TSTP Solution File: GEO220+2 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO220+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n016.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 15:18:31 EDT 2022
% Result : Theorem 208.97s 52.28s
% Output : Proof 208.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO220+2 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.32 % Computer : n016.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Wed Aug 31 07:24:02 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33 [DMT] DMT loaded with preskolemization
% 0.12/0.33 [EQ] equality loaded.
% 0.12/0.33 [0.000035s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.33 Conjecture not found
% 0.12/0.33 Conjecture not found
% 0.12/0.33 Start search
% 0.12/0.33 nb_step : 1 - limit : 16
% 0.12/0.33 Launch Gotab with destructive = true
% 208.94/52.24 % SZS output start Proof for theBenchmark.p
% 208.97/52.28 [0] ALPHA_AND : ((! [X8_8] : (~distinct_points(X8_8, X8_8)) & ! [X9_9] : (~distinct_lines(X9_9, X9_9)) & ! [X10_10] : (~convergent_lines(X10_10, X10_10)) & ! [X11_11, Y12_12, Z13_13] : ((distinct_points(X11_11, Y12_12) => (distinct_points(X11_11, Z13_13) | distinct_points(Y12_12, Z13_13)))) & ! [X14_14, Y15_15, Z16_16] : ((distinct_lines(X14_14, Y15_15) => (distinct_lines(X14_14, Z16_16) | distinct_lines(Y15_15, Z16_16)))) & ! [X17_17, Y18_18, Z19_19] : ((convergent_lines(X17_17, Y18_18) => (convergent_lines(X17_17, Z19_19) | convergent_lines(Y18_18, Z19_19)))) & ! [X20_20, Y21_21, Z22_22] : ((distinct_points(X20_20, Y21_21) => (apart_point_and_line(Z22_22, line_connecting(X20_20, Y21_21)) => (distinct_points(Z22_22, X20_20) & distinct_points(Z22_22, Y21_21))))) & ! [X23_23, Y24_24, Z25_25] : ((convergent_lines(X23_23, Y24_24) => ((apart_point_and_line(Z25_25, X23_23) | apart_point_and_line(Z25_25, Y24_24)) => distinct_points(Z25_25, intersection_point(X23_23, Y24_24))))) & ! [X26_26, Y27_27, U28_28, V29_29] : (((distinct_points(X26_26, Y27_27) & distinct_lines(U28_28, V29_29)) => (((apart_point_and_line(X26_26, U28_28) | apart_point_and_line(X26_26, V29_29)) | apart_point_and_line(Y27_27, U28_28)) | apart_point_and_line(Y27_27, V29_29)))) & ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_points(X30_30, Z32_32) | apart_point_and_line(Z32_32, Y31_31)))) & ! [X33_33, Y34_34, Z35_35] : ((apart_point_and_line(X33_33, Y34_34) => (distinct_lines(Y34_34, Z35_35) | apart_point_and_line(X33_33, Z35_35)))) & ! [X36_36, Y37_37] : ((convergent_lines(X36_36, Y37_37) => distinct_lines(X36_36, Y37_37)))) & (! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39))) & ! [L40_40, M41_41, N42_42] : ((((~convergent_lines(L40_40, M41_41) | ~unorthogonal_lines(L40_40, M41_41)) & (~convergent_lines(L40_40, N42_42) | ~unorthogonal_lines(L40_40, N42_42))) => (~convergent_lines(M41_41, N42_42) | ~unorthogonal_lines(M41_41, N42_42)))) & ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45)))) & ~! [L46_46, M47_47, N48_48] : (((~unorthogonal_lines(L46_46, M47_47) & ~unorthogonal_lines(L46_46, N48_48)) => ~convergent_lines(M47_47, N48_48))))
% 208.97/52.28 -> [1] (! [X8_8] : (~distinct_points(X8_8, X8_8)) & ! [X9_9] : (~distinct_lines(X9_9, X9_9)) & ! [X10_10] : (~convergent_lines(X10_10, X10_10)) & ! [X11_11, Y12_12, Z13_13] : ((distinct_points(X11_11, Y12_12) => (distinct_points(X11_11, Z13_13) | distinct_points(Y12_12, Z13_13)))) & ! [X14_14, Y15_15, Z16_16] : ((distinct_lines(X14_14, Y15_15) => (distinct_lines(X14_14, Z16_16) | distinct_lines(Y15_15, Z16_16)))) & ! [X17_17, Y18_18, Z19_19] : ((convergent_lines(X17_17, Y18_18) => (convergent_lines(X17_17, Z19_19) | convergent_lines(Y18_18, Z19_19)))) & ! [X20_20, Y21_21, Z22_22] : ((distinct_points(X20_20, Y21_21) => (apart_point_and_line(Z22_22, line_connecting(X20_20, Y21_21)) => (distinct_points(Z22_22, X20_20) & distinct_points(Z22_22, Y21_21))))) & ! [X23_23, Y24_24, Z25_25] : ((convergent_lines(X23_23, Y24_24) => ((apart_point_and_line(Z25_25, X23_23) | apart_point_and_line(Z25_25, Y24_24)) => distinct_points(Z25_25, intersection_point(X23_23, Y24_24))))) & ! [X26_26, Y27_27, U28_28, V29_29] : (((distinct_points(X26_26, Y27_27) & distinct_lines(U28_28, V29_29)) => (((apart_point_and_line(X26_26, U28_28) | apart_point_and_line(X26_26, V29_29)) | apart_point_and_line(Y27_27, U28_28)) | apart_point_and_line(Y27_27, V29_29)))) & ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_points(X30_30, Z32_32) | apart_point_and_line(Z32_32, Y31_31)))) & ! [X33_33, Y34_34, Z35_35] : ((apart_point_and_line(X33_33, Y34_34) => (distinct_lines(Y34_34, Z35_35) | apart_point_and_line(X33_33, Z35_35)))) & ! [X36_36, Y37_37] : ((convergent_lines(X36_36, Y37_37) => distinct_lines(X36_36, Y37_37)))), (! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39))) & ! [L40_40, M41_41, N42_42] : ((((~convergent_lines(L40_40, M41_41) | ~unorthogonal_lines(L40_40, M41_41)) & (~convergent_lines(L40_40, N42_42) | ~unorthogonal_lines(L40_40, N42_42))) => (~convergent_lines(M41_41, N42_42) | ~unorthogonal_lines(M41_41, N42_42)))) & ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45)))), ~! [L46_46, M47_47, N48_48] : (((~unorthogonal_lines(L46_46, M47_47) & ~unorthogonal_lines(L46_46, N48_48)) => ~convergent_lines(M47_47, N48_48)))
% 208.97/52.28
% 208.97/52.28 [1] ALPHA_AND : (! [X8_8] : (~distinct_points(X8_8, X8_8)) & ! [X9_9] : (~distinct_lines(X9_9, X9_9)) & ! [X10_10] : (~convergent_lines(X10_10, X10_10)) & ! [X11_11, Y12_12, Z13_13] : ((distinct_points(X11_11, Y12_12) => (distinct_points(X11_11, Z13_13) | distinct_points(Y12_12, Z13_13)))) & ! [X14_14, Y15_15, Z16_16] : ((distinct_lines(X14_14, Y15_15) => (distinct_lines(X14_14, Z16_16) | distinct_lines(Y15_15, Z16_16)))) & ! [X17_17, Y18_18, Z19_19] : ((convergent_lines(X17_17, Y18_18) => (convergent_lines(X17_17, Z19_19) | convergent_lines(Y18_18, Z19_19)))) & ! [X20_20, Y21_21, Z22_22] : ((distinct_points(X20_20, Y21_21) => (apart_point_and_line(Z22_22, line_connecting(X20_20, Y21_21)) => (distinct_points(Z22_22, X20_20) & distinct_points(Z22_22, Y21_21))))) & ! [X23_23, Y24_24, Z25_25] : ((convergent_lines(X23_23, Y24_24) => ((apart_point_and_line(Z25_25, X23_23) | apart_point_and_line(Z25_25, Y24_24)) => distinct_points(Z25_25, intersection_point(X23_23, Y24_24))))) & ! [X26_26, Y27_27, U28_28, V29_29] : (((distinct_points(X26_26, Y27_27) & distinct_lines(U28_28, V29_29)) => (((apart_point_and_line(X26_26, U28_28) | apart_point_and_line(X26_26, V29_29)) | apart_point_and_line(Y27_27, U28_28)) | apart_point_and_line(Y27_27, V29_29)))) & ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_points(X30_30, Z32_32) | apart_point_and_line(Z32_32, Y31_31)))) & ! [X33_33, Y34_34, Z35_35] : ((apart_point_and_line(X33_33, Y34_34) => (distinct_lines(Y34_34, Z35_35) | apart_point_and_line(X33_33, Z35_35)))) & ! [X36_36, Y37_37] : ((convergent_lines(X36_36, Y37_37) => distinct_lines(X36_36, Y37_37))))
% 208.97/52.28 -> [2] ! [X8_8] : (~distinct_points(X8_8, X8_8)), ! [X9_9] : (~distinct_lines(X9_9, X9_9)), ! [X10_10] : (~convergent_lines(X10_10, X10_10)), ! [X11_11, Y12_12, Z13_13] : ((distinct_points(X11_11, Y12_12) => (distinct_points(X11_11, Z13_13) | distinct_points(Y12_12, Z13_13)))), ! [X14_14, Y15_15, Z16_16] : ((distinct_lines(X14_14, Y15_15) => (distinct_lines(X14_14, Z16_16) | distinct_lines(Y15_15, Z16_16)))), ! [X17_17, Y18_18, Z19_19] : ((convergent_lines(X17_17, Y18_18) => (convergent_lines(X17_17, Z19_19) | convergent_lines(Y18_18, Z19_19)))), ! [X20_20, Y21_21, Z22_22] : ((distinct_points(X20_20, Y21_21) => (apart_point_and_line(Z22_22, line_connecting(X20_20, Y21_21)) => (distinct_points(Z22_22, X20_20) & distinct_points(Z22_22, Y21_21))))), ! [X23_23, Y24_24, Z25_25] : ((convergent_lines(X23_23, Y24_24) => ((apart_point_and_line(Z25_25, X23_23) | apart_point_and_line(Z25_25, Y24_24)) => distinct_points(Z25_25, intersection_point(X23_23, Y24_24))))), ! [X26_26, Y27_27, U28_28, V29_29] : (((distinct_points(X26_26, Y27_27) & distinct_lines(U28_28, V29_29)) => (((apart_point_and_line(X26_26, U28_28) | apart_point_and_line(X26_26, V29_29)) | apart_point_and_line(Y27_27, U28_28)) | apart_point_and_line(Y27_27, V29_29)))), ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_points(X30_30, Z32_32) | apart_point_and_line(Z32_32, Y31_31)))), ! [X33_33, Y34_34, Z35_35] : ((apart_point_and_line(X33_33, Y34_34) => (distinct_lines(Y34_34, Z35_35) | apart_point_and_line(X33_33, Z35_35)))), ! [X36_36, Y37_37] : ((convergent_lines(X36_36, Y37_37) => distinct_lines(X36_36, Y37_37)))
% 208.97/52.28
% 208.97/52.28 [2] ALPHA_AND : (! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39))) & ! [L40_40, M41_41, N42_42] : ((((~convergent_lines(L40_40, M41_41) | ~unorthogonal_lines(L40_40, M41_41)) & (~convergent_lines(L40_40, N42_42) | ~unorthogonal_lines(L40_40, N42_42))) => (~convergent_lines(M41_41, N42_42) | ~unorthogonal_lines(M41_41, N42_42)))) & ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45))))
% 208.97/52.28 -> [3] ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39))), ! [L40_40, M41_41, N42_42] : ((((~convergent_lines(L40_40, M41_41) | ~unorthogonal_lines(L40_40, M41_41)) & (~convergent_lines(L40_40, N42_42) | ~unorthogonal_lines(L40_40, N42_42))) => (~convergent_lines(M41_41, N42_42) | ~unorthogonal_lines(M41_41, N42_42)))), ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45)))
% 208.97/52.28
% 208.97/52.28 [3] DELTA_NOT_FORALL : ~! [L46_46, M47_47, N48_48] : (((~unorthogonal_lines(L46_46, M47_47) & ~unorthogonal_lines(L46_46, N48_48)) => ~convergent_lines(M47_47, N48_48)))
% 208.97/52.28 -> [4] ~((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [4] ALPHA_NOT_IMPLY : ~((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [5] (~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)), ~~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [5] ALPHA_AND : (~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [6] ~unorthogonal_lines(skolem_L4646, skolem_M4747), ~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [6] ALPHA_NOT_NOT : ~~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [7] convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [7] GAMMA_FORALL : ! [X8_8] : (~distinct_points(X8_8, X8_8))
% 208.97/52.28 -> [8] ~distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [8] GAMMA_FORALL : ! [X9_9] : (~distinct_lines(X9_9, X9_9))
% 208.97/52.28 -> [9] ~distinct_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28
% 208.97/52.28 [9] GAMMA_FORALL : ! [X10_10] : (~convergent_lines(X10_10, X10_10))
% 208.97/52.28 -> [10] ~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [10] GAMMA_FORALL : ! [X11_11, Y12_12, Z13_13] : ((distinct_points(X11_11, Y12_12) => (distinct_points(X11_11, Z13_13) | distinct_points(Y12_12, Z13_13))))
% 208.97/52.28 -> [11] (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) => (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) | distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28
% 208.97/52.28 [11] BETA_IMPLY : (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) => (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) | distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [12] ~distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [13] (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) | distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [13] BETA_OR : (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) | distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28 -> [14] distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [15] distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [14] CLOSURE : distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [15] CLOSURE : distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [16] BETA_IMPLY : (distinct_lines(skolem_L4646, skolem_M4747) => (distinct_lines(skolem_L4646, line_connecting(X20_4_6, intersection_point(skolem_M4747, skolem_N4848))) | distinct_lines(skolem_M4747, line_connecting(X20_4_6, intersection_point(skolem_M4747, skolem_N4848)))))
% 208.97/52.28 -> [8768] ~distinct_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [8769] (distinct_lines(skolem_L4646, line_connecting(X20_4_6, intersection_point(skolem_M4747, skolem_N4848))) | distinct_lines(skolem_M4747, line_connecting(X20_4_6, intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28
% 208.97/52.28 [8768] GAMMA_FORALL : ! [X17_17, Y18_18, Z19_19] : ((convergent_lines(X17_17, Y18_18) => (convergent_lines(X17_17, Z19_19) | convergent_lines(Y18_18, Z19_19))))
% 208.97/52.28 -> [8772] (convergent_lines(skolem_M4747, skolem_N4848) => (convergent_lines(skolem_M4747, skolem_N4848) | convergent_lines(skolem_N4848, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [8772] BETA_IMPLY : (convergent_lines(skolem_M4747, skolem_N4848) => (convergent_lines(skolem_M4747, skolem_N4848) | convergent_lines(skolem_N4848, skolem_N4848)))
% 208.97/52.28 -> [8773] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [8774] (convergent_lines(skolem_M4747, skolem_N4848) | convergent_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [8773] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [8774] BETA_OR : (convergent_lines(skolem_M4747, skolem_N4848) | convergent_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28 -> [8777] convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [8778] convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [8778] CLOSURE : convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [8777] GAMMA_FORALL : ! [X20_20, Y21_21, Z22_22] : ((distinct_points(X20_20, Y21_21) => (apart_point_and_line(Z22_22, line_connecting(X20_20, Y21_21)) => (distinct_points(Z22_22, X20_20) & distinct_points(Z22_22, Y21_21)))))
% 208.97/52.28 -> [8779] (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) => (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) => (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))))
% 208.97/52.28
% 208.97/52.28 [8779] BETA_IMPLY : (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) => (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) => (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))))
% 208.97/52.28 -> [8780] ~distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [8781] (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) => (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28
% 208.97/52.28 [8780] GAMMA_FORALL : ! [X23_23, Y24_24, Z25_25] : ((convergent_lines(X23_23, Y24_24) => ((apart_point_and_line(Z25_25, X23_23) | apart_point_and_line(Z25_25, Y24_24)) => distinct_points(Z25_25, intersection_point(X23_23, Y24_24)))))
% 208.97/52.28 -> [8784] (convergent_lines(skolem_M4747, skolem_N4848) => ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) => distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28
% 208.97/52.28 [8784] BETA_IMPLY : (convergent_lines(skolem_M4747, skolem_N4848) => ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) => distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [8786] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [8787] ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) => distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [8786] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [8787] BETA_IMPLY : ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) => distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28 -> [9064] ~(apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28 -> [9065] distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [9064] ALPHA_NOT_OR : ~(apart_point_and_line(X26_27_8, skolem_M4747) | apart_point_and_line(X26_27_8, skolem_N4848))
% 208.97/52.28 -> [9068] ~apart_point_and_line(X26_27_8, skolem_M4747), ~apart_point_and_line(X26_27_8, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9068] GAMMA_FORALL : ! [X26_26, Y27_27, U28_28, V29_29] : (((distinct_points(X26_26, Y27_27) & distinct_lines(U28_28, V29_29)) => (((apart_point_and_line(X26_26, U28_28) | apart_point_and_line(X26_26, V29_29)) | apart_point_and_line(Y27_27, U28_28)) | apart_point_and_line(Y27_27, V29_29))))
% 208.97/52.28 -> [9069] ((distinct_points(X26_27_8, X26_27_8) & distinct_lines(skolem_M4747, skolem_N4848)) => (((apart_point_and_line(X26_27_8, skolem_M4747) | apart_point_and_line(X26_27_8, skolem_N4848)) | apart_point_and_line(X26_27_8, skolem_M4747)) | apart_point_and_line(X26_27_8, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [9069] BETA_IMPLY : ((distinct_points(X26_27_8, X26_27_8) & distinct_lines(skolem_M4747, skolem_N4848)) => (((apart_point_and_line(X26_27_8, skolem_M4747) | apart_point_and_line(X26_27_8, skolem_N4848)) | apart_point_and_line(X26_27_8, skolem_M4747)) | apart_point_and_line(X26_27_8, skolem_N4848)))
% 208.97/52.28 -> [9070] ~(distinct_points(X26_27_8, X26_27_8) & distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [9071] (((apart_point_and_line(X26_27_8, skolem_M4747) | apart_point_and_line(X26_27_8, skolem_N4848)) | apart_point_and_line(X26_27_8, skolem_M4747)) | apart_point_and_line(X26_27_8, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [9070] BETA_NOT_AND : ~(distinct_points(X26_27_8, X26_27_8) & distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [9072] ~distinct_points(X26_27_8, X26_27_8)
% 208.97/52.28 -> [9073] ~distinct_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9073] GAMMA_FORALL : ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_points(X30_30, Z32_32) | apart_point_and_line(Z32_32, Y31_31))))
% 208.97/52.28 -> [9081] (apart_point_and_line(Z32_84_9, skolem_N4848) => (distinct_points(Z32_84_9, Z32_84_9) | apart_point_and_line(Z32_84_9, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [9081] BETA_IMPLY : (apart_point_and_line(Z32_84_9, skolem_N4848) => (distinct_points(Z32_84_9, Z32_84_9) | apart_point_and_line(Z32_84_9, skolem_N4848)))
% 208.97/52.28 -> [9086] ~apart_point_and_line(Z32_84_9, skolem_N4848)
% 208.97/52.28 -> [9087] (distinct_points(Z32_84_9, Z32_84_9) | apart_point_and_line(Z32_84_9, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [9087] BETA_OR : (distinct_points(Z32_84_9, Z32_84_9) | apart_point_and_line(Z32_84_9, skolem_N4848))
% 208.97/52.28 -> [9088] distinct_points(Z32_84_9, Z32_84_9)
% 208.97/52.28 -> [9089] apart_point_and_line(Z32_84_9, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9089] CLOSURE : apart_point_and_line(Z32_84_9, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9088] CLOSURE : distinct_points(Z32_84_9, Z32_84_9)
% 208.97/52.28
% 208.97/52.28 [9092] BETA_IMPLY : (apart_point_and_line(X33_111_10, Y34_111_10) => (distinct_lines(Y34_111_10, skolem_M4747) | apart_point_and_line(X33_111_10, skolem_M4747)))
% 208.97/52.28 -> [9130] ~apart_point_and_line(X33_111_10, Y34_111_10)
% 208.97/52.28 -> [9131] (distinct_lines(Y34_111_10, skolem_M4747) | apart_point_and_line(X33_111_10, skolem_M4747))
% 208.97/52.28
% 208.97/52.28 [9131] BETA_OR : (distinct_lines(Y34_111_10, skolem_N4848) | apart_point_and_line(X33_111_10, skolem_N4848))
% 208.97/52.28 -> [9132] distinct_lines(Y34_111_10, skolem_N4848)
% 208.97/52.28 -> [9133] apart_point_and_line(X33_111_10, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9132] CLOSURE : distinct_lines(Y34_111_10, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9133] CLOSURE : apart_point_and_line(X33_111_10, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9134] BETA_IMPLY : (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [9158] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [9159] distinct_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9159] CLOSURE : distinct_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9158] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9080] BETA_IMPLY : (apart_point_and_line(Z32_83_9, skolem_M4747) => (distinct_points(Z32_83_9, Z32_83_9) | apart_point_and_line(Z32_83_9, skolem_M4747)))
% 208.97/52.28 -> [9298] ~apart_point_and_line(Z32_83_9, skolem_M4747)
% 208.97/52.28 -> [9299] (distinct_points(Z32_83_9, Z32_83_9) | apart_point_and_line(Z32_83_9, skolem_M4747))
% 208.97/52.28
% 208.97/52.28 [9298] GAMMA_FORALL : ! [X33_33, Y34_34, Z35_35] : ((apart_point_and_line(X33_33, Y34_34) => (distinct_lines(Y34_34, Z35_35) | apart_point_and_line(X33_33, Z35_35))))
% 208.97/52.28 -> [9302] (apart_point_and_line(X33_114_10, Y34_114_10) => (distinct_lines(Y34_114_10, skolem_M4747) | apart_point_and_line(X33_114_10, skolem_M4747)))
% 208.97/52.28
% 208.97/52.28 [9302] BETA_IMPLY : (apart_point_and_line(X33_114_10, Y34_114_10) => (distinct_lines(Y34_114_10, skolem_M4747) | apart_point_and_line(X33_114_10, skolem_M4747)))
% 208.97/52.28 -> [9303] ~apart_point_and_line(X33_114_10, Y34_114_10)
% 208.97/52.28 -> [9304] (distinct_lines(Y34_114_10, skolem_M4747) | apart_point_and_line(X33_114_10, skolem_M4747))
% 208.97/52.28
% 208.97/52.28 [9304] BETA_OR : (distinct_lines(Y34_114_10, skolem_M4747) | apart_point_and_line(X33_114_10, skolem_M4747))
% 208.97/52.28 -> [9305] distinct_lines(Y34_114_10, skolem_M4747)
% 208.97/52.28 -> [9306] apart_point_and_line(X33_114_10, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [9305] CLOSURE : distinct_lines(Y34_114_10, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [9306] CLOSURE : apart_point_and_line(X33_114_10, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [9303] GAMMA_FORALL : ! [X36_36, Y37_37] : ((convergent_lines(X36_36, Y37_37) => distinct_lines(X36_36, Y37_37)))
% 208.97/52.28 -> [9307] (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [9307] BETA_IMPLY : (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [9308] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [9309] distinct_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9308] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9309] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 208.97/52.28 -> [9316] ~(~convergent_lines(skolem_N4848, skolem_N4848) & ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [9316] BETA_NOT_AND : ~(~convergent_lines(skolem_N4848, skolem_N4848) & ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28 -> [9317] ~~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [9318] ~~unorthogonal_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9317] ALPHA_NOT_NOT : ~~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [9320] convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9320] CLOSURE : convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9319] GAMMA_FORALL : ! [L40_40, M41_41, N42_42] : ((((~convergent_lines(L40_40, M41_41) | ~unorthogonal_lines(L40_40, M41_41)) & (~convergent_lines(L40_40, N42_42) | ~unorthogonal_lines(L40_40, N42_42))) => (~convergent_lines(M41_41, N42_42) | ~unorthogonal_lines(M41_41, N42_42))))
% 208.97/52.28 -> [9324] (((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_N4848, skolem_N4848) | ~unorthogonal_lines(skolem_N4848, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [9324] BETA_IMPLY : (((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_N4848, skolem_N4848) | ~unorthogonal_lines(skolem_N4848, skolem_N4848)))
% 208.97/52.28 -> [9325] ~((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [9326] (~convergent_lines(skolem_N4848, skolem_N4848) | ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [9325] BETA_NOT_AND : ~((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [9329] ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [9330] ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [9330] ALPHA_NOT_OR : ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [9334] ~~convergent_lines(skolem_L4646, skolem_N4848), ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9334] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [9336] convergent_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9336] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [9338] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9338] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9337] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9326] BETA_OR : (~convergent_lines(skolem_N4848, skolem_N4848) | ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28 -> [9359] ~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [9360] ~unorthogonal_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9360] CLOSURE : ~unorthogonal_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9359] GAMMA_FORALL : ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45)))
% 208.97/52.28 -> [9361] ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [9361] BETA_IMPLY : ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [9362] ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [9363] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9363] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9362] BETA_NOT_AND : ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [9368] ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [9369] ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9368] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [9370] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [9370] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [9369] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [9371] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9371] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9299] BETA_OR : (distinct_points(Z32_83_9, Z32_83_9) | apart_point_and_line(Z32_83_9, skolem_M4747))
% 208.97/52.28 -> [9372] distinct_points(Z32_83_9, Z32_83_9)
% 208.97/52.28 -> [9373] apart_point_and_line(Z32_83_9, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [9373] CLOSURE : apart_point_and_line(Z32_83_9, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [9372] CLOSURE : distinct_points(Z32_83_9, Z32_83_9)
% 208.97/52.28
% 208.97/52.28 [9071] BETA_OR : (((apart_point_and_line(X26_27_8, skolem_M4747) | apart_point_and_line(X26_27_8, skolem_N4848)) | apart_point_and_line(X26_27_8, skolem_M4747)) | apart_point_and_line(X26_27_8, skolem_N4848))
% 208.97/52.28 -> [9400] ((apart_point_and_line(X26_27_8, skolem_M4747) | apart_point_and_line(X26_27_8, skolem_N4848)) | apart_point_and_line(X26_27_8, skolem_M4747))
% 208.97/52.28 -> [9401] apart_point_and_line(X26_27_8, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9400] BETA_OR : ((apart_point_and_line(X26_27_8, skolem_M4747) | apart_point_and_line(X26_27_8, skolem_N4848)) | apart_point_and_line(X26_27_8, skolem_M4747))
% 208.97/52.28 -> [9402] (apart_point_and_line(X26_27_8, skolem_M4747) | apart_point_and_line(X26_27_8, skolem_N4848))
% 208.97/52.28 -> [9403] apart_point_and_line(X26_27_8, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [9403] CLOSURE : apart_point_and_line(X26_27_8, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [9402] BETA_OR : (apart_point_and_line(X26_27_8, skolem_M4747) | apart_point_and_line(X26_27_8, skolem_N4848))
% 208.97/52.28 -> [9406] apart_point_and_line(X26_27_8, skolem_M4747)
% 208.97/52.28 -> [9407] apart_point_and_line(X26_27_8, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9406] CLOSURE : apart_point_and_line(X26_27_8, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [9407] CLOSURE : apart_point_and_line(X26_27_8, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9401] CLOSURE : apart_point_and_line(X26_27_8, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [9065] CLOSURE : distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [8781] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) => (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [10195] ~apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28 -> [10196] (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [10196] ALPHA_AND : (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28 -> [10197] distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [10197] CLOSURE : distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [10198] BETA_IMPLY : (convergent_lines(skolem_M4747, skolem_N4848) => ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) => distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [11859] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [11860] ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) => distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [11859] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [11860] BETA_IMPLY : ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) => distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28 -> [12669] ~(apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28 -> [12670] distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [12669] ALPHA_NOT_OR : ~(apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28 -> [12671] ~apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747), ~apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12671] GAMMA_FORALL : ! [X26_26, Y27_27, U28_28, V29_29] : (((distinct_points(X26_26, Y27_27) & distinct_lines(U28_28, V29_29)) => (((apart_point_and_line(X26_26, U28_28) | apart_point_and_line(X26_26, V29_29)) | apart_point_and_line(Y27_27, U28_28)) | apart_point_and_line(Y27_27, V29_29))))
% 208.97/52.28 -> [12672] ((distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_lines(line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))) => (((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))))
% 208.97/52.28
% 208.97/52.28 [12672] BETA_IMPLY : ((distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_lines(line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))) => (((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))))
% 208.97/52.28 -> [12673] ~(distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_lines(line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [12674] (((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28
% 208.97/52.28 [12673] BETA_NOT_AND : ~(distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_lines(line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [12675] ~distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [12676] ~distinct_lines(line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [12676] GAMMA_FORALL : ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_points(X30_30, Z32_32) | apart_point_and_line(Z32_32, Y31_31))))
% 208.97/52.28 -> [12682] (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) => (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))))
% 208.97/52.28
% 208.97/52.28 [12682] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) => (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))))
% 208.97/52.28 -> [12687] ~apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28 -> [12688] (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28
% 208.97/52.28 [12688] BETA_OR : (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [12691] distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [12692] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [12691] CLOSURE : distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [12692] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [12694] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), Y34_166_10) => (distinct_lines(Y34_166_10, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))))
% 208.97/52.28 -> [12731] ~apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), Y34_166_10)
% 208.97/52.28 -> [12732] (distinct_lines(Y34_166_10, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28
% 208.97/52.28 [12732] BETA_OR : (distinct_lines(Y34_166_10, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [12735] distinct_lines(Y34_166_10, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28 -> [12736] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [12736] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [12735] CLOSURE : distinct_lines(Y34_166_10, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [12737] BETA_IMPLY : (convergent_lines(skolem_L4646, skolem_L4646) => distinct_lines(skolem_L4646, skolem_L4646))
% 208.97/52.28 -> [12758] ~convergent_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28 -> [12759] distinct_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28
% 208.97/52.28 [12759] CLOSURE : distinct_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28
% 208.97/52.28 [12758] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 208.97/52.28 -> [12760] ~(~convergent_lines(skolem_N4848, skolem_N4848) & ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [12760] BETA_NOT_AND : ~(~convergent_lines(skolem_N4848, skolem_N4848) & ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28 -> [12761] ~~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [12762] ~~unorthogonal_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12761] ALPHA_NOT_NOT : ~~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [12763] convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12763] CLOSURE : convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12764] GAMMA_FORALL : ! [L40_40, M41_41, N42_42] : ((((~convergent_lines(L40_40, M41_41) | ~unorthogonal_lines(L40_40, M41_41)) & (~convergent_lines(L40_40, N42_42) | ~unorthogonal_lines(L40_40, N42_42))) => (~convergent_lines(M41_41, N42_42) | ~unorthogonal_lines(M41_41, N42_42))))
% 208.97/52.28 -> [12773] (((~convergent_lines(skolem_L4646, skolem_L4646) | ~unorthogonal_lines(skolem_L4646, skolem_L4646)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [12773] BETA_IMPLY : (((~convergent_lines(skolem_L4646, skolem_L4646) | ~unorthogonal_lines(skolem_L4646, skolem_L4646)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [12774] ~((~convergent_lines(skolem_L4646, skolem_L4646) | ~unorthogonal_lines(skolem_L4646, skolem_L4646)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [12775] (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [12774] BETA_NOT_AND : ~((~convergent_lines(skolem_L4646, skolem_L4646) | ~unorthogonal_lines(skolem_L4646, skolem_L4646)) & (~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)))
% 208.97/52.28 -> [12776] ~(~convergent_lines(skolem_L4646, skolem_L4646) | ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 208.97/52.28 -> [12777] ~(~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747))
% 208.97/52.28
% 208.97/52.28 [12776] ALPHA_NOT_OR : ~(~convergent_lines(skolem_L4646, skolem_L4646) | ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 208.97/52.28 -> [12780] ~~convergent_lines(skolem_L4646, skolem_L4646), ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28
% 208.97/52.28 [12780] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28 -> [12782] convergent_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28
% 208.97/52.28 [12782] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28 -> [12784] unorthogonal_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28
% 208.97/52.28 [12784] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28
% 208.97/52.28 [12785] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [12775] BETA_OR : (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [12812] ~convergent_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [12813] ~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12812] GAMMA_FORALL : ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45)))
% 208.97/52.28 -> [12815] ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [12815] BETA_IMPLY : ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [12819] ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [12820] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12820] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12819] BETA_NOT_AND : ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [12846] ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [12847] ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12846] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [12850] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [12850] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [12847] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [12851] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12851] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12813] GAMMA_FORALL : ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45)))
% 208.97/52.28 -> [12818] ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [12818] BETA_IMPLY : ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [12821] ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [12822] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12822] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12821] BETA_NOT_AND : ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [12848] ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [12849] ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12848] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [12852] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [12852] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [12849] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [12853] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12853] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12681] BETA_IMPLY : (apart_point_and_line(X30_122_9, skolem_L4646) => (distinct_points(X30_122_9, Z32_122_9) | apart_point_and_line(Z32_122_9, skolem_L4646)))
% 208.97/52.28 -> [12884] ~apart_point_and_line(X30_122_9, skolem_L4646)
% 208.97/52.28 -> [12885] (distinct_points(X30_122_9, Z32_122_9) | apart_point_and_line(Z32_122_9, skolem_L4646))
% 208.97/52.28
% 208.97/52.28 [12884] GAMMA_FORALL : ! [X33_33, Y34_34, Z35_35] : ((apart_point_and_line(X33_33, Y34_34) => (distinct_lines(Y34_34, Z35_35) | apart_point_and_line(X33_33, Z35_35))))
% 208.97/52.28 -> [12888] (apart_point_and_line(X33_167_10, Y34_167_10) => (distinct_lines(Y34_167_10, skolem_M4747) | apart_point_and_line(X33_167_10, skolem_M4747)))
% 208.97/52.28
% 208.97/52.28 [12888] BETA_IMPLY : (apart_point_and_line(X33_167_10, Y34_167_10) => (distinct_lines(Y34_167_10, skolem_M4747) | apart_point_and_line(X33_167_10, skolem_M4747)))
% 208.97/52.28 -> [12889] ~apart_point_and_line(X33_167_10, Y34_167_10)
% 208.97/52.28 -> [12890] (distinct_lines(Y34_167_10, skolem_M4747) | apart_point_and_line(X33_167_10, skolem_M4747))
% 208.97/52.28
% 208.97/52.28 [12890] BETA_OR : (distinct_lines(Y34_167_10, skolem_M4747) | apart_point_and_line(X33_167_10, skolem_M4747))
% 208.97/52.28 -> [12891] distinct_lines(Y34_167_10, skolem_M4747)
% 208.97/52.28 -> [12892] apart_point_and_line(X33_167_10, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [12892] CLOSURE : apart_point_and_line(X33_167_10, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [12891] CLOSURE : distinct_lines(Y34_167_10, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [12889] GAMMA_FORALL : ! [X36_36, Y37_37] : ((convergent_lines(X36_36, Y37_37) => distinct_lines(X36_36, Y37_37)))
% 208.97/52.28 -> [12893] (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [12893] BETA_IMPLY : (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [12894] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [12895] distinct_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12894] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12895] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 208.97/52.28 -> [12896] ~(~convergent_lines(skolem_N4848, skolem_N4848) & ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [12896] BETA_NOT_AND : ~(~convergent_lines(skolem_N4848, skolem_N4848) & ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28 -> [12897] ~~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [12898] ~~unorthogonal_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12897] ALPHA_NOT_NOT : ~~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [12899] convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12899] CLOSURE : convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12900] GAMMA_FORALL : ! [L40_40, M41_41, N42_42] : ((((~convergent_lines(L40_40, M41_41) | ~unorthogonal_lines(L40_40, M41_41)) & (~convergent_lines(L40_40, N42_42) | ~unorthogonal_lines(L40_40, N42_42))) => (~convergent_lines(M41_41, N42_42) | ~unorthogonal_lines(M41_41, N42_42))))
% 208.97/52.28 -> [12901] (((~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_M4747, skolem_N4848) | ~unorthogonal_lines(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [12901] BETA_IMPLY : (((~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_M4747, skolem_N4848) | ~unorthogonal_lines(skolem_M4747, skolem_N4848)))
% 208.97/52.28 -> [12902] ~((~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [12903] (~convergent_lines(skolem_M4747, skolem_N4848) | ~unorthogonal_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [12902] BETA_NOT_AND : ~((~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [12904] ~(~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747))
% 208.97/52.28 -> [12905] ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [12904] ALPHA_NOT_OR : ~(~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747))
% 208.97/52.28 -> [12909] ~~convergent_lines(skolem_L4646, skolem_M4747), ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [12909] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [12911] convergent_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [12911] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [12913] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [12913] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [12912] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12903] BETA_OR : (~convergent_lines(skolem_M4747, skolem_N4848) | ~unorthogonal_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [12925] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [12926] ~unorthogonal_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12925] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12926] GAMMA_FORALL : ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45)))
% 208.97/52.28 -> [12927] ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [12927] BETA_IMPLY : ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [12928] ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [12929] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12929] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12928] BETA_NOT_AND : ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [12934] ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [12935] ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12934] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [12936] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [12936] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [12935] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [12937] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12937] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12885] BETA_OR : (distinct_points(X30_122_9, Z32_122_9) | apart_point_and_line(Z32_122_9, skolem_L4646))
% 208.97/52.28 -> [12938] distinct_points(X30_122_9, Z32_122_9)
% 208.97/52.28 -> [12939] apart_point_and_line(Z32_122_9, skolem_L4646)
% 208.97/52.28
% 208.97/52.28 [12938] CLOSURE : distinct_points(X30_122_9, Z32_122_9)
% 208.97/52.28
% 208.97/52.28 [12940] BETA_IMPLY : (apart_point_and_line(X33_168_10, skolem_L4646) => (distinct_lines(skolem_L4646, skolem_M4747) | apart_point_and_line(X33_168_10, skolem_M4747)))
% 208.97/52.28 -> [12945] ~apart_point_and_line(X33_168_10, skolem_L4646)
% 208.97/52.28 -> [12946] (distinct_lines(skolem_L4646, skolem_M4747) | apart_point_and_line(X33_168_10, skolem_M4747))
% 208.97/52.28
% 208.97/52.28 [12946] BETA_OR : (distinct_lines(skolem_L4646, skolem_M4747) | apart_point_and_line(X33_168_10, skolem_M4747))
% 208.97/52.28 -> [12947] distinct_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [12948] apart_point_and_line(X33_168_10, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [12947] CLOSURE : distinct_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [12948] CLOSURE : apart_point_and_line(X33_168_10, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [12945] CLOSURE : ~apart_point_and_line(X33_168_10, skolem_L4646)
% 208.97/52.28
% 208.97/52.28 [12674] BETA_OR : (((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [12949] ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [12950] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [12950] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [12949] BETA_OR : ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [12957] (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [12958] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [12957] BETA_OR : (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [12959] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28 -> [12960] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [12960] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [12959] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12958] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [12670] CLOSURE : distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [8769] BETA_OR : (distinct_lines(skolem_L4646, line_connecting(X20_4_6, intersection_point(skolem_M4747, skolem_N4848))) | distinct_lines(skolem_M4747, line_connecting(X20_4_6, intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [12961] distinct_lines(skolem_L4646, line_connecting(X20_4_6, intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28 -> [12962] distinct_lines(skolem_M4747, line_connecting(X20_4_6, intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [12962] GAMMA_FORALL : ! [X17_17, Y18_18, Z19_19] : ((convergent_lines(X17_17, Y18_18) => (convergent_lines(X17_17, Z19_19) | convergent_lines(Y18_18, Z19_19))))
% 208.97/52.28 -> [12963] (convergent_lines(skolem_M4747, skolem_N4848) => (convergent_lines(skolem_M4747, skolem_N4848) | convergent_lines(skolem_N4848, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [12963] BETA_IMPLY : (convergent_lines(skolem_M4747, skolem_N4848) => (convergent_lines(skolem_M4747, skolem_N4848) | convergent_lines(skolem_N4848, skolem_N4848)))
% 208.97/52.28 -> [12964] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [12965] (convergent_lines(skolem_M4747, skolem_N4848) | convergent_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [12964] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12965] BETA_OR : (convergent_lines(skolem_M4747, skolem_N4848) | convergent_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28 -> [12968] convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [12969] convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12968] GAMMA_FORALL : ! [X20_20, Y21_21, Z22_22] : ((distinct_points(X20_20, Y21_21) => (apart_point_and_line(Z22_22, line_connecting(X20_20, Y21_21)) => (distinct_points(Z22_22, X20_20) & distinct_points(Z22_22, Y21_21)))))
% 208.97/52.28 -> [12970] (distinct_points(X20_4_6, intersection_point(skolem_M4747, skolem_N4848)) => (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(X20_4_6, intersection_point(skolem_M4747, skolem_N4848))) => (distinct_points(intersection_point(skolem_M4747, skolem_N4848), X20_4_6) & distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))))
% 208.97/52.28
% 208.97/52.28 [12970] BETA_IMPLY : (distinct_points(X20_4_6, intersection_point(skolem_M4747, skolem_N4848)) => (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(X20_4_6, intersection_point(skolem_M4747, skolem_N4848))) => (distinct_points(intersection_point(skolem_M4747, skolem_N4848), X20_4_6) & distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))))
% 208.97/52.28 -> [12971] ~distinct_points(X20_4_6, intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [12972] (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(X20_4_6, intersection_point(skolem_M4747, skolem_N4848))) => (distinct_points(intersection_point(skolem_M4747, skolem_N4848), X20_4_6) & distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28
% 208.97/52.28 [12972] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) => (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [12973] ~apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28 -> [12974] (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [12973] GAMMA_FORALL : ! [X23_23, Y24_24, Z25_25] : ((convergent_lines(X23_23, Y24_24) => ((apart_point_and_line(Z25_25, X23_23) | apart_point_and_line(Z25_25, Y24_24)) => distinct_points(Z25_25, intersection_point(X23_23, Y24_24)))))
% 208.97/52.28 -> [12979] (convergent_lines(skolem_M4747, skolem_N4848) => ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) => distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28
% 208.97/52.28 [12979] BETA_IMPLY : (convergent_lines(skolem_M4747, skolem_N4848) => ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) => distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [12980] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [12981] ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) => distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [12980] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12981] BETA_IMPLY : ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) => distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28 -> [13963] ~(apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28 -> [13964] distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [13964] CLOSURE : distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [13966] BETA_IMPLY : ((distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_lines(skolem_M4747, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))) => (((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))))
% 208.97/52.28 -> [14788] ~(distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_lines(skolem_M4747, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [14789] (((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28
% 208.97/52.28 [14788] BETA_NOT_AND : ~(distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_lines(skolem_M4747, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [14790] ~distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [14791] ~distinct_lines(skolem_M4747, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [14791] CLOSURE : ~distinct_lines(skolem_M4747, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [14798] BETA_IMPLY : (apart_point_and_line(X30_132_9, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) => (distinct_points(X30_132_9, Z32_132_9) | apart_point_and_line(Z32_132_9, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))))
% 208.97/52.28 -> [15138] ~apart_point_and_line(X30_132_9, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28 -> [15139] (distinct_points(X30_132_9, Z32_132_9) | apart_point_and_line(Z32_132_9, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28
% 208.97/52.28 [15139] BETA_OR : (distinct_points(X30_132_9, Z32_132_9) | apart_point_and_line(Z32_132_9, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [15140] distinct_points(X30_132_9, Z32_132_9)
% 208.97/52.28 -> [15141] apart_point_and_line(Z32_132_9, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [15140] CLOSURE : distinct_points(X30_132_9, Z32_132_9)
% 208.97/52.28
% 208.97/52.28 [15141] CLOSURE : apart_point_and_line(Z32_132_9, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [15138] GAMMA_FORALL : ! [X33_33, Y34_34, Z35_35] : ((apart_point_and_line(X33_33, Y34_34) => (distinct_lines(Y34_34, Z35_35) | apart_point_and_line(X33_33, Z35_35))))
% 208.97/52.28 -> [15142] (apart_point_and_line(X33_183_10, Y34_183_10) => (distinct_lines(Y34_183_10, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) | apart_point_and_line(X33_183_10, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))))
% 208.97/52.28
% 208.97/52.28 [15142] BETA_IMPLY : (apart_point_and_line(X33_183_10, Y34_183_10) => (distinct_lines(Y34_183_10, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) | apart_point_and_line(X33_183_10, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))))
% 208.97/52.28 -> [15143] ~apart_point_and_line(X33_183_10, Y34_183_10)
% 208.97/52.28 -> [15144] (distinct_lines(Y34_183_10, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) | apart_point_and_line(X33_183_10, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28
% 208.97/52.28 [15144] BETA_OR : (distinct_lines(Y34_183_10, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) | apart_point_and_line(X33_183_10, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [15145] distinct_lines(Y34_183_10, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28 -> [15146] apart_point_and_line(X33_183_10, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [15146] CLOSURE : apart_point_and_line(X33_183_10, line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [15145] GAMMA_FORALL : ! [X36_36, Y37_37] : ((convergent_lines(X36_36, Y37_37) => distinct_lines(X36_36, Y37_37)))
% 208.97/52.28 -> [15154] (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [15154] BETA_IMPLY : (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [15155] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [15156] distinct_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15155] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15156] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 208.97/52.28 -> [15170] ~(~convergent_lines(skolem_N4848, skolem_N4848) & ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [15170] BETA_NOT_AND : ~(~convergent_lines(skolem_N4848, skolem_N4848) & ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28 -> [15171] ~~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [15172] ~~unorthogonal_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15171] ALPHA_NOT_NOT : ~~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [15173] convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15173] CLOSURE : convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15174] GAMMA_FORALL : ! [L40_40, M41_41, N42_42] : ((((~convergent_lines(L40_40, M41_41) | ~unorthogonal_lines(L40_40, M41_41)) & (~convergent_lines(L40_40, N42_42) | ~unorthogonal_lines(L40_40, N42_42))) => (~convergent_lines(M41_41, N42_42) | ~unorthogonal_lines(M41_41, N42_42))))
% 208.97/52.28 -> [15192] (((~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_M4747, skolem_N4848) | ~unorthogonal_lines(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [15192] BETA_IMPLY : (((~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_M4747, skolem_N4848) | ~unorthogonal_lines(skolem_M4747, skolem_N4848)))
% 208.97/52.28 -> [15193] ~((~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [15194] (~convergent_lines(skolem_M4747, skolem_N4848) | ~unorthogonal_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [15193] BETA_NOT_AND : ~((~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [15195] ~(~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747))
% 208.97/52.28 -> [15196] ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [15195] ALPHA_NOT_OR : ~(~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747))
% 208.97/52.28 -> [15197] ~~convergent_lines(skolem_L4646, skolem_M4747), ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [15197] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [15201] convergent_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [15201] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [15204] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [15204] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [15205] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15194] BETA_OR : (~convergent_lines(skolem_M4747, skolem_N4848) | ~unorthogonal_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [15239] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [15240] ~unorthogonal_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15239] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15240] GAMMA_FORALL : ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45)))
% 208.97/52.28 -> [15242] ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [15242] BETA_IMPLY : ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [15246] ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [15247] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15247] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15246] BETA_NOT_AND : ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [15273] ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [15274] ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15273] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [15277] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [15277] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [15274] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [15278] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15278] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15143] GAMMA_FORALL : ! [X36_36, Y37_37] : ((convergent_lines(X36_36, Y37_37) => distinct_lines(X36_36, Y37_37)))
% 208.97/52.28 -> [15147] (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [15147] BETA_IMPLY : (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [15148] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [15149] distinct_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15148] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15149] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 208.97/52.28 -> [15157] ~(~convergent_lines(skolem_N4848, skolem_N4848) & ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [15157] BETA_NOT_AND : ~(~convergent_lines(skolem_N4848, skolem_N4848) & ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28 -> [15158] ~~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [15159] ~~unorthogonal_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15158] ALPHA_NOT_NOT : ~~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [15160] convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15160] CLOSURE : convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15161] GAMMA_FORALL : ! [L40_40, M41_41, N42_42] : ((((~convergent_lines(L40_40, M41_41) | ~unorthogonal_lines(L40_40, M41_41)) & (~convergent_lines(L40_40, N42_42) | ~unorthogonal_lines(L40_40, N42_42))) => (~convergent_lines(M41_41, N42_42) | ~unorthogonal_lines(M41_41, N42_42))))
% 208.97/52.28 -> [15179] (((~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_M4747, skolem_N4848) | ~unorthogonal_lines(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [15179] BETA_IMPLY : (((~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_M4747, skolem_N4848) | ~unorthogonal_lines(skolem_M4747, skolem_N4848)))
% 208.97/52.28 -> [15180] ~((~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [15181] (~convergent_lines(skolem_M4747, skolem_N4848) | ~unorthogonal_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [15180] BETA_NOT_AND : ~((~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [15182] ~(~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747))
% 208.97/52.28 -> [15183] ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [15182] ALPHA_NOT_OR : ~(~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747))
% 208.97/52.28 -> [15186] ~~convergent_lines(skolem_L4646, skolem_M4747), ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [15186] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [15188] convergent_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [15188] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [15190] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [15190] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [15191] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15181] BETA_OR : (~convergent_lines(skolem_M4747, skolem_N4848) | ~unorthogonal_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [15237] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [15238] ~unorthogonal_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15237] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15238] GAMMA_FORALL : ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45)))
% 208.97/52.28 -> [15241] ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [15241] BETA_IMPLY : ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [15243] ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [15244] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15244] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15243] BETA_NOT_AND : ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [15275] ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [15276] ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15276] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [15282] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15282] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [15275] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [15285] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [15285] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [14789] BETA_OR : (((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [15303] ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747))
% 208.97/52.28 -> [15304] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [15304] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [15303] BETA_OR : ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747))
% 208.97/52.28 -> [15317] (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [15318] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [15318] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [15317] BETA_OR : (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [15319] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28 -> [15320] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [15319] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [15320] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [12976] CLOSURE : distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [12975] BETA_IMPLY : (convergent_lines(skolem_M4747, skolem_N4848) => ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) => distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [16145] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [16146] ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) => distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [16145] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [16146] BETA_IMPLY : ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) => distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28 -> [17286] ~(apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28 -> [17287] distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [17287] CLOSURE : distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [17289] BETA_IMPLY : ((distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_lines(skolem_N4848, skolem_N4848)) => (((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)))
% 208.97/52.28 -> [17732] ~(distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28 -> [17733] (((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [17733] BETA_OR : (((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28 -> [17736] ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28 -> [17737] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17737] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17736] BETA_OR : ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28 -> [17773] (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28 -> [17774] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17773] BETA_OR : (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28 -> [17779] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28 -> [17780] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17780] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17779] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17774] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17732] BETA_NOT_AND : ~(distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28 -> [17865] ~distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [17866] ~distinct_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17865] GAMMA_FORALL : ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_points(X30_30, Z32_32) | apart_point_and_line(Z32_32, Y31_31))))
% 208.97/52.28 -> [17867] (apart_point_and_line(X30_146_9, skolem_M4747) => (distinct_points(X30_146_9, intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)))
% 208.97/52.28
% 208.97/52.28 [17867] BETA_IMPLY : (apart_point_and_line(X30_146_9, skolem_M4747) => (distinct_points(X30_146_9, intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)))
% 208.97/52.28 -> [17869] ~apart_point_and_line(X30_146_9, skolem_M4747)
% 208.97/52.28 -> [17870] (distinct_points(X30_146_9, intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747))
% 208.97/52.28
% 208.97/52.28 [17870] BETA_OR : (distinct_points(X30_146_9, intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747))
% 208.97/52.28 -> [17873] distinct_points(X30_146_9, intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [17874] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [17874] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [17873] CLOSURE : distinct_points(X30_146_9, intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [17869] GAMMA_FORALL : ! [X33_33, Y34_34, Z35_35] : ((apart_point_and_line(X33_33, Y34_34) => (distinct_lines(Y34_34, Z35_35) | apart_point_and_line(X33_33, Z35_35))))
% 208.97/52.28 -> [17877] (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), Y34_202_10) => (distinct_lines(Y34_202_10, skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)))
% 208.97/52.28
% 208.97/52.28 [17877] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), Y34_202_10) => (distinct_lines(Y34_202_10, skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)))
% 208.97/52.28 -> [17881] ~apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), Y34_202_10)
% 208.97/52.28 -> [17882] (distinct_lines(Y34_202_10, skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747))
% 208.97/52.28
% 208.97/52.28 [17881] GAMMA_FORALL : ! [X36_36, Y37_37] : ((convergent_lines(X36_36, Y37_37) => distinct_lines(X36_36, Y37_37)))
% 208.97/52.28 -> [17888] (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [17888] BETA_IMPLY : (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [17891] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [17892] distinct_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17891] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17892] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 208.97/52.28 -> [17897] ~(~convergent_lines(skolem_N4848, skolem_N4848) & ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [17897] BETA_NOT_AND : ~(~convergent_lines(skolem_N4848, skolem_N4848) & ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28 -> [17900] ~~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [17901] ~~unorthogonal_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17900] ALPHA_NOT_NOT : ~~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [17903] convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17903] CLOSURE : convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17906] GAMMA_FORALL : ! [L40_40, M41_41, N42_42] : ((((~convergent_lines(L40_40, M41_41) | ~unorthogonal_lines(L40_40, M41_41)) & (~convergent_lines(L40_40, N42_42) | ~unorthogonal_lines(L40_40, N42_42))) => (~convergent_lines(M41_41, N42_42) | ~unorthogonal_lines(M41_41, N42_42))))
% 208.97/52.28 -> [17913] (((~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_M4747, skolem_N4848) | ~unorthogonal_lines(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [17913] BETA_IMPLY : (((~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_M4747, skolem_N4848) | ~unorthogonal_lines(skolem_M4747, skolem_N4848)))
% 208.97/52.28 -> [17917] ~((~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [17918] (~convergent_lines(skolem_M4747, skolem_N4848) | ~unorthogonal_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [17918] BETA_OR : (~convergent_lines(skolem_M4747, skolem_N4848) | ~unorthogonal_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [17925] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [17926] ~unorthogonal_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17925] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17926] GAMMA_FORALL : ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45)))
% 208.97/52.28 -> [17957] ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [17957] BETA_IMPLY : ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [17960] ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [17961] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17961] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17960] BETA_NOT_AND : ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [18008] ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [18009] ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18008] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [18012] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [18012] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [18009] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [18013] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18013] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17917] BETA_NOT_AND : ~((~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [18033] ~(~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747))
% 208.97/52.28 -> [18034] ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [18034] ALPHA_NOT_OR : ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [18039] ~~convergent_lines(skolem_L4646, skolem_N4848), ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18039] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [18042] convergent_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18042] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [18043] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18043] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18033] ALPHA_NOT_OR : ~(~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747))
% 208.97/52.28 -> [18037] ~~convergent_lines(skolem_L4646, skolem_M4747), ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [18037] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [18040] convergent_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [18040] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [18044] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [18044] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [17882] BETA_OR : (distinct_lines(Y34_202_10, skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747))
% 208.97/52.28 -> [17885] distinct_lines(Y34_202_10, skolem_M4747)
% 208.97/52.28 -> [17886] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [17886] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [17885] GAMMA_FORALL : ! [X36_36, Y37_37] : ((convergent_lines(X36_36, Y37_37) => distinct_lines(X36_36, Y37_37)))
% 208.97/52.28 -> [17896] (convergent_lines(skolem_L4646, skolem_L4646) => distinct_lines(skolem_L4646, skolem_L4646))
% 208.97/52.28
% 208.97/52.28 [17896] BETA_IMPLY : (convergent_lines(skolem_L4646, skolem_L4646) => distinct_lines(skolem_L4646, skolem_L4646))
% 208.97/52.28 -> [17898] ~convergent_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28 -> [17899] distinct_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28
% 208.97/52.28 [17899] CLOSURE : distinct_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28
% 208.97/52.28 [17898] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 208.97/52.28 -> [17912] ~(~convergent_lines(skolem_L4646, skolem_N4848) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [17912] BETA_NOT_AND : ~(~convergent_lines(skolem_L4646, skolem_N4848) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [17914] ~~convergent_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [17915] ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17915] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [17920] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17920] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17924] GAMMA_FORALL : ! [L40_40, M41_41, N42_42] : ((((~convergent_lines(L40_40, M41_41) | ~unorthogonal_lines(L40_40, M41_41)) & (~convergent_lines(L40_40, N42_42) | ~unorthogonal_lines(L40_40, N42_42))) => (~convergent_lines(M41_41, N42_42) | ~unorthogonal_lines(M41_41, N42_42))))
% 208.97/52.28 -> [17946] (((~convergent_lines(skolem_L4646, skolem_L4646) | ~unorthogonal_lines(skolem_L4646, skolem_L4646)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [17946] BETA_IMPLY : (((~convergent_lines(skolem_L4646, skolem_L4646) | ~unorthogonal_lines(skolem_L4646, skolem_L4646)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [17949] ~((~convergent_lines(skolem_L4646, skolem_L4646) | ~unorthogonal_lines(skolem_L4646, skolem_L4646)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [17950] (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [17949] BETA_NOT_AND : ~((~convergent_lines(skolem_L4646, skolem_L4646) | ~unorthogonal_lines(skolem_L4646, skolem_L4646)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [17953] ~(~convergent_lines(skolem_L4646, skolem_L4646) | ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 208.97/52.28 -> [17954] ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [17953] ALPHA_NOT_OR : ~(~convergent_lines(skolem_L4646, skolem_L4646) | ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 208.97/52.28 -> [17964] ~~convergent_lines(skolem_L4646, skolem_L4646), ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28
% 208.97/52.28 [17964] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28 -> [17967] convergent_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28
% 208.97/52.28 [17967] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28 -> [17971] unorthogonal_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28
% 208.97/52.28 [17971] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28
% 208.97/52.28 [17978] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17950] BETA_OR : (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [18069] ~convergent_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [18070] ~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18069] CLOSURE : ~convergent_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18070] GAMMA_FORALL : ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45)))
% 208.97/52.28 -> [18077] ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [18077] BETA_IMPLY : ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [18080] ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [18081] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18081] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18080] BETA_NOT_AND : ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [18124] ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [18125] ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18124] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [18127] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [18127] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [18125] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [18128] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18128] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17866] GAMMA_FORALL : ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_points(X30_30, Z32_32) | apart_point_and_line(Z32_32, Y31_31))))
% 208.97/52.28 -> [17868] (apart_point_and_line(X30_147_9, skolem_N4848) => (distinct_points(X30_147_9, intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [17868] BETA_IMPLY : (apart_point_and_line(X30_147_9, skolem_N4848) => (distinct_points(X30_147_9, intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)))
% 208.97/52.28 -> [17871] ~apart_point_and_line(X30_147_9, skolem_N4848)
% 208.97/52.28 -> [17872] (distinct_points(X30_147_9, intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [17872] BETA_OR : (distinct_points(X30_147_9, intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28 -> [17875] distinct_points(X30_147_9, intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [17876] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17876] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17875] CLOSURE : distinct_points(X30_147_9, intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [17871] GAMMA_FORALL : ! [X33_33, Y34_34, Z35_35] : ((apart_point_and_line(X33_33, Y34_34) => (distinct_lines(Y34_34, Z35_35) | apart_point_and_line(X33_33, Z35_35))))
% 208.97/52.28 -> [17878] (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), Y34_203_10) => (distinct_lines(Y34_203_10, skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)))
% 208.97/52.28
% 208.97/52.28 [17878] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), Y34_203_10) => (distinct_lines(Y34_203_10, skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)))
% 208.97/52.28 -> [17879] ~apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), Y34_203_10)
% 208.97/52.28 -> [17880] (distinct_lines(Y34_203_10, skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747))
% 208.97/52.28
% 208.97/52.28 [17879] GAMMA_FORALL : ! [X36_36, Y37_37] : ((convergent_lines(X36_36, Y37_37) => distinct_lines(X36_36, Y37_37)))
% 208.97/52.28 -> [17887] (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [17887] BETA_IMPLY : (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [17889] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [17890] distinct_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17889] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17890] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 208.97/52.28 -> [17902] ~(~convergent_lines(skolem_N4848, skolem_N4848) & ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [17902] BETA_NOT_AND : ~(~convergent_lines(skolem_N4848, skolem_N4848) & ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28 -> [17904] ~~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [17905] ~~unorthogonal_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17904] ALPHA_NOT_NOT : ~~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [17907] convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17907] CLOSURE : convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17908] GAMMA_FORALL : ! [L40_40, M41_41, N42_42] : ((((~convergent_lines(L40_40, M41_41) | ~unorthogonal_lines(L40_40, M41_41)) & (~convergent_lines(L40_40, N42_42) | ~unorthogonal_lines(L40_40, N42_42))) => (~convergent_lines(M41_41, N42_42) | ~unorthogonal_lines(M41_41, N42_42))))
% 208.97/52.28 -> [17921] (((~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_M4747, skolem_N4848) | ~unorthogonal_lines(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [17921] BETA_IMPLY : (((~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_M4747, skolem_N4848) | ~unorthogonal_lines(skolem_M4747, skolem_N4848)))
% 208.97/52.28 -> [17927] ~((~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [17928] (~convergent_lines(skolem_M4747, skolem_N4848) | ~unorthogonal_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [17927] BETA_NOT_AND : ~((~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [17935] ~(~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747))
% 208.97/52.28 -> [17936] ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [17935] ALPHA_NOT_OR : ~(~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747))
% 208.97/52.28 -> [17937] ~~convergent_lines(skolem_L4646, skolem_M4747), ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [17937] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [17940] convergent_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [17940] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [17942] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [17942] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [17943] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17928] BETA_OR : (~convergent_lines(skolem_M4747, skolem_N4848) | ~unorthogonal_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [18026] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [18027] ~unorthogonal_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18026] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18027] GAMMA_FORALL : ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45)))
% 208.97/52.28 -> [18028] ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [18028] BETA_IMPLY : ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [18030] ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [18031] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18031] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18030] BETA_NOT_AND : ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [18051] ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [18052] ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18051] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [18053] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [18053] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [18052] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [18056] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18056] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17880] BETA_OR : (distinct_lines(Y34_203_10, skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747))
% 208.97/52.28 -> [17883] distinct_lines(Y34_203_10, skolem_M4747)
% 208.97/52.28 -> [17884] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [17884] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [17883] GAMMA_FORALL : ! [X36_36, Y37_37] : ((convergent_lines(X36_36, Y37_37) => distinct_lines(X36_36, Y37_37)))
% 208.97/52.28 -> [17893] (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [17893] BETA_IMPLY : (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [17894] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [17895] distinct_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17894] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17895] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 208.97/52.28 -> [17909] ~(~convergent_lines(skolem_L4646, skolem_N4848) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [17909] BETA_NOT_AND : ~(~convergent_lines(skolem_L4646, skolem_N4848) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [17910] ~~convergent_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [17911] ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17911] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [17916] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17916] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17919] GAMMA_FORALL : ! [L40_40, M41_41, N42_42] : ((((~convergent_lines(L40_40, M41_41) | ~unorthogonal_lines(L40_40, M41_41)) & (~convergent_lines(L40_40, N42_42) | ~unorthogonal_lines(L40_40, N42_42))) => (~convergent_lines(M41_41, N42_42) | ~unorthogonal_lines(M41_41, N42_42))))
% 208.97/52.28 -> [17945] (((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_N4848, skolem_N4848) | ~unorthogonal_lines(skolem_N4848, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [17945] BETA_IMPLY : (((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_N4848, skolem_N4848) | ~unorthogonal_lines(skolem_N4848, skolem_N4848)))
% 208.97/52.28 -> [17947] ~((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [17948] (~convergent_lines(skolem_N4848, skolem_N4848) | ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [17947] BETA_NOT_AND : ~((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [17951] ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [17952] ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [17952] ALPHA_NOT_OR : ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [17962] ~~convergent_lines(skolem_L4646, skolem_N4848), ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17962] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [17965] convergent_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17965] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [17968] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17968] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17981] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [17948] BETA_OR : (~convergent_lines(skolem_N4848, skolem_N4848) | ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28 -> [18067] ~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [18068] ~unorthogonal_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18067] GAMMA_FORALL : ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45)))
% 208.97/52.28 -> [18071] ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [18071] BETA_IMPLY : ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [18073] ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [18074] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18074] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18073] BETA_NOT_AND : ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [18122] ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [18123] ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18122] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [18126] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [18126] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [18123] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [18129] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18129] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18068] GAMMA_FORALL : ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45)))
% 208.97/52.28 -> [18072] ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [18072] BETA_IMPLY : ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [18075] ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [18076] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18076] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18075] BETA_NOT_AND : ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [18130] ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [18131] ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18130] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [18132] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [18132] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [18131] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [18133] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18133] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12969] CLOSURE : convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [12961] GAMMA_FORALL : ! [X17_17, Y18_18, Z19_19] : ((convergent_lines(X17_17, Y18_18) => (convergent_lines(X17_17, Z19_19) | convergent_lines(Y18_18, Z19_19))))
% 208.97/52.28 -> [18134] (convergent_lines(skolem_M4747, skolem_N4848) => (convergent_lines(skolem_M4747, skolem_N4848) | convergent_lines(skolem_N4848, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [18134] BETA_IMPLY : (convergent_lines(skolem_M4747, skolem_N4848) => (convergent_lines(skolem_M4747, skolem_N4848) | convergent_lines(skolem_N4848, skolem_N4848)))
% 208.97/52.28 -> [18135] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [18136] (convergent_lines(skolem_M4747, skolem_N4848) | convergent_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [18135] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18136] BETA_OR : (convergent_lines(skolem_M4747, skolem_N4848) | convergent_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28 -> [18139] convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [18140] convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18140] CLOSURE : convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18139] GAMMA_FORALL : ! [X20_20, Y21_21, Z22_22] : ((distinct_points(X20_20, Y21_21) => (apart_point_and_line(Z22_22, line_connecting(X20_20, Y21_21)) => (distinct_points(Z22_22, X20_20) & distinct_points(Z22_22, Y21_21)))))
% 208.97/52.28 -> [18141] (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) => (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) => (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))))
% 208.97/52.28
% 208.97/52.28 [18141] BETA_IMPLY : (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) => (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) => (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))))
% 208.97/52.28 -> [18142] ~distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [18143] (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) => (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28
% 208.97/52.28 [18142] GAMMA_FORALL : ! [X23_23, Y24_24, Z25_25] : ((convergent_lines(X23_23, Y24_24) => ((apart_point_and_line(Z25_25, X23_23) | apart_point_and_line(Z25_25, Y24_24)) => distinct_points(Z25_25, intersection_point(X23_23, Y24_24)))))
% 208.97/52.28 -> [18146] (convergent_lines(skolem_M4747, skolem_N4848) => ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) => distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28
% 208.97/52.28 [18146] BETA_IMPLY : (convergent_lines(skolem_M4747, skolem_N4848) => ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) => distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [18148] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [18149] ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) => distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [18148] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18149] BETA_IMPLY : ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) => distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28 -> [19073] ~(apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28 -> [19074] distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [19074] CLOSURE : distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [19077] BETA_IMPLY : ((distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_lines(skolem_M4747, skolem_M4747)) => (((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)))
% 208.97/52.28 -> [20200] ~(distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_lines(skolem_M4747, skolem_M4747))
% 208.97/52.28 -> [20201] (((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747))
% 208.97/52.28
% 208.97/52.28 [20201] BETA_OR : (((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747))
% 208.97/52.28 -> [20208] ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747))
% 208.97/52.28 -> [20209] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [20208] BETA_OR : ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747))
% 208.97/52.28 -> [20210] (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747))
% 208.97/52.28 -> [20211] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [20211] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [20210] BETA_OR : (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747))
% 208.97/52.28 -> [20230] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28 -> [20231] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [20231] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [20230] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [20209] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [20200] BETA_NOT_AND : ~(distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_lines(skolem_M4747, skolem_M4747))
% 208.97/52.28 -> [20913] ~distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [20914] ~distinct_lines(skolem_M4747, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [20914] GAMMA_FORALL : ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_points(X30_30, Z32_32) | apart_point_and_line(Z32_32, Y31_31))))
% 208.97/52.28 -> [20918] (apart_point_and_line(X30_163_9, skolem_N4848) => (distinct_points(X30_163_9, intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [20918] BETA_IMPLY : (apart_point_and_line(X30_163_9, skolem_N4848) => (distinct_points(X30_163_9, intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)))
% 208.97/52.28 -> [20922] ~apart_point_and_line(X30_163_9, skolem_N4848)
% 208.97/52.28 -> [20923] (distinct_points(X30_163_9, intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [20923] BETA_OR : (distinct_points(X30_163_9, intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28 -> [20926] distinct_points(X30_163_9, intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [20927] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [20927] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [20926] CLOSURE : distinct_points(X30_163_9, intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [20922] GAMMA_FORALL : ! [X33_33, Y34_34, Z35_35] : ((apart_point_and_line(X33_33, Y34_34) => (distinct_lines(Y34_34, Z35_35) | apart_point_and_line(X33_33, Z35_35))))
% 208.97/52.28 -> [20930] (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) => (distinct_lines(skolem_M4747, skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)))
% 208.97/52.28
% 208.97/52.28 [20930] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) => (distinct_lines(skolem_M4747, skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)))
% 208.97/52.28 -> [20935] ~apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28 -> [20936] (distinct_lines(skolem_M4747, skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747))
% 208.97/52.28
% 208.97/52.28 [20936] BETA_OR : (distinct_lines(skolem_M4747, skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747))
% 208.97/52.28 -> [20941] distinct_lines(skolem_M4747, skolem_M4747)
% 208.97/52.28 -> [20942] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [20941] CLOSURE : distinct_lines(skolem_M4747, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [20942] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [20944] BETA_IMPLY : (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [20979] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [20980] distinct_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [20979] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [20980] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 208.97/52.28 -> [21004] ~(~convergent_lines(skolem_N4848, skolem_N4848) & ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [21004] BETA_NOT_AND : ~(~convergent_lines(skolem_N4848, skolem_N4848) & ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28 -> [21007] ~~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [21008] ~~unorthogonal_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21007] ALPHA_NOT_NOT : ~~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [21018] convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21018] CLOSURE : convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21015] GAMMA_FORALL : ! [L40_40, M41_41, N42_42] : ((((~convergent_lines(L40_40, M41_41) | ~unorthogonal_lines(L40_40, M41_41)) & (~convergent_lines(L40_40, N42_42) | ~unorthogonal_lines(L40_40, N42_42))) => (~convergent_lines(M41_41, N42_42) | ~unorthogonal_lines(M41_41, N42_42))))
% 208.97/52.28 -> [21049] (((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_N4848, skolem_N4848) | ~unorthogonal_lines(skolem_N4848, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [21049] BETA_IMPLY : (((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_N4848, skolem_N4848) | ~unorthogonal_lines(skolem_N4848, skolem_N4848)))
% 208.97/52.28 -> [21050] ~((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [21051] (~convergent_lines(skolem_N4848, skolem_N4848) | ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [21050] BETA_NOT_AND : ~((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [21053] ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [21054] ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [21053] ALPHA_NOT_OR : ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [21061] ~~convergent_lines(skolem_L4646, skolem_N4848), ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21061] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [21062] convergent_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21062] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [21064] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21064] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21063] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21051] BETA_OR : (~convergent_lines(skolem_N4848, skolem_N4848) | ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28 -> [21114] ~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [21115] ~unorthogonal_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21115] CLOSURE : ~unorthogonal_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21114] GAMMA_FORALL : ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45)))
% 208.97/52.28 -> [21121] ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [21121] BETA_IMPLY : ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [21123] ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [21124] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21124] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21123] BETA_NOT_AND : ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [21149] ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [21150] ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21150] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [21158] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21158] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21149] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [21163] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [21163] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [20913] GAMMA_FORALL : ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_points(X30_30, Z32_32) | apart_point_and_line(Z32_32, Y31_31))))
% 208.97/52.28 -> [20917] (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) => (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)))
% 208.97/52.28
% 208.97/52.28 [20917] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) => (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)))
% 208.97/52.28 -> [20920] ~apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28 -> [20921] (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747))
% 208.97/52.28
% 208.97/52.28 [20921] BETA_OR : (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747))
% 208.97/52.28 -> [20924] distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [20925] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [20924] CLOSURE : distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [20925] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [20929] BETA_IMPLY : (apart_point_and_line(X33_221_10, skolem_L4646) => (distinct_lines(skolem_L4646, skolem_L4646) | apart_point_and_line(X33_221_10, skolem_L4646)))
% 208.97/52.28 -> [21144] ~apart_point_and_line(X33_221_10, skolem_L4646)
% 208.97/52.28 -> [21145] (distinct_lines(skolem_L4646, skolem_L4646) | apart_point_and_line(X33_221_10, skolem_L4646))
% 208.97/52.28
% 208.97/52.28 [21144] GAMMA_FORALL : ! [X36_36, Y37_37] : ((convergent_lines(X36_36, Y37_37) => distinct_lines(X36_36, Y37_37)))
% 208.97/52.28 -> [21159] (convergent_lines(skolem_L4646, skolem_L4646) => distinct_lines(skolem_L4646, skolem_L4646))
% 208.97/52.28
% 208.97/52.28 [21159] BETA_IMPLY : (convergent_lines(skolem_L4646, skolem_L4646) => distinct_lines(skolem_L4646, skolem_L4646))
% 208.97/52.28 -> [21161] ~convergent_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28 -> [21162] distinct_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28
% 208.97/52.28 [21162] CLOSURE : distinct_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28
% 208.97/52.28 [21161] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 208.97/52.28 -> [21168] ~(~convergent_lines(skolem_N4848, skolem_N4848) & ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [21168] BETA_NOT_AND : ~(~convergent_lines(skolem_N4848, skolem_N4848) & ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28 -> [21169] ~~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [21170] ~~unorthogonal_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21169] ALPHA_NOT_NOT : ~~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [21171] convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21171] CLOSURE : convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21172] GAMMA_FORALL : ! [L40_40, M41_41, N42_42] : ((((~convergent_lines(L40_40, M41_41) | ~unorthogonal_lines(L40_40, M41_41)) & (~convergent_lines(L40_40, N42_42) | ~unorthogonal_lines(L40_40, N42_42))) => (~convergent_lines(M41_41, N42_42) | ~unorthogonal_lines(M41_41, N42_42))))
% 208.97/52.28 -> [21184] (((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747))) => (~convergent_lines(skolem_N4848, skolem_M4747) | ~unorthogonal_lines(skolem_N4848, skolem_M4747)))
% 208.97/52.28
% 208.97/52.28 [21184] BETA_IMPLY : (((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747))) => (~convergent_lines(skolem_N4848, skolem_M4747) | ~unorthogonal_lines(skolem_N4848, skolem_M4747)))
% 208.97/52.28 -> [21187] ~((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)))
% 208.97/52.28 -> [21188] (~convergent_lines(skolem_N4848, skolem_M4747) | ~unorthogonal_lines(skolem_N4848, skolem_M4747))
% 208.97/52.28
% 208.97/52.28 [21187] BETA_NOT_AND : ~((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)))
% 208.97/52.28 -> [21191] ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [21192] ~(~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747))
% 208.97/52.28
% 208.97/52.28 [21192] ALPHA_NOT_OR : ~(~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747))
% 208.97/52.28 -> [21196] ~~convergent_lines(skolem_L4646, skolem_M4747), ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [21196] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [21198] convergent_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [21198] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [21201] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [21201] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [21200] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21188] BETA_OR : (~convergent_lines(skolem_N4848, skolem_M4747) | ~unorthogonal_lines(skolem_N4848, skolem_M4747))
% 208.97/52.28 -> [21242] ~convergent_lines(skolem_N4848, skolem_M4747)
% 208.97/52.28 -> [21243] ~unorthogonal_lines(skolem_N4848, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [21243] GAMMA_FORALL : ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45)))
% 208.97/52.28 -> [21245] ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [21245] BETA_IMPLY : ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [21248] ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [21249] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21249] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21248] BETA_NOT_AND : ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [21262] ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [21263] ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21262] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [21266] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [21266] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [21263] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [21267] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21267] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21242] GAMMA_FORALL : ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45)))
% 208.97/52.28 -> [21244] ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [21244] BETA_IMPLY : ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [21246] ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [21247] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21247] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21246] BETA_NOT_AND : ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [21268] ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [21269] ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21268] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [21272] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [21272] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [21269] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [21273] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21273] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21145] BETA_OR : (distinct_lines(skolem_L4646, skolem_L4646) | apart_point_and_line(X33_221_10, skolem_L4646))
% 208.97/52.28 -> [21153] distinct_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28 -> [21154] apart_point_and_line(X33_221_10, skolem_L4646)
% 208.97/52.28
% 208.97/52.28 [21153] CLOSURE : distinct_lines(skolem_L4646, skolem_L4646)
% 208.97/52.28
% 208.97/52.28 [21154] GAMMA_FORALL : ! [X36_36, Y37_37] : ((convergent_lines(X36_36, Y37_37) => distinct_lines(X36_36, Y37_37)))
% 208.97/52.28 -> [21165] (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [21165] BETA_IMPLY : (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [21166] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [21167] distinct_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21166] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21167] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 208.97/52.28 -> [21177] ~(~convergent_lines(skolem_N4848, skolem_N4848) & ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [21177] BETA_NOT_AND : ~(~convergent_lines(skolem_N4848, skolem_N4848) & ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28 -> [21178] ~~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [21179] ~~unorthogonal_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21178] ALPHA_NOT_NOT : ~~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [21189] convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21189] CLOSURE : convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21185] GAMMA_FORALL : ! [L40_40, M41_41, N42_42] : ((((~convergent_lines(L40_40, M41_41) | ~unorthogonal_lines(L40_40, M41_41)) & (~convergent_lines(L40_40, N42_42) | ~unorthogonal_lines(L40_40, N42_42))) => (~convergent_lines(M41_41, N42_42) | ~unorthogonal_lines(M41_41, N42_42))))
% 208.97/52.28 -> [21203] (((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747))) => (~convergent_lines(skolem_N4848, skolem_M4747) | ~unorthogonal_lines(skolem_N4848, skolem_M4747)))
% 208.97/52.28
% 208.97/52.28 [21203] BETA_IMPLY : (((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747))) => (~convergent_lines(skolem_N4848, skolem_M4747) | ~unorthogonal_lines(skolem_N4848, skolem_M4747)))
% 208.97/52.28 -> [21204] ~((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)))
% 208.97/52.28 -> [21205] (~convergent_lines(skolem_N4848, skolem_M4747) | ~unorthogonal_lines(skolem_N4848, skolem_M4747))
% 208.97/52.28
% 208.97/52.28 [21204] BETA_NOT_AND : ~((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747)))
% 208.97/52.28 -> [21213] ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [21214] ~(~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747))
% 208.97/52.28
% 208.97/52.28 [21214] ALPHA_NOT_OR : ~(~convergent_lines(skolem_L4646, skolem_M4747) | ~unorthogonal_lines(skolem_L4646, skolem_M4747))
% 208.97/52.28 -> [21217] ~~convergent_lines(skolem_L4646, skolem_M4747), ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [21217] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [21218] convergent_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [21218] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [21221] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [21221] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [21222] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21205] BETA_OR : (~convergent_lines(skolem_N4848, skolem_M4747) | ~unorthogonal_lines(skolem_N4848, skolem_M4747))
% 208.97/52.28 -> [21264] ~convergent_lines(skolem_N4848, skolem_M4747)
% 208.97/52.28 -> [21265] ~unorthogonal_lines(skolem_N4848, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [21264] GAMMA_FORALL : ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45)))
% 208.97/52.28 -> [21274] ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [21274] BETA_IMPLY : ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [21275] ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [21276] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21276] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21275] BETA_NOT_AND : ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [21302] ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [21303] ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21302] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [21306] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [21306] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [21303] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [21307] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21307] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21265] GAMMA_FORALL : ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45)))
% 208.97/52.28 -> [21277] ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [21277] BETA_IMPLY : ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [21278] ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [21279] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21279] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21278] BETA_NOT_AND : ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [21310] ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [21311] ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21310] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [21312] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [21312] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [21311] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [21313] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [21313] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [18143] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))) => (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [24148] ~apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), line_connecting(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28 -> [24149] (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [24149] ALPHA_AND : (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28 -> [24150] distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [24150] CLOSURE : distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [24148] GAMMA_FORALL : ! [X23_23, Y24_24, Z25_25] : ((convergent_lines(X23_23, Y24_24) => ((apart_point_and_line(Z25_25, X23_23) | apart_point_and_line(Z25_25, Y24_24)) => distinct_points(Z25_25, intersection_point(X23_23, Y24_24)))))
% 208.97/52.28 -> [24151] (convergent_lines(skolem_M4747, skolem_N4848) => ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) => distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28
% 208.97/52.28 [24151] BETA_IMPLY : (convergent_lines(skolem_M4747, skolem_N4848) => ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) => distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))))
% 208.97/52.28 -> [24152] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [24153] ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) => distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [24152] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [24153] BETA_IMPLY : ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) => distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)))
% 208.97/52.28 -> [26064] ~(apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28 -> [26065] distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [26065] CLOSURE : distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [26064] ALPHA_NOT_OR : ~(apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28 -> [26066] ~apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747), ~apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26066] GAMMA_FORALL : ! [X26_26, Y27_27, U28_28, V29_29] : (((distinct_points(X26_26, Y27_27) & distinct_lines(U28_28, V29_29)) => (((apart_point_and_line(X26_26, U28_28) | apart_point_and_line(X26_26, V29_29)) | apart_point_and_line(Y27_27, U28_28)) | apart_point_and_line(Y27_27, V29_29))))
% 208.97/52.28 -> [26067] ((distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_lines(skolem_M4747, skolem_N4848)) => (((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [26067] BETA_IMPLY : ((distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_lines(skolem_M4747, skolem_N4848)) => (((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)))
% 208.97/52.28 -> [26068] ~(distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [26069] (((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [26069] BETA_OR : (((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28 -> [26072] ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747))
% 208.97/52.28 -> [26073] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26073] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26072] BETA_OR : ((apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747))
% 208.97/52.28 -> [26099] (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28 -> [26100] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [26099] BETA_OR : (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28 -> [26104] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28 -> [26105] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26104] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [26105] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26100] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [26068] BETA_NOT_AND : ~(distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) & distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [26575] ~distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [26576] ~distinct_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26576] GAMMA_FORALL : ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_points(X30_30, Z32_32) | apart_point_and_line(Z32_32, Y31_31))))
% 208.97/52.28 -> [26578] (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848) => (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [26578] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848) => (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)))
% 208.97/52.28 -> [26581] ~apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28 -> [26582] (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [26581] GAMMA_FORALL : ! [X33_33, Y34_34, Z35_35] : ((apart_point_and_line(X33_33, Y34_34) => (distinct_lines(Y34_34, Z35_35) | apart_point_and_line(X33_33, Z35_35))))
% 208.97/52.28 -> [26590] (apart_point_and_line(X33_261_10, skolem_M4747) => (distinct_lines(skolem_M4747, skolem_N4848) | apart_point_and_line(X33_261_10, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [26590] BETA_IMPLY : (apart_point_and_line(X33_261_10, skolem_M4747) => (distinct_lines(skolem_M4747, skolem_N4848) | apart_point_and_line(X33_261_10, skolem_N4848)))
% 208.97/52.28 -> [26591] ~apart_point_and_line(X33_261_10, skolem_M4747)
% 208.97/52.28 -> [26592] (distinct_lines(skolem_M4747, skolem_N4848) | apart_point_and_line(X33_261_10, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [26591] GAMMA_FORALL : ! [X36_36, Y37_37] : ((convergent_lines(X36_36, Y37_37) => distinct_lines(X36_36, Y37_37)))
% 208.97/52.28 -> [26600] (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [26600] BETA_IMPLY : (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [26601] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [26602] distinct_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26601] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26602] CLOSURE : distinct_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26592] BETA_OR : (distinct_lines(skolem_M4747, skolem_N4848) | apart_point_and_line(X33_261_10, skolem_N4848))
% 208.97/52.28 -> [26598] distinct_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [26599] apart_point_and_line(X33_261_10, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26599] CLOSURE : apart_point_and_line(X33_261_10, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26598] CLOSURE : distinct_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26582] BETA_OR : (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28 -> [26608] distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [26609] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26608] CLOSURE : distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [26609] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26575] GAMMA_FORALL : ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_points(X30_30, Z32_32) | apart_point_and_line(Z32_32, Y31_31))))
% 208.97/52.28 -> [26577] (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848) => (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [26577] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848) => (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)))
% 208.97/52.28 -> [26579] ~apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28 -> [26580] (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [26580] BETA_OR : (distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848)) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28 -> [26583] distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [26584] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26584] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26583] CLOSURE : distinct_points(intersection_point(skolem_M4747, skolem_N4848), intersection_point(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [26587] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), Y34_260_10) => (distinct_lines(Y34_260_10, skolem_N4848) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)))
% 208.97/52.28 -> [26647] ~apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), Y34_260_10)
% 208.97/52.28 -> [26648] (distinct_lines(Y34_260_10, skolem_N4848) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [26648] BETA_OR : (distinct_lines(Y34_260_10, skolem_N4848) | apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848))
% 208.97/52.28 -> [26649] distinct_lines(Y34_260_10, skolem_N4848)
% 208.97/52.28 -> [26650] apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26650] CLOSURE : apart_point_and_line(intersection_point(skolem_M4747, skolem_N4848), skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26649] GAMMA_FORALL : ! [X36_36, Y37_37] : ((convergent_lines(X36_36, Y37_37) => distinct_lines(X36_36, Y37_37)))
% 208.97/52.28 -> [26654] (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [26654] BETA_IMPLY : (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [26655] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [26656] distinct_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26655] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26656] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 208.97/52.28 -> [26662] ~(~convergent_lines(skolem_N4848, skolem_N4848) & ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [26662] BETA_NOT_AND : ~(~convergent_lines(skolem_N4848, skolem_N4848) & ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28 -> [26663] ~~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [26664] ~~unorthogonal_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26663] ALPHA_NOT_NOT : ~~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [26665] convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26665] CLOSURE : convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26666] GAMMA_FORALL : ! [L40_40, M41_41, N42_42] : ((((~convergent_lines(L40_40, M41_41) | ~unorthogonal_lines(L40_40, M41_41)) & (~convergent_lines(L40_40, N42_42) | ~unorthogonal_lines(L40_40, N42_42))) => (~convergent_lines(M41_41, N42_42) | ~unorthogonal_lines(M41_41, N42_42))))
% 208.97/52.28 -> [26674] (((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_N4848, skolem_N4848) | ~unorthogonal_lines(skolem_N4848, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [26674] BETA_IMPLY : (((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_N4848, skolem_N4848) | ~unorthogonal_lines(skolem_N4848, skolem_N4848)))
% 208.97/52.28 -> [26676] ~((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [26677] (~convergent_lines(skolem_N4848, skolem_N4848) | ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [26676] BETA_NOT_AND : ~((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [26681] ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [26682] ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [26681] ALPHA_NOT_OR : ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [26685] ~~convergent_lines(skolem_L4646, skolem_N4848), ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26685] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [26689] convergent_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26689] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [26696] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26696] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26697] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26677] BETA_OR : (~convergent_lines(skolem_N4848, skolem_N4848) | ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28 -> [26717] ~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [26718] ~unorthogonal_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26718] CLOSURE : ~unorthogonal_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26717] GAMMA_FORALL : ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45)))
% 208.97/52.28 -> [26719] ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [26719] BETA_IMPLY : ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [26720] ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [26721] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26721] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26720] BETA_NOT_AND : ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [26732] ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [26733] ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26733] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [26735] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26735] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26732] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [26734] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [26734] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [26647] GAMMA_FORALL : ! [X36_36, Y37_37] : ((convergent_lines(X36_36, Y37_37) => distinct_lines(X36_36, Y37_37)))
% 208.97/52.28 -> [26651] (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [26651] BETA_IMPLY : (convergent_lines(skolem_M4747, skolem_N4848) => distinct_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [26652] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28 -> [26653] distinct_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26652] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26653] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 208.97/52.28 -> [26657] ~(~convergent_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_M4747))
% 208.97/52.28
% 208.97/52.28 [26657] BETA_NOT_AND : ~(~convergent_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_M4747))
% 208.97/52.28 -> [26658] ~~convergent_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [26659] ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [26659] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [26660] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [26660] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [26661] GAMMA_FORALL : ! [L40_40, M41_41, N42_42] : ((((~convergent_lines(L40_40, M41_41) | ~unorthogonal_lines(L40_40, M41_41)) & (~convergent_lines(L40_40, N42_42) | ~unorthogonal_lines(L40_40, N42_42))) => (~convergent_lines(M41_41, N42_42) | ~unorthogonal_lines(M41_41, N42_42))))
% 208.97/52.28 -> [26667] (((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_N4848, skolem_N4848) | ~unorthogonal_lines(skolem_N4848, skolem_N4848)))
% 208.97/52.28
% 208.97/52.28 [26667] BETA_IMPLY : (((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))) => (~convergent_lines(skolem_N4848, skolem_N4848) | ~unorthogonal_lines(skolem_N4848, skolem_N4848)))
% 208.97/52.28 -> [26668] ~((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [26669] (~convergent_lines(skolem_N4848, skolem_N4848) | ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [26668] BETA_NOT_AND : ~((~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)) & (~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848)))
% 208.97/52.28 -> [26670] ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [26671] ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [26671] ALPHA_NOT_OR : ~(~convergent_lines(skolem_L4646, skolem_N4848) | ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [26678] ~~convergent_lines(skolem_L4646, skolem_N4848), ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26678] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [26679] convergent_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26679] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [26686] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26686] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26693] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26669] BETA_OR : (~convergent_lines(skolem_N4848, skolem_N4848) | ~unorthogonal_lines(skolem_N4848, skolem_N4848))
% 208.97/52.28 -> [26748] ~convergent_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28 -> [26749] ~unorthogonal_lines(skolem_N4848, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26748] GAMMA_FORALL : ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45)))
% 208.97/52.28 -> [26753] ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [26753] BETA_IMPLY : ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [26754] ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [26755] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26754] BETA_NOT_AND : ~(~unorthogonal_lines(skolem_L4646, skolem_N4848) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [26758] ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [26759] ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26759] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [26763] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26763] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26761] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26755] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26749] GAMMA_FORALL : ! [L43_43, M44_44, N45_45] : (((~unorthogonal_lines(L43_43, M44_44) & ~unorthogonal_lines(L43_43, N45_45)) => ~convergent_lines(M44_44, N45_45)))
% 208.97/52.28 -> [26750] ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28
% 208.97/52.28 [26750] BETA_IMPLY : ((~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848)) => ~convergent_lines(skolem_M4747, skolem_N4848))
% 208.97/52.28 -> [26751] ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [26752] ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26752] CLOSURE : ~convergent_lines(skolem_M4747, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26751] BETA_NOT_AND : ~(~unorthogonal_lines(skolem_L4646, skolem_M4747) & ~unorthogonal_lines(skolem_L4646, skolem_N4848))
% 208.97/52.28 -> [26778] ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [26779] ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26779] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28 -> [26781] unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26781] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_N4848)
% 208.97/52.28
% 208.97/52.28 [26778] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28 -> [26780] unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 [26780] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_M4747)
% 208.97/52.28
% 208.97/52.28 % SZS output end Proof for theBenchmark.p
% 208.97/52.28 [51.952020s][1][Res] 468119 goroutines created
% 208.97/52.28 ==== Result ====
% 208.97/52.28 [51.952054s][1][Res] VALID
% 208.97/52.28 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------