | unequally_directed_lines(L36_36, reverse_line(M37_37))))), ! [L38_38, M39_39] : (((unequally_directed_lines(L38_38, M39_39) & unequally_directed_lines(L38_38, reverse_line(M39_39))) => (left_convergent_lines(L38_38, M39_39) | left_convergent_lines(L38_38, reverse_line(M39_39))))), ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41)))), ! [L42_42, M43_43] : (~(left_convergent_lines(L42_42, M43_43) | left_convergent_lines(L42_42, reverse_line(M43_43)))), ! [A44_44, B45_45] : ((((point(A44_44) & point(B45_45)) & distinct_points(A44_44, B45_45)) => line(line_connecting(A44_44, B45_45)))), ! [L46_46, M47_47] : (((((line(L46_46) & line(M47_47)) & unequally_directed_lines(L46_46, M47_47)) & unequally_directed_lines(L46_46, reverse_line(M47_47))) => point(intersection_point(L46_46, M47_47)))), ! [L48_48, A49_49] : (((point(A49_49) & line(L48_48)) => line(parallel_through_point(L48_48, A49_49)))), ! [L50_50] : ((line(L50_50) => line(reverse_line(L50_50)))), ! [A51_51, B52_52] : ((distinct_points(A51_51, B52_52) => (~apart_point_and_line(A51_51, line_connecting(A51_51, B52_52)) & ~apart_point_and_line(B52_52, line_connecting(A51_51, B52_52))))), ! [L53_53, M54_54] : (((unequally_directed_lines(L53_53, M54_54) & unequally_directed_lines(L53_53, reverse_line(M54_54))) => (~apart_point_and_line(intersection_point(L53_53, M54_54), L53_53) & ~apart_point_and_line(intersection_point(L53_53, M54_54), M54_54)))), ! [A55_55, L56_56] : (~apart_point_and_line(A55_55, parallel_through_point(L56_56, A55_55))), ! [L57_57] : (~distinct_lines(L57_57, reverse_line(L57_57))), ! [A58_58, B59_59] : (~unequally_directed_lines(line_connecting(A58_58, B59_59), reverse_line(line_connecting(B59_59, A58_58)))), ! [A60_60, L61_61] : (~unequally_directed_lines(parallel_through_point(L61_61, A60_60), L61_61)), ! [A62_62, B63_63, L64_64, M65_65] : (((distinct_points(A62_62, B63_63) & distinct_lines(L64_64, M65_65)) => (((((((left_apart_point(A62_62, L64_64) | left_apart_point(B63_63, L64_64)) | left_apart_point(A62_62, M65_65)) | left_apart_point(B63_63, M65_65)) | left_apart_point(A62_62, reverse_line(L64_64))) | left_apart_point(B63_63, reverse_line(L64_64))) | left_apart_point(A62_62, reverse_line(M65_65))) | left_apart_point(B63_63, reverse_line(M65_65))))), ! [A66_66, B67_67, L68_68] : (((distinct_points(A66_66, B67_67) & left_apart_point(A66_66, L68_68)) => (left_apart_point(B67_67, L68_68) | left_convergent_lines(line_connecting(A66_66, B67_67), L68_68)))), ! [A69_69, B70_70, L71_71] : ((left_apart_point(A69_69, L71_71) => (distinct_points(A69_69, B70_70) | left_apart_point(B70_70, L71_71)))), ! [A72_72, L73_73, M74_74] : (((left_apart_point(A72_72, L73_73) & unequally_directed_lines(L73_73, M74_74)) => (distinct_lines(L73_73, M74_74) | left_apart_point(A72_72, reverse_line(M74_74))))), ! [L75_75, M76_76, N77_77] : ((left_convergent_lines(L75_75, M76_76) => (unequally_directed_lines(M76_76, N77_77) | left_convergent_lines(L75_75, N77_77))))
% 2.70/0.94
% 2.70/0.94 [2] DELTA_NOT_FORALL : ~! [A78_78, B79_79, C80_80, D81_81] : ((left_apart_point(C80_80, line_connecting(A78_78, B79_79)) => ((left_apart_point(D81_81, reverse_line(line_connecting(B79_79, C80_80))) & left_apart_point(D81_81, reverse_line(line_connecting(C80_80, A78_78)))) => left_apart_point(D81_81, line_connecting(A78_78, B79_79)))))
% 2.70/0.94 -> [3] ~(left_apart_point(skolem_C8080, line_connecting(skolem_A7878, skolem_B7979)) => ((left_apart_point(skolem_D8181, reverse_line(line_connecting(skolem_B7979, skolem_C8080))) & left_apart_point(skolem_D8181, reverse_line(line_connecting(skolem_C8080, skolem_A7878)))) => left_apart_point(skolem_D8181, line_connecting(skolem_A7878, skolem_B7979))))
% 2.70/0.94
% 2.70/0.94 [3] ALPHA_NOT_IMPLY : ~(left_apart_point(skolem_C8080, line_connecting(skolem_A7878, skolem_B7979)) => ((left_apart_point(skolem_D8181, reverse_line(line_connecting(skolem_B7979, skolem_C8080))) & left_apart_point(skolem_D8181, reverse_line(line_connecting(skolem_C8080, skolem_A7878)))) => left_apart_point(skolem_D8181, line_connecting(skolem_A7878, skolem_B7979))))
% 2.70/0.94 -> [4] left_apart_point(skolem_C8080, line_connecting(skolem_A7878, skolem_B7979)), ~((left_apart_point(skolem_D8181, reverse_line(line_connecting(skolem_B7979, skolem_C8080))) & left_apart_point(skolem_D8181, reverse_line(line_connecting(skolem_C8080, skolem_A7878)))) => left_apart_point(skolem_D8181, line_connecting(skolem_A7878, skolem_B7979)))
% 2.70/0.94
% 2.70/0.94 [4] ALPHA_NOT_IMPLY : ~((left_apart_point(skolem_D8181, reverse_line(line_connecting(skolem_B7979, skolem_C8080))) & left_apart_point(skolem_D8181, reverse_line(line_connecting(skolem_C8080, skolem_A7878)))) => left_apart_point(skolem_D8181, line_connecting(skolem_A7878, skolem_B7979)))
% 2.70/0.94 -> [5] (left_apart_point(skolem_D8181, reverse_line(line_connecting(skolem_B7979, skolem_C8080))) & left_apart_point(skolem_D8181, reverse_line(line_connecting(skolem_C8080, skolem_A7878)))), ~left_apart_point(skolem_D8181, line_connecting(skolem_A7878, skolem_B7979))
% 2.70/0.94
% 2.70/0.94 [5] ALPHA_AND : (left_apart_point(skolem_D8181, reverse_line(line_connecting(skolem_B7979, skolem_C8080))) & left_apart_point(skolem_D8181, reverse_line(line_connecting(skolem_C8080, skolem_A7878))))
% 2.70/0.94 -> [6] left_apart_point(skolem_D8181, reverse_line(line_connecting(skolem_B7979, skolem_C8080))), left_apart_point(skolem_D8181, reverse_line(line_connecting(skolem_C8080, skolem_A7878)))
% 2.70/0.94
% 2.70/0.94 [6] GAMMA_FORALL : ! [A21_21] : (~distinct_points(A21_21, A21_21))
% 2.70/0.94 -> [7] ~distinct_points(C24_0_1, C24_0_1)
% 2.70/0.94
% 2.70/0.94 [7] GAMMA_FORALL : ! [A22_22, B23_23, C24_24] : ((distinct_points(A22_22, B23_23) => (distinct_points(A22_22, C24_24) | distinct_points(B23_23, C24_24))))
% 2.70/0.94 -> [8] (distinct_points(C24_0_1, C24_0_1) => (distinct_points(C24_0_1, C24_0_1) | distinct_points(C24_0_1, C24_0_1)))
% 2.70/0.94
% 2.70/0.94 [8] BETA_IMPLY : (distinct_points(C24_0_1, C24_0_1) => (distinct_points(C24_0_1, C24_0_1) | distinct_points(C24_0_1, C24_0_1)))
% 2.70/0.94 -> [9] ~distinct_points(C24_0_1, C24_0_1)
% 2.70/0.94 -> [10] (distinct_points(C24_0_1, C24_0_1) | distinct_points(C24_0_1, C24_0_1))
% 2.70/0.94
% 2.70/0.94 [10] BETA_OR : (distinct_points(C24_0_1, C24_0_1) | distinct_points(C24_0_1, C24_0_1))
% 2.70/0.94 -> [11] distinct_points(C24_0_1, C24_0_1)
% 2.70/0.94 -> [12] distinct_points(C24_0_1, C24_0_1)
% 2.70/0.94
% 2.70/0.94 [12] CLOSURE : distinct_points(C24_0_1, C24_0_1)
% 2.70/0.94
% 2.70/0.94 [11] CLOSURE : distinct_points(C24_0_1, C24_0_1)
% 2.70/0.94
% 2.70/0.94 [9] GAMMA_FORALL : ! [L25_25] : (~distinct_lines(L25_25, L25_25))
% 2.70/0.94 -> [13] ~distinct_lines(N28_0_3, N28_0_3)
% 2.70/0.94
% 2.70/0.94 [13] GAMMA_FORALL : ! [L26_26, M27_27, N28_28] : ((distinct_lines(L26_26, M27_27) => (distinct_lines(L26_26, N28_28) | distinct_lines(M27_27, N28_28))))
% 2.70/0.94 -> [14] (distinct_lines(N28_0_3, N28_0_3) => (distinct_lines(N28_0_3, N28_0_3) | distinct_lines(N28_0_3, N28_0_3)))
% 2.70/0.94
% 2.70/0.94 [14] BETA_IMPLY : (distinct_lines(N28_0_3, N28_0_3) => (distinct_lines(N28_0_3, N28_0_3) | distinct_lines(N28_0_3, N28_0_3)))
% 2.70/0.94 -> [15] ~distinct_lines(N28_0_3, N28_0_3)
% 2.70/0.94 -> [16] (distinct_lines(N28_0_3, N28_0_3) | distinct_lines(N28_0_3, N28_0_3))
% 2.70/0.94
% 2.70/0.94 [16] BETA_OR : (distinct_lines(N28_0_3, N28_0_3) | distinct_lines(N28_0_3, N28_0_3))
% 2.70/0.94 -> [17] distinct_lines(N28_0_3, N28_0_3)
% 2.70/0.94 -> [18] distinct_lines(N28_0_3, N28_0_3)
% 2.70/0.94
% 2.70/0.94 [18] CLOSURE : distinct_lines(N28_0_3, N28_0_3)
% 2.70/0.94
% 2.70/0.94 [17] CLOSURE : distinct_lines(N28_0_3, N28_0_3)
% 2.70/0.94
% 2.70/0.94 [15] GAMMA_FORALL : ! [L29_29] : (~unequally_directed_lines(L29_29, L29_29))
% 2.70/0.94 -> [19] ~unequally_directed_lines(reverse_line(N35_0_6), reverse_line(N35_0_6))
% 2.70/0.94
% 2.70/0.94 [19] GAMMA_FORALL : ! [L30_30, M31_31, N32_32] : ((unequally_directed_lines(L30_30, M31_31) => (unequally_directed_lines(L30_30, N32_32) | unequally_directed_lines(M31_31, N32_32))))
% 2.70/0.94 -> [20] (unequally_directed_lines(reverse_line(N35_0_6), reverse_line(N35_0_6)) => (unequally_directed_lines(reverse_line(N35_0_6), reverse_line(N35_0_6)) | unequally_directed_lines(reverse_line(N35_0_6), reverse_line(N35_0_6))))
% 2.70/0.94
% 2.70/0.94 [20] BETA_IMPLY : (unequally_directed_lines(reverse_line(N35_0_6), reverse_line(N35_0_6)) => (unequally_directed_lines(reverse_line(N35_0_6), reverse_line(N35_0_6)) | unequally_directed_lines(reverse_line(N35_0_6), reverse_line(N35_0_6))))
% 2.70/0.94 -> [21] ~unequally_directed_lines(reverse_line(N35_0_6), reverse_line(N35_0_6))
% 2.70/0.94 -> [22] (unequally_directed_lines(reverse_line(N35_0_6), reverse_line(N35_0_6)) | unequally_directed_lines(reverse_line(N35_0_6), reverse_line(N35_0_6)))
% 2.70/0.94
% 2.70/0.94 [22] BETA_OR : (unequally_directed_lines(reverse_line(N35_0_6), reverse_line(N35_0_6)) | unequally_directed_lines(reverse_line(N35_0_6), reverse_line(N35_0_6)))
% 2.70/0.94 -> [23] unequally_directed_lines(reverse_line(N35_0_6), reverse_line(N35_0_6))
% 2.70/0.94 -> [24] unequally_directed_lines(reverse_line(N35_0_6), reverse_line(N35_0_6))
% 2.70/0.94
% 2.70/0.94 [24] CLOSURE : unequally_directed_lines(reverse_line(N35_0_6), reverse_line(N35_0_6))
% 2.70/0.94
% 2.70/0.94 [23] CLOSURE : unequally_directed_lines(reverse_line(N35_0_6), reverse_line(N35_0_6))
% 2.70/0.94
% 2.70/0.94 [25] BETA_IMPLY : ((unequally_directed_lines(N35_0_6, N35_0_6) & unequally_directed_lines(N35_0_6, reverse_line(N35_0_6))) => ((unequally_directed_lines(N35_0_6, N35_0_6) & unequally_directed_lines(N35_0_6, reverse_line(N35_0_6))) | (unequally_directed_lines(N35_0_6, N35_0_6) & unequally_directed_lines(N35_0_6, reverse_line(N35_0_6)))))
% 2.70/0.94 -> [282] ~(unequally_directed_lines(N35_0_6, N35_0_6) & unequally_directed_lines(N35_0_6, reverse_line(N35_0_6)))
% 2.70/0.94 -> [283] ((unequally_directed_lines(N35_0_6, N35_0_6) & unequally_directed_lines(N35_0_6, reverse_line(N35_0_6))) | (unequally_directed_lines(N35_0_6, N35_0_6) & unequally_directed_lines(N35_0_6, reverse_line(N35_0_6))))
% 2.70/0.94
% 2.70/0.94 [282] BETA_NOT_AND : ~(unequally_directed_lines(N35_0_6, N35_0_6) & unequally_directed_lines(N35_0_6, reverse_line(N35_0_6)))
% 2.70/0.94 -> [284] ~unequally_directed_lines(N35_0_6, N35_0_6)
% 2.70/0.94 -> [285] ~unequally_directed_lines(N35_0_6, reverse_line(N35_0_6))
% 2.70/0.94
% 2.70/0.94 [285] GAMMA_FORALL : ! [L36_36, M37_37] : (((line(L36_36) & line(M37_37)) => (unequally_directed_lines(L36_36, M37_37) | unequally_directed_lines(L36_36, reverse_line(M37_37)))))
% 2.70/0.94 -> [291] ((line(M37_5_7) & line(M37_5_7)) => (unequally_directed_lines(M37_5_7, M37_5_7) | unequally_directed_lines(M37_5_7, reverse_line(M37_5_7))))
% 2.70/0.94
% 2.70/0.94 [291] BETA_IMPLY : ((line(M37_5_7) & line(M37_5_7)) => (unequally_directed_lines(M37_5_7, M37_5_7) | unequally_directed_lines(M37_5_7, reverse_line(M37_5_7))))
% 2.70/0.94 -> [294] ~(line(M37_5_7) & line(M37_5_7))
% 2.70/0.94 -> [295] (unequally_directed_lines(M37_5_7, M37_5_7) | unequally_directed_lines(M37_5_7, reverse_line(M37_5_7)))
% 2.70/0.94
% 2.70/0.94 [295] BETA_OR : (unequally_directed_lines(M37_5_7, M37_5_7) | unequally_directed_lines(M37_5_7, reverse_line(M37_5_7)))
% 2.70/0.94 -> [302] unequally_directed_lines(M37_5_7, M37_5_7)
% 2.70/0.94 -> [303] unequally_directed_lines(M37_5_7, reverse_line(M37_5_7))
% 2.70/0.94
% 2.70/0.94 [303] CLOSURE : unequally_directed_lines(M37_5_7, reverse_line(M37_5_7))
% 2.70/0.94
% 2.70/0.94 [302] CLOSURE : unequally_directed_lines(M37_5_7, M37_5_7)
% 2.70/0.94
% 2.70/0.94 [294] BETA_NOT_AND : ~(line(M37_5_7) & line(M37_5_7))
% 2.70/0.94 -> [300] ~line(M37_5_7)
% 2.70/0.94 -> [301] ~line(M37_5_7)
% 2.70/0.94
% 2.70/0.94 [301] GAMMA_FORALL : ! [L38_38, M39_39] : (((unequally_directed_lines(L38_38, M39_39) & unequally_directed_lines(L38_38, reverse_line(M39_39))) => (left_convergent_lines(L38_38, M39_39) | left_convergent_lines(L38_38, reverse_line(M39_39)))))
% 2.70/0.94 -> [308] ((unequally_directed_lines(L38_16_8, M39_16_8) & unequally_directed_lines(L38_16_8, reverse_line(M39_16_8))) => (left_convergent_lines(L38_16_8, M39_16_8) | left_convergent_lines(L38_16_8, reverse_line(M39_16_8))))
% 2.70/0.94
% 2.70/0.94 [308] BETA_IMPLY : ((unequally_directed_lines(L38_16_8, M39_16_8) & unequally_directed_lines(L38_16_8, reverse_line(M39_16_8))) => (left_convergent_lines(L38_16_8, M39_16_8) | left_convergent_lines(L38_16_8, reverse_line(M39_16_8))))
% 2.70/0.94 -> [310] ~(unequally_directed_lines(L38_16_8, M39_16_8) & unequally_directed_lines(L38_16_8, reverse_line(M39_16_8)))
% 2.70/0.94 -> [311] (left_convergent_lines(L38_16_8, M39_16_8) | left_convergent_lines(L38_16_8, reverse_line(M39_16_8)))
% 2.70/0.94
% 2.70/0.94 [311] BETA_OR : (left_convergent_lines(L38_16_8, M39_16_8) | left_convergent_lines(L38_16_8, reverse_line(M39_16_8)))
% 2.70/0.94 -> [324] left_convergent_lines(L38_16_8, M39_16_8)
% 2.70/0.94 -> [325] left_convergent_lines(L38_16_8, reverse_line(M39_16_8))
% 2.70/0.94
% 2.70/0.94 [325] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.70/0.94 -> [340] ~(left_apart_point(A40_59_9, L41_59_9) | left_apart_point(A40_59_9, reverse_line(L41_59_9)))
% 2.70/0.94
% 2.70/0.94 [340] ALPHA_NOT_OR : ~(left_apart_point(A40_59_9, L41_59_9) | left_apart_point(A40_59_9, reverse_line(L41_59_9)))
% 2.70/0.94 -> [343] ~left_apart_point(A40_59_9, L41_59_9), ~left_apart_point(A40_59_9, reverse_line(L41_59_9))
% 2.70/0.94
% 2.70/0.94 [343] CLOSURE : ~left_apart_point(A40_59_9, L41_59_9)
% 2.70/0.94
% 2.70/0.94 [324] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.70/0.94 -> [353] ~(left_apart_point(A40_65_9, L41_65_9) | left_apart_point(A40_65_9, reverse_line(L41_65_9)))
% 2.70/0.94
% 2.70/0.94 [353] ALPHA_NOT_OR : ~(left_apart_point(A40_65_9, L41_65_9) | left_apart_point(A40_65_9, reverse_line(L41_65_9)))
% 2.70/0.94 -> [356] ~left_apart_point(A40_65_9, L41_65_9), ~left_apart_point(A40_65_9, reverse_line(L41_65_9))
% 2.70/0.94
% 2.70/0.94 [356] CLOSURE : ~left_apart_point(A40_65_9, L41_65_9)
% 2.70/0.94
% 2.70/0.94 [310] BETA_NOT_AND : ~(unequally_directed_lines(L38_16_8, M39_16_8) & unequally_directed_lines(L38_16_8, reverse_line(M39_16_8)))
% 2.70/0.94 -> [326] ~unequally_directed_lines(L38_16_8, M39_16_8)
% 2.70/0.94 -> [327] ~unequally_directed_lines(L38_16_8, reverse_line(M39_16_8))
% 2.70/0.94
% 2.70/0.94 [326] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.70/0.94 -> [341] ~(left_apart_point(A40_60_9, L41_60_9) | left_apart_point(A40_60_9, reverse_line(L41_60_9)))
% 2.70/0.94
% 2.70/0.94 [341] ALPHA_NOT_OR : ~(left_apart_point(A40_60_9, L41_60_9) | left_apart_point(A40_60_9, reverse_line(L41_60_9)))
% 2.70/0.94 -> [344] ~left_apart_point(A40_60_9, L41_60_9), ~left_apart_point(A40_60_9, reverse_line(L41_60_9))
% 2.70/0.94
% 2.70/0.94 [344] CLOSURE : ~left_apart_point(A40_60_9, L41_60_9)
% 2.70/0.94
% 2.70/0.94 [327] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.70/0.94 -> [355] ~(left_apart_point(A40_67_9, L41_67_9) | left_apart_point(A40_67_9, reverse_line(L41_67_9)))
% 2.70/0.94
% 2.70/0.94 [355] ALPHA_NOT_OR : ~(left_apart_point(A40_67_9, L41_67_9) | left_apart_point(A40_67_9, reverse_line(L41_67_9)))
% 2.70/0.94 -> [359] ~left_apart_point(A40_67_9, L41_67_9), ~left_apart_point(A40_67_9, reverse_line(L41_67_9))
% 2.70/0.94
% 2.70/0.94 [359] CLOSURE : ~left_apart_point(A40_67_9, L41_67_9)
% 2.70/0.94
% 2.70/0.94 [300] GAMMA_FORALL : ! [L38_38, M39_39] : (((unequally_directed_lines(L38_38, M39_39) & unequally_directed_lines(L38_38, reverse_line(M39_39))) => (left_convergent_lines(L38_38, M39_39) | left_convergent_lines(L38_38, reverse_line(M39_39)))))
% 2.70/0.94 -> [309] ((unequally_directed_lines(L38_17_8, M39_17_8) & unequally_directed_lines(L38_17_8, reverse_line(M39_17_8))) => (left_convergent_lines(L38_17_8, M39_17_8) | left_convergent_lines(L38_17_8, reverse_line(M39_17_8))))
% 2.70/0.94
% 2.70/0.94 [309] BETA_IMPLY : ((unequally_directed_lines(L38_17_8, M39_17_8) & unequally_directed_lines(L38_17_8, reverse_line(M39_17_8))) => (left_convergent_lines(L38_17_8, M39_17_8) | left_convergent_lines(L38_17_8, reverse_line(M39_17_8))))
% 2.70/0.94 -> [316] ~(unequally_directed_lines(L38_17_8, M39_17_8) & unequally_directed_lines(L38_17_8, reverse_line(M39_17_8)))
% 2.70/0.94 -> [317] (left_convergent_lines(L38_17_8, M39_17_8) | left_convergent_lines(L38_17_8, reverse_line(M39_17_8)))
% 2.70/0.94
% 2.70/0.94 [316] BETA_NOT_AND : ~(unequally_directed_lines(L38_17_8, M39_17_8) & unequally_directed_lines(L38_17_8, reverse_line(M39_17_8)))
% 2.70/0.94 -> [322] ~unequally_directed_lines(L38_17_8, M39_17_8)
% 2.70/0.94 -> [323] ~unequally_directed_lines(L38_17_8, reverse_line(M39_17_8))
% 2.70/0.94
% 2.70/0.94 [323] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.70/0.94 -> [345] ~(left_apart_point(A40_61_9, L41_61_9) | left_apart_point(A40_61_9, reverse_line(L41_61_9)))
% 2.70/0.94
% 2.70/0.94 [345] ALPHA_NOT_OR : ~(left_apart_point(A40_61_9, L41_61_9) | left_apart_point(A40_61_9, reverse_line(L41_61_9)))
% 2.70/0.94 -> [346] ~left_apart_point(A40_61_9, L41_61_9), ~left_apart_point(A40_61_9, reverse_line(L41_61_9))
% 2.70/0.94
% 2.70/0.94 [346] CLOSURE : ~left_apart_point(A40_61_9, L41_61_9)
% 2.70/0.94
% 2.70/0.94 [322] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.70/0.94 -> [348] ~(left_apart_point(A40_63_9, L41_63_9) | left_apart_point(A40_63_9, reverse_line(L41_63_9)))
% 2.70/0.94
% 2.70/0.94 [348] ALPHA_NOT_OR : ~(left_apart_point(A40_63_9, L41_63_9) | left_apart_point(A40_63_9, reverse_line(L41_63_9)))
% 2.70/0.94 -> [351] ~left_apart_point(A40_63_9, L41_63_9), ~left_apart_point(A40_63_9, reverse_line(L41_63_9))
% 2.70/0.94
% 2.70/0.94 [351] CLOSURE : ~left_apart_point(A40_63_9, L41_63_9)
% 2.70/0.94
% 2.70/0.94 [317] BETA_OR : (left_convergent_lines(L38_17_8, M39_17_8) | left_convergent_lines(L38_17_8, reverse_line(M39_17_8)))
% 2.70/0.94 -> [328] left_convergent_lines(L38_17_8, M39_17_8)
% 2.70/0.94 -> [329] left_convergent_lines(L38_17_8, reverse_line(M39_17_8))
% 2.70/0.94
% 2.70/0.94 [328] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.70/0.94 -> [339] ~(left_apart_point(A40_58_9, L41_58_9) | left_apart_point(A40_58_9, reverse_line(L41_58_9)))
% 2.70/0.94
% 2.70/0.94 [339] ALPHA_NOT_OR : ~(left_apart_point(A40_58_9, L41_58_9) | left_apart_point(A40_58_9, reverse_line(L41_58_9)))
% 2.70/0.94 -> [342] ~left_apart_point(A40_58_9, L41_58_9), ~left_apart_point(A40_58_9, reverse_line(L41_58_9))
% 2.70/0.94
% 2.70/0.94 [342] CLOSURE : ~left_apart_point(A40_58_9, L41_58_9)
% 2.70/0.94
% 2.70/0.94 [329] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.70/0.94 -> [362] ~(left_apart_point(A40_69_9, L41_69_9) | left_apart_point(A40_69_9, reverse_line(L41_69_9)))
% 2.70/0.94
% 2.70/0.94 [362] ALPHA_NOT_OR : ~(left_apart_point(A40_69_9, L41_69_9) | left_apart_point(A40_69_9, reverse_line(L41_69_9)))
% 2.70/0.94 -> [363] ~left_apart_point(A40_69_9, L41_69_9), ~left_apart_point(A40_69_9, reverse_line(L41_69_9))
% 2.70/0.94
% 2.70/0.94 [363] CLOSURE : ~left_apart_point(A40_69_9, L41_69_9)
% 2.70/0.94
% 2.70/0.94 [288] BETA_IMPLY : ((line(M37_4_7) & line(M37_4_7)) => (unequally_directed_lines(M37_4_7, M37_4_7) | unequally_directed_lines(M37_4_7, reverse_line(M37_4_7))))
% 2.70/0.94 -> [364] ~(line(M37_4_7) & line(M37_4_7))
% 2.70/0.94 -> [365] (unequally_directed_lines(M37_4_7, M37_4_7) | unequally_directed_lines(M37_4_7, reverse_line(M37_4_7)))
% 2.70/0.94
% 2.70/0.94 [364] BETA_NOT_AND : ~(line(M37_4_7) & line(M37_4_7))
% 2.70/0.94 -> [366] ~line(M37_4_7)
% 2.70/0.94 -> [367] ~line(M37_4_7)
% 2.70/0.94
% 2.70/0.94 [366] GAMMA_FORALL : ! [L38_38, M39_39] : (((unequally_directed_lines(L38_38, M39_39) & unequally_directed_lines(L38_38, reverse_line(M39_39))) => (left_convergent_lines(L38_38, M39_39) | left_convergent_lines(L38_38, reverse_line(M39_39)))))
% 2.70/0.94 -> [370] ((unequally_directed_lines(L38_18_8, M39_18_8) & unequally_directed_lines(L38_18_8, reverse_line(M39_18_8))) => (left_convergent_lines(L38_18_8, M39_18_8) | left_convergent_lines(L38_18_8, reverse_line(M39_18_8))))
% 2.70/0.94
% 2.70/0.94 [370] BETA_IMPLY : ((unequally_directed_lines(L38_18_8, M39_18_8) & unequally_directed_lines(L38_18_8, reverse_line(M39_18_8))) => (left_convergent_lines(L38_18_8, M39_18_8) | left_convergent_lines(L38_18_8, reverse_line(M39_18_8))))
% 2.70/0.94 -> [372] ~(unequally_directed_lines(L38_18_8, M39_18_8) & unequally_directed_lines(L38_18_8, reverse_line(M39_18_8)))
% 2.70/0.94 -> [373] (left_convergent_lines(L38_18_8, M39_18_8) | left_convergent_lines(L38_18_8, reverse_line(M39_18_8)))
% 2.70/0.94
% 2.70/0.94 [372] BETA_NOT_AND : ~(unequally_directed_lines(L38_18_8, M39_18_8) & unequally_directed_lines(L38_18_8, reverse_line(M39_18_8)))
% 2.70/0.94 -> [376] ~unequally_directed_lines(L38_18_8, M39_18_8)
% 2.70/0.94 -> [377] ~unequally_directed_lines(L38_18_8, reverse_line(M39_18_8))
% 2.70/0.94
% 2.70/0.94 [377] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.70/0.94 -> [384] ~(left_apart_point(A40_70_9, L41_70_9) | left_apart_point(A40_70_9, reverse_line(L41_70_9)))
% 2.70/0.94
% 2.70/0.94 [384] ALPHA_NOT_OR : ~(left_apart_point(A40_70_9, L41_70_9) | left_apart_point(A40_70_9, reverse_line(L41_70_9)))
% 2.70/0.94 -> [385] ~left_apart_point(A40_70_9, L41_70_9), ~left_apart_point(A40_70_9, reverse_line(L41_70_9))
% 2.70/0.94
% 2.70/0.94 [385] CLOSURE : ~left_apart_point(A40_70_9, L41_70_9)
% 2.70/0.94
% 2.70/0.94 [376] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.70/0.94 -> [388] ~(left_apart_point(A40_72_9, L41_72_9) | left_apart_point(A40_72_9, reverse_line(L41_72_9)))
% 2.70/0.94
% 2.70/0.94 [388] ALPHA_NOT_OR : ~(left_apart_point(A40_72_9, L41_72_9) | left_apart_point(A40_72_9, reverse_line(L41_72_9)))
% 2.70/0.94 -> [391] ~left_apart_point(A40_72_9, L41_72_9), ~left_apart_point(A40_72_9, reverse_line(L41_72_9))
% 2.70/0.94
% 2.70/0.94 [391] CLOSURE : ~left_apart_point(A40_72_9, L41_72_9)
% 2.70/0.94
% 2.70/0.94 [373] BETA_OR : (left_convergent_lines(L38_18_8, M39_18_8) | left_convergent_lines(L38_18_8, reverse_line(M39_18_8)))
% 2.70/0.94 -> [382] left_convergent_lines(L38_18_8, M39_18_8)
% 2.70/0.94 -> [383] left_convergent_lines(L38_18_8, reverse_line(M39_18_8))
% 2.70/0.94
% 2.70/0.94 [382] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.70/0.94 -> [394] ~(left_apart_point(A40_74_9, L41_74_9) | left_apart_point(A40_74_9, reverse_line(L41_74_9)))
% 2.70/0.94
% 2.70/0.94 [394] ALPHA_NOT_OR : ~(left_apart_point(A40_74_9, L41_74_9) | left_apart_point(A40_74_9, reverse_line(L41_74_9)))
% 2.70/0.94 -> [401] ~left_apart_point(A40_74_9, L41_74_9), ~left_apart_point(A40_74_9, reverse_line(L41_74_9))
% 2.70/0.94
% 2.70/0.94 [401] CLOSURE : ~left_apart_point(A40_74_9, L41_74_9)
% 2.70/0.94
% 2.70/0.94 [383] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.70/0.94 -> [395] ~(left_apart_point(A40_75_9, L41_75_9) | left_apart_point(A40_75_9, reverse_line(L41_75_9)))
% 2.70/0.94
% 2.70/0.94 [395] ALPHA_NOT_OR : ~(left_apart_point(A40_75_9, L41_75_9) | left_apart_point(A40_75_9, reverse_line(L41_75_9)))
% 2.70/0.94 -> [397] ~left_apart_point(A40_75_9, L41_75_9), ~left_apart_point(A40_75_9, reverse_line(L41_75_9))
% 2.70/0.94
% 2.70/0.94 [397] CLOSURE : ~left_apart_point(A40_75_9, L41_75_9)
% 2.70/0.94
% 2.70/0.94 [367] GAMMA_FORALL : ! [L38_38, M39_39] : (((unequally_directed_lines(L38_38, M39_39) & unequally_directed_lines(L38_38, reverse_line(M39_39))) => (left_convergent_lines(L38_38, M39_39) | left_convergent_lines(L38_38, reverse_line(M39_39)))))
% 2.70/0.94 -> [371] ((unequally_directed_lines(L38_19_8, M39_19_8) & unequally_directed_lines(L38_19_8, reverse_line(M39_19_8))) => (left_convergent_lines(L38_19_8, M39_19_8) | left_convergent_lines(L38_19_8, reverse_line(M39_19_8))))
% 2.70/0.94
% 2.70/0.94 [371] BETA_IMPLY : ((unequally_directed_lines(L38_19_8, M39_19_8) & unequally_directed_lines(L38_19_8, reverse_line(M39_19_8))) => (left_convergent_lines(L38_19_8, M39_19_8) | left_convergent_lines(L38_19_8, reverse_line(M39_19_8))))
% 2.70/0.94 -> [374] ~(unequally_directed_lines(L38_19_8, M39_19_8) & unequally_directed_lines(L38_19_8, reverse_line(M39_19_8)))
% 2.70/0.94 -> [375] (left_convergent_lines(L38_19_8, M39_19_8) | left_convergent_lines(L38_19_8, reverse_line(M39_19_8)))
% 2.70/0.94
% 2.70/0.94 [375] BETA_OR : (left_convergent_lines(L38_19_8, M39_19_8) | left_convergent_lines(L38_19_8, reverse_line(M39_19_8)))
% 2.70/0.94 -> [380] left_convergent_lines(L38_19_8, M39_19_8)
% 2.70/0.94 -> [381] left_convergent_lines(L38_19_8, reverse_line(M39_19_8))
% 2.70/0.94
% 2.70/0.94 [381] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.70/0.94 -> [390] ~(left_apart_point(A40_73_9, L41_73_9) | left_apart_point(A40_73_9, reverse_line(L41_73_9)))
% 2.70/0.94
% 2.70/0.94 [390] ALPHA_NOT_OR : ~(left_apart_point(A40_73_9, L41_73_9) | left_apart_point(A40_73_9, reverse_line(L41_73_9)))
% 2.70/0.94 -> [396] ~left_apart_point(A40_73_9, L41_73_9), ~left_apart_point(A40_73_9, reverse_line(L41_73_9))
% 2.70/0.94
% 2.70/0.94 [396] CLOSURE : ~left_apart_point(A40_73_9, L41_73_9)
% 2.70/0.94
% 2.70/0.94 [380] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.70/0.94 -> [398] ~(left_apart_point(A40_76_9, L41_76_9) | left_apart_point(A40_76_9, reverse_line(L41_76_9)))
% 2.70/0.94
% 2.70/0.94 [398] ALPHA_NOT_OR : ~(left_apart_point(A40_76_9, L41_76_9) | left_apart_point(A40_76_9, reverse_line(L41_76_9)))
% 2.70/0.94 -> [404] ~left_apart_point(A40_76_9, L41_76_9), ~left_apart_point(A40_76_9, reverse_line(L41_76_9))
% 2.70/0.94
% 2.70/0.94 [404] CLOSURE : ~left_apart_point(A40_76_9, L41_76_9)
% 2.70/0.94
% 2.70/0.94 [374] BETA_NOT_AND : ~(unequally_directed_lines(L38_19_8, M39_19_8) & unequally_directed_lines(L38_19_8, reverse_line(M39_19_8)))
% 2.70/0.94 -> [378] ~unequally_directed_lines(L38_19_8, M39_19_8)
% 2.70/0.94 -> [379] ~unequally_directed_lines(L38_19_8, reverse_line(M39_19_8))
% 2.70/0.94
% 2.70/0.94 [378] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.70/0.94 -> [386] ~(left_apart_point(A40_71_9, L41_71_9) | left_apart_point(A40_71_9, reverse_line(L41_71_9)))
% 2.70/0.94
% 2.70/0.94 [386] ALPHA_NOT_OR : ~(left_apart_point(A40_71_9, L41_71_9) | left_apart_point(A40_71_9, reverse_line(L41_71_9)))
% 2.70/0.94 -> [389] ~left_apart_point(A40_71_9, L41_71_9), ~left_apart_point(A40_71_9, reverse_line(L41_71_9))
% 2.70/0.94
% 2.70/0.94 [389] CLOSURE : ~left_apart_point(A40_71_9, L41_71_9)
% 2.70/0.94
% 2.70/0.94 [379] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.70/0.94 -> [405] ~(left_apart_point(A40_77_9, L41_77_9) | left_apart_point(A40_77_9, reverse_line(L41_77_9)))
% 2.70/0.94
% 2.70/0.94 [405] ALPHA_NOT_OR : ~(left_apart_point(A40_77_9, L41_77_9) | left_apart_point(A40_77_9, reverse_line(L41_77_9)))
% 2.70/0.94 -> [406] ~left_apart_point(A40_77_9, L41_77_9), ~left_apart_point(A40_77_9, reverse_line(L41_77_9))
% 2.70/0.94
% 2.70/0.94 [406] CLOSURE : ~left_apart_point(A40_77_9, L41_77_9)
% 2.70/0.94
% 2.70/0.94 [365] BETA_OR : (unequally_directed_lines(M37_4_7, M37_4_7) | unequally_directed_lines(M37_4_7, reverse_line(M37_4_7)))
% 2.70/0.94 -> [368] unequally_directed_lines(M37_4_7, M37_4_7)
% 2.70/0.94 -> [369] unequally_directed_lines(M37_4_7, reverse_line(M37_4_7))
% 2.70/0.94
% 2.70/0.94 [368] CLOSURE : unequally_directed_lines(M37_4_7, M37_4_7)
% 2.70/0.94
% 2.70/0.94 [369] GAMMA_FORALL : ! [L38_38, M39_39] : (((unequally_directed_lines(L38_38, M39_39) & unequally_directed_lines(L38_38, reverse_line(M39_39))) => (left_convergent_lines(L38_38, M39_39) | left_convergent_lines(L38_38, reverse_line(M39_39)))))
% 2.70/0.94 -> [387] ((unequally_directed_lines(M39_20_8, M39_20_8) & unequally_directed_lines(M39_20_8, reverse_line(M39_20_8))) => (left_convergent_lines(M39_20_8, M39_20_8) | left_convergent_lines(M39_20_8, reverse_line(M39_20_8))))
% 2.70/0.94
% 2.70/0.94 [387] BETA_IMPLY : ((unequally_directed_lines(M39_20_8, M39_20_8) & unequally_directed_lines(M39_20_8, reverse_line(M39_20_8))) => (left_convergent_lines(M39_20_8, M39_20_8) | left_convergent_lines(M39_20_8, reverse_line(M39_20_8))))
% 2.70/0.94 -> [392] ~(unequally_directed_lines(M39_20_8, M39_20_8) & unequally_directed_lines(M39_20_8, reverse_line(M39_20_8)))
% 2.70/0.94 -> [393] (left_convergent_lines(M39_20_8, M39_20_8) | left_convergent_lines(M39_20_8, reverse_line(M39_20_8)))
% 2.70/0.94
% 2.70/0.94 [393] BETA_OR : (left_convergent_lines(M39_20_8, M39_20_8) | left_convergent_lines(M39_20_8, reverse_line(M39_20_8)))
% 2.70/0.94 -> [399] left_convergent_lines(M39_20_8, M39_20_8)
% 2.70/0.94 -> [400] left_convergent_lines(M39_20_8, reverse_line(M39_20_8))
% 2.70/0.94
% 2.70/0.94 [400] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.70/0.94 -> [407] ~(left_apart_point(A40_78_9, L41_78_9) | left_apart_point(A40_78_9, reverse_line(L41_78_9)))
% 2.70/0.94
% 2.70/0.94 [407] ALPHA_NOT_OR : ~(left_apart_point(A40_78_9, L41_78_9) | left_apart_point(A40_78_9, reverse_line(L41_78_9)))
% 2.70/0.94 -> [409] ~left_apart_point(A40_78_9, L41_78_9), ~left_apart_point(A40_78_9, reverse_line(L41_78_9))
% 2.70/0.94
% 2.70/0.94 [409] CLOSURE : ~left_apart_point(A40_78_9, L41_78_9)
% 2.70/0.94
% 2.70/0.94 [399] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.70/0.94 -> [408] ~(left_apart_point(A40_79_9, L41_79_9) | left_apart_point(A40_79_9, reverse_line(L41_79_9)))
% 2.70/0.94
% 2.70/0.94 [408] ALPHA_NOT_OR : ~(left_apart_point(A40_79_9, L41_79_9) | left_apart_point(A40_79_9, reverse_line(L41_79_9)))
% 2.70/0.94 -> [410] ~left_apart_point(A40_79_9, L41_79_9), ~left_apart_point(A40_79_9, reverse_line(L41_79_9))
% 2.70/0.94
% 2.70/0.94 [410] CLOSURE : ~left_apart_point(A40_79_9, L41_79_9)
% 2.70/0.94
% 2.70/0.94 [392] BETA_NOT_AND : ~(unequally_directed_lines(M39_20_8, M39_20_8) & unequally_directed_lines(M39_20_8, reverse_line(M39_20_8)))
% 2.70/0.94 -> [402] ~unequally_directed_lines(M39_20_8, M39_20_8)
% 2.70/0.94 -> [403] ~unequally_directed_lines(M39_20_8, reverse_line(M39_20_8))
% 2.70/0.94
% 2.70/0.94 [403] CLOSURE : ~unequally_directed_lines(M39_20_8, reverse_line(M39_20_8))
% 2.70/0.94
% 2.70/0.94 [402] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.70/0.94 -> [411] ~(left_apart_point(A40_80_9, L41_80_9) | left_apart_point(A40_80_9, reverse_line(L41_80_9)))
% 2.70/0.94
% 2.70/0.94 [411] ALPHA_NOT_OR : ~(left_apart_point(A40_80_9, L41_80_9) | left_apart_point(A40_80_9, reverse_line(L41_80_9)))
% 2.70/0.94 -> [412] ~left_apart_point(A40_80_9, L41_80_9), ~left_apart_point(A40_80_9, reverse_line(L41_80_9))
% 2.70/0.94
% 2.70/0.94 [412] CLOSURE : ~left_apart_point(A40_80_9, L41_80_9)
% 2.70/0.94
% 2.70/0.94 [283] BETA_OR : ((unequally_directed_lines(N35_0_6, N35_0_6) & unequally_directed_lines(N35_0_6, reverse_line(N35_0_6))) | (unequally_directed_lines(N35_0_6, N35_0_6) & unequally_directed_lines(N35_0_6, reverse_line(N35_0_6))))
% 2.70/0.94 -> [413] (unequally_directed_lines(N35_0_6, N35_0_6) & unequally_directed_lines(N35_0_6, reverse_line(N35_0_6)))
% 2.70/0.94 -> [414] (unequally_directed_lines(N35_0_6, N35_0_6) & unequally_directed_lines(N35_0_6, reverse_line(N35_0_6)))
% 2.70/0.94
% 2.70/0.94 [413] ALPHA_AND : (unequally_directed_lines(N35_0_6, N35_0_6) & unequally_directed_lines(N35_0_6, reverse_line(N35_0_6)))
% 2.70/0.94 -> [415] unequally_directed_lines(N35_0_6, N35_0_6), unequally_directed_lines(N35_0_6, reverse_line(N35_0_6))
% 2.70/0.94
% 2.70/0.94 [415] CLOSURE : unequally_directed_lines(N35_0_6, reverse_line(N35_0_6))
% 2.70/0.94
% 2.70/0.94 [414] ALPHA_AND : (unequally_directed_lines(N35_0_6, N35_0_6) & unequally_directed_lines(N35_0_6, reverse_line(N35_0_6)))
% 2.70/0.94 -> [416] unequally_directed_lines(N35_0_6, N35_0_6), unequally_directed_lines(N35_0_6, reverse_line(N35_0_6))
% 2.70/0.94
% 2.70/0.94 [416] CLOSURE : unequally_directed_lines(N35_0_6, reverse_line(N35_0_6))
% 2.70/0.94
% 2.70/0.94 % SZS output end Proof for theBenchmark.p
% 2.70/0.94 [0.587637s][1][Res] 2383 goroutines created
% 2.70/0.94 ==== Result ====
% 2.70/0.94 [0.587660s][1][Res] VALID
% 2.70/0.94 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------