TSTP Solution File: GEO247+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO247+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n013.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 15:18:42 EDT 2022
% Result : Theorem 4.84s 1.20s
% Output : Proof 4.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO247+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.07/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 07:07:02 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 [DMT] DMT loaded with preskolemization
% 0.13/0.36 [EQ] equality loaded.
% 0.13/0.36 [0.000052s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.37 Conjecture not found
% 0.13/0.37 Start search
% 0.13/0.37 nb_step : 1 - limit : 32
% 0.13/0.37 Launch Gotab with destructive = true
% 4.84/1.19 % SZS output start Proof for theBenchmark.p
% 4.84/1.20 [0] ALPHA_AND : ((! [A21_21] : (~distinct_points(A21_21, A21_21)) & ! [A22_22, B23_23, C24_24] : ((distinct_points(A22_22, B23_23) => (distinct_points(A22_22, C24_24) | distinct_points(B23_23, C24_24)))) & ! [L25_25] : (~distinct_lines(L25_25, L25_25)) & ! [L26_26, M27_27, N28_28] : ((distinct_lines(L26_26, M27_27) => (distinct_lines(L26_26, N28_28) | distinct_lines(M27_27, N28_28)))) & ! [L29_29] : (~unequally_directed_lines(L29_29, L29_29)) & ! [L30_30, M31_31, N32_32] : ((unequally_directed_lines(L30_30, M31_31) => (unequally_directed_lines(L30_30, N32_32) | unequally_directed_lines(M31_31, N32_32)))) & ! [L33_33, M34_34, N35_35] : (((unequally_directed_lines(L33_33, M34_34) & unequally_directed_lines(L33_33, reverse_line(M34_34))) => ((unequally_directed_lines(L33_33, N35_35) & unequally_directed_lines(L33_33, reverse_line(N35_35))) | (unequally_directed_lines(M34_34, N35_35) & unequally_directed_lines(M34_34, reverse_line(N35_35)))))) & ! [L36_36, M37_37] : (((line(L36_36) & line(M37_37)) => (unequally_directed_lines(L36_36, M37_37) | unequally_directed_lines(L36_36, reverse_line(M37_37))))) & ! [L38_38, M39_39] : (((unequally_directed_lines(L38_38, M39_39) & unequally_directed_lines(L38_38, reverse_line(M39_39))) => (left_convergent_lines(L38_38, M39_39) | left_convergent_lines(L38_38, reverse_line(M39_39))))) & ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41)))) & ! [L42_42, M43_43] : (~(left_convergent_lines(L42_42, M43_43) | left_convergent_lines(L42_42, reverse_line(M43_43)))) & ! [A44_44, B45_45] : ((((point(A44_44) & point(B45_45)) & distinct_points(A44_44, B45_45)) => line(line_connecting(A44_44, B45_45)))) & ! [L46_46, M47_47] : (((((line(L46_46) & line(M47_47)) & unequally_directed_lines(L46_46, M47_47)) & unequally_directed_lines(L46_46, reverse_line(M47_47))) => point(intersection_point(L46_46, M47_47)))) & ! [L48_48, A49_49] : (((point(A49_49) & line(L48_48)) => line(parallel_through_point(L48_48, A49_49)))) & ! [L50_50] : ((line(L50_50) => line(reverse_line(L50_50)))) & ! [A51_51, B52_52] : ((distinct_points(A51_51, B52_52) => (~apart_point_and_line(A51_51, line_connecting(A51_51, B52_52)) & ~apart_point_and_line(B52_52, line_connecting(A51_51, B52_52))))) & ! [L53_53, M54_54] : (((unequally_directed_lines(L53_53, M54_54) & unequally_directed_lines(L53_53, reverse_line(M54_54))) => (~apart_point_and_line(intersection_point(L53_53, M54_54), L53_53) & ~apart_point_and_line(intersection_point(L53_53, M54_54), M54_54)))) & ! [A55_55, L56_56] : (~apart_point_and_line(A55_55, parallel_through_point(L56_56, A55_55))) & ! [L57_57] : (~distinct_lines(L57_57, reverse_line(L57_57))) & ! [A58_58, B59_59] : (~unequally_directed_lines(line_connecting(A58_58, B59_59), reverse_line(line_connecting(B59_59, A58_58)))) & ! [A60_60, L61_61] : (~unequally_directed_lines(parallel_through_point(L61_61, A60_60), L61_61)) & ! [A62_62, B63_63, L64_64, M65_65] : (((distinct_points(A62_62, B63_63) & distinct_lines(L64_64, M65_65)) => (((((((left_apart_point(A62_62, L64_64) | left_apart_point(B63_63, L64_64)) | left_apart_point(A62_62, M65_65)) | left_apart_point(B63_63, M65_65)) | left_apart_point(A62_62, reverse_line(L64_64))) | left_apart_point(B63_63, reverse_line(L64_64))) | left_apart_point(A62_62, reverse_line(M65_65))) | left_apart_point(B63_63, reverse_line(M65_65))))) & ! [A66_66, B67_67, L68_68] : (((distinct_points(A66_66, B67_67) & left_apart_point(A66_66, L68_68)) => (left_apart_point(B67_67, L68_68) | left_convergent_lines(line_connecting(A66_66, B67_67), L68_68)))) & ! [A69_69, B70_70, L71_71] : ((left_apart_point(A69_69, L71_71) => (distinct_points(A69_69, B70_70) | left_apart_point(B70_70, L71_71)))) & ! [A72_72, L73_73, M74_74] : (((left_apart_point(A72_72, L73_73) & unequally_directed_lines(L73_73, M74_74)) => (distinct_lines(L73_73, M74_74) | left_apart_point(A72_72, reverse_line(M74_74))))) & ! [L75_75, M76_76, N77_77] : ((left_convergent_lines(L75_75, M76_76) => (unequally_directed_lines(M76_76, N77_77) | left_convergent_lines(L75_75, N77_77))))) & ~! [A78_78, B79_79, C80_80, D81_81, L82_82, M83_83] : (((((((((left_apart_point(A78_78, L82_82) & left_apart_point(A78_78, M83_83)) & left_apart_point(B79_79, reverse_line(L82_82))) & left_apart_point(B79_79, reverse_line(M83_83))) & left_apart_point(C80_80, L82_82)) & left_apart_point(C80_80, reverse_line(M83_83))) & left_apart_point(D81_81, reverse_line(L82_82))) & left_apart_point(D81_81, M83_83)) => convergent_lines(L82_82, M83_83))))
% 4.84/1.20 -> [1] (! [A21_21] : (~distinct_points(A21_21, A21_21)) & ! [A22_22, B23_23, C24_24] : ((distinct_points(A22_22, B23_23) => (distinct_points(A22_22, C24_24) | distinct_points(B23_23, C24_24)))) & ! [L25_25] : (~distinct_lines(L25_25, L25_25)) & ! [L26_26, M27_27, N28_28] : ((distinct_lines(L26_26, M27_27) => (distinct_lines(L26_26, N28_28) | distinct_lines(M27_27, N28_28)))) & ! [L29_29] : (~unequally_directed_lines(L29_29, L29_29)) & ! [L30_30, M31_31, N32_32] : ((unequally_directed_lines(L30_30, M31_31) => (unequally_directed_lines(L30_30, N32_32) | unequally_directed_lines(M31_31, N32_32)))) & ! [L33_33, M34_34, N35_35] : (((unequally_directed_lines(L33_33, M34_34) & unequally_directed_lines(L33_33, reverse_line(M34_34))) => ((unequally_directed_lines(L33_33, N35_35) & unequally_directed_lines(L33_33, reverse_line(N35_35))) | (unequally_directed_lines(M34_34, N35_35) & unequally_directed_lines(M34_34, reverse_line(N35_35)))))) & ! [L36_36, M37_37] : (((line(L36_36) & line(M37_37)) => (unequally_directed_lines(L36_36, M37_37) | unequally_directed_lines(L36_36, reverse_line(M37_37))))) & ! [L38_38, M39_39] : (((unequally_directed_lines(L38_38, M39_39) & unequally_directed_lines(L38_38, reverse_line(M39_39))) => (left_convergent_lines(L38_38, M39_39) | left_convergent_lines(L38_38, reverse_line(M39_39))))) & ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41)))) & ! [L42_42, M43_43] : (~(left_convergent_lines(L42_42, M43_43) | left_convergent_lines(L42_42, reverse_line(M43_43)))) & ! [A44_44, B45_45] : ((((point(A44_44) & point(B45_45)) & distinct_points(A44_44, B45_45)) => line(line_connecting(A44_44, B45_45)))) & ! [L46_46, M47_47] : (((((line(L46_46) & line(M47_47)) & unequally_directed_lines(L46_46, M47_47)) & unequally_directed_lines(L46_46, reverse_line(M47_47))) => point(intersection_point(L46_46, M47_47)))) & ! [L48_48, A49_49] : (((point(A49_49) & line(L48_48)) => line(parallel_through_point(L48_48, A49_49)))) & ! [L50_50] : ((line(L50_50) => line(reverse_line(L50_50)))) & ! [A51_51, B52_52] : ((distinct_points(A51_51, B52_52) => (~apart_point_and_line(A51_51, line_connecting(A51_51, B52_52)) & ~apart_point_and_line(B52_52, line_connecting(A51_51, B52_52))))) & ! [L53_53, M54_54] : (((unequally_directed_lines(L53_53, M54_54) & unequally_directed_lines(L53_53, reverse_line(M54_54))) => (~apart_point_and_line(intersection_point(L53_53, M54_54), L53_53) & ~apart_point_and_line(intersection_point(L53_53, M54_54), M54_54)))) & ! [A55_55, L56_56] : (~apart_point_and_line(A55_55, parallel_through_point(L56_56, A55_55))) & ! [L57_57] : (~distinct_lines(L57_57, reverse_line(L57_57))) & ! [A58_58, B59_59] : (~unequally_directed_lines(line_connecting(A58_58, B59_59), reverse_line(line_connecting(B59_59, A58_58)))) & ! [A60_60, L61_61] : (~unequally_directed_lines(parallel_through_point(L61_61, A60_60), L61_61)) & ! [A62_62, B63_63, L64_64, M65_65] : (((distinct_points(A62_62, B63_63) & distinct_lines(L64_64, M65_65)) => (((((((left_apart_point(A62_62, L64_64) | left_apart_point(B63_63, L64_64)) | left_apart_point(A62_62, M65_65)) | left_apart_point(B63_63, M65_65)) | left_apart_point(A62_62, reverse_line(L64_64))) | left_apart_point(B63_63, reverse_line(L64_64))) | left_apart_point(A62_62, reverse_line(M65_65))) | left_apart_point(B63_63, reverse_line(M65_65))))) & ! [A66_66, B67_67, L68_68] : (((distinct_points(A66_66, B67_67) & left_apart_point(A66_66, L68_68)) => (left_apart_point(B67_67, L68_68) | left_convergent_lines(line_connecting(A66_66, B67_67), L68_68)))) & ! [A69_69, B70_70, L71_71] : ((left_apart_point(A69_69, L71_71) => (distinct_points(A69_69, B70_70) | left_apart_point(B70_70, L71_71)))) & ! [A72_72, L73_73, M74_74] : (((left_apart_point(A72_72, L73_73) & unequally_directed_lines(L73_73, M74_74)) => (distinct_lines(L73_73, M74_74) | left_apart_point(A72_72, reverse_line(M74_74))))) & ! [L75_75, M76_76, N77_77] : ((left_convergent_lines(L75_75, M76_76) => (unequally_directed_lines(M76_76, N77_77) | left_convergent_lines(L75_75, N77_77))))), ~! [A78_78, B79_79, C80_80, D81_81, L82_82, M83_83] : (((((((((left_apart_point(A78_78, L82_82) & left_apart_point(A78_78, M83_83)) & left_apart_point(B79_79, reverse_line(L82_82))) & left_apart_point(B79_79, reverse_line(M83_83))) & left_apart_point(C80_80, L82_82)) & left_apart_point(C80_80, reverse_line(M83_83))) & left_apart_point(D81_81, reverse_line(L82_82))) & left_apart_point(D81_81, M83_83)) => convergent_lines(L82_82, M83_83)))
% 4.84/1.20
% 4.84/1.20 [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)))))
% 4.84/1.20 -> [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))))
% 4.84/1.20
% 4.84/1.20 [2] DELTA_NOT_FORALL : ~! [A78_78, B79_79, C80_80, D81_81, L82_82, M83_83] : (((((((((left_apart_point(A78_78, L82_82) & left_apart_point(A78_78, M83_83)) & left_apart_point(B79_79, reverse_line(L82_82))) & left_apart_point(B79_79, reverse_line(M83_83))) & left_apart_point(C80_80, L82_82)) & left_apart_point(C80_80, reverse_line(M83_83))) & left_apart_point(D81_81, reverse_line(L82_82))) & left_apart_point(D81_81, M83_83)) => convergent_lines(L82_82, M83_83)))
% 4.84/1.20 -> [3] ~((((((((left_apart_point(skolem_A7878, skolem_L8282) & left_apart_point(skolem_A7878, skolem_M8383)) & left_apart_point(skolem_B7979, reverse_line(skolem_L8282))) & left_apart_point(skolem_B7979, reverse_line(skolem_M8383))) & left_apart_point(skolem_C8080, skolem_L8282)) & left_apart_point(skolem_C8080, reverse_line(skolem_M8383))) & left_apart_point(skolem_D8181, reverse_line(skolem_L8282))) & left_apart_point(skolem_D8181, skolem_M8383)) => convergent_lines(skolem_L8282, skolem_M8383))
% 4.84/1.20
% 4.84/1.20 [3] ALPHA_NOT_IMPLY : ~((((((((left_apart_point(skolem_A7878, skolem_L8282) & left_apart_point(skolem_A7878, skolem_M8383)) & left_apart_point(skolem_B7979, reverse_line(skolem_L8282))) & left_apart_point(skolem_B7979, reverse_line(skolem_M8383))) & left_apart_point(skolem_C8080, skolem_L8282)) & left_apart_point(skolem_C8080, reverse_line(skolem_M8383))) & left_apart_point(skolem_D8181, reverse_line(skolem_L8282))) & left_apart_point(skolem_D8181, skolem_M8383)) => convergent_lines(skolem_L8282, skolem_M8383))
% 4.84/1.20 -> [4] (((((((left_apart_point(skolem_A7878, skolem_L8282) & left_apart_point(skolem_A7878, skolem_M8383)) & left_apart_point(skolem_B7979, reverse_line(skolem_L8282))) & left_apart_point(skolem_B7979, reverse_line(skolem_M8383))) & left_apart_point(skolem_C8080, skolem_L8282)) & left_apart_point(skolem_C8080, reverse_line(skolem_M8383))) & left_apart_point(skolem_D8181, reverse_line(skolem_L8282))) & left_apart_point(skolem_D8181, skolem_M8383)), ~convergent_lines(skolem_L8282, skolem_M8383)
% 4.84/1.20
% 4.84/1.20 [4] Rewrite : ~convergent_lines(skolem_L8282, skolem_M8383)
% 4.84/1.20 -> [5] ~(unequally_directed_lines(skolem_L8282, skolem_M8383) & unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)))
% 4.84/1.20
% 4.84/1.20 [5] ALPHA_AND : (((((((left_apart_point(skolem_A7878, skolem_L8282) & left_apart_point(skolem_A7878, skolem_M8383)) & left_apart_point(skolem_B7979, reverse_line(skolem_L8282))) & left_apart_point(skolem_B7979, reverse_line(skolem_M8383))) & left_apart_point(skolem_C8080, skolem_L8282)) & left_apart_point(skolem_C8080, reverse_line(skolem_M8383))) & left_apart_point(skolem_D8181, reverse_line(skolem_L8282))) & left_apart_point(skolem_D8181, skolem_M8383))
% 4.84/1.20 -> [6] ((((((left_apart_point(skolem_A7878, skolem_L8282) & left_apart_point(skolem_A7878, skolem_M8383)) & left_apart_point(skolem_B7979, reverse_line(skolem_L8282))) & left_apart_point(skolem_B7979, reverse_line(skolem_M8383))) & left_apart_point(skolem_C8080, skolem_L8282)) & left_apart_point(skolem_C8080, reverse_line(skolem_M8383))) & left_apart_point(skolem_D8181, reverse_line(skolem_L8282))), left_apart_point(skolem_D8181, skolem_M8383)
% 4.84/1.20
% 4.84/1.20 [6] ALPHA_AND : ((((((left_apart_point(skolem_A7878, skolem_L8282) & left_apart_point(skolem_A7878, skolem_M8383)) & left_apart_point(skolem_B7979, reverse_line(skolem_L8282))) & left_apart_point(skolem_B7979, reverse_line(skolem_M8383))) & left_apart_point(skolem_C8080, skolem_L8282)) & left_apart_point(skolem_C8080, reverse_line(skolem_M8383))) & left_apart_point(skolem_D8181, reverse_line(skolem_L8282)))
% 4.84/1.20 -> [7] (((((left_apart_point(skolem_A7878, skolem_L8282) & left_apart_point(skolem_A7878, skolem_M8383)) & left_apart_point(skolem_B7979, reverse_line(skolem_L8282))) & left_apart_point(skolem_B7979, reverse_line(skolem_M8383))) & left_apart_point(skolem_C8080, skolem_L8282)) & left_apart_point(skolem_C8080, reverse_line(skolem_M8383))), left_apart_point(skolem_D8181, reverse_line(skolem_L8282))
% 4.84/1.20
% 4.84/1.20 [7] ALPHA_AND : (((((left_apart_point(skolem_A7878, skolem_L8282) & left_apart_point(skolem_A7878, skolem_M8383)) & left_apart_point(skolem_B7979, reverse_line(skolem_L8282))) & left_apart_point(skolem_B7979, reverse_line(skolem_M8383))) & left_apart_point(skolem_C8080, skolem_L8282)) & left_apart_point(skolem_C8080, reverse_line(skolem_M8383)))
% 4.84/1.20 -> [8] ((((left_apart_point(skolem_A7878, skolem_L8282) & left_apart_point(skolem_A7878, skolem_M8383)) & left_apart_point(skolem_B7979, reverse_line(skolem_L8282))) & left_apart_point(skolem_B7979, reverse_line(skolem_M8383))) & left_apart_point(skolem_C8080, skolem_L8282)), left_apart_point(skolem_C8080, reverse_line(skolem_M8383))
% 4.84/1.20
% 4.84/1.20 [8] ALPHA_AND : ((((left_apart_point(skolem_A7878, skolem_L8282) & left_apart_point(skolem_A7878, skolem_M8383)) & left_apart_point(skolem_B7979, reverse_line(skolem_L8282))) & left_apart_point(skolem_B7979, reverse_line(skolem_M8383))) & left_apart_point(skolem_C8080, skolem_L8282))
% 4.84/1.20 -> [9] (((left_apart_point(skolem_A7878, skolem_L8282) & left_apart_point(skolem_A7878, skolem_M8383)) & left_apart_point(skolem_B7979, reverse_line(skolem_L8282))) & left_apart_point(skolem_B7979, reverse_line(skolem_M8383))), left_apart_point(skolem_C8080, skolem_L8282)
% 4.84/1.20
% 4.84/1.20 [9] ALPHA_AND : (((left_apart_point(skolem_A7878, skolem_L8282) & left_apart_point(skolem_A7878, skolem_M8383)) & left_apart_point(skolem_B7979, reverse_line(skolem_L8282))) & left_apart_point(skolem_B7979, reverse_line(skolem_M8383)))
% 4.84/1.20 -> [10] ((left_apart_point(skolem_A7878, skolem_L8282) & left_apart_point(skolem_A7878, skolem_M8383)) & left_apart_point(skolem_B7979, reverse_line(skolem_L8282))), left_apart_point(skolem_B7979, reverse_line(skolem_M8383))
% 4.84/1.20
% 4.84/1.20 [10] ALPHA_AND : ((left_apart_point(skolem_A7878, skolem_L8282) & left_apart_point(skolem_A7878, skolem_M8383)) & left_apart_point(skolem_B7979, reverse_line(skolem_L8282)))
% 4.84/1.20 -> [11] (left_apart_point(skolem_A7878, skolem_L8282) & left_apart_point(skolem_A7878, skolem_M8383)), left_apart_point(skolem_B7979, reverse_line(skolem_L8282))
% 4.84/1.20
% 4.84/1.20 [11] ALPHA_AND : (left_apart_point(skolem_A7878, skolem_L8282) & left_apart_point(skolem_A7878, skolem_M8383))
% 4.84/1.20 -> [12] left_apart_point(skolem_A7878, skolem_L8282), left_apart_point(skolem_A7878, skolem_M8383)
% 4.84/1.20
% 4.84/1.20 [12] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L8282, skolem_M8383) & unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)))
% 4.84/1.20 -> [13] ~unequally_directed_lines(skolem_L8282, skolem_M8383)
% 4.84/1.20 -> [14] ~unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383))
% 4.84/1.20
% 4.84/1.20 [13] GAMMA_FORALL : ! [A21_21] : (~distinct_points(A21_21, A21_21))
% 4.84/1.20 -> [15] ~distinct_points(A22_0_1, A22_0_1)
% 4.84/1.20
% 4.84/1.20 [15] 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))))
% 4.84/1.20 -> [17] (distinct_points(A22_0_1, A22_0_1) => (distinct_points(A22_0_1, A22_0_1) | distinct_points(A22_0_1, A22_0_1)))
% 4.84/1.20
% 4.84/1.20 [17] BETA_IMPLY : (distinct_points(A22_0_1, A22_0_1) => (distinct_points(A22_0_1, A22_0_1) | distinct_points(A22_0_1, A22_0_1)))
% 4.84/1.20 -> [19] ~distinct_points(A22_0_1, A22_0_1)
% 4.84/1.20 -> [20] (distinct_points(A22_0_1, A22_0_1) | distinct_points(A22_0_1, A22_0_1))
% 4.84/1.20
% 4.84/1.20 [20] BETA_OR : (distinct_points(A22_0_1, A22_0_1) | distinct_points(A22_0_1, A22_0_1))
% 4.84/1.20 -> [23] distinct_points(A22_0_1, A22_0_1)
% 4.84/1.20 -> [24] distinct_points(A22_0_1, A22_0_1)
% 4.84/1.20
% 4.84/1.20 [24] CLOSURE : distinct_points(A22_0_1, A22_0_1)
% 4.84/1.20
% 4.84/1.20 [23] CLOSURE : distinct_points(A22_0_1, A22_0_1)
% 4.84/1.20
% 4.84/1.20 [19] GAMMA_FORALL : ! [L25_25] : (~distinct_lines(L25_25, L25_25))
% 4.84/1.20 -> [27] ~distinct_lines(N28_0_3, N28_0_3)
% 4.84/1.20
% 4.84/1.20 [27] 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))))
% 4.84/1.20 -> [29] (distinct_lines(N28_0_3, N28_0_3) => (distinct_lines(N28_0_3, N28_0_3) | distinct_lines(N28_0_3, N28_0_3)))
% 4.84/1.20
% 4.84/1.20 [29] 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)))
% 4.84/1.20 -> [31] ~distinct_lines(N28_0_3, N28_0_3)
% 4.84/1.20 -> [32] (distinct_lines(N28_0_3, N28_0_3) | distinct_lines(N28_0_3, N28_0_3))
% 4.84/1.20
% 4.84/1.20 [32] BETA_OR : (distinct_lines(N28_0_3, N28_0_3) | distinct_lines(N28_0_3, N28_0_3))
% 4.84/1.20 -> [35] distinct_lines(N28_0_3, N28_0_3)
% 4.84/1.20 -> [36] distinct_lines(N28_0_3, N28_0_3)
% 4.84/1.20
% 4.84/1.20 [36] CLOSURE : distinct_lines(N28_0_3, N28_0_3)
% 4.84/1.20
% 4.84/1.20 [35] CLOSURE : distinct_lines(N28_0_3, N28_0_3)
% 4.84/1.20
% 4.84/1.20 [31] GAMMA_FORALL : ! [L29_29] : (~unequally_directed_lines(L29_29, L29_29))
% 4.84/1.20 -> [39] ~unequally_directed_lines(skolem_M8383, skolem_M8383)
% 4.84/1.20
% 4.84/1.20 [39] 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))))
% 4.84/1.20 -> [41] (unequally_directed_lines(skolem_L8282, skolem_M8383) => (unequally_directed_lines(skolem_L8282, skolem_M8383) | unequally_directed_lines(skolem_M8383, skolem_M8383)))
% 4.84/1.20
% 4.84/1.20 [41] BETA_IMPLY : (unequally_directed_lines(skolem_L8282, skolem_M8383) => (unequally_directed_lines(skolem_L8282, skolem_M8383) | unequally_directed_lines(skolem_M8383, skolem_M8383)))
% 4.84/1.20 -> [43] ~unequally_directed_lines(skolem_L8282, skolem_M8383)
% 4.84/1.20 -> [44] (unequally_directed_lines(skolem_L8282, skolem_M8383) | unequally_directed_lines(skolem_M8383, skolem_M8383))
% 4.84/1.20
% 4.84/1.20 [44] BETA_OR : (unequally_directed_lines(skolem_L8282, skolem_M8383) | unequally_directed_lines(skolem_M8383, skolem_M8383))
% 4.84/1.20 -> [49] unequally_directed_lines(skolem_L8282, skolem_M8383)
% 4.84/1.20 -> [50] unequally_directed_lines(skolem_M8383, skolem_M8383)
% 4.84/1.20
% 4.84/1.20 [49] CLOSURE : unequally_directed_lines(skolem_L8282, skolem_M8383)
% 4.84/1.20
% 4.84/1.20 [50] CLOSURE : unequally_directed_lines(skolem_M8383, skolem_M8383)
% 4.84/1.20
% 4.84/1.20 [51] BETA_IMPLY : ((unequally_directed_lines(skolem_L8282, skolem_M8383) & unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383))) => ((unequally_directed_lines(skolem_L8282, skolem_M8383) & unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383))) | (unequally_directed_lines(skolem_M8383, skolem_M8383) & unequally_directed_lines(skolem_M8383, reverse_line(skolem_M8383)))))
% 4.84/1.20 -> [502] ~(unequally_directed_lines(skolem_L8282, skolem_M8383) & unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)))
% 4.84/1.20 -> [503] ((unequally_directed_lines(skolem_L8282, skolem_M8383) & unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383))) | (unequally_directed_lines(skolem_M8383, skolem_M8383) & unequally_directed_lines(skolem_M8383, reverse_line(skolem_M8383))))
% 4.84/1.20
% 4.84/1.20 [502] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L8282, skolem_M8383) & unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)))
% 4.84/1.20 -> [508] ~unequally_directed_lines(skolem_L8282, skolem_M8383)
% 4.84/1.20 -> [509] ~unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383))
% 4.84/1.20
% 4.84/1.20 [509] 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)))))
% 4.84/1.20 -> [523] ((line(skolem_L8282) & line(skolem_M8383)) => (unequally_directed_lines(skolem_L8282, skolem_M8383) | unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383))))
% 4.84/1.20
% 4.84/1.20 [523] BETA_IMPLY : ((line(skolem_L8282) & line(skolem_M8383)) => (unequally_directed_lines(skolem_L8282, skolem_M8383) | unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383))))
% 4.84/1.20 -> [531] ~(line(skolem_L8282) & line(skolem_M8383))
% 4.84/1.20 -> [532] (unequally_directed_lines(skolem_L8282, skolem_M8383) | unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)))
% 4.84/1.20
% 4.84/1.20 [531] BETA_NOT_AND : ~(line(skolem_L8282) & line(skolem_M8383))
% 4.84/1.20 -> [537] ~line(skolem_L8282)
% 4.84/1.20 -> [538] ~line(skolem_M8383)
% 4.84/1.20
% 4.84/1.20 [537] 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)))))
% 4.84/1.20 -> [552] ((unequally_directed_lines(L38_27_8, M39_27_8) & unequally_directed_lines(L38_27_8, reverse_line(M39_27_8))) => (left_convergent_lines(L38_27_8, M39_27_8) | left_convergent_lines(L38_27_8, reverse_line(M39_27_8))))
% 4.84/1.20
% 4.84/1.20 [552] BETA_IMPLY : ((unequally_directed_lines(L38_27_8, M39_27_8) & unequally_directed_lines(L38_27_8, reverse_line(M39_27_8))) => (left_convergent_lines(L38_27_8, M39_27_8) | left_convergent_lines(L38_27_8, reverse_line(M39_27_8))))
% 4.84/1.20 -> [558] ~(unequally_directed_lines(L38_27_8, M39_27_8) & unequally_directed_lines(L38_27_8, reverse_line(M39_27_8)))
% 4.84/1.20 -> [559] (left_convergent_lines(L38_27_8, M39_27_8) | left_convergent_lines(L38_27_8, reverse_line(M39_27_8)))
% 4.84/1.20
% 4.84/1.20 [558] BETA_NOT_AND : ~(unequally_directed_lines(L38_27_8, M39_27_8) & unequally_directed_lines(L38_27_8, reverse_line(M39_27_8)))
% 4.84/1.20 -> [566] ~unequally_directed_lines(L38_27_8, M39_27_8)
% 4.84/1.20 -> [567] ~unequally_directed_lines(L38_27_8, reverse_line(M39_27_8))
% 4.84/1.20
% 4.84/1.20 [566] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [588] ~(left_apart_point(A40_97_9, L41_97_9) | left_apart_point(A40_97_9, reverse_line(L41_97_9)))
% 4.84/1.20
% 4.84/1.20 [588] ALPHA_NOT_OR : ~(left_apart_point(A40_97_9, L41_97_9) | left_apart_point(A40_97_9, reverse_line(L41_97_9)))
% 4.84/1.20 -> [591] ~left_apart_point(A40_97_9, L41_97_9), ~left_apart_point(A40_97_9, reverse_line(L41_97_9))
% 4.84/1.20
% 4.84/1.20 [591] CLOSURE : ~left_apart_point(A40_97_9, L41_97_9)
% 4.84/1.20
% 4.84/1.20 [567] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [616] ~(left_apart_point(A40_105_9, L41_105_9) | left_apart_point(A40_105_9, reverse_line(L41_105_9)))
% 4.84/1.20
% 4.84/1.20 [616] ALPHA_NOT_OR : ~(left_apart_point(A40_105_9, L41_105_9) | left_apart_point(A40_105_9, reverse_line(L41_105_9)))
% 4.84/1.20 -> [617] ~left_apart_point(A40_105_9, L41_105_9), ~left_apart_point(A40_105_9, reverse_line(L41_105_9))
% 4.84/1.20
% 4.84/1.20 [617] CLOSURE : ~left_apart_point(A40_105_9, L41_105_9)
% 4.84/1.20
% 4.84/1.20 [559] BETA_OR : (left_convergent_lines(L38_27_8, M39_27_8) | left_convergent_lines(L38_27_8, reverse_line(M39_27_8)))
% 4.84/1.20 -> [585] left_convergent_lines(L38_27_8, M39_27_8)
% 4.84/1.20 -> [586] left_convergent_lines(L38_27_8, reverse_line(M39_27_8))
% 4.84/1.20
% 4.84/1.20 [585] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [618] ~(left_apart_point(A40_106_9, L41_106_9) | left_apart_point(A40_106_9, reverse_line(L41_106_9)))
% 4.84/1.20
% 4.84/1.20 [618] ALPHA_NOT_OR : ~(left_apart_point(A40_106_9, L41_106_9) | left_apart_point(A40_106_9, reverse_line(L41_106_9)))
% 4.84/1.20 -> [620] ~left_apart_point(A40_106_9, L41_106_9), ~left_apart_point(A40_106_9, reverse_line(L41_106_9))
% 4.84/1.20
% 4.84/1.20 [620] CLOSURE : ~left_apart_point(A40_106_9, L41_106_9)
% 4.84/1.20
% 4.84/1.20 [586] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [598] ~(left_apart_point(A40_99_9, L41_99_9) | left_apart_point(A40_99_9, reverse_line(L41_99_9)))
% 4.84/1.20
% 4.84/1.20 [598] ALPHA_NOT_OR : ~(left_apart_point(A40_99_9, L41_99_9) | left_apart_point(A40_99_9, reverse_line(L41_99_9)))
% 4.84/1.20 -> [601] ~left_apart_point(A40_99_9, L41_99_9), ~left_apart_point(A40_99_9, reverse_line(L41_99_9))
% 4.84/1.20
% 4.84/1.20 [601] CLOSURE : ~left_apart_point(A40_99_9, L41_99_9)
% 4.84/1.20
% 4.84/1.20 [538] 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)))))
% 4.84/1.20 -> [577] ((unequally_directed_lines(L38_30_8, M39_30_8) & unequally_directed_lines(L38_30_8, reverse_line(M39_30_8))) => (left_convergent_lines(L38_30_8, M39_30_8) | left_convergent_lines(L38_30_8, reverse_line(M39_30_8))))
% 4.84/1.20
% 4.84/1.20 [577] BETA_IMPLY : ((unequally_directed_lines(L38_30_8, M39_30_8) & unequally_directed_lines(L38_30_8, reverse_line(M39_30_8))) => (left_convergent_lines(L38_30_8, M39_30_8) | left_convergent_lines(L38_30_8, reverse_line(M39_30_8))))
% 4.84/1.20 -> [596] ~(unequally_directed_lines(L38_30_8, M39_30_8) & unequally_directed_lines(L38_30_8, reverse_line(M39_30_8)))
% 4.84/1.20 -> [597] (left_convergent_lines(L38_30_8, M39_30_8) | left_convergent_lines(L38_30_8, reverse_line(M39_30_8)))
% 4.84/1.20
% 4.84/1.20 [597] BETA_OR : (left_convergent_lines(L38_30_8, M39_30_8) | left_convergent_lines(L38_30_8, reverse_line(M39_30_8)))
% 4.84/1.20 -> [602] left_convergent_lines(L38_30_8, M39_30_8)
% 4.84/1.20 -> [603] left_convergent_lines(L38_30_8, reverse_line(M39_30_8))
% 4.84/1.20
% 4.84/1.20 [603] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [621] ~(left_apart_point(A40_108_9, L41_108_9) | left_apart_point(A40_108_9, reverse_line(L41_108_9)))
% 4.84/1.20
% 4.84/1.20 [621] ALPHA_NOT_OR : ~(left_apart_point(A40_108_9, L41_108_9) | left_apart_point(A40_108_9, reverse_line(L41_108_9)))
% 4.84/1.20 -> [626] ~left_apart_point(A40_108_9, L41_108_9), ~left_apart_point(A40_108_9, reverse_line(L41_108_9))
% 4.84/1.20
% 4.84/1.20 [626] CLOSURE : ~left_apart_point(A40_108_9, L41_108_9)
% 4.84/1.20
% 4.84/1.20 [602] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [636] ~(left_apart_point(A40_114_9, L41_114_9) | left_apart_point(A40_114_9, reverse_line(L41_114_9)))
% 4.84/1.20
% 4.84/1.20 [636] ALPHA_NOT_OR : ~(left_apart_point(A40_114_9, L41_114_9) | left_apart_point(A40_114_9, reverse_line(L41_114_9)))
% 4.84/1.20 -> [638] ~left_apart_point(A40_114_9, L41_114_9), ~left_apart_point(A40_114_9, reverse_line(L41_114_9))
% 4.84/1.20
% 4.84/1.20 [638] CLOSURE : ~left_apart_point(A40_114_9, L41_114_9)
% 4.84/1.20
% 4.84/1.20 [596] BETA_NOT_AND : ~(unequally_directed_lines(L38_30_8, M39_30_8) & unequally_directed_lines(L38_30_8, reverse_line(M39_30_8)))
% 4.84/1.20 -> [599] ~unequally_directed_lines(L38_30_8, M39_30_8)
% 4.84/1.20 -> [600] ~unequally_directed_lines(L38_30_8, reverse_line(M39_30_8))
% 4.84/1.20
% 4.84/1.20 [599] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [627] ~(left_apart_point(A40_110_9, L41_110_9) | left_apart_point(A40_110_9, reverse_line(L41_110_9)))
% 4.84/1.20
% 4.84/1.20 [627] ALPHA_NOT_OR : ~(left_apart_point(A40_110_9, L41_110_9) | left_apart_point(A40_110_9, reverse_line(L41_110_9)))
% 4.84/1.20 -> [630] ~left_apart_point(A40_110_9, L41_110_9), ~left_apart_point(A40_110_9, reverse_line(L41_110_9))
% 4.84/1.20
% 4.84/1.20 [630] CLOSURE : ~left_apart_point(A40_110_9, L41_110_9)
% 4.84/1.20
% 4.84/1.20 [600] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [641] ~(left_apart_point(A40_117_9, L41_117_9) | left_apart_point(A40_117_9, reverse_line(L41_117_9)))
% 4.84/1.20
% 4.84/1.20 [641] ALPHA_NOT_OR : ~(left_apart_point(A40_117_9, L41_117_9) | left_apart_point(A40_117_9, reverse_line(L41_117_9)))
% 4.84/1.20 -> [643] ~left_apart_point(A40_117_9, L41_117_9), ~left_apart_point(A40_117_9, reverse_line(L41_117_9))
% 4.84/1.20
% 4.84/1.20 [643] CLOSURE : ~left_apart_point(A40_117_9, L41_117_9)
% 4.84/1.20
% 4.84/1.20 [532] BETA_OR : (unequally_directed_lines(skolem_L8282, skolem_M8383) | unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)))
% 4.84/1.20 -> [539] unequally_directed_lines(skolem_L8282, skolem_M8383)
% 4.84/1.20 -> [540] unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383))
% 4.84/1.20
% 4.84/1.20 [539] CLOSURE : unequally_directed_lines(skolem_L8282, skolem_M8383)
% 4.84/1.20
% 4.84/1.20 [540] CLOSURE : unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383))
% 4.84/1.20
% 4.84/1.20 [522] BETA_IMPLY : ((line(skolem_L8282) & line(skolem_M8383)) => (unequally_directed_lines(skolem_L8282, skolem_M8383) | unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383))))
% 4.84/1.20 -> [660] ~(line(skolem_L8282) & line(skolem_M8383))
% 4.84/1.20 -> [661] (unequally_directed_lines(skolem_L8282, skolem_M8383) | unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)))
% 4.84/1.20
% 4.84/1.20 [660] BETA_NOT_AND : ~(line(skolem_L8282) & line(skolem_M8383))
% 4.84/1.20 -> [662] ~line(skolem_L8282)
% 4.84/1.20 -> [663] ~line(skolem_M8383)
% 4.84/1.20
% 4.84/1.20 [662] 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)))))
% 4.84/1.20 -> [673] ((unequally_directed_lines(L38_34_8, M39_34_8) & unequally_directed_lines(L38_34_8, reverse_line(M39_34_8))) => (left_convergent_lines(L38_34_8, M39_34_8) | left_convergent_lines(L38_34_8, reverse_line(M39_34_8))))
% 4.84/1.20
% 4.84/1.20 [673] BETA_IMPLY : ((unequally_directed_lines(L38_34_8, M39_34_8) & unequally_directed_lines(L38_34_8, reverse_line(M39_34_8))) => (left_convergent_lines(L38_34_8, M39_34_8) | left_convergent_lines(L38_34_8, reverse_line(M39_34_8))))
% 4.84/1.20 -> [687] ~(unequally_directed_lines(L38_34_8, M39_34_8) & unequally_directed_lines(L38_34_8, reverse_line(M39_34_8)))
% 4.84/1.20 -> [688] (left_convergent_lines(L38_34_8, M39_34_8) | left_convergent_lines(L38_34_8, reverse_line(M39_34_8)))
% 4.84/1.20
% 4.84/1.20 [687] BETA_NOT_AND : ~(unequally_directed_lines(L38_34_8, M39_34_8) & unequally_directed_lines(L38_34_8, reverse_line(M39_34_8)))
% 4.84/1.20 -> [701] ~unequally_directed_lines(L38_34_8, M39_34_8)
% 4.84/1.20 -> [702] ~unequally_directed_lines(L38_34_8, reverse_line(M39_34_8))
% 4.84/1.20
% 4.84/1.20 [701] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [719] ~(left_apart_point(A40_131_9, L41_131_9) | left_apart_point(A40_131_9, reverse_line(L41_131_9)))
% 4.84/1.20
% 4.84/1.20 [719] ALPHA_NOT_OR : ~(left_apart_point(A40_131_9, L41_131_9) | left_apart_point(A40_131_9, reverse_line(L41_131_9)))
% 4.84/1.20 -> [723] ~left_apart_point(A40_131_9, L41_131_9), ~left_apart_point(A40_131_9, reverse_line(L41_131_9))
% 4.84/1.20
% 4.84/1.20 [723] CLOSURE : ~left_apart_point(A40_131_9, L41_131_9)
% 4.84/1.20
% 4.84/1.20 [702] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [724] ~(left_apart_point(A40_132_9, L41_132_9) | left_apart_point(A40_132_9, reverse_line(L41_132_9)))
% 4.84/1.20
% 4.84/1.20 [724] ALPHA_NOT_OR : ~(left_apart_point(A40_132_9, L41_132_9) | left_apart_point(A40_132_9, reverse_line(L41_132_9)))
% 4.84/1.20 -> [725] ~left_apart_point(A40_132_9, L41_132_9), ~left_apart_point(A40_132_9, reverse_line(L41_132_9))
% 4.84/1.20
% 4.84/1.20 [725] CLOSURE : ~left_apart_point(A40_132_9, L41_132_9)
% 4.84/1.20
% 4.84/1.20 [688] BETA_OR : (left_convergent_lines(L38_34_8, M39_34_8) | left_convergent_lines(L38_34_8, reverse_line(M39_34_8)))
% 4.84/1.20 -> [696] left_convergent_lines(L38_34_8, M39_34_8)
% 4.84/1.20 -> [697] left_convergent_lines(L38_34_8, reverse_line(M39_34_8))
% 4.84/1.20
% 4.84/1.20 [696] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [736] ~(left_apart_point(A40_138_9, L41_138_9) | left_apart_point(A40_138_9, reverse_line(L41_138_9)))
% 4.84/1.20
% 4.84/1.20 [736] ALPHA_NOT_OR : ~(left_apart_point(A40_138_9, L41_138_9) | left_apart_point(A40_138_9, reverse_line(L41_138_9)))
% 4.84/1.20 -> [739] ~left_apart_point(A40_138_9, L41_138_9), ~left_apart_point(A40_138_9, reverse_line(L41_138_9))
% 4.84/1.20
% 4.84/1.20 [739] CLOSURE : ~left_apart_point(A40_138_9, L41_138_9)
% 4.84/1.20
% 4.84/1.20 [697] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [732] ~(left_apart_point(A40_135_9, L41_135_9) | left_apart_point(A40_135_9, reverse_line(L41_135_9)))
% 4.84/1.20
% 4.84/1.20 [732] ALPHA_NOT_OR : ~(left_apart_point(A40_135_9, L41_135_9) | left_apart_point(A40_135_9, reverse_line(L41_135_9)))
% 4.84/1.20 -> [741] ~left_apart_point(A40_135_9, L41_135_9), ~left_apart_point(A40_135_9, reverse_line(L41_135_9))
% 4.84/1.20
% 4.84/1.20 [741] CLOSURE : ~left_apart_point(A40_135_9, L41_135_9)
% 4.84/1.20
% 4.84/1.20 [663] 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)))))
% 4.84/1.20 -> [672] ((unequally_directed_lines(L38_33_8, M39_33_8) & unequally_directed_lines(L38_33_8, reverse_line(M39_33_8))) => (left_convergent_lines(L38_33_8, M39_33_8) | left_convergent_lines(L38_33_8, reverse_line(M39_33_8))))
% 4.84/1.20
% 4.84/1.20 [672] BETA_IMPLY : ((unequally_directed_lines(L38_33_8, M39_33_8) & unequally_directed_lines(L38_33_8, reverse_line(M39_33_8))) => (left_convergent_lines(L38_33_8, M39_33_8) | left_convergent_lines(L38_33_8, reverse_line(M39_33_8))))
% 4.84/1.20 -> [676] ~(unequally_directed_lines(L38_33_8, M39_33_8) & unequally_directed_lines(L38_33_8, reverse_line(M39_33_8)))
% 4.84/1.20 -> [677] (left_convergent_lines(L38_33_8, M39_33_8) | left_convergent_lines(L38_33_8, reverse_line(M39_33_8)))
% 4.84/1.20
% 4.84/1.20 [676] BETA_NOT_AND : ~(unequally_directed_lines(L38_33_8, M39_33_8) & unequally_directed_lines(L38_33_8, reverse_line(M39_33_8)))
% 4.84/1.20 -> [698] ~unequally_directed_lines(L38_33_8, M39_33_8)
% 4.84/1.20 -> [699] ~unequally_directed_lines(L38_33_8, reverse_line(M39_33_8))
% 4.84/1.20
% 4.84/1.20 [698] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [716] ~(left_apart_point(A40_130_9, L41_130_9) | left_apart_point(A40_130_9, reverse_line(L41_130_9)))
% 4.84/1.20
% 4.84/1.20 [716] ALPHA_NOT_OR : ~(left_apart_point(A40_130_9, L41_130_9) | left_apart_point(A40_130_9, reverse_line(L41_130_9)))
% 4.84/1.20 -> [722] ~left_apart_point(A40_130_9, L41_130_9), ~left_apart_point(A40_130_9, reverse_line(L41_130_9))
% 4.84/1.20
% 4.84/1.20 [722] CLOSURE : ~left_apart_point(A40_130_9, L41_130_9)
% 4.84/1.20
% 4.84/1.20 [699] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [729] ~(left_apart_point(A40_134_9, L41_134_9) | left_apart_point(A40_134_9, reverse_line(L41_134_9)))
% 4.84/1.20
% 4.84/1.20 [729] ALPHA_NOT_OR : ~(left_apart_point(A40_134_9, L41_134_9) | left_apart_point(A40_134_9, reverse_line(L41_134_9)))
% 4.84/1.20 -> [731] ~left_apart_point(A40_134_9, L41_134_9), ~left_apart_point(A40_134_9, reverse_line(L41_134_9))
% 4.84/1.20
% 4.84/1.20 [731] CLOSURE : ~left_apart_point(A40_134_9, L41_134_9)
% 4.84/1.20
% 4.84/1.20 [677] BETA_OR : (left_convergent_lines(L38_33_8, M39_33_8) | left_convergent_lines(L38_33_8, reverse_line(M39_33_8)))
% 4.84/1.20 -> [689] left_convergent_lines(L38_33_8, M39_33_8)
% 4.84/1.20 -> [690] left_convergent_lines(L38_33_8, reverse_line(M39_33_8))
% 4.84/1.20
% 4.84/1.20 [689] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [714] ~(left_apart_point(A40_129_9, L41_129_9) | left_apart_point(A40_129_9, reverse_line(L41_129_9)))
% 4.84/1.20
% 4.84/1.20 [714] ALPHA_NOT_OR : ~(left_apart_point(A40_129_9, L41_129_9) | left_apart_point(A40_129_9, reverse_line(L41_129_9)))
% 4.84/1.20 -> [721] ~left_apart_point(A40_129_9, L41_129_9), ~left_apart_point(A40_129_9, reverse_line(L41_129_9))
% 4.84/1.20
% 4.84/1.20 [721] CLOSURE : ~left_apart_point(A40_129_9, L41_129_9)
% 4.84/1.20
% 4.84/1.20 [690] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [744] ~(left_apart_point(A40_141_9, L41_141_9) | left_apart_point(A40_141_9, reverse_line(L41_141_9)))
% 4.84/1.20
% 4.84/1.20 [744] ALPHA_NOT_OR : ~(left_apart_point(A40_141_9, L41_141_9) | left_apart_point(A40_141_9, reverse_line(L41_141_9)))
% 4.84/1.20 -> [745] ~left_apart_point(A40_141_9, L41_141_9), ~left_apart_point(A40_141_9, reverse_line(L41_141_9))
% 4.84/1.20
% 4.84/1.20 [745] CLOSURE : ~left_apart_point(A40_141_9, L41_141_9)
% 4.84/1.20
% 4.84/1.20 [661] BETA_OR : (unequally_directed_lines(skolem_L8282, skolem_M8383) | unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)))
% 4.84/1.20 -> [664] unequally_directed_lines(skolem_L8282, skolem_M8383)
% 4.84/1.20 -> [665] unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383))
% 4.84/1.20
% 4.84/1.20 [664] CLOSURE : unequally_directed_lines(skolem_L8282, skolem_M8383)
% 4.84/1.20
% 4.84/1.20 [665] 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)))))
% 4.84/1.20 -> [680] ((unequally_directed_lines(L38_35_8, reverse_line(skolem_M8383)) & unequally_directed_lines(L38_35_8, reverse_line(reverse_line(skolem_M8383)))) => (left_convergent_lines(L38_35_8, reverse_line(skolem_M8383)) | left_convergent_lines(L38_35_8, reverse_line(reverse_line(skolem_M8383)))))
% 4.84/1.20
% 4.84/1.20 [680] BETA_IMPLY : ((unequally_directed_lines(L38_35_8, reverse_line(skolem_M8383)) & unequally_directed_lines(L38_35_8, reverse_line(reverse_line(skolem_M8383)))) => (left_convergent_lines(L38_35_8, reverse_line(skolem_M8383)) | left_convergent_lines(L38_35_8, reverse_line(reverse_line(skolem_M8383)))))
% 4.84/1.20 -> [685] ~(unequally_directed_lines(L38_35_8, reverse_line(skolem_M8383)) & unequally_directed_lines(L38_35_8, reverse_line(reverse_line(skolem_M8383))))
% 4.84/1.20 -> [686] (left_convergent_lines(L38_35_8, reverse_line(skolem_M8383)) | left_convergent_lines(L38_35_8, reverse_line(reverse_line(skolem_M8383))))
% 4.84/1.20
% 4.84/1.20 [686] BETA_OR : (left_convergent_lines(L38_35_8, reverse_line(skolem_M8383)) | left_convergent_lines(L38_35_8, reverse_line(reverse_line(skolem_M8383))))
% 4.84/1.20 -> [692] left_convergent_lines(L38_35_8, reverse_line(skolem_M8383))
% 4.84/1.20 -> [693] left_convergent_lines(L38_35_8, reverse_line(reverse_line(skolem_M8383)))
% 4.84/1.20
% 4.84/1.20 [693] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [728] ~(left_apart_point(A40_133_9, L41_133_9) | left_apart_point(A40_133_9, reverse_line(L41_133_9)))
% 4.84/1.20
% 4.84/1.20 [728] ALPHA_NOT_OR : ~(left_apart_point(A40_133_9, L41_133_9) | left_apart_point(A40_133_9, reverse_line(L41_133_9)))
% 4.84/1.20 -> [730] ~left_apart_point(A40_133_9, L41_133_9), ~left_apart_point(A40_133_9, reverse_line(L41_133_9))
% 4.84/1.20
% 4.84/1.20 [730] CLOSURE : ~left_apart_point(A40_133_9, L41_133_9)
% 4.84/1.20
% 4.84/1.20 [692] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [737] ~(left_apart_point(A40_139_9, L41_139_9) | left_apart_point(A40_139_9, reverse_line(L41_139_9)))
% 4.84/1.20
% 4.84/1.20 [737] ALPHA_NOT_OR : ~(left_apart_point(A40_139_9, L41_139_9) | left_apart_point(A40_139_9, reverse_line(L41_139_9)))
% 4.84/1.20 -> [740] ~left_apart_point(A40_139_9, L41_139_9), ~left_apart_point(A40_139_9, reverse_line(L41_139_9))
% 4.84/1.20
% 4.84/1.20 [740] CLOSURE : ~left_apart_point(A40_139_9, L41_139_9)
% 4.84/1.20
% 4.84/1.20 [685] BETA_NOT_AND : ~(unequally_directed_lines(L38_35_8, reverse_line(skolem_M8383)) & unequally_directed_lines(L38_35_8, reverse_line(reverse_line(skolem_M8383))))
% 4.84/1.20 -> [703] ~unequally_directed_lines(L38_35_8, reverse_line(skolem_M8383))
% 4.84/1.20 -> [704] ~unequally_directed_lines(L38_35_8, reverse_line(reverse_line(skolem_M8383)))
% 4.84/1.20
% 4.84/1.20 [703] CLOSURE : ~unequally_directed_lines(L38_35_8, reverse_line(skolem_M8383))
% 4.84/1.20
% 4.84/1.20 [704] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [748] ~(left_apart_point(A40_143_9, L41_143_9) | left_apart_point(A40_143_9, reverse_line(L41_143_9)))
% 4.84/1.20
% 4.84/1.20 [748] ALPHA_NOT_OR : ~(left_apart_point(A40_143_9, L41_143_9) | left_apart_point(A40_143_9, reverse_line(L41_143_9)))
% 4.84/1.20 -> [750] ~left_apart_point(A40_143_9, L41_143_9), ~left_apart_point(A40_143_9, reverse_line(L41_143_9))
% 4.84/1.20
% 4.84/1.20 [750] CLOSURE : ~left_apart_point(A40_143_9, L41_143_9)
% 4.84/1.20
% 4.84/1.20 [503] BETA_OR : ((unequally_directed_lines(skolem_L8282, skolem_M8383) & unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383))) | (unequally_directed_lines(skolem_M8383, skolem_M8383) & unequally_directed_lines(skolem_M8383, reverse_line(skolem_M8383))))
% 4.84/1.20 -> [752] (unequally_directed_lines(skolem_L8282, skolem_M8383) & unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)))
% 4.84/1.20 -> [753] (unequally_directed_lines(skolem_M8383, skolem_M8383) & unequally_directed_lines(skolem_M8383, reverse_line(skolem_M8383)))
% 4.84/1.20
% 4.84/1.20 [753] ALPHA_AND : (unequally_directed_lines(skolem_M8383, skolem_M8383) & unequally_directed_lines(skolem_M8383, reverse_line(skolem_M8383)))
% 4.84/1.20 -> [755] unequally_directed_lines(skolem_M8383, skolem_M8383), unequally_directed_lines(skolem_M8383, reverse_line(skolem_M8383))
% 4.84/1.20
% 4.84/1.20 [755] CLOSURE : unequally_directed_lines(skolem_M8383, skolem_M8383)
% 4.84/1.20
% 4.84/1.20 [752] ALPHA_AND : (unequally_directed_lines(skolem_L8282, skolem_M8383) & unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)))
% 4.84/1.20 -> [754] unequally_directed_lines(skolem_L8282, skolem_M8383), unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383))
% 4.84/1.20
% 4.84/1.20 [754] CLOSURE : unequally_directed_lines(skolem_L8282, skolem_M8383)
% 4.84/1.20
% 4.84/1.20 [14] GAMMA_FORALL : ! [A21_21] : (~distinct_points(A21_21, A21_21))
% 4.84/1.20 -> [16] ~distinct_points(C24_1_1, C24_1_1)
% 4.84/1.20
% 4.84/1.20 [16] 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))))
% 4.84/1.20 -> [18] (distinct_points(C24_1_1, C24_1_1) => (distinct_points(C24_1_1, C24_1_1) | distinct_points(C24_1_1, C24_1_1)))
% 4.84/1.20
% 4.84/1.20 [18] BETA_IMPLY : (distinct_points(C24_1_1, C24_1_1) => (distinct_points(C24_1_1, C24_1_1) | distinct_points(C24_1_1, C24_1_1)))
% 4.84/1.20 -> [21] ~distinct_points(C24_1_1, C24_1_1)
% 4.84/1.20 -> [22] (distinct_points(C24_1_1, C24_1_1) | distinct_points(C24_1_1, C24_1_1))
% 4.84/1.20
% 4.84/1.20 [22] BETA_OR : (distinct_points(C24_1_1, C24_1_1) | distinct_points(C24_1_1, C24_1_1))
% 4.84/1.20 -> [25] distinct_points(C24_1_1, C24_1_1)
% 4.84/1.20 -> [26] distinct_points(C24_1_1, C24_1_1)
% 4.84/1.20
% 4.84/1.20 [26] CLOSURE : distinct_points(C24_1_1, C24_1_1)
% 4.84/1.20
% 4.84/1.20 [25] CLOSURE : distinct_points(C24_1_1, C24_1_1)
% 4.84/1.20
% 4.84/1.20 [21] GAMMA_FORALL : ! [L25_25] : (~distinct_lines(L25_25, L25_25))
% 4.84/1.20 -> [28] ~distinct_lines(N28_1_3, N28_1_3)
% 4.84/1.20
% 4.84/1.20 [28] 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))))
% 4.84/1.20 -> [30] (distinct_lines(N28_1_3, N28_1_3) => (distinct_lines(N28_1_3, N28_1_3) | distinct_lines(N28_1_3, N28_1_3)))
% 4.84/1.20
% 4.84/1.20 [30] BETA_IMPLY : (distinct_lines(N28_1_3, N28_1_3) => (distinct_lines(N28_1_3, N28_1_3) | distinct_lines(N28_1_3, N28_1_3)))
% 4.84/1.20 -> [33] ~distinct_lines(N28_1_3, N28_1_3)
% 4.84/1.20 -> [34] (distinct_lines(N28_1_3, N28_1_3) | distinct_lines(N28_1_3, N28_1_3))
% 4.84/1.20
% 4.84/1.20 [34] BETA_OR : (distinct_lines(N28_1_3, N28_1_3) | distinct_lines(N28_1_3, N28_1_3))
% 4.84/1.20 -> [37] distinct_lines(N28_1_3, N28_1_3)
% 4.84/1.20 -> [38] distinct_lines(N28_1_3, N28_1_3)
% 4.84/1.20
% 4.84/1.20 [38] CLOSURE : distinct_lines(N28_1_3, N28_1_3)
% 4.84/1.20
% 4.84/1.20 [37] CLOSURE : distinct_lines(N28_1_3, N28_1_3)
% 4.84/1.20
% 4.84/1.20 [33] GAMMA_FORALL : ! [L29_29] : (~unequally_directed_lines(L29_29, L29_29))
% 4.84/1.20 -> [40] ~unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(reverse_line(M39_36_8)))
% 4.84/1.20
% 4.84/1.20 [40] 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))))
% 4.84/1.20 -> [42] (unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(reverse_line(M39_36_8))) => (unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(reverse_line(M39_36_8))) | unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(reverse_line(M39_36_8)))))
% 4.84/1.20
% 4.84/1.20 [42] BETA_IMPLY : (unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(reverse_line(M39_36_8))) => (unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(reverse_line(M39_36_8))) | unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(reverse_line(M39_36_8)))))
% 4.84/1.20 -> [45] ~unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(reverse_line(M39_36_8)))
% 4.84/1.20 -> [46] (unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(reverse_line(M39_36_8))) | unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(reverse_line(M39_36_8))))
% 4.84/1.20
% 4.84/1.20 [46] BETA_OR : (unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(reverse_line(M39_36_8))) | unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(reverse_line(M39_36_8))))
% 4.84/1.20 -> [47] unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(reverse_line(M39_36_8)))
% 4.84/1.20 -> [48] unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(reverse_line(M39_36_8)))
% 4.84/1.20
% 4.84/1.20 [48] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(reverse_line(M39_36_8)))
% 4.84/1.20
% 4.84/1.20 [47] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(reverse_line(M39_36_8)))
% 4.84/1.20
% 4.84/1.20 [52] BETA_IMPLY : ((unequally_directed_lines(skolem_L8282, skolem_M8383) & unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383))) => ((unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)) & unequally_directed_lines(skolem_L8282, reverse_line(reverse_line(skolem_M8383)))) | (unequally_directed_lines(skolem_M8383, reverse_line(skolem_M8383)) & unequally_directed_lines(skolem_M8383, reverse_line(reverse_line(skolem_M8383))))))
% 4.84/1.20 -> [490] ~(unequally_directed_lines(skolem_L8282, skolem_M8383) & unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)))
% 4.84/1.20 -> [491] ((unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)) & unequally_directed_lines(skolem_L8282, reverse_line(reverse_line(skolem_M8383)))) | (unequally_directed_lines(skolem_M8383, reverse_line(skolem_M8383)) & unequally_directed_lines(skolem_M8383, reverse_line(reverse_line(skolem_M8383)))))
% 4.84/1.20
% 4.84/1.20 [490] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L8282, skolem_M8383) & unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)))
% 4.84/1.20 -> [492] ~unequally_directed_lines(skolem_L8282, skolem_M8383)
% 4.84/1.20 -> [493] ~unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383))
% 4.84/1.20
% 4.84/1.20 [492] 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)))))
% 4.84/1.20 -> [498] ((line(skolem_L8282) & line(skolem_M8383)) => (unequally_directed_lines(skolem_L8282, skolem_M8383) | unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383))))
% 4.84/1.20
% 4.84/1.20 [498] BETA_IMPLY : ((line(skolem_L8282) & line(skolem_M8383)) => (unequally_directed_lines(skolem_L8282, skolem_M8383) | unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383))))
% 4.84/1.20 -> [500] ~(line(skolem_L8282) & line(skolem_M8383))
% 4.84/1.20 -> [501] (unequally_directed_lines(skolem_L8282, skolem_M8383) | unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)))
% 4.84/1.20
% 4.84/1.20 [501] BETA_OR : (unequally_directed_lines(skolem_L8282, skolem_M8383) | unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)))
% 4.84/1.20 -> [512] unequally_directed_lines(skolem_L8282, skolem_M8383)
% 4.84/1.20 -> [513] unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383))
% 4.84/1.20
% 4.84/1.20 [513] CLOSURE : unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383))
% 4.84/1.20
% 4.84/1.20 [512] CLOSURE : unequally_directed_lines(skolem_L8282, skolem_M8383)
% 4.84/1.20
% 4.84/1.20 [500] BETA_NOT_AND : ~(line(skolem_L8282) & line(skolem_M8383))
% 4.84/1.20 -> [506] ~line(skolem_L8282)
% 4.84/1.20 -> [507] ~line(skolem_M8383)
% 4.84/1.20
% 4.84/1.20 [506] 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)))))
% 4.84/1.20 -> [519] ((unequally_directed_lines(L38_23_8, M39_23_8) & unequally_directed_lines(L38_23_8, reverse_line(M39_23_8))) => (left_convergent_lines(L38_23_8, M39_23_8) | left_convergent_lines(L38_23_8, reverse_line(M39_23_8))))
% 4.84/1.20
% 4.84/1.20 [519] BETA_IMPLY : ((unequally_directed_lines(L38_23_8, M39_23_8) & unequally_directed_lines(L38_23_8, reverse_line(M39_23_8))) => (left_convergent_lines(L38_23_8, M39_23_8) | left_convergent_lines(L38_23_8, reverse_line(M39_23_8))))
% 4.84/1.20 -> [524] ~(unequally_directed_lines(L38_23_8, M39_23_8) & unequally_directed_lines(L38_23_8, reverse_line(M39_23_8)))
% 4.84/1.20 -> [525] (left_convergent_lines(L38_23_8, M39_23_8) | left_convergent_lines(L38_23_8, reverse_line(M39_23_8)))
% 4.84/1.20
% 4.84/1.20 [524] BETA_NOT_AND : ~(unequally_directed_lines(L38_23_8, M39_23_8) & unequally_directed_lines(L38_23_8, reverse_line(M39_23_8)))
% 4.84/1.20 -> [548] ~unequally_directed_lines(L38_23_8, M39_23_8)
% 4.84/1.20 -> [549] ~unequally_directed_lines(L38_23_8, reverse_line(M39_23_8))
% 4.84/1.20
% 4.84/1.20 [549] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [578] ~(left_apart_point(A40_95_9, L41_95_9) | left_apart_point(A40_95_9, reverse_line(L41_95_9)))
% 4.84/1.20
% 4.84/1.20 [578] ALPHA_NOT_OR : ~(left_apart_point(A40_95_9, L41_95_9) | left_apart_point(A40_95_9, reverse_line(L41_95_9)))
% 4.84/1.20 -> [584] ~left_apart_point(A40_95_9, L41_95_9), ~left_apart_point(A40_95_9, reverse_line(L41_95_9))
% 4.84/1.20
% 4.84/1.20 [584] CLOSURE : ~left_apart_point(A40_95_9, L41_95_9)
% 4.84/1.20
% 4.84/1.20 [548] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [613] ~(left_apart_point(A40_104_9, L41_104_9) | left_apart_point(A40_104_9, reverse_line(L41_104_9)))
% 4.84/1.20
% 4.84/1.20 [613] ALPHA_NOT_OR : ~(left_apart_point(A40_104_9, L41_104_9) | left_apart_point(A40_104_9, reverse_line(L41_104_9)))
% 4.84/1.20 -> [615] ~left_apart_point(A40_104_9, L41_104_9), ~left_apart_point(A40_104_9, reverse_line(L41_104_9))
% 4.84/1.20
% 4.84/1.20 [615] CLOSURE : ~left_apart_point(A40_104_9, L41_104_9)
% 4.84/1.20
% 4.84/1.20 [525] BETA_OR : (left_convergent_lines(L38_23_8, M39_23_8) | left_convergent_lines(L38_23_8, reverse_line(M39_23_8)))
% 4.84/1.20 -> [535] left_convergent_lines(L38_23_8, M39_23_8)
% 4.84/1.20 -> [536] left_convergent_lines(L38_23_8, reverse_line(M39_23_8))
% 4.84/1.20
% 4.84/1.20 [536] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [576] ~(left_apart_point(A40_94_9, L41_94_9) | left_apart_point(A40_94_9, reverse_line(L41_94_9)))
% 4.84/1.20
% 4.84/1.20 [576] ALPHA_NOT_OR : ~(left_apart_point(A40_94_9, L41_94_9) | left_apart_point(A40_94_9, reverse_line(L41_94_9)))
% 4.84/1.20 -> [595] ~left_apart_point(A40_94_9, L41_94_9), ~left_apart_point(A40_94_9, reverse_line(L41_94_9))
% 4.84/1.20
% 4.84/1.20 [595] CLOSURE : ~left_apart_point(A40_94_9, L41_94_9)
% 4.84/1.20
% 4.84/1.20 [535] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [631] ~(left_apart_point(A40_113_9, L41_113_9) | left_apart_point(A40_113_9, reverse_line(L41_113_9)))
% 4.84/1.20
% 4.84/1.20 [631] ALPHA_NOT_OR : ~(left_apart_point(A40_113_9, L41_113_9) | left_apart_point(A40_113_9, reverse_line(L41_113_9)))
% 4.84/1.20 -> [634] ~left_apart_point(A40_113_9, L41_113_9), ~left_apart_point(A40_113_9, reverse_line(L41_113_9))
% 4.84/1.20
% 4.84/1.20 [634] CLOSURE : ~left_apart_point(A40_113_9, L41_113_9)
% 4.84/1.20
% 4.84/1.20 [507] 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)))))
% 4.84/1.20 -> [530] ((unequally_directed_lines(L38_25_8, M39_25_8) & unequally_directed_lines(L38_25_8, reverse_line(M39_25_8))) => (left_convergent_lines(L38_25_8, M39_25_8) | left_convergent_lines(L38_25_8, reverse_line(M39_25_8))))
% 4.84/1.20
% 4.84/1.20 [530] BETA_IMPLY : ((unequally_directed_lines(L38_25_8, M39_25_8) & unequally_directed_lines(L38_25_8, reverse_line(M39_25_8))) => (left_convergent_lines(L38_25_8, M39_25_8) | left_convergent_lines(L38_25_8, reverse_line(M39_25_8))))
% 4.84/1.20 -> [533] ~(unequally_directed_lines(L38_25_8, M39_25_8) & unequally_directed_lines(L38_25_8, reverse_line(M39_25_8)))
% 4.84/1.20 -> [534] (left_convergent_lines(L38_25_8, M39_25_8) | left_convergent_lines(L38_25_8, reverse_line(M39_25_8)))
% 4.84/1.20
% 4.84/1.20 [533] BETA_NOT_AND : ~(unequally_directed_lines(L38_25_8, M39_25_8) & unequally_directed_lines(L38_25_8, reverse_line(M39_25_8)))
% 4.84/1.20 -> [541] ~unequally_directed_lines(L38_25_8, M39_25_8)
% 4.84/1.20 -> [542] ~unequally_directed_lines(L38_25_8, reverse_line(M39_25_8))
% 4.84/1.20
% 4.84/1.20 [541] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [573] ~(left_apart_point(A40_92_9, L41_92_9) | left_apart_point(A40_92_9, reverse_line(L41_92_9)))
% 4.84/1.20
% 4.84/1.20 [573] ALPHA_NOT_OR : ~(left_apart_point(A40_92_9, L41_92_9) | left_apart_point(A40_92_9, reverse_line(L41_92_9)))
% 4.84/1.20 -> [575] ~left_apart_point(A40_92_9, L41_92_9), ~left_apart_point(A40_92_9, reverse_line(L41_92_9))
% 4.84/1.20
% 4.84/1.20 [575] CLOSURE : ~left_apart_point(A40_92_9, L41_92_9)
% 4.84/1.20
% 4.84/1.20 [542] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [553] ~(left_apart_point(A40_91_9, L41_91_9) | left_apart_point(A40_91_9, reverse_line(L41_91_9)))
% 4.84/1.20
% 4.84/1.20 [553] ALPHA_NOT_OR : ~(left_apart_point(A40_91_9, L41_91_9) | left_apart_point(A40_91_9, reverse_line(L41_91_9)))
% 4.84/1.20 -> [563] ~left_apart_point(A40_91_9, L41_91_9), ~left_apart_point(A40_91_9, reverse_line(L41_91_9))
% 4.84/1.20
% 4.84/1.20 [563] CLOSURE : ~left_apart_point(A40_91_9, L41_91_9)
% 4.84/1.20
% 4.84/1.20 [534] BETA_OR : (left_convergent_lines(L38_25_8, M39_25_8) | left_convergent_lines(L38_25_8, reverse_line(M39_25_8)))
% 4.84/1.20 -> [543] left_convergent_lines(L38_25_8, M39_25_8)
% 4.84/1.20 -> [544] left_convergent_lines(L38_25_8, reverse_line(M39_25_8))
% 4.84/1.20
% 4.84/1.20 [543] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [574] ~(left_apart_point(A40_93_9, L41_93_9) | left_apart_point(A40_93_9, reverse_line(L41_93_9)))
% 4.84/1.20
% 4.84/1.20 [574] ALPHA_NOT_OR : ~(left_apart_point(A40_93_9, L41_93_9) | left_apart_point(A40_93_9, reverse_line(L41_93_9)))
% 4.84/1.20 -> [594] ~left_apart_point(A40_93_9, L41_93_9), ~left_apart_point(A40_93_9, reverse_line(L41_93_9))
% 4.84/1.20
% 4.84/1.20 [594] CLOSURE : ~left_apart_point(A40_93_9, L41_93_9)
% 4.84/1.20
% 4.84/1.20 [544] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [637] ~(left_apart_point(A40_115_9, L41_115_9) | left_apart_point(A40_115_9, reverse_line(L41_115_9)))
% 4.84/1.20
% 4.84/1.20 [637] ALPHA_NOT_OR : ~(left_apart_point(A40_115_9, L41_115_9) | left_apart_point(A40_115_9, reverse_line(L41_115_9)))
% 4.84/1.20 -> [640] ~left_apart_point(A40_115_9, L41_115_9), ~left_apart_point(A40_115_9, reverse_line(L41_115_9))
% 4.84/1.20
% 4.84/1.20 [640] CLOSURE : ~left_apart_point(A40_115_9, L41_115_9)
% 4.84/1.20
% 4.84/1.20 [499] BETA_IMPLY : ((line(reverse_line(reverse_line(M39_36_8))) & line(reverse_line(M39_36_8))) => (unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(M39_36_8)) | unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(reverse_line(M39_36_8)))))
% 4.84/1.20 -> [654] ~(line(reverse_line(reverse_line(M39_36_8))) & line(reverse_line(M39_36_8)))
% 4.84/1.20 -> [655] (unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(M39_36_8)) | unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(reverse_line(M39_36_8))))
% 4.84/1.20
% 4.84/1.20 [654] BETA_NOT_AND : ~(line(reverse_line(reverse_line(M39_36_8))) & line(reverse_line(M39_36_8)))
% 4.84/1.20 -> [656] ~line(reverse_line(reverse_line(M39_36_8)))
% 4.84/1.20 -> [657] ~line(reverse_line(M39_36_8))
% 4.84/1.20
% 4.84/1.20 [657] 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)))))
% 4.84/1.20 -> [667] ((unequally_directed_lines(L38_32_8, M39_32_8) & unequally_directed_lines(L38_32_8, reverse_line(M39_32_8))) => (left_convergent_lines(L38_32_8, M39_32_8) | left_convergent_lines(L38_32_8, reverse_line(M39_32_8))))
% 4.84/1.20
% 4.84/1.20 [667] BETA_IMPLY : ((unequally_directed_lines(L38_32_8, M39_32_8) & unequally_directed_lines(L38_32_8, reverse_line(M39_32_8))) => (left_convergent_lines(L38_32_8, M39_32_8) | left_convergent_lines(L38_32_8, reverse_line(M39_32_8))))
% 4.84/1.20 -> [670] ~(unequally_directed_lines(L38_32_8, M39_32_8) & unequally_directed_lines(L38_32_8, reverse_line(M39_32_8)))
% 4.84/1.20 -> [671] (left_convergent_lines(L38_32_8, M39_32_8) | left_convergent_lines(L38_32_8, reverse_line(M39_32_8)))
% 4.84/1.20
% 4.84/1.20 [671] BETA_OR : (left_convergent_lines(L38_32_8, M39_32_8) | left_convergent_lines(L38_32_8, reverse_line(M39_32_8)))
% 4.84/1.20 -> [681] left_convergent_lines(L38_32_8, M39_32_8)
% 4.84/1.20 -> [682] left_convergent_lines(L38_32_8, reverse_line(M39_32_8))
% 4.84/1.20
% 4.84/1.20 [682] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [705] ~(left_apart_point(A40_125_9, L41_125_9) | left_apart_point(A40_125_9, reverse_line(L41_125_9)))
% 4.84/1.20
% 4.84/1.20 [705] ALPHA_NOT_OR : ~(left_apart_point(A40_125_9, L41_125_9) | left_apart_point(A40_125_9, reverse_line(L41_125_9)))
% 4.84/1.20 -> [708] ~left_apart_point(A40_125_9, L41_125_9), ~left_apart_point(A40_125_9, reverse_line(L41_125_9))
% 4.84/1.20
% 4.84/1.20 [708] CLOSURE : ~left_apart_point(A40_125_9, L41_125_9)
% 4.84/1.20
% 4.84/1.20 [681] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [710] ~(left_apart_point(A40_127_9, L41_127_9) | left_apart_point(A40_127_9, reverse_line(L41_127_9)))
% 4.84/1.20
% 4.84/1.20 [710] ALPHA_NOT_OR : ~(left_apart_point(A40_127_9, L41_127_9) | left_apart_point(A40_127_9, reverse_line(L41_127_9)))
% 4.84/1.20 -> [720] ~left_apart_point(A40_127_9, L41_127_9), ~left_apart_point(A40_127_9, reverse_line(L41_127_9))
% 4.84/1.20
% 4.84/1.20 [720] CLOSURE : ~left_apart_point(A40_127_9, L41_127_9)
% 4.84/1.20
% 4.84/1.20 [670] BETA_NOT_AND : ~(unequally_directed_lines(L38_32_8, M39_32_8) & unequally_directed_lines(L38_32_8, reverse_line(M39_32_8)))
% 4.84/1.20 -> [683] ~unequally_directed_lines(L38_32_8, M39_32_8)
% 4.84/1.20 -> [684] ~unequally_directed_lines(L38_32_8, reverse_line(M39_32_8))
% 4.84/1.20
% 4.84/1.20 [683] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [713] ~(left_apart_point(A40_128_9, L41_128_9) | left_apart_point(A40_128_9, reverse_line(L41_128_9)))
% 4.84/1.20
% 4.84/1.20 [713] ALPHA_NOT_OR : ~(left_apart_point(A40_128_9, L41_128_9) | left_apart_point(A40_128_9, reverse_line(L41_128_9)))
% 4.84/1.20 -> [715] ~left_apart_point(A40_128_9, L41_128_9), ~left_apart_point(A40_128_9, reverse_line(L41_128_9))
% 4.84/1.20
% 4.84/1.20 [715] CLOSURE : ~left_apart_point(A40_128_9, L41_128_9)
% 4.84/1.20
% 4.84/1.20 [684] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [735] ~(left_apart_point(A40_137_9, L41_137_9) | left_apart_point(A40_137_9, reverse_line(L41_137_9)))
% 4.84/1.20
% 4.84/1.20 [735] ALPHA_NOT_OR : ~(left_apart_point(A40_137_9, L41_137_9) | left_apart_point(A40_137_9, reverse_line(L41_137_9)))
% 4.84/1.20 -> [738] ~left_apart_point(A40_137_9, L41_137_9), ~left_apart_point(A40_137_9, reverse_line(L41_137_9))
% 4.84/1.20
% 4.84/1.20 [738] CLOSURE : ~left_apart_point(A40_137_9, L41_137_9)
% 4.84/1.20
% 4.84/1.20 [656] 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)))))
% 4.84/1.20 -> [666] ((unequally_directed_lines(L38_31_8, M39_31_8) & unequally_directed_lines(L38_31_8, reverse_line(M39_31_8))) => (left_convergent_lines(L38_31_8, M39_31_8) | left_convergent_lines(L38_31_8, reverse_line(M39_31_8))))
% 4.84/1.20
% 4.84/1.20 [666] BETA_IMPLY : ((unequally_directed_lines(L38_31_8, M39_31_8) & unequally_directed_lines(L38_31_8, reverse_line(M39_31_8))) => (left_convergent_lines(L38_31_8, M39_31_8) | left_convergent_lines(L38_31_8, reverse_line(M39_31_8))))
% 4.84/1.20 -> [668] ~(unequally_directed_lines(L38_31_8, M39_31_8) & unequally_directed_lines(L38_31_8, reverse_line(M39_31_8)))
% 4.84/1.20 -> [669] (left_convergent_lines(L38_31_8, M39_31_8) | left_convergent_lines(L38_31_8, reverse_line(M39_31_8)))
% 4.84/1.20
% 4.84/1.20 [668] BETA_NOT_AND : ~(unequally_directed_lines(L38_31_8, M39_31_8) & unequally_directed_lines(L38_31_8, reverse_line(M39_31_8)))
% 4.84/1.20 -> [674] ~unequally_directed_lines(L38_31_8, M39_31_8)
% 4.84/1.20 -> [675] ~unequally_directed_lines(L38_31_8, reverse_line(M39_31_8))
% 4.84/1.20
% 4.84/1.20 [675] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [691] ~(left_apart_point(A40_123_9, L41_123_9) | left_apart_point(A40_123_9, reverse_line(L41_123_9)))
% 4.84/1.20
% 4.84/1.20 [691] ALPHA_NOT_OR : ~(left_apart_point(A40_123_9, L41_123_9) | left_apart_point(A40_123_9, reverse_line(L41_123_9)))
% 4.84/1.20 -> [694] ~left_apart_point(A40_123_9, L41_123_9), ~left_apart_point(A40_123_9, reverse_line(L41_123_9))
% 4.84/1.20
% 4.84/1.20 [694] CLOSURE : ~left_apart_point(A40_123_9, L41_123_9)
% 4.84/1.20
% 4.84/1.20 [674] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [695] ~(left_apart_point(A40_124_9, L41_124_9) | left_apart_point(A40_124_9, reverse_line(L41_124_9)))
% 4.84/1.20
% 4.84/1.20 [695] ALPHA_NOT_OR : ~(left_apart_point(A40_124_9, L41_124_9) | left_apart_point(A40_124_9, reverse_line(L41_124_9)))
% 4.84/1.20 -> [700] ~left_apart_point(A40_124_9, L41_124_9), ~left_apart_point(A40_124_9, reverse_line(L41_124_9))
% 4.84/1.20
% 4.84/1.20 [700] CLOSURE : ~left_apart_point(A40_124_9, L41_124_9)
% 4.84/1.20
% 4.84/1.20 [669] BETA_OR : (left_convergent_lines(L38_31_8, M39_31_8) | left_convergent_lines(L38_31_8, reverse_line(M39_31_8)))
% 4.84/1.20 -> [678] left_convergent_lines(L38_31_8, M39_31_8)
% 4.84/1.20 -> [679] left_convergent_lines(L38_31_8, reverse_line(M39_31_8))
% 4.84/1.20
% 4.84/1.20 [678] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [733] ~(left_apart_point(A40_136_9, L41_136_9) | left_apart_point(A40_136_9, reverse_line(L41_136_9)))
% 4.84/1.20
% 4.84/1.20 [733] ALPHA_NOT_OR : ~(left_apart_point(A40_136_9, L41_136_9) | left_apart_point(A40_136_9, reverse_line(L41_136_9)))
% 4.84/1.20 -> [734] ~left_apart_point(A40_136_9, L41_136_9), ~left_apart_point(A40_136_9, reverse_line(L41_136_9))
% 4.84/1.20
% 4.84/1.20 [734] CLOSURE : ~left_apart_point(A40_136_9, L41_136_9)
% 4.84/1.20
% 4.84/1.20 [679] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [706] ~(left_apart_point(A40_126_9, L41_126_9) | left_apart_point(A40_126_9, reverse_line(L41_126_9)))
% 4.84/1.20
% 4.84/1.20 [706] ALPHA_NOT_OR : ~(left_apart_point(A40_126_9, L41_126_9) | left_apart_point(A40_126_9, reverse_line(L41_126_9)))
% 4.84/1.20 -> [709] ~left_apart_point(A40_126_9, L41_126_9), ~left_apart_point(A40_126_9, reverse_line(L41_126_9))
% 4.84/1.20
% 4.84/1.20 [709] CLOSURE : ~left_apart_point(A40_126_9, L41_126_9)
% 4.84/1.20
% 4.84/1.20 [655] BETA_OR : (unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(M39_36_8)) | unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(reverse_line(M39_36_8))))
% 4.84/1.20 -> [658] unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(M39_36_8))
% 4.84/1.20 -> [659] unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(reverse_line(M39_36_8)))
% 4.84/1.20
% 4.84/1.20 [659] CLOSURE : unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(reverse_line(M39_36_8)))
% 4.84/1.20
% 4.84/1.20 [658] 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)))))
% 4.84/1.20 -> [707] ((unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), M39_36_8) & unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(M39_36_8))) => (left_convergent_lines(reverse_line(reverse_line(M39_36_8)), M39_36_8) | left_convergent_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(M39_36_8))))
% 4.84/1.20
% 4.84/1.20 [707] BETA_IMPLY : ((unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), M39_36_8) & unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(M39_36_8))) => (left_convergent_lines(reverse_line(reverse_line(M39_36_8)), M39_36_8) | left_convergent_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(M39_36_8))))
% 4.84/1.20 -> [711] ~(unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), M39_36_8) & unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(M39_36_8)))
% 4.84/1.20 -> [712] (left_convergent_lines(reverse_line(reverse_line(M39_36_8)), M39_36_8) | left_convergent_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(M39_36_8)))
% 4.84/1.20
% 4.84/1.20 [712] BETA_OR : (left_convergent_lines(reverse_line(reverse_line(M39_36_8)), M39_36_8) | left_convergent_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(M39_36_8)))
% 4.84/1.20 -> [717] left_convergent_lines(reverse_line(reverse_line(M39_36_8)), M39_36_8)
% 4.84/1.20 -> [718] left_convergent_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(M39_36_8))
% 4.84/1.20
% 4.84/1.20 [717] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [742] ~(left_apart_point(A40_140_9, L41_140_9) | left_apart_point(A40_140_9, reverse_line(L41_140_9)))
% 4.84/1.20
% 4.84/1.20 [742] ALPHA_NOT_OR : ~(left_apart_point(A40_140_9, L41_140_9) | left_apart_point(A40_140_9, reverse_line(L41_140_9)))
% 4.84/1.20 -> [743] ~left_apart_point(A40_140_9, L41_140_9), ~left_apart_point(A40_140_9, reverse_line(L41_140_9))
% 4.84/1.20
% 4.84/1.20 [743] CLOSURE : ~left_apart_point(A40_140_9, L41_140_9)
% 4.84/1.20
% 4.84/1.20 [718] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [746] ~(left_apart_point(A40_142_9, L41_142_9) | left_apart_point(A40_142_9, reverse_line(L41_142_9)))
% 4.84/1.20
% 4.84/1.20 [746] ALPHA_NOT_OR : ~(left_apart_point(A40_142_9, L41_142_9) | left_apart_point(A40_142_9, reverse_line(L41_142_9)))
% 4.84/1.20 -> [747] ~left_apart_point(A40_142_9, L41_142_9), ~left_apart_point(A40_142_9, reverse_line(L41_142_9))
% 4.84/1.20
% 4.84/1.20 [747] CLOSURE : ~left_apart_point(A40_142_9, L41_142_9)
% 4.84/1.20
% 4.84/1.20 [711] BETA_NOT_AND : ~(unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), M39_36_8) & unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(M39_36_8)))
% 4.84/1.20 -> [726] ~unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), M39_36_8)
% 4.84/1.20 -> [727] ~unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(M39_36_8))
% 4.84/1.20
% 4.84/1.20 [727] CLOSURE : ~unequally_directed_lines(reverse_line(reverse_line(M39_36_8)), reverse_line(M39_36_8))
% 4.84/1.20
% 4.84/1.20 [726] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [749] ~(left_apart_point(A40_144_9, L41_144_9) | left_apart_point(A40_144_9, reverse_line(L41_144_9)))
% 4.84/1.20
% 4.84/1.20 [749] ALPHA_NOT_OR : ~(left_apart_point(A40_144_9, L41_144_9) | left_apart_point(A40_144_9, reverse_line(L41_144_9)))
% 4.84/1.20 -> [751] ~left_apart_point(A40_144_9, L41_144_9), ~left_apart_point(A40_144_9, reverse_line(L41_144_9))
% 4.84/1.20
% 4.84/1.20 [751] CLOSURE : ~left_apart_point(A40_144_9, L41_144_9)
% 4.84/1.20
% 4.84/1.20 [491] BETA_OR : ((unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)) & unequally_directed_lines(skolem_L8282, reverse_line(reverse_line(skolem_M8383)))) | (unequally_directed_lines(skolem_M8383, reverse_line(skolem_M8383)) & unequally_directed_lines(skolem_M8383, reverse_line(reverse_line(skolem_M8383)))))
% 4.84/1.20 -> [756] (unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)) & unequally_directed_lines(skolem_L8282, reverse_line(reverse_line(skolem_M8383))))
% 4.84/1.20 -> [757] (unequally_directed_lines(skolem_M8383, reverse_line(skolem_M8383)) & unequally_directed_lines(skolem_M8383, reverse_line(reverse_line(skolem_M8383))))
% 4.84/1.20
% 4.84/1.20 [756] ALPHA_AND : (unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)) & unequally_directed_lines(skolem_L8282, reverse_line(reverse_line(skolem_M8383))))
% 4.84/1.20 -> [758] unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)), unequally_directed_lines(skolem_L8282, reverse_line(reverse_line(skolem_M8383)))
% 4.84/1.20
% 4.84/1.20 [758] CLOSURE : unequally_directed_lines(skolem_L8282, reverse_line(reverse_line(skolem_M8383)))
% 4.84/1.20
% 4.84/1.20 [757] ALPHA_AND : (unequally_directed_lines(skolem_M8383, reverse_line(skolem_M8383)) & unequally_directed_lines(skolem_M8383, reverse_line(reverse_line(skolem_M8383))))
% 4.84/1.20 -> [759] unequally_directed_lines(skolem_M8383, reverse_line(skolem_M8383)), unequally_directed_lines(skolem_M8383, reverse_line(reverse_line(skolem_M8383)))
% 4.84/1.20
% 4.84/1.20 [759] 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)))))
% 4.84/1.20 -> [760] ((line(skolem_L8282) & line(reverse_line(skolem_M8383))) => (unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)) | unequally_directed_lines(skolem_L8282, reverse_line(reverse_line(skolem_M8383)))))
% 4.84/1.20
% 4.84/1.20 [760] BETA_IMPLY : ((line(skolem_L8282) & line(reverse_line(skolem_M8383))) => (unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)) | unequally_directed_lines(skolem_L8282, reverse_line(reverse_line(skolem_M8383)))))
% 4.84/1.20 -> [761] ~(line(skolem_L8282) & line(reverse_line(skolem_M8383)))
% 4.84/1.20 -> [762] (unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)) | unequally_directed_lines(skolem_L8282, reverse_line(reverse_line(skolem_M8383))))
% 4.84/1.20
% 4.84/1.20 [761] BETA_NOT_AND : ~(line(skolem_L8282) & line(reverse_line(skolem_M8383)))
% 4.84/1.20 -> [763] ~line(skolem_L8282)
% 4.84/1.20 -> [764] ~line(reverse_line(skolem_M8383))
% 4.84/1.20
% 4.84/1.20 [763] 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)))))
% 4.84/1.20 -> [767] ((unequally_directed_lines(skolem_M8383, M39_37_8) & unequally_directed_lines(skolem_M8383, reverse_line(M39_37_8))) => (left_convergent_lines(skolem_M8383, M39_37_8) | left_convergent_lines(skolem_M8383, reverse_line(M39_37_8))))
% 4.84/1.20
% 4.84/1.20 [767] BETA_IMPLY : ((unequally_directed_lines(skolem_M8383, M39_37_8) & unequally_directed_lines(skolem_M8383, reverse_line(M39_37_8))) => (left_convergent_lines(skolem_M8383, M39_37_8) | left_convergent_lines(skolem_M8383, reverse_line(M39_37_8))))
% 4.84/1.20 -> [769] ~(unequally_directed_lines(skolem_M8383, M39_37_8) & unequally_directed_lines(skolem_M8383, reverse_line(M39_37_8)))
% 4.84/1.20 -> [770] (left_convergent_lines(skolem_M8383, M39_37_8) | left_convergent_lines(skolem_M8383, reverse_line(M39_37_8)))
% 4.84/1.20
% 4.84/1.20 [769] BETA_NOT_AND : ~(unequally_directed_lines(skolem_M8383, M39_37_8) & unequally_directed_lines(skolem_M8383, reverse_line(M39_37_8)))
% 4.84/1.20 -> [773] ~unequally_directed_lines(skolem_M8383, M39_37_8)
% 4.84/1.20 -> [774] ~unequally_directed_lines(skolem_M8383, reverse_line(M39_37_8))
% 4.84/1.20
% 4.84/1.20 [774] CLOSURE : ~unequally_directed_lines(skolem_M8383, reverse_line(M39_37_8))
% 4.84/1.20
% 4.84/1.20 [773] CLOSURE : ~unequally_directed_lines(skolem_M8383, M39_37_8)
% 4.84/1.20
% 4.84/1.20 [770] BETA_OR : (left_convergent_lines(skolem_M8383, M39_37_8) | left_convergent_lines(skolem_M8383, reverse_line(M39_37_8)))
% 4.84/1.20 -> [777] left_convergent_lines(skolem_M8383, M39_37_8)
% 4.84/1.20 -> [778] left_convergent_lines(skolem_M8383, reverse_line(M39_37_8))
% 4.84/1.20
% 4.84/1.20 [778] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [781] ~(left_apart_point(A40_145_9, L41_145_9) | left_apart_point(A40_145_9, reverse_line(L41_145_9)))
% 4.84/1.20
% 4.84/1.20 [781] ALPHA_NOT_OR : ~(left_apart_point(A40_145_9, L41_145_9) | left_apart_point(A40_145_9, reverse_line(L41_145_9)))
% 4.84/1.20 -> [783] ~left_apart_point(A40_145_9, L41_145_9), ~left_apart_point(A40_145_9, reverse_line(L41_145_9))
% 4.84/1.20
% 4.84/1.20 [783] CLOSURE : ~left_apart_point(A40_145_9, L41_145_9)
% 4.84/1.20
% 4.84/1.20 [777] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [785] ~(left_apart_point(A40_147_9, L41_147_9) | left_apart_point(A40_147_9, reverse_line(L41_147_9)))
% 4.84/1.20
% 4.84/1.20 [785] ALPHA_NOT_OR : ~(left_apart_point(A40_147_9, L41_147_9) | left_apart_point(A40_147_9, reverse_line(L41_147_9)))
% 4.84/1.20 -> [790] ~left_apart_point(A40_147_9, L41_147_9), ~left_apart_point(A40_147_9, reverse_line(L41_147_9))
% 4.84/1.20
% 4.84/1.20 [790] CLOSURE : ~left_apart_point(A40_147_9, L41_147_9)
% 4.84/1.20
% 4.84/1.20 [764] 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)))))
% 4.84/1.20 -> [768] ((unequally_directed_lines(skolem_M8383, M39_38_8) & unequally_directed_lines(skolem_M8383, reverse_line(M39_38_8))) => (left_convergent_lines(skolem_M8383, M39_38_8) | left_convergent_lines(skolem_M8383, reverse_line(M39_38_8))))
% 4.84/1.20
% 4.84/1.20 [768] BETA_IMPLY : ((unequally_directed_lines(skolem_M8383, M39_38_8) & unequally_directed_lines(skolem_M8383, reverse_line(M39_38_8))) => (left_convergent_lines(skolem_M8383, M39_38_8) | left_convergent_lines(skolem_M8383, reverse_line(M39_38_8))))
% 4.84/1.20 -> [771] ~(unequally_directed_lines(skolem_M8383, M39_38_8) & unequally_directed_lines(skolem_M8383, reverse_line(M39_38_8)))
% 4.84/1.20 -> [772] (left_convergent_lines(skolem_M8383, M39_38_8) | left_convergent_lines(skolem_M8383, reverse_line(M39_38_8)))
% 4.84/1.20
% 4.84/1.20 [771] BETA_NOT_AND : ~(unequally_directed_lines(skolem_M8383, M39_38_8) & unequally_directed_lines(skolem_M8383, reverse_line(M39_38_8)))
% 4.84/1.20 -> [775] ~unequally_directed_lines(skolem_M8383, M39_38_8)
% 4.84/1.20 -> [776] ~unequally_directed_lines(skolem_M8383, reverse_line(M39_38_8))
% 4.84/1.20
% 4.84/1.20 [775] CLOSURE : ~unequally_directed_lines(skolem_M8383, M39_38_8)
% 4.84/1.20
% 4.84/1.20 [776] CLOSURE : ~unequally_directed_lines(skolem_M8383, reverse_line(M39_38_8))
% 4.84/1.20
% 4.84/1.20 [772] BETA_OR : (left_convergent_lines(skolem_M8383, M39_38_8) | left_convergent_lines(skolem_M8383, reverse_line(M39_38_8)))
% 4.84/1.20 -> [779] left_convergent_lines(skolem_M8383, M39_38_8)
% 4.84/1.20 -> [780] left_convergent_lines(skolem_M8383, reverse_line(M39_38_8))
% 4.84/1.20
% 4.84/1.20 [780] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [782] ~(left_apart_point(A40_146_9, L41_146_9) | left_apart_point(A40_146_9, reverse_line(L41_146_9)))
% 4.84/1.20
% 4.84/1.20 [782] ALPHA_NOT_OR : ~(left_apart_point(A40_146_9, L41_146_9) | left_apart_point(A40_146_9, reverse_line(L41_146_9)))
% 4.84/1.20 -> [786] ~left_apart_point(A40_146_9, L41_146_9), ~left_apart_point(A40_146_9, reverse_line(L41_146_9))
% 4.84/1.20
% 4.84/1.20 [786] CLOSURE : ~left_apart_point(A40_146_9, L41_146_9)
% 4.84/1.20
% 4.84/1.20 [779] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [787] ~(left_apart_point(A40_148_9, L41_148_9) | left_apart_point(A40_148_9, reverse_line(L41_148_9)))
% 4.84/1.20
% 4.84/1.20 [787] ALPHA_NOT_OR : ~(left_apart_point(A40_148_9, L41_148_9) | left_apart_point(A40_148_9, reverse_line(L41_148_9)))
% 4.84/1.20 -> [791] ~left_apart_point(A40_148_9, L41_148_9), ~left_apart_point(A40_148_9, reverse_line(L41_148_9))
% 4.84/1.20
% 4.84/1.20 [791] CLOSURE : ~left_apart_point(A40_148_9, L41_148_9)
% 4.84/1.20
% 4.84/1.20 [762] BETA_OR : (unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383)) | unequally_directed_lines(skolem_L8282, reverse_line(reverse_line(skolem_M8383))))
% 4.84/1.20 -> [765] unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383))
% 4.84/1.20 -> [766] unequally_directed_lines(skolem_L8282, reverse_line(reverse_line(skolem_M8383)))
% 4.84/1.20
% 4.84/1.20 [765] CLOSURE : unequally_directed_lines(skolem_L8282, reverse_line(skolem_M8383))
% 4.84/1.20
% 4.84/1.20 [766] 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)))))
% 4.84/1.20 -> [784] ((unequally_directed_lines(skolem_M8383, M39_39_8) & unequally_directed_lines(skolem_M8383, reverse_line(M39_39_8))) => (left_convergent_lines(skolem_M8383, M39_39_8) | left_convergent_lines(skolem_M8383, reverse_line(M39_39_8))))
% 4.84/1.20
% 4.84/1.20 [784] BETA_IMPLY : ((unequally_directed_lines(skolem_M8383, M39_39_8) & unequally_directed_lines(skolem_M8383, reverse_line(M39_39_8))) => (left_convergent_lines(skolem_M8383, M39_39_8) | left_convergent_lines(skolem_M8383, reverse_line(M39_39_8))))
% 4.84/1.20 -> [788] ~(unequally_directed_lines(skolem_M8383, M39_39_8) & unequally_directed_lines(skolem_M8383, reverse_line(M39_39_8)))
% 4.84/1.20 -> [789] (left_convergent_lines(skolem_M8383, M39_39_8) | left_convergent_lines(skolem_M8383, reverse_line(M39_39_8)))
% 4.84/1.20
% 4.84/1.20 [788] BETA_NOT_AND : ~(unequally_directed_lines(skolem_M8383, M39_39_8) & unequally_directed_lines(skolem_M8383, reverse_line(M39_39_8)))
% 4.84/1.20 -> [792] ~unequally_directed_lines(skolem_M8383, M39_39_8)
% 4.84/1.20 -> [793] ~unequally_directed_lines(skolem_M8383, reverse_line(M39_39_8))
% 4.84/1.20
% 4.84/1.20 [792] CLOSURE : ~unequally_directed_lines(skolem_M8383, M39_39_8)
% 4.84/1.20
% 4.84/1.20 [793] CLOSURE : ~unequally_directed_lines(skolem_M8383, reverse_line(M39_39_8))
% 4.84/1.20
% 4.84/1.20 [789] BETA_OR : (left_convergent_lines(skolem_M8383, M39_39_8) | left_convergent_lines(skolem_M8383, reverse_line(M39_39_8)))
% 4.84/1.20 -> [794] left_convergent_lines(skolem_M8383, M39_39_8)
% 4.84/1.20 -> [795] left_convergent_lines(skolem_M8383, reverse_line(M39_39_8))
% 4.84/1.20
% 4.84/1.20 [794] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [796] ~(left_apart_point(A40_149_9, L41_149_9) | left_apart_point(A40_149_9, reverse_line(L41_149_9)))
% 4.84/1.20
% 4.84/1.20 [796] ALPHA_NOT_OR : ~(left_apart_point(A40_149_9, L41_149_9) | left_apart_point(A40_149_9, reverse_line(L41_149_9)))
% 4.84/1.20 -> [798] ~left_apart_point(A40_149_9, L41_149_9), ~left_apart_point(A40_149_9, reverse_line(L41_149_9))
% 4.84/1.20
% 4.84/1.20 [798] CLOSURE : ~left_apart_point(A40_149_9, L41_149_9)
% 4.84/1.20
% 4.84/1.20 [795] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 4.84/1.20 -> [797] ~(left_apart_point(A40_150_9, L41_150_9) | left_apart_point(A40_150_9, reverse_line(L41_150_9)))
% 4.84/1.20
% 4.84/1.20 [797] ALPHA_NOT_OR : ~(left_apart_point(A40_150_9, L41_150_9) | left_apart_point(A40_150_9, reverse_line(L41_150_9)))
% 4.84/1.20 -> [799] ~left_apart_point(A40_150_9, L41_150_9), ~left_apart_point(A40_150_9, reverse_line(L41_150_9))
% 4.84/1.20
% 4.84/1.20 [799] CLOSURE : ~left_apart_point(A40_150_9, L41_150_9)
% 4.84/1.20
% 4.84/1.20 % SZS output end Proof for theBenchmark.p
% 4.84/1.20 [0.844565s][1][Res] 6092 goroutines created
% 4.84/1.20 ==== Result ====
% 4.84/1.20 [0.844585s][1][Res] VALID
% 4.84/1.20 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------