TSTP Solution File: GEO216+2 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO216+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n026.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 15:18:29 EDT 2022
% Result : Theorem 158.60s 31.92s
% Output : Proof 158.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO216+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 07:13:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 [DMT] DMT loaded with preskolemization
% 0.12/0.34 [EQ] equality loaded.
% 0.12/0.34 [0.000039s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.34 Conjecture not found
% 0.12/0.34 Conjecture not found
% 0.12/0.34 Start search
% 0.12/0.34 nb_step : 1 - limit : 16
% 0.12/0.34 Launch Gotab with destructive = true
% 158.56/31.89 % SZS output start Proof for theBenchmark.p
% 158.60/31.91 [0] ALPHA_AND : ((! [X6_6] : (~distinct_points(X6_6, X6_6)) & ! [X7_7] : (~distinct_lines(X7_7, X7_7)) & ! [X8_8] : (~convergent_lines(X8_8, X8_8)) & ! [X9_9, Y10_10, Z11_11] : ((distinct_points(X9_9, Y10_10) => (distinct_points(X9_9, Z11_11) | distinct_points(Y10_10, Z11_11)))) & ! [X12_12, Y13_13, Z14_14] : ((distinct_lines(X12_12, Y13_13) => (distinct_lines(X12_12, Z14_14) | distinct_lines(Y13_13, Z14_14)))) & ! [X15_15, Y16_16, Z17_17] : ((convergent_lines(X15_15, Y16_16) => (convergent_lines(X15_15, Z17_17) | convergent_lines(Y16_16, Z17_17)))) & ! [X18_18, Y19_19, Z20_20] : ((distinct_points(X18_18, Y19_19) => (apart_point_and_line(Z20_20, line_connecting(X18_18, Y19_19)) => (distinct_points(Z20_20, X18_18) & distinct_points(Z20_20, Y19_19))))) & ! [X21_21, Y22_22, Z23_23] : ((convergent_lines(X21_21, Y22_22) => ((apart_point_and_line(Z23_23, X21_21) | apart_point_and_line(Z23_23, Y22_22)) => distinct_points(Z23_23, intersection_point(X21_21, Y22_22))))) & ! [X24_24, Y25_25, U26_26, V27_27] : (((distinct_points(X24_24, Y25_25) & distinct_lines(U26_26, V27_27)) => (((apart_point_and_line(X24_24, U26_26) | apart_point_and_line(X24_24, V27_27)) | apart_point_and_line(Y25_25, U26_26)) | apart_point_and_line(Y25_25, V27_27)))) & ! [X28_28, Y29_29, Z30_30] : ((apart_point_and_line(X28_28, Y29_29) => (distinct_points(X28_28, Z30_30) | apart_point_and_line(Z30_30, Y29_29)))) & ! [X31_31, Y32_32, Z33_33] : ((apart_point_and_line(X31_31, Y32_32) => (distinct_lines(Y32_32, Z33_33) | apart_point_and_line(X31_31, Z33_33)))) & ! [X34_34, Y35_35] : ((convergent_lines(X34_34, Y35_35) => distinct_lines(X34_34, Y35_35)))) & (! [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] : (~~unorthogonal_lines(L46_46, L46_46)))
% 158.60/31.91 -> [1] (! [X6_6] : (~distinct_points(X6_6, X6_6)) & ! [X7_7] : (~distinct_lines(X7_7, X7_7)) & ! [X8_8] : (~convergent_lines(X8_8, X8_8)) & ! [X9_9, Y10_10, Z11_11] : ((distinct_points(X9_9, Y10_10) => (distinct_points(X9_9, Z11_11) | distinct_points(Y10_10, Z11_11)))) & ! [X12_12, Y13_13, Z14_14] : ((distinct_lines(X12_12, Y13_13) => (distinct_lines(X12_12, Z14_14) | distinct_lines(Y13_13, Z14_14)))) & ! [X15_15, Y16_16, Z17_17] : ((convergent_lines(X15_15, Y16_16) => (convergent_lines(X15_15, Z17_17) | convergent_lines(Y16_16, Z17_17)))) & ! [X18_18, Y19_19, Z20_20] : ((distinct_points(X18_18, Y19_19) => (apart_point_and_line(Z20_20, line_connecting(X18_18, Y19_19)) => (distinct_points(Z20_20, X18_18) & distinct_points(Z20_20, Y19_19))))) & ! [X21_21, Y22_22, Z23_23] : ((convergent_lines(X21_21, Y22_22) => ((apart_point_and_line(Z23_23, X21_21) | apart_point_and_line(Z23_23, Y22_22)) => distinct_points(Z23_23, intersection_point(X21_21, Y22_22))))) & ! [X24_24, Y25_25, U26_26, V27_27] : (((distinct_points(X24_24, Y25_25) & distinct_lines(U26_26, V27_27)) => (((apart_point_and_line(X24_24, U26_26) | apart_point_and_line(X24_24, V27_27)) | apart_point_and_line(Y25_25, U26_26)) | apart_point_and_line(Y25_25, V27_27)))) & ! [X28_28, Y29_29, Z30_30] : ((apart_point_and_line(X28_28, Y29_29) => (distinct_points(X28_28, Z30_30) | apart_point_and_line(Z30_30, Y29_29)))) & ! [X31_31, Y32_32, Z33_33] : ((apart_point_and_line(X31_31, Y32_32) => (distinct_lines(Y32_32, Z33_33) | apart_point_and_line(X31_31, Z33_33)))) & ! [X34_34, Y35_35] : ((convergent_lines(X34_34, Y35_35) => distinct_lines(X34_34, Y35_35)))), (! [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] : (~~unorthogonal_lines(L46_46, L46_46))
% 158.60/31.91
% 158.60/31.91 [1] ALPHA_AND : (! [X6_6] : (~distinct_points(X6_6, X6_6)) & ! [X7_7] : (~distinct_lines(X7_7, X7_7)) & ! [X8_8] : (~convergent_lines(X8_8, X8_8)) & ! [X9_9, Y10_10, Z11_11] : ((distinct_points(X9_9, Y10_10) => (distinct_points(X9_9, Z11_11) | distinct_points(Y10_10, Z11_11)))) & ! [X12_12, Y13_13, Z14_14] : ((distinct_lines(X12_12, Y13_13) => (distinct_lines(X12_12, Z14_14) | distinct_lines(Y13_13, Z14_14)))) & ! [X15_15, Y16_16, Z17_17] : ((convergent_lines(X15_15, Y16_16) => (convergent_lines(X15_15, Z17_17) | convergent_lines(Y16_16, Z17_17)))) & ! [X18_18, Y19_19, Z20_20] : ((distinct_points(X18_18, Y19_19) => (apart_point_and_line(Z20_20, line_connecting(X18_18, Y19_19)) => (distinct_points(Z20_20, X18_18) & distinct_points(Z20_20, Y19_19))))) & ! [X21_21, Y22_22, Z23_23] : ((convergent_lines(X21_21, Y22_22) => ((apart_point_and_line(Z23_23, X21_21) | apart_point_and_line(Z23_23, Y22_22)) => distinct_points(Z23_23, intersection_point(X21_21, Y22_22))))) & ! [X24_24, Y25_25, U26_26, V27_27] : (((distinct_points(X24_24, Y25_25) & distinct_lines(U26_26, V27_27)) => (((apart_point_and_line(X24_24, U26_26) | apart_point_and_line(X24_24, V27_27)) | apart_point_and_line(Y25_25, U26_26)) | apart_point_and_line(Y25_25, V27_27)))) & ! [X28_28, Y29_29, Z30_30] : ((apart_point_and_line(X28_28, Y29_29) => (distinct_points(X28_28, Z30_30) | apart_point_and_line(Z30_30, Y29_29)))) & ! [X31_31, Y32_32, Z33_33] : ((apart_point_and_line(X31_31, Y32_32) => (distinct_lines(Y32_32, Z33_33) | apart_point_and_line(X31_31, Z33_33)))) & ! [X34_34, Y35_35] : ((convergent_lines(X34_34, Y35_35) => distinct_lines(X34_34, Y35_35))))
% 158.60/31.91 -> [2] ! [X6_6] : (~distinct_points(X6_6, X6_6)), ! [X7_7] : (~distinct_lines(X7_7, X7_7)), ! [X8_8] : (~convergent_lines(X8_8, X8_8)), ! [X9_9, Y10_10, Z11_11] : ((distinct_points(X9_9, Y10_10) => (distinct_points(X9_9, Z11_11) | distinct_points(Y10_10, Z11_11)))), ! [X12_12, Y13_13, Z14_14] : ((distinct_lines(X12_12, Y13_13) => (distinct_lines(X12_12, Z14_14) | distinct_lines(Y13_13, Z14_14)))), ! [X15_15, Y16_16, Z17_17] : ((convergent_lines(X15_15, Y16_16) => (convergent_lines(X15_15, Z17_17) | convergent_lines(Y16_16, Z17_17)))), ! [X18_18, Y19_19, Z20_20] : ((distinct_points(X18_18, Y19_19) => (apart_point_and_line(Z20_20, line_connecting(X18_18, Y19_19)) => (distinct_points(Z20_20, X18_18) & distinct_points(Z20_20, Y19_19))))), ! [X21_21, Y22_22, Z23_23] : ((convergent_lines(X21_21, Y22_22) => ((apart_point_and_line(Z23_23, X21_21) | apart_point_and_line(Z23_23, Y22_22)) => distinct_points(Z23_23, intersection_point(X21_21, Y22_22))))), ! [X24_24, Y25_25, U26_26, V27_27] : (((distinct_points(X24_24, Y25_25) & distinct_lines(U26_26, V27_27)) => (((apart_point_and_line(X24_24, U26_26) | apart_point_and_line(X24_24, V27_27)) | apart_point_and_line(Y25_25, U26_26)) | apart_point_and_line(Y25_25, V27_27)))), ! [X28_28, Y29_29, Z30_30] : ((apart_point_and_line(X28_28, Y29_29) => (distinct_points(X28_28, Z30_30) | apart_point_and_line(Z30_30, Y29_29)))), ! [X31_31, Y32_32, Z33_33] : ((apart_point_and_line(X31_31, Y32_32) => (distinct_lines(Y32_32, Z33_33) | apart_point_and_line(X31_31, Z33_33)))), ! [X34_34, Y35_35] : ((convergent_lines(X34_34, Y35_35) => distinct_lines(X34_34, Y35_35)))
% 158.60/31.91
% 158.60/31.91 [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))))
% 158.60/31.91 -> [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)))
% 158.60/31.91
% 158.60/31.91 [3] DELTA_NOT_FORALL : ~! [L46_46] : (~~unorthogonal_lines(L46_46, L46_46))
% 158.60/31.91 -> [4] ~~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [4] ALPHA_NOT_NOT : ~~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91 -> [5] ~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [5] GAMMA_FORALL : ! [X6_6] : (~distinct_points(X6_6, X6_6))
% 158.60/31.91 -> [6] ~distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.91
% 158.60/31.91 [6] GAMMA_FORALL : ! [X7_7] : (~distinct_lines(X7_7, X7_7))
% 158.60/31.91 -> [7] ~distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [7] GAMMA_FORALL : ! [X8_8] : (~convergent_lines(X8_8, X8_8))
% 158.60/31.91 -> [8] ~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [8] GAMMA_FORALL : ! [X9_9, Y10_10, Z11_11] : ((distinct_points(X9_9, Y10_10) => (distinct_points(X9_9, Z11_11) | distinct_points(Y10_10, Z11_11))))
% 158.60/31.91 -> [9] (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) => (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) | distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91
% 158.60/31.91 [9] BETA_IMPLY : (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) => (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) | distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [10] ~distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.91 -> [11] (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) | distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [11] BETA_OR : (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) | distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91 -> [12] distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.91 -> [13] distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.91
% 158.60/31.91 [12] CLOSURE : distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.91
% 158.60/31.91 [13] CLOSURE : distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.91
% 158.60/31.91 [14] BETA_IMPLY : (distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) => (distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91 -> [16034] ~distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91 -> [16035] (distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91
% 158.60/31.91 [16035] BETA_OR : (distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [16036] distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91 -> [16037] distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [16037] CLOSURE : distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [16036] CLOSURE : distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [16038] BETA_IMPLY : (convergent_lines(skolem_L4646, skolem_L4646) => (convergent_lines(skolem_L4646, skolem_L4646) | convergent_lines(skolem_L4646, skolem_L4646)))
% 158.60/31.91 -> [28650] ~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91 -> [28651] (convergent_lines(skolem_L4646, skolem_L4646) | convergent_lines(skolem_L4646, skolem_L4646))
% 158.60/31.91
% 158.60/31.91 [28650] GAMMA_FORALL : ! [X18_18, Y19_19, Z20_20] : ((distinct_points(X18_18, Y19_19) => (apart_point_and_line(Z20_20, line_connecting(X18_18, Y19_19)) => (distinct_points(Z20_20, X18_18) & distinct_points(Z20_20, Y19_19)))))
% 158.60/31.91 -> [28654] (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) => (apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) => (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) & distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91
% 158.60/31.91 [28654] BETA_IMPLY : (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) => (apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) => (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) & distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91 -> [28655] ~distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.91 -> [28656] (apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) => (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) & distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91
% 158.60/31.91 [28656] BETA_IMPLY : (apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) => (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) & distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [28657] ~apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91 -> [28658] (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) & distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [28658] ALPHA_AND : (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) & distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91 -> [28660] distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.91
% 158.60/31.91 [28660] CLOSURE : distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.91
% 158.60/31.91 [28663] BETA_IMPLY : (convergent_lines(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) => ((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), X21_16_7) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) => distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))))
% 158.60/31.91 -> [30760] ~convergent_lines(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91 -> [30761] ((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), X21_16_7) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) => distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91
% 158.60/31.91 [30760] GAMMA_FORALL : ! [X24_24, Y25_25, U26_26, V27_27] : (((distinct_points(X24_24, Y25_25) & distinct_lines(U26_26, V27_27)) => (((apart_point_and_line(X24_24, U26_26) | apart_point_and_line(X24_24, V27_27)) | apart_point_and_line(Y25_25, U26_26)) | apart_point_and_line(Y25_25, V27_27))))
% 158.60/31.91 -> [30764] ((distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) & distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) => (((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91
% 158.60/31.91 [30764] BETA_IMPLY : ((distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) & distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) => (((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91 -> [30766] ~(distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) & distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [30767] (((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91
% 158.60/31.91 [30766] BETA_NOT_AND : ~(distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) & distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [30771] ~distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.91 -> [30772] ~distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [30772] GAMMA_FORALL : ! [X28_28, Y29_29, Z30_30] : ((apart_point_and_line(X28_28, Y29_29) => (distinct_points(X28_28, Z30_30) | apart_point_and_line(Z30_30, Y29_29))))
% 158.60/31.91 -> [30782] (apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) => (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91
% 158.60/31.91 [30782] BETA_IMPLY : (apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) => (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91 -> [30785] ~apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91 -> [30786] (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91
% 158.60/31.91 [30786] BETA_OR : (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [30791] distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.91 -> [30792] apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [30792] CLOSURE : apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [30791] CLOSURE : distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.91
% 158.60/31.91 [30802] BETA_IMPLY : (apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y32_912_10) => (distinct_lines(Y32_912_10, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91 -> [31019] ~apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y32_912_10)
% 158.60/31.91 -> [31020] (distinct_lines(Y32_912_10, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91
% 158.60/31.91 [31019] GAMMA_FORALL : ! [X34_34, Y35_35] : ((convergent_lines(X34_34, Y35_35) => distinct_lines(X34_34, Y35_35)))
% 158.60/31.91 -> [31028] (convergent_lines(X34_1806_11, Y35_1806_11) => distinct_lines(X34_1806_11, Y35_1806_11))
% 158.60/31.91
% 158.60/31.91 [31028] BETA_IMPLY : (convergent_lines(X34_1806_11, Y35_1806_11) => distinct_lines(X34_1806_11, Y35_1806_11))
% 158.60/31.91 -> [31029] ~convergent_lines(X34_1806_11, Y35_1806_11)
% 158.60/31.91 -> [31030] distinct_lines(X34_1806_11, Y35_1806_11)
% 158.60/31.91
% 158.60/31.91 [31030] CLOSURE : distinct_lines(X34_1806_11, Y35_1806_11)
% 158.60/31.91
% 158.60/31.91 [31036] BETA_NOT_AND : ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.91 -> [31055] ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91 -> [31056] ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31055] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91 -> [31059] convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31059] CLOSURE : convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31060] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31020] BETA_OR : (distinct_lines(Y32_912_10, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31066] distinct_lines(Y32_912_10, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91 -> [31067] apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31066] CLOSURE : distinct_lines(Y32_912_10, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31067] CLOSURE : apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [30781] BETA_IMPLY : (apart_point_and_line(X28_502_9, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) => (distinct_points(X28_502_9, intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91 -> [31116] ~apart_point_and_line(X28_502_9, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91 -> [31117] (distinct_points(X28_502_9, intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91
% 158.60/31.91 [31116] GAMMA_FORALL : ! [X31_31, Y32_32, Z33_33] : ((apart_point_and_line(X31_31, Y32_32) => (distinct_lines(Y32_32, Z33_33) | apart_point_and_line(X31_31, Z33_33))))
% 158.60/31.91 -> [31128] (apart_point_and_line(X31_923_10, Z33_923_10) => (distinct_lines(Z33_923_10, Z33_923_10) | apart_point_and_line(X31_923_10, Z33_923_10)))
% 158.60/31.91
% 158.60/31.91 [31128] BETA_IMPLY : (apart_point_and_line(X31_923_10, Z33_923_10) => (distinct_lines(Z33_923_10, Z33_923_10) | apart_point_and_line(X31_923_10, Z33_923_10)))
% 158.60/31.91 -> [31133] ~apart_point_and_line(X31_923_10, Z33_923_10)
% 158.60/31.91 -> [31134] (distinct_lines(Z33_923_10, Z33_923_10) | apart_point_and_line(X31_923_10, Z33_923_10))
% 158.60/31.91
% 158.60/31.91 [31134] BETA_OR : (distinct_lines(Z33_923_10, Z33_923_10) | apart_point_and_line(X31_923_10, Z33_923_10))
% 158.60/31.91 -> [31140] distinct_lines(Z33_923_10, Z33_923_10)
% 158.60/31.91 -> [31141] apart_point_and_line(X31_923_10, Z33_923_10)
% 158.60/31.91
% 158.60/31.91 [31141] CLOSURE : apart_point_and_line(X31_923_10, Z33_923_10)
% 158.60/31.91
% 158.60/31.91 [31140] CLOSURE : distinct_lines(Z33_923_10, Z33_923_10)
% 158.60/31.91
% 158.60/31.91 [31133] GAMMA_FORALL : ! [X34_34, Y35_35] : ((convergent_lines(X34_34, Y35_35) => distinct_lines(X34_34, Y35_35)))
% 158.60/31.91 -> [31163] (convergent_lines(Y35_1812_11, Y35_1812_11) => distinct_lines(Y35_1812_11, Y35_1812_11))
% 158.60/31.91
% 158.60/31.91 [31163] BETA_IMPLY : (convergent_lines(Y35_1812_11, Y35_1812_11) => distinct_lines(Y35_1812_11, Y35_1812_11))
% 158.60/31.91 -> [31164] ~convergent_lines(Y35_1812_11, Y35_1812_11)
% 158.60/31.91 -> [31165] distinct_lines(Y35_1812_11, Y35_1812_11)
% 158.60/31.91
% 158.60/31.91 [31165] CLOSURE : distinct_lines(Y35_1812_11, Y35_1812_11)
% 158.60/31.91
% 158.60/31.91 [31164] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 158.60/31.91 -> [31167] ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.91
% 158.60/31.91 [31167] BETA_NOT_AND : ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.91 -> [31170] ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91 -> [31171] ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31171] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91 -> [31175] unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31175] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31170] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91 -> [31177] convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31177] CLOSURE : convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31117] BETA_OR : (distinct_points(X28_502_9, intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31178] distinct_points(X28_502_9, intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.91 -> [31179] apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31178] CLOSURE : distinct_points(X28_502_9, intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.91
% 158.60/31.91 [31179] CLOSURE : apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [30767] BETA_OR : (((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31195] ((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31196] apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31196] CLOSURE : apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31195] BETA_OR : ((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31197] (apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31198] apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31198] CLOSURE : apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31197] BETA_OR : (apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31218] apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91 -> [31219] apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31219] CLOSURE : apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31218] CLOSURE : apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [30761] BETA_IMPLY : ((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), X21_16_7) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) => distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91 -> [31558] ~(apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), X21_16_7) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31559] distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91
% 158.60/31.91 [31558] ALPHA_NOT_OR : ~(apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), X21_16_7) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31563] ~apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), X21_16_7), ~apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31563] GAMMA_FORALL : ! [X24_24, Y25_25, U26_26, V27_27] : (((distinct_points(X24_24, Y25_25) & distinct_lines(U26_26, V27_27)) => (((apart_point_and_line(X24_24, U26_26) | apart_point_and_line(X24_24, V27_27)) | apart_point_and_line(Y25_25, U26_26)) | apart_point_and_line(Y25_25, V27_27))))
% 158.60/31.91 -> [31566] ((distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) & distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) => (((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91
% 158.60/31.91 [31566] BETA_IMPLY : ((distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) & distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) => (((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91 -> [31567] ~(distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) & distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31568] (((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91
% 158.60/31.91 [31567] BETA_NOT_AND : ~(distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) & distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31569] ~distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.91 -> [31570] ~distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31570] GAMMA_FORALL : ! [X28_28, Y29_29, Z30_30] : ((apart_point_and_line(X28_28, Y29_29) => (distinct_points(X28_28, Z30_30) | apart_point_and_line(Z30_30, Y29_29))))
% 158.60/31.91 -> [31577] (apart_point_and_line(Z30_518_9, Y29_518_9) => (distinct_points(Z30_518_9, Z30_518_9) | apart_point_and_line(Z30_518_9, Y29_518_9)))
% 158.60/31.91
% 158.60/31.91 [31577] BETA_IMPLY : (apart_point_and_line(Z30_518_9, Y29_518_9) => (distinct_points(Z30_518_9, Z30_518_9) | apart_point_and_line(Z30_518_9, Y29_518_9)))
% 158.60/31.91 -> [31579] ~apart_point_and_line(Z30_518_9, Y29_518_9)
% 158.60/31.91 -> [31580] (distinct_points(Z30_518_9, Z30_518_9) | apart_point_and_line(Z30_518_9, Y29_518_9))
% 158.60/31.91
% 158.60/31.91 [31579] GAMMA_FORALL : ! [X31_31, Y32_32, Z33_33] : ((apart_point_and_line(X31_31, Y32_32) => (distinct_lines(Y32_32, Z33_33) | apart_point_and_line(X31_31, Z33_33))))
% 158.60/31.91 -> [31589] (apart_point_and_line(X31_935_10, Y32_935_10) => (distinct_lines(Y32_935_10, Z33_935_10) | apart_point_and_line(X31_935_10, Z33_935_10)))
% 158.60/31.91
% 158.60/31.91 [31589] BETA_IMPLY : (apart_point_and_line(X31_935_10, Y32_935_10) => (distinct_lines(Y32_935_10, Z33_935_10) | apart_point_and_line(X31_935_10, Z33_935_10)))
% 158.60/31.91 -> [31590] ~apart_point_and_line(X31_935_10, Y32_935_10)
% 158.60/31.91 -> [31591] (distinct_lines(Y32_935_10, Z33_935_10) | apart_point_and_line(X31_935_10, Z33_935_10))
% 158.60/31.91
% 158.60/31.91 [31591] BETA_OR : (distinct_lines(Y32_935_10, Z33_935_10) | apart_point_and_line(X31_935_10, Z33_935_10))
% 158.60/31.91 -> [31592] distinct_lines(Y32_935_10, Z33_935_10)
% 158.60/31.91 -> [31593] apart_point_and_line(X31_935_10, Z33_935_10)
% 158.60/31.91
% 158.60/31.91 [31593] CLOSURE : apart_point_and_line(X31_935_10, Z33_935_10)
% 158.60/31.91
% 158.60/31.91 [31592] CLOSURE : distinct_lines(Y32_935_10, Z33_935_10)
% 158.60/31.91
% 158.60/31.91 [31590] GAMMA_FORALL : ! [X34_34, Y35_35] : ((convergent_lines(X34_34, Y35_35) => distinct_lines(X34_34, Y35_35)))
% 158.60/31.91 -> [31594] (convergent_lines(X34_1829_11, Y35_1829_11) => distinct_lines(X34_1829_11, Y35_1829_11))
% 158.60/31.91
% 158.60/31.91 [31594] BETA_IMPLY : (convergent_lines(X34_1829_11, Y35_1829_11) => distinct_lines(X34_1829_11, Y35_1829_11))
% 158.60/31.91 -> [31596] ~convergent_lines(X34_1829_11, Y35_1829_11)
% 158.60/31.91 -> [31597] distinct_lines(X34_1829_11, Y35_1829_11)
% 158.60/31.91
% 158.60/31.91 [31597] CLOSURE : distinct_lines(X34_1829_11, Y35_1829_11)
% 158.60/31.91
% 158.60/31.91 [31596] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 158.60/31.91 -> [31600] ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.91
% 158.60/31.91 [31600] BETA_NOT_AND : ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.91 -> [31603] ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91 -> [31604] ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31604] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91 -> [31609] unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31609] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31603] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91 -> [31608] convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31608] CLOSURE : convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31580] BETA_OR : (distinct_points(Z30_518_9, Z30_518_9) | apart_point_and_line(Z30_518_9, Y29_518_9))
% 158.60/31.91 -> [31615] distinct_points(Z30_518_9, Z30_518_9)
% 158.60/31.91 -> [31616] apart_point_and_line(Z30_518_9, Y29_518_9)
% 158.60/31.91
% 158.60/31.91 [31616] CLOSURE : apart_point_and_line(Z30_518_9, Y29_518_9)
% 158.60/31.91
% 158.60/31.91 [31615] CLOSURE : distinct_points(Z30_518_9, Z30_518_9)
% 158.60/31.91
% 158.60/31.91 [31569] GAMMA_FORALL : ! [X28_28, Y29_29, Z30_30] : ((apart_point_and_line(X28_28, Y29_29) => (distinct_points(X28_28, Z30_30) | apart_point_and_line(Z30_30, Y29_29))))
% 158.60/31.91 -> [31578] (apart_point_and_line(X31_936_10, line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9))) => (distinct_points(X31_936_10, X31_936_10) | apart_point_and_line(X31_936_10, line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91
% 158.60/31.91 [31578] BETA_IMPLY : (apart_point_and_line(X31_936_10, line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9))) => (distinct_points(X31_936_10, X31_936_10) | apart_point_and_line(X31_936_10, line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91 -> [31581] ~apart_point_and_line(X31_936_10, line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91 -> [31582] (distinct_points(X31_936_10, X31_936_10) | apart_point_and_line(X31_936_10, line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91
% 158.60/31.91 [31582] BETA_OR : (distinct_points(X31_936_10, X31_936_10) | apart_point_and_line(X31_936_10, line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31587] distinct_points(X31_936_10, X31_936_10)
% 158.60/31.91 -> [31588] apart_point_and_line(X31_936_10, line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31588] CLOSURE : apart_point_and_line(X31_936_10, line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31587] CLOSURE : distinct_points(X31_936_10, X31_936_10)
% 158.60/31.91
% 158.60/31.91 [31595] BETA_IMPLY : (apart_point_and_line(X31_936_10, line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9))) => (distinct_lines(line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(X31_936_10, line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91 -> [31617] ~apart_point_and_line(X31_936_10, line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91 -> [31618] (distinct_lines(line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(X31_936_10, line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91
% 158.60/31.91 [31617] GAMMA_FORALL : ! [X34_34, Y35_35] : ((convergent_lines(X34_34, Y35_35) => distinct_lines(X34_34, Y35_35)))
% 158.60/31.91 -> [31621] (convergent_lines(line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9))) => distinct_lines(line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91
% 158.60/31.91 [31621] BETA_IMPLY : (convergent_lines(line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9))) => distinct_lines(line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31622] ~convergent_lines(line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91 -> [31623] distinct_lines(line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31623] CLOSURE : distinct_lines(line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31622] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 158.60/31.91 -> [31626] ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.91
% 158.60/31.91 [31626] BETA_NOT_AND : ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.91 -> [31627] ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91 -> [31628] ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31627] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91 -> [31631] convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31631] CLOSURE : convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31628] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91 -> [31632] unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31632] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31618] BETA_OR : (distinct_lines(line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(X31_936_10, line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31619] distinct_lines(line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91 -> [31620] apart_point_and_line(X31_936_10, line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31620] CLOSURE : apart_point_and_line(X31_936_10, line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31619] CLOSURE : distinct_lines(line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_936_10, intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31568] BETA_OR : (((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31633] ((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31634] apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31633] BETA_OR : ((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31635] (apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31636] apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31635] BETA_OR : (apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31637] apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91 -> [31638] apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31638] CLOSURE : apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31637] CLOSURE : apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31636] CLOSURE : apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31634] CLOSURE : apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31559] GAMMA_FORALL : ! [X24_24, Y25_25, U26_26, V27_27] : (((distinct_points(X24_24, Y25_25) & distinct_lines(U26_26, V27_27)) => (((apart_point_and_line(X24_24, U26_26) | apart_point_and_line(X24_24, V27_27)) | apart_point_and_line(Y25_25, U26_26)) | apart_point_and_line(Y25_25, V27_27))))
% 158.60/31.91 -> [31639] ((distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) & distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) => (((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91
% 158.60/31.91 [31639] BETA_IMPLY : ((distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) & distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) => (((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91 -> [31640] ~(distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) & distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31641] (((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91
% 158.60/31.91 [31640] BETA_NOT_AND : ~(distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) & distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31642] ~distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31643] ~distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31643] GAMMA_FORALL : ! [X28_28, Y29_29, Z30_30] : ((apart_point_and_line(X28_28, Y29_29) => (distinct_points(X28_28, Z30_30) | apart_point_and_line(Z30_30, Y29_29))))
% 158.60/31.91 -> [31648] (apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) => (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91
% 158.60/31.91 [31648] BETA_IMPLY : (apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) => (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91 -> [31651] ~apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91 -> [31652] (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91
% 158.60/31.91 [31651] GAMMA_FORALL : ! [X31_31, Y32_32, Z33_33] : ((apart_point_and_line(X31_31, Y32_32) => (distinct_lines(Y32_32, Z33_33) | apart_point_and_line(X31_31, Z33_33))))
% 158.60/31.91 -> [31655] (apart_point_and_line(X31_937_10, Y32_937_10) => (distinct_lines(Y32_937_10, Z33_937_10) | apart_point_and_line(X31_937_10, Z33_937_10)))
% 158.60/31.91
% 158.60/31.91 [31655] BETA_IMPLY : (apart_point_and_line(X31_937_10, Y32_937_10) => (distinct_lines(Y32_937_10, Z33_937_10) | apart_point_and_line(X31_937_10, Z33_937_10)))
% 158.60/31.91 -> [31656] ~apart_point_and_line(X31_937_10, Y32_937_10)
% 158.60/31.91 -> [31657] (distinct_lines(Y32_937_10, Z33_937_10) | apart_point_and_line(X31_937_10, Z33_937_10))
% 158.60/31.91
% 158.60/31.91 [31656] GAMMA_FORALL : ! [X34_34, Y35_35] : ((convergent_lines(X34_34, Y35_35) => distinct_lines(X34_34, Y35_35)))
% 158.60/31.91 -> [31660] (convergent_lines(X34_1832_11, Y35_1832_11) => distinct_lines(X34_1832_11, Y35_1832_11))
% 158.60/31.91
% 158.60/31.91 [31660] BETA_IMPLY : (convergent_lines(X34_1832_11, Y35_1832_11) => distinct_lines(X34_1832_11, Y35_1832_11))
% 158.60/31.91 -> [31661] ~convergent_lines(X34_1832_11, Y35_1832_11)
% 158.60/31.91 -> [31662] distinct_lines(X34_1832_11, Y35_1832_11)
% 158.60/31.91
% 158.60/31.91 [31662] CLOSURE : distinct_lines(X34_1832_11, Y35_1832_11)
% 158.60/31.91
% 158.60/31.91 [31661] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 158.60/31.91 -> [31663] ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.91
% 158.60/31.91 [31663] BETA_NOT_AND : ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.91 -> [31664] ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91 -> [31665] ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31665] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91 -> [31667] unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31667] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31664] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91 -> [31666] convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31666] CLOSURE : convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31657] BETA_OR : (distinct_lines(Y32_937_10, Z33_937_10) | apart_point_and_line(X31_937_10, Z33_937_10))
% 158.60/31.91 -> [31658] distinct_lines(Y32_937_10, Z33_937_10)
% 158.60/31.91 -> [31659] apart_point_and_line(X31_937_10, Z33_937_10)
% 158.60/31.91
% 158.60/31.91 [31659] CLOSURE : apart_point_and_line(X31_937_10, Z33_937_10)
% 158.60/31.91
% 158.60/31.91 [31658] CLOSURE : distinct_lines(Y32_937_10, Z33_937_10)
% 158.60/31.91
% 158.60/31.91 [31652] BETA_OR : (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31668] distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.91 -> [31669] apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31668] CLOSURE : distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.91
% 158.60/31.91 [31669] CLOSURE : apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31642] CLOSURE : ~distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91
% 158.60/31.91 [31641] BETA_OR : (((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31670] ((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31671] apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31670] BETA_OR : ((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))) | apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31672] (apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31673] apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31672] BETA_OR : (apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31674] apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91 -> [31675] apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31675] CLOSURE : apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31674] CLOSURE : apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31673] GAMMA_FORALL : ! [X28_28, Y29_29, Z30_30] : ((apart_point_and_line(X28_28, Y29_29) => (distinct_points(X28_28, Z30_30) | apart_point_and_line(Z30_30, Y29_29))))
% 158.60/31.91 -> [31679] (apart_point_and_line(X31_938_10, line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9))) => (distinct_points(X31_938_10, X31_938_10) | apart_point_and_line(X31_938_10, line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91
% 158.60/31.91 [31679] BETA_IMPLY : (apart_point_and_line(X31_938_10, line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9))) => (distinct_points(X31_938_10, X31_938_10) | apart_point_and_line(X31_938_10, line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91 -> [31680] ~apart_point_and_line(X31_938_10, line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91 -> [31681] (distinct_points(X31_938_10, X31_938_10) | apart_point_and_line(X31_938_10, line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91
% 158.60/31.91 [31681] BETA_OR : (distinct_points(X31_938_10, X31_938_10) | apart_point_and_line(X31_938_10, line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31684] distinct_points(X31_938_10, X31_938_10)
% 158.60/31.91 -> [31685] apart_point_and_line(X31_938_10, line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31684] CLOSURE : distinct_points(X31_938_10, X31_938_10)
% 158.60/31.91
% 158.60/31.91 [31685] CLOSURE : apart_point_and_line(X31_938_10, line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31680] GAMMA_FORALL : ! [X31_31, Y32_32, Z33_33] : ((apart_point_and_line(X31_31, Y32_32) => (distinct_lines(Y32_32, Z33_33) | apart_point_and_line(X31_31, Z33_33))))
% 158.60/31.91 -> [31688] (apart_point_and_line(X31_938_10, line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9))) => (distinct_lines(line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(X31_938_10, line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91
% 158.60/31.91 [31688] BETA_IMPLY : (apart_point_and_line(X31_938_10, line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9))) => (distinct_lines(line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(X31_938_10, line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91 -> [31689] ~apart_point_and_line(X31_938_10, line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91 -> [31690] (distinct_lines(line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(X31_938_10, line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91
% 158.60/31.91 [31690] BETA_OR : (distinct_lines(line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(X31_938_10, line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31694] distinct_lines(line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91 -> [31695] apart_point_and_line(X31_938_10, line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31695] CLOSURE : apart_point_and_line(X31_938_10, line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31694] CLOSURE : distinct_lines(line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31689] GAMMA_FORALL : ! [X34_34, Y35_35] : ((convergent_lines(X34_34, Y35_35) => distinct_lines(X34_34, Y35_35)))
% 158.60/31.91 -> [31698] (convergent_lines(line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9))) => distinct_lines(line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91
% 158.60/31.91 [31698] BETA_IMPLY : (convergent_lines(line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9))) => distinct_lines(line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31699] ~convergent_lines(line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91 -> [31700] distinct_lines(line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31700] CLOSURE : distinct_lines(line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)), line_connecting(X31_938_10, intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31699] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 158.60/31.91 -> [31703] ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.91
% 158.60/31.91 [31703] BETA_NOT_AND : ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.91 -> [31704] ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91 -> [31705] ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31705] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91 -> [31710] unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31710] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31704] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91 -> [31709] convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31709] CLOSURE : convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.91
% 158.60/31.91 [31671] GAMMA_FORALL : ! [X28_28, Y29_29, Z30_30] : ((apart_point_and_line(X28_28, Y29_29) => (distinct_points(X28_28, Z30_30) | apart_point_and_line(Z30_30, Y29_29))))
% 158.60/31.91 -> [31676] (apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) => (distinct_points(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91
% 158.60/31.91 [31676] BETA_IMPLY : (apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) => (distinct_points(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.91 -> [31677] ~apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91 -> [31678] (distinct_points(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91
% 158.60/31.91 [31677] CLOSURE : ~apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31678] BETA_OR : (distinct_points(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.91 -> [31686] distinct_points(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.91 -> [31687] apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31687] CLOSURE : apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.91
% 158.60/31.91 [31686] GAMMA_FORALL : ! [X31_31, Y32_32, Z33_33] : ((apart_point_and_line(X31_31, Y32_32) => (distinct_lines(Y32_32, Z33_33) | apart_point_and_line(X31_31, Z33_33))))
% 158.60/31.92 -> [31691] (apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) => (distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.92
% 158.60/31.92 [31691] BETA_IMPLY : (apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) => (distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))))
% 158.60/31.92 -> [31692] ~apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.92 -> [31693] (distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.92
% 158.60/31.92 [31692] CLOSURE : ~apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.92
% 158.60/31.92 [31693] BETA_OR : (distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) | apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.92 -> [31701] distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.92 -> [31702] apart_point_and_line(intersection_point(X21_16_7, line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.92
% 158.60/31.92 [31701] CLOSURE : distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.92
% 158.60/31.92 [31702] GAMMA_FORALL : ! [X34_34, Y35_35] : ((convergent_lines(X34_34, Y35_35) => distinct_lines(X34_34, Y35_35)))
% 158.60/31.92 -> [31706] (convergent_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) => distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.92
% 158.60/31.92 [31706] BETA_IMPLY : (convergent_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))) => distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.92 -> [31707] ~convergent_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.92 -> [31708] distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.92
% 158.60/31.92 [31708] CLOSURE : distinct_lines(line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)), line_connecting(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.92
% 158.60/31.92 [31707] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 158.60/31.92 -> [31711] ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92
% 158.60/31.92 [31711] BETA_NOT_AND : ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92 -> [31712] ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [31713] ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [31713] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [31715] unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [31715] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [31712] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [31714] convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [31714] CLOSURE : convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [28659] BETA_IMPLY : (convergent_lines(Y29_536_9, Y29_536_9) => ((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)) => distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))))
% 158.60/31.92 -> [31716] ~convergent_lines(Y29_536_9, Y29_536_9)
% 158.60/31.92 -> [31717] ((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)) => distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.92
% 158.60/31.92 [31717] BETA_IMPLY : ((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)) => distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)))
% 158.60/31.92 -> [31718] ~(apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9))
% 158.60/31.92 -> [31719] distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.92
% 158.60/31.92 [31719] CLOSURE : distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.92
% 158.60/31.92 [31724] BETA_IMPLY : ((distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) & distinct_lines(Y29_536_9, Y29_536_9)) => (((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)))
% 158.60/31.92 -> [32315] ~(distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) & distinct_lines(Y29_536_9, Y29_536_9))
% 158.60/31.92 -> [32316] (((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9))
% 158.60/31.92
% 158.60/31.92 [32316] BETA_OR : (((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9))
% 158.60/31.92 -> [32321] ((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9))
% 158.60/31.92 -> [32322] apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)
% 158.60/31.92
% 158.60/31.92 [32321] BETA_OR : ((apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9))
% 158.60/31.92 -> [32324] (apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9))
% 158.60/31.92 -> [32325] apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)
% 158.60/31.92
% 158.60/31.92 [32325] CLOSURE : apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)
% 158.60/31.92
% 158.60/31.92 [32324] BETA_OR : (apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9))
% 158.60/31.92 -> [32366] apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)
% 158.60/31.92 -> [32367] apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)
% 158.60/31.92
% 158.60/31.92 [32366] CLOSURE : apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)
% 158.60/31.92
% 158.60/31.92 [32367] CLOSURE : apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)
% 158.60/31.92
% 158.60/31.92 [32322] CLOSURE : apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)
% 158.60/31.92
% 158.60/31.92 [32315] BETA_NOT_AND : ~(distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) & distinct_lines(Y29_536_9, Y29_536_9))
% 158.60/31.92 -> [32398] ~distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.92 -> [32399] ~distinct_lines(Y29_536_9, Y29_536_9)
% 158.60/31.92
% 158.60/31.92 [32399] GAMMA_FORALL : ! [X28_28, Y29_29, Z30_30] : ((apart_point_and_line(X28_28, Y29_29) => (distinct_points(X28_28, Z30_30) | apart_point_and_line(Z30_30, Y29_29))))
% 158.60/31.92 -> [32404] (apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9) => (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)))
% 158.60/31.92
% 158.60/31.92 [32404] BETA_IMPLY : (apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9) => (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)))
% 158.60/31.92 -> [32408] ~apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)
% 158.60/31.92 -> [32409] (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9))
% 158.60/31.92
% 158.60/31.92 [32409] BETA_OR : (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9))
% 158.60/31.92 -> [32410] distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.92 -> [32411] apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)
% 158.60/31.92
% 158.60/31.92 [32410] CLOSURE : distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.92
% 158.60/31.92 [32411] CLOSURE : apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)
% 158.60/31.92
% 158.60/31.92 [32408] GAMMA_FORALL : ! [X31_31, Y32_32, Z33_33] : ((apart_point_and_line(X31_31, Y32_32) => (distinct_lines(Y32_32, Z33_33) | apart_point_and_line(X31_31, Z33_33))))
% 158.60/31.92 -> [32413] (apart_point_and_line(X31_964_10, Y32_964_10) => (distinct_lines(Y32_964_10, Y32_964_10) | apart_point_and_line(X31_964_10, Y32_964_10)))
% 158.60/31.92
% 158.60/31.92 [32413] BETA_IMPLY : (apart_point_and_line(X31_964_10, Y32_964_10) => (distinct_lines(Y32_964_10, Y32_964_10) | apart_point_and_line(X31_964_10, Y32_964_10)))
% 158.60/31.92 -> [32418] ~apart_point_and_line(X31_964_10, Y32_964_10)
% 158.60/31.92 -> [32419] (distinct_lines(Y32_964_10, Y32_964_10) | apart_point_and_line(X31_964_10, Y32_964_10))
% 158.60/31.92
% 158.60/31.92 [32418] GAMMA_FORALL : ! [X34_34, Y35_35] : ((convergent_lines(X34_34, Y35_35) => distinct_lines(X34_34, Y35_35)))
% 158.60/31.92 -> [32427] (convergent_lines(Y35_1882_11, Y35_1882_11) => distinct_lines(Y35_1882_11, Y35_1882_11))
% 158.60/31.92
% 158.60/31.92 [32427] BETA_IMPLY : (convergent_lines(Y35_1882_11, Y35_1882_11) => distinct_lines(Y35_1882_11, Y35_1882_11))
% 158.60/31.92 -> [32428] ~convergent_lines(Y35_1882_11, Y35_1882_11)
% 158.60/31.92 -> [32429] distinct_lines(Y35_1882_11, Y35_1882_11)
% 158.60/31.92
% 158.60/31.92 [32429] CLOSURE : distinct_lines(Y35_1882_11, Y35_1882_11)
% 158.60/31.92
% 158.60/31.92 [32428] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 158.60/31.92 -> [32434] ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92
% 158.60/31.92 [32434] BETA_NOT_AND : ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92 -> [32436] ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32437] ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32437] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32439] unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32439] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32436] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32438] convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32438] CLOSURE : convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32419] BETA_OR : (distinct_lines(Y32_964_10, Y32_964_10) | apart_point_and_line(X31_964_10, Y32_964_10))
% 158.60/31.92 -> [32425] distinct_lines(Y32_964_10, Y32_964_10)
% 158.60/31.92 -> [32426] apart_point_and_line(X31_964_10, Y32_964_10)
% 158.60/31.92
% 158.60/31.92 [32426] CLOSURE : apart_point_and_line(X31_964_10, Y32_964_10)
% 158.60/31.92
% 158.60/31.92 [32425] CLOSURE : distinct_lines(Y32_964_10, Y32_964_10)
% 158.60/31.92
% 158.60/31.92 [32398] GAMMA_FORALL : ! [X28_28, Y29_29, Z30_30] : ((apart_point_and_line(X28_28, Y29_29) => (distinct_points(X28_28, Z30_30) | apart_point_and_line(Z30_30, Y29_29))))
% 158.60/31.92 -> [32403] (apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9) => (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)))
% 158.60/31.92
% 158.60/31.92 [32403] BETA_IMPLY : (apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9) => (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)))
% 158.60/31.92 -> [32406] ~apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)
% 158.60/31.92 -> [32407] (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9))
% 158.60/31.92
% 158.60/31.92 [32407] BETA_OR : (distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9)) | apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9))
% 158.60/31.92 -> [32416] distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.92 -> [32417] apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)
% 158.60/31.92
% 158.60/31.92 [32416] CLOSURE : distinct_points(intersection_point(Y29_536_9, Y29_536_9), intersection_point(Y29_536_9, Y29_536_9))
% 158.60/31.92
% 158.60/31.92 [32417] CLOSURE : apart_point_and_line(intersection_point(Y29_536_9, Y29_536_9), Y29_536_9)
% 158.60/31.92
% 158.60/31.92 [32412] BETA_IMPLY : (apart_point_and_line(X31_963_10, Y32_963_10) => (distinct_lines(Y32_963_10, Z33_963_10) | apart_point_and_line(X31_963_10, Z33_963_10)))
% 158.60/31.92 -> [32440] ~apart_point_and_line(X31_963_10, Y32_963_10)
% 158.60/31.92 -> [32441] (distinct_lines(Y32_963_10, Z33_963_10) | apart_point_and_line(X31_963_10, Z33_963_10))
% 158.60/31.92
% 158.60/31.92 [32440] GAMMA_FORALL : ! [X34_34, Y35_35] : ((convergent_lines(X34_34, Y35_35) => distinct_lines(X34_34, Y35_35)))
% 158.60/31.92 -> [32444] (convergent_lines(line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10)), line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10))) => distinct_lines(line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10)), line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10))))
% 158.60/31.92
% 158.60/31.92 [32444] BETA_IMPLY : (convergent_lines(line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10)), line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10))) => distinct_lines(line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10)), line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10))))
% 158.60/31.92 -> [32445] ~convergent_lines(line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10)), line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10)))
% 158.60/31.92 -> [32446] distinct_lines(line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10)), line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10)))
% 158.60/31.92
% 158.60/31.92 [32446] CLOSURE : distinct_lines(line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10)), line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10)))
% 158.60/31.92
% 158.60/31.92 [32445] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 158.60/31.92 -> [32447] ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92
% 158.60/31.92 [32447] BETA_NOT_AND : ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92 -> [32449] ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32450] ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32449] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32454] convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32454] CLOSURE : convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32450] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32453] unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32453] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32441] BETA_OR : (distinct_lines(Y32_963_10, Z33_963_10) | apart_point_and_line(X31_963_10, Z33_963_10))
% 158.60/31.92 -> [32442] distinct_lines(Y32_963_10, Z33_963_10)
% 158.60/31.92 -> [32443] apart_point_and_line(X31_963_10, Z33_963_10)
% 158.60/31.92
% 158.60/31.92 [32443] CLOSURE : apart_point_and_line(X31_963_10, Z33_963_10)
% 158.60/31.92
% 158.60/31.92 [32442] GAMMA_FORALL : ! [X34_34, Y35_35] : ((convergent_lines(X34_34, Y35_35) => distinct_lines(X34_34, Y35_35)))
% 158.60/31.92 -> [32448] (convergent_lines(line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10)), line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10))) => distinct_lines(line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10)), line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10))))
% 158.60/31.92
% 158.60/31.92 [32448] BETA_IMPLY : (convergent_lines(line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10)), line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10))) => distinct_lines(line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10)), line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10))))
% 158.60/31.92 -> [32451] ~convergent_lines(line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10)), line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10)))
% 158.60/31.92 -> [32452] distinct_lines(line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10)), line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10)))
% 158.60/31.92
% 158.60/31.92 [32452] CLOSURE : distinct_lines(line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10)), line_connecting(X31_963_10, intersection_point(Z33_963_10, Z33_963_10)))
% 158.60/31.92
% 158.60/31.92 [32451] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 158.60/31.92 -> [32455] ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92
% 158.60/31.92 [32455] BETA_NOT_AND : ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92 -> [32456] ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32457] ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32457] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32459] unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32459] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32456] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32458] convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32458] CLOSURE : convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [31716] GAMMA_FORALL : ! [X24_24, Y25_25, U26_26, V27_27] : (((distinct_points(X24_24, Y25_25) & distinct_lines(U26_26, V27_27)) => (((apart_point_and_line(X24_24, U26_26) | apart_point_and_line(X24_24, V27_27)) | apart_point_and_line(Y25_25, U26_26)) | apart_point_and_line(Y25_25, V27_27))))
% 158.60/31.92 -> [31721] ((distinct_points(X28_524_9, X28_524_9) & distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9))) => (((apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9)) | apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9))) | apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9))) | apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9))))
% 158.60/31.92
% 158.60/31.92 [31721] BETA_IMPLY : ((distinct_points(X28_524_9, X28_524_9) & distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9))) => (((apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9)) | apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9))) | apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9))) | apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9))))
% 158.60/31.92 -> [31722] ~(distinct_points(X28_524_9, X28_524_9) & distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9)))
% 158.60/31.92 -> [31723] (((apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9)) | apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9))) | apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9))) | apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9)))
% 158.60/31.92
% 158.60/31.92 [31723] BETA_OR : (((apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9)) | apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9))) | apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9))) | apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9)))
% 158.60/31.92 -> [31729] ((apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9)) | apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9))) | apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9)))
% 158.60/31.92 -> [31730] apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92
% 158.60/31.92 [31729] BETA_OR : ((apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9)) | apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9))) | apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9)))
% 158.60/31.92 -> [31735] (apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9)) | apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9)))
% 158.60/31.92 -> [31736] apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92
% 158.60/31.92 [31735] BETA_OR : (apart_point_and_line(X28_529_9, line_connecting(X28_529_9, X28_524_9)) | apart_point_and_line(X28_529_9, line_connecting(X28_529_9, X28_524_9)))
% 158.60/31.92 -> [31758] apart_point_and_line(X28_529_9, line_connecting(X28_529_9, X28_524_9))
% 158.60/31.92 -> [31759] apart_point_and_line(X28_529_9, line_connecting(X28_529_9, X28_524_9))
% 158.60/31.92
% 158.60/31.92 [31758] GAMMA_FORALL : ! [X28_28, Y29_29, Z30_30] : ((apart_point_and_line(X28_28, Y29_29) => (distinct_points(X28_28, Z30_30) | apart_point_and_line(Z30_30, Y29_29))))
% 158.60/31.92 -> [31810] (apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_530_9)) => (distinct_points(X28_524_9, Z30_530_9) | apart_point_and_line(Z30_530_9, line_connecting(X28_524_9, Z30_530_9))))
% 158.60/31.92
% 158.60/31.92 [31810] BETA_IMPLY : (apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_530_9)) => (distinct_points(X28_524_9, Z30_530_9) | apart_point_and_line(Z30_530_9, line_connecting(X28_524_9, Z30_530_9))))
% 158.60/31.92 -> [31814] ~apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_530_9))
% 158.60/31.92 -> [31815] (distinct_points(X28_524_9, Z30_530_9) | apart_point_and_line(Z30_530_9, line_connecting(X28_524_9, Z30_530_9)))
% 158.60/31.92
% 158.60/31.92 [31814] CLOSURE : ~apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_530_9))
% 158.60/31.92
% 158.60/31.92 [31815] BETA_OR : (distinct_points(X28_524_9, Z30_530_9) | apart_point_and_line(Z30_530_9, line_connecting(X28_524_9, Z30_530_9)))
% 158.60/31.92 -> [32035] distinct_points(X28_524_9, Z30_530_9)
% 158.60/31.92 -> [32036] apart_point_and_line(Z30_530_9, line_connecting(X28_524_9, Z30_530_9))
% 158.60/31.92
% 158.60/31.92 [32035] CLOSURE : distinct_points(X28_524_9, Z30_530_9)
% 158.60/31.92
% 158.60/31.92 [32040] BETA_IMPLY : (apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_530_9)) => (distinct_lines(line_connecting(X28_524_9, Z30_530_9), line_connecting(X28_524_9, Z30_530_9)) | apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_530_9))))
% 158.60/31.92 -> [32135] ~apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_530_9))
% 158.60/31.92 -> [32136] (distinct_lines(line_connecting(X28_524_9, Z30_530_9), line_connecting(X28_524_9, Z30_530_9)) | apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_530_9)))
% 158.60/31.92
% 158.60/31.92 [32136] BETA_OR : (distinct_lines(line_connecting(X28_524_9, Z30_530_9), line_connecting(X28_524_9, Z30_530_9)) | apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_530_9)))
% 158.60/31.92 -> [32143] distinct_lines(line_connecting(X28_524_9, Z30_530_9), line_connecting(X28_524_9, Z30_530_9))
% 158.60/31.92 -> [32144] apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_530_9))
% 158.60/31.92
% 158.60/31.92 [32143] CLOSURE : distinct_lines(line_connecting(X28_524_9, Z30_530_9), line_connecting(X28_524_9, Z30_530_9))
% 158.60/31.92
% 158.60/31.92 [32144] GAMMA_FORALL : ! [X34_34, Y35_35] : ((convergent_lines(X34_34, Y35_35) => distinct_lines(X34_34, Y35_35)))
% 158.60/31.92 -> [32149] (convergent_lines(line_connecting(X28_524_9, Z30_530_9), line_connecting(X28_524_9, Z30_530_9)) => distinct_lines(line_connecting(X28_524_9, Z30_530_9), line_connecting(X28_524_9, Z30_530_9)))
% 158.60/31.92
% 158.60/31.92 [32149] BETA_IMPLY : (convergent_lines(line_connecting(X28_524_9, Z30_530_9), line_connecting(X28_524_9, Z30_530_9)) => distinct_lines(line_connecting(X28_524_9, Z30_530_9), line_connecting(X28_524_9, Z30_530_9)))
% 158.60/31.92 -> [32150] ~convergent_lines(line_connecting(X28_524_9, Z30_530_9), line_connecting(X28_524_9, Z30_530_9))
% 158.60/31.92 -> [32151] distinct_lines(line_connecting(X28_524_9, Z30_530_9), line_connecting(X28_524_9, Z30_530_9))
% 158.60/31.92
% 158.60/31.92 [32151] CLOSURE : distinct_lines(line_connecting(X28_524_9, Z30_530_9), line_connecting(X28_524_9, Z30_530_9))
% 158.60/31.92
% 158.60/31.92 [32150] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 158.60/31.92 -> [32154] ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92
% 158.60/31.92 [32154] BETA_NOT_AND : ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92 -> [32155] ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32156] ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32155] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32157] convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32157] CLOSURE : convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32156] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32159] unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32159] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32135] CLOSURE : ~apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_530_9))
% 158.60/31.92
% 158.60/31.92 [31791] BETA_IMPLY : (apart_point_and_line(X28_529_9, line_connecting(X28_529_9, X28_524_9)) => (distinct_points(X28_529_9, X28_524_9) | apart_point_and_line(X28_524_9, line_connecting(X28_529_9, X28_524_9))))
% 158.60/31.92 -> [32270] ~apart_point_and_line(X28_529_9, line_connecting(X28_529_9, X28_524_9))
% 158.60/31.92 -> [32271] (distinct_points(X28_529_9, X28_524_9) | apart_point_and_line(X28_524_9, line_connecting(X28_529_9, X28_524_9)))
% 158.60/31.92
% 158.60/31.92 [32270] CLOSURE : ~apart_point_and_line(X28_529_9, line_connecting(X28_529_9, X28_524_9))
% 158.60/31.92
% 158.60/31.92 [32271] BETA_OR : (distinct_points(X28_529_9, X28_524_9) | apart_point_and_line(X28_524_9, line_connecting(X28_529_9, X28_524_9)))
% 158.60/31.92 -> [32373] distinct_points(X28_529_9, X28_524_9)
% 158.60/31.92 -> [32374] apart_point_and_line(X28_524_9, line_connecting(X28_529_9, X28_524_9))
% 158.60/31.92
% 158.60/31.92 [32374] GAMMA_FORALL : ! [X31_31, Y32_32, Z33_33] : ((apart_point_and_line(X31_31, Y32_32) => (distinct_lines(Y32_32, Z33_33) | apart_point_and_line(X31_31, Z33_33))))
% 158.60/31.92 -> [32377] (apart_point_and_line(X31_962_10, line_connecting(X28_529_9, X28_524_9)) => (distinct_lines(line_connecting(X28_529_9, X28_524_9), line_connecting(X28_529_9, X28_524_9)) | apart_point_and_line(X31_962_10, line_connecting(X28_529_9, X28_524_9))))
% 158.60/31.92
% 158.60/31.92 [32377] BETA_IMPLY : (apart_point_and_line(X31_962_10, line_connecting(X28_529_9, X28_524_9)) => (distinct_lines(line_connecting(X28_529_9, X28_524_9), line_connecting(X28_529_9, X28_524_9)) | apart_point_and_line(X31_962_10, line_connecting(X28_529_9, X28_524_9))))
% 158.60/31.92 -> [32378] ~apart_point_and_line(X31_962_10, line_connecting(X28_529_9, X28_524_9))
% 158.60/31.92 -> [32379] (distinct_lines(line_connecting(X28_529_9, X28_524_9), line_connecting(X28_529_9, X28_524_9)) | apart_point_and_line(X31_962_10, line_connecting(X28_529_9, X28_524_9)))
% 158.60/31.92
% 158.60/31.92 [32378] CLOSURE : ~apart_point_and_line(X31_962_10, line_connecting(X28_529_9, X28_524_9))
% 158.60/31.92
% 158.60/31.92 [32379] BETA_OR : (distinct_lines(line_connecting(X28_529_9, X28_524_9), line_connecting(X28_529_9, X28_524_9)) | apart_point_and_line(X31_962_10, line_connecting(X28_529_9, X28_524_9)))
% 158.60/31.92 -> [32392] distinct_lines(line_connecting(X28_529_9, X28_524_9), line_connecting(X28_529_9, X28_524_9))
% 158.60/31.92 -> [32393] apart_point_and_line(X31_962_10, line_connecting(X28_529_9, X28_524_9))
% 158.60/31.92
% 158.60/31.92 [32392] CLOSURE : distinct_lines(line_connecting(X28_529_9, X28_524_9), line_connecting(X28_529_9, X28_524_9))
% 158.60/31.92
% 158.60/31.92 [32393] GAMMA_FORALL : ! [X34_34, Y35_35] : ((convergent_lines(X34_34, Y35_35) => distinct_lines(X34_34, Y35_35)))
% 158.60/31.92 -> [32394] (convergent_lines(line_connecting(X28_529_9, X28_524_9), line_connecting(X28_529_9, X28_524_9)) => distinct_lines(line_connecting(X28_529_9, X28_524_9), line_connecting(X28_529_9, X28_524_9)))
% 158.60/31.92
% 158.60/31.92 [32394] BETA_IMPLY : (convergent_lines(line_connecting(X28_529_9, X28_524_9), line_connecting(X28_529_9, X28_524_9)) => distinct_lines(line_connecting(X28_529_9, X28_524_9), line_connecting(X28_529_9, X28_524_9)))
% 158.60/31.92 -> [32395] ~convergent_lines(line_connecting(X28_529_9, X28_524_9), line_connecting(X28_529_9, X28_524_9))
% 158.60/31.92 -> [32396] distinct_lines(line_connecting(X28_529_9, X28_524_9), line_connecting(X28_529_9, X28_524_9))
% 158.60/31.92
% 158.60/31.92 [32396] CLOSURE : distinct_lines(line_connecting(X28_529_9, X28_524_9), line_connecting(X28_529_9, X28_524_9))
% 158.60/31.92
% 158.60/31.92 [32395] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 158.60/31.92 -> [32397] ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92
% 158.60/31.92 [32397] BETA_NOT_AND : ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92 -> [32400] ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32401] ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32401] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32405] unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32405] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32400] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32402] convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32402] CLOSURE : convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32373] CLOSURE : distinct_points(X28_529_9, X28_524_9)
% 158.60/31.92
% 158.60/31.92 [31763] BETA_IMPLY : (apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9)) => (distinct_points(X28_524_9, Z30_524_9) | apart_point_and_line(Z30_524_9, line_connecting(X28_524_9, Z30_524_9))))
% 158.60/31.92 -> [32460] ~apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92 -> [32461] (distinct_points(X28_524_9, Z30_524_9) | apart_point_and_line(Z30_524_9, line_connecting(X28_524_9, Z30_524_9)))
% 158.60/31.92
% 158.60/31.92 [32461] BETA_OR : (distinct_points(X28_524_9, Z30_524_9) | apart_point_and_line(Z30_524_9, line_connecting(X28_524_9, Z30_524_9)))
% 158.60/31.92 -> [32462] distinct_points(X28_524_9, Z30_524_9)
% 158.60/31.92 -> [32463] apart_point_and_line(Z30_524_9, line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92
% 158.60/31.92 [32463] GAMMA_FORALL : ! [X31_31, Y32_32, Z33_33] : ((apart_point_and_line(X31_31, Y32_32) => (distinct_lines(Y32_32, Z33_33) | apart_point_and_line(X31_31, Z33_33))))
% 158.60/31.92 -> [32464] (apart_point_and_line(X31_965_10, line_connecting(X28_524_9, Z30_524_9)) => (distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9)) | apart_point_and_line(X31_965_10, line_connecting(X28_524_9, Z30_524_9))))
% 158.60/31.92
% 158.60/31.92 [32464] BETA_IMPLY : (apart_point_and_line(X31_965_10, line_connecting(X28_524_9, Z30_524_9)) => (distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9)) | apart_point_and_line(X31_965_10, line_connecting(X28_524_9, Z30_524_9))))
% 158.60/31.92 -> [32465] ~apart_point_and_line(X31_965_10, line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92 -> [32466] (distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9)) | apart_point_and_line(X31_965_10, line_connecting(X28_524_9, Z30_524_9)))
% 158.60/31.92
% 158.60/31.92 [32466] BETA_OR : (distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9)) | apart_point_and_line(X31_965_10, line_connecting(X28_524_9, Z30_524_9)))
% 158.60/31.92 -> [32467] distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92 -> [32468] apart_point_and_line(X31_965_10, line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92
% 158.60/31.92 [32467] CLOSURE : distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92
% 158.60/31.92 [32468] GAMMA_FORALL : ! [X34_34, Y35_35] : ((convergent_lines(X34_34, Y35_35) => distinct_lines(X34_34, Y35_35)))
% 158.60/31.92 -> [32469] (convergent_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9)) => distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9)))
% 158.60/31.92
% 158.60/31.92 [32469] BETA_IMPLY : (convergent_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9)) => distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9)))
% 158.60/31.92 -> [32470] ~convergent_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92 -> [32471] distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92
% 158.60/31.92 [32471] CLOSURE : distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92
% 158.60/31.92 [32470] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 158.60/31.92 -> [32472] ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92
% 158.60/31.92 [32472] BETA_NOT_AND : ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92 -> [32473] ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32474] ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32474] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32476] unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32476] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32473] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32475] convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32475] CLOSURE : convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32465] CLOSURE : ~apart_point_and_line(X31_965_10, line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92
% 158.60/31.92 [32462] CLOSURE : distinct_points(X28_524_9, Z30_524_9)
% 158.60/31.92
% 158.60/31.92 [32460] CLOSURE : ~apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92
% 158.60/31.92 [31740] BETA_IMPLY : (apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9)) => (distinct_points(X28_524_9, Z30_524_9) | apart_point_and_line(Z30_524_9, line_connecting(X28_524_9, Z30_524_9))))
% 158.60/31.92 -> [32477] ~apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92 -> [32478] (distinct_points(X28_524_9, Z30_524_9) | apart_point_and_line(Z30_524_9, line_connecting(X28_524_9, Z30_524_9)))
% 158.60/31.92
% 158.60/31.92 [32478] BETA_OR : (distinct_points(X28_524_9, Z30_524_9) | apart_point_and_line(Z30_524_9, line_connecting(X28_524_9, Z30_524_9)))
% 158.60/31.92 -> [32479] distinct_points(X28_524_9, Z30_524_9)
% 158.60/31.92 -> [32480] apart_point_and_line(Z30_524_9, line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92
% 158.60/31.92 [32480] GAMMA_FORALL : ! [X31_31, Y32_32, Z33_33] : ((apart_point_and_line(X31_31, Y32_32) => (distinct_lines(Y32_32, Z33_33) | apart_point_and_line(X31_31, Z33_33))))
% 158.60/31.92 -> [32481] (apart_point_and_line(X31_966_10, line_connecting(X28_524_9, Z30_524_9)) => (distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9)) | apart_point_and_line(X31_966_10, line_connecting(X28_524_9, Z30_524_9))))
% 158.60/31.92
% 158.60/31.92 [32481] BETA_IMPLY : (apart_point_and_line(X31_966_10, line_connecting(X28_524_9, Z30_524_9)) => (distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9)) | apart_point_and_line(X31_966_10, line_connecting(X28_524_9, Z30_524_9))))
% 158.60/31.92 -> [32482] ~apart_point_and_line(X31_966_10, line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92 -> [32483] (distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9)) | apart_point_and_line(X31_966_10, line_connecting(X28_524_9, Z30_524_9)))
% 158.60/31.92
% 158.60/31.92 [32482] CLOSURE : ~apart_point_and_line(X31_966_10, line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92
% 158.60/31.92 [32483] BETA_OR : (distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9)) | apart_point_and_line(X31_966_10, line_connecting(X28_524_9, Z30_524_9)))
% 158.60/31.92 -> [32494] distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92 -> [32495] apart_point_and_line(X31_966_10, line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92
% 158.60/31.92 [32494] CLOSURE : distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92
% 158.60/31.92 [32495] GAMMA_FORALL : ! [X34_34, Y35_35] : ((convergent_lines(X34_34, Y35_35) => distinct_lines(X34_34, Y35_35)))
% 158.60/31.92 -> [32496] (convergent_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9)) => distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9)))
% 158.60/31.92
% 158.60/31.92 [32496] BETA_IMPLY : (convergent_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9)) => distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9)))
% 158.60/31.92 -> [32497] ~convergent_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92 -> [32498] distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92
% 158.60/31.92 [32498] CLOSURE : distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92
% 158.60/31.92 [32497] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 158.60/31.92 -> [32499] ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92
% 158.60/31.92 [32499] BETA_NOT_AND : ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92 -> [32500] ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32501] ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32501] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32502] unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32502] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32500] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32503] convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32503] CLOSURE : convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32479] CLOSURE : distinct_points(X28_524_9, Z30_524_9)
% 158.60/31.92
% 158.60/31.92 [32477] CLOSURE : ~apart_point_and_line(X28_524_9, line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92
% 158.60/31.92 [31722] BETA_NOT_AND : ~(distinct_points(X28_524_9, X28_524_9) & distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9)))
% 158.60/31.92 -> [32504] ~distinct_points(X28_524_9, X28_524_9)
% 158.60/31.92 -> [32505] ~distinct_lines(line_connecting(X28_524_9, Z30_524_9), line_connecting(X28_524_9, Z30_524_9))
% 158.60/31.92
% 158.60/31.92 [32505] GAMMA_FORALL : ! [X28_28, Y29_29, Z30_30] : ((apart_point_and_line(X28_28, Y29_29) => (distinct_points(X28_28, Z30_30) | apart_point_and_line(Z30_30, Y29_29))))
% 158.60/31.92 -> [32506] (apart_point_and_line(X28_537_9, line_connecting(X28_537_9, Z30_537_9)) => (distinct_points(X28_537_9, Z30_537_9) | apart_point_and_line(Z30_537_9, line_connecting(X28_537_9, Z30_537_9))))
% 158.60/31.92
% 158.60/31.92 [32506] BETA_IMPLY : (apart_point_and_line(X28_537_9, line_connecting(X28_537_9, Z30_537_9)) => (distinct_points(X28_537_9, Z30_537_9) | apart_point_and_line(Z30_537_9, line_connecting(X28_537_9, Z30_537_9))))
% 158.60/31.92 -> [32508] ~apart_point_and_line(X28_537_9, line_connecting(X28_537_9, Z30_537_9))
% 158.60/31.92 -> [32509] (distinct_points(X28_537_9, Z30_537_9) | apart_point_and_line(Z30_537_9, line_connecting(X28_537_9, Z30_537_9)))
% 158.60/31.92
% 158.60/31.92 [32508] GAMMA_FORALL : ! [X31_31, Y32_32, Z33_33] : ((apart_point_and_line(X31_31, Y32_32) => (distinct_lines(Y32_32, Z33_33) | apart_point_and_line(X31_31, Z33_33))))
% 158.60/31.92 -> [32516] (apart_point_and_line(X31_967_10, line_connecting(X28_537_9, Z30_537_9)) => (distinct_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9)) | apart_point_and_line(X31_967_10, line_connecting(X28_537_9, Z30_537_9))))
% 158.60/31.92
% 158.60/31.92 [32516] BETA_IMPLY : (apart_point_and_line(X31_967_10, line_connecting(X28_537_9, Z30_537_9)) => (distinct_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9)) | apart_point_and_line(X31_967_10, line_connecting(X28_537_9, Z30_537_9))))
% 158.60/31.92 -> [32517] ~apart_point_and_line(X31_967_10, line_connecting(X28_537_9, Z30_537_9))
% 158.60/31.92 -> [32518] (distinct_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9)) | apart_point_and_line(X31_967_10, line_connecting(X28_537_9, Z30_537_9)))
% 158.60/31.92
% 158.60/31.92 [32518] BETA_OR : (distinct_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9)) | apart_point_and_line(X31_967_10, line_connecting(X28_537_9, Z30_537_9)))
% 158.60/31.92 -> [32523] distinct_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9))
% 158.60/31.92 -> [32524] apart_point_and_line(X31_967_10, line_connecting(X28_537_9, Z30_537_9))
% 158.60/31.92
% 158.60/31.92 [32523] CLOSURE : distinct_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9))
% 158.60/31.92
% 158.60/31.92 [32524] CLOSURE : apart_point_and_line(X31_967_10, line_connecting(X28_537_9, Z30_537_9))
% 158.60/31.92
% 158.60/31.92 [32517] GAMMA_FORALL : ! [X34_34, Y35_35] : ((convergent_lines(X34_34, Y35_35) => distinct_lines(X34_34, Y35_35)))
% 158.60/31.92 -> [32532] (convergent_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9)) => distinct_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9)))
% 158.60/31.92
% 158.60/31.92 [32532] BETA_IMPLY : (convergent_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9)) => distinct_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9)))
% 158.60/31.92 -> [32534] ~convergent_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9))
% 158.60/31.92 -> [32535] distinct_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9))
% 158.60/31.92
% 158.60/31.92 [32535] CLOSURE : distinct_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9))
% 158.60/31.92
% 158.60/31.92 [32534] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 158.60/31.92 -> [32548] ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92
% 158.60/31.92 [32548] BETA_NOT_AND : ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92 -> [32550] ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32551] ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32550] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32552] convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32552] CLOSURE : convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32551] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32555] unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32555] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32509] BETA_OR : (distinct_points(X28_537_9, Z30_537_9) | apart_point_and_line(Z30_537_9, line_connecting(X28_537_9, Z30_537_9)))
% 158.60/31.92 -> [32612] distinct_points(X28_537_9, Z30_537_9)
% 158.60/31.92 -> [32613] apart_point_and_line(Z30_537_9, line_connecting(X28_537_9, Z30_537_9))
% 158.60/31.92
% 158.60/31.92 [32612] CLOSURE : distinct_points(X28_537_9, Z30_537_9)
% 158.60/31.92
% 158.60/31.92 [32613] GAMMA_FORALL : ! [X31_31, Y32_32, Z33_33] : ((apart_point_and_line(X31_31, Y32_32) => (distinct_lines(Y32_32, Z33_33) | apart_point_and_line(X31_31, Z33_33))))
% 158.60/31.92 -> [32614] (apart_point_and_line(X31_971_10, line_connecting(X28_537_9, Z30_537_9)) => (distinct_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9)) | apart_point_and_line(X31_971_10, line_connecting(X28_537_9, Z30_537_9))))
% 158.60/31.92
% 158.60/31.92 [32614] BETA_IMPLY : (apart_point_and_line(X31_971_10, line_connecting(X28_537_9, Z30_537_9)) => (distinct_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9)) | apart_point_and_line(X31_971_10, line_connecting(X28_537_9, Z30_537_9))))
% 158.60/31.92 -> [32615] ~apart_point_and_line(X31_971_10, line_connecting(X28_537_9, Z30_537_9))
% 158.60/31.92 -> [32616] (distinct_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9)) | apart_point_and_line(X31_971_10, line_connecting(X28_537_9, Z30_537_9)))
% 158.60/31.92
% 158.60/31.92 [32616] BETA_OR : (distinct_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9)) | apart_point_and_line(X31_971_10, line_connecting(X28_537_9, Z30_537_9)))
% 158.60/31.92 -> [32617] distinct_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9))
% 158.60/31.92 -> [32618] apart_point_and_line(X31_971_10, line_connecting(X28_537_9, Z30_537_9))
% 158.60/31.92
% 158.60/31.92 [32617] CLOSURE : distinct_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9))
% 158.60/31.92
% 158.60/31.92 [32618] GAMMA_FORALL : ! [X34_34, Y35_35] : ((convergent_lines(X34_34, Y35_35) => distinct_lines(X34_34, Y35_35)))
% 158.60/31.92 -> [32619] (convergent_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9)) => distinct_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9)))
% 158.60/31.92
% 158.60/31.92 [32619] BETA_IMPLY : (convergent_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9)) => distinct_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9)))
% 158.60/31.92 -> [32620] ~convergent_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9))
% 158.60/31.92 -> [32621] distinct_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9))
% 158.60/31.92
% 158.60/31.92 [32621] CLOSURE : distinct_lines(line_connecting(X28_537_9, Z30_537_9), line_connecting(X28_537_9, Z30_537_9))
% 158.60/31.92
% 158.60/31.92 [32620] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 158.60/31.92 -> [32622] ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92
% 158.60/31.92 [32622] BETA_NOT_AND : ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92 -> [32623] ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32624] ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32624] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32628] unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32628] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32623] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32627] convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32627] CLOSURE : convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32615] CLOSURE : ~apart_point_and_line(X31_971_10, line_connecting(X28_537_9, Z30_537_9))
% 158.60/31.92
% 158.60/31.92 [32504] GAMMA_FORALL : ! [X28_28, Y29_29, Z30_30] : ((apart_point_and_line(X28_28, Y29_29) => (distinct_points(X28_28, Z30_30) | apart_point_and_line(Z30_30, Y29_29))))
% 158.60/31.92 -> [32507] (apart_point_and_line(X28_538_9, line_connecting(X28_538_9, Z30_538_9)) => (distinct_points(X28_538_9, Z30_538_9) | apart_point_and_line(Z30_538_9, line_connecting(X28_538_9, Z30_538_9))))
% 158.60/31.92
% 158.60/31.92 [32507] BETA_IMPLY : (apart_point_and_line(X28_538_9, line_connecting(X28_538_9, Z30_538_9)) => (distinct_points(X28_538_9, Z30_538_9) | apart_point_and_line(Z30_538_9, line_connecting(X28_538_9, Z30_538_9))))
% 158.60/31.92 -> [32510] ~apart_point_and_line(X28_538_9, line_connecting(X28_538_9, Z30_538_9))
% 158.60/31.92 -> [32511] (distinct_points(X28_538_9, Z30_538_9) | apart_point_and_line(Z30_538_9, line_connecting(X28_538_9, Z30_538_9)))
% 158.60/31.92
% 158.60/31.92 [32510] GAMMA_FORALL : ! [X31_31, Y32_32, Z33_33] : ((apart_point_and_line(X31_31, Y32_32) => (distinct_lines(Y32_32, Z33_33) | apart_point_and_line(X31_31, Z33_33))))
% 158.60/31.92 -> [32519] (apart_point_and_line(X31_968_10, line_connecting(X28_538_9, Z30_538_9)) => (distinct_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9)) | apart_point_and_line(X31_968_10, line_connecting(X28_538_9, Z30_538_9))))
% 158.60/31.92
% 158.60/31.92 [32519] BETA_IMPLY : (apart_point_and_line(X31_968_10, line_connecting(X28_538_9, Z30_538_9)) => (distinct_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9)) | apart_point_and_line(X31_968_10, line_connecting(X28_538_9, Z30_538_9))))
% 158.60/31.92 -> [32520] ~apart_point_and_line(X31_968_10, line_connecting(X28_538_9, Z30_538_9))
% 158.60/31.92 -> [32521] (distinct_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9)) | apart_point_and_line(X31_968_10, line_connecting(X28_538_9, Z30_538_9)))
% 158.60/31.92
% 158.60/31.92 [32521] BETA_OR : (distinct_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9)) | apart_point_and_line(X31_968_10, line_connecting(X28_538_9, Z30_538_9)))
% 158.60/31.92 -> [32528] distinct_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9))
% 158.60/31.92 -> [32529] apart_point_and_line(X31_968_10, line_connecting(X28_538_9, Z30_538_9))
% 158.60/31.92
% 158.60/31.92 [32529] CLOSURE : apart_point_and_line(X31_968_10, line_connecting(X28_538_9, Z30_538_9))
% 158.60/31.92
% 158.60/31.92 [32528] CLOSURE : distinct_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9))
% 158.60/31.92
% 158.60/31.92 [32520] GAMMA_FORALL : ! [X34_34, Y35_35] : ((convergent_lines(X34_34, Y35_35) => distinct_lines(X34_34, Y35_35)))
% 158.60/31.92 -> [32533] (convergent_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9)) => distinct_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9)))
% 158.60/31.92
% 158.60/31.92 [32533] BETA_IMPLY : (convergent_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9)) => distinct_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9)))
% 158.60/31.92 -> [32538] ~convergent_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9))
% 158.60/31.92 -> [32539] distinct_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9))
% 158.60/31.92
% 158.60/31.92 [32539] CLOSURE : distinct_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9))
% 158.60/31.92
% 158.60/31.92 [32538] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 158.60/31.92 -> [32549] ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92
% 158.60/31.92 [32549] BETA_NOT_AND : ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92 -> [32553] ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32554] ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32553] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32558] convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32558] CLOSURE : convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32554] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32563] unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32563] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32511] BETA_OR : (distinct_points(X28_538_9, Z30_538_9) | apart_point_and_line(Z30_538_9, line_connecting(X28_538_9, Z30_538_9)))
% 158.60/31.92 -> [32625] distinct_points(X28_538_9, Z30_538_9)
% 158.60/31.92 -> [32626] apart_point_and_line(Z30_538_9, line_connecting(X28_538_9, Z30_538_9))
% 158.60/31.92
% 158.60/31.92 [32625] CLOSURE : distinct_points(X28_538_9, Z30_538_9)
% 158.60/31.92
% 158.60/31.92 [32626] GAMMA_FORALL : ! [X31_31, Y32_32, Z33_33] : ((apart_point_and_line(X31_31, Y32_32) => (distinct_lines(Y32_32, Z33_33) | apart_point_and_line(X31_31, Z33_33))))
% 158.60/31.92 -> [32629] (apart_point_and_line(X31_972_10, line_connecting(X28_538_9, Z30_538_9)) => (distinct_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9)) | apart_point_and_line(X31_972_10, line_connecting(X28_538_9, Z30_538_9))))
% 158.60/31.92
% 158.60/31.92 [32629] BETA_IMPLY : (apart_point_and_line(X31_972_10, line_connecting(X28_538_9, Z30_538_9)) => (distinct_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9)) | apart_point_and_line(X31_972_10, line_connecting(X28_538_9, Z30_538_9))))
% 158.60/31.92 -> [32630] ~apart_point_and_line(X31_972_10, line_connecting(X28_538_9, Z30_538_9))
% 158.60/31.92 -> [32631] (distinct_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9)) | apart_point_and_line(X31_972_10, line_connecting(X28_538_9, Z30_538_9)))
% 158.60/31.92
% 158.60/31.92 [32631] BETA_OR : (distinct_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9)) | apart_point_and_line(X31_972_10, line_connecting(X28_538_9, Z30_538_9)))
% 158.60/31.92 -> [32632] distinct_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9))
% 158.60/31.92 -> [32633] apart_point_and_line(X31_972_10, line_connecting(X28_538_9, Z30_538_9))
% 158.60/31.92
% 158.60/31.92 [32632] CLOSURE : distinct_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9))
% 158.60/31.92
% 158.60/31.92 [32633] GAMMA_FORALL : ! [X34_34, Y35_35] : ((convergent_lines(X34_34, Y35_35) => distinct_lines(X34_34, Y35_35)))
% 158.60/31.92 -> [32634] (convergent_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9)) => distinct_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9)))
% 158.60/31.92
% 158.60/31.92 [32634] BETA_IMPLY : (convergent_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9)) => distinct_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9)))
% 158.60/31.92 -> [32635] ~convergent_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9))
% 158.60/31.92 -> [32636] distinct_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9))
% 158.60/31.92
% 158.60/31.92 [32636] CLOSURE : distinct_lines(line_connecting(X28_538_9, Z30_538_9), line_connecting(X28_538_9, Z30_538_9))
% 158.60/31.92
% 158.60/31.92 [32635] GAMMA_FORALL : ! [L38_38, M39_39] : (~(~convergent_lines(L38_38, M39_39) & ~unorthogonal_lines(L38_38, M39_39)))
% 158.60/31.92 -> [32637] ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92
% 158.60/31.92 [32637] BETA_NOT_AND : ~(~convergent_lines(skolem_L4646, skolem_L4646) & ~unorthogonal_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92 -> [32638] ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32639] ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32639] ALPHA_NOT_NOT : ~~unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32641] unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32641] CLOSURE : unorthogonal_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32638] ALPHA_NOT_NOT : ~~convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32640] convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32640] CLOSURE : convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32630] CLOSURE : ~apart_point_and_line(X31_972_10, line_connecting(X28_538_9, Z30_538_9))
% 158.60/31.92
% 158.60/31.92 [28651] BETA_OR : (convergent_lines(skolem_L4646, skolem_L4646) | convergent_lines(skolem_L4646, skolem_L4646))
% 158.60/31.92 -> [32642] convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92 -> [32643] convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32643] CLOSURE : convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 [32642] CLOSURE : convergent_lines(skolem_L4646, skolem_L4646)
% 158.60/31.92
% 158.60/31.92 % SZS output end Proof for theBenchmark.p
% 158.60/31.92 [31.575041s][1][Res] 185839 goroutines created
% 158.60/31.92 ==== Result ====
% 158.60/31.92 [31.575082s][1][Res] VALID
% 158.60/31.92 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------