TSTP Solution File: GEO256+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO256+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n017.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 15:18:46 EDT 2022
% Result : Theorem 3.35s 1.13s
% Output : Proof 3.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO256+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.11/0.13 % Command : goeland -dmt -presko -proof %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 06:36:21 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 [DMT] DMT loaded with preskolemization
% 0.12/0.35 [EQ] equality loaded.
% 0.12/0.35 [0.000037s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.36 Conjecture not found
% 0.12/0.36 Start search
% 0.12/0.36 nb_step : 1 - limit : 32
% 0.12/0.36 Launch Gotab with destructive = true
% 3.35/1.12 % SZS output start Proof for theBenchmark.p
% 3.35/1.13 [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))))) & ~! [L78_78, A79_79, B80_80, C81_81, D82_82] : (((((distinct_points(A79_79, C81_81) & distinct_points(B80_80, C81_81)) & ~apart_point_and_line(C81_81, L78_78)) & left_apart_point(D82_82, L78_78)) => (before_on_line(L78_78, A79_79, B80_80) => (before_on_line(L78_78, A79_79, C81_81) | before_on_line(L78_78, C81_81, B80_80))))))
% 3.35/1.13 -> [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))))), ~! [L78_78, A79_79, B80_80, C81_81, D82_82] : (((((distinct_points(A79_79, C81_81) & distinct_points(B80_80, C81_81)) & ~apart_point_and_line(C81_81, L78_78)) & left_apart_point(D82_82, L78_78)) => (before_on_line(L78_78, A79_79, B80_80) => (before_on_line(L78_78, A79_79, C81_81) | before_on_line(L78_78, C81_81, B80_80)))))
% 3.35/1.13
% 3.35/1.13 [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)))))
% 3.35/1.13 -> [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))))
% 3.35/1.13
% 3.35/1.13 [2] DELTA_NOT_FORALL : ~! [L78_78, A79_79, B80_80, C81_81, D82_82] : (((((distinct_points(A79_79, C81_81) & distinct_points(B80_80, C81_81)) & ~apart_point_and_line(C81_81, L78_78)) & left_apart_point(D82_82, L78_78)) => (before_on_line(L78_78, A79_79, B80_80) => (before_on_line(L78_78, A79_79, C81_81) | before_on_line(L78_78, C81_81, B80_80)))))
% 3.35/1.13 -> [3] ~((((distinct_points(skolem_A7979, skolem_C8181) & distinct_points(skolem_B8080, skolem_C8181)) & ~apart_point_and_line(skolem_C8181, skolem_L7878)) & left_apart_point(skolem_D8282, skolem_L7878)) => (before_on_line(skolem_L7878, skolem_A7979, skolem_B8080) => (before_on_line(skolem_L7878, skolem_A7979, skolem_C8181) | before_on_line(skolem_L7878, skolem_C8181, skolem_B8080))))
% 3.35/1.13
% 3.35/1.13 [3] ALPHA_NOT_IMPLY : ~((((distinct_points(skolem_A7979, skolem_C8181) & distinct_points(skolem_B8080, skolem_C8181)) & ~apart_point_and_line(skolem_C8181, skolem_L7878)) & left_apart_point(skolem_D8282, skolem_L7878)) => (before_on_line(skolem_L7878, skolem_A7979, skolem_B8080) => (before_on_line(skolem_L7878, skolem_A7979, skolem_C8181) | before_on_line(skolem_L7878, skolem_C8181, skolem_B8080))))
% 3.35/1.13 -> [4] (((distinct_points(skolem_A7979, skolem_C8181) & distinct_points(skolem_B8080, skolem_C8181)) & ~apart_point_and_line(skolem_C8181, skolem_L7878)) & left_apart_point(skolem_D8282, skolem_L7878)), ~(before_on_line(skolem_L7878, skolem_A7979, skolem_B8080) => (before_on_line(skolem_L7878, skolem_A7979, skolem_C8181) | before_on_line(skolem_L7878, skolem_C8181, skolem_B8080)))
% 3.35/1.13
% 3.35/1.13 [4] ALPHA_AND : (((distinct_points(skolem_A7979, skolem_C8181) & distinct_points(skolem_B8080, skolem_C8181)) & ~apart_point_and_line(skolem_C8181, skolem_L7878)) & left_apart_point(skolem_D8282, skolem_L7878))
% 3.35/1.13 -> [5] ((distinct_points(skolem_A7979, skolem_C8181) & distinct_points(skolem_B8080, skolem_C8181)) & ~apart_point_and_line(skolem_C8181, skolem_L7878)), left_apart_point(skolem_D8282, skolem_L7878)
% 3.35/1.13
% 3.35/1.13 [5] ALPHA_NOT_IMPLY : ~(before_on_line(skolem_L7878, skolem_A7979, skolem_B8080) => (before_on_line(skolem_L7878, skolem_A7979, skolem_C8181) | before_on_line(skolem_L7878, skolem_C8181, skolem_B8080)))
% 3.35/1.13 -> [6] before_on_line(skolem_L7878, skolem_A7979, skolem_B8080), ~(before_on_line(skolem_L7878, skolem_A7979, skolem_C8181) | before_on_line(skolem_L7878, skolem_C8181, skolem_B8080))
% 3.35/1.13
% 3.35/1.13 [6] Rewrite : before_on_line(skolem_L7878, skolem_A7979, skolem_B8080)
% 3.35/1.13 -> [7] (((distinct_points(skolem_A7979, skolem_B8080) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))) & ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080)))
% 3.35/1.13
% 3.35/1.13 [7] ALPHA_AND : ((distinct_points(skolem_A7979, skolem_C8181) & distinct_points(skolem_B8080, skolem_C8181)) & ~apart_point_and_line(skolem_C8181, skolem_L7878))
% 3.35/1.13 -> [8] (distinct_points(skolem_A7979, skolem_C8181) & distinct_points(skolem_B8080, skolem_C8181)), ~apart_point_and_line(skolem_C8181, skolem_L7878)
% 3.35/1.13
% 3.35/1.13 [8] Rewrite : ~apart_point_and_line(skolem_C8181, skolem_L7878)
% 3.35/1.13 -> [9] ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [9] ALPHA_NOT_OR : ~(before_on_line(skolem_L7878, skolem_A7979, skolem_C8181) | before_on_line(skolem_L7878, skolem_C8181, skolem_B8080))
% 3.35/1.13 -> [10] ~before_on_line(skolem_L7878, skolem_A7979, skolem_C8181), ~before_on_line(skolem_L7878, skolem_C8181, skolem_B8080)
% 3.35/1.13
% 3.35/1.13 [10] Rewrite : ~before_on_line(skolem_L7878, skolem_A7979, skolem_C8181)
% 3.35/1.13 -> [11] ~(((distinct_points(skolem_A7979, skolem_C8181) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))) & ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)))
% 3.35/1.13
% 3.35/1.13 [11] Rewrite : ~before_on_line(skolem_L7878, skolem_C8181, skolem_B8080)
% 3.35/1.13 -> [12] ~(((distinct_points(skolem_C8181, skolem_B8080) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))) & ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_C8181, skolem_B8080)))
% 3.35/1.13
% 3.35/1.13 [12] ALPHA_AND : (((distinct_points(skolem_A7979, skolem_B8080) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))) & ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080)))
% 3.35/1.13 -> [13] ((distinct_points(skolem_A7979, skolem_B8080) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))), ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13
% 3.35/1.13 [13] ALPHA_AND : (distinct_points(skolem_A7979, skolem_C8181) & distinct_points(skolem_B8080, skolem_C8181))
% 3.35/1.13 -> [14] distinct_points(skolem_A7979, skolem_C8181), distinct_points(skolem_B8080, skolem_C8181)
% 3.35/1.13
% 3.35/1.13 [14] ALPHA_NOT_OR : ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [15] ~left_apart_point(skolem_C8181, skolem_L7878), ~left_apart_point(skolem_C8181, reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [15] ALPHA_AND : ((distinct_points(skolem_A7979, skolem_B8080) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878))))
% 3.35/1.13 -> [16] (distinct_points(skolem_A7979, skolem_B8080) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))), ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [16] ALPHA_AND : (distinct_points(skolem_A7979, skolem_B8080) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878))))
% 3.35/1.13 -> [17] distinct_points(skolem_A7979, skolem_B8080), ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [17] ALPHA_NOT_OR : ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [18] ~left_apart_point(skolem_B8080, skolem_L7878), ~left_apart_point(skolem_B8080, reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [18] ALPHA_NOT_OR : ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [19] ~left_apart_point(skolem_A7979, skolem_L7878), ~left_apart_point(skolem_A7979, reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [19] BETA_NOT_AND : ~(((distinct_points(skolem_A7979, skolem_C8181) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))) & ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)))
% 3.35/1.13 -> [20] ~((distinct_points(skolem_A7979, skolem_C8181) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878))))
% 3.35/1.13 -> [21] ~~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13
% 3.35/1.13 [20] BETA_NOT_AND : ~(((distinct_points(skolem_C8181, skolem_B8080) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))) & ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_C8181, skolem_B8080)))
% 3.35/1.13 -> [22] ~((distinct_points(skolem_C8181, skolem_B8080) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878))))
% 3.35/1.13 -> [23] ~~unequally_directed_lines(skolem_L7878, line_connecting(skolem_C8181, skolem_B8080))
% 3.35/1.13
% 3.35/1.13 [23] ALPHA_NOT_NOT : ~~unequally_directed_lines(skolem_L7878, line_connecting(skolem_C8181, skolem_B8080))
% 3.35/1.13 -> [27] unequally_directed_lines(skolem_L7878, line_connecting(skolem_C8181, skolem_B8080))
% 3.35/1.13
% 3.35/1.13 [27] BETA_NOT_AND : ~((distinct_points(skolem_A7979, skolem_C8181) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878))))
% 3.35/1.13 -> [41] ~(distinct_points(skolem_A7979, skolem_C8181) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878))))
% 3.35/1.13 -> [42] ~~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [42] ALPHA_NOT_NOT : ~~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [56] (left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [56] BETA_OR : (left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [62] left_apart_point(skolem_C8181, skolem_L7878)
% 3.35/1.13 -> [63] left_apart_point(skolem_C8181, reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [62] CLOSURE : left_apart_point(skolem_C8181, skolem_L7878)
% 3.35/1.13
% 3.35/1.13 [63] CLOSURE : left_apart_point(skolem_C8181, reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [41] BETA_NOT_AND : ~(distinct_points(skolem_A7979, skolem_C8181) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878))))
% 3.35/1.13 -> [49] ~distinct_points(skolem_A7979, skolem_C8181)
% 3.35/1.13 -> [50] ~~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [49] CLOSURE : ~distinct_points(skolem_A7979, skolem_C8181)
% 3.35/1.13
% 3.35/1.13 [50] ALPHA_NOT_NOT : ~~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [66] (left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [66] BETA_OR : (left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [74] left_apart_point(skolem_A7979, skolem_L7878)
% 3.35/1.13 -> [75] left_apart_point(skolem_A7979, reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [75] CLOSURE : left_apart_point(skolem_A7979, reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [74] CLOSURE : left_apart_point(skolem_A7979, skolem_L7878)
% 3.35/1.13
% 3.35/1.13 [22] BETA_NOT_AND : ~((distinct_points(skolem_A7979, skolem_C8181) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878))))
% 3.35/1.13 -> [25] ~(distinct_points(skolem_A7979, skolem_C8181) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878))))
% 3.35/1.13 -> [26] ~~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [26] ALPHA_NOT_NOT : ~~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [32] (left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [32] BETA_NOT_AND : ~((distinct_points(skolem_C8181, skolem_B8080) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878))))
% 3.35/1.13 -> [33] ~(distinct_points(skolem_C8181, skolem_B8080) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878))))
% 3.35/1.13 -> [34] ~~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [33] BETA_OR : (left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [45] left_apart_point(skolem_C8181, skolem_L7878)
% 3.35/1.13 -> [46] left_apart_point(skolem_C8181, reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [46] CLOSURE : left_apart_point(skolem_C8181, reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [45] CLOSURE : left_apart_point(skolem_C8181, skolem_L7878)
% 3.35/1.13
% 3.35/1.13 [34] ALPHA_NOT_NOT : ~~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [51] (left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [51] BETA_OR : (left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [60] left_apart_point(skolem_C8181, skolem_L7878)
% 3.35/1.13 -> [61] left_apart_point(skolem_C8181, reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [60] CLOSURE : left_apart_point(skolem_C8181, skolem_L7878)
% 3.35/1.13
% 3.35/1.13 [61] CLOSURE : left_apart_point(skolem_C8181, reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [25] BETA_NOT_AND : ~((distinct_points(skolem_C8181, skolem_B8080) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878))))
% 3.35/1.13 -> [28] ~(distinct_points(skolem_C8181, skolem_B8080) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878))))
% 3.35/1.13 -> [29] ~~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [29] ALPHA_NOT_NOT : ~~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [37] (left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [37] BETA_NOT_AND : ~(distinct_points(skolem_A7979, skolem_C8181) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878))))
% 3.35/1.13 -> [43] ~distinct_points(skolem_A7979, skolem_C8181)
% 3.35/1.13 -> [44] ~~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [43] CLOSURE : ~distinct_points(skolem_A7979, skolem_C8181)
% 3.35/1.13
% 3.35/1.13 [44] ALPHA_NOT_NOT : ~~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [57] (left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [57] BETA_OR : (left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [67] left_apart_point(skolem_B8080, skolem_L7878)
% 3.35/1.13 -> [68] left_apart_point(skolem_B8080, reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [67] CLOSURE : left_apart_point(skolem_B8080, skolem_L7878)
% 3.35/1.13
% 3.35/1.13 [68] CLOSURE : left_apart_point(skolem_B8080, reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [28] BETA_NOT_AND : ~(distinct_points(skolem_A7979, skolem_C8181) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878))))
% 3.35/1.13 -> [35] ~distinct_points(skolem_A7979, skolem_C8181)
% 3.35/1.13 -> [36] ~~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [35] CLOSURE : ~distinct_points(skolem_A7979, skolem_C8181)
% 3.35/1.13
% 3.35/1.13 [36] ALPHA_NOT_NOT : ~~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [47] (left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [47] BETA_NOT_AND : ~(distinct_points(skolem_C8181, skolem_B8080) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878))))
% 3.35/1.13 -> [52] ~distinct_points(skolem_C8181, skolem_B8080)
% 3.35/1.13 -> [53] ~~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [53] ALPHA_NOT_NOT : ~~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [65] (left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [65] BETA_OR : (left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [70] left_apart_point(skolem_A7979, skolem_L7878)
% 3.35/1.13 -> [71] left_apart_point(skolem_A7979, reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [70] CLOSURE : left_apart_point(skolem_A7979, skolem_L7878)
% 3.35/1.13
% 3.35/1.13 [71] CLOSURE : left_apart_point(skolem_A7979, reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [52] BETA_OR : (left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [77] left_apart_point(skolem_A7979, skolem_L7878)
% 3.35/1.13 -> [78] left_apart_point(skolem_A7979, reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [77] CLOSURE : left_apart_point(skolem_A7979, skolem_L7878)
% 3.35/1.13
% 3.35/1.13 [78] CLOSURE : left_apart_point(skolem_A7979, reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [21] ALPHA_NOT_NOT : ~~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13 -> [24] unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13
% 3.35/1.13 [24] BETA_NOT_AND : ~(((distinct_points(skolem_C8181, skolem_B8080) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))) & ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_C8181, skolem_B8080)))
% 3.35/1.13 -> [30] ~((distinct_points(skolem_C8181, skolem_B8080) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878))))
% 3.35/1.13 -> [31] ~~unequally_directed_lines(skolem_L7878, line_connecting(skolem_C8181, skolem_B8080))
% 3.35/1.13
% 3.35/1.13 [30] BETA_NOT_AND : ~((distinct_points(skolem_C8181, skolem_B8080) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878))))
% 3.35/1.13 -> [39] ~(distinct_points(skolem_C8181, skolem_B8080) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878))))
% 3.35/1.13 -> [40] ~~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [40] ALPHA_NOT_NOT : ~~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [48] (left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [48] BETA_OR : (left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [54] left_apart_point(skolem_B8080, skolem_L7878)
% 3.35/1.13 -> [55] left_apart_point(skolem_B8080, reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [54] CLOSURE : left_apart_point(skolem_B8080, skolem_L7878)
% 3.35/1.13
% 3.35/1.13 [55] CLOSURE : left_apart_point(skolem_B8080, reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [39] BETA_NOT_AND : ~(distinct_points(skolem_C8181, skolem_B8080) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878))))
% 3.35/1.13 -> [58] ~distinct_points(skolem_C8181, skolem_B8080)
% 3.35/1.13 -> [59] ~~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [59] ALPHA_NOT_NOT : ~~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [64] (left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [64] BETA_OR : (left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [72] left_apart_point(skolem_C8181, skolem_L7878)
% 3.35/1.13 -> [73] left_apart_point(skolem_C8181, reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [73] CLOSURE : left_apart_point(skolem_C8181, reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [72] CLOSURE : left_apart_point(skolem_C8181, skolem_L7878)
% 3.35/1.13
% 3.35/1.13 [58] GAMMA_FORALL : ! [A21_21] : (~distinct_points(A21_21, A21_21))
% 3.35/1.13 -> [76] ~distinct_points(skolem_C8181, skolem_C8181)
% 3.35/1.13
% 3.35/1.13 [76] 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))))
% 3.35/1.13 -> [80] (distinct_points(skolem_B8080, skolem_C8181) => (distinct_points(skolem_B8080, skolem_C8181) | distinct_points(skolem_C8181, skolem_C8181)))
% 3.35/1.13
% 3.35/1.13 [80] BETA_IMPLY : (distinct_points(skolem_B8080, skolem_C8181) => (distinct_points(skolem_B8080, skolem_C8181) | distinct_points(skolem_C8181, skolem_C8181)))
% 3.35/1.13 -> [81] ~distinct_points(skolem_B8080, skolem_C8181)
% 3.35/1.13 -> [82] (distinct_points(skolem_B8080, skolem_C8181) | distinct_points(skolem_C8181, skolem_C8181))
% 3.35/1.13
% 3.35/1.13 [81] CLOSURE : ~distinct_points(skolem_B8080, skolem_C8181)
% 3.35/1.13
% 3.35/1.13 [82] BETA_OR : (distinct_points(skolem_B8080, skolem_C8181) | distinct_points(skolem_C8181, skolem_C8181))
% 3.35/1.13 -> [89] distinct_points(skolem_B8080, skolem_C8181)
% 3.35/1.13 -> [90] distinct_points(skolem_C8181, skolem_C8181)
% 3.35/1.13
% 3.35/1.13 [90] CLOSURE : distinct_points(skolem_C8181, skolem_C8181)
% 3.35/1.13
% 3.35/1.13 [89] GAMMA_FORALL : ! [L25_25] : (~distinct_lines(L25_25, L25_25))
% 3.35/1.13 -> [93] ~distinct_lines(N28_0_3, N28_0_3)
% 3.35/1.13
% 3.35/1.13 [93] 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))))
% 3.35/1.13 -> [94] (distinct_lines(N28_0_3, N28_0_3) => (distinct_lines(N28_0_3, N28_0_3) | distinct_lines(N28_0_3, N28_0_3)))
% 3.35/1.13
% 3.35/1.13 [94] 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)))
% 3.35/1.13 -> [96] ~distinct_lines(N28_0_3, N28_0_3)
% 3.35/1.13 -> [97] (distinct_lines(N28_0_3, N28_0_3) | distinct_lines(N28_0_3, N28_0_3))
% 3.35/1.13
% 3.35/1.13 [97] BETA_OR : (distinct_lines(N28_0_3, N28_0_3) | distinct_lines(N28_0_3, N28_0_3))
% 3.35/1.13 -> [98] distinct_lines(N28_0_3, N28_0_3)
% 3.35/1.13 -> [99] distinct_lines(N28_0_3, N28_0_3)
% 3.35/1.13
% 3.35/1.13 [98] CLOSURE : distinct_lines(N28_0_3, N28_0_3)
% 3.35/1.13
% 3.35/1.13 [99] CLOSURE : distinct_lines(N28_0_3, N28_0_3)
% 3.35/1.13
% 3.35/1.13 [96] GAMMA_FORALL : ! [L29_29] : (~unequally_directed_lines(L29_29, L29_29))
% 3.35/1.13 -> [100] ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13
% 3.35/1.13 [100] 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))))
% 3.35/1.13 -> [104] (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) => (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080)) | unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13
% 3.35/1.13 [104] BETA_IMPLY : (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) => (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080)) | unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13 -> [105] ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13 -> [106] (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080)) | unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080)))
% 3.35/1.13
% 3.35/1.13 [105] CLOSURE : ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13
% 3.35/1.13 [106] BETA_OR : (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080)) | unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080)))
% 3.35/1.13 -> [117] unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13 -> [118] unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13
% 3.35/1.13 [117] CLOSURE : unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13
% 3.35/1.13 [118] GAMMA_FORALL : ! [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))))))
% 3.35/1.13 -> [121] ((unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))) => ((unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))) | (unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_C8181))))))
% 3.35/1.13
% 3.35/1.13 [121] BETA_IMPLY : ((unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))) => ((unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))) | (unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_C8181))))))
% 3.35/1.13 -> [122] ~(unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13 -> [123] ((unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))) | (unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_C8181)))))
% 3.35/1.13
% 3.35/1.13 [122] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13 -> [124] ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13 -> [125] ~unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))
% 3.35/1.13
% 3.35/1.13 [124] CLOSURE : ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13
% 3.35/1.13 [130] BETA_IMPLY : ((line(skolem_L7878) & line(line_connecting(skolem_A7979, skolem_B8080))) => (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080)) | unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_B8080)))))
% 3.35/1.13 -> [205] ~(line(skolem_L7878) & line(line_connecting(skolem_A7979, skolem_B8080)))
% 3.35/1.13 -> [206] (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080)) | unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13
% 3.35/1.13 [205] BETA_NOT_AND : ~(line(skolem_L7878) & line(line_connecting(skolem_A7979, skolem_B8080)))
% 3.35/1.13 -> [207] ~line(skolem_L7878)
% 3.35/1.13 -> [208] ~line(line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13
% 3.35/1.13 [208] 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)))))
% 3.35/1.13 -> [212] ((unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080)) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))) => (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080)) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))))
% 3.35/1.13
% 3.35/1.13 [212] BETA_IMPLY : ((unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080)) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))) => (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080)) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))))
% 3.35/1.13 -> [213] ~(unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080)) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13 -> [214] (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080)) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13
% 3.35/1.13 [213] BETA_NOT_AND : ~(unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080)) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13 -> [217] ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13 -> [218] ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))
% 3.35/1.13
% 3.35/1.13 [217] CLOSURE : ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13
% 3.35/1.13 [218] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [231] ~(left_apart_point(A40_12_9, L41_12_9) | left_apart_point(A40_12_9, reverse_line(L41_12_9)))
% 3.35/1.13
% 3.35/1.13 [231] ALPHA_NOT_OR : ~(left_apart_point(A40_12_9, L41_12_9) | left_apart_point(A40_12_9, reverse_line(L41_12_9)))
% 3.35/1.13 -> [233] ~left_apart_point(A40_12_9, L41_12_9), ~left_apart_point(A40_12_9, reverse_line(L41_12_9))
% 3.35/1.13
% 3.35/1.13 [233] CLOSURE : ~left_apart_point(A40_12_9, L41_12_9)
% 3.35/1.13
% 3.35/1.13 [214] BETA_OR : (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080)) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13 -> [219] left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13 -> [220] left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))
% 3.35/1.13
% 3.35/1.13 [220] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [234] ~(left_apart_point(A40_14_9, L41_14_9) | left_apart_point(A40_14_9, reverse_line(L41_14_9)))
% 3.35/1.13
% 3.35/1.13 [234] ALPHA_NOT_OR : ~(left_apart_point(A40_14_9, L41_14_9) | left_apart_point(A40_14_9, reverse_line(L41_14_9)))
% 3.35/1.13 -> [236] ~left_apart_point(A40_14_9, L41_14_9), ~left_apart_point(A40_14_9, reverse_line(L41_14_9))
% 3.35/1.13
% 3.35/1.13 [236] CLOSURE : ~left_apart_point(A40_14_9, L41_14_9)
% 3.35/1.13
% 3.35/1.13 [219] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [237] ~(left_apart_point(A40_15_9, L41_15_9) | left_apart_point(A40_15_9, reverse_line(L41_15_9)))
% 3.35/1.13
% 3.35/1.13 [237] ALPHA_NOT_OR : ~(left_apart_point(A40_15_9, L41_15_9) | left_apart_point(A40_15_9, reverse_line(L41_15_9)))
% 3.35/1.13 -> [238] ~left_apart_point(A40_15_9, L41_15_9), ~left_apart_point(A40_15_9, reverse_line(L41_15_9))
% 3.35/1.13
% 3.35/1.13 [238] CLOSURE : ~left_apart_point(A40_15_9, L41_15_9)
% 3.35/1.13
% 3.35/1.13 [207] 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)))))
% 3.35/1.13 -> [211] ((unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))) => (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))))
% 3.35/1.13
% 3.35/1.13 [211] BETA_IMPLY : ((unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))) => (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))))
% 3.35/1.13 -> [215] ~(unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13 -> [216] (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13
% 3.35/1.13 [215] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13 -> [221] ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13 -> [222] ~unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))
% 3.35/1.13
% 3.35/1.13 [221] CLOSURE : ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13
% 3.35/1.13 [222] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [232] ~(left_apart_point(A40_13_9, L41_13_9) | left_apart_point(A40_13_9, reverse_line(L41_13_9)))
% 3.35/1.13
% 3.35/1.13 [232] ALPHA_NOT_OR : ~(left_apart_point(A40_13_9, L41_13_9) | left_apart_point(A40_13_9, reverse_line(L41_13_9)))
% 3.35/1.13 -> [235] ~left_apart_point(A40_13_9, L41_13_9), ~left_apart_point(A40_13_9, reverse_line(L41_13_9))
% 3.35/1.13
% 3.35/1.13 [235] CLOSURE : ~left_apart_point(A40_13_9, L41_13_9)
% 3.35/1.13
% 3.35/1.13 [216] BETA_OR : (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13 -> [229] left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13 -> [230] left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))
% 3.35/1.13
% 3.35/1.13 [230] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [245] ~(left_apart_point(A40_16_9, L41_16_9) | left_apart_point(A40_16_9, reverse_line(L41_16_9)))
% 3.35/1.13
% 3.35/1.13 [245] ALPHA_NOT_OR : ~(left_apart_point(A40_16_9, L41_16_9) | left_apart_point(A40_16_9, reverse_line(L41_16_9)))
% 3.35/1.13 -> [248] ~left_apart_point(A40_16_9, L41_16_9), ~left_apart_point(A40_16_9, reverse_line(L41_16_9))
% 3.35/1.13
% 3.35/1.13 [248] CLOSURE : ~left_apart_point(A40_16_9, L41_16_9)
% 3.35/1.13
% 3.35/1.13 [229] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [255] ~(left_apart_point(A40_17_9, L41_17_9) | left_apart_point(A40_17_9, reverse_line(L41_17_9)))
% 3.35/1.13
% 3.35/1.13 [255] ALPHA_NOT_OR : ~(left_apart_point(A40_17_9, L41_17_9) | left_apart_point(A40_17_9, reverse_line(L41_17_9)))
% 3.35/1.13 -> [257] ~left_apart_point(A40_17_9, L41_17_9), ~left_apart_point(A40_17_9, reverse_line(L41_17_9))
% 3.35/1.13
% 3.35/1.13 [257] CLOSURE : ~left_apart_point(A40_17_9, L41_17_9)
% 3.35/1.13
% 3.35/1.13 [206] BETA_OR : (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080)) | unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13 -> [209] unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13 -> [210] unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_B8080)))
% 3.35/1.13
% 3.35/1.13 [209] CLOSURE : unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13
% 3.35/1.13 [210] 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)))))
% 3.35/1.13 -> [256] ((unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080)) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))) => (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080)) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))))
% 3.35/1.13
% 3.35/1.13 [256] BETA_IMPLY : ((unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080)) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))) => (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080)) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))))
% 3.35/1.13 -> [258] ~(unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080)) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13 -> [259] (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080)) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13
% 3.35/1.13 [259] BETA_OR : (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080)) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13 -> [260] left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13 -> [261] left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))
% 3.35/1.13
% 3.35/1.13 [261] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [275] ~(left_apart_point(A40_24_9, L41_24_9) | left_apart_point(A40_24_9, reverse_line(L41_24_9)))
% 3.35/1.13
% 3.35/1.13 [275] ALPHA_NOT_OR : ~(left_apart_point(A40_24_9, L41_24_9) | left_apart_point(A40_24_9, reverse_line(L41_24_9)))
% 3.35/1.13 -> [277] ~left_apart_point(A40_24_9, L41_24_9), ~left_apart_point(A40_24_9, reverse_line(L41_24_9))
% 3.35/1.13
% 3.35/1.13 [277] CLOSURE : ~left_apart_point(A40_24_9, L41_24_9)
% 3.35/1.13
% 3.35/1.13 [260] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [278] ~(left_apart_point(A40_25_9, L41_25_9) | left_apart_point(A40_25_9, reverse_line(L41_25_9)))
% 3.35/1.13
% 3.35/1.13 [278] ALPHA_NOT_OR : ~(left_apart_point(A40_25_9, L41_25_9) | left_apart_point(A40_25_9, reverse_line(L41_25_9)))
% 3.35/1.13 -> [279] ~left_apart_point(A40_25_9, L41_25_9), ~left_apart_point(A40_25_9, reverse_line(L41_25_9))
% 3.35/1.13
% 3.35/1.13 [279] CLOSURE : ~left_apart_point(A40_25_9, L41_25_9)
% 3.35/1.13
% 3.35/1.13 [258] BETA_NOT_AND : ~(unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080)) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13 -> [264] ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13 -> [265] ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))
% 3.35/1.13
% 3.35/1.13 [264] CLOSURE : ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13
% 3.35/1.13 [265] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [287] ~(left_apart_point(A40_26_9, L41_26_9) | left_apart_point(A40_26_9, reverse_line(L41_26_9)))
% 3.35/1.13
% 3.35/1.13 [287] ALPHA_NOT_OR : ~(left_apart_point(A40_26_9, L41_26_9) | left_apart_point(A40_26_9, reverse_line(L41_26_9)))
% 3.35/1.13 -> [289] ~left_apart_point(A40_26_9, L41_26_9), ~left_apart_point(A40_26_9, reverse_line(L41_26_9))
% 3.35/1.13
% 3.35/1.13 [289] CLOSURE : ~left_apart_point(A40_26_9, L41_26_9)
% 3.35/1.13
% 3.35/1.13 [123] BETA_OR : ((unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))) | (unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_C8181)))))
% 3.35/1.13 -> [295] (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13 -> [296] (unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13
% 3.35/1.13 [296] ALPHA_AND : (unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13 -> [298] unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_C8181)), unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_C8181)))
% 3.35/1.13
% 3.35/1.13 [298] CLOSURE : unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13
% 3.35/1.13 [297] 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)))))
% 3.35/1.13 -> [299] ((line(line_connecting(skolem_A7979, skolem_C8181)) & line(line_connecting(skolem_A7979, skolem_C8181))) => (unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_C8181)) | unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_C8181)))))
% 3.35/1.13
% 3.35/1.13 [299] BETA_IMPLY : ((line(line_connecting(skolem_A7979, skolem_C8181)) & line(line_connecting(skolem_A7979, skolem_C8181))) => (unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_C8181)) | unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_C8181)))))
% 3.35/1.13 -> [300] ~(line(line_connecting(skolem_A7979, skolem_C8181)) & line(line_connecting(skolem_A7979, skolem_C8181)))
% 3.35/1.13 -> [301] (unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_C8181)) | unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13
% 3.35/1.13 [300] BETA_NOT_AND : ~(line(line_connecting(skolem_A7979, skolem_C8181)) & line(line_connecting(skolem_A7979, skolem_C8181)))
% 3.35/1.13 -> [302] ~line(line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13 -> [303] ~line(line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13
% 3.35/1.13 [302] 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)))))
% 3.35/1.13 -> [311] ((unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))) => (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))))
% 3.35/1.13
% 3.35/1.13 [311] BETA_IMPLY : ((unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))) => (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))))
% 3.35/1.13 -> [314] ~(unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13 -> [315] (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13
% 3.35/1.13 [314] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13 -> [319] ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13 -> [320] ~unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))
% 3.35/1.13
% 3.35/1.13 [320] CLOSURE : ~unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))
% 3.35/1.13
% 3.35/1.13 [319] CLOSURE : ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13
% 3.35/1.13 [315] BETA_OR : (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13 -> [323] left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13 -> [324] left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))
% 3.35/1.13
% 3.35/1.13 [323] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [333] ~(left_apart_point(A40_31_9, L41_31_9) | left_apart_point(A40_31_9, reverse_line(L41_31_9)))
% 3.35/1.13
% 3.35/1.13 [333] ALPHA_NOT_OR : ~(left_apart_point(A40_31_9, L41_31_9) | left_apart_point(A40_31_9, reverse_line(L41_31_9)))
% 3.35/1.13 -> [334] ~left_apart_point(A40_31_9, L41_31_9), ~left_apart_point(A40_31_9, reverse_line(L41_31_9))
% 3.35/1.13
% 3.35/1.13 [334] CLOSURE : ~left_apart_point(A40_31_9, L41_31_9)
% 3.35/1.13
% 3.35/1.13 [324] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [331] ~(left_apart_point(A40_30_9, L41_30_9) | left_apart_point(A40_30_9, reverse_line(L41_30_9)))
% 3.35/1.13
% 3.35/1.13 [331] ALPHA_NOT_OR : ~(left_apart_point(A40_30_9, L41_30_9) | left_apart_point(A40_30_9, reverse_line(L41_30_9)))
% 3.35/1.13 -> [332] ~left_apart_point(A40_30_9, L41_30_9), ~left_apart_point(A40_30_9, reverse_line(L41_30_9))
% 3.35/1.13
% 3.35/1.13 [332] CLOSURE : ~left_apart_point(A40_30_9, L41_30_9)
% 3.35/1.13
% 3.35/1.13 [303] 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)))))
% 3.35/1.13 -> [310] ((unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))) => (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))))
% 3.35/1.13
% 3.35/1.13 [310] BETA_IMPLY : ((unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))) => (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))))
% 3.35/1.13 -> [312] ~(unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13 -> [313] (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13
% 3.35/1.13 [312] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13 -> [317] ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13 -> [318] ~unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))
% 3.35/1.13
% 3.35/1.13 [318] CLOSURE : ~unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))
% 3.35/1.13
% 3.35/1.13 [317] CLOSURE : ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13
% 3.35/1.13 [313] BETA_OR : (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13 -> [325] left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13 -> [326] left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))
% 3.35/1.13
% 3.35/1.13 [326] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [335] ~(left_apart_point(A40_32_9, L41_32_9) | left_apart_point(A40_32_9, reverse_line(L41_32_9)))
% 3.35/1.13
% 3.35/1.13 [335] ALPHA_NOT_OR : ~(left_apart_point(A40_32_9, L41_32_9) | left_apart_point(A40_32_9, reverse_line(L41_32_9)))
% 3.35/1.13 -> [338] ~left_apart_point(A40_32_9, L41_32_9), ~left_apart_point(A40_32_9, reverse_line(L41_32_9))
% 3.35/1.13
% 3.35/1.13 [338] CLOSURE : ~left_apart_point(A40_32_9, L41_32_9)
% 3.35/1.13
% 3.35/1.13 [325] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [336] ~(left_apart_point(A40_33_9, L41_33_9) | left_apart_point(A40_33_9, reverse_line(L41_33_9)))
% 3.35/1.13
% 3.35/1.13 [336] ALPHA_NOT_OR : ~(left_apart_point(A40_33_9, L41_33_9) | left_apart_point(A40_33_9, reverse_line(L41_33_9)))
% 3.35/1.13 -> [340] ~left_apart_point(A40_33_9, L41_33_9), ~left_apart_point(A40_33_9, reverse_line(L41_33_9))
% 3.35/1.13
% 3.35/1.13 [340] CLOSURE : ~left_apart_point(A40_33_9, L41_33_9)
% 3.35/1.13
% 3.35/1.13 [301] BETA_OR : (unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_C8181)) | unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13 -> [304] unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13 -> [305] unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(line_connecting(skolem_A7979, skolem_C8181)))
% 3.35/1.13
% 3.35/1.13 [304] CLOSURE : unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13
% 3.35/1.13 [305] 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)))))
% 3.35/1.13 -> [316] ((unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))) => (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))))
% 3.35/1.13
% 3.35/1.13 [316] BETA_IMPLY : ((unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))) => (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))))
% 3.35/1.13 -> [321] ~(unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13 -> [322] (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13
% 3.35/1.13 [321] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13 -> [329] ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13 -> [330] ~unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))
% 3.35/1.13
% 3.35/1.13 [330] CLOSURE : ~unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))
% 3.35/1.13
% 3.35/1.13 [329] CLOSURE : ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13
% 3.35/1.13 [322] BETA_OR : (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13 -> [327] left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13 -> [328] left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))
% 3.35/1.13
% 3.35/1.13 [327] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [337] ~(left_apart_point(A40_34_9, L41_34_9) | left_apart_point(A40_34_9, reverse_line(L41_34_9)))
% 3.35/1.13
% 3.35/1.13 [337] ALPHA_NOT_OR : ~(left_apart_point(A40_34_9, L41_34_9) | left_apart_point(A40_34_9, reverse_line(L41_34_9)))
% 3.35/1.13 -> [341] ~left_apart_point(A40_34_9, L41_34_9), ~left_apart_point(A40_34_9, reverse_line(L41_34_9))
% 3.35/1.13
% 3.35/1.13 [341] CLOSURE : ~left_apart_point(A40_34_9, L41_34_9)
% 3.35/1.13
% 3.35/1.13 [328] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [339] ~(left_apart_point(A40_35_9, L41_35_9) | left_apart_point(A40_35_9, reverse_line(L41_35_9)))
% 3.35/1.13
% 3.35/1.13 [339] ALPHA_NOT_OR : ~(left_apart_point(A40_35_9, L41_35_9) | left_apart_point(A40_35_9, reverse_line(L41_35_9)))
% 3.35/1.13 -> [342] ~left_apart_point(A40_35_9, L41_35_9), ~left_apart_point(A40_35_9, reverse_line(L41_35_9))
% 3.35/1.13
% 3.35/1.13 [342] CLOSURE : ~left_apart_point(A40_35_9, L41_35_9)
% 3.35/1.13
% 3.35/1.13 [31] ALPHA_NOT_NOT : ~~unequally_directed_lines(skolem_L7878, line_connecting(skolem_C8181, skolem_B8080))
% 3.35/1.13 -> [38] unequally_directed_lines(skolem_L7878, line_connecting(skolem_C8181, skolem_B8080))
% 3.35/1.13
% 3.35/1.13 [38] GAMMA_FORALL : ! [A21_21] : (~distinct_points(A21_21, A21_21))
% 3.35/1.13 -> [69] ~distinct_points(skolem_B8080, skolem_B8080)
% 3.35/1.13
% 3.35/1.13 [69] 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))))
% 3.35/1.13 -> [79] (distinct_points(skolem_B8080, skolem_C8181) => (distinct_points(skolem_B8080, skolem_B8080) | distinct_points(skolem_C8181, skolem_B8080)))
% 3.35/1.13
% 3.35/1.13 [79] BETA_IMPLY : (distinct_points(skolem_B8080, skolem_C8181) => (distinct_points(skolem_B8080, skolem_B8080) | distinct_points(skolem_C8181, skolem_B8080)))
% 3.35/1.13 -> [83] ~distinct_points(skolem_B8080, skolem_C8181)
% 3.35/1.13 -> [84] (distinct_points(skolem_B8080, skolem_B8080) | distinct_points(skolem_C8181, skolem_B8080))
% 3.35/1.13
% 3.35/1.13 [83] CLOSURE : ~distinct_points(skolem_B8080, skolem_C8181)
% 3.35/1.13
% 3.35/1.13 [84] BETA_OR : (distinct_points(skolem_B8080, skolem_B8080) | distinct_points(skolem_C8181, skolem_B8080))
% 3.35/1.13 -> [91] distinct_points(skolem_B8080, skolem_B8080)
% 3.35/1.13 -> [92] distinct_points(skolem_C8181, skolem_B8080)
% 3.35/1.13
% 3.35/1.13 [91] CLOSURE : distinct_points(skolem_B8080, skolem_B8080)
% 3.35/1.13
% 3.35/1.13 [92] GAMMA_FORALL : ! [L25_25] : (~distinct_lines(L25_25, L25_25))
% 3.35/1.13 -> [95] ~distinct_lines(L26_1_3, L26_1_3)
% 3.35/1.13
% 3.35/1.13 [95] 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))))
% 3.35/1.13 -> [101] (distinct_lines(L26_1_3, L26_1_3) => (distinct_lines(L26_1_3, L26_1_3) | distinct_lines(L26_1_3, L26_1_3)))
% 3.35/1.13
% 3.35/1.13 [101] BETA_IMPLY : (distinct_lines(L26_1_3, L26_1_3) => (distinct_lines(L26_1_3, L26_1_3) | distinct_lines(L26_1_3, L26_1_3)))
% 3.35/1.13 -> [102] ~distinct_lines(L26_1_3, L26_1_3)
% 3.35/1.13 -> [103] (distinct_lines(L26_1_3, L26_1_3) | distinct_lines(L26_1_3, L26_1_3))
% 3.35/1.13
% 3.35/1.13 [103] BETA_OR : (distinct_lines(L26_1_3, L26_1_3) | distinct_lines(L26_1_3, L26_1_3))
% 3.35/1.13 -> [109] distinct_lines(L26_1_3, L26_1_3)
% 3.35/1.13 -> [110] distinct_lines(L26_1_3, L26_1_3)
% 3.35/1.13
% 3.35/1.13 [110] CLOSURE : distinct_lines(L26_1_3, L26_1_3)
% 3.35/1.13
% 3.35/1.13 [109] CLOSURE : distinct_lines(L26_1_3, L26_1_3)
% 3.35/1.13
% 3.35/1.13 [102] GAMMA_FORALL : ! [L29_29] : (~unequally_directed_lines(L29_29, L29_29))
% 3.35/1.13 -> [111] ~unequally_directed_lines(skolem_L7878, skolem_L7878)
% 3.35/1.13
% 3.35/1.13 [111] 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))))
% 3.35/1.13 -> [112] (unequally_directed_lines(skolem_L7878, line_connecting(skolem_C8181, skolem_B8080)) => (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080)) | unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13
% 3.35/1.13 [112] BETA_IMPLY : (unequally_directed_lines(skolem_L7878, line_connecting(skolem_C8181, skolem_B8080)) => (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080)) | unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13 -> [113] ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_C8181, skolem_B8080))
% 3.35/1.13 -> [114] (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080)) | unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080)))
% 3.35/1.13
% 3.35/1.13 [113] CLOSURE : ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_C8181, skolem_B8080))
% 3.35/1.13
% 3.35/1.13 [114] BETA_OR : (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080)) | unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080)))
% 3.35/1.13 -> [119] unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13 -> [120] unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13
% 3.35/1.13 [119] CLOSURE : unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13
% 3.35/1.13 [120] GAMMA_FORALL : ! [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))))))
% 3.35/1.13 -> [133] ((unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))) => ((unequally_directed_lines(skolem_L7878, skolem_L7878) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878))) | (unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))))
% 3.35/1.13
% 3.35/1.13 [133] BETA_IMPLY : ((unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))) => ((unequally_directed_lines(skolem_L7878, skolem_L7878) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878))) | (unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))))
% 3.35/1.13 -> [134] ~(unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13 -> [135] ((unequally_directed_lines(skolem_L7878, skolem_L7878) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878))) | (unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))))
% 3.35/1.13
% 3.35/1.13 [134] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 3.35/1.13 -> [140] ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13 -> [141] ~unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))
% 3.35/1.13
% 3.35/1.13 [140] CLOSURE : ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 3.35/1.13
% 3.35/1.13 [152] BETA_IMPLY : ((line(L36_1_7) & line(L36_1_7)) => (unequally_directed_lines(L36_1_7, L36_1_7) | unequally_directed_lines(L36_1_7, reverse_line(L36_1_7))))
% 3.35/1.13 -> [223] ~(line(L36_1_7) & line(L36_1_7))
% 3.35/1.13 -> [224] (unequally_directed_lines(L36_1_7, L36_1_7) | unequally_directed_lines(L36_1_7, reverse_line(L36_1_7)))
% 3.35/1.13
% 3.35/1.13 [223] BETA_NOT_AND : ~(line(L36_1_7) & line(L36_1_7))
% 3.35/1.13 -> [225] ~line(L36_1_7)
% 3.35/1.13 -> [226] ~line(L36_1_7)
% 3.35/1.13
% 3.35/1.13 [226] 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)))))
% 3.35/1.13 -> [240] ((unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080)) & unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))) => (left_convergent_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080)) | left_convergent_lines(line_connecting(skolem_C8181, skolem_B8080), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))))
% 3.35/1.13
% 3.35/1.13 [240] BETA_IMPLY : ((unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080)) & unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))) => (left_convergent_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080)) | left_convergent_lines(line_connecting(skolem_C8181, skolem_B8080), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))))
% 3.35/1.13 -> [243] ~(unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080)) & unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), reverse_line(line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13 -> [244] (left_convergent_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080)) | left_convergent_lines(line_connecting(skolem_C8181, skolem_B8080), reverse_line(line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13
% 3.35/1.13 [244] BETA_OR : (left_convergent_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080)) | left_convergent_lines(line_connecting(skolem_C8181, skolem_B8080), reverse_line(line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13 -> [251] left_convergent_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13 -> [252] left_convergent_lines(line_connecting(skolem_C8181, skolem_B8080), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))
% 3.35/1.13
% 3.35/1.13 [251] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [262] ~(left_apart_point(A40_18_9, L41_18_9) | left_apart_point(A40_18_9, reverse_line(L41_18_9)))
% 3.35/1.13
% 3.35/1.13 [262] ALPHA_NOT_OR : ~(left_apart_point(A40_18_9, L41_18_9) | left_apart_point(A40_18_9, reverse_line(L41_18_9)))
% 3.35/1.13 -> [263] ~left_apart_point(A40_18_9, L41_18_9), ~left_apart_point(A40_18_9, reverse_line(L41_18_9))
% 3.35/1.13
% 3.35/1.13 [263] CLOSURE : ~left_apart_point(A40_18_9, L41_18_9)
% 3.35/1.13
% 3.35/1.13 [252] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [266] ~(left_apart_point(A40_19_9, L41_19_9) | left_apart_point(A40_19_9, reverse_line(L41_19_9)))
% 3.35/1.13
% 3.35/1.13 [266] ALPHA_NOT_OR : ~(left_apart_point(A40_19_9, L41_19_9) | left_apart_point(A40_19_9, reverse_line(L41_19_9)))
% 3.35/1.13 -> [267] ~left_apart_point(A40_19_9, L41_19_9), ~left_apart_point(A40_19_9, reverse_line(L41_19_9))
% 3.35/1.13
% 3.35/1.13 [267] CLOSURE : ~left_apart_point(A40_19_9, L41_19_9)
% 3.35/1.13
% 3.35/1.13 [243] BETA_NOT_AND : ~(unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080)) & unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), reverse_line(line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13 -> [253] ~unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13 -> [254] ~unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))
% 3.35/1.13
% 3.35/1.13 [253] CLOSURE : ~unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13
% 3.35/1.13 [254] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [268] ~(left_apart_point(A40_20_9, L41_20_9) | left_apart_point(A40_20_9, reverse_line(L41_20_9)))
% 3.35/1.13
% 3.35/1.13 [268] ALPHA_NOT_OR : ~(left_apart_point(A40_20_9, L41_20_9) | left_apart_point(A40_20_9, reverse_line(L41_20_9)))
% 3.35/1.13 -> [269] ~left_apart_point(A40_20_9, L41_20_9), ~left_apart_point(A40_20_9, reverse_line(L41_20_9))
% 3.35/1.13
% 3.35/1.13 [269] CLOSURE : ~left_apart_point(A40_20_9, L41_20_9)
% 3.35/1.13
% 3.35/1.13 [225] 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)))))
% 3.35/1.13 -> [239] ((unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080)) & unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))) => (left_convergent_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080)) | left_convergent_lines(line_connecting(skolem_C8181, skolem_B8080), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))))
% 3.35/1.13
% 3.35/1.13 [239] BETA_IMPLY : ((unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080)) & unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))) => (left_convergent_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080)) | left_convergent_lines(line_connecting(skolem_C8181, skolem_B8080), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))))
% 3.35/1.13 -> [241] ~(unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080)) & unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), reverse_line(line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13 -> [242] (left_convergent_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080)) | left_convergent_lines(line_connecting(skolem_C8181, skolem_B8080), reverse_line(line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13
% 3.35/1.13 [241] BETA_NOT_AND : ~(unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080)) & unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), reverse_line(line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13 -> [246] ~unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13 -> [247] ~unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))
% 3.35/1.13
% 3.35/1.13 [246] CLOSURE : ~unequally_directed_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13
% 3.35/1.13 [247] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [270] ~(left_apart_point(A40_21_9, L41_21_9) | left_apart_point(A40_21_9, reverse_line(L41_21_9)))
% 3.35/1.13
% 3.35/1.13 [270] ALPHA_NOT_OR : ~(left_apart_point(A40_21_9, L41_21_9) | left_apart_point(A40_21_9, reverse_line(L41_21_9)))
% 3.35/1.13 -> [273] ~left_apart_point(A40_21_9, L41_21_9), ~left_apart_point(A40_21_9, reverse_line(L41_21_9))
% 3.35/1.13
% 3.35/1.13 [273] CLOSURE : ~left_apart_point(A40_21_9, L41_21_9)
% 3.35/1.13
% 3.35/1.13 [242] BETA_OR : (left_convergent_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080)) | left_convergent_lines(line_connecting(skolem_C8181, skolem_B8080), reverse_line(line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13 -> [249] left_convergent_lines(line_connecting(skolem_C8181, skolem_B8080), line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13 -> [250] left_convergent_lines(line_connecting(skolem_C8181, skolem_B8080), reverse_line(line_connecting(skolem_A7979, skolem_B8080)))
% 3.35/1.13
% 3.35/1.13 [250] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [271] ~(left_apart_point(A40_22_9, L41_22_9) | left_apart_point(A40_22_9, reverse_line(L41_22_9)))
% 3.35/1.13
% 3.35/1.13 [271] ALPHA_NOT_OR : ~(left_apart_point(A40_22_9, L41_22_9) | left_apart_point(A40_22_9, reverse_line(L41_22_9)))
% 3.35/1.13 -> [276] ~left_apart_point(A40_22_9, L41_22_9), ~left_apart_point(A40_22_9, reverse_line(L41_22_9))
% 3.35/1.13
% 3.35/1.13 [276] CLOSURE : ~left_apart_point(A40_22_9, L41_22_9)
% 3.35/1.13
% 3.35/1.13 [249] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [272] ~(left_apart_point(A40_23_9, L41_23_9) | left_apart_point(A40_23_9, reverse_line(L41_23_9)))
% 3.35/1.13
% 3.35/1.13 [272] ALPHA_NOT_OR : ~(left_apart_point(A40_23_9, L41_23_9) | left_apart_point(A40_23_9, reverse_line(L41_23_9)))
% 3.35/1.13 -> [274] ~left_apart_point(A40_23_9, L41_23_9), ~left_apart_point(A40_23_9, reverse_line(L41_23_9))
% 3.35/1.13
% 3.35/1.13 [274] CLOSURE : ~left_apart_point(A40_23_9, L41_23_9)
% 3.35/1.13
% 3.35/1.13 [224] BETA_OR : (unequally_directed_lines(L36_1_7, L36_1_7) | unequally_directed_lines(L36_1_7, reverse_line(L36_1_7)))
% 3.35/1.13 -> [227] unequally_directed_lines(L36_1_7, L36_1_7)
% 3.35/1.13 -> [228] unequally_directed_lines(L36_1_7, reverse_line(L36_1_7))
% 3.35/1.13
% 3.35/1.13 [227] CLOSURE : unequally_directed_lines(L36_1_7, L36_1_7)
% 3.35/1.13
% 3.35/1.13 [228] 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)))))
% 3.35/1.13 -> [280] ((unequally_directed_lines(L38_9_8, reverse_line(L38_9_8)) & unequally_directed_lines(L38_9_8, reverse_line(reverse_line(L38_9_8)))) => (left_convergent_lines(L38_9_8, reverse_line(L38_9_8)) | left_convergent_lines(L38_9_8, reverse_line(reverse_line(L38_9_8)))))
% 3.35/1.13
% 3.35/1.13 [280] BETA_IMPLY : ((unequally_directed_lines(L38_9_8, reverse_line(L38_9_8)) & unequally_directed_lines(L38_9_8, reverse_line(reverse_line(L38_9_8)))) => (left_convergent_lines(L38_9_8, reverse_line(L38_9_8)) | left_convergent_lines(L38_9_8, reverse_line(reverse_line(L38_9_8)))))
% 3.35/1.13 -> [281] ~(unequally_directed_lines(L38_9_8, reverse_line(L38_9_8)) & unequally_directed_lines(L38_9_8, reverse_line(reverse_line(L38_9_8))))
% 3.35/1.13 -> [282] (left_convergent_lines(L38_9_8, reverse_line(L38_9_8)) | left_convergent_lines(L38_9_8, reverse_line(reverse_line(L38_9_8))))
% 3.35/1.13
% 3.35/1.13 [282] BETA_OR : (left_convergent_lines(L38_9_8, reverse_line(L38_9_8)) | left_convergent_lines(L38_9_8, reverse_line(reverse_line(L38_9_8))))
% 3.35/1.13 -> [285] left_convergent_lines(L38_9_8, reverse_line(L38_9_8))
% 3.35/1.13 -> [286] left_convergent_lines(L38_9_8, reverse_line(reverse_line(L38_9_8)))
% 3.35/1.13
% 3.35/1.13 [286] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [290] ~(left_apart_point(A40_28_9, L41_28_9) | left_apart_point(A40_28_9, reverse_line(L41_28_9)))
% 3.35/1.13
% 3.35/1.13 [290] ALPHA_NOT_OR : ~(left_apart_point(A40_28_9, L41_28_9) | left_apart_point(A40_28_9, reverse_line(L41_28_9)))
% 3.35/1.13 -> [292] ~left_apart_point(A40_28_9, L41_28_9), ~left_apart_point(A40_28_9, reverse_line(L41_28_9))
% 3.35/1.13
% 3.35/1.13 [292] CLOSURE : ~left_apart_point(A40_28_9, L41_28_9)
% 3.35/1.13
% 3.35/1.13 [285] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [288] ~(left_apart_point(A40_27_9, L41_27_9) | left_apart_point(A40_27_9, reverse_line(L41_27_9)))
% 3.35/1.13
% 3.35/1.13 [288] ALPHA_NOT_OR : ~(left_apart_point(A40_27_9, L41_27_9) | left_apart_point(A40_27_9, reverse_line(L41_27_9)))
% 3.35/1.13 -> [291] ~left_apart_point(A40_27_9, L41_27_9), ~left_apart_point(A40_27_9, reverse_line(L41_27_9))
% 3.35/1.13
% 3.35/1.13 [291] CLOSURE : ~left_apart_point(A40_27_9, L41_27_9)
% 3.35/1.13
% 3.35/1.13 [281] BETA_NOT_AND : ~(unequally_directed_lines(L38_9_8, reverse_line(L38_9_8)) & unequally_directed_lines(L38_9_8, reverse_line(reverse_line(L38_9_8))))
% 3.35/1.13 -> [283] ~unequally_directed_lines(L38_9_8, reverse_line(L38_9_8))
% 3.35/1.13 -> [284] ~unequally_directed_lines(L38_9_8, reverse_line(reverse_line(L38_9_8)))
% 3.35/1.13
% 3.35/1.13 [283] CLOSURE : ~unequally_directed_lines(L38_9_8, reverse_line(L38_9_8))
% 3.35/1.13
% 3.35/1.13 [284] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [293] ~(left_apart_point(A40_29_9, L41_29_9) | left_apart_point(A40_29_9, reverse_line(L41_29_9)))
% 3.35/1.13
% 3.35/1.13 [293] ALPHA_NOT_OR : ~(left_apart_point(A40_29_9, L41_29_9) | left_apart_point(A40_29_9, reverse_line(L41_29_9)))
% 3.35/1.13 -> [294] ~left_apart_point(A40_29_9, L41_29_9), ~left_apart_point(A40_29_9, reverse_line(L41_29_9))
% 3.35/1.13
% 3.35/1.13 [294] CLOSURE : ~left_apart_point(A40_29_9, L41_29_9)
% 3.35/1.13
% 3.35/1.13 [135] BETA_OR : ((unequally_directed_lines(skolem_L7878, skolem_L7878) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878))) | (unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))))
% 3.35/1.13 -> [306] (unequally_directed_lines(skolem_L7878, skolem_L7878) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [307] (unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [306] ALPHA_AND : (unequally_directed_lines(skolem_L7878, skolem_L7878) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878)))
% 3.35/1.13 -> [308] unequally_directed_lines(skolem_L7878, skolem_L7878), unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [308] CLOSURE : unequally_directed_lines(skolem_L7878, skolem_L7878)
% 3.35/1.13
% 3.35/1.13 [309] 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)))))
% 3.35/1.13 -> [343] ((line(skolem_L7878) & line(line_connecting(skolem_A7979, skolem_B8080))) => (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080)) | unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_B8080)))))
% 3.35/1.13
% 3.35/1.13 [343] BETA_IMPLY : ((line(skolem_L7878) & line(line_connecting(skolem_A7979, skolem_B8080))) => (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080)) | unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_B8080)))))
% 3.35/1.13 -> [344] ~(line(skolem_L7878) & line(line_connecting(skolem_A7979, skolem_B8080)))
% 3.35/1.13 -> [345] (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080)) | unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13
% 3.35/1.13 [344] BETA_NOT_AND : ~(line(skolem_L7878) & line(line_connecting(skolem_A7979, skolem_B8080)))
% 3.35/1.13 -> [348] ~line(skolem_L7878)
% 3.35/1.13 -> [349] ~line(line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13
% 3.35/1.13 [349] 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)))))
% 3.35/1.13 -> [352] ((unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))) => (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))))
% 3.35/1.13
% 3.35/1.13 [352] BETA_IMPLY : ((unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))) => (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))))
% 3.35/1.13 -> [357] ~(unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 3.35/1.13 -> [358] (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [357] BETA_NOT_AND : ~(unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 3.35/1.13 -> [369] ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)
% 3.35/1.13 -> [370] ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [370] CLOSURE : ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [369] CLOSURE : ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)
% 3.35/1.13
% 3.35/1.13 [358] BETA_OR : (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 3.35/1.13 -> [367] left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)
% 3.35/1.13 -> [368] left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [367] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [372] ~(left_apart_point(A40_37_9, L41_37_9) | left_apart_point(A40_37_9, reverse_line(L41_37_9)))
% 3.35/1.13
% 3.35/1.13 [372] ALPHA_NOT_OR : ~(left_apart_point(A40_37_9, L41_37_9) | left_apart_point(A40_37_9, reverse_line(L41_37_9)))
% 3.35/1.13 -> [374] ~left_apart_point(A40_37_9, L41_37_9), ~left_apart_point(A40_37_9, reverse_line(L41_37_9))
% 3.35/1.13
% 3.35/1.13 [374] CLOSURE : ~left_apart_point(A40_37_9, L41_37_9)
% 3.35/1.13
% 3.35/1.13 [368] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [377] ~(left_apart_point(A40_40_9, L41_40_9) | left_apart_point(A40_40_9, reverse_line(L41_40_9)))
% 3.35/1.13
% 3.35/1.13 [377] ALPHA_NOT_OR : ~(left_apart_point(A40_40_9, L41_40_9) | left_apart_point(A40_40_9, reverse_line(L41_40_9)))
% 3.35/1.13 -> [381] ~left_apart_point(A40_40_9, L41_40_9), ~left_apart_point(A40_40_9, reverse_line(L41_40_9))
% 3.35/1.13
% 3.35/1.13 [381] CLOSURE : ~left_apart_point(A40_40_9, L41_40_9)
% 3.35/1.13
% 3.35/1.13 [348] 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)))))
% 3.35/1.13 -> [350] ((unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))) => (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))))
% 3.35/1.13
% 3.35/1.13 [350] BETA_IMPLY : ((unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))) => (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))))
% 3.35/1.13 -> [353] ~(unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 3.35/1.13 -> [354] (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [353] BETA_NOT_AND : ~(unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 3.35/1.13 -> [359] ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)
% 3.35/1.13 -> [360] ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [360] CLOSURE : ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [359] CLOSURE : ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)
% 3.35/1.13
% 3.35/1.13 [354] BETA_OR : (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 3.35/1.13 -> [361] left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)
% 3.35/1.13 -> [362] left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [361] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [371] ~(left_apart_point(A40_36_9, L41_36_9) | left_apart_point(A40_36_9, reverse_line(L41_36_9)))
% 3.35/1.13
% 3.35/1.13 [371] ALPHA_NOT_OR : ~(left_apart_point(A40_36_9, L41_36_9) | left_apart_point(A40_36_9, reverse_line(L41_36_9)))
% 3.35/1.13 -> [373] ~left_apart_point(A40_36_9, L41_36_9), ~left_apart_point(A40_36_9, reverse_line(L41_36_9))
% 3.35/1.13
% 3.35/1.13 [373] CLOSURE : ~left_apart_point(A40_36_9, L41_36_9)
% 3.35/1.13
% 3.35/1.13 [362] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [380] ~(left_apart_point(A40_41_9, L41_41_9) | left_apart_point(A40_41_9, reverse_line(L41_41_9)))
% 3.35/1.13
% 3.35/1.13 [380] ALPHA_NOT_OR : ~(left_apart_point(A40_41_9, L41_41_9) | left_apart_point(A40_41_9, reverse_line(L41_41_9)))
% 3.35/1.13 -> [382] ~left_apart_point(A40_41_9, L41_41_9), ~left_apart_point(A40_41_9, reverse_line(L41_41_9))
% 3.35/1.13
% 3.35/1.13 [382] CLOSURE : ~left_apart_point(A40_41_9, L41_41_9)
% 3.35/1.13
% 3.35/1.13 [345] BETA_OR : (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080)) | unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_B8080))))
% 3.35/1.13 -> [346] unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13 -> [347] unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_B8080)))
% 3.35/1.13
% 3.35/1.13 [346] CLOSURE : unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080))
% 3.35/1.13
% 3.35/1.13 [347] 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)))))
% 3.35/1.13 -> [351] ((unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))) => (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))))
% 3.35/1.13
% 3.35/1.13 [351] BETA_IMPLY : ((unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))) => (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))))
% 3.35/1.13 -> [355] ~(unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 3.35/1.13 -> [356] (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 3.35/1.13
% 3.35/1.13 [355] BETA_NOT_AND : ~(unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 3.35/1.13 -> [363] ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)
% 3.35/1.13 -> [364] ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [363] CLOSURE : ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)
% 3.35/1.13
% 3.35/1.13 [364] CLOSURE : ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [356] BETA_OR : (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 3.35/1.13 -> [365] left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)
% 3.35/1.13 -> [366] left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))
% 3.35/1.13
% 3.35/1.13 [366] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [376] ~(left_apart_point(A40_39_9, L41_39_9) | left_apart_point(A40_39_9, reverse_line(L41_39_9)))
% 3.35/1.13
% 3.35/1.13 [376] ALPHA_NOT_OR : ~(left_apart_point(A40_39_9, L41_39_9) | left_apart_point(A40_39_9, reverse_line(L41_39_9)))
% 3.35/1.13 -> [379] ~left_apart_point(A40_39_9, L41_39_9), ~left_apart_point(A40_39_9, reverse_line(L41_39_9))
% 3.35/1.13
% 3.35/1.13 [379] CLOSURE : ~left_apart_point(A40_39_9, L41_39_9)
% 3.35/1.13
% 3.35/1.13 [365] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 3.35/1.13 -> [375] ~(left_apart_point(A40_38_9, L41_38_9) | left_apart_point(A40_38_9, reverse_line(L41_38_9)))
% 3.35/1.13
% 3.35/1.13 [375] ALPHA_NOT_OR : ~(left_apart_point(A40_38_9, L41_38_9) | left_apart_point(A40_38_9, reverse_line(L41_38_9)))
% 3.35/1.13 -> [378] ~left_apart_point(A40_38_9, L41_38_9), ~left_apart_point(A40_38_9, reverse_line(L41_38_9))
% 3.35/1.13
% 3.35/1.13 [378] CLOSURE : ~left_apart_point(A40_38_9, L41_38_9)
% 3.35/1.13
% 3.35/1.13 % SZS output end Proof for theBenchmark.p
% 3.35/1.13 [0.778494s][1][Res] 4831 goroutines created
% 3.35/1.13 ==== Result ====
% 3.35/1.13 [0.778521s][1][Res] VALID
% 3.35/1.13 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------