TSTP Solution File: GEO185+2 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO185+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n002.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 65.79s 16.69s
% Output : Proof 65.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO185+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n002.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 07:00:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 [DMT] DMT loaded with preskolemization
% 0.13/0.34 [EQ] equality loaded.
% 0.13/0.34 [0.000030s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.34 Conjecture not found
% 0.13/0.34 Start search
% 0.13/0.35 nb_step : 1 - limit : 13
% 0.13/0.35 Launch Gotab with destructive = true
% 65.79/16.68 % SZS output start Proof for theBenchmark.p
% 65.79/16.69 [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)))))
% 65.79/16.69 -> [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))))
% 65.79/16.69
% 65.79/16.69 [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))))
% 65.79/16.69 -> [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)))
% 65.79/16.69
% 65.79/16.69 [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))))
% 65.79/16.69 -> [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)))
% 65.79/16.69
% 65.79/16.69 [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)))
% 65.79/16.69 -> [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))
% 65.79/16.69
% 65.79/16.69 [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)))
% 65.79/16.69 -> [5] (distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)), ~distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 65.79/16.69
% 65.79/16.69 [5] ALPHA_AND : (distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838))
% 65.79/16.69 -> [6] distinct_points(skolem_X3535, skolem_Y3636), convergent_lines(skolem_U3737, skolem_V3838)
% 65.79/16.69
% 65.79/16.69 [6] BETA_NOT_AND : ~(~apart_point_and_line(skolem_X3535, skolem_U3737) & ~apart_point_and_line(skolem_X3535, skolem_V3838))
% 65.79/16.69 -> [7] ~~apart_point_and_line(skolem_X3535, skolem_U3737)
% 65.79/16.69 -> [8] ~~apart_point_and_line(skolem_X3535, skolem_V3838)
% 65.79/16.69
% 65.79/16.69 [7] ALPHA_NOT_NOT : ~~apart_point_and_line(skolem_X3535, skolem_U3737)
% 65.79/16.69 -> [9] apart_point_and_line(skolem_X3535, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [9] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 65.79/16.69 -> [11] ~distinct_points(skolem_X3535, skolem_X3535)
% 65.79/16.69
% 65.79/16.69 [11] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 65.79/16.69 -> [14] ~distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69
% 65.79/16.69 [14] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 65.79/16.69 -> [16] ~convergent_lines(skolem_U3737, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [16] 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))))
% 65.79/16.69 -> [18] (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_X3535) | distinct_points(skolem_Y3636, skolem_X3535)))
% 65.79/16.69
% 65.79/16.69 [18] BETA_IMPLY : (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_X3535) | distinct_points(skolem_Y3636, skolem_X3535)))
% 65.79/16.69 -> [21] ~distinct_points(skolem_X3535, skolem_Y3636)
% 65.79/16.69 -> [22] (distinct_points(skolem_X3535, skolem_X3535) | distinct_points(skolem_Y3636, skolem_X3535))
% 65.79/16.69
% 65.79/16.69 [21] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 65.79/16.69
% 65.79/16.69 [22] BETA_OR : (distinct_points(skolem_X3535, skolem_X3535) | distinct_points(skolem_Y3636, skolem_X3535))
% 65.79/16.69 -> [29] distinct_points(skolem_X3535, skolem_X3535)
% 65.79/16.69 -> [30] distinct_points(skolem_Y3636, skolem_X3535)
% 65.79/16.69
% 65.79/16.69 [29] CLOSURE : distinct_points(skolem_X3535, skolem_X3535)
% 65.79/16.69
% 65.79/16.69 [30] 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))))
% 65.79/16.69 -> [32] (distinct_lines(skolem_V3838, skolem_U3737) => (distinct_lines(skolem_V3838, Z13_1_4) | distinct_lines(skolem_U3737, Z13_1_4)))
% 65.79/16.69
% 65.79/16.69 [32] BETA_IMPLY : (distinct_lines(skolem_V3838, skolem_U3737) => (distinct_lines(skolem_V3838, Z13_1_4) | distinct_lines(skolem_U3737, Z13_1_4)))
% 65.79/16.69 -> [35] ~distinct_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69 -> [36] (distinct_lines(skolem_V3838, Z13_1_4) | distinct_lines(skolem_U3737, Z13_1_4))
% 65.79/16.69
% 65.79/16.69 [35] 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))))
% 65.79/16.69 -> [42] (convergent_lines(skolem_U3737, skolem_V3838) => (convergent_lines(skolem_U3737, skolem_U3737) | convergent_lines(skolem_V3838, skolem_U3737)))
% 65.79/16.69
% 65.79/16.69 [42] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => (convergent_lines(skolem_U3737, skolem_U3737) | convergent_lines(skolem_V3838, skolem_U3737)))
% 65.79/16.69 -> [45] ~convergent_lines(skolem_U3737, skolem_V3838)
% 65.79/16.69 -> [46] (convergent_lines(skolem_U3737, skolem_U3737) | convergent_lines(skolem_V3838, skolem_U3737))
% 65.79/16.69
% 65.79/16.69 [45] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 65.79/16.69
% 65.79/16.69 [46] BETA_OR : (convergent_lines(skolem_U3737, skolem_U3737) | convergent_lines(skolem_V3838, skolem_U3737))
% 65.79/16.69 -> [53] convergent_lines(skolem_U3737, skolem_U3737)
% 65.79/16.69 -> [54] convergent_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [53] CLOSURE : convergent_lines(skolem_U3737, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [54] 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)))))
% 65.79/16.69 -> [58] (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))))
% 65.79/16.69
% 65.79/16.69 [58] 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))))
% 65.79/16.69 -> [61] ~distinct_points(skolem_X3535, skolem_Y3636)
% 65.79/16.69 -> [62] (apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_X3535, skolem_X3535) & distinct_points(skolem_X3535, skolem_Y3636)))
% 65.79/16.69
% 65.79/16.69 [61] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 65.79/16.69
% 65.79/16.69 [62] 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)))
% 65.79/16.69 -> [1265] ~apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69 -> [1266] (distinct_points(skolem_X3535, skolem_X3535) & distinct_points(skolem_X3535, skolem_Y3636))
% 65.79/16.69
% 65.79/16.69 [1266] ALPHA_AND : (distinct_points(skolem_X3535, skolem_X3535) & distinct_points(skolem_X3535, skolem_Y3636))
% 65.79/16.69 -> [1267] distinct_points(skolem_X3535, skolem_X3535), distinct_points(skolem_X3535, skolem_Y3636)
% 65.79/16.69
% 65.79/16.69 [1267] CLOSURE : distinct_points(skolem_X3535, skolem_X3535)
% 65.79/16.69
% 65.79/16.69 [1268] BETA_IMPLY : (convergent_lines(skolem_V3838, skolem_U3737) => ((apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737)) => distinct_points(skolem_X3535, intersection_point(skolem_V3838, skolem_U3737))))
% 65.79/16.69 -> [1874] ~convergent_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69 -> [1875] ((apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737)) => distinct_points(skolem_X3535, intersection_point(skolem_V3838, skolem_U3737)))
% 65.79/16.69
% 65.79/16.69 [1874] CLOSURE : ~convergent_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [1875] BETA_IMPLY : ((apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737)) => distinct_points(skolem_X3535, intersection_point(skolem_V3838, skolem_U3737)))
% 65.79/16.69 -> [1884] ~(apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 65.79/16.69 -> [1885] distinct_points(skolem_X3535, intersection_point(skolem_V3838, skolem_U3737))
% 65.79/16.69
% 65.79/16.69 [1884] ALPHA_NOT_OR : ~(apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 65.79/16.69 -> [1886] ~apart_point_and_line(skolem_X3535, skolem_V3838), ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [1886] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [1887] BETA_IMPLY : ((distinct_points(skolem_X3535, skolem_Y3636) & distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))) => (((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_Y3636, skolem_U3737)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))))
% 65.79/16.69 -> [2041] ~(distinct_points(skolem_X3535, skolem_Y3636) & distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)))
% 65.79/16.69 -> [2042] (((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_Y3636, skolem_U3737)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 65.79/16.69
% 65.79/16.69 [2041] BETA_NOT_AND : ~(distinct_points(skolem_Y3636, skolem_X3535) & distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)))
% 65.79/16.69 -> [2043] ~distinct_points(skolem_Y3636, skolem_X3535)
% 65.79/16.69 -> [2044] ~distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69
% 65.79/16.69 [2044] 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))))
% 65.79/16.69 -> [2051] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 65.79/16.69
% 65.79/16.69 [2051] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 65.79/16.69 -> [2052] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 65.79/16.69 -> [2053] (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 65.79/16.69
% 65.79/16.69 [2052] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2053] BETA_OR : (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 65.79/16.69 -> [2107] distinct_points(skolem_X3535, skolem_X3535)
% 65.79/16.69 -> [2108] apart_point_and_line(skolem_X3535, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2108] 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))))
% 65.79/16.69 -> [2109] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))))
% 65.79/16.69
% 65.79/16.69 [2109] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))))
% 65.79/16.69 -> [2110] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 65.79/16.69 -> [2111] (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 65.79/16.69
% 65.79/16.69 [2110] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2111] BETA_OR : (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 65.79/16.69 -> [2116] distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69 -> [2117] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69
% 65.79/16.69 [2116] CLOSURE : distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69
% 65.79/16.69 [2117] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69
% 65.79/16.69 [2107] CLOSURE : distinct_points(skolem_X3535, skolem_X3535)
% 65.79/16.69
% 65.79/16.69 [2043] CLOSURE : ~distinct_points(skolem_Y3636, skolem_X3535)
% 65.79/16.69
% 65.79/16.69 [2042] BETA_OR : (((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_Y3636, skolem_U3737)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 65.79/16.69 -> [2124] ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_Y3636, skolem_U3737))
% 65.79/16.69 -> [2125] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69
% 65.79/16.69 [2125] 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))))
% 65.79/16.69 -> [2130] (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_X3535) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))))
% 65.79/16.69
% 65.79/16.69 [2130] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_X3535) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))))
% 65.79/16.69 -> [2131] ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69 -> [2132] (distinct_points(skolem_Y3636, skolem_X3535) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 65.79/16.69
% 65.79/16.69 [2131] CLOSURE : ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69
% 65.79/16.69 [2132] BETA_OR : (distinct_points(skolem_Y3636, skolem_X3535) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 65.79/16.69 -> [2154] distinct_points(skolem_Y3636, skolem_X3535)
% 65.79/16.69 -> [2155] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69
% 65.79/16.69 [2155] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69
% 65.79/16.69 [2162] 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))))
% 65.79/16.69 -> [2202] ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69 -> [2203] (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)))
% 65.79/16.69
% 65.79/16.69 [2202] CLOSURE : ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69
% 65.79/16.69 [2203] 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)))
% 65.79/16.69 -> [2213] distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69 -> [2214] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69
% 65.79/16.69 [2213] CLOSURE : distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69
% 65.79/16.69 [2221] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 65.79/16.69 -> [2271] ~convergent_lines(skolem_U3737, skolem_V3838)
% 65.79/16.69 -> [2272] distinct_lines(skolem_U3737, skolem_V3838)
% 65.79/16.69
% 65.79/16.69 [2272] CLOSURE : distinct_lines(skolem_U3737, skolem_V3838)
% 65.79/16.69
% 65.79/16.69 [2271] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 65.79/16.69
% 65.79/16.69 [2124] BETA_OR : ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_Y3636, skolem_U3737))
% 65.79/16.69 -> [2126] (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 65.79/16.69 -> [2127] apart_point_and_line(skolem_Y3636, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2126] BETA_OR : (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 65.79/16.69 -> [2128] apart_point_and_line(skolem_X3535, skolem_U3737)
% 65.79/16.69 -> [2129] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69
% 65.79/16.69 [2129] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69
% 65.79/16.69 [2128] 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))))
% 65.79/16.69 -> [2138] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737)))
% 65.79/16.69
% 65.79/16.69 [2138] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737)))
% 65.79/16.69 -> [2139] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 65.79/16.69 -> [2140] (distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737))
% 65.79/16.69
% 65.79/16.69 [2139] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2140] BETA_OR : (distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)) | apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737))
% 65.79/16.69 -> [2152] distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 65.79/16.69 -> [2153] apart_point_and_line(intersection_point(skolem_U3737, skolem_V3838), skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2152] CLOSURE : distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 65.79/16.69
% 65.79/16.69 [2161] BETA_IMPLY : (apart_point_and_line(skolem_X3535, 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_X3535, line_connecting(skolem_X3535, skolem_Y3636))))
% 65.79/16.69 -> [2198] ~apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69 -> [2199] (distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 65.79/16.69
% 65.79/16.69 [2199] BETA_OR : (distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 65.79/16.69 -> [2200] distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69 -> [2201] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69
% 65.79/16.69 [2200] CLOSURE : distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69
% 65.79/16.69 [2201] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69
% 65.79/16.69 [2198] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 65.79/16.69 -> [2216] (convergent_lines(skolem_V3838, skolem_U3737) => distinct_lines(skolem_V3838, skolem_U3737))
% 65.79/16.69
% 65.79/16.69 [2216] BETA_IMPLY : (convergent_lines(skolem_V3838, skolem_U3737) => distinct_lines(skolem_V3838, skolem_U3737))
% 65.79/16.69 -> [2222] ~convergent_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69 -> [2223] distinct_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2222] CLOSURE : ~convergent_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2223] CLOSURE : distinct_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2133] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, skolem_U3737) => (distinct_points(skolem_Y3636, Z29_47_9) | apart_point_and_line(Z29_47_9, skolem_U3737)))
% 65.79/16.69 -> [2252] ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 65.79/16.69 -> [2253] (distinct_points(skolem_Y3636, Z29_47_9) | apart_point_and_line(Z29_47_9, skolem_U3737))
% 65.79/16.69
% 65.79/16.69 [2252] CLOSURE : ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2253] BETA_OR : (distinct_points(skolem_Y3636, Z29_47_9) | apart_point_and_line(Z29_47_9, skolem_U3737))
% 65.79/16.69 -> [2263] distinct_points(skolem_Y3636, Z29_47_9)
% 65.79/16.69 -> [2264] apart_point_and_line(Z29_47_9, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2263] 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))))
% 65.79/16.69 -> [2265] (apart_point_and_line(skolem_Y3636, skolem_U3737) => (distinct_lines(skolem_U3737, Z32_97_10) | apart_point_and_line(skolem_Y3636, Z32_97_10)))
% 65.79/16.69
% 65.79/16.69 [2265] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, skolem_U3737) => (distinct_lines(skolem_U3737, Z32_97_10) | apart_point_and_line(skolem_Y3636, Z32_97_10)))
% 65.79/16.69 -> [2267] ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 65.79/16.69 -> [2268] (distinct_lines(skolem_U3737, Z32_97_10) | apart_point_and_line(skolem_Y3636, Z32_97_10))
% 65.79/16.69
% 65.79/16.69 [2267] CLOSURE : ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2268] BETA_OR : (distinct_lines(skolem_U3737, Z32_97_10) | apart_point_and_line(skolem_Y3636, Z32_97_10))
% 65.79/16.69 -> [2286] distinct_lines(skolem_U3737, Z32_97_10)
% 65.79/16.69 -> [2287] apart_point_and_line(skolem_Y3636, Z32_97_10)
% 65.79/16.69
% 65.79/16.69 [2287] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 65.79/16.69 -> [2291] (convergent_lines(skolem_V3838, skolem_U3737) => distinct_lines(skolem_V3838, skolem_U3737))
% 65.79/16.69
% 65.79/16.69 [2291] BETA_IMPLY : (convergent_lines(skolem_V3838, skolem_U3737) => distinct_lines(skolem_V3838, skolem_U3737))
% 65.79/16.69 -> [2293] ~convergent_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69 -> [2294] distinct_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2293] CLOSURE : ~convergent_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2294] CLOSURE : distinct_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2286] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 65.79/16.69 -> [2295] (convergent_lines(skolem_V3838, skolem_U3737) => distinct_lines(skolem_V3838, skolem_U3737))
% 65.79/16.69
% 65.79/16.69 [2295] BETA_IMPLY : (convergent_lines(skolem_V3838, skolem_U3737) => distinct_lines(skolem_V3838, skolem_U3737))
% 65.79/16.69 -> [2296] ~convergent_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69 -> [2297] distinct_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2296] CLOSURE : ~convergent_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2297] CLOSURE : distinct_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2264] 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))))
% 65.79/16.69 -> [2266] (apart_point_and_line(skolem_Y3636, skolem_U3737) => (distinct_lines(skolem_U3737, Z32_98_10) | apart_point_and_line(skolem_Y3636, Z32_98_10)))
% 65.79/16.69
% 65.79/16.69 [2266] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, skolem_U3737) => (distinct_lines(skolem_U3737, Z32_98_10) | apart_point_and_line(skolem_Y3636, Z32_98_10)))
% 65.79/16.69 -> [2269] ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 65.79/16.69 -> [2270] (distinct_lines(skolem_U3737, Z32_98_10) | apart_point_and_line(skolem_Y3636, Z32_98_10))
% 65.79/16.69
% 65.79/16.69 [2269] CLOSURE : ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2270] BETA_OR : (distinct_lines(skolem_U3737, Z32_98_10) | apart_point_and_line(skolem_Y3636, Z32_98_10))
% 65.79/16.69 -> [2284] distinct_lines(skolem_U3737, Z32_98_10)
% 65.79/16.69 -> [2285] apart_point_and_line(skolem_Y3636, Z32_98_10)
% 65.79/16.69
% 65.79/16.69 [2284] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 65.79/16.69 -> [2288] (convergent_lines(skolem_V3838, skolem_U3737) => distinct_lines(skolem_V3838, skolem_U3737))
% 65.79/16.69
% 65.79/16.69 [2288] BETA_IMPLY : (convergent_lines(skolem_V3838, skolem_U3737) => distinct_lines(skolem_V3838, skolem_U3737))
% 65.79/16.69 -> [2289] ~convergent_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69 -> [2290] distinct_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2289] CLOSURE : ~convergent_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2290] CLOSURE : distinct_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2285] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 65.79/16.69 -> [2292] (convergent_lines(skolem_V3838, skolem_U3737) => distinct_lines(skolem_V3838, skolem_U3737))
% 65.79/16.69
% 65.79/16.69 [2292] BETA_IMPLY : (convergent_lines(skolem_V3838, skolem_U3737) => distinct_lines(skolem_V3838, skolem_U3737))
% 65.79/16.69 -> [2298] ~convergent_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69 -> [2299] distinct_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2299] CLOSURE : distinct_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2298] CLOSURE : ~convergent_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [36] BETA_OR : (distinct_lines(skolem_V3838, Z13_1_4) | distinct_lines(skolem_U3737, Z13_1_4))
% 65.79/16.69 -> [2342] distinct_lines(skolem_V3838, Z13_1_4)
% 65.79/16.69 -> [2343] distinct_lines(skolem_U3737, Z13_1_4)
% 65.79/16.69
% 65.79/16.69 [2343] 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))))
% 65.79/16.69 -> [2349] (convergent_lines(skolem_U3737, skolem_V3838) => (convergent_lines(skolem_U3737, skolem_U3737) | convergent_lines(skolem_V3838, skolem_U3737)))
% 65.79/16.69
% 65.79/16.69 [2349] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => (convergent_lines(skolem_U3737, skolem_U3737) | convergent_lines(skolem_V3838, skolem_U3737)))
% 65.79/16.69 -> [2352] ~convergent_lines(skolem_U3737, skolem_V3838)
% 65.79/16.69 -> [2353] (convergent_lines(skolem_U3737, skolem_U3737) | convergent_lines(skolem_V3838, skolem_U3737))
% 65.79/16.69
% 65.79/16.69 [2352] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 65.79/16.69
% 65.79/16.69 [2353] BETA_OR : (convergent_lines(skolem_U3737, skolem_U3737) | convergent_lines(skolem_V3838, skolem_U3737))
% 65.79/16.69 -> [2362] convergent_lines(skolem_U3737, skolem_U3737)
% 65.79/16.69 -> [2363] convergent_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2362] CLOSURE : convergent_lines(skolem_U3737, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2363] 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)))))
% 65.79/16.69 -> [2364] (distinct_points(skolem_Y3636, skolem_X3535) => (apart_point_and_line(skolem_X3535, line_connecting(skolem_Y3636, skolem_X3535)) => (distinct_points(skolem_X3535, skolem_Y3636) & distinct_points(skolem_X3535, skolem_X3535))))
% 65.79/16.69
% 65.79/16.69 [2364] BETA_IMPLY : (distinct_points(skolem_Y3636, skolem_X3535) => (apart_point_and_line(skolem_X3535, line_connecting(skolem_Y3636, skolem_X3535)) => (distinct_points(skolem_X3535, skolem_Y3636) & distinct_points(skolem_X3535, skolem_X3535))))
% 65.79/16.69 -> [2366] ~distinct_points(skolem_Y3636, skolem_X3535)
% 65.79/16.69 -> [2367] (apart_point_and_line(skolem_X3535, line_connecting(skolem_Y3636, skolem_X3535)) => (distinct_points(skolem_X3535, skolem_Y3636) & distinct_points(skolem_X3535, skolem_X3535)))
% 65.79/16.69
% 65.79/16.69 [2366] CLOSURE : ~distinct_points(skolem_Y3636, skolem_X3535)
% 65.79/16.69
% 65.79/16.69 [2367] BETA_IMPLY : (apart_point_and_line(skolem_X3535, line_connecting(skolem_Y3636, skolem_X3535)) => (distinct_points(skolem_X3535, skolem_Y3636) & distinct_points(skolem_X3535, skolem_X3535)))
% 65.79/16.69 -> [2400] ~apart_point_and_line(skolem_X3535, line_connecting(skolem_Y3636, skolem_X3535))
% 65.79/16.69 -> [2401] (distinct_points(skolem_X3535, skolem_Y3636) & distinct_points(skolem_X3535, skolem_X3535))
% 65.79/16.69
% 65.79/16.69 [2401] ALPHA_AND : (distinct_points(skolem_X3535, skolem_Y3636) & distinct_points(skolem_X3535, skolem_X3535))
% 65.79/16.69 -> [2405] distinct_points(skolem_X3535, skolem_Y3636), distinct_points(skolem_X3535, skolem_X3535)
% 65.79/16.69
% 65.79/16.69 [2405] CLOSURE : distinct_points(skolem_X3535, skolem_X3535)
% 65.79/16.69
% 65.79/16.69 [2400] 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)))))
% 65.79/16.69 -> [2409] (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))))
% 65.79/16.69
% 65.79/16.69 [2409] 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))))
% 65.79/16.69 -> [2410] ~convergent_lines(skolem_U3737, skolem_V3838)
% 65.79/16.69 -> [2411] ((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)))
% 65.79/16.69
% 65.79/16.69 [2410] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 65.79/16.69
% 65.79/16.69 [2411] 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)))
% 65.79/16.69 -> [2425] ~(apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 65.79/16.69 -> [2426] distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 65.79/16.69
% 65.79/16.69 [2426] CLOSURE : distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 65.79/16.69
% 65.79/16.69 [2425] ALPHA_NOT_OR : ~(apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 65.79/16.69 -> [2430] ~apart_point_and_line(skolem_X3535, skolem_U3737), ~apart_point_and_line(skolem_X3535, skolem_V3838)
% 65.79/16.69
% 65.79/16.69 [2430] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2342] 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))))
% 65.79/16.69 -> [2348] (convergent_lines(skolem_U3737, skolem_V3838) => (convergent_lines(skolem_U3737, skolem_U3737) | convergent_lines(skolem_V3838, skolem_U3737)))
% 65.79/16.69
% 65.79/16.69 [2348] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => (convergent_lines(skolem_U3737, skolem_U3737) | convergent_lines(skolem_V3838, skolem_U3737)))
% 65.79/16.69 -> [2350] ~convergent_lines(skolem_U3737, skolem_V3838)
% 65.79/16.69 -> [2351] (convergent_lines(skolem_U3737, skolem_U3737) | convergent_lines(skolem_V3838, skolem_U3737))
% 65.79/16.69
% 65.79/16.69 [2350] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 65.79/16.69
% 65.79/16.69 [2351] BETA_OR : (convergent_lines(skolem_U3737, skolem_U3737) | convergent_lines(skolem_V3838, skolem_U3737))
% 65.79/16.69 -> [2360] convergent_lines(skolem_U3737, skolem_U3737)
% 65.79/16.69 -> [2361] convergent_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2360] CLOSURE : convergent_lines(skolem_U3737, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2361] 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)))))
% 65.79/16.69 -> [2365] (distinct_points(skolem_Y3636, skolem_X3535) => (apart_point_and_line(skolem_X3535, line_connecting(skolem_Y3636, skolem_X3535)) => (distinct_points(skolem_X3535, skolem_Y3636) & distinct_points(skolem_X3535, skolem_X3535))))
% 65.79/16.69
% 65.79/16.69 [2365] BETA_IMPLY : (distinct_points(skolem_Y3636, skolem_X3535) => (apart_point_and_line(skolem_X3535, line_connecting(skolem_Y3636, skolem_X3535)) => (distinct_points(skolem_X3535, skolem_Y3636) & distinct_points(skolem_X3535, skolem_X3535))))
% 65.79/16.69 -> [2368] ~distinct_points(skolem_Y3636, skolem_X3535)
% 65.79/16.69 -> [2369] (apart_point_and_line(skolem_X3535, line_connecting(skolem_Y3636, skolem_X3535)) => (distinct_points(skolem_X3535, skolem_Y3636) & distinct_points(skolem_X3535, skolem_X3535)))
% 65.79/16.69
% 65.79/16.69 [2368] CLOSURE : ~distinct_points(skolem_Y3636, skolem_X3535)
% 65.79/16.69
% 65.79/16.69 [2369] BETA_IMPLY : (apart_point_and_line(skolem_X3535, line_connecting(skolem_Y3636, skolem_X3535)) => (distinct_points(skolem_X3535, skolem_Y3636) & distinct_points(skolem_X3535, skolem_X3535)))
% 65.79/16.69 -> [2398] ~apart_point_and_line(skolem_X3535, line_connecting(skolem_Y3636, skolem_X3535))
% 65.79/16.69 -> [2399] (distinct_points(skolem_X3535, skolem_Y3636) & distinct_points(skolem_X3535, skolem_X3535))
% 65.79/16.69
% 65.79/16.69 [2399] ALPHA_AND : (distinct_points(skolem_X3535, skolem_Y3636) & distinct_points(skolem_X3535, skolem_X3535))
% 65.79/16.69 -> [2402] distinct_points(skolem_X3535, skolem_Y3636), distinct_points(skolem_X3535, skolem_X3535)
% 65.79/16.69
% 65.79/16.69 [2402] CLOSURE : distinct_points(skolem_X3535, skolem_X3535)
% 65.79/16.69
% 65.79/16.69 [2398] 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)))))
% 65.79/16.69 -> [2406] (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))))
% 65.79/16.69
% 65.79/16.69 [2406] 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))))
% 65.79/16.69 -> [2407] ~convergent_lines(skolem_U3737, skolem_V3838)
% 65.79/16.69 -> [2408] ((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)))
% 65.79/16.69
% 65.79/16.69 [2407] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 65.79/16.69
% 65.79/16.69 [2408] 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)))
% 65.79/16.69 -> [2423] ~(apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 65.79/16.69 -> [2424] distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 65.79/16.69
% 65.79/16.69 [2424] CLOSURE : distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 65.79/16.69
% 65.79/16.69 [2423] ALPHA_NOT_OR : ~(apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 65.79/16.69 -> [2427] ~apart_point_and_line(skolem_X3535, skolem_U3737), ~apart_point_and_line(skolem_X3535, skolem_V3838)
% 65.79/16.69
% 65.79/16.69 [2427] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [8] ALPHA_NOT_NOT : ~~apart_point_and_line(skolem_X3535, skolem_V3838)
% 65.79/16.69 -> [10] apart_point_and_line(skolem_X3535, skolem_V3838)
% 65.79/16.69
% 65.79/16.69 [10] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 65.79/16.69 -> [12] ~distinct_points(skolem_Y3636, skolem_Y3636)
% 65.79/16.69
% 65.79/16.69 [12] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 65.79/16.69 -> [13] ~distinct_lines(X6_0_1, X6_0_1)
% 65.79/16.69
% 65.79/16.69 [13] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 65.79/16.69 -> [15] ~convergent_lines(skolem_U3737, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [15] 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))))
% 65.79/16.69 -> [17] (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636)))
% 65.79/16.69
% 65.79/16.69 [17] BETA_IMPLY : (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636)))
% 65.79/16.69 -> [19] ~distinct_points(skolem_X3535, skolem_Y3636)
% 65.79/16.69 -> [20] (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636))
% 65.79/16.69
% 65.79/16.69 [19] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 65.79/16.69
% 65.79/16.69 [20] BETA_OR : (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636))
% 65.79/16.69 -> [27] distinct_points(skolem_X3535, skolem_Y3636)
% 65.79/16.69 -> [28] distinct_points(skolem_Y3636, skolem_Y3636)
% 65.79/16.69
% 65.79/16.69 [28] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 65.79/16.69
% 65.79/16.69 [27] 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))))
% 65.79/16.69 -> [31] (distinct_lines(Z13_0_4, Z13_0_4) => (distinct_lines(Z13_0_4, Z13_0_4) | distinct_lines(Z13_0_4, Z13_0_4)))
% 65.79/16.69
% 65.79/16.69 [31] BETA_IMPLY : (distinct_lines(Z13_0_4, Z13_0_4) => (distinct_lines(Z13_0_4, Z13_0_4) | distinct_lines(Z13_0_4, Z13_0_4)))
% 65.79/16.69 -> [33] ~distinct_lines(Z13_0_4, Z13_0_4)
% 65.79/16.69 -> [34] (distinct_lines(Z13_0_4, Z13_0_4) | distinct_lines(Z13_0_4, Z13_0_4))
% 65.79/16.69
% 65.79/16.69 [34] BETA_OR : (distinct_lines(Z13_0_4, Z13_0_4) | distinct_lines(Z13_0_4, Z13_0_4))
% 65.79/16.69 -> [37] distinct_lines(Z13_0_4, Z13_0_4)
% 65.79/16.69 -> [38] distinct_lines(Z13_0_4, Z13_0_4)
% 65.79/16.69
% 65.79/16.69 [38] CLOSURE : distinct_lines(Z13_0_4, Z13_0_4)
% 65.79/16.69
% 65.79/16.69 [37] CLOSURE : distinct_lines(Z13_0_4, Z13_0_4)
% 65.79/16.69
% 65.79/16.69 [41] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => (convergent_lines(skolem_U3737, skolem_U3737) | convergent_lines(skolem_V3838, skolem_U3737)))
% 65.79/16.69 -> [2037] ~convergent_lines(skolem_U3737, skolem_V3838)
% 65.79/16.69 -> [2038] (convergent_lines(skolem_U3737, skolem_U3737) | convergent_lines(skolem_V3838, skolem_U3737))
% 65.79/16.69
% 65.79/16.69 [2037] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 65.79/16.69
% 65.79/16.69 [2038] BETA_OR : (convergent_lines(skolem_U3737, skolem_U3737) | convergent_lines(skolem_V3838, skolem_U3737))
% 65.79/16.69 -> [2056] convergent_lines(skolem_U3737, skolem_U3737)
% 65.79/16.69 -> [2057] convergent_lines(skolem_V3838, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2056] CLOSURE : convergent_lines(skolem_U3737, skolem_U3737)
% 65.79/16.69
% 65.79/16.69 [2057] 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)))))
% 65.79/16.69 -> [2061] (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))))
% 65.79/16.69
% 65.79/16.69 [2061] 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))))
% 65.79/16.69 -> [2062] ~distinct_points(skolem_X3535, skolem_Y3636)
% 65.79/16.69 -> [2063] (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636)))
% 65.79/16.69
% 65.79/16.69 [2062] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 65.79/16.69
% 65.79/16.69 [2063] 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)))
% 65.79/16.69 -> [3662] ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 65.79/16.69 -> [3663] (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636))
% 65.79/16.69
% 65.79/16.69 [3663] ALPHA_AND : (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636))
% 65.79/16.69 -> [3664] distinct_points(skolem_Y3636, skolem_X3535), distinct_points(skolem_Y3636, skolem_Y3636)
% 65.79/16.69
% 65.79/16.69 [3664] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 65.79/16.69
% 65.79/16.69 [3662] 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)))))
% 65.79/16.69 -> [3665] (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))))
% 65.79/16.69
% 65.79/16.69 [3665] 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))))
% 65.79/16.69 -> [3666] ~convergent_lines(skolem_U3737, skolem_V3838)
% 65.79/16.69 -> [3667] ((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)))
% 65.79/16.69
% 65.79/16.69 [3667] 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)))
% 65.79/16.69 -> [3668] ~(apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 65.79/16.69 -> [3669] distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 65.79/16.69
% 65.79/16.69 [3669] CLOSURE : distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 65.79/16.69
% 65.79/16.69 [3670] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_V3838)
% 65.79/16.69
% 65.79/16.69 [3666] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 65.79/16.69
% 65.79/16.69 % SZS output end Proof for theBenchmark.p
% 65.79/16.69 [16.347460s][1][Res] 219779 goroutines created
% 65.79/16.69 ==== Result ====
% 65.79/16.69 [16.347495s][1][Res] VALID
% 65.79/16.69 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------