TSTP Solution File: GEO171+2 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO171+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n028.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 15:18:11 EDT 2022
% Result : Theorem 32.46s 9.04s
% Output : Proof 32.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO171+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : goeland -dmt -presko -proof %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 06:52:49 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 [DMT] DMT loaded with preskolemization
% 0.12/0.34 [EQ] equality loaded.
% 0.12/0.34 [0.000041s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.35 Conjecture not found
% 0.12/0.35 Start search
% 0.12/0.35 nb_step : 1 - limit : 13
% 0.12/0.35 Launch Gotab with destructive = true
% 32.45/9.02 % SZS output start Proof for theBenchmark.p
% 32.46/9.03 [0] ALPHA_AND : ((! [X5_5] : (~distinct_points(X5_5, X5_5)) & ! [X6_6] : (~distinct_lines(X6_6, X6_6)) & ! [X7_7] : (~convergent_lines(X7_7, X7_7)) & ! [X8_8, Y9_9, Z10_10] : ((distinct_points(X8_8, Y9_9) => (distinct_points(X8_8, Z10_10) | distinct_points(Y9_9, Z10_10)))) & ! [X11_11, Y12_12, Z13_13] : ((distinct_lines(X11_11, Y12_12) => (distinct_lines(X11_11, Z13_13) | distinct_lines(Y12_12, Z13_13)))) & ! [X14_14, Y15_15, Z16_16] : ((convergent_lines(X14_14, Y15_15) => (convergent_lines(X14_14, Z16_16) | convergent_lines(Y15_15, Z16_16)))) & ! [X17_17, Y18_18, Z19_19] : ((distinct_points(X17_17, Y18_18) => (apart_point_and_line(Z19_19, line_connecting(X17_17, Y18_18)) => (distinct_points(Z19_19, X17_17) & distinct_points(Z19_19, Y18_18))))) & ! [X20_20, Y21_21, Z22_22] : ((convergent_lines(X20_20, Y21_21) => ((apart_point_and_line(Z22_22, X20_20) | apart_point_and_line(Z22_22, Y21_21)) => distinct_points(Z22_22, intersection_point(X20_20, Y21_21))))) & ! [X23_23, Y24_24, U25_25, V26_26] : (((distinct_points(X23_23, Y24_24) & distinct_lines(U25_25, V26_26)) => (((apart_point_and_line(X23_23, U25_25) | apart_point_and_line(X23_23, V26_26)) | apart_point_and_line(Y24_24, U25_25)) | apart_point_and_line(Y24_24, V26_26)))) & ! [X27_27, Y28_28, Z29_29] : ((apart_point_and_line(X27_27, Y28_28) => (distinct_points(X27_27, Z29_29) | apart_point_and_line(Z29_29, Y28_28)))) & ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_lines(Y31_31, Z32_32) | apart_point_and_line(X30_30, Z32_32)))) & ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))) & ~! [X35_35, Y36_36] : ((convergent_lines(X35_35, Y36_36) => distinct_lines(X35_35, Y36_36))))
% 32.46/9.03 -> [1] (! [X5_5] : (~distinct_points(X5_5, X5_5)) & ! [X6_6] : (~distinct_lines(X6_6, X6_6)) & ! [X7_7] : (~convergent_lines(X7_7, X7_7)) & ! [X8_8, Y9_9, Z10_10] : ((distinct_points(X8_8, Y9_9) => (distinct_points(X8_8, Z10_10) | distinct_points(Y9_9, Z10_10)))) & ! [X11_11, Y12_12, Z13_13] : ((distinct_lines(X11_11, Y12_12) => (distinct_lines(X11_11, Z13_13) | distinct_lines(Y12_12, Z13_13)))) & ! [X14_14, Y15_15, Z16_16] : ((convergent_lines(X14_14, Y15_15) => (convergent_lines(X14_14, Z16_16) | convergent_lines(Y15_15, Z16_16)))) & ! [X17_17, Y18_18, Z19_19] : ((distinct_points(X17_17, Y18_18) => (apart_point_and_line(Z19_19, line_connecting(X17_17, Y18_18)) => (distinct_points(Z19_19, X17_17) & distinct_points(Z19_19, Y18_18))))) & ! [X20_20, Y21_21, Z22_22] : ((convergent_lines(X20_20, Y21_21) => ((apart_point_and_line(Z22_22, X20_20) | apart_point_and_line(Z22_22, Y21_21)) => distinct_points(Z22_22, intersection_point(X20_20, Y21_21))))) & ! [X23_23, Y24_24, U25_25, V26_26] : (((distinct_points(X23_23, Y24_24) & distinct_lines(U25_25, V26_26)) => (((apart_point_and_line(X23_23, U25_25) | apart_point_and_line(X23_23, V26_26)) | apart_point_and_line(Y24_24, U25_25)) | apart_point_and_line(Y24_24, V26_26)))) & ! [X27_27, Y28_28, Z29_29] : ((apart_point_and_line(X27_27, Y28_28) => (distinct_points(X27_27, Z29_29) | apart_point_and_line(Z29_29, Y28_28)))) & ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_lines(Y31_31, Z32_32) | apart_point_and_line(X30_30, Z32_32)))) & ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))), ~! [X35_35, Y36_36] : ((convergent_lines(X35_35, Y36_36) => distinct_lines(X35_35, Y36_36)))
% 32.46/9.03
% 32.46/9.03 [1] ALPHA_AND : (! [X5_5] : (~distinct_points(X5_5, X5_5)) & ! [X6_6] : (~distinct_lines(X6_6, X6_6)) & ! [X7_7] : (~convergent_lines(X7_7, X7_7)) & ! [X8_8, Y9_9, Z10_10] : ((distinct_points(X8_8, Y9_9) => (distinct_points(X8_8, Z10_10) | distinct_points(Y9_9, Z10_10)))) & ! [X11_11, Y12_12, Z13_13] : ((distinct_lines(X11_11, Y12_12) => (distinct_lines(X11_11, Z13_13) | distinct_lines(Y12_12, Z13_13)))) & ! [X14_14, Y15_15, Z16_16] : ((convergent_lines(X14_14, Y15_15) => (convergent_lines(X14_14, Z16_16) | convergent_lines(Y15_15, Z16_16)))) & ! [X17_17, Y18_18, Z19_19] : ((distinct_points(X17_17, Y18_18) => (apart_point_and_line(Z19_19, line_connecting(X17_17, Y18_18)) => (distinct_points(Z19_19, X17_17) & distinct_points(Z19_19, Y18_18))))) & ! [X20_20, Y21_21, Z22_22] : ((convergent_lines(X20_20, Y21_21) => ((apart_point_and_line(Z22_22, X20_20) | apart_point_and_line(Z22_22, Y21_21)) => distinct_points(Z22_22, intersection_point(X20_20, Y21_21))))) & ! [X23_23, Y24_24, U25_25, V26_26] : (((distinct_points(X23_23, Y24_24) & distinct_lines(U25_25, V26_26)) => (((apart_point_and_line(X23_23, U25_25) | apart_point_and_line(X23_23, V26_26)) | apart_point_and_line(Y24_24, U25_25)) | apart_point_and_line(Y24_24, V26_26)))) & ! [X27_27, Y28_28, Z29_29] : ((apart_point_and_line(X27_27, Y28_28) => (distinct_points(X27_27, Z29_29) | apart_point_and_line(Z29_29, Y28_28)))) & ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_lines(Y31_31, Z32_32) | apart_point_and_line(X30_30, Z32_32)))) & ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34))))
% 32.46/9.03 -> [2] ! [X5_5] : (~distinct_points(X5_5, X5_5)), ! [X6_6] : (~distinct_lines(X6_6, X6_6)), ! [X7_7] : (~convergent_lines(X7_7, X7_7)), ! [X8_8, Y9_9, Z10_10] : ((distinct_points(X8_8, Y9_9) => (distinct_points(X8_8, Z10_10) | distinct_points(Y9_9, Z10_10)))), ! [X11_11, Y12_12, Z13_13] : ((distinct_lines(X11_11, Y12_12) => (distinct_lines(X11_11, Z13_13) | distinct_lines(Y12_12, Z13_13)))), ! [X14_14, Y15_15, Z16_16] : ((convergent_lines(X14_14, Y15_15) => (convergent_lines(X14_14, Z16_16) | convergent_lines(Y15_15, Z16_16)))), ! [X17_17, Y18_18, Z19_19] : ((distinct_points(X17_17, Y18_18) => (apart_point_and_line(Z19_19, line_connecting(X17_17, Y18_18)) => (distinct_points(Z19_19, X17_17) & distinct_points(Z19_19, Y18_18))))), ! [X20_20, Y21_21, Z22_22] : ((convergent_lines(X20_20, Y21_21) => ((apart_point_and_line(Z22_22, X20_20) | apart_point_and_line(Z22_22, Y21_21)) => distinct_points(Z22_22, intersection_point(X20_20, Y21_21))))), ! [X23_23, Y24_24, U25_25, V26_26] : (((distinct_points(X23_23, Y24_24) & distinct_lines(U25_25, V26_26)) => (((apart_point_and_line(X23_23, U25_25) | apart_point_and_line(X23_23, V26_26)) | apart_point_and_line(Y24_24, U25_25)) | apart_point_and_line(Y24_24, V26_26)))), ! [X27_27, Y28_28, Z29_29] : ((apart_point_and_line(X27_27, Y28_28) => (distinct_points(X27_27, Z29_29) | apart_point_and_line(Z29_29, Y28_28)))), ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_lines(Y31_31, Z32_32) | apart_point_and_line(X30_30, Z32_32)))), ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 32.46/9.03
% 32.46/9.03 [2] DELTA_NOT_FORALL : ~! [X35_35, Y36_36] : ((convergent_lines(X35_35, Y36_36) => distinct_lines(X35_35, Y36_36)))
% 32.46/9.03 -> [3] ~(convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.03
% 32.46/9.03 [3] ALPHA_NOT_IMPLY : ~(convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.03 -> [4] convergent_lines(skolem_X3535, skolem_Y3636), ~distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.03
% 32.46/9.03 [4] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 32.46/9.03 -> [5] ~distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.03
% 32.46/9.03 [5] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 32.46/9.03 -> [6] ~distinct_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.03
% 32.46/9.03 [6] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 32.46/9.03 -> [7] ~convergent_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.03
% 32.46/9.03 [7] GAMMA_FORALL : ! [X8_8, Y9_9, Z10_10] : ((distinct_points(X8_8, Y9_9) => (distinct_points(X8_8, Z10_10) | distinct_points(Y9_9, Z10_10))))
% 32.46/9.03 -> [8] (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) => (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.03
% 32.46/9.03 [8] BETA_IMPLY : (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) => (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.03 -> [9] ~distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.03 -> [10] (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.03
% 32.46/9.03 [10] BETA_OR : (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.03 -> [11] distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.03 -> [12] distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.03
% 32.46/9.03 [12] CLOSURE : distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.03
% 32.46/9.03 [11] CLOSURE : distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.03
% 32.46/9.03 [13] BETA_IMPLY : (distinct_lines(skolem_X3535, skolem_Y3636) => (distinct_lines(skolem_X3535, skolem_Y3636) | distinct_lines(skolem_Y3636, skolem_Y3636)))
% 32.46/9.03 -> [2361] ~distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.03 -> [2362] (distinct_lines(skolem_X3535, skolem_Y3636) | distinct_lines(skolem_Y3636, skolem_Y3636))
% 32.46/9.03
% 32.46/9.03 [2362] BETA_OR : (distinct_lines(skolem_X3535, skolem_Y3636) | distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.03 -> [2363] distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.03 -> [2364] distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.03
% 32.46/9.03 [2363] CLOSURE : distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.03
% 32.46/9.03 [2364] CLOSURE : distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.03
% 32.46/9.03 [2365] BETA_IMPLY : (convergent_lines(skolem_X3535, skolem_Y3636) => (convergent_lines(skolem_X3535, skolem_Y3636) | convergent_lines(skolem_Y3636, skolem_Y3636)))
% 32.46/9.03 -> [3604] ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.03 -> [3605] (convergent_lines(skolem_X3535, skolem_Y3636) | convergent_lines(skolem_Y3636, skolem_Y3636))
% 32.46/9.03
% 32.46/9.03 [3604] CLOSURE : ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.03
% 32.46/9.03 [3605] BETA_OR : (convergent_lines(skolem_X3535, skolem_Y3636) | convergent_lines(skolem_Y3636, skolem_Y3636))
% 32.46/9.03 -> [3608] convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.03 -> [3609] convergent_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.03
% 32.46/9.03 [3609] CLOSURE : convergent_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.03
% 32.46/9.03 [3608] GAMMA_FORALL : ! [X17_17, Y18_18, Z19_19] : ((distinct_points(X17_17, Y18_18) => (apart_point_and_line(Z19_19, line_connecting(X17_17, Y18_18)) => (distinct_points(Z19_19, X17_17) & distinct_points(Z19_19, Y18_18)))))
% 32.46/9.03 -> [3610] (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) => (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))) => (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) & distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))))
% 32.46/9.03
% 32.46/9.03 [3610] BETA_IMPLY : (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) => (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))) => (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) & distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))))
% 32.46/9.03 -> [3611] ~distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.03 -> [3612] (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))) => (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) & distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.03
% 32.46/9.03 [3612] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))) => (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) & distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.03 -> [3613] ~apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.03 -> [3614] (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) & distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.03
% 32.46/9.03 [3614] ALPHA_AND : (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) & distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.03 -> [3618] distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.03
% 32.46/9.03 [3618] CLOSURE : distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.03
% 32.46/9.03 [3619] BETA_IMPLY : (convergent_lines(skolem_Y3636, skolem_Y3636) => ((apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)) => distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.03 -> [3957] ~convergent_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.03 -> [3958] ((apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)) => distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.03
% 32.46/9.03 [3958] BETA_IMPLY : ((apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)) => distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.03 -> [3959] ~(apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636))
% 32.46/9.03 -> [3960] distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.03
% 32.46/9.03 [3959] ALPHA_NOT_OR : ~(apart_point_and_line(X23_26_8, skolem_Y3636) | apart_point_and_line(X23_26_8, skolem_Y3636))
% 32.46/9.03 -> [3961] ~apart_point_and_line(X23_26_8, skolem_Y3636)
% 32.46/9.03
% 32.46/9.03 [3961] GAMMA_FORALL : ! [X23_23, Y24_24, U25_25, V26_26] : (((distinct_points(X23_23, Y24_24) & distinct_lines(U25_25, V26_26)) => (((apart_point_and_line(X23_23, U25_25) | apart_point_and_line(X23_23, V26_26)) | apart_point_and_line(Y24_24, U25_25)) | apart_point_and_line(Y24_24, V26_26))))
% 32.46/9.03 -> [3962] ((distinct_points(X23_26_8, X23_26_8) & distinct_lines(line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)), line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))) => (((apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636))) | apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))) | apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))) | apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))))
% 32.46/9.03
% 32.46/9.03 [3962] BETA_IMPLY : ((distinct_points(X23_26_8, X23_26_8) & distinct_lines(line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)), line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))) => (((apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636))) | apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))) | apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))) | apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))))
% 32.46/9.03 -> [3963] ~(distinct_points(X23_26_8, X23_26_8) & distinct_lines(line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)), line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.03 -> [3964] (((apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636))) | apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))) | apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))) | apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.03
% 32.46/9.03 [3963] BETA_NOT_AND : ~(distinct_points(X23_26_8, X23_26_8) & distinct_lines(line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)), line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.03 -> [3965] ~distinct_points(X23_26_8, X23_26_8)
% 32.46/9.03 -> [3966] ~distinct_lines(line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)), line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.03
% 32.46/9.03 [3966] GAMMA_FORALL : ! [X27_27, Y28_28, Z29_29] : ((apart_point_and_line(X27_27, Y28_28) => (distinct_points(X27_27, Z29_29) | apart_point_and_line(Z29_29, Y28_28))))
% 32.46/9.03 -> [3972] (apart_point_and_line(Z29_115_9, Y28_115_9) => (distinct_points(Z29_115_9, Z29_115_9) | apart_point_and_line(Z29_115_9, Y28_115_9)))
% 32.46/9.03
% 32.46/9.03 [3972] BETA_IMPLY : (apart_point_and_line(Z29_115_9, Y28_115_9) => (distinct_points(Z29_115_9, Z29_115_9) | apart_point_and_line(Z29_115_9, Y28_115_9)))
% 32.46/9.03 -> [3975] ~apart_point_and_line(Z29_115_9, Y28_115_9)
% 32.46/9.03 -> [3976] (distinct_points(Z29_115_9, Z29_115_9) | apart_point_and_line(Z29_115_9, Y28_115_9))
% 32.46/9.03
% 32.46/9.03 [3976] BETA_OR : (distinct_points(Z29_115_9, Z29_115_9) | apart_point_and_line(Z29_115_9, Y28_115_9))
% 32.46/9.03 -> [3981] distinct_points(Z29_115_9, Z29_115_9)
% 32.46/9.03 -> [3982] apart_point_and_line(Z29_115_9, Y28_115_9)
% 32.46/9.03
% 32.46/9.03 [3982] CLOSURE : apart_point_and_line(Z29_115_9, Y28_115_9)
% 32.46/9.03
% 32.46/9.03 [3981] CLOSURE : distinct_points(Z29_115_9, Z29_115_9)
% 32.46/9.03
% 32.46/9.03 [3984] BETA_IMPLY : (apart_point_and_line(X23_26_8, Y31_179_10) => (distinct_lines(Y31_179_10, Z32_179_10) | apart_point_and_line(X23_26_8, Z32_179_10)))
% 32.46/9.03 -> [4029] ~apart_point_and_line(X23_26_8, Y31_179_10)
% 32.46/9.03 -> [4030] (distinct_lines(Y31_179_10, Z32_179_10) | apart_point_and_line(X23_26_8, Z32_179_10))
% 32.46/9.03
% 32.46/9.03 [4029] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 32.46/9.03 -> [4033] (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.03
% 32.46/9.03 [4033] BETA_IMPLY : (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.03 -> [4034] ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.03 -> [4035] distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.03
% 32.46/9.03 [4034] CLOSURE : ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.03
% 32.46/9.03 [4035] CLOSURE : distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.03
% 32.46/9.03 [4030] BETA_OR : (distinct_lines(Y31_179_10, Z32_179_10) | apart_point_and_line(X23_26_8, Z32_179_10))
% 32.46/9.03 -> [4031] distinct_lines(Y31_179_10, Z32_179_10)
% 32.46/9.03 -> [4032] apart_point_and_line(X23_26_8, Z32_179_10)
% 32.46/9.03
% 32.46/9.03 [4031] CLOSURE : distinct_lines(Y31_179_10, Z32_179_10)
% 32.46/9.03
% 32.46/9.03 [4032] CLOSURE : apart_point_and_line(X23_26_8, Z32_179_10)
% 32.46/9.04
% 32.46/9.04 [3971] BETA_IMPLY : (apart_point_and_line(X23_26_8, Y28_114_9) => (distinct_points(X23_26_8, X23_26_8) | apart_point_and_line(X23_26_8, Y28_114_9)))
% 32.46/9.04 -> [4045] ~apart_point_and_line(X23_26_8, Y28_114_9)
% 32.46/9.04 -> [4046] (distinct_points(X23_26_8, X23_26_8) | apart_point_and_line(X23_26_8, Y28_114_9))
% 32.46/9.04
% 32.46/9.04 [4045] GAMMA_FORALL : ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_lines(Y31_31, Z32_32) | apart_point_and_line(X30_30, Z32_32))))
% 32.46/9.04 -> [4049] (apart_point_and_line(X30_182_10, skolem_X3535) => (distinct_lines(skolem_X3535, skolem_Y3636) | apart_point_and_line(X30_182_10, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4049] BETA_IMPLY : (apart_point_and_line(X30_182_10, skolem_X3535) => (distinct_lines(skolem_X3535, skolem_Y3636) | apart_point_and_line(X30_182_10, skolem_Y3636)))
% 32.46/9.04 -> [4050] ~apart_point_and_line(X30_182_10, skolem_X3535)
% 32.46/9.04 -> [4051] (distinct_lines(skolem_X3535, skolem_Y3636) | apart_point_and_line(X30_182_10, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4050] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 32.46/9.04 -> [4054] (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4054] BETA_IMPLY : (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04 -> [4055] ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04 -> [4056] distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4055] CLOSURE : ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4056] CLOSURE : distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4051] BETA_OR : (distinct_lines(skolem_X3535, skolem_Y3636) | apart_point_and_line(X30_182_10, skolem_Y3636))
% 32.46/9.04 -> [4052] distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04 -> [4053] apart_point_and_line(X30_182_10, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4052] CLOSURE : distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4053] CLOSURE : apart_point_and_line(X30_182_10, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4046] BETA_OR : (distinct_points(X23_26_8, X23_26_8) | apart_point_and_line(X23_26_8, Y28_114_9))
% 32.46/9.04 -> [4057] distinct_points(X23_26_8, X23_26_8)
% 32.46/9.04 -> [4058] apart_point_and_line(X23_26_8, Y28_114_9)
% 32.46/9.04
% 32.46/9.04 [4057] CLOSURE : distinct_points(X23_26_8, X23_26_8)
% 32.46/9.04
% 32.46/9.04 [4058] CLOSURE : apart_point_and_line(X23_26_8, Y28_114_9)
% 32.46/9.04
% 32.46/9.04 [3964] BETA_OR : (((apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636))) | apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))) | apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))) | apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.04 -> [4099] ((apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636))) | apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))) | apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.04 -> [4100] apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4100] CLOSURE : apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4099] BETA_OR : ((apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636))) | apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))) | apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.04 -> [4122] (apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636))) | apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.04 -> [4123] apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4122] BETA_OR : (apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636))) | apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.04 -> [4127] apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04 -> [4128] apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4127] CLOSURE : apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4128] CLOSURE : apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4123] CLOSURE : apart_point_and_line(X23_26_8, line_connecting(X23_26_8, intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [3960] CLOSURE : distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [3957] GAMMA_FORALL : ! [X23_23, Y24_24, U25_25, V26_26] : (((distinct_points(X23_23, Y24_24) & distinct_lines(U25_25, V26_26)) => (((apart_point_and_line(X23_23, U25_25) | apart_point_and_line(X23_23, V26_26)) | apart_point_and_line(Y24_24, U25_25)) | apart_point_and_line(Y24_24, V26_26))))
% 32.46/9.04 -> [4155] ((distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) & distinct_lines(line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))) => (((apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))))
% 32.46/9.04
% 32.46/9.04 [4155] BETA_IMPLY : ((distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) & distinct_lines(line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))) => (((apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))))
% 32.46/9.04 -> [4160] ~(distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) & distinct_lines(line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.04 -> [4161] (((apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.04
% 32.46/9.04 [4161] BETA_OR : (((apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.04 -> [4168] ((apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.04 -> [4169] apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4168] BETA_OR : ((apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.04 -> [4182] (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.04 -> [4183] apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4182] BETA_OR : (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.04 -> [4186] apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04 -> [4187] apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4186] CLOSURE : apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4187] CLOSURE : apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4183] CLOSURE : apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4169] CLOSURE : apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4160] BETA_NOT_AND : ~(distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) & distinct_lines(line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.04 -> [4263] ~distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.04 -> [4264] ~distinct_lines(line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4263] GAMMA_FORALL : ! [X27_27, Y28_28, Z29_29] : ((apart_point_and_line(X27_27, Y28_28) => (distinct_points(X27_27, Z29_29) | apart_point_and_line(Z29_29, Y28_28))))
% 32.46/9.04 -> [4269] (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))) => (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))))
% 32.46/9.04
% 32.46/9.04 [4269] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))) => (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))))
% 32.46/9.04 -> [4271] ~apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04 -> [4272] (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.04
% 32.46/9.04 [4272] BETA_OR : (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.04 -> [4275] distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.04 -> [4276] apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4275] CLOSURE : distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4276] CLOSURE : apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4271] GAMMA_FORALL : ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_lines(Y31_31, Z32_32) | apart_point_and_line(X30_30, Z32_32))))
% 32.46/9.04 -> [4281] (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), Y31_192_10) => (distinct_lines(Y31_192_10, line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))))
% 32.46/9.04
% 32.46/9.04 [4281] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), Y31_192_10) => (distinct_lines(Y31_192_10, line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))))
% 32.46/9.04 -> [4285] ~apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), Y31_192_10)
% 32.46/9.04 -> [4286] (distinct_lines(Y31_192_10, line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.04
% 32.46/9.04 [4285] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 32.46/9.04 -> [4291] (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4291] BETA_IMPLY : (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04 -> [4292] ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04 -> [4293] distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4292] CLOSURE : ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4293] CLOSURE : distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4286] BETA_OR : (distinct_lines(Y31_192_10, line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.04 -> [4287] distinct_lines(Y31_192_10, line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04 -> [4288] apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4288] CLOSURE : apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4287] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 32.46/9.04 -> [4301] (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4301] BETA_IMPLY : (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04 -> [4305] ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04 -> [4306] distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4305] CLOSURE : ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4306] CLOSURE : distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4264] GAMMA_FORALL : ! [X27_27, Y28_28, Z29_29] : ((apart_point_and_line(X27_27, Y28_28) => (distinct_points(X27_27, Z29_29) | apart_point_and_line(Z29_29, Y28_28))))
% 32.46/9.04 -> [4270] (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))) => (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))))
% 32.46/9.04
% 32.46/9.04 [4270] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))) => (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))))
% 32.46/9.04 -> [4273] ~apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04 -> [4274] (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.04
% 32.46/9.04 [4274] BETA_OR : (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.04 -> [4277] distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.04 -> [4278] apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4278] CLOSURE : apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), line_connecting(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4277] CLOSURE : distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4282] BETA_IMPLY : (apart_point_and_line(X30_193_10, skolem_Y3636) => (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(X30_193_10, skolem_Y3636)))
% 32.46/9.04 -> [4314] ~apart_point_and_line(X30_193_10, skolem_Y3636)
% 32.46/9.04 -> [4315] (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(X30_193_10, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4314] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 32.46/9.04 -> [4318] (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4318] BETA_IMPLY : (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04 -> [4319] ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04 -> [4320] distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4319] CLOSURE : ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4320] CLOSURE : distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4315] BETA_OR : (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(X30_193_10, skolem_Y3636))
% 32.46/9.04 -> [4316] distinct_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.04 -> [4317] apart_point_and_line(X30_193_10, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4316] CLOSURE : distinct_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4317] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 32.46/9.04 -> [4321] (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4321] BETA_IMPLY : (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04 -> [4322] ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04 -> [4323] distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4322] CLOSURE : ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4323] CLOSURE : distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [3615] BETA_IMPLY : (convergent_lines(skolem_Y3636, skolem_Y3636) => ((apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)) => distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))))
% 32.46/9.04 -> [4351] ~convergent_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.04 -> [4352] ((apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)) => distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4352] BETA_IMPLY : ((apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)) => distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)))
% 32.46/9.04 -> [4353] ~(apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636))
% 32.46/9.04 -> [4354] distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4353] ALPHA_NOT_OR : ~(apart_point_and_line(X23_29_8, U25_29_8) | apart_point_and_line(X23_29_8, skolem_Y3636))
% 32.46/9.04 -> [4355] ~apart_point_and_line(X23_29_8, U25_29_8), ~apart_point_and_line(X23_29_8, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4355] GAMMA_FORALL : ! [X23_23, Y24_24, U25_25, V26_26] : (((distinct_points(X23_23, Y24_24) & distinct_lines(U25_25, V26_26)) => (((apart_point_and_line(X23_23, U25_25) | apart_point_and_line(X23_23, V26_26)) | apart_point_and_line(Y24_24, U25_25)) | apart_point_and_line(Y24_24, V26_26))))
% 32.46/9.04 -> [4356] ((distinct_points(X23_29_8, X23_29_8) & distinct_lines(U25_29_8, U25_29_8)) => (((apart_point_and_line(X23_29_8, U25_29_8) | apart_point_and_line(X23_29_8, U25_29_8)) | apart_point_and_line(X23_29_8, U25_29_8)) | apart_point_and_line(X23_29_8, U25_29_8)))
% 32.46/9.04
% 32.46/9.04 [4356] BETA_IMPLY : ((distinct_points(X23_29_8, X23_29_8) & distinct_lines(U25_29_8, U25_29_8)) => (((apart_point_and_line(X23_29_8, U25_29_8) | apart_point_and_line(X23_29_8, U25_29_8)) | apart_point_and_line(X23_29_8, U25_29_8)) | apart_point_and_line(X23_29_8, U25_29_8)))
% 32.46/9.04 -> [4357] ~(distinct_points(X23_29_8, X23_29_8) & distinct_lines(U25_29_8, U25_29_8))
% 32.46/9.04 -> [4358] (((apart_point_and_line(X23_29_8, U25_29_8) | apart_point_and_line(X23_29_8, U25_29_8)) | apart_point_and_line(X23_29_8, U25_29_8)) | apart_point_and_line(X23_29_8, U25_29_8))
% 32.46/9.04
% 32.46/9.04 [4357] BETA_NOT_AND : ~(distinct_points(X23_29_8, X23_29_8) & distinct_lines(U25_29_8, U25_29_8))
% 32.46/9.04 -> [4359] ~distinct_points(X23_29_8, X23_29_8)
% 32.46/9.04 -> [4360] ~distinct_lines(U25_29_8, U25_29_8)
% 32.46/9.04
% 32.46/9.04 [4359] GAMMA_FORALL : ! [X27_27, Y28_28, Z29_29] : ((apart_point_and_line(X27_27, Y28_28) => (distinct_points(X27_27, Z29_29) | apart_point_and_line(Z29_29, Y28_28))))
% 32.46/9.04 -> [4365] (apart_point_and_line(X27_128_9, Y28_128_9) => (distinct_points(X27_128_9, Z29_128_9) | apart_point_and_line(Z29_128_9, Y28_128_9)))
% 32.46/9.04
% 32.46/9.04 [4365] BETA_IMPLY : (apart_point_and_line(X27_128_9, Y28_128_9) => (distinct_points(X27_128_9, Z29_128_9) | apart_point_and_line(Z29_128_9, Y28_128_9)))
% 32.46/9.04 -> [4367] ~apart_point_and_line(X27_128_9, Y28_128_9)
% 32.46/9.04 -> [4368] (distinct_points(X27_128_9, Z29_128_9) | apart_point_and_line(Z29_128_9, Y28_128_9))
% 32.46/9.04
% 32.46/9.04 [4368] BETA_OR : (distinct_points(X27_128_9, Z29_128_9) | apart_point_and_line(Z29_128_9, Y28_128_9))
% 32.46/9.04 -> [4373] distinct_points(X27_128_9, Z29_128_9)
% 32.46/9.04 -> [4374] apart_point_and_line(Z29_128_9, Y28_128_9)
% 32.46/9.04
% 32.46/9.04 [4373] CLOSURE : distinct_points(X27_128_9, Z29_128_9)
% 32.46/9.04
% 32.46/9.04 [4374] CLOSURE : apart_point_and_line(Z29_128_9, Y28_128_9)
% 32.46/9.04
% 32.46/9.04 [4377] BETA_IMPLY : (apart_point_and_line(X30_195_10, skolem_Y3636) => (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(X30_195_10, skolem_Y3636)))
% 32.46/9.04 -> [4395] ~apart_point_and_line(X30_195_10, skolem_Y3636)
% 32.46/9.04 -> [4396] (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(X30_195_10, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4395] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 32.46/9.04 -> [4399] (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4399] BETA_IMPLY : (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04 -> [4402] ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04 -> [4403] distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4402] CLOSURE : ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4403] CLOSURE : distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4396] BETA_OR : (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(X30_195_10, skolem_Y3636))
% 32.46/9.04 -> [4397] distinct_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.04 -> [4398] apart_point_and_line(X30_195_10, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4398] CLOSURE : apart_point_and_line(X30_195_10, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4397] CLOSURE : distinct_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4366] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) => (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), Z29_129_9) | apart_point_and_line(Z29_129_9, skolem_Y3636)))
% 32.46/9.04 -> [4408] ~apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04 -> [4409] (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), Z29_129_9) | apart_point_and_line(Z29_129_9, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4408] GAMMA_FORALL : ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_lines(Y31_31, Z32_32) | apart_point_and_line(X30_30, Z32_32))))
% 32.46/9.04 -> [4412] (apart_point_and_line(X30_197_10, Y31_197_10) => (distinct_lines(Y31_197_10, Z32_197_10) | apart_point_and_line(X30_197_10, Z32_197_10)))
% 32.46/9.04
% 32.46/9.04 [4412] BETA_IMPLY : (apart_point_and_line(X30_197_10, Y31_197_10) => (distinct_lines(Y31_197_10, Z32_197_10) | apart_point_and_line(X30_197_10, Z32_197_10)))
% 32.46/9.04 -> [4413] ~apart_point_and_line(X30_197_10, Y31_197_10)
% 32.46/9.04 -> [4414] (distinct_lines(Y31_197_10, Z32_197_10) | apart_point_and_line(X30_197_10, Z32_197_10))
% 32.46/9.04
% 32.46/9.04 [4413] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 32.46/9.04 -> [4417] (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4417] BETA_IMPLY : (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04 -> [4418] ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04 -> [4419] distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4418] CLOSURE : ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4419] CLOSURE : distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4414] BETA_OR : (distinct_lines(Y31_197_10, Z32_197_10) | apart_point_and_line(X30_197_10, Z32_197_10))
% 32.46/9.04 -> [4415] distinct_lines(Y31_197_10, Z32_197_10)
% 32.46/9.04 -> [4416] apart_point_and_line(X30_197_10, Z32_197_10)
% 32.46/9.04
% 32.46/9.04 [4416] CLOSURE : apart_point_and_line(X30_197_10, Z32_197_10)
% 32.46/9.04
% 32.46/9.04 [4415] CLOSURE : distinct_lines(Y31_197_10, Z32_197_10)
% 32.46/9.04
% 32.46/9.04 [4409] BETA_OR : (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), Z29_129_9) | apart_point_and_line(Z29_129_9, skolem_Y3636))
% 32.46/9.04 -> [4420] distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), Z29_129_9)
% 32.46/9.04 -> [4421] apart_point_and_line(Z29_129_9, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4421] CLOSURE : apart_point_and_line(Z29_129_9, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4420] CLOSURE : distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), Z29_129_9)
% 32.46/9.04
% 32.46/9.04 [4358] BETA_OR : (((apart_point_and_line(X23_29_8, U25_29_8) | apart_point_and_line(X23_29_8, U25_29_8)) | apart_point_and_line(X23_29_8, U25_29_8)) | apart_point_and_line(X23_29_8, U25_29_8))
% 32.46/9.04 -> [4422] ((apart_point_and_line(X23_29_8, U25_29_8) | apart_point_and_line(X23_29_8, U25_29_8)) | apart_point_and_line(X23_29_8, U25_29_8))
% 32.46/9.04 -> [4423] apart_point_and_line(X23_29_8, U25_29_8)
% 32.46/9.04
% 32.46/9.04 [4422] BETA_OR : ((apart_point_and_line(X23_29_8, U25_29_8) | apart_point_and_line(X23_29_8, U25_29_8)) | apart_point_and_line(X23_29_8, U25_29_8))
% 32.46/9.04 -> [4424] (apart_point_and_line(X23_29_8, U25_29_8) | apart_point_and_line(X23_29_8, U25_29_8))
% 32.46/9.04 -> [4425] apart_point_and_line(X23_29_8, U25_29_8)
% 32.46/9.04
% 32.46/9.04 [4424] BETA_OR : (apart_point_and_line(X23_29_8, skolem_Y3636) | apart_point_and_line(X23_29_8, U25_29_8))
% 32.46/9.04 -> [4426] apart_point_and_line(X23_29_8, skolem_Y3636)
% 32.46/9.04 -> [4427] apart_point_and_line(X23_29_8, U25_29_8)
% 32.46/9.04
% 32.46/9.04 [4427] CLOSURE : apart_point_and_line(X23_29_8, U25_29_8)
% 32.46/9.04
% 32.46/9.04 [4426] CLOSURE : apart_point_and_line(X23_29_8, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4425] CLOSURE : apart_point_and_line(X23_29_8, U25_29_8)
% 32.46/9.04
% 32.46/9.04 [4423] CLOSURE : apart_point_and_line(X23_29_8, U25_29_8)
% 32.46/9.04
% 32.46/9.04 [4354] CLOSURE : distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4351] GAMMA_FORALL : ! [X23_23, Y24_24, U25_25, V26_26] : (((distinct_points(X23_23, Y24_24) & distinct_lines(U25_25, V26_26)) => (((apart_point_and_line(X23_23, U25_25) | apart_point_and_line(X23_23, V26_26)) | apart_point_and_line(Y24_24, U25_25)) | apart_point_and_line(Y24_24, V26_26))))
% 32.46/9.04 -> [4428] ((distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) & distinct_lines(skolem_Y3636, skolem_Y3636)) => (((apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4428] BETA_IMPLY : ((distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) & distinct_lines(skolem_Y3636, skolem_Y3636)) => (((apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)))
% 32.46/9.04 -> [4429] ~(distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) & distinct_lines(skolem_Y3636, skolem_Y3636))
% 32.46/9.04 -> [4430] (((apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4429] BETA_NOT_AND : ~(distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) & distinct_lines(skolem_Y3636, skolem_Y3636))
% 32.46/9.04 -> [4431] ~distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.04 -> [4432] ~distinct_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4432] GAMMA_FORALL : ! [X27_27, Y28_28, Z29_29] : ((apart_point_and_line(X27_27, Y28_28) => (distinct_points(X27_27, Z29_29) | apart_point_and_line(Z29_29, Y28_28))))
% 32.46/9.04 -> [4438] (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) => (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4438] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) => (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)))
% 32.46/9.04 -> [4443] ~apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04 -> [4444] (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4443] GAMMA_FORALL : ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_lines(Y31_31, Z32_32) | apart_point_and_line(X30_30, Z32_32))))
% 32.46/9.04 -> [4457] (apart_point_and_line(X30_199_10, Y31_199_10) => (distinct_lines(Y31_199_10, Z32_199_10) | apart_point_and_line(X30_199_10, Z32_199_10)))
% 32.46/9.04
% 32.46/9.04 [4457] BETA_IMPLY : (apart_point_and_line(X30_199_10, Y31_199_10) => (distinct_lines(Y31_199_10, Z32_199_10) | apart_point_and_line(X30_199_10, Z32_199_10)))
% 32.46/9.04 -> [4458] ~apart_point_and_line(X30_199_10, Y31_199_10)
% 32.46/9.04 -> [4459] (distinct_lines(Y31_199_10, Z32_199_10) | apart_point_and_line(X30_199_10, Z32_199_10))
% 32.46/9.04
% 32.46/9.04 [4458] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 32.46/9.04 -> [4469] (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4469] BETA_IMPLY : (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04 -> [4472] ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04 -> [4473] distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4472] CLOSURE : ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4473] CLOSURE : distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4459] BETA_OR : (distinct_lines(Y31_199_10, Z32_199_10) | apart_point_and_line(X30_199_10, Z32_199_10))
% 32.46/9.04 -> [4476] distinct_lines(Y31_199_10, Z32_199_10)
% 32.46/9.04 -> [4477] apart_point_and_line(X30_199_10, Z32_199_10)
% 32.46/9.04
% 32.46/9.04 [4476] CLOSURE : distinct_lines(Y31_199_10, Z32_199_10)
% 32.46/9.04
% 32.46/9.04 [4477] CLOSURE : apart_point_and_line(X30_199_10, Z32_199_10)
% 32.46/9.04
% 32.46/9.04 [4444] BETA_OR : (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636))
% 32.46/9.04 -> [4540] distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.04 -> [4541] apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4541] GAMMA_FORALL : ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_lines(Y31_31, Z32_32) | apart_point_and_line(X30_30, Z32_32))))
% 32.46/9.04 -> [4544] (apart_point_and_line(X30_206_10, skolem_Y3636) => (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(X30_206_10, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4544] BETA_IMPLY : (apart_point_and_line(X30_206_10, skolem_Y3636) => (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(X30_206_10, skolem_Y3636)))
% 32.46/9.04 -> [4547] ~apart_point_and_line(X30_206_10, skolem_Y3636)
% 32.46/9.04 -> [4548] (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(X30_206_10, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4548] BETA_OR : (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(X30_206_10, skolem_Y3636))
% 32.46/9.04 -> [4549] distinct_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.04 -> [4550] apart_point_and_line(X30_206_10, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4549] CLOSURE : distinct_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4550] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 32.46/9.04 -> [4554] (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4554] BETA_IMPLY : (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04 -> [4555] ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04 -> [4556] distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4555] CLOSURE : ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4556] CLOSURE : distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4547] CLOSURE : ~apart_point_and_line(X30_206_10, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4540] CLOSURE : distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4431] GAMMA_FORALL : ! [X27_27, Y28_28, Z29_29] : ((apart_point_and_line(X27_27, Y28_28) => (distinct_points(X27_27, Z29_29) | apart_point_and_line(Z29_29, Y28_28))))
% 32.46/9.04 -> [4437] (apart_point_and_line(X27_130_9, skolem_Y3636) => (distinct_points(X27_130_9, Z29_130_9) | apart_point_and_line(Z29_130_9, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4437] BETA_IMPLY : (apart_point_and_line(X27_130_9, skolem_Y3636) => (distinct_points(X27_130_9, Z29_130_9) | apart_point_and_line(Z29_130_9, skolem_Y3636)))
% 32.46/9.04 -> [4439] ~apart_point_and_line(X27_130_9, skolem_Y3636)
% 32.46/9.04 -> [4440] (distinct_points(X27_130_9, Z29_130_9) | apart_point_and_line(Z29_130_9, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4439] GAMMA_FORALL : ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_lines(Y31_31, Z32_32) | apart_point_and_line(X30_30, Z32_32))))
% 32.46/9.04 -> [4449] (apart_point_and_line(X30_198_10, skolem_X3535) => (distinct_lines(skolem_X3535, skolem_Y3636) | apart_point_and_line(X30_198_10, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4449] BETA_IMPLY : (apart_point_and_line(X30_198_10, skolem_X3535) => (distinct_lines(skolem_X3535, skolem_Y3636) | apart_point_and_line(X30_198_10, skolem_Y3636)))
% 32.46/9.04 -> [4462] ~apart_point_and_line(X30_198_10, skolem_X3535)
% 32.46/9.04 -> [4463] (distinct_lines(skolem_X3535, skolem_Y3636) | apart_point_and_line(X30_198_10, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4463] BETA_OR : (distinct_lines(skolem_X3535, skolem_Y3636) | apart_point_and_line(X30_198_10, skolem_Y3636))
% 32.46/9.04 -> [4474] distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04 -> [4475] apart_point_and_line(X30_198_10, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4474] CLOSURE : distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4475] CLOSURE : apart_point_and_line(X30_198_10, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4462] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 32.46/9.04 -> [4501] (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4501] BETA_IMPLY : (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04 -> [4504] ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04 -> [4505] distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4504] CLOSURE : ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4505] CLOSURE : distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4440] BETA_OR : (distinct_points(X27_130_9, Z29_130_9) | apart_point_and_line(Z29_130_9, skolem_Y3636))
% 32.46/9.04 -> [4557] distinct_points(X27_130_9, Z29_130_9)
% 32.46/9.04 -> [4558] apart_point_and_line(Z29_130_9, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4557] CLOSURE : distinct_points(X27_130_9, Z29_130_9)
% 32.46/9.04
% 32.46/9.04 [4558] GAMMA_FORALL : ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_lines(Y31_31, Z32_32) | apart_point_and_line(X30_30, Z32_32))))
% 32.46/9.04 -> [4561] (apart_point_and_line(X30_207_10, skolem_Y3636) => (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(X30_207_10, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4561] BETA_IMPLY : (apart_point_and_line(X30_207_10, skolem_Y3636) => (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(X30_207_10, skolem_Y3636)))
% 32.46/9.04 -> [4562] ~apart_point_and_line(X30_207_10, skolem_Y3636)
% 32.46/9.04 -> [4563] (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(X30_207_10, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4563] BETA_OR : (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(X30_207_10, skolem_Y3636))
% 32.46/9.04 -> [4564] distinct_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.04 -> [4565] apart_point_and_line(X30_207_10, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4564] CLOSURE : distinct_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4565] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 32.46/9.04 -> [4571] (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4571] BETA_IMPLY : (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04 -> [4574] ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04 -> [4575] distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4574] CLOSURE : ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4575] CLOSURE : distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4562] CLOSURE : ~apart_point_and_line(X30_207_10, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4430] BETA_OR : (((apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636))
% 32.46/9.04 -> [4821] ((apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636))
% 32.46/9.04 -> [4822] apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4821] BETA_OR : ((apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636))
% 32.46/9.04 -> [4823] (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636))
% 32.46/9.04 -> [4824] apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4824] GAMMA_FORALL : ! [X27_27, Y28_28, Z29_29] : ((apart_point_and_line(X27_27, Y28_28) => (distinct_points(X27_27, Z29_29) | apart_point_and_line(Z29_29, Y28_28))))
% 32.46/9.04 -> [4830] (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) => (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4830] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) => (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)))
% 32.46/9.04 -> [4831] ~apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04 -> [4832] (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4831] CLOSURE : ~apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4832] BETA_OR : (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636))
% 32.46/9.04 -> [4890] distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.04 -> [4891] apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4890] CLOSURE : distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4895] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) => (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)))
% 32.46/9.04 -> [4925] ~apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04 -> [4926] (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4926] BETA_OR : (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636))
% 32.46/9.04 -> [4927] distinct_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.04 -> [4928] apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4927] CLOSURE : distinct_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4928] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 32.46/9.04 -> [4930] (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4930] BETA_IMPLY : (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04 -> [4933] ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04 -> [4934] distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4933] CLOSURE : ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4934] CLOSURE : distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4925] CLOSURE : ~apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4823] BETA_OR : (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636))
% 32.46/9.04 -> [4969] apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04 -> [4970] apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4969] GAMMA_FORALL : ! [X27_27, Y28_28, Z29_29] : ((apart_point_and_line(X27_27, Y28_28) => (distinct_points(X27_27, Z29_29) | apart_point_and_line(Z29_29, Y28_28))))
% 32.46/9.04 -> [4971] (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) => (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4971] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) => (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)))
% 32.46/9.04 -> [4973] ~apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04 -> [4974] (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4974] BETA_OR : (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636))
% 32.46/9.04 -> [4977] distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.04 -> [4978] apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4978] GAMMA_FORALL : ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_lines(Y31_31, Z32_32) | apart_point_and_line(X30_30, Z32_32))))
% 32.46/9.04 -> [4981] (apart_point_and_line(X30_235_10, skolem_Y3636) => (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(X30_235_10, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4981] BETA_IMPLY : (apart_point_and_line(X30_235_10, skolem_Y3636) => (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(X30_235_10, skolem_Y3636)))
% 32.46/9.04 -> [4983] ~apart_point_and_line(X30_235_10, skolem_Y3636)
% 32.46/9.04 -> [4984] (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(X30_235_10, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4984] BETA_OR : (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(X30_235_10, skolem_Y3636))
% 32.46/9.04 -> [4987] distinct_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.04 -> [4988] apart_point_and_line(X30_235_10, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4987] CLOSURE : distinct_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4988] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 32.46/9.04 -> [4991] (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4991] BETA_IMPLY : (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04 -> [4993] ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04 -> [4994] distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4993] CLOSURE : ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4994] CLOSURE : distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4983] CLOSURE : ~apart_point_and_line(X30_235_10, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4977] CLOSURE : distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4973] CLOSURE : ~apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4970] GAMMA_FORALL : ! [X27_27, Y28_28, Z29_29] : ((apart_point_and_line(X27_27, Y28_28) => (distinct_points(X27_27, Z29_29) | apart_point_and_line(Z29_29, Y28_28))))
% 32.46/9.04 -> [4972] (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) => (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4972] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) => (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)))
% 32.46/9.04 -> [4975] ~apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04 -> [4976] (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4976] BETA_OR : (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636))
% 32.46/9.04 -> [4979] distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.04 -> [4980] apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4980] GAMMA_FORALL : ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_lines(Y31_31, Z32_32) | apart_point_and_line(X30_30, Z32_32))))
% 32.46/9.04 -> [4982] (apart_point_and_line(X30_236_10, skolem_Y3636) => (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(X30_236_10, skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [4982] BETA_IMPLY : (apart_point_and_line(X30_236_10, skolem_Y3636) => (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(X30_236_10, skolem_Y3636)))
% 32.46/9.04 -> [4985] ~apart_point_and_line(X30_236_10, skolem_Y3636)
% 32.46/9.04 -> [4986] (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(X30_236_10, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4986] BETA_OR : (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(X30_236_10, skolem_Y3636))
% 32.46/9.04 -> [4989] distinct_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.04 -> [4990] apart_point_and_line(X30_236_10, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4989] CLOSURE : distinct_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4990] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 32.46/9.04 -> [4992] (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4992] BETA_IMPLY : (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04 -> [4995] ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04 -> [4996] distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4995] CLOSURE : ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4996] CLOSURE : distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4985] CLOSURE : ~apart_point_and_line(X30_236_10, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4979] CLOSURE : distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4975] CLOSURE : ~apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4825] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) => (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)))
% 32.46/9.04 -> [4997] ~apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04 -> [4998] (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [4997] CLOSURE : ~apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [4998] BETA_OR : (distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636))
% 32.46/9.04 -> [5014] distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.04 -> [5015] apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [5014] CLOSURE : distinct_points(intersection_point(skolem_Y3636, skolem_Y3636), intersection_point(skolem_Y3636, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [5015] GAMMA_FORALL : ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_lines(Y31_31, Z32_32) | apart_point_and_line(X30_30, Z32_32))))
% 32.46/9.04 -> [5016] (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) => (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)))
% 32.46/9.04
% 32.46/9.04 [5016] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636) => (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)))
% 32.46/9.04 -> [5017] ~apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04 -> [5018] (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [5017] CLOSURE : ~apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [5018] BETA_OR : (distinct_lines(skolem_Y3636, skolem_Y3636) | apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636))
% 32.46/9.04 -> [5024] distinct_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.04 -> [5025] apart_point_and_line(intersection_point(skolem_Y3636, skolem_Y3636), skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [5024] CLOSURE : distinct_lines(skolem_Y3636, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [5025] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 32.46/9.04 -> [5026] (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04
% 32.46/9.04 [5026] BETA_IMPLY : (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 32.46/9.04 -> [5027] ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04 -> [5028] distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [5027] CLOSURE : ~convergent_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 [5028] CLOSURE : distinct_lines(skolem_X3535, skolem_Y3636)
% 32.46/9.04
% 32.46/9.04 % SZS output end Proof for theBenchmark.p
% 32.46/9.04 [8.690125s][1][Res] 46747 goroutines created
% 32.46/9.04 ==== Result ====
% 32.46/9.04 [8.690164s][1][Res] VALID
% 32.46/9.04 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------