TSTP Solution File: GEO257+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO257+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 15:18:46 EDT 2022
% Result : Theorem 2.27s 1.05s
% Output : Proof 2.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO257+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.12/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 06:36:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 [DMT] DMT loaded with preskolemization
% 0.12/0.34 [EQ] equality loaded.
% 0.12/0.34 [0.000041s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.35 Conjecture not found
% 0.12/0.35 Start search
% 0.12/0.35 nb_step : 1 - limit : 32
% 0.12/0.35 Launch Gotab with destructive = true
% 2.27/1.04 % SZS output start Proof for theBenchmark.p
% 2.27/1.05 [0] ALPHA_AND : ((! [A21_21] : (~distinct_points(A21_21, A21_21)) & ! [A22_22, B23_23, C24_24] : ((distinct_points(A22_22, B23_23) => (distinct_points(A22_22, C24_24) | distinct_points(B23_23, C24_24)))) & ! [L25_25] : (~distinct_lines(L25_25, L25_25)) & ! [L26_26, M27_27, N28_28] : ((distinct_lines(L26_26, M27_27) => (distinct_lines(L26_26, N28_28) | distinct_lines(M27_27, N28_28)))) & ! [L29_29] : (~unequally_directed_lines(L29_29, L29_29)) & ! [L30_30, M31_31, N32_32] : ((unequally_directed_lines(L30_30, M31_31) => (unequally_directed_lines(L30_30, N32_32) | unequally_directed_lines(M31_31, N32_32)))) & ! [L33_33, M34_34, N35_35] : (((unequally_directed_lines(L33_33, M34_34) & unequally_directed_lines(L33_33, reverse_line(M34_34))) => ((unequally_directed_lines(L33_33, N35_35) & unequally_directed_lines(L33_33, reverse_line(N35_35))) | (unequally_directed_lines(M34_34, N35_35) & unequally_directed_lines(M34_34, reverse_line(N35_35)))))) & ! [L36_36, M37_37] : (((line(L36_36) & line(M37_37)) => (unequally_directed_lines(L36_36, M37_37) | unequally_directed_lines(L36_36, reverse_line(M37_37))))) & ! [L38_38, M39_39] : (((unequally_directed_lines(L38_38, M39_39) & unequally_directed_lines(L38_38, reverse_line(M39_39))) => (left_convergent_lines(L38_38, M39_39) | left_convergent_lines(L38_38, reverse_line(M39_39))))) & ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41)))) & ! [L42_42, M43_43] : (~(left_convergent_lines(L42_42, M43_43) | left_convergent_lines(L42_42, reverse_line(M43_43)))) & ! [A44_44, B45_45] : ((((point(A44_44) & point(B45_45)) & distinct_points(A44_44, B45_45)) => line(line_connecting(A44_44, B45_45)))) & ! [L46_46, M47_47] : (((((line(L46_46) & line(M47_47)) & unequally_directed_lines(L46_46, M47_47)) & unequally_directed_lines(L46_46, reverse_line(M47_47))) => point(intersection_point(L46_46, M47_47)))) & ! [L48_48, A49_49] : (((point(A49_49) & line(L48_48)) => line(parallel_through_point(L48_48, A49_49)))) & ! [L50_50] : ((line(L50_50) => line(reverse_line(L50_50)))) & ! [A51_51, B52_52] : ((distinct_points(A51_51, B52_52) => (~apart_point_and_line(A51_51, line_connecting(A51_51, B52_52)) & ~apart_point_and_line(B52_52, line_connecting(A51_51, B52_52))))) & ! [L53_53, M54_54] : (((unequally_directed_lines(L53_53, M54_54) & unequally_directed_lines(L53_53, reverse_line(M54_54))) => (~apart_point_and_line(intersection_point(L53_53, M54_54), L53_53) & ~apart_point_and_line(intersection_point(L53_53, M54_54), M54_54)))) & ! [A55_55, L56_56] : (~apart_point_and_line(A55_55, parallel_through_point(L56_56, A55_55))) & ! [L57_57] : (~distinct_lines(L57_57, reverse_line(L57_57))) & ! [A58_58, B59_59] : (~unequally_directed_lines(line_connecting(A58_58, B59_59), reverse_line(line_connecting(B59_59, A58_58)))) & ! [A60_60, L61_61] : (~unequally_directed_lines(parallel_through_point(L61_61, A60_60), L61_61)) & ! [A62_62, B63_63, L64_64, M65_65] : (((distinct_points(A62_62, B63_63) & distinct_lines(L64_64, M65_65)) => (((((((left_apart_point(A62_62, L64_64) | left_apart_point(B63_63, L64_64)) | left_apart_point(A62_62, M65_65)) | left_apart_point(B63_63, M65_65)) | left_apart_point(A62_62, reverse_line(L64_64))) | left_apart_point(B63_63, reverse_line(L64_64))) | left_apart_point(A62_62, reverse_line(M65_65))) | left_apart_point(B63_63, reverse_line(M65_65))))) & ! [A66_66, B67_67, L68_68] : (((distinct_points(A66_66, B67_67) & left_apart_point(A66_66, L68_68)) => (left_apart_point(B67_67, L68_68) | left_convergent_lines(line_connecting(A66_66, B67_67), L68_68)))) & ! [A69_69, B70_70, L71_71] : ((left_apart_point(A69_69, L71_71) => (distinct_points(A69_69, B70_70) | left_apart_point(B70_70, L71_71)))) & ! [A72_72, L73_73, M74_74] : (((left_apart_point(A72_72, L73_73) & unequally_directed_lines(L73_73, M74_74)) => (distinct_lines(L73_73, M74_74) | left_apart_point(A72_72, reverse_line(M74_74))))) & ! [L75_75, M76_76, N77_77] : ((left_convergent_lines(L75_75, M76_76) => (unequally_directed_lines(M76_76, N77_77) | left_convergent_lines(L75_75, N77_77))))) & ~! [L78_78, A79_79, B80_80, C81_81, D82_82] : (((((distinct_points(A79_79, C81_81) & distinct_points(B80_80, C81_81)) & ~apart_point_and_line(C81_81, L78_78)) & left_apart_point(D82_82, L78_78)) => ((before_on_line(L78_78, A79_79, B80_80) & before_on_line(L78_78, B80_80, C81_81)) => before_on_line(L78_78, A79_79, C81_81)))))
% 2.27/1.05 -> [1] (! [A21_21] : (~distinct_points(A21_21, A21_21)) & ! [A22_22, B23_23, C24_24] : ((distinct_points(A22_22, B23_23) => (distinct_points(A22_22, C24_24) | distinct_points(B23_23, C24_24)))) & ! [L25_25] : (~distinct_lines(L25_25, L25_25)) & ! [L26_26, M27_27, N28_28] : ((distinct_lines(L26_26, M27_27) => (distinct_lines(L26_26, N28_28) | distinct_lines(M27_27, N28_28)))) & ! [L29_29] : (~unequally_directed_lines(L29_29, L29_29)) & ! [L30_30, M31_31, N32_32] : ((unequally_directed_lines(L30_30, M31_31) => (unequally_directed_lines(L30_30, N32_32) | unequally_directed_lines(M31_31, N32_32)))) & ! [L33_33, M34_34, N35_35] : (((unequally_directed_lines(L33_33, M34_34) & unequally_directed_lines(L33_33, reverse_line(M34_34))) => ((unequally_directed_lines(L33_33, N35_35) & unequally_directed_lines(L33_33, reverse_line(N35_35))) | (unequally_directed_lines(M34_34, N35_35) & unequally_directed_lines(M34_34, reverse_line(N35_35)))))) & ! [L36_36, M37_37] : (((line(L36_36) & line(M37_37)) => (unequally_directed_lines(L36_36, M37_37) | unequally_directed_lines(L36_36, reverse_line(M37_37))))) & ! [L38_38, M39_39] : (((unequally_directed_lines(L38_38, M39_39) & unequally_directed_lines(L38_38, reverse_line(M39_39))) => (left_convergent_lines(L38_38, M39_39) | left_convergent_lines(L38_38, reverse_line(M39_39))))) & ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41)))) & ! [L42_42, M43_43] : (~(left_convergent_lines(L42_42, M43_43) | left_convergent_lines(L42_42, reverse_line(M43_43)))) & ! [A44_44, B45_45] : ((((point(A44_44) & point(B45_45)) & distinct_points(A44_44, B45_45)) => line(line_connecting(A44_44, B45_45)))) & ! [L46_46, M47_47] : (((((line(L46_46) & line(M47_47)) & unequally_directed_lines(L46_46, M47_47)) & unequally_directed_lines(L46_46, reverse_line(M47_47))) => point(intersection_point(L46_46, M47_47)))) & ! [L48_48, A49_49] : (((point(A49_49) & line(L48_48)) => line(parallel_through_point(L48_48, A49_49)))) & ! [L50_50] : ((line(L50_50) => line(reverse_line(L50_50)))) & ! [A51_51, B52_52] : ((distinct_points(A51_51, B52_52) => (~apart_point_and_line(A51_51, line_connecting(A51_51, B52_52)) & ~apart_point_and_line(B52_52, line_connecting(A51_51, B52_52))))) & ! [L53_53, M54_54] : (((unequally_directed_lines(L53_53, M54_54) & unequally_directed_lines(L53_53, reverse_line(M54_54))) => (~apart_point_and_line(intersection_point(L53_53, M54_54), L53_53) & ~apart_point_and_line(intersection_point(L53_53, M54_54), M54_54)))) & ! [A55_55, L56_56] : (~apart_point_and_line(A55_55, parallel_through_point(L56_56, A55_55))) & ! [L57_57] : (~distinct_lines(L57_57, reverse_line(L57_57))) & ! [A58_58, B59_59] : (~unequally_directed_lines(line_connecting(A58_58, B59_59), reverse_line(line_connecting(B59_59, A58_58)))) & ! [A60_60, L61_61] : (~unequally_directed_lines(parallel_through_point(L61_61, A60_60), L61_61)) & ! [A62_62, B63_63, L64_64, M65_65] : (((distinct_points(A62_62, B63_63) & distinct_lines(L64_64, M65_65)) => (((((((left_apart_point(A62_62, L64_64) | left_apart_point(B63_63, L64_64)) | left_apart_point(A62_62, M65_65)) | left_apart_point(B63_63, M65_65)) | left_apart_point(A62_62, reverse_line(L64_64))) | left_apart_point(B63_63, reverse_line(L64_64))) | left_apart_point(A62_62, reverse_line(M65_65))) | left_apart_point(B63_63, reverse_line(M65_65))))) & ! [A66_66, B67_67, L68_68] : (((distinct_points(A66_66, B67_67) & left_apart_point(A66_66, L68_68)) => (left_apart_point(B67_67, L68_68) | left_convergent_lines(line_connecting(A66_66, B67_67), L68_68)))) & ! [A69_69, B70_70, L71_71] : ((left_apart_point(A69_69, L71_71) => (distinct_points(A69_69, B70_70) | left_apart_point(B70_70, L71_71)))) & ! [A72_72, L73_73, M74_74] : (((left_apart_point(A72_72, L73_73) & unequally_directed_lines(L73_73, M74_74)) => (distinct_lines(L73_73, M74_74) | left_apart_point(A72_72, reverse_line(M74_74))))) & ! [L75_75, M76_76, N77_77] : ((left_convergent_lines(L75_75, M76_76) => (unequally_directed_lines(M76_76, N77_77) | left_convergent_lines(L75_75, N77_77))))), ~! [L78_78, A79_79, B80_80, C81_81, D82_82] : (((((distinct_points(A79_79, C81_81) & distinct_points(B80_80, C81_81)) & ~apart_point_and_line(C81_81, L78_78)) & left_apart_point(D82_82, L78_78)) => ((before_on_line(L78_78, A79_79, B80_80) & before_on_line(L78_78, B80_80, C81_81)) => before_on_line(L78_78, A79_79, C81_81))))
% 2.27/1.05
% 2.27/1.05 [1] ALPHA_AND : (! [A21_21] : (~distinct_points(A21_21, A21_21)) & ! [A22_22, B23_23, C24_24] : ((distinct_points(A22_22, B23_23) => (distinct_points(A22_22, C24_24) | distinct_points(B23_23, C24_24)))) & ! [L25_25] : (~distinct_lines(L25_25, L25_25)) & ! [L26_26, M27_27, N28_28] : ((distinct_lines(L26_26, M27_27) => (distinct_lines(L26_26, N28_28) | distinct_lines(M27_27, N28_28)))) & ! [L29_29] : (~unequally_directed_lines(L29_29, L29_29)) & ! [L30_30, M31_31, N32_32] : ((unequally_directed_lines(L30_30, M31_31) => (unequally_directed_lines(L30_30, N32_32) | unequally_directed_lines(M31_31, N32_32)))) & ! [L33_33, M34_34, N35_35] : (((unequally_directed_lines(L33_33, M34_34) & unequally_directed_lines(L33_33, reverse_line(M34_34))) => ((unequally_directed_lines(L33_33, N35_35) & unequally_directed_lines(L33_33, reverse_line(N35_35))) | (unequally_directed_lines(M34_34, N35_35) & unequally_directed_lines(M34_34, reverse_line(N35_35)))))) & ! [L36_36, M37_37] : (((line(L36_36) & line(M37_37)) => (unequally_directed_lines(L36_36, M37_37) | unequally_directed_lines(L36_36, reverse_line(M37_37))))) & ! [L38_38, M39_39] : (((unequally_directed_lines(L38_38, M39_39) & unequally_directed_lines(L38_38, reverse_line(M39_39))) => (left_convergent_lines(L38_38, M39_39) | left_convergent_lines(L38_38, reverse_line(M39_39))))) & ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41)))) & ! [L42_42, M43_43] : (~(left_convergent_lines(L42_42, M43_43) | left_convergent_lines(L42_42, reverse_line(M43_43)))) & ! [A44_44, B45_45] : ((((point(A44_44) & point(B45_45)) & distinct_points(A44_44, B45_45)) => line(line_connecting(A44_44, B45_45)))) & ! [L46_46, M47_47] : (((((line(L46_46) & line(M47_47)) & unequally_directed_lines(L46_46, M47_47)) & unequally_directed_lines(L46_46, reverse_line(M47_47))) => point(intersection_point(L46_46, M47_47)))) & ! [L48_48, A49_49] : (((point(A49_49) & line(L48_48)) => line(parallel_through_point(L48_48, A49_49)))) & ! [L50_50] : ((line(L50_50) => line(reverse_line(L50_50)))) & ! [A51_51, B52_52] : ((distinct_points(A51_51, B52_52) => (~apart_point_and_line(A51_51, line_connecting(A51_51, B52_52)) & ~apart_point_and_line(B52_52, line_connecting(A51_51, B52_52))))) & ! [L53_53, M54_54] : (((unequally_directed_lines(L53_53, M54_54) & unequally_directed_lines(L53_53, reverse_line(M54_54))) => (~apart_point_and_line(intersection_point(L53_53, M54_54), L53_53) & ~apart_point_and_line(intersection_point(L53_53, M54_54), M54_54)))) & ! [A55_55, L56_56] : (~apart_point_and_line(A55_55, parallel_through_point(L56_56, A55_55))) & ! [L57_57] : (~distinct_lines(L57_57, reverse_line(L57_57))) & ! [A58_58, B59_59] : (~unequally_directed_lines(line_connecting(A58_58, B59_59), reverse_line(line_connecting(B59_59, A58_58)))) & ! [A60_60, L61_61] : (~unequally_directed_lines(parallel_through_point(L61_61, A60_60), L61_61)) & ! [A62_62, B63_63, L64_64, M65_65] : (((distinct_points(A62_62, B63_63) & distinct_lines(L64_64, M65_65)) => (((((((left_apart_point(A62_62, L64_64) | left_apart_point(B63_63, L64_64)) | left_apart_point(A62_62, M65_65)) | left_apart_point(B63_63, M65_65)) | left_apart_point(A62_62, reverse_line(L64_64))) | left_apart_point(B63_63, reverse_line(L64_64))) | left_apart_point(A62_62, reverse_line(M65_65))) | left_apart_point(B63_63, reverse_line(M65_65))))) & ! [A66_66, B67_67, L68_68] : (((distinct_points(A66_66, B67_67) & left_apart_point(A66_66, L68_68)) => (left_apart_point(B67_67, L68_68) | left_convergent_lines(line_connecting(A66_66, B67_67), L68_68)))) & ! [A69_69, B70_70, L71_71] : ((left_apart_point(A69_69, L71_71) => (distinct_points(A69_69, B70_70) | left_apart_point(B70_70, L71_71)))) & ! [A72_72, L73_73, M74_74] : (((left_apart_point(A72_72, L73_73) & unequally_directed_lines(L73_73, M74_74)) => (distinct_lines(L73_73, M74_74) | left_apart_point(A72_72, reverse_line(M74_74))))) & ! [L75_75, M76_76, N77_77] : ((left_convergent_lines(L75_75, M76_76) => (unequally_directed_lines(M76_76, N77_77) | left_convergent_lines(L75_75, N77_77)))))
% 2.27/1.05 -> [2] ! [A21_21] : (~distinct_points(A21_21, A21_21)), ! [A22_22, B23_23, C24_24] : ((distinct_points(A22_22, B23_23) => (distinct_points(A22_22, C24_24) | distinct_points(B23_23, C24_24)))), ! [L25_25] : (~distinct_lines(L25_25, L25_25)), ! [L26_26, M27_27, N28_28] : ((distinct_lines(L26_26, M27_27) => (distinct_lines(L26_26, N28_28) | distinct_lines(M27_27, N28_28)))), ! [L29_29] : (~unequally_directed_lines(L29_29, L29_29)), ! [L30_30, M31_31, N32_32] : ((unequally_directed_lines(L30_30, M31_31) => (unequally_directed_lines(L30_30, N32_32) | unequally_directed_lines(M31_31, N32_32)))), ! [L33_33, M34_34, N35_35] : (((unequally_directed_lines(L33_33, M34_34) & unequally_directed_lines(L33_33, reverse_line(M34_34))) => ((unequally_directed_lines(L33_33, N35_35) & unequally_directed_lines(L33_33, reverse_line(N35_35))) | (unequally_directed_lines(M34_34, N35_35) & unequally_directed_lines(M34_34, reverse_line(N35_35)))))), ! [L36_36, M37_37] : (((line(L36_36) & line(M37_37)) => (unequally_directed_lines(L36_36, M37_37) | unequally_directed_lines(L36_36, reverse_line(M37_37))))), ! [L38_38, M39_39] : (((unequally_directed_lines(L38_38, M39_39) & unequally_directed_lines(L38_38, reverse_line(M39_39))) => (left_convergent_lines(L38_38, M39_39) | left_convergent_lines(L38_38, reverse_line(M39_39))))), ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41)))), ! [L42_42, M43_43] : (~(left_convergent_lines(L42_42, M43_43) | left_convergent_lines(L42_42, reverse_line(M43_43)))), ! [A44_44, B45_45] : ((((point(A44_44) & point(B45_45)) & distinct_points(A44_44, B45_45)) => line(line_connecting(A44_44, B45_45)))), ! [L46_46, M47_47] : (((((line(L46_46) & line(M47_47)) & unequally_directed_lines(L46_46, M47_47)) & unequally_directed_lines(L46_46, reverse_line(M47_47))) => point(intersection_point(L46_46, M47_47)))), ! [L48_48, A49_49] : (((point(A49_49) & line(L48_48)) => line(parallel_through_point(L48_48, A49_49)))), ! [L50_50] : ((line(L50_50) => line(reverse_line(L50_50)))), ! [A51_51, B52_52] : ((distinct_points(A51_51, B52_52) => (~apart_point_and_line(A51_51, line_connecting(A51_51, B52_52)) & ~apart_point_and_line(B52_52, line_connecting(A51_51, B52_52))))), ! [L53_53, M54_54] : (((unequally_directed_lines(L53_53, M54_54) & unequally_directed_lines(L53_53, reverse_line(M54_54))) => (~apart_point_and_line(intersection_point(L53_53, M54_54), L53_53) & ~apart_point_and_line(intersection_point(L53_53, M54_54), M54_54)))), ! [A55_55, L56_56] : (~apart_point_and_line(A55_55, parallel_through_point(L56_56, A55_55))), ! [L57_57] : (~distinct_lines(L57_57, reverse_line(L57_57))), ! [A58_58, B59_59] : (~unequally_directed_lines(line_connecting(A58_58, B59_59), reverse_line(line_connecting(B59_59, A58_58)))), ! [A60_60, L61_61] : (~unequally_directed_lines(parallel_through_point(L61_61, A60_60), L61_61)), ! [A62_62, B63_63, L64_64, M65_65] : (((distinct_points(A62_62, B63_63) & distinct_lines(L64_64, M65_65)) => (((((((left_apart_point(A62_62, L64_64) | left_apart_point(B63_63, L64_64)) | left_apart_point(A62_62, M65_65)) | left_apart_point(B63_63, M65_65)) | left_apart_point(A62_62, reverse_line(L64_64))) | left_apart_point(B63_63, reverse_line(L64_64))) | left_apart_point(A62_62, reverse_line(M65_65))) | left_apart_point(B63_63, reverse_line(M65_65))))), ! [A66_66, B67_67, L68_68] : (((distinct_points(A66_66, B67_67) & left_apart_point(A66_66, L68_68)) => (left_apart_point(B67_67, L68_68) | left_convergent_lines(line_connecting(A66_66, B67_67), L68_68)))), ! [A69_69, B70_70, L71_71] : ((left_apart_point(A69_69, L71_71) => (distinct_points(A69_69, B70_70) | left_apart_point(B70_70, L71_71)))), ! [A72_72, L73_73, M74_74] : (((left_apart_point(A72_72, L73_73) & unequally_directed_lines(L73_73, M74_74)) => (distinct_lines(L73_73, M74_74) | left_apart_point(A72_72, reverse_line(M74_74))))), ! [L75_75, M76_76, N77_77] : ((left_convergent_lines(L75_75, M76_76) => (unequally_directed_lines(M76_76, N77_77) | left_convergent_lines(L75_75, N77_77))))
% 2.27/1.05
% 2.27/1.05 [2] DELTA_NOT_FORALL : ~! [L78_78, A79_79, B80_80, C81_81, D82_82] : (((((distinct_points(A79_79, C81_81) & distinct_points(B80_80, C81_81)) & ~apart_point_and_line(C81_81, L78_78)) & left_apart_point(D82_82, L78_78)) => ((before_on_line(L78_78, A79_79, B80_80) & before_on_line(L78_78, B80_80, C81_81)) => before_on_line(L78_78, A79_79, C81_81))))
% 2.27/1.05 -> [3] ~((((distinct_points(skolem_A7979, skolem_C8181) & distinct_points(skolem_B8080, skolem_C8181)) & ~apart_point_and_line(skolem_C8181, skolem_L7878)) & left_apart_point(skolem_D8282, skolem_L7878)) => ((before_on_line(skolem_L7878, skolem_A7979, skolem_B8080) & before_on_line(skolem_L7878, skolem_B8080, skolem_C8181)) => before_on_line(skolem_L7878, skolem_A7979, skolem_C8181)))
% 2.27/1.05
% 2.27/1.05 [3] ALPHA_NOT_IMPLY : ~((((distinct_points(skolem_A7979, skolem_C8181) & distinct_points(skolem_B8080, skolem_C8181)) & ~apart_point_and_line(skolem_C8181, skolem_L7878)) & left_apart_point(skolem_D8282, skolem_L7878)) => ((before_on_line(skolem_L7878, skolem_A7979, skolem_B8080) & before_on_line(skolem_L7878, skolem_B8080, skolem_C8181)) => before_on_line(skolem_L7878, skolem_A7979, skolem_C8181)))
% 2.27/1.05 -> [4] (((distinct_points(skolem_A7979, skolem_C8181) & distinct_points(skolem_B8080, skolem_C8181)) & ~apart_point_and_line(skolem_C8181, skolem_L7878)) & left_apart_point(skolem_D8282, skolem_L7878)), ~((before_on_line(skolem_L7878, skolem_A7979, skolem_B8080) & before_on_line(skolem_L7878, skolem_B8080, skolem_C8181)) => before_on_line(skolem_L7878, skolem_A7979, skolem_C8181))
% 2.27/1.05
% 2.27/1.05 [4] ALPHA_AND : (((distinct_points(skolem_A7979, skolem_C8181) & distinct_points(skolem_B8080, skolem_C8181)) & ~apart_point_and_line(skolem_C8181, skolem_L7878)) & left_apart_point(skolem_D8282, skolem_L7878))
% 2.27/1.05 -> [5] ((distinct_points(skolem_A7979, skolem_C8181) & distinct_points(skolem_B8080, skolem_C8181)) & ~apart_point_and_line(skolem_C8181, skolem_L7878)), left_apart_point(skolem_D8282, skolem_L7878)
% 2.27/1.05
% 2.27/1.05 [5] ALPHA_NOT_IMPLY : ~((before_on_line(skolem_L7878, skolem_A7979, skolem_B8080) & before_on_line(skolem_L7878, skolem_B8080, skolem_C8181)) => before_on_line(skolem_L7878, skolem_A7979, skolem_C8181))
% 2.27/1.05 -> [6] (before_on_line(skolem_L7878, skolem_A7979, skolem_B8080) & before_on_line(skolem_L7878, skolem_B8080, skolem_C8181)), ~before_on_line(skolem_L7878, skolem_A7979, skolem_C8181)
% 2.27/1.05
% 2.27/1.05 [6] Rewrite : ~before_on_line(skolem_L7878, skolem_A7979, skolem_C8181)
% 2.27/1.05 -> [7] ~(((distinct_points(skolem_A7979, skolem_C8181) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))) & ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)))
% 2.27/1.05
% 2.27/1.05 [7] ALPHA_AND : ((distinct_points(skolem_A7979, skolem_C8181) & distinct_points(skolem_B8080, skolem_C8181)) & ~apart_point_and_line(skolem_C8181, skolem_L7878))
% 2.27/1.05 -> [8] (distinct_points(skolem_A7979, skolem_C8181) & distinct_points(skolem_B8080, skolem_C8181)), ~apart_point_and_line(skolem_C8181, skolem_L7878)
% 2.27/1.05
% 2.27/1.05 [8] Rewrite : ~apart_point_and_line(skolem_C8181, skolem_L7878)
% 2.27/1.05 -> [9] ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 2.27/1.05
% 2.27/1.05 [9] ALPHA_AND : (before_on_line(skolem_L7878, skolem_A7979, skolem_B8080) & before_on_line(skolem_L7878, skolem_B8080, skolem_C8181))
% 2.27/1.05 -> [10] before_on_line(skolem_L7878, skolem_A7979, skolem_B8080), before_on_line(skolem_L7878, skolem_B8080, skolem_C8181)
% 2.27/1.05
% 2.27/1.05 [10] Rewrite : before_on_line(skolem_L7878, skolem_A7979, skolem_B8080)
% 2.27/1.05 -> [11] (((distinct_points(skolem_A7979, skolem_B8080) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))) & ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080)))
% 2.27/1.05
% 2.27/1.05 [11] Rewrite : before_on_line(skolem_L7878, skolem_B8080, skolem_C8181)
% 2.27/1.05 -> [12] (((distinct_points(skolem_B8080, skolem_C8181) & ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))) & ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_B8080, skolem_C8181)))
% 2.27/1.05
% 2.27/1.05 [12] ALPHA_AND : (distinct_points(skolem_A7979, skolem_C8181) & distinct_points(skolem_B8080, skolem_C8181))
% 2.27/1.05 -> [13] distinct_points(skolem_A7979, skolem_C8181), distinct_points(skolem_B8080, skolem_C8181)
% 2.27/1.05
% 2.27/1.05 [13] ALPHA_NOT_OR : ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 2.27/1.05 -> [14] ~left_apart_point(skolem_C8181, skolem_L7878), ~left_apart_point(skolem_C8181, reverse_line(skolem_L7878))
% 2.27/1.05
% 2.27/1.05 [14] ALPHA_AND : (((distinct_points(skolem_A7979, skolem_B8080) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))) & ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080)))
% 2.27/1.05 -> [15] ((distinct_points(skolem_A7979, skolem_B8080) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))), ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_B8080))
% 2.27/1.05
% 2.27/1.05 [15] ALPHA_AND : (((distinct_points(skolem_B8080, skolem_C8181) & ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))) & ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_B8080, skolem_C8181)))
% 2.27/1.05 -> [16] ((distinct_points(skolem_B8080, skolem_C8181) & ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))), ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_B8080, skolem_C8181))
% 2.27/1.05
% 2.27/1.05 [16] ALPHA_AND : ((distinct_points(skolem_A7979, skolem_B8080) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878))))
% 2.27/1.05 -> [17] (distinct_points(skolem_A7979, skolem_B8080) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))), ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))
% 2.27/1.05
% 2.27/1.05 [17] ALPHA_AND : ((distinct_points(skolem_B8080, skolem_C8181) & ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878))))
% 2.27/1.05 -> [18] (distinct_points(skolem_B8080, skolem_C8181) & ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))), ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 2.27/1.05
% 2.27/1.05 [18] ALPHA_AND : (distinct_points(skolem_A7979, skolem_B8080) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878))))
% 2.27/1.05 -> [19] distinct_points(skolem_A7979, skolem_B8080), ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))
% 2.27/1.05
% 2.27/1.05 [19] ALPHA_NOT_OR : ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))
% 2.27/1.05 -> [20] ~left_apart_point(skolem_B8080, skolem_L7878), ~left_apart_point(skolem_B8080, reverse_line(skolem_L7878))
% 2.27/1.05
% 2.27/1.05 [20] ALPHA_AND : (distinct_points(skolem_B8080, skolem_C8181) & ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878))))
% 2.27/1.05 -> [21] distinct_points(skolem_B8080, skolem_C8181), ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))
% 2.27/1.05
% 2.27/1.05 [21] ALPHA_NOT_OR : ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 2.27/1.05 -> [22] ~left_apart_point(skolem_C8181, skolem_L7878), ~left_apart_point(skolem_C8181, reverse_line(skolem_L7878))
% 2.27/1.05
% 2.27/1.05 [22] ALPHA_NOT_OR : ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))
% 2.27/1.05 -> [23] ~left_apart_point(skolem_A7979, skolem_L7878), ~left_apart_point(skolem_A7979, reverse_line(skolem_L7878))
% 2.27/1.05
% 2.27/1.05 [23] ALPHA_NOT_OR : ~(left_apart_point(skolem_B8080, skolem_L7878) | left_apart_point(skolem_B8080, reverse_line(skolem_L7878)))
% 2.27/1.05 -> [24] ~left_apart_point(skolem_B8080, skolem_L7878), ~left_apart_point(skolem_B8080, reverse_line(skolem_L7878))
% 2.27/1.05
% 2.27/1.05 [24] BETA_NOT_AND : ~(((distinct_points(skolem_A7979, skolem_C8181) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))) & ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)))
% 2.27/1.05 -> [25] ~((distinct_points(skolem_A7979, skolem_C8181) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878))))
% 2.27/1.05 -> [26] ~~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 2.27/1.05
% 2.27/1.05 [25] BETA_NOT_AND : ~((distinct_points(skolem_A7979, skolem_C8181) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))) & ~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878))))
% 2.27/1.05 -> [27] ~(distinct_points(skolem_A7979, skolem_C8181) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878))))
% 2.27/1.05 -> [28] ~~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 2.27/1.05
% 2.27/1.05 [28] ALPHA_NOT_NOT : ~~(left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 2.27/1.05 -> [32] (left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 2.27/1.05
% 2.27/1.05 [32] BETA_OR : (left_apart_point(skolem_C8181, skolem_L7878) | left_apart_point(skolem_C8181, reverse_line(skolem_L7878)))
% 2.27/1.05 -> [33] left_apart_point(skolem_C8181, skolem_L7878)
% 2.27/1.05 -> [34] left_apart_point(skolem_C8181, reverse_line(skolem_L7878))
% 2.27/1.05
% 2.27/1.05 [33] CLOSURE : left_apart_point(skolem_C8181, skolem_L7878)
% 2.27/1.05
% 2.27/1.05 [34] CLOSURE : left_apart_point(skolem_C8181, reverse_line(skolem_L7878))
% 2.27/1.05
% 2.27/1.05 [27] BETA_NOT_AND : ~(distinct_points(skolem_A7979, skolem_C8181) & ~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878))))
% 2.27/1.05 -> [30] ~distinct_points(skolem_A7979, skolem_C8181)
% 2.27/1.05 -> [31] ~~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))
% 2.27/1.05
% 2.27/1.05 [30] CLOSURE : ~distinct_points(skolem_A7979, skolem_C8181)
% 2.27/1.05
% 2.27/1.05 [31] ALPHA_NOT_NOT : ~~(left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))
% 2.27/1.05 -> [35] (left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))
% 2.27/1.05
% 2.27/1.05 [35] BETA_OR : (left_apart_point(skolem_A7979, skolem_L7878) | left_apart_point(skolem_A7979, reverse_line(skolem_L7878)))
% 2.27/1.05 -> [36] left_apart_point(skolem_A7979, skolem_L7878)
% 2.27/1.05 -> [37] left_apart_point(skolem_A7979, reverse_line(skolem_L7878))
% 2.27/1.05
% 2.27/1.05 [36] CLOSURE : left_apart_point(skolem_A7979, skolem_L7878)
% 2.27/1.05
% 2.27/1.05 [37] CLOSURE : left_apart_point(skolem_A7979, reverse_line(skolem_L7878))
% 2.27/1.05
% 2.27/1.05 [26] ALPHA_NOT_NOT : ~~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 2.27/1.05 -> [29] unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 2.27/1.05
% 2.27/1.05 [29] GAMMA_FORALL : ! [A21_21] : (~distinct_points(A21_21, A21_21))
% 2.27/1.05 -> [38] ~distinct_points(skolem_C8181, skolem_C8181)
% 2.27/1.05
% 2.27/1.05 [38] GAMMA_FORALL : ! [A22_22, B23_23, C24_24] : ((distinct_points(A22_22, B23_23) => (distinct_points(A22_22, C24_24) | distinct_points(B23_23, C24_24))))
% 2.27/1.05 -> [39] (distinct_points(skolem_B8080, skolem_C8181) => (distinct_points(skolem_B8080, skolem_C8181) | distinct_points(skolem_C8181, skolem_C8181)))
% 2.27/1.05
% 2.27/1.05 [39] BETA_IMPLY : (distinct_points(skolem_B8080, skolem_C8181) => (distinct_points(skolem_B8080, skolem_C8181) | distinct_points(skolem_C8181, skolem_C8181)))
% 2.27/1.05 -> [40] ~distinct_points(skolem_B8080, skolem_C8181)
% 2.27/1.05 -> [41] (distinct_points(skolem_B8080, skolem_C8181) | distinct_points(skolem_C8181, skolem_C8181))
% 2.27/1.05
% 2.27/1.05 [40] CLOSURE : ~distinct_points(skolem_B8080, skolem_C8181)
% 2.27/1.05
% 2.27/1.05 [41] BETA_OR : (distinct_points(skolem_B8080, skolem_C8181) | distinct_points(skolem_C8181, skolem_C8181))
% 2.27/1.05 -> [44] distinct_points(skolem_B8080, skolem_C8181)
% 2.27/1.05 -> [45] distinct_points(skolem_C8181, skolem_C8181)
% 2.27/1.05
% 2.27/1.05 [45] CLOSURE : distinct_points(skolem_C8181, skolem_C8181)
% 2.27/1.05
% 2.27/1.05 [44] GAMMA_FORALL : ! [L25_25] : (~distinct_lines(L25_25, L25_25))
% 2.27/1.05 -> [46] ~distinct_lines(L26_0_3, L26_0_3)
% 2.27/1.05
% 2.27/1.05 [46] GAMMA_FORALL : ! [L26_26, M27_27, N28_28] : ((distinct_lines(L26_26, M27_27) => (distinct_lines(L26_26, N28_28) | distinct_lines(M27_27, N28_28))))
% 2.27/1.05 -> [47] (distinct_lines(L26_0_3, L26_0_3) => (distinct_lines(L26_0_3, L26_0_3) | distinct_lines(L26_0_3, L26_0_3)))
% 2.27/1.05
% 2.27/1.05 [47] BETA_IMPLY : (distinct_lines(L26_0_3, L26_0_3) => (distinct_lines(L26_0_3, L26_0_3) | distinct_lines(L26_0_3, L26_0_3)))
% 2.27/1.05 -> [48] ~distinct_lines(L26_0_3, L26_0_3)
% 2.27/1.05 -> [49] (distinct_lines(L26_0_3, L26_0_3) | distinct_lines(L26_0_3, L26_0_3))
% 2.27/1.05
% 2.27/1.05 [49] BETA_OR : (distinct_lines(L26_0_3, L26_0_3) | distinct_lines(L26_0_3, L26_0_3))
% 2.27/1.05 -> [50] distinct_lines(L26_0_3, L26_0_3)
% 2.27/1.05 -> [51] distinct_lines(L26_0_3, L26_0_3)
% 2.27/1.05
% 2.27/1.05 [51] CLOSURE : distinct_lines(L26_0_3, L26_0_3)
% 2.27/1.05
% 2.27/1.05 [50] CLOSURE : distinct_lines(L26_0_3, L26_0_3)
% 2.27/1.05
% 2.27/1.05 [48] GAMMA_FORALL : ! [L29_29] : (~unequally_directed_lines(L29_29, L29_29))
% 2.27/1.05 -> [52] ~unequally_directed_lines(skolem_L7878, skolem_L7878)
% 2.27/1.05
% 2.27/1.05 [52] GAMMA_FORALL : ! [L30_30, M31_31, N32_32] : ((unequally_directed_lines(L30_30, M31_31) => (unequally_directed_lines(L30_30, N32_32) | unequally_directed_lines(M31_31, N32_32))))
% 2.27/1.05 -> [53] (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) => (unequally_directed_lines(skolem_L7878, skolem_L7878) | unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)))
% 2.27/1.05
% 2.27/1.05 [53] BETA_IMPLY : (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) => (unequally_directed_lines(skolem_L7878, skolem_L7878) | unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)))
% 2.27/1.05 -> [54] ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 2.27/1.05 -> [55] (unequally_directed_lines(skolem_L7878, skolem_L7878) | unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878))
% 2.27/1.05
% 2.27/1.05 [54] CLOSURE : ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 2.27/1.05
% 2.27/1.05 [55] BETA_OR : (unequally_directed_lines(skolem_L7878, skolem_L7878) | unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878))
% 2.27/1.05 -> [58] unequally_directed_lines(skolem_L7878, skolem_L7878)
% 2.27/1.05 -> [59] unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)
% 2.27/1.05
% 2.27/1.05 [58] CLOSURE : unequally_directed_lines(skolem_L7878, skolem_L7878)
% 2.27/1.05
% 2.27/1.05 [59] GAMMA_FORALL : ! [L33_33, M34_34, N35_35] : (((unequally_directed_lines(L33_33, M34_34) & unequally_directed_lines(L33_33, reverse_line(M34_34))) => ((unequally_directed_lines(L33_33, N35_35) & unequally_directed_lines(L33_33, reverse_line(N35_35))) | (unequally_directed_lines(M34_34, N35_35) & unequally_directed_lines(M34_34, reverse_line(N35_35))))))
% 2.27/1.05 -> [60] ((unequally_directed_lines(skolem_L7878, skolem_L7878) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878))) => ((unequally_directed_lines(skolem_L7878, skolem_L7878) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878))) | (unequally_directed_lines(skolem_L7878, skolem_L7878) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878)))))
% 2.27/1.05
% 2.27/1.05 [60] BETA_IMPLY : ((unequally_directed_lines(skolem_L7878, skolem_L7878) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878))) => ((unequally_directed_lines(skolem_L7878, skolem_L7878) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878))) | (unequally_directed_lines(skolem_L7878, skolem_L7878) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878)))))
% 2.27/1.05 -> [61] ~(unequally_directed_lines(skolem_L7878, skolem_L7878) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878)))
% 2.27/1.05 -> [62] ((unequally_directed_lines(skolem_L7878, skolem_L7878) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878))) | (unequally_directed_lines(skolem_L7878, skolem_L7878) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878))))
% 2.27/1.05
% 2.27/1.05 [62] BETA_OR : ((unequally_directed_lines(skolem_L7878, skolem_L7878) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878))) | (unequally_directed_lines(skolem_L7878, skolem_L7878) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878))))
% 2.27/1.05 -> [65] (unequally_directed_lines(skolem_L7878, skolem_L7878) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878)))
% 2.27/1.05 -> [66] (unequally_directed_lines(skolem_L7878, skolem_L7878) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878)))
% 2.27/1.05
% 2.27/1.05 [65] ALPHA_AND : (unequally_directed_lines(skolem_L7878, skolem_L7878) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878)))
% 2.27/1.05 -> [67] unequally_directed_lines(skolem_L7878, skolem_L7878), unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878))
% 2.27/1.05
% 2.27/1.05 [67] CLOSURE : unequally_directed_lines(skolem_L7878, skolem_L7878)
% 2.27/1.05
% 2.27/1.05 [68] CLOSURE : unequally_directed_lines(skolem_L7878, skolem_L7878)
% 2.27/1.05
% 2.27/1.05 [61] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L7878, skolem_L7878) & unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878)))
% 2.27/1.05 -> [147] ~unequally_directed_lines(skolem_L7878, skolem_L7878)
% 2.27/1.05 -> [148] ~unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878))
% 2.27/1.05
% 2.27/1.05 [148] GAMMA_FORALL : ! [L36_36, M37_37] : (((line(L36_36) & line(M37_37)) => (unequally_directed_lines(L36_36, M37_37) | unequally_directed_lines(L36_36, reverse_line(M37_37)))))
% 2.27/1.05 -> [150] ((line(skolem_L7878) & line(skolem_L7878)) => (unequally_directed_lines(skolem_L7878, skolem_L7878) | unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878))))
% 2.27/1.05
% 2.27/1.05 [150] BETA_IMPLY : ((line(skolem_L7878) & line(skolem_L7878)) => (unequally_directed_lines(skolem_L7878, skolem_L7878) | unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878))))
% 2.27/1.05 -> [153] ~(line(skolem_L7878) & line(skolem_L7878))
% 2.27/1.05 -> [154] (unequally_directed_lines(skolem_L7878, skolem_L7878) | unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878)))
% 2.27/1.05
% 2.27/1.05 [154] BETA_OR : (unequally_directed_lines(skolem_L7878, skolem_L7878) | unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878)))
% 2.27/1.05 -> [161] unequally_directed_lines(skolem_L7878, skolem_L7878)
% 2.27/1.05 -> [162] unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878))
% 2.27/1.05
% 2.27/1.05 [162] CLOSURE : unequally_directed_lines(skolem_L7878, reverse_line(skolem_L7878))
% 2.27/1.05
% 2.27/1.05 [161] CLOSURE : unequally_directed_lines(skolem_L7878, skolem_L7878)
% 2.27/1.05
% 2.27/1.05 [153] BETA_NOT_AND : ~(line(skolem_L7878) & line(skolem_L7878))
% 2.27/1.05 -> [159] ~line(skolem_L7878)
% 2.27/1.05 -> [160] ~line(skolem_L7878)
% 2.27/1.05
% 2.27/1.05 [159] GAMMA_FORALL : ! [L38_38, M39_39] : (((unequally_directed_lines(L38_38, M39_39) & unequally_directed_lines(L38_38, reverse_line(M39_39))) => (left_convergent_lines(L38_38, M39_39) | left_convergent_lines(L38_38, reverse_line(M39_39)))))
% 2.27/1.05 -> [167] ((unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))) => (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))))
% 2.27/1.05
% 2.27/1.05 [167] BETA_IMPLY : ((unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))) => (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))))
% 2.27/1.05 -> [176] ~(unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 2.27/1.05 -> [177] (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 2.27/1.05
% 2.27/1.05 [176] BETA_NOT_AND : ~(unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 2.27/1.05 -> [186] ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)
% 2.27/1.05 -> [187] ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))
% 2.27/1.05
% 2.27/1.05 [186] CLOSURE : ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)
% 2.27/1.05
% 2.27/1.05 [187] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.27/1.05 -> [196] ~(left_apart_point(A40_15_9, L41_15_9) | left_apart_point(A40_15_9, reverse_line(L41_15_9)))
% 2.27/1.05
% 2.27/1.05 [196] ALPHA_NOT_OR : ~(left_apart_point(A40_15_9, L41_15_9) | left_apart_point(A40_15_9, reverse_line(L41_15_9)))
% 2.27/1.05 -> [197] ~left_apart_point(A40_15_9, L41_15_9), ~left_apart_point(A40_15_9, reverse_line(L41_15_9))
% 2.27/1.05
% 2.27/1.05 [197] CLOSURE : ~left_apart_point(A40_15_9, L41_15_9)
% 2.27/1.05
% 2.27/1.05 [177] BETA_OR : (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 2.27/1.05 -> [188] left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)
% 2.27/1.05 -> [189] left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))
% 2.27/1.05
% 2.27/1.05 [188] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.27/1.05 -> [201] ~(left_apart_point(A40_17_9, L41_17_9) | left_apart_point(A40_17_9, reverse_line(L41_17_9)))
% 2.27/1.05
% 2.27/1.05 [201] ALPHA_NOT_OR : ~(left_apart_point(A40_17_9, L41_17_9) | left_apart_point(A40_17_9, reverse_line(L41_17_9)))
% 2.27/1.05 -> [204] ~left_apart_point(A40_17_9, L41_17_9), ~left_apart_point(A40_17_9, reverse_line(L41_17_9))
% 2.27/1.05
% 2.27/1.05 [204] CLOSURE : ~left_apart_point(A40_17_9, L41_17_9)
% 2.27/1.05
% 2.27/1.05 [189] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.27/1.05 -> [222] ~(left_apart_point(A40_28_9, L41_28_9) | left_apart_point(A40_28_9, reverse_line(L41_28_9)))
% 2.27/1.05
% 2.27/1.05 [222] ALPHA_NOT_OR : ~(left_apart_point(A40_28_9, L41_28_9) | left_apart_point(A40_28_9, reverse_line(L41_28_9)))
% 2.27/1.05 -> [225] ~left_apart_point(A40_28_9, L41_28_9), ~left_apart_point(A40_28_9, reverse_line(L41_28_9))
% 2.27/1.05
% 2.27/1.05 [225] CLOSURE : ~left_apart_point(A40_28_9, L41_28_9)
% 2.27/1.05
% 2.27/1.05 [160] GAMMA_FORALL : ! [L38_38, M39_39] : (((unequally_directed_lines(L38_38, M39_39) & unequally_directed_lines(L38_38, reverse_line(M39_39))) => (left_convergent_lines(L38_38, M39_39) | left_convergent_lines(L38_38, reverse_line(M39_39)))))
% 2.27/1.05 -> [174] ((unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))) => (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))))
% 2.27/1.05
% 2.27/1.05 [174] BETA_IMPLY : ((unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))) => (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))))
% 2.27/1.05 -> [178] ~(unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 2.27/1.05 -> [179] (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 2.27/1.05
% 2.27/1.05 [178] BETA_NOT_AND : ~(unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 2.27/1.05 -> [190] ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)
% 2.27/1.05 -> [191] ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))
% 2.27/1.05
% 2.27/1.05 [190] CLOSURE : ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)
% 2.27/1.05
% 2.27/1.05 [191] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.27/1.05 -> [210] ~(left_apart_point(A40_21_9, L41_21_9) | left_apart_point(A40_21_9, reverse_line(L41_21_9)))
% 2.27/1.05
% 2.27/1.05 [210] ALPHA_NOT_OR : ~(left_apart_point(A40_21_9, L41_21_9) | left_apart_point(A40_21_9, reverse_line(L41_21_9)))
% 2.27/1.05 -> [211] ~left_apart_point(A40_21_9, L41_21_9), ~left_apart_point(A40_21_9, reverse_line(L41_21_9))
% 2.27/1.05
% 2.27/1.05 [211] CLOSURE : ~left_apart_point(A40_21_9, L41_21_9)
% 2.27/1.05
% 2.27/1.05 [179] BETA_OR : (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 2.27/1.05 -> [199] left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)
% 2.27/1.05 -> [200] left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))
% 2.27/1.05
% 2.27/1.05 [199] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.27/1.05 -> [214] ~(left_apart_point(A40_23_9, L41_23_9) | left_apart_point(A40_23_9, reverse_line(L41_23_9)))
% 2.27/1.05
% 2.27/1.05 [214] ALPHA_NOT_OR : ~(left_apart_point(A40_23_9, L41_23_9) | left_apart_point(A40_23_9, reverse_line(L41_23_9)))
% 2.27/1.05 -> [219] ~left_apart_point(A40_23_9, L41_23_9), ~left_apart_point(A40_23_9, reverse_line(L41_23_9))
% 2.27/1.05
% 2.27/1.05 [219] CLOSURE : ~left_apart_point(A40_23_9, L41_23_9)
% 2.27/1.05
% 2.27/1.05 [200] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.27/1.05 -> [221] ~(left_apart_point(A40_27_9, L41_27_9) | left_apart_point(A40_27_9, reverse_line(L41_27_9)))
% 2.27/1.05
% 2.27/1.05 [221] ALPHA_NOT_OR : ~(left_apart_point(A40_27_9, L41_27_9) | left_apart_point(A40_27_9, reverse_line(L41_27_9)))
% 2.27/1.05 -> [224] ~left_apart_point(A40_27_9, L41_27_9), ~left_apart_point(A40_27_9, reverse_line(L41_27_9))
% 2.27/1.05
% 2.27/1.05 [224] CLOSURE : ~left_apart_point(A40_27_9, L41_27_9)
% 2.27/1.05
% 2.27/1.05 [147] GAMMA_FORALL : ! [L36_36, M37_37] : (((line(L36_36) & line(M37_37)) => (unequally_directed_lines(L36_36, M37_37) | unequally_directed_lines(L36_36, reverse_line(M37_37)))))
% 2.27/1.05 -> [149] ((line(skolem_L7878) & line(line_connecting(skolem_A7979, skolem_C8181))) => (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))))
% 2.27/1.05
% 2.27/1.05 [149] BETA_IMPLY : ((line(skolem_L7878) & line(line_connecting(skolem_A7979, skolem_C8181))) => (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))))
% 2.27/1.05 -> [151] ~(line(skolem_L7878) & line(line_connecting(skolem_A7979, skolem_C8181)))
% 2.27/1.05 -> [152] (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 2.27/1.05
% 2.27/1.05 [151] BETA_NOT_AND : ~(line(skolem_L7878) & line(line_connecting(skolem_A7979, skolem_C8181)))
% 2.27/1.05 -> [155] ~line(skolem_L7878)
% 2.27/1.05 -> [156] ~line(line_connecting(skolem_A7979, skolem_C8181))
% 2.27/1.05
% 2.27/1.05 [155] GAMMA_FORALL : ! [L38_38, M39_39] : (((unequally_directed_lines(L38_38, M39_39) & unequally_directed_lines(L38_38, reverse_line(M39_39))) => (left_convergent_lines(L38_38, M39_39) | left_convergent_lines(L38_38, reverse_line(M39_39)))))
% 2.27/1.05 -> [163] ((unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))) => (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))))
% 2.27/1.05
% 2.27/1.05 [163] BETA_IMPLY : ((unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))) => (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))))
% 2.27/1.05 -> [164] ~(unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 2.27/1.05 -> [165] (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 2.27/1.05
% 2.27/1.05 [164] BETA_NOT_AND : ~(unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 2.27/1.05 -> [168] ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)
% 2.27/1.05 -> [169] ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))
% 2.27/1.05
% 2.27/1.05 [168] CLOSURE : ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)
% 2.27/1.05
% 2.27/1.05 [169] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.27/1.05 -> [203] ~(left_apart_point(A40_18_9, L41_18_9) | left_apart_point(A40_18_9, reverse_line(L41_18_9)))
% 2.27/1.05
% 2.27/1.05 [203] ALPHA_NOT_OR : ~(left_apart_point(A40_18_9, L41_18_9) | left_apart_point(A40_18_9, reverse_line(L41_18_9)))
% 2.27/1.05 -> [205] ~left_apart_point(A40_18_9, L41_18_9), ~left_apart_point(A40_18_9, reverse_line(L41_18_9))
% 2.27/1.05
% 2.27/1.05 [205] CLOSURE : ~left_apart_point(A40_18_9, L41_18_9)
% 2.27/1.05
% 2.27/1.05 [165] BETA_OR : (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 2.27/1.05 -> [170] left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)
% 2.27/1.05 -> [171] left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))
% 2.27/1.05
% 2.27/1.05 [170] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.27/1.05 -> [207] ~(left_apart_point(A40_20_9, L41_20_9) | left_apart_point(A40_20_9, reverse_line(L41_20_9)))
% 2.27/1.05
% 2.27/1.05 [207] ALPHA_NOT_OR : ~(left_apart_point(A40_20_9, L41_20_9) | left_apart_point(A40_20_9, reverse_line(L41_20_9)))
% 2.27/1.05 -> [209] ~left_apart_point(A40_20_9, L41_20_9), ~left_apart_point(A40_20_9, reverse_line(L41_20_9))
% 2.27/1.05
% 2.27/1.05 [209] CLOSURE : ~left_apart_point(A40_20_9, L41_20_9)
% 2.27/1.05
% 2.27/1.05 [171] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.27/1.05 -> [216] ~(left_apart_point(A40_25_9, L41_25_9) | left_apart_point(A40_25_9, reverse_line(L41_25_9)))
% 2.27/1.05
% 2.27/1.05 [216] ALPHA_NOT_OR : ~(left_apart_point(A40_25_9, L41_25_9) | left_apart_point(A40_25_9, reverse_line(L41_25_9)))
% 2.27/1.05 -> [218] ~left_apart_point(A40_25_9, L41_25_9), ~left_apart_point(A40_25_9, reverse_line(L41_25_9))
% 2.27/1.05
% 2.27/1.05 [218] CLOSURE : ~left_apart_point(A40_25_9, L41_25_9)
% 2.27/1.05
% 2.27/1.05 [156] GAMMA_FORALL : ! [L38_38, M39_39] : (((unequally_directed_lines(L38_38, M39_39) & unequally_directed_lines(L38_38, reverse_line(M39_39))) => (left_convergent_lines(L38_38, M39_39) | left_convergent_lines(L38_38, reverse_line(M39_39)))))
% 2.27/1.05 -> [175] ((unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))) => (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))))
% 2.27/1.05
% 2.27/1.05 [175] BETA_IMPLY : ((unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))) => (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))))
% 2.27/1.05 -> [180] ~(unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 2.27/1.05 -> [181] (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 2.27/1.05
% 2.27/1.05 [180] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 2.27/1.05 -> [194] ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 2.27/1.05 -> [195] ~unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))
% 2.27/1.05
% 2.27/1.05 [194] CLOSURE : ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 2.27/1.05
% 2.27/1.05 [195] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.27/1.05 -> [212] ~(left_apart_point(A40_22_9, L41_22_9) | left_apart_point(A40_22_9, reverse_line(L41_22_9)))
% 2.27/1.05
% 2.27/1.05 [212] ALPHA_NOT_OR : ~(left_apart_point(A40_22_9, L41_22_9) | left_apart_point(A40_22_9, reverse_line(L41_22_9)))
% 2.27/1.05 -> [213] ~left_apart_point(A40_22_9, L41_22_9), ~left_apart_point(A40_22_9, reverse_line(L41_22_9))
% 2.27/1.05
% 2.27/1.05 [213] CLOSURE : ~left_apart_point(A40_22_9, L41_22_9)
% 2.27/1.05
% 2.27/1.05 [181] BETA_OR : (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 2.27/1.05 -> [192] left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 2.27/1.05 -> [193] left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))
% 2.27/1.05
% 2.27/1.05 [192] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.27/1.05 -> [215] ~(left_apart_point(A40_24_9, L41_24_9) | left_apart_point(A40_24_9, reverse_line(L41_24_9)))
% 2.27/1.05
% 2.27/1.05 [215] ALPHA_NOT_OR : ~(left_apart_point(A40_24_9, L41_24_9) | left_apart_point(A40_24_9, reverse_line(L41_24_9)))
% 2.27/1.05 -> [217] ~left_apart_point(A40_24_9, L41_24_9), ~left_apart_point(A40_24_9, reverse_line(L41_24_9))
% 2.27/1.05
% 2.27/1.05 [217] CLOSURE : ~left_apart_point(A40_24_9, L41_24_9)
% 2.27/1.05
% 2.27/1.05 [193] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.27/1.05 -> [220] ~(left_apart_point(A40_26_9, L41_26_9) | left_apart_point(A40_26_9, reverse_line(L41_26_9)))
% 2.27/1.05
% 2.27/1.05 [220] ALPHA_NOT_OR : ~(left_apart_point(A40_26_9, L41_26_9) | left_apart_point(A40_26_9, reverse_line(L41_26_9)))
% 2.27/1.05 -> [223] ~left_apart_point(A40_26_9, L41_26_9), ~left_apart_point(A40_26_9, reverse_line(L41_26_9))
% 2.27/1.05
% 2.27/1.05 [223] CLOSURE : ~left_apart_point(A40_26_9, L41_26_9)
% 2.27/1.05
% 2.27/1.05 [152] BETA_OR : (unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 2.27/1.05 -> [157] unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 2.27/1.05 -> [158] unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))
% 2.27/1.05
% 2.27/1.05 [158] GAMMA_FORALL : ! [L38_38, M39_39] : (((unequally_directed_lines(L38_38, M39_39) & unequally_directed_lines(L38_38, reverse_line(M39_39))) => (left_convergent_lines(L38_38, M39_39) | left_convergent_lines(L38_38, reverse_line(M39_39)))))
% 2.27/1.05 -> [166] ((unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))) => (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))))
% 2.27/1.05
% 2.27/1.05 [166] BETA_IMPLY : ((unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))) => (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))))
% 2.27/1.05 -> [172] ~(unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 2.27/1.05 -> [173] (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 2.27/1.05
% 2.27/1.05 [173] BETA_OR : (left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) | left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 2.27/1.05 -> [184] left_convergent_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 2.27/1.05 -> [185] left_convergent_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))
% 2.27/1.05
% 2.27/1.05 [184] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.27/1.05 -> [198] ~(left_apart_point(A40_16_9, L41_16_9) | left_apart_point(A40_16_9, reverse_line(L41_16_9)))
% 2.27/1.05
% 2.27/1.05 [198] ALPHA_NOT_OR : ~(left_apart_point(A40_16_9, L41_16_9) | left_apart_point(A40_16_9, reverse_line(L41_16_9)))
% 2.27/1.05 -> [202] ~left_apart_point(A40_16_9, L41_16_9), ~left_apart_point(A40_16_9, reverse_line(L41_16_9))
% 2.27/1.05
% 2.27/1.05 [202] CLOSURE : ~left_apart_point(A40_16_9, L41_16_9)
% 2.27/1.05
% 2.27/1.05 [185] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.27/1.05 -> [206] ~(left_apart_point(A40_19_9, L41_19_9) | left_apart_point(A40_19_9, reverse_line(L41_19_9)))
% 2.27/1.05
% 2.27/1.05 [206] ALPHA_NOT_OR : ~(left_apart_point(A40_19_9, L41_19_9) | left_apart_point(A40_19_9, reverse_line(L41_19_9)))
% 2.27/1.05 -> [208] ~left_apart_point(A40_19_9, L41_19_9), ~left_apart_point(A40_19_9, reverse_line(L41_19_9))
% 2.27/1.05
% 2.27/1.05 [208] CLOSURE : ~left_apart_point(A40_19_9, L41_19_9)
% 2.27/1.05
% 2.27/1.05 [172] BETA_NOT_AND : ~(unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181)) & unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181))))
% 2.27/1.05 -> [182] ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 2.27/1.05 -> [183] ~unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))
% 2.27/1.05
% 2.27/1.05 [182] CLOSURE : ~unequally_directed_lines(skolem_L7878, line_connecting(skolem_A7979, skolem_C8181))
% 2.27/1.05
% 2.27/1.05 [183] CLOSURE : ~unequally_directed_lines(skolem_L7878, reverse_line(line_connecting(skolem_A7979, skolem_C8181)))
% 2.27/1.05
% 2.27/1.05 [157] GAMMA_FORALL : ! [L38_38, M39_39] : (((unequally_directed_lines(L38_38, M39_39) & unequally_directed_lines(L38_38, reverse_line(M39_39))) => (left_convergent_lines(L38_38, M39_39) | left_convergent_lines(L38_38, reverse_line(M39_39)))))
% 2.27/1.05 -> [226] ((unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))) => (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))))
% 2.27/1.05
% 2.27/1.05 [226] BETA_IMPLY : ((unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))) => (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))))
% 2.27/1.05 -> [227] ~(unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 2.27/1.05 -> [228] (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 2.27/1.05
% 2.27/1.05 [227] BETA_NOT_AND : ~(unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) & unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 2.27/1.05 -> [229] ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)
% 2.27/1.05 -> [230] ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))
% 2.27/1.05
% 2.27/1.05 [229] CLOSURE : ~unequally_directed_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)
% 2.27/1.05
% 2.27/1.05 [230] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.27/1.05 -> [233] ~(left_apart_point(A40_29_9, L41_29_9) | left_apart_point(A40_29_9, reverse_line(L41_29_9)))
% 2.27/1.05
% 2.27/1.05 [233] ALPHA_NOT_OR : ~(left_apart_point(A40_29_9, L41_29_9) | left_apart_point(A40_29_9, reverse_line(L41_29_9)))
% 2.27/1.05 -> [236] ~left_apart_point(A40_29_9, L41_29_9), ~left_apart_point(A40_29_9, reverse_line(L41_29_9))
% 2.27/1.05
% 2.27/1.05 [236] CLOSURE : ~left_apart_point(A40_29_9, L41_29_9)
% 2.27/1.05
% 2.27/1.05 [228] BETA_OR : (left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878) | left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878)))
% 2.27/1.05 -> [231] left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), skolem_L7878)
% 2.27/1.05 -> [232] left_convergent_lines(line_connecting(skolem_A7979, skolem_C8181), reverse_line(skolem_L7878))
% 2.27/1.05
% 2.27/1.05 [231] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.27/1.05 -> [234] ~(left_apart_point(A40_30_9, L41_30_9) | left_apart_point(A40_30_9, reverse_line(L41_30_9)))
% 2.27/1.05
% 2.27/1.05 [234] ALPHA_NOT_OR : ~(left_apart_point(A40_30_9, L41_30_9) | left_apart_point(A40_30_9, reverse_line(L41_30_9)))
% 2.27/1.05 -> [237] ~left_apart_point(A40_30_9, L41_30_9), ~left_apart_point(A40_30_9, reverse_line(L41_30_9))
% 2.27/1.05
% 2.27/1.05 [237] CLOSURE : ~left_apart_point(A40_30_9, L41_30_9)
% 2.27/1.05
% 2.27/1.05 [232] GAMMA_FORALL : ! [A40_40, L41_41] : (~(left_apart_point(A40_40, L41_41) | left_apart_point(A40_40, reverse_line(L41_41))))
% 2.27/1.05 -> [235] ~(left_apart_point(A40_31_9, L41_31_9) | left_apart_point(A40_31_9, reverse_line(L41_31_9)))
% 2.27/1.05
% 2.27/1.05 [235] ALPHA_NOT_OR : ~(left_apart_point(A40_31_9, L41_31_9) | left_apart_point(A40_31_9, reverse_line(L41_31_9)))
% 2.27/1.05 -> [238] ~left_apart_point(A40_31_9, L41_31_9), ~left_apart_point(A40_31_9, reverse_line(L41_31_9))
% 2.27/1.05
% 2.27/1.05 [238] CLOSURE : ~left_apart_point(A40_31_9, L41_31_9)
% 2.27/1.05
% 2.27/1.05 % SZS output end Proof for theBenchmark.p
% 2.27/1.05 [0.705795s][1][Res] 2752 goroutines created
% 2.27/1.05 ==== Result ====
% 2.27/1.05 [0.705839s][1][Res] VALID
% 2.27/1.05 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------