TSTP Solution File: GEO186+2 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO186+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n022.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 15:18:17 EDT 2022
% Result : Theorem 191.49s 52.72s
% Output : Proof 191.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO186+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 06:50:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 [DMT] DMT loaded with preskolemization
% 0.13/0.34 [EQ] equality loaded.
% 0.13/0.35 [0.000041s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.35 Conjecture not found
% 0.13/0.35 Start search
% 0.13/0.35 nb_step : 1 - limit : 13
% 0.13/0.35 Launch Gotab with destructive = true
% 191.39/52.70 % SZS output start Proof for theBenchmark.p
% 191.49/52.71 [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, U37_37, V38_38] : (((((distinct_points(X35_35, Y36_36) & convergent_lines(U37_37, V38_38)) & ~apart_point_and_line(X35_35, U37_37)) & ~apart_point_and_line(X35_35, V38_38)) => ~distinct_points(X35_35, intersection_point(U37_37, V38_38)))))
% 191.49/52.71 -> [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, U37_37, V38_38] : (((((distinct_points(X35_35, Y36_36) & convergent_lines(U37_37, V38_38)) & ~apart_point_and_line(X35_35, U37_37)) & ~apart_point_and_line(X35_35, V38_38)) => ~distinct_points(X35_35, intersection_point(U37_37, V38_38))))
% 191.49/52.71
% 191.49/52.71 [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))))
% 191.49/52.71 -> [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)))
% 191.49/52.71
% 191.49/52.71 [2] DELTA_NOT_FORALL : ~! [X35_35, Y36_36, U37_37, V38_38] : (((((distinct_points(X35_35, Y36_36) & convergent_lines(U37_37, V38_38)) & ~apart_point_and_line(X35_35, U37_37)) & ~apart_point_and_line(X35_35, V38_38)) => ~distinct_points(X35_35, intersection_point(U37_37, V38_38))))
% 191.49/52.71 -> [3] ~((((distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)) & ~apart_point_and_line(skolem_X3535, skolem_U3737)) & ~apart_point_and_line(skolem_X3535, skolem_V3838)) => ~distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.71
% 191.49/52.71 [3] ALPHA_NOT_IMPLY : ~((((distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)) & ~apart_point_and_line(skolem_X3535, skolem_U3737)) & ~apart_point_and_line(skolem_X3535, skolem_V3838)) => ~distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.71 -> [4] (((distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)) & ~apart_point_and_line(skolem_X3535, skolem_U3737)) & ~apart_point_and_line(skolem_X3535, skolem_V3838)), ~~distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 191.49/52.71
% 191.49/52.71 [4] ALPHA_AND : (((distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)) & ~apart_point_and_line(skolem_X3535, skolem_U3737)) & ~apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.71 -> [5] ((distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)) & ~apart_point_and_line(skolem_X3535, skolem_U3737)), ~apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.71
% 191.49/52.71 [5] ALPHA_NOT_NOT : ~~distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 191.49/52.71 -> [6] distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 191.49/52.71
% 191.49/52.71 [6] ALPHA_AND : ((distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)) & ~apart_point_and_line(skolem_X3535, skolem_U3737))
% 191.49/52.71 -> [7] (distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)), ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.71
% 191.49/52.71 [7] ALPHA_AND : (distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838))
% 191.49/52.71 -> [8] distinct_points(skolem_X3535, skolem_Y3636), convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.71
% 191.49/52.71 [8] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.71 -> [9] ~distinct_points(skolem_Y3636, skolem_Y3636)
% 191.49/52.71
% 191.49/52.71 [9] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 191.49/52.71 -> [10] ~distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.71
% 191.49/52.71 [10] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 191.49/52.71 -> [11] ~convergent_lines(skolem_V3838, skolem_V3838)
% 191.49/52.71
% 191.49/52.71 [11] 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))))
% 191.49/52.71 -> [12] (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636)))
% 191.49/52.71
% 191.49/52.71 [12] BETA_IMPLY : (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636)))
% 191.49/52.71 -> [13] ~distinct_points(skolem_X3535, skolem_Y3636)
% 191.49/52.71 -> [14] (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636))
% 191.49/52.71
% 191.49/52.71 [13] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 191.49/52.71
% 191.49/52.71 [14] BETA_OR : (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636))
% 191.49/52.71 -> [17] distinct_points(skolem_X3535, skolem_Y3636)
% 191.49/52.71 -> [18] distinct_points(skolem_Y3636, skolem_Y3636)
% 191.49/52.71
% 191.49/52.71 [18] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 191.49/52.71
% 191.49/52.71 [17] GAMMA_FORALL : ! [X11_11, Y12_12, Z13_13] : ((distinct_lines(X11_11, Y12_12) => (distinct_lines(X11_11, Z13_13) | distinct_lines(Y12_12, Z13_13))))
% 191.49/52.71 -> [19] (distinct_lines(skolem_U3737, skolem_V3838) => (distinct_lines(skolem_U3737, skolem_V3838) | distinct_lines(skolem_V3838, skolem_V3838)))
% 191.49/52.71
% 191.49/52.71 [19] BETA_IMPLY : (distinct_lines(skolem_U3737, skolem_V3838) => (distinct_lines(skolem_U3737, skolem_V3838) | distinct_lines(skolem_V3838, skolem_V3838)))
% 191.49/52.71 -> [20] ~distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.71 -> [21] (distinct_lines(skolem_U3737, skolem_V3838) | distinct_lines(skolem_V3838, skolem_V3838))
% 191.49/52.71
% 191.49/52.71 [20] GAMMA_FORALL : ! [X14_14, Y15_15, Z16_16] : ((convergent_lines(X14_14, Y15_15) => (convergent_lines(X14_14, Z16_16) | convergent_lines(Y15_15, Z16_16))))
% 191.49/52.71 -> [24] (convergent_lines(skolem_U3737, skolem_V3838) => (convergent_lines(skolem_U3737, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838)))
% 191.49/52.71
% 191.49/52.71 [24] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => (convergent_lines(skolem_U3737, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838)))
% 191.49/52.71 -> [25] ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.71 -> [26] (convergent_lines(skolem_U3737, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838))
% 191.49/52.71
% 191.49/52.71 [25] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.71
% 191.49/52.71 [26] BETA_OR : (convergent_lines(skolem_U3737, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838))
% 191.49/52.71 -> [29] convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.71 -> [30] convergent_lines(skolem_V3838, skolem_V3838)
% 191.49/52.71
% 191.49/52.71 [30] CLOSURE : convergent_lines(skolem_V3838, skolem_V3838)
% 191.49/52.71
% 191.49/52.71 [29] 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)))))
% 191.49/52.71 -> [31] (distinct_points(skolem_X3535, skolem_Y3636) => (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636))))
% 191.49/52.71
% 191.49/52.71 [31] BETA_IMPLY : (distinct_points(skolem_X3535, skolem_Y3636) => (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636))))
% 191.49/52.71 -> [32] ~distinct_points(skolem_X3535, skolem_Y3636)
% 191.49/52.71 -> [33] (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636)))
% 191.49/52.71
% 191.49/52.71 [32] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 191.49/52.72
% 191.49/52.72 [33] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636)))
% 191.49/52.72 -> [1773] ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72 -> [1774] (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [1773] GAMMA_FORALL : ! [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)))))
% 191.49/52.72 -> [1776] (convergent_lines(skolem_U3737, skolem_V3838) => ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) => distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72
% 191.49/52.72 [1776] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) => distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72 -> [1777] ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72 -> [1778] ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) => distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [1777] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [1778] BETA_IMPLY : ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) => distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72 -> [3000] ~(apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72 -> [3001] distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [3001] 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))))
% 191.49/52.72 -> [3003] ((distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(skolem_V3838, skolem_U3737)) => (((apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737)) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 191.49/52.72
% 191.49/52.72 [3003] BETA_IMPLY : ((distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(skolem_V3838, skolem_U3737)) => (((apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737)) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 191.49/52.72 -> [3005] ~(distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(skolem_V3838, skolem_U3737))
% 191.49/52.72 -> [3006] (((apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737)) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 191.49/52.72
% 191.49/52.72 [3006] BETA_OR : (((apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737)) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 191.49/52.72 -> [3013] ((apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737)) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72 -> [3014] apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [3013] BETA_OR : ((apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737)) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72 -> [3017] (apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 191.49/52.72 -> [3018] apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3018] CLOSURE : apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3017] BETA_OR : (apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 191.49/52.72 -> [3051] apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72 -> [3052] apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [3052] CLOSURE : apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [3051] CLOSURE : apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3014] CLOSURE : apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [3005] BETA_NOT_AND : ~(distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(skolem_V3838, skolem_U3737))
% 191.49/52.72 -> [3135] ~distinct_points(skolem_X3535, skolem_X3535)
% 191.49/52.72 -> [3136] ~distinct_lines(skolem_V3838, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [3135] 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))))
% 191.49/52.72 -> [3138] (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))))
% 191.49/52.72
% 191.49/52.72 [3138] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))))
% 191.49/52.72 -> [3141] ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72 -> [3142] (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 191.49/52.72
% 191.49/52.72 [3141] 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))))
% 191.49/52.72 -> [3148] (apart_point_and_line(X30_129_10, Z32_129_10) => (distinct_lines(Z32_129_10, Z32_129_10) | apart_point_and_line(X30_129_10, Z32_129_10)))
% 191.49/52.72
% 191.49/52.72 [3148] BETA_IMPLY : (apart_point_and_line(X30_129_10, Z32_129_10) => (distinct_lines(Z32_129_10, Z32_129_10) | apart_point_and_line(X30_129_10, Z32_129_10)))
% 191.49/52.72 -> [3151] ~apart_point_and_line(X30_129_10, Z32_129_10)
% 191.49/52.72 -> [3152] (distinct_lines(Z32_129_10, Z32_129_10) | apart_point_and_line(X30_129_10, Z32_129_10))
% 191.49/52.72
% 191.49/52.72 [3152] BETA_OR : (distinct_lines(Z32_129_10, Z32_129_10) | apart_point_and_line(X30_129_10, Z32_129_10))
% 191.49/52.72 -> [3155] distinct_lines(Z32_129_10, Z32_129_10)
% 191.49/52.72 -> [3156] apart_point_and_line(X30_129_10, Z32_129_10)
% 191.49/52.72
% 191.49/52.72 [3156] CLOSURE : apart_point_and_line(X30_129_10, Z32_129_10)
% 191.49/52.72
% 191.49/52.72 [3155] CLOSURE : distinct_lines(Z32_129_10, Z32_129_10)
% 191.49/52.72
% 191.49/52.72 [3157] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [3167] ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72 -> [3168] distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3167] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3168] CLOSURE : distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3142] BETA_OR : (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 191.49/52.72 -> [3171] distinct_points(skolem_Y3636, skolem_Y3636)
% 191.49/52.72 -> [3172] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [3171] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 191.49/52.72
% 191.49/52.72 [3172] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [3137] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))))
% 191.49/52.72 -> [3182] ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72 -> [3183] (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 191.49/52.72
% 191.49/52.72 [3182] 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))))
% 191.49/52.72 -> [3186] (apart_point_and_line(X30_130_10, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(X30_130_10, line_connecting(skolem_X3535, skolem_Y3636))))
% 191.49/52.72
% 191.49/52.72 [3186] BETA_IMPLY : (apart_point_and_line(X30_130_10, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(X30_130_10, line_connecting(skolem_X3535, skolem_Y3636))))
% 191.49/52.72 -> [3187] ~apart_point_and_line(X30_130_10, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72 -> [3188] (distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(X30_130_10, line_connecting(skolem_X3535, skolem_Y3636)))
% 191.49/52.72
% 191.49/52.72 [3187] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 191.49/52.72 -> [3191] (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [3191] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [3192] ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72 -> [3193] distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3192] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3193] CLOSURE : distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3188] BETA_OR : (distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(X30_130_10, line_connecting(skolem_X3535, skolem_Y3636)))
% 191.49/52.72 -> [3189] distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72 -> [3190] apart_point_and_line(X30_130_10, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [3189] CLOSURE : distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [3190] CLOSURE : apart_point_and_line(X30_130_10, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [3183] BETA_OR : (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 191.49/52.72 -> [3194] distinct_points(skolem_Y3636, skolem_Y3636)
% 191.49/52.72 -> [3195] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [3195] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [3194] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 191.49/52.72
% 191.49/52.72 [3004] BETA_IMPLY : ((distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(skolem_U3737, skolem_V3838)) => (((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737)) | apart_point_and_line(skolem_X3535, skolem_V3838)))
% 191.49/52.72 -> [3196] ~(distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [3197] (((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737)) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [3197] BETA_OR : (((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737)) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72 -> [3200] ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 191.49/52.72 -> [3201] apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3201] CLOSURE : apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3200] BETA_OR : ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 191.49/52.72 -> [3223] (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72 -> [3224] apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [3224] CLOSURE : apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [3223] BETA_OR : (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72 -> [3230] apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72 -> [3231] apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3230] CLOSURE : apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [3231] CLOSURE : apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3196] BETA_NOT_AND : ~(distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [3251] ~distinct_points(skolem_X3535, skolem_X3535)
% 191.49/52.72 -> [3252] ~distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3252] 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))))
% 191.49/52.72 -> [3253] (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))))
% 191.49/52.72
% 191.49/52.72 [3253] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))))
% 191.49/52.72 -> [3255] ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72 -> [3256] (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 191.49/52.72
% 191.49/52.72 [3256] BETA_OR : (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 191.49/52.72 -> [3259] distinct_points(skolem_Y3636, skolem_Y3636)
% 191.49/52.72 -> [3260] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [3259] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 191.49/52.72
% 191.49/52.72 [3260] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [3255] 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))))
% 191.49/52.72 -> [3263] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [3263] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_V3838)))
% 191.49/52.72 -> [3265] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72 -> [3266] (distinct_lines(skolem_U3737, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [3265] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 191.49/52.72 -> [3273] (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [3273] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [3274] ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72 -> [3275] distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3274] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3275] CLOSURE : distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3266] BETA_OR : (distinct_lines(skolem_U3737, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72 -> [3269] distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72 -> [3270] apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3270] CLOSURE : apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3269] CLOSURE : distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3251] 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))))
% 191.49/52.72 -> [3254] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 191.49/52.72
% 191.49/52.72 [3254] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 191.49/52.72 -> [3257] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72 -> [3258] (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 191.49/52.72
% 191.49/52.72 [3258] BETA_OR : (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 191.49/52.72 -> [3261] distinct_points(skolem_X3535, skolem_X3535)
% 191.49/52.72 -> [3262] apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [3262] CLOSURE : apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [3261] CLOSURE : distinct_points(skolem_X3535, skolem_X3535)
% 191.49/52.72
% 191.49/52.72 [3264] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))))
% 191.49/52.72 -> [3279] ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72 -> [3280] (distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 191.49/52.72
% 191.49/52.72 [3279] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 191.49/52.72 -> [3283] (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [3283] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [3284] ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72 -> [3285] distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3284] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3285] CLOSURE : distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [3280] BETA_OR : (distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 191.49/52.72 -> [3281] distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72 -> [3282] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [3281] CLOSURE : distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [3282] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [1775] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 191.49/52.72
% 191.49/52.72 [21] BETA_OR : (distinct_lines(skolem_U3737, skolem_V3838) | distinct_lines(skolem_V3838, skolem_V3838))
% 191.49/52.72 -> [7615] distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72 -> [7616] distinct_lines(skolem_V3838, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [7616] GAMMA_FORALL : ! [X14_14, Y15_15, Z16_16] : ((convergent_lines(X14_14, Y15_15) => (convergent_lines(X14_14, Z16_16) | convergent_lines(Y15_15, Z16_16))))
% 191.49/52.72 -> [7618] (convergent_lines(skolem_V3838, skolem_V3838) => (convergent_lines(skolem_V3838, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [7618] BETA_IMPLY : (convergent_lines(skolem_V3838, skolem_V3838) => (convergent_lines(skolem_V3838, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838)))
% 191.49/52.72 -> [7621] ~convergent_lines(skolem_V3838, skolem_V3838)
% 191.49/52.72 -> [7622] (convergent_lines(skolem_V3838, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [7622] BETA_OR : (convergent_lines(skolem_V3838, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838))
% 191.49/52.72 -> [7625] convergent_lines(skolem_V3838, skolem_V3838)
% 191.49/52.72 -> [7626] convergent_lines(skolem_V3838, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [7626] CLOSURE : convergent_lines(skolem_V3838, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [7625] CLOSURE : convergent_lines(skolem_V3838, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [7621] 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)))))
% 191.49/52.72 -> [9762] (distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)) => (apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) => (distinct_points(skolem_Y3636, skolem_Y3636) & distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))))
% 191.49/52.72
% 191.49/52.72 [9762] BETA_IMPLY : (distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)) => (apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) => (distinct_points(skolem_Y3636, skolem_Y3636) & distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))))
% 191.49/52.72 -> [9763] ~distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [9764] (apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) => (distinct_points(skolem_Y3636, skolem_Y3636) & distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72
% 191.49/52.72 [9764] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) => (distinct_points(skolem_Y3636, skolem_Y3636) & distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72 -> [9765] ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72 -> [9766] (distinct_points(skolem_Y3636, skolem_Y3636) & distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [9766] ALPHA_AND : (distinct_points(skolem_Y3636, skolem_Y3636) & distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72 -> [9767] distinct_points(skolem_Y3636, skolem_Y3636), distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [9767] CLOSURE : distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [9768] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => ((apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)) => distinct_points(intersection_point(skolem_U3737, skolem_V3838), intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72 -> [12140] ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72 -> [12141] ((apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)) => distinct_points(intersection_point(skolem_U3737, skolem_V3838), intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [12141] BETA_IMPLY : ((apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)) => distinct_points(intersection_point(skolem_U3737, skolem_V3838), intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72 -> [12142] ~(apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838))
% 191.49/52.72 -> [12143] distinct_points(intersection_point(skolem_U3737, skolem_V3838), intersection_point(skolem_U3737, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [12142] ALPHA_NOT_OR : ~(apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838))
% 191.49/52.72 -> [12144] ~apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737), ~apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [12144] 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))))
% 191.49/52.72 -> [12148] ((distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)) & distinct_lines(skolem_V3838, skolem_V3838)) => (((apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [12148] BETA_IMPLY : ((distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)) & distinct_lines(skolem_V3838, skolem_V3838)) => (((apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)))
% 191.49/52.72 -> [12153] ~(distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)) & distinct_lines(skolem_V3838, skolem_V3838))
% 191.49/52.72 -> [12154] (((apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [12153] BETA_NOT_AND : ~(distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)) & distinct_lines(skolem_V3838, skolem_V3838))
% 191.49/52.72 -> [12157] ~distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [12158] ~distinct_lines(skolem_V3838, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [12157] CLOSURE : ~distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [12158] CLOSURE : ~distinct_lines(skolem_V3838, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [12154] BETA_OR : (((apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838))
% 191.49/52.72 -> [12266] ((apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838))
% 191.49/52.72 -> [12267] apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [12266] BETA_OR : ((apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838))
% 191.49/52.72 -> [12268] (apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72 -> [12269] apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [12268] BETA_OR : (apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72 -> [12270] apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72 -> [12271] apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [12270] CLOSURE : apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [12271] CLOSURE : apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [12269] CLOSURE : apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [12267] CLOSURE : apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [12145] BETA_IMPLY : ((distinct_points(skolem_Y3636, skolem_Y3636) & distinct_lines(line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)), line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))) => (((apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))))
% 191.49/52.72 -> [12684] ~(distinct_points(skolem_Y3636, skolem_Y3636) & distinct_lines(line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)), line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72 -> [12685] (((apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72
% 191.49/52.72 [12685] BETA_OR : (((apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72 -> [12688] ((apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72 -> [12689] apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [12689] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [12688] BETA_OR : ((apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72 -> [12794] (apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72 -> [12795] apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [12794] BETA_OR : (apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72 -> [12796] apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72 -> [12797] apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [12796] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [12797] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [12795] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [12684] BETA_NOT_AND : ~(distinct_points(skolem_Y3636, skolem_Y3636) & distinct_lines(line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)), line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72 -> [12804] ~distinct_points(skolem_Y3636, skolem_Y3636)
% 191.49/52.72 -> [12805] ~distinct_lines(line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)), line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [12804] 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))))
% 191.49/52.72 -> [12809] (apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) => (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))))
% 191.49/52.72
% 191.49/52.72 [12809] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) => (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))))
% 191.49/52.72 -> [12810] ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72 -> [12811] (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72
% 191.49/52.72 [12811] BETA_OR : (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72 -> [12815] distinct_points(skolem_Y3636, skolem_Y3636)
% 191.49/52.72 -> [12816] apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [12816] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [12815] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 191.49/52.72
% 191.49/52.72 [12819] BETA_IMPLY : (apart_point_and_line(skolem_X3535, Y31_434_10) => (distinct_lines(Y31_434_10, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 191.49/52.72 -> [12875] ~apart_point_and_line(skolem_X3535, Y31_434_10)
% 191.49/52.72 -> [12876] (distinct_lines(Y31_434_10, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 191.49/52.72
% 191.49/52.72 [12876] BETA_OR : (distinct_lines(Y31_434_10, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 191.49/52.72 -> [12877] distinct_lines(Y31_434_10, skolem_U3737)
% 191.49/52.72 -> [12878] apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [12878] CLOSURE : apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [12877] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 191.49/52.72 -> [12884] (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [12884] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [12885] ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72 -> [12886] distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [12885] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [12886] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72 -> [12898] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72
% 191.49/52.72 [12898] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72 -> [12899] ~distinct_points(X5_1867_0, X5_1867_0)
% 191.49/52.72
% 191.49/52.72 [12899] CLOSURE : ~distinct_points(X5_1867_0, X5_1867_0)
% 191.49/52.72
% 191.49/52.72 [12881] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [12904] ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72 -> [12905] distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [12904] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [12905] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72 -> [12908] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72
% 191.49/52.72 [12908] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72 -> [12910] ~distinct_points(X5_1870_0, X5_1870_0)
% 191.49/52.72
% 191.49/52.72 [12910] CLOSURE : ~distinct_points(X5_1870_0, X5_1870_0)
% 191.49/52.72
% 191.49/52.72 [12805] 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))))
% 191.49/52.72 -> [12806] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 191.49/52.72
% 191.49/52.72 [12806] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 191.49/52.72 -> [12807] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72 -> [12808] (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 191.49/52.72
% 191.49/52.72 [12808] BETA_OR : (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 191.49/52.72 -> [12812] distinct_points(skolem_X3535, skolem_X3535)
% 191.49/52.72 -> [12813] apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [12813] CLOSURE : apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [12812] 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))))
% 191.49/52.72 -> [12834] (apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) => (distinct_lines(line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)), line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))))
% 191.49/52.72
% 191.49/52.72 [12834] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) => (distinct_lines(line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)), line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))))
% 191.49/52.72 -> [12835] ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72 -> [12836] (distinct_lines(line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)), line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72
% 191.49/52.72 [12836] BETA_OR : (distinct_lines(line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)), line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72 -> [12837] distinct_lines(line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)), line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72 -> [12838] apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [12838] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [12837] CLOSURE : distinct_lines(line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)), line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [12842] BETA_IMPLY : (convergent_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)) => distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)))
% 191.49/52.72 -> [12862] ~convergent_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72 -> [12863] distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [12863] CLOSURE : distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [12862] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72 -> [12872] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72
% 191.49/52.72 [12872] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72 -> [12874] ~distinct_points(X5_1863_0, X5_1863_0)
% 191.49/52.72
% 191.49/52.72 [12874] CLOSURE : ~distinct_points(X5_1863_0, X5_1863_0)
% 191.49/52.72
% 191.49/52.72 [12814] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) => (distinct_lines(line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)), line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))))
% 191.49/52.72 -> [12887] ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72 -> [12888] (distinct_lines(line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)), line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72
% 191.49/52.72 [12888] BETA_OR : (distinct_lines(line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)), line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72 -> [12891] distinct_lines(line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)), line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72 -> [12892] apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [12892] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [12891] CLOSURE : distinct_lines(line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)), line_connecting(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [12893] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [12906] ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72 -> [12907] distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [12906] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [12907] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72 -> [12913] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72
% 191.49/52.72 [12913] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72 -> [12914] ~distinct_points(X5_1871_0, X5_1871_0)
% 191.49/52.72
% 191.49/52.72 [12914] CLOSURE : ~distinct_points(X5_1871_0, X5_1871_0)
% 191.49/52.72
% 191.49/52.72 [12140] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [9763] GAMMA_FORALL : ! [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)))))
% 191.49/52.72 -> [15182] (convergent_lines(skolem_U3737, skolem_V3838) => ((apart_point_and_line(skolem_Y3636, skolem_U3737) | apart_point_and_line(skolem_Y3636, skolem_V3838)) => distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72
% 191.49/52.72 [15182] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => ((apart_point_and_line(skolem_Y3636, skolem_U3737) | apart_point_and_line(skolem_Y3636, skolem_V3838)) => distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72 -> [15183] ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72 -> [15184] ((apart_point_and_line(skolem_Y3636, skolem_U3737) | apart_point_and_line(skolem_Y3636, skolem_V3838)) => distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [15183] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [15184] BETA_IMPLY : ((apart_point_and_line(skolem_Y3636, skolem_U3737) | apart_point_and_line(skolem_Y3636, skolem_V3838)) => distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72 -> [15232] ~(apart_point_and_line(skolem_Y3636, skolem_U3737) | apart_point_and_line(skolem_Y3636, skolem_V3838))
% 191.49/52.72 -> [15233] distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [15233] CLOSURE : distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [15235] BETA_IMPLY : ((distinct_points(skolem_X3535, skolem_Y3636) & distinct_lines(skolem_V3838, skolem_V3838)) => (((apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_Y3636, skolem_V3838)) | apart_point_and_line(skolem_Y3636, skolem_V3838)))
% 191.49/52.72 -> [15269] ~(distinct_points(skolem_X3535, skolem_Y3636) & distinct_lines(skolem_V3838, skolem_V3838))
% 191.49/52.72 -> [15270] (((apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_Y3636, skolem_V3838)) | apart_point_and_line(skolem_Y3636, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [15270] BETA_OR : (((apart_point_and_line(skolem_Y3636, skolem_V3838) | apart_point_and_line(skolem_Y3636, skolem_V3838)) | apart_point_and_line(skolem_Y3636, skolem_V3838)) | apart_point_and_line(skolem_Y3636, skolem_V3838))
% 191.49/52.72 -> [15273] ((apart_point_and_line(skolem_Y3636, skolem_V3838) | apart_point_and_line(skolem_Y3636, skolem_V3838)) | apart_point_and_line(skolem_Y3636, skolem_V3838))
% 191.49/52.72 -> [15274] apart_point_and_line(skolem_Y3636, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [15274] CLOSURE : apart_point_and_line(skolem_Y3636, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [15273] BETA_OR : ((apart_point_and_line(skolem_Y3636, skolem_V3838) | apart_point_and_line(skolem_Y3636, skolem_V3838)) | apart_point_and_line(skolem_Y3636, skolem_V3838))
% 191.49/52.72 -> [15288] (apart_point_and_line(skolem_Y3636, skolem_V3838) | apart_point_and_line(skolem_Y3636, skolem_V3838))
% 191.49/52.72 -> [15289] apart_point_and_line(skolem_Y3636, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [15289] CLOSURE : apart_point_and_line(skolem_Y3636, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [15288] BETA_OR : (apart_point_and_line(skolem_Y3636, skolem_V3838) | apart_point_and_line(skolem_Y3636, skolem_V3838))
% 191.49/52.72 -> [15294] apart_point_and_line(skolem_Y3636, skolem_V3838)
% 191.49/52.72 -> [15295] apart_point_and_line(skolem_Y3636, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [15294] CLOSURE : apart_point_and_line(skolem_Y3636, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [15295] CLOSURE : apart_point_and_line(skolem_Y3636, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [15269] BETA_NOT_AND : ~(distinct_points(skolem_X3535, skolem_Y3636) & distinct_lines(skolem_V3838, skolem_V3838))
% 191.49/52.72 -> [15298] ~distinct_points(skolem_X3535, skolem_Y3636)
% 191.49/52.72 -> [15299] ~distinct_lines(skolem_V3838, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [15298] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 191.49/52.72
% 191.49/52.72 [15299] CLOSURE : ~distinct_lines(skolem_V3838, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [7615] GAMMA_FORALL : ! [X14_14, Y15_15, Z16_16] : ((convergent_lines(X14_14, Y15_15) => (convergent_lines(X14_14, Z16_16) | convergent_lines(Y15_15, Z16_16))))
% 191.49/52.72 -> [7617] (convergent_lines(skolem_U3737, skolem_V3838) => (convergent_lines(skolem_U3737, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [7617] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => (convergent_lines(skolem_U3737, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838)))
% 191.49/52.72 -> [7619] ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72 -> [7620] (convergent_lines(skolem_U3737, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [7619] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [7620] BETA_OR : (convergent_lines(skolem_U3737, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838))
% 191.49/52.72 -> [7627] convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72 -> [7628] convergent_lines(skolem_V3838, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [7627] 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)))))
% 191.49/52.72 -> [7631] (distinct_points(skolem_X3535, skolem_Y3636) => (apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_X3535, skolem_X3535) & distinct_points(skolem_X3535, skolem_Y3636))))
% 191.49/52.72
% 191.49/52.72 [7631] BETA_IMPLY : (distinct_points(skolem_X3535, skolem_Y3636) => (apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_X3535, skolem_X3535) & distinct_points(skolem_X3535, skolem_Y3636))))
% 191.49/52.72 -> [7632] ~distinct_points(skolem_X3535, skolem_Y3636)
% 191.49/52.72 -> [7633] (apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_X3535, skolem_X3535) & distinct_points(skolem_X3535, skolem_Y3636)))
% 191.49/52.72
% 191.49/52.72 [7632] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 191.49/52.72
% 191.49/52.72 [7633] BETA_IMPLY : (apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_X3535, skolem_X3535) & distinct_points(skolem_X3535, skolem_Y3636)))
% 191.49/52.72 -> [13886] ~apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72 -> [13887] (distinct_points(skolem_X3535, skolem_X3535) & distinct_points(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [13886] GAMMA_FORALL : ! [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)))))
% 191.49/52.72 -> [13889] (convergent_lines(skolem_U3737, skolem_V3838) => ((apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)) => distinct_points(intersection_point(skolem_U3737, skolem_V3838), intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72
% 191.49/52.72 [13889] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => ((apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)) => distinct_points(intersection_point(skolem_U3737, skolem_V3838), intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72 -> [13890] ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72 -> [13891] ((apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)) => distinct_points(intersection_point(skolem_U3737, skolem_V3838), intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [13890] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [13891] BETA_IMPLY : ((apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)) => distinct_points(intersection_point(skolem_U3737, skolem_V3838), intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72 -> [16300] ~(apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838))
% 191.49/52.72 -> [16301] distinct_points(intersection_point(skolem_U3737, skolem_V3838), intersection_point(skolem_U3737, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [16300] ALPHA_NOT_OR : ~(apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838))
% 191.49/52.72 -> [16302] ~apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737), ~apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16302] 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))))
% 191.49/52.72 -> [16306] ((distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)) & distinct_lines(skolem_U3737, skolem_V3838)) => (((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [16306] BETA_IMPLY : ((distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)) & distinct_lines(skolem_U3737, skolem_V3838)) => (((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)))
% 191.49/52.72 -> [16309] ~(distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)) & distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [16310] (((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [16309] BETA_NOT_AND : ~(distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)) & distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [16313] ~distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [16314] ~distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16313] CLOSURE : ~distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [16314] CLOSURE : ~distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16310] BETA_OR : (((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838))
% 191.49/52.72 -> [16335] ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737))
% 191.49/52.72 -> [16336] apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16336] CLOSURE : apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16335] BETA_OR : ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737))
% 191.49/52.72 -> [16339] (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72 -> [16340] apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [16339] BETA_OR : (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72 -> [16341] apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72 -> [16342] apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16341] CLOSURE : apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [16342] CLOSURE : apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16340] CLOSURE : apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [16303] BETA_IMPLY : ((distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), skolem_V3838)) => (((apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, skolem_V3838)))
% 191.49/52.72 -> [16398] ~(distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), skolem_V3838))
% 191.49/52.72 -> [16399] (((apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [16399] BETA_OR : (((apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72 -> [16402] ((apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 191.49/52.72 -> [16403] apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16403] CLOSURE : apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16402] BETA_OR : ((apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 191.49/52.72 -> [16410] (apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72 -> [16411] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [16411] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [16410] BETA_OR : (apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72 -> [16414] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72 -> [16415] apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16414] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [16415] CLOSURE : apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16398] BETA_NOT_AND : ~(distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), skolem_V3838))
% 191.49/52.72 -> [16416] ~distinct_points(skolem_X3535, skolem_X3535)
% 191.49/52.72 -> [16417] ~distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16416] 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))))
% 191.49/52.72 -> [16418] (apart_point_and_line(skolem_X3535, skolem_V3838) => (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [16418] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_V3838) => (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_V3838)))
% 191.49/52.72 -> [16420] ~apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72 -> [16421] (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [16421] BETA_OR : (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72 -> [16424] distinct_points(skolem_X3535, skolem_X3535)
% 191.49/52.72 -> [16425] apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16424] CLOSURE : distinct_points(skolem_X3535, skolem_X3535)
% 191.49/52.72
% 191.49/52.72 [16425] CLOSURE : apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16429] BETA_IMPLY : (apart_point_and_line(skolem_X3535, Y31_519_10) => (distinct_lines(Y31_519_10, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 191.49/52.72 -> [16458] ~apart_point_and_line(skolem_X3535, Y31_519_10)
% 191.49/52.72 -> [16459] (distinct_lines(Y31_519_10, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 191.49/52.72
% 191.49/52.72 [16458] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 191.49/52.72 -> [16462] (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [16462] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [16463] ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72 -> [16464] distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16463] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16464] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72 -> [16470] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72
% 191.49/52.72 [16470] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72 -> [16471] ~distinct_points(X5_2537_0, X5_2537_0)
% 191.49/52.72
% 191.49/52.72 [16471] CLOSURE : ~distinct_points(X5_2537_0, X5_2537_0)
% 191.49/52.72
% 191.49/52.72 [16459] BETA_OR : (distinct_lines(Y31_519_10, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 191.49/52.72 -> [16460] distinct_lines(Y31_519_10, skolem_U3737)
% 191.49/52.72 -> [16461] apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [16461] CLOSURE : apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [16460] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 191.49/52.72 -> [16467] (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [16467] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [16468] ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72 -> [16469] distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16468] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16469] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72 -> [16480] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72
% 191.49/52.72 [16480] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72 -> [16481] ~distinct_points(X5_2538_0, X5_2538_0)
% 191.49/52.72
% 191.49/52.72 [16481] CLOSURE : ~distinct_points(X5_2538_0, X5_2538_0)
% 191.49/52.72
% 191.49/52.72 [16417] 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))))
% 191.49/52.72 -> [16419] (apart_point_and_line(X27_210_9, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(X27_210_9, skolem_X3535) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))))
% 191.49/52.72
% 191.49/52.72 [16419] BETA_IMPLY : (apart_point_and_line(X27_210_9, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(X27_210_9, skolem_X3535) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))))
% 191.49/52.72 -> [16422] ~apart_point_and_line(X27_210_9, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72 -> [16423] (distinct_points(X27_210_9, skolem_X3535) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 191.49/52.72
% 191.49/52.72 [16422] 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))))
% 191.49/52.72 -> [16428] (apart_point_and_line(X30_518_10, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(X30_518_10, line_connecting(skolem_X3535, skolem_Y3636))))
% 191.49/52.72
% 191.49/52.72 [16428] BETA_IMPLY : (apart_point_and_line(X30_518_10, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(X30_518_10, line_connecting(skolem_X3535, skolem_Y3636))))
% 191.49/52.72 -> [16430] ~apart_point_and_line(X30_518_10, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72 -> [16431] (distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(X30_518_10, line_connecting(skolem_X3535, skolem_Y3636)))
% 191.49/52.72
% 191.49/52.72 [16431] BETA_OR : (distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(X30_518_10, line_connecting(skolem_X3535, skolem_Y3636)))
% 191.49/52.72 -> [16434] distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72 -> [16435] apart_point_and_line(X30_518_10, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [16435] CLOSURE : apart_point_and_line(X30_518_10, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [16434] CLOSURE : distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [16430] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 191.49/52.72 -> [16438] (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [16438] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [16440] ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72 -> [16441] distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16440] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16441] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72 -> [16452] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72
% 191.49/52.72 [16452] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72 -> [16453] ~distinct_points(X5_2534_0, X5_2534_0)
% 191.49/52.72
% 191.49/52.72 [16453] CLOSURE : ~distinct_points(X5_2534_0, X5_2534_0)
% 191.49/52.72
% 191.49/52.72 [16423] BETA_OR : (distinct_points(X27_210_9, skolem_X3535) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 191.49/52.72 -> [16465] distinct_points(X27_210_9, skolem_X3535)
% 191.49/52.72 -> [16466] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [16466] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 191.49/52.72
% 191.49/52.72 [16465] 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))))
% 191.49/52.72 -> [16472] (apart_point_and_line(skolem_X3535, Y31_521_10) => (distinct_lines(Y31_521_10, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 191.49/52.72
% 191.49/52.72 [16472] BETA_IMPLY : (apart_point_and_line(skolem_X3535, Y31_521_10) => (distinct_lines(Y31_521_10, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 191.49/52.72 -> [16473] ~apart_point_and_line(skolem_X3535, Y31_521_10)
% 191.49/52.72 -> [16474] (distinct_lines(Y31_521_10, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 191.49/52.72
% 191.49/52.72 [16473] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 191.49/52.72 -> [16477] (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [16477] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [16478] ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72 -> [16479] distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16478] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16479] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72 -> [16485] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72
% 191.49/52.72 [16485] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72 -> [16486] ~distinct_points(X5_2539_0, X5_2539_0)
% 191.49/52.72
% 191.49/52.72 [16486] CLOSURE : ~distinct_points(X5_2539_0, X5_2539_0)
% 191.49/52.72
% 191.49/52.72 [16474] BETA_OR : (distinct_lines(Y31_521_10, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 191.49/52.72 -> [16475] distinct_lines(Y31_521_10, skolem_U3737)
% 191.49/52.72 -> [16476] apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [16476] CLOSURE : apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [16475] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 191.49/52.72 -> [16482] (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [16482] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [16483] ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72 -> [16484] distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16483] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [16484] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72 -> [16487] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72
% 191.49/52.72 [16487] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 191.49/52.72 -> [16488] ~distinct_points(X5_2540_0, X5_2540_0)
% 191.49/52.72
% 191.49/52.72 [16488] CLOSURE : ~distinct_points(X5_2540_0, X5_2540_0)
% 191.49/52.72
% 191.49/52.72 [13888] GAMMA_FORALL : ! [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)))))
% 191.49/52.72 -> [18602] (convergent_lines(skolem_U3737, skolem_V3838) => ((apart_point_and_line(Z22_11_7, skolem_U3737) | apart_point_and_line(Z22_11_7, skolem_V3838)) => distinct_points(Z22_11_7, intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72
% 191.49/52.72 [18602] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => ((apart_point_and_line(Z22_11_7, skolem_U3737) | apart_point_and_line(Z22_11_7, skolem_V3838)) => distinct_points(Z22_11_7, intersection_point(skolem_U3737, skolem_V3838))))
% 191.49/52.72 -> [18603] ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72 -> [18604] ((apart_point_and_line(Z22_11_7, skolem_U3737) | apart_point_and_line(Z22_11_7, skolem_V3838)) => distinct_points(Z22_11_7, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [18603] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [18604] BETA_IMPLY : ((apart_point_and_line(Z22_11_7, skolem_U3737) | apart_point_and_line(Z22_11_7, skolem_V3838)) => distinct_points(Z22_11_7, intersection_point(skolem_U3737, skolem_V3838)))
% 191.49/52.72 -> [18652] ~(apart_point_and_line(Z22_11_7, skolem_U3737) | apart_point_and_line(Z22_11_7, skolem_V3838))
% 191.49/52.72 -> [18653] distinct_points(Z22_11_7, intersection_point(skolem_U3737, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [18653] 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))))
% 191.49/52.72 -> [18655] ((distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(skolem_U3737, skolem_V3838)) => (((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737)) | apart_point_and_line(skolem_X3535, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [18655] BETA_IMPLY : ((distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(skolem_U3737, skolem_V3838)) => (((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737)) | apart_point_and_line(skolem_X3535, skolem_V3838)))
% 191.49/52.72 -> [18656] ~(distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [18657] (((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737)) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [18656] BETA_NOT_AND : ~(distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [18659] ~distinct_points(skolem_X3535, skolem_X3535)
% 191.49/52.72 -> [18660] ~distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [18659] CLOSURE : ~distinct_points(skolem_X3535, skolem_X3535)
% 191.49/52.72
% 191.49/52.72 [18660] CLOSURE : ~distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [18657] BETA_OR : (((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737)) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72 -> [18661] ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 191.49/52.72 -> [18662] apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [18662] CLOSURE : apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [18661] BETA_OR : ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 191.49/52.72 -> [18677] (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72 -> [18678] apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [18678] CLOSURE : apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [18677] BETA_OR : (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72 -> [18685] apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72 -> [18686] apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [18685] CLOSURE : apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [18686] CLOSURE : apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [18652] ALPHA_NOT_OR : ~(apart_point_and_line(Z22_11_7, skolem_U3737) | apart_point_and_line(Z22_11_7, skolem_V3838))
% 191.49/52.72 -> [18654] ~apart_point_and_line(Z22_11_7, skolem_U3737), ~apart_point_and_line(Z22_11_7, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [18654] 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))))
% 191.49/52.72 -> [18658] ((distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(skolem_U3737, skolem_V3838)) => (((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737)) | apart_point_and_line(skolem_X3535, skolem_V3838)))
% 191.49/52.72
% 191.49/52.72 [18658] BETA_IMPLY : ((distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(skolem_U3737, skolem_V3838)) => (((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737)) | apart_point_and_line(skolem_X3535, skolem_V3838)))
% 191.49/52.72 -> [18663] ~(distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [18664] (((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737)) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72
% 191.49/52.72 [18663] BETA_NOT_AND : ~(distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(skolem_U3737, skolem_V3838))
% 191.49/52.72 -> [18667] ~distinct_points(skolem_X3535, skolem_X3535)
% 191.49/52.72 -> [18668] ~distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [18667] CLOSURE : ~distinct_points(skolem_X3535, skolem_X3535)
% 191.49/52.72
% 191.49/52.72 [18668] CLOSURE : ~distinct_lines(skolem_U3737, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [18664] BETA_OR : (((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737)) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72 -> [18669] ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 191.49/52.72 -> [18670] apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [18670] CLOSURE : apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [18669] BETA_OR : ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 191.49/52.72 -> [18681] (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72 -> [18682] apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [18681] BETA_OR : (apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 191.49/52.72 -> [18683] apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72 -> [18684] apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [18684] CLOSURE : apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [18683] CLOSURE : apart_point_and_line(skolem_X3535, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 [18682] CLOSURE : apart_point_and_line(skolem_X3535, skolem_U3737)
% 191.49/52.72
% 191.49/52.72 [7628] CLOSURE : convergent_lines(skolem_V3838, skolem_V3838)
% 191.49/52.72
% 191.49/52.72 % SZS output end Proof for theBenchmark.p
% 191.49/52.72 [52.370541s][1][Res] 569701 goroutines created
% 191.49/52.72 ==== Result ====
% 191.49/52.72 [52.370581s][1][Res] VALID
% 191.49/52.72 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------