TSTP Solution File: GEO175+2 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO175+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 15:18:13 EDT 2022
% Result : Theorem 138.71s 41.83s
% Output : Proof 138.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO175+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.32 % Computer : n022.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Wed Aug 31 06:46:40 EDT 2022
% 0.13/0.32 % CPUTime :
% 0.13/0.33 [DMT] DMT loaded with preskolemization
% 0.13/0.33 [EQ] equality loaded.
% 0.13/0.33 [0.000048s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.33 Conjecture not found
% 0.13/0.33 Start search
% 0.13/0.34 nb_step : 1 - limit : 13
% 0.13/0.34 Launch Gotab with destructive = true
% 138.71/41.83 % SZS output start Proof for theBenchmark.p
% 138.71/41.83 [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)) & distinct_points(X35_35, intersection_point(U37_37, V38_38))) => (apart_point_and_line(X35_35, U37_37) | apart_point_and_line(X35_35, V38_38)))))
% 138.71/41.83 -> [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)) & distinct_points(X35_35, intersection_point(U37_37, V38_38))) => (apart_point_and_line(X35_35, U37_37) | apart_point_and_line(X35_35, V38_38))))
% 138.71/41.83
% 138.71/41.83 [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))))
% 138.71/41.83 -> [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)))
% 138.71/41.83
% 138.71/41.83 [2] DELTA_NOT_FORALL : ~! [X35_35, Y36_36, U37_37, V38_38] : ((((distinct_points(X35_35, Y36_36) & convergent_lines(U37_37, V38_38)) & distinct_points(X35_35, intersection_point(U37_37, V38_38))) => (apart_point_and_line(X35_35, U37_37) | apart_point_and_line(X35_35, V38_38))))
% 138.71/41.83 -> [3] ~(((distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)) & distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))) => (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)))
% 138.71/41.83
% 138.71/41.83 [3] ALPHA_NOT_IMPLY : ~(((distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)) & distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))) => (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)))
% 138.71/41.83 -> [4] ((distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)) & distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))), ~(apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 138.71/41.83
% 138.71/41.83 [4] ALPHA_AND : ((distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)) & distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)))
% 138.71/41.83 -> [5] (distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)), distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 138.71/41.83
% 138.71/41.83 [5] ALPHA_NOT_OR : ~(apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 138.71/41.83 -> [6] ~apart_point_and_line(skolem_X3535, skolem_U3737), ~apart_point_and_line(skolem_X3535, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [6] ALPHA_AND : (distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838))
% 138.71/41.83 -> [7] distinct_points(skolem_X3535, skolem_Y3636), convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [7] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 138.71/41.83 -> [8] ~distinct_points(skolem_Y3636, skolem_Y3636)
% 138.71/41.83
% 138.71/41.83 [8] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 138.71/41.83 -> [9] ~distinct_lines(skolem_V3838, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [9] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 138.71/41.83 -> [10] ~convergent_lines(skolem_V3838, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [10] 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))))
% 138.71/41.83 -> [11] (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636)))
% 138.71/41.83
% 138.71/41.83 [11] BETA_IMPLY : (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636)))
% 138.71/41.83 -> [12] ~distinct_points(skolem_X3535, skolem_Y3636)
% 138.71/41.83 -> [13] (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636))
% 138.71/41.83
% 138.71/41.83 [12] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 138.71/41.83
% 138.71/41.83 [13] BETA_OR : (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636))
% 138.71/41.83 -> [16] distinct_points(skolem_X3535, skolem_Y3636)
% 138.71/41.83 -> [17] distinct_points(skolem_Y3636, skolem_Y3636)
% 138.71/41.83
% 138.71/41.83 [17] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 138.71/41.83
% 138.71/41.83 [16] 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))))
% 138.71/41.83 -> [18] (distinct_lines(skolem_U3737, skolem_V3838) => (distinct_lines(skolem_U3737, skolem_V3838) | distinct_lines(skolem_V3838, skolem_V3838)))
% 138.71/41.83
% 138.71/41.83 [18] BETA_IMPLY : (distinct_lines(skolem_U3737, skolem_V3838) => (distinct_lines(skolem_U3737, skolem_V3838) | distinct_lines(skolem_V3838, skolem_V3838)))
% 138.71/41.83 -> [19] ~distinct_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83 -> [20] (distinct_lines(skolem_U3737, skolem_V3838) | distinct_lines(skolem_V3838, skolem_V3838))
% 138.71/41.83
% 138.71/41.83 [19] 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))))
% 138.71/41.83 -> [23] (convergent_lines(skolem_U3737, skolem_V3838) => (convergent_lines(skolem_U3737, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838)))
% 138.71/41.83
% 138.71/41.83 [23] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => (convergent_lines(skolem_U3737, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838)))
% 138.71/41.83 -> [24] ~convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83 -> [25] (convergent_lines(skolem_U3737, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838))
% 138.71/41.83
% 138.71/41.83 [24] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [25] BETA_OR : (convergent_lines(skolem_U3737, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838))
% 138.71/41.83 -> [28] convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83 -> [29] convergent_lines(skolem_V3838, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [29] CLOSURE : convergent_lines(skolem_V3838, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [28] 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)))))
% 138.71/41.83 -> [30] (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))))
% 138.71/41.83
% 138.71/41.83 [30] 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))))
% 138.71/41.83 -> [31] ~distinct_points(skolem_X3535, skolem_Y3636)
% 138.71/41.83 -> [32] (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636)))
% 138.71/41.83
% 138.71/41.83 [31] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 138.71/41.83
% 138.71/41.83 [32] 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)))
% 138.71/41.83 -> [1446] ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 138.71/41.83 -> [1447] (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636))
% 138.71/41.83
% 138.71/41.83 [1446] 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)))))
% 138.71/41.83 -> [1449] (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))))
% 138.71/41.83
% 138.71/41.83 [1449] 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))))
% 138.71/41.83 -> [1450] ~convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83 -> [1451] ((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)))
% 138.71/41.83
% 138.71/41.83 [1450] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [1451] 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)))
% 138.71/41.83 -> [1889] ~(apart_point_and_line(skolem_Y3636, skolem_U3737) | apart_point_and_line(skolem_Y3636, skolem_V3838))
% 138.71/41.83 -> [1890] distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))
% 138.71/41.83
% 138.71/41.83 [1890] 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))))
% 138.71/41.83 -> [1892] ((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)))
% 138.71/41.83
% 138.71/41.83 [1892] 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)))
% 138.71/41.83 -> [1894] ~(distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)) & distinct_lines(skolem_U3737, skolem_V3838))
% 138.71/41.83 -> [1895] (((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))
% 138.71/41.83
% 138.71/41.83 [1894] BETA_NOT_AND : ~(distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)) & distinct_lines(skolem_U3737, skolem_V3838))
% 138.71/41.83 -> [1898] ~distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 138.71/41.83 -> [1899] ~distinct_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [1898] CLOSURE : ~distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 138.71/41.83
% 138.71/41.83 [1912] 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))))
% 138.71/41.83 -> [1974] ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 138.71/41.83 -> [1975] (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 138.71/41.83
% 138.71/41.83 [1975] BETA_OR : (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 138.71/41.83 -> [1976] distinct_points(skolem_Y3636, skolem_Y3636)
% 138.71/41.83 -> [1977] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 138.71/41.83
% 138.71/41.83 [1977] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 138.71/41.83
% 138.71/41.83 [1976] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 138.71/41.83
% 138.71/41.83 [1981] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_V3838)))
% 138.71/41.83 -> [2002] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 138.71/41.83 -> [2003] (distinct_lines(skolem_U3737, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 138.71/41.83
% 138.71/41.83 [2002] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 138.71/41.83 -> [2006] (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 138.71/41.83
% 138.71/41.83 [2006] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 138.71/41.83 -> [2007] ~convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83 -> [2008] distinct_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2007] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2008] CLOSURE : distinct_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2003] BETA_OR : (distinct_lines(skolem_U3737, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 138.71/41.83 -> [2016] distinct_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83 -> [2017] apart_point_and_line(skolem_X3535, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2017] CLOSURE : apart_point_and_line(skolem_X3535, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2016] CLOSURE : distinct_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [1895] 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))
% 138.71/41.83 -> [2033] ((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))
% 138.71/41.83 -> [2034] apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2033] 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))
% 138.71/41.83 -> [2037] (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 138.71/41.83 -> [2038] apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737)
% 138.71/41.83
% 138.71/41.83 [2037] BETA_OR : (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 138.71/41.83 -> [2039] apart_point_and_line(skolem_X3535, skolem_U3737)
% 138.71/41.83 -> [2040] apart_point_and_line(skolem_X3535, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2039] CLOSURE : apart_point_and_line(skolem_X3535, skolem_U3737)
% 138.71/41.83
% 138.71/41.83 [2040] CLOSURE : apart_point_and_line(skolem_X3535, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2038] 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))))
% 138.71/41.83 -> [2044] (apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737) => (distinct_points(intersection_point(skolem_U3737, skolem_V3838), skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 138.71/41.83
% 138.71/41.83 [2044] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737) => (distinct_points(intersection_point(skolem_U3737, skolem_V3838), skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 138.71/41.83 -> [2045] ~apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737)
% 138.71/41.83 -> [2046] (distinct_points(intersection_point(skolem_U3737, skolem_V3838), skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 138.71/41.83
% 138.71/41.83 [2045] CLOSURE : ~apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737)
% 138.71/41.83
% 138.71/41.83 [2046] BETA_OR : (distinct_points(intersection_point(skolem_U3737, skolem_V3838), skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 138.71/41.83 -> [2064] distinct_points(intersection_point(skolem_U3737, skolem_V3838), skolem_X3535)
% 138.71/41.83 -> [2065] apart_point_and_line(skolem_X3535, skolem_U3737)
% 138.71/41.83
% 138.71/41.83 [2065] CLOSURE : apart_point_and_line(skolem_X3535, skolem_U3737)
% 138.71/41.83
% 138.71/41.83 [2066] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737) => (distinct_lines(skolem_U3737, skolem_V3838) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)))
% 138.71/41.83 -> [2100] ~apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737)
% 138.71/41.83 -> [2101] (distinct_lines(skolem_U3737, skolem_V3838) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838))
% 138.71/41.83
% 138.71/41.83 [2100] CLOSURE : ~apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737)
% 138.71/41.83
% 138.71/41.83 [2101] BETA_OR : (distinct_lines(skolem_U3737, skolem_V3838) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838))
% 138.71/41.83 -> [2109] distinct_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83 -> [2110] apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2110] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 138.71/41.83 -> [2111] (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 138.71/41.83
% 138.71/41.83 [2111] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 138.71/41.83 -> [2112] ~convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83 -> [2113] distinct_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2112] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2113] CLOSURE : distinct_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2109] CLOSURE : distinct_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2041] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838) => (distinct_points(intersection_point(skolem_U3737, skolem_V3838), skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_V3838)))
% 138.71/41.83 -> [2125] ~apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)
% 138.71/41.83 -> [2126] (distinct_points(intersection_point(skolem_U3737, skolem_V3838), skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 138.71/41.83
% 138.71/41.83 [2125] CLOSURE : ~apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2126] BETA_OR : (distinct_points(intersection_point(skolem_U3737, skolem_V3838), skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 138.71/41.83 -> [2139] distinct_points(intersection_point(skolem_U3737, skolem_V3838), skolem_X3535)
% 138.71/41.83 -> [2140] apart_point_and_line(skolem_X3535, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2139] 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))))
% 138.71/41.83 -> [2141] (apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838) => (distinct_lines(skolem_V3838, skolem_V3838) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)))
% 138.71/41.83
% 138.71/41.83 [2141] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838) => (distinct_lines(skolem_V3838, skolem_V3838) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)))
% 138.71/41.83 -> [2142] ~apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)
% 138.71/41.83 -> [2143] (distinct_lines(skolem_V3838, skolem_V3838) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838))
% 138.71/41.83
% 138.71/41.83 [2142] CLOSURE : ~apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2143] BETA_OR : (distinct_lines(skolem_V3838, skolem_V3838) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838))
% 138.71/41.83 -> [2146] distinct_lines(skolem_V3838, skolem_V3838)
% 138.71/41.83 -> [2147] apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2146] CLOSURE : distinct_lines(skolem_V3838, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2147] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 138.71/41.83 -> [2148] (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 138.71/41.83
% 138.71/41.83 [2148] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 138.71/41.83 -> [2149] ~convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83 -> [2150] distinct_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2149] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2150] CLOSURE : distinct_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2140] CLOSURE : apart_point_and_line(skolem_X3535, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [1893] BETA_IMPLY : ((distinct_points(skolem_X3535, skolem_Y3636) & 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_Y3636, skolem_U3737)) | apart_point_and_line(skolem_Y3636, skolem_V3838)))
% 138.71/41.83 -> [2151] ~(distinct_points(skolem_X3535, skolem_Y3636) & distinct_lines(skolem_U3737, skolem_V3838))
% 138.71/41.83 -> [2152] (((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_Y3636, skolem_U3737)) | apart_point_and_line(skolem_Y3636, skolem_V3838))
% 138.71/41.83
% 138.71/41.83 [2151] BETA_NOT_AND : ~(distinct_points(skolem_X3535, skolem_Y3636) & distinct_lines(skolem_U3737, skolem_V3838))
% 138.71/41.83 -> [2153] ~distinct_points(skolem_X3535, skolem_Y3636)
% 138.71/41.83 -> [2154] ~distinct_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2153] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 138.71/41.83
% 138.71/41.83 [2159] 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))))
% 138.71/41.83 -> [2185] ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 138.71/41.83 -> [2186] (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 138.71/41.83
% 138.71/41.83 [2186] BETA_OR : (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 138.71/41.83 -> [2189] distinct_points(skolem_Y3636, skolem_Y3636)
% 138.71/41.83 -> [2190] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 138.71/41.83
% 138.71/41.83 [2190] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 138.71/41.83
% 138.71/41.83 [2189] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 138.71/41.83
% 138.71/41.83 [2191] BETA_IMPLY : (apart_point_and_line(X30_118_10, Y31_118_10) => (distinct_lines(Y31_118_10, skolem_V3838) | apart_point_and_line(X30_118_10, skolem_V3838)))
% 138.71/41.83 -> [2199] ~apart_point_and_line(X30_118_10, Y31_118_10)
% 138.71/41.83 -> [2200] (distinct_lines(Y31_118_10, skolem_V3838) | apart_point_and_line(X30_118_10, skolem_V3838))
% 138.71/41.83
% 138.71/41.83 [2199] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 138.71/41.83 -> [2203] (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 138.71/41.83
% 138.71/41.83 [2203] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 138.71/41.83 -> [2204] ~convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83 -> [2205] distinct_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2204] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2205] CLOSURE : distinct_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2200] BETA_OR : (distinct_lines(Y31_118_10, skolem_V3838) | apart_point_and_line(X30_118_10, skolem_V3838))
% 138.71/41.83 -> [2201] distinct_lines(Y31_118_10, skolem_V3838)
% 138.71/41.83 -> [2202] apart_point_and_line(X30_118_10, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2202] CLOSURE : apart_point_and_line(X30_118_10, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2201] CLOSURE : distinct_lines(Y31_118_10, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2152] BETA_OR : (((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_Y3636, skolem_U3737)) | apart_point_and_line(skolem_Y3636, skolem_V3838))
% 138.71/41.83 -> [2206] ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_Y3636, skolem_U3737))
% 138.71/41.83 -> [2207] apart_point_and_line(skolem_Y3636, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2206] BETA_OR : ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_Y3636, skolem_U3737))
% 138.71/41.83 -> [2208] (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 138.71/41.83 -> [2209] apart_point_and_line(skolem_Y3636, skolem_U3737)
% 138.71/41.83
% 138.71/41.83 [2208] BETA_OR : (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 138.71/41.83 -> [2210] apart_point_and_line(skolem_X3535, skolem_U3737)
% 138.71/41.83 -> [2211] apart_point_and_line(skolem_X3535, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2211] CLOSURE : apart_point_and_line(skolem_X3535, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [2210] CLOSURE : apart_point_and_line(skolem_X3535, skolem_U3737)
% 138.71/41.83
% 138.71/41.83 [2209] CLOSURE : apart_point_and_line(skolem_Y3636, skolem_U3737)
% 138.71/41.83
% 138.71/41.83 [2207] CLOSURE : apart_point_and_line(skolem_Y3636, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [1448] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 138.71/41.83
% 138.71/41.83 [20] BETA_OR : (distinct_lines(skolem_U3737, skolem_V3838) | distinct_lines(skolem_V3838, skolem_V3838))
% 138.71/41.83 -> [7188] distinct_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83 -> [7189] distinct_lines(skolem_V3838, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [7189] CLOSURE : distinct_lines(skolem_V3838, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [7188] 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))))
% 138.71/41.83 -> [7190] (convergent_lines(skolem_U3737, skolem_V3838) => (convergent_lines(skolem_U3737, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838)))
% 138.71/41.83
% 138.71/41.83 [7190] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => (convergent_lines(skolem_U3737, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838)))
% 138.71/41.83 -> [7191] ~convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83 -> [7192] (convergent_lines(skolem_U3737, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838))
% 138.71/41.83
% 138.71/41.83 [7191] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [7192] BETA_OR : (convergent_lines(skolem_U3737, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838))
% 138.71/41.83 -> [7195] convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83 -> [7196] convergent_lines(skolem_V3838, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [7195] 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)))))
% 138.71/41.83 -> [7197] (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))))
% 138.71/41.83
% 138.71/41.83 [7197] 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))))
% 138.71/41.83 -> [7198] ~distinct_points(skolem_X3535, skolem_Y3636)
% 138.71/41.83 -> [7199] (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636)))
% 138.71/41.83
% 138.71/41.83 [7199] 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)))
% 138.71/41.83 -> [7200] ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 138.71/41.83 -> [7201] (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636))
% 138.71/41.83
% 138.71/41.83 [7201] ALPHA_AND : (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636))
% 138.71/41.83 -> [7202] distinct_points(skolem_Y3636, skolem_X3535), distinct_points(skolem_Y3636, skolem_Y3636)
% 138.71/41.83
% 138.71/41.83 [7202] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 138.71/41.83
% 138.71/41.83 [7203] 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))))
% 138.71/41.83 -> [9784] ~convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83 -> [9785] ((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)))
% 138.71/41.83
% 138.71/41.83 [9785] 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)))
% 138.71/41.83 -> [9786] ~(apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838))
% 138.71/41.83 -> [9787] distinct_points(intersection_point(skolem_U3737, skolem_V3838), intersection_point(skolem_U3737, skolem_V3838))
% 138.71/41.83
% 138.71/41.83 [9787] 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))))
% 138.71/41.83 -> [9789] ((distinct_points(skolem_X3535, skolem_Y3636) & 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_Y3636, skolem_U3737)) | apart_point_and_line(skolem_Y3636, skolem_V3838)))
% 138.71/41.83
% 138.71/41.83 [9789] BETA_IMPLY : ((distinct_points(skolem_X3535, skolem_Y3636) & 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_Y3636, skolem_U3737)) | apart_point_and_line(skolem_Y3636, skolem_V3838)))
% 138.71/41.83 -> [9791] ~(distinct_points(skolem_X3535, skolem_Y3636) & distinct_lines(skolem_U3737, skolem_V3838))
% 138.71/41.83 -> [9792] (((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_Y3636, skolem_U3737)) | apart_point_and_line(skolem_Y3636, skolem_V3838))
% 138.71/41.83
% 138.71/41.83 [9791] BETA_NOT_AND : ~(distinct_points(skolem_X3535, skolem_Y3636) & distinct_lines(skolem_U3737, skolem_V3838))
% 138.71/41.83 -> [9795] ~distinct_points(skolem_X3535, skolem_Y3636)
% 138.71/41.83 -> [9796] ~distinct_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [9795] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 138.71/41.83
% 138.71/41.83 [9796] CLOSURE : ~distinct_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [9792] BETA_OR : (((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_Y3636, skolem_U3737)) | apart_point_and_line(skolem_Y3636, skolem_V3838))
% 138.71/41.83 -> [9969] ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_Y3636, skolem_U3737))
% 138.71/41.83 -> [9970] apart_point_and_line(skolem_Y3636, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [9969] BETA_OR : ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_Y3636, skolem_U3737))
% 138.71/41.83 -> [9972] (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 138.71/41.83 -> [9973] apart_point_and_line(skolem_Y3636, skolem_U3737)
% 138.71/41.83
% 138.71/41.83 [9972] BETA_OR : (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 138.71/41.83 -> [9976] apart_point_and_line(skolem_X3535, skolem_U3737)
% 138.71/41.83 -> [9977] apart_point_and_line(skolem_X3535, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [9976] CLOSURE : apart_point_and_line(skolem_X3535, skolem_U3737)
% 138.71/41.83
% 138.71/41.83 [9977] CLOSURE : apart_point_and_line(skolem_X3535, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [9978] 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))))
% 138.71/41.83 -> [10065] ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 138.71/41.83 -> [10066] (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 138.71/41.83
% 138.71/41.83 [10066] BETA_OR : (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 138.71/41.83 -> [10067] distinct_points(skolem_Y3636, skolem_Y3636)
% 138.71/41.83 -> [10068] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 138.71/41.83
% 138.71/41.83 [10067] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 138.71/41.83
% 138.71/41.83 [10068] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 138.71/41.83
% 138.71/41.83 [10065] 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))))
% 138.71/41.83 -> [10072] (apart_point_and_line(skolem_Y3636, skolem_U3737) => (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))))
% 138.71/41.83
% 138.71/41.83 [10072] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, skolem_U3737) => (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))))
% 138.71/41.83 -> [10075] ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 138.71/41.83 -> [10076] (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 138.71/41.83
% 138.71/41.83 [10075] CLOSURE : ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 138.71/41.83
% 138.71/41.83 [10076] BETA_OR : (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 138.71/41.83 -> [10081] distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 138.71/41.83 -> [10082] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 138.71/41.83
% 138.71/41.83 [10082] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 138.71/41.83
% 138.71/41.83 [10083] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 138.71/41.83 -> [10092] ~convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83 -> [10093] distinct_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [10092] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [10093] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 138.71/41.83 -> [10094] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 138.71/41.83
% 138.71/41.83 [10094] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 138.71/41.83 -> [10096] ~distinct_points(X5_1380_0, X5_1380_0)
% 138.71/41.83
% 138.71/41.83 [10096] CLOSURE : ~distinct_points(X5_1380_0, X5_1380_0)
% 138.71/41.83
% 138.71/41.83 [9970] 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))))
% 138.71/41.83 -> [10101] (apart_point_and_line(skolem_Y3636, skolem_V3838) => (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, skolem_V3838)))
% 138.71/41.83
% 138.71/41.83 [10101] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, skolem_V3838) => (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, skolem_V3838)))
% 138.71/41.83 -> [10102] ~apart_point_and_line(skolem_Y3636, skolem_V3838)
% 138.71/41.83 -> [10103] (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, skolem_V3838))
% 138.71/41.83
% 138.71/41.83 [10102] CLOSURE : ~apart_point_and_line(skolem_Y3636, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [10103] BETA_OR : (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, skolem_V3838))
% 138.71/41.83 -> [10110] distinct_points(skolem_Y3636, skolem_Y3636)
% 138.71/41.83 -> [10111] apart_point_and_line(skolem_Y3636, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [10110] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 138.71/41.83
% 138.71/41.83 [10111] 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))))
% 138.71/41.83 -> [10112] (apart_point_and_line(skolem_Y3636, skolem_V3838) => (distinct_lines(skolem_V3838, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))))
% 138.71/41.83
% 138.71/41.83 [10112] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, skolem_V3838) => (distinct_lines(skolem_V3838, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))))
% 138.71/41.83 -> [10113] ~apart_point_and_line(skolem_Y3636, skolem_V3838)
% 138.71/41.83 -> [10114] (distinct_lines(skolem_V3838, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 138.71/41.83
% 138.71/41.83 [10113] CLOSURE : ~apart_point_and_line(skolem_Y3636, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [10114] BETA_OR : (distinct_lines(skolem_V3838, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 138.71/41.83 -> [10122] distinct_lines(skolem_V3838, line_connecting(skolem_X3535, skolem_Y3636))
% 138.71/41.83 -> [10123] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 138.71/41.83
% 138.71/41.83 [10123] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 138.71/41.83
% 138.71/41.83 [10122] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 138.71/41.83 -> [10126] (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 138.71/41.83
% 138.71/41.83 [10126] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 138.71/41.83 -> [10127] ~convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83 -> [10128] distinct_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [10127] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [10128] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 138.71/41.83 -> [10131] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 138.71/41.83
% 138.71/41.83 [10131] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 138.71/41.83 -> [10132] ~distinct_points(X5_1387_0, X5_1387_0)
% 138.71/41.83
% 138.71/41.83 [10132] CLOSURE : ~distinct_points(X5_1387_0, X5_1387_0)
% 138.71/41.83
% 138.71/41.83 [9790] 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)))
% 138.71/41.83 -> [12027] ~(distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)) & distinct_lines(skolem_U3737, skolem_V3838))
% 138.71/41.83 -> [12028] (((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))
% 138.71/41.83
% 138.71/41.83 [12027] BETA_NOT_AND : ~(distinct_points(skolem_X3535, skolem_Y3636) & distinct_lines(skolem_U3737, skolem_V3838))
% 138.71/41.83 -> [12029] ~distinct_points(skolem_X3535, skolem_Y3636)
% 138.71/41.83 -> [12030] ~distinct_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [12030] CLOSURE : ~distinct_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [12029] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 138.71/41.83
% 138.71/41.83 [12028] 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))
% 138.71/41.83 -> [12045] ((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))
% 138.71/41.83 -> [12046] apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [12046] CLOSURE : apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [12045] 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))
% 138.71/41.83 -> [12047] (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 138.71/41.83 -> [12048] apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737)
% 138.71/41.83
% 138.71/41.83 [12048] CLOSURE : apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737)
% 138.71/41.83
% 138.71/41.83 [12047] BETA_OR : (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 138.71/41.83 -> [12049] apart_point_and_line(skolem_X3535, skolem_U3737)
% 138.71/41.83 -> [12050] apart_point_and_line(skolem_X3535, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [12049] CLOSURE : apart_point_and_line(skolem_X3535, skolem_U3737)
% 138.71/41.83
% 138.71/41.83 [12050] CLOSURE : apart_point_and_line(skolem_X3535, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [9784] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 [7198] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 138.71/41.83
% 138.71/41.83 [7196] CLOSURE : convergent_lines(skolem_V3838, skolem_V3838)
% 138.71/41.83
% 138.71/41.83 % SZS output end Proof for theBenchmark.p
% 138.71/41.83 [41.500287s][1][Res] 436512 goroutines created
% 138.71/41.83 ==== Result ====
% 138.71/41.83 [41.500321s][1][Res] VALID
% 138.71/41.83 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------