TSTP Solution File: GEO174+2 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO174+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n025.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 133.09s 29.50s
% Output : Proof 133.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO174+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : goeland -dmt -presko -proof %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 06:54:00 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.35 [DMT] DMT loaded with preskolemization
% 0.19/0.35 [EQ] equality loaded.
% 0.19/0.35 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.19/0.35 Conjecture not found
% 0.19/0.35 Start search
% 0.19/0.35 nb_step : 1 - limit : 13
% 0.19/0.35 Launch Gotab with destructive = true
% 133.09/29.48 % SZS output start Proof for theBenchmark.p
% 133.09/29.50 [0] ALPHA_AND : ((! [X5_5] : (~distinct_points(X5_5, X5_5)) & ! [X6_6] : (~distinct_lines(X6_6, X6_6)) & ! [X7_7] : (~convergent_lines(X7_7, X7_7)) & ! [X8_8, Y9_9, Z10_10] : ((distinct_points(X8_8, Y9_9) => (distinct_points(X8_8, Z10_10) | distinct_points(Y9_9, Z10_10)))) & ! [X11_11, Y12_12, Z13_13] : ((distinct_lines(X11_11, Y12_12) => (distinct_lines(X11_11, Z13_13) | distinct_lines(Y12_12, Z13_13)))) & ! [X14_14, Y15_15, Z16_16] : ((convergent_lines(X14_14, Y15_15) => (convergent_lines(X14_14, Z16_16) | convergent_lines(Y15_15, Z16_16)))) & ! [X17_17, Y18_18, Z19_19] : ((distinct_points(X17_17, Y18_18) => (apart_point_and_line(Z19_19, line_connecting(X17_17, Y18_18)) => (distinct_points(Z19_19, X17_17) & distinct_points(Z19_19, Y18_18))))) & ! [X20_20, Y21_21, Z22_22] : ((convergent_lines(X20_20, Y21_21) => ((apart_point_and_line(Z22_22, X20_20) | apart_point_and_line(Z22_22, Y21_21)) => distinct_points(Z22_22, intersection_point(X20_20, Y21_21))))) & ! [X23_23, Y24_24, U25_25, V26_26] : (((distinct_points(X23_23, Y24_24) & distinct_lines(U25_25, V26_26)) => (((apart_point_and_line(X23_23, U25_25) | apart_point_and_line(X23_23, V26_26)) | apart_point_and_line(Y24_24, U25_25)) | apart_point_and_line(Y24_24, V26_26)))) & ! [X27_27, Y28_28, Z29_29] : ((apart_point_and_line(X27_27, Y28_28) => (distinct_points(X27_27, Z29_29) | apart_point_and_line(Z29_29, Y28_28)))) & ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_lines(Y31_31, Z32_32) | apart_point_and_line(X30_30, Z32_32)))) & ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))) & ~! [X35_35, Y36_36, U37_37, V38_38] : ((((distinct_points(X35_35, Y36_36) & convergent_lines(U37_37, V38_38)) & (apart_point_and_line(X35_35, U37_37) | apart_point_and_line(Y36_36, U37_37))) => distinct_lines(U37_37, line_connecting(X35_35, Y36_36)))))
% 133.09/29.50 -> [1] (! [X5_5] : (~distinct_points(X5_5, X5_5)) & ! [X6_6] : (~distinct_lines(X6_6, X6_6)) & ! [X7_7] : (~convergent_lines(X7_7, X7_7)) & ! [X8_8, Y9_9, Z10_10] : ((distinct_points(X8_8, Y9_9) => (distinct_points(X8_8, Z10_10) | distinct_points(Y9_9, Z10_10)))) & ! [X11_11, Y12_12, Z13_13] : ((distinct_lines(X11_11, Y12_12) => (distinct_lines(X11_11, Z13_13) | distinct_lines(Y12_12, Z13_13)))) & ! [X14_14, Y15_15, Z16_16] : ((convergent_lines(X14_14, Y15_15) => (convergent_lines(X14_14, Z16_16) | convergent_lines(Y15_15, Z16_16)))) & ! [X17_17, Y18_18, Z19_19] : ((distinct_points(X17_17, Y18_18) => (apart_point_and_line(Z19_19, line_connecting(X17_17, Y18_18)) => (distinct_points(Z19_19, X17_17) & distinct_points(Z19_19, Y18_18))))) & ! [X20_20, Y21_21, Z22_22] : ((convergent_lines(X20_20, Y21_21) => ((apart_point_and_line(Z22_22, X20_20) | apart_point_and_line(Z22_22, Y21_21)) => distinct_points(Z22_22, intersection_point(X20_20, Y21_21))))) & ! [X23_23, Y24_24, U25_25, V26_26] : (((distinct_points(X23_23, Y24_24) & distinct_lines(U25_25, V26_26)) => (((apart_point_and_line(X23_23, U25_25) | apart_point_and_line(X23_23, V26_26)) | apart_point_and_line(Y24_24, U25_25)) | apart_point_and_line(Y24_24, V26_26)))) & ! [X27_27, Y28_28, Z29_29] : ((apart_point_and_line(X27_27, Y28_28) => (distinct_points(X27_27, Z29_29) | apart_point_and_line(Z29_29, Y28_28)))) & ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_lines(Y31_31, Z32_32) | apart_point_and_line(X30_30, Z32_32)))) & ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))), ~! [X35_35, Y36_36, U37_37, V38_38] : ((((distinct_points(X35_35, Y36_36) & convergent_lines(U37_37, V38_38)) & (apart_point_and_line(X35_35, U37_37) | apart_point_and_line(Y36_36, U37_37))) => distinct_lines(U37_37, line_connecting(X35_35, Y36_36))))
% 133.09/29.50
% 133.09/29.50 [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))))
% 133.09/29.50 -> [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)))
% 133.09/29.50
% 133.09/29.50 [2] DELTA_NOT_FORALL : ~! [X35_35, Y36_36, U37_37, V38_38] : ((((distinct_points(X35_35, Y36_36) & convergent_lines(U37_37, V38_38)) & (apart_point_and_line(X35_35, U37_37) | apart_point_and_line(Y36_36, U37_37))) => distinct_lines(U37_37, line_connecting(X35_35, Y36_36))))
% 133.09/29.50 -> [3] ~(((distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)) & (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_Y3636, skolem_U3737))) => distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50
% 133.09/29.50 [3] ALPHA_NOT_IMPLY : ~(((distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)) & (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_Y3636, skolem_U3737))) => distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50 -> [4] ((distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)) & (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_Y3636, skolem_U3737))), ~distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [4] ALPHA_AND : ((distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)) & (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_Y3636, skolem_U3737)))
% 133.09/29.50 -> [5] (distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)), (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_Y3636, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [5] ALPHA_AND : (distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838))
% 133.09/29.50 -> [6] distinct_points(skolem_X3535, skolem_Y3636), convergent_lines(skolem_U3737, skolem_V3838)
% 133.09/29.50
% 133.09/29.50 [6] BETA_OR : (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_Y3636, skolem_U3737))
% 133.09/29.50 -> [7] apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [8] apart_point_and_line(skolem_Y3636, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [8] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50 -> [10] ~distinct_points(skolem_Y3636, skolem_Y3636)
% 133.09/29.50
% 133.09/29.50 [10] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 133.09/29.50 -> [12] ~distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [12] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 133.09/29.50 -> [13] ~convergent_lines(skolem_V3838, skolem_V3838)
% 133.09/29.50
% 133.09/29.50 [13] 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))))
% 133.09/29.50 -> [16] (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636)))
% 133.09/29.50
% 133.09/29.50 [16] BETA_IMPLY : (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636)))
% 133.09/29.50 -> [19] ~distinct_points(skolem_X3535, skolem_Y3636)
% 133.09/29.50 -> [20] (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [19] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 133.09/29.50
% 133.09/29.50 [20] BETA_OR : (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636))
% 133.09/29.50 -> [25] distinct_points(skolem_X3535, skolem_Y3636)
% 133.09/29.50 -> [26] distinct_points(skolem_Y3636, skolem_Y3636)
% 133.09/29.50
% 133.09/29.50 [26] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 133.09/29.50
% 133.09/29.50 [25] 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))))
% 133.09/29.50 -> [30] (distinct_lines(skolem_U3737, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | distinct_lines(skolem_U3737, skolem_U3737)))
% 133.09/29.50
% 133.09/29.50 [30] BETA_IMPLY : (distinct_lines(skolem_U3737, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | distinct_lines(skolem_U3737, skolem_U3737)))
% 133.09/29.50 -> [33] ~distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50 -> [34] (distinct_lines(skolem_U3737, skolem_U3737) | distinct_lines(skolem_U3737, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [34] BETA_OR : (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50 -> [35] distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50 -> [36] distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [36] CLOSURE : distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [35] CLOSURE : distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [42] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => (convergent_lines(skolem_U3737, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838)))
% 133.09/29.50 -> [3052] ~convergent_lines(skolem_U3737, skolem_V3838)
% 133.09/29.50 -> [3053] (convergent_lines(skolem_U3737, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838))
% 133.09/29.50
% 133.09/29.50 [3052] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 133.09/29.50
% 133.09/29.50 [3053] BETA_OR : (convergent_lines(skolem_U3737, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838))
% 133.09/29.50 -> [3076] convergent_lines(skolem_U3737, skolem_V3838)
% 133.09/29.50 -> [3077] convergent_lines(skolem_V3838, skolem_V3838)
% 133.09/29.50
% 133.09/29.50 [3077] CLOSURE : convergent_lines(skolem_V3838, skolem_V3838)
% 133.09/29.50
% 133.09/29.50 [3076] 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)))))
% 133.09/29.50 -> [3085] (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))))
% 133.09/29.50
% 133.09/29.50 [3085] 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))))
% 133.09/29.50 -> [3088] ~distinct_points(skolem_X3535, skolem_Y3636)
% 133.09/29.50 -> [3089] (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636)))
% 133.09/29.50
% 133.09/29.50 [3088] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 133.09/29.50
% 133.09/29.50 [3089] 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)))
% 133.09/29.50 -> [4518] ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50 -> [4519] (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [4518] 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)))))
% 133.09/29.50 -> [4521] (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))))
% 133.09/29.50
% 133.09/29.50 [4521] 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))))
% 133.09/29.50 -> [4522] ~convergent_lines(skolem_U3737, skolem_V3838)
% 133.09/29.50 -> [4523] ((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)))
% 133.09/29.50
% 133.09/29.50 [4522] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 133.09/29.50
% 133.09/29.50 [4523] 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)))
% 133.09/29.50 -> [5102] ~(apart_point_and_line(skolem_Y3636, skolem_U3737) | apart_point_and_line(skolem_Y3636, skolem_V3838))
% 133.09/29.50 -> [5103] distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))
% 133.09/29.50
% 133.09/29.50 [5102] ALPHA_NOT_OR : ~(apart_point_and_line(skolem_Y3636, skolem_U3737) | apart_point_and_line(skolem_Y3636, skolem_V3838))
% 133.09/29.50 -> [5104] ~apart_point_and_line(skolem_Y3636, skolem_U3737), ~apart_point_and_line(skolem_Y3636, skolem_V3838)
% 133.09/29.50
% 133.09/29.50 [5104] CLOSURE : ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [5110] 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))))
% 133.09/29.50 -> [5343] ~(distinct_points(skolem_X3535, skolem_Y3636) & distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50 -> [5344] (((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)))
% 133.09/29.50
% 133.09/29.50 [5343] BETA_NOT_AND : ~(distinct_points(skolem_X3535, skolem_Y3636) & distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50 -> [5345] ~distinct_points(skolem_X3535, skolem_Y3636)
% 133.09/29.50 -> [5346] ~distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [5345] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 133.09/29.50
% 133.09/29.50 [5353] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, skolem_U3737) => (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, skolem_U3737)))
% 133.09/29.50 -> [5410] ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 133.09/29.50 -> [5411] (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [5410] CLOSURE : ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [5411] BETA_OR : (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, skolem_U3737))
% 133.09/29.50 -> [5423] distinct_points(skolem_Y3636, skolem_Y3636)
% 133.09/29.50 -> [5424] apart_point_and_line(skolem_Y3636, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [5424] 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))))
% 133.09/29.50 -> [5425] (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))))
% 133.09/29.50
% 133.09/29.50 [5425] 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))))
% 133.09/29.50 -> [5426] ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 133.09/29.50 -> [5427] (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50
% 133.09/29.50 [5426] CLOSURE : ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [5427] BETA_OR : (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50 -> [5433] distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50 -> [5434] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [5433] CLOSURE : distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [5434] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [5423] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 133.09/29.50
% 133.09/29.50 [5344] 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)))
% 133.09/29.50 -> [5461] ((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))
% 133.09/29.50 -> [5462] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [5462] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [5461] 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))
% 133.09/29.50 -> [5463] (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50 -> [5464] apart_point_and_line(skolem_Y3636, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [5464] 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))))
% 133.09/29.50 -> [5467] (apart_point_and_line(skolem_Y3636, skolem_U3737) => (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, skolem_U3737)))
% 133.09/29.50
% 133.09/29.50 [5467] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, skolem_U3737) => (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, skolem_U3737)))
% 133.09/29.50 -> [5468] ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 133.09/29.50 -> [5469] (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [5468] CLOSURE : ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [5469] BETA_OR : (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, skolem_U3737))
% 133.09/29.50 -> [5528] distinct_points(skolem_Y3636, skolem_Y3636)
% 133.09/29.50 -> [5529] apart_point_and_line(skolem_Y3636, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [5528] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 133.09/29.50
% 133.09/29.50 [5529] 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))))
% 133.09/29.50 -> [5554] (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))))
% 133.09/29.50
% 133.09/29.50 [5554] 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))))
% 133.09/29.50 -> [5555] ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 133.09/29.50 -> [5556] (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50
% 133.09/29.50 [5555] CLOSURE : ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [5556] BETA_OR : (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50 -> [5579] distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50 -> [5580] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [5580] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [5579] CLOSURE : distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [5463] BETA_OR : (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50 -> [5465] apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [5466] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [5466] 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))))
% 133.09/29.50 -> [5471] (apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_X3535, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))))
% 133.09/29.50
% 133.09/29.50 [5471] BETA_IMPLY : (apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_X3535, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))))
% 133.09/29.50 -> [5478] ~apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50 -> [5479] (distinct_points(skolem_X3535, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50
% 133.09/29.50 [5478] CLOSURE : ~apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [5479] BETA_OR : (distinct_points(skolem_X3535, skolem_Y3636) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50 -> [5534] distinct_points(skolem_X3535, skolem_Y3636)
% 133.09/29.50 -> [5535] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [5535] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [5549] 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))))
% 133.09/29.50 -> [5644] ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 133.09/29.50 -> [5645] (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50
% 133.09/29.50 [5644] CLOSURE : ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [5645] BETA_OR : (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50 -> [5662] distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50 -> [5663] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [5663] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [5662] CLOSURE : distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [5465] 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))))
% 133.09/29.50 -> [5470] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50
% 133.09/29.50 [5470] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50 -> [5472] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [5473] (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [5472] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [5473] BETA_OR : (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50 -> [5524] distinct_points(skolem_X3535, skolem_X3535)
% 133.09/29.50 -> [5525] apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [5524] 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))))
% 133.09/29.50 -> [5532] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50
% 133.09/29.50 [5532] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50 -> [5536] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [5537] (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [5536] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [5537] BETA_OR : (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50 -> [5565] distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50 -> [5566] apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [5565] CLOSURE : distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [5567] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => distinct_lines(skolem_U3737, skolem_V3838))
% 133.09/29.50 -> [5608] ~convergent_lines(skolem_U3737, skolem_V3838)
% 133.09/29.50 -> [5609] distinct_lines(skolem_U3737, skolem_V3838)
% 133.09/29.50
% 133.09/29.50 [5608] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 133.09/29.50
% 133.09/29.50 [5609] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50 -> [5622] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50
% 133.09/29.50 [5622] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50 -> [5624] ~distinct_points(X5_326_0, X5_326_0)
% 133.09/29.50
% 133.09/29.50 [5624] CLOSURE : ~distinct_points(X5_326_0, X5_326_0)
% 133.09/29.50
% 133.09/29.50 [5525] 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))))
% 133.09/29.50 -> [5533] (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))))
% 133.09/29.50
% 133.09/29.50 [5533] 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))))
% 133.09/29.50 -> [5538] ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 133.09/29.50 -> [5539] (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50
% 133.09/29.50 [5539] BETA_OR : (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50 -> [5544] distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50 -> [5545] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [5544] CLOSURE : distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [5545] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [5538] CLOSURE : ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [4520] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 133.09/29.50
% 133.09/29.50 [7] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50 -> [9] ~distinct_points(skolem_Y3636, skolem_Y3636)
% 133.09/29.50
% 133.09/29.50 [9] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 133.09/29.50 -> [11] ~distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [11] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 133.09/29.50 -> [14] ~convergent_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14] 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))))
% 133.09/29.50 -> [15] (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636)))
% 133.09/29.50
% 133.09/29.50 [15] BETA_IMPLY : (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636)))
% 133.09/29.50 -> [17] ~distinct_points(skolem_X3535, skolem_Y3636)
% 133.09/29.50 -> [18] (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [17] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 133.09/29.50
% 133.09/29.50 [18] BETA_OR : (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636))
% 133.09/29.50 -> [27] distinct_points(skolem_X3535, skolem_Y3636)
% 133.09/29.50 -> [28] distinct_points(skolem_Y3636, skolem_Y3636)
% 133.09/29.50
% 133.09/29.50 [28] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 133.09/29.50
% 133.09/29.50 [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))))
% 133.09/29.50 -> [29] (distinct_lines(skolem_U3737, skolem_U3737) => (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))))
% 133.09/29.50
% 133.09/29.50 [29] BETA_IMPLY : (distinct_lines(skolem_U3737, skolem_U3737) => (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))))
% 133.09/29.50 -> [31] ~distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50 -> [32] (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50
% 133.09/29.50 [32] BETA_OR : (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50 -> [37] distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50 -> [38] distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [37] CLOSURE : distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [38] CLOSURE : distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [39] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => (convergent_lines(skolem_U3737, skolem_U3737) | convergent_lines(skolem_V3838, skolem_U3737)))
% 133.09/29.50 -> [4039] ~convergent_lines(skolem_U3737, skolem_V3838)
% 133.09/29.50 -> [4040] (convergent_lines(skolem_U3737, skolem_U3737) | convergent_lines(skolem_V3838, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [4039] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 133.09/29.50
% 133.09/29.50 [4040] BETA_OR : (convergent_lines(skolem_U3737, skolem_U3737) | convergent_lines(skolem_V3838, skolem_U3737))
% 133.09/29.50 -> [4053] convergent_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50 -> [4054] convergent_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [4053] CLOSURE : convergent_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [4054] 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)))))
% 133.09/29.50 -> [4055] (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))))
% 133.09/29.50
% 133.09/29.50 [4055] 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))))
% 133.09/29.50 -> [4056] ~distinct_points(skolem_X3535, skolem_Y3636)
% 133.09/29.50 -> [4057] (apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_X3535, skolem_X3535) & distinct_points(skolem_X3535, skolem_Y3636)))
% 133.09/29.50
% 133.09/29.50 [4056] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 133.09/29.50
% 133.09/29.50 [4057] 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)))
% 133.09/29.50 -> [6885] ~apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50 -> [6886] (distinct_points(skolem_X3535, skolem_X3535) & distinct_points(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [6885] 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)))))
% 133.09/29.50 -> [6888] (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))))
% 133.09/29.50
% 133.09/29.50 [6888] 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))))
% 133.09/29.50 -> [6889] ~convergent_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50 -> [6890] ((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)))
% 133.09/29.50
% 133.09/29.50 [6889] CLOSURE : ~convergent_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [6890] 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)))
% 133.09/29.50 -> [7158] ~(apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50 -> [7159] distinct_points(skolem_X3535, intersection_point(skolem_V3838, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [7158] ALPHA_NOT_OR : ~(apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50 -> [7160] ~apart_point_and_line(skolem_X3535, skolem_V3838), ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [7160] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [7161] BETA_IMPLY : ((distinct_points(skolem_X3535, skolem_X3535) & 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)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))))
% 133.09/29.50 -> [7309] ~(distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50 -> [7310] (((apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50
% 133.09/29.50 [7310] BETA_OR : (((apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50 -> [7313] ((apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50 -> [7314] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [7313] BETA_OR : ((apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50 -> [7315] (apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50 -> [7316] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [7315] BETA_OR : (apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50 -> [7320] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50 -> [7321] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [7320] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [7321] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [7316] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [7314] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [7309] BETA_NOT_AND : ~(distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50 -> [8246] ~distinct_points(skolem_X3535, skolem_X3535)
% 133.09/29.50 -> [8247] ~distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [8246] 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))))
% 133.09/29.50 -> [8248] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50
% 133.09/29.50 [8248] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50 -> [8250] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [8251] (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [8250] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [8251] BETA_OR : (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50 -> [8260] distinct_points(skolem_X3535, skolem_X3535)
% 133.09/29.50 -> [8261] apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [8261] 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))))
% 133.09/29.50 -> [8263] (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))))
% 133.09/29.50
% 133.09/29.50 [8263] 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))))
% 133.09/29.50 -> [8267] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [8268] (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50
% 133.09/29.50 [8267] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [8268] BETA_OR : (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50 -> [8279] distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50 -> [8280] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [8279] CLOSURE : distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [8280] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [8260] CLOSURE : distinct_points(skolem_X3535, skolem_X3535)
% 133.09/29.50
% 133.09/29.50 [8247] 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))))
% 133.09/29.50 -> [8249] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50
% 133.09/29.50 [8249] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50 -> [8252] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [8253] (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [8252] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [8253] BETA_OR : (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50 -> [8258] distinct_points(skolem_X3535, skolem_X3535)
% 133.09/29.50 -> [8259] apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [8258] 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))))
% 133.09/29.50 -> [8262] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50
% 133.09/29.50 [8262] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50 -> [8265] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [8266] (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [8265] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [8266] BETA_OR : (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50 -> [8277] distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50 -> [8278] apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [8277] CLOSURE : distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [8278] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 133.09/29.50 -> [8283] (convergent_lines(skolem_V3838, skolem_U3737) => distinct_lines(skolem_V3838, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [8283] BETA_IMPLY : (convergent_lines(skolem_V3838, skolem_U3737) => distinct_lines(skolem_V3838, skolem_U3737))
% 133.09/29.50 -> [8284] ~convergent_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50 -> [8285] distinct_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [8284] CLOSURE : ~convergent_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [8285] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50 -> [8289] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50
% 133.09/29.50 [8289] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50 -> [8290] ~distinct_points(X5_750_0, X5_750_0)
% 133.09/29.50
% 133.09/29.50 [8290] CLOSURE : ~distinct_points(X5_750_0, X5_750_0)
% 133.09/29.50
% 133.09/29.50 [8264] 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))))
% 133.09/29.50 -> [8303] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [8304] (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50
% 133.09/29.50 [8304] 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)))
% 133.09/29.50 -> [8305] distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50 -> [8306] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [8306] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [8305] CLOSURE : distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [8303] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [6887] 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)))))
% 133.09/29.50 -> [12119] (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))))
% 133.09/29.50
% 133.09/29.50 [12119] 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))))
% 133.09/29.50 -> [12120] ~convergent_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50 -> [12121] ((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)))
% 133.09/29.50
% 133.09/29.50 [12120] CLOSURE : ~convergent_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [12121] 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)))
% 133.09/29.50 -> [13163] ~(apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50 -> [13164] distinct_points(skolem_X3535, intersection_point(skolem_V3838, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [13163] ALPHA_NOT_OR : ~(apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50 -> [13165] ~apart_point_and_line(skolem_X3535, skolem_V3838), ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [13165] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [13166] BETA_IMPLY : ((distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(skolem_V3838, skolem_U3737)) => (((apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737)) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50 -> [14103] ~(distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(skolem_V3838, skolem_U3737))
% 133.09/29.50 -> [14104] (((apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737)) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14104] BETA_OR : (((apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737)) | apart_point_and_line(skolem_X3535, skolem_V3838)) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50 -> [14107] ((apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737)) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 133.09/29.50 -> [14108] apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14108] 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))))
% 133.09/29.50 -> [14116] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, Z29_226_9) | apart_point_and_line(Z29_226_9, skolem_U3737)))
% 133.09/29.50
% 133.09/29.50 [14116] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, Z29_226_9) | apart_point_and_line(Z29_226_9, skolem_U3737)))
% 133.09/29.50 -> [14117] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [14118] (distinct_points(skolem_X3535, Z29_226_9) | apart_point_and_line(Z29_226_9, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14117] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14118] BETA_OR : (distinct_points(skolem_X3535, Z29_226_9) | apart_point_and_line(Z29_226_9, skolem_U3737))
% 133.09/29.50 -> [14275] distinct_points(skolem_X3535, Z29_226_9)
% 133.09/29.50 -> [14276] apart_point_and_line(Z29_226_9, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14275] 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))))
% 133.09/29.50 -> [14279] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50
% 133.09/29.50 [14279] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50 -> [14286] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [14287] (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14286] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14287] BETA_OR : (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50 -> [14366] distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50 -> [14367] apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14366] CLOSURE : distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14367] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 133.09/29.50 -> [14373] (convergent_lines(skolem_U3737, skolem_U3737) => distinct_lines(skolem_U3737, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14373] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_U3737) => distinct_lines(skolem_U3737, skolem_U3737))
% 133.09/29.50 -> [14376] ~convergent_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50 -> [14377] distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14377] CLOSURE : distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14376] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50 -> [14414] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50
% 133.09/29.50 [14414] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50 -> [14415] ~distinct_points(X5_1889_0, X5_1889_0)
% 133.09/29.50
% 133.09/29.50 [14415] CLOSURE : ~distinct_points(X5_1889_0, X5_1889_0)
% 133.09/29.50
% 133.09/29.50 [14276] 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))))
% 133.09/29.50 -> [14278] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50
% 133.09/29.50 [14278] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50 -> [14284] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [14285] (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14284] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14285] BETA_OR : (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50 -> [14358] distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50 -> [14359] apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14358] CLOSURE : distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14359] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 133.09/29.50 -> [14372] (convergent_lines(skolem_V3838, skolem_U3737) => distinct_lines(skolem_V3838, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14372] BETA_IMPLY : (convergent_lines(skolem_V3838, skolem_U3737) => distinct_lines(skolem_V3838, skolem_U3737))
% 133.09/29.50 -> [14374] ~convergent_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50 -> [14375] distinct_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14374] CLOSURE : ~convergent_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14375] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50 -> [14422] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50
% 133.09/29.50 [14422] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50 -> [14423] ~distinct_points(X5_1890_0, X5_1890_0)
% 133.09/29.50
% 133.09/29.50 [14423] CLOSURE : ~distinct_points(X5_1890_0, X5_1890_0)
% 133.09/29.50
% 133.09/29.50 [14107] BETA_OR : ((apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737)) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 133.09/29.50 -> [14109] (apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50 -> [14110] apart_point_and_line(skolem_X3535, skolem_V3838)
% 133.09/29.50
% 133.09/29.50 [14109] BETA_OR : (apart_point_and_line(skolem_X3535, skolem_V3838) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50 -> [14111] apart_point_and_line(skolem_X3535, skolem_V3838)
% 133.09/29.50 -> [14112] apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14112] 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))))
% 133.09/29.50 -> [14127] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, Z29_229_9) | apart_point_and_line(Z29_229_9, skolem_U3737)))
% 133.09/29.50
% 133.09/29.50 [14127] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, Z29_229_9) | apart_point_and_line(Z29_229_9, skolem_U3737)))
% 133.09/29.50 -> [14130] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [14131] (distinct_points(skolem_X3535, Z29_229_9) | apart_point_and_line(Z29_229_9, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14130] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14131] BETA_OR : (distinct_points(skolem_X3535, Z29_229_9) | apart_point_and_line(Z29_229_9, skolem_U3737))
% 133.09/29.50 -> [14280] distinct_points(skolem_X3535, Z29_229_9)
% 133.09/29.50 -> [14281] apart_point_and_line(Z29_229_9, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14281] 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))))
% 133.09/29.50 -> [14292] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50
% 133.09/29.50 [14292] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50 -> [14294] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [14295] (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14294] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14295] BETA_OR : (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50 -> [14370] distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50 -> [14371] apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14370] CLOSURE : distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14371] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 133.09/29.50 -> [14381] (convergent_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) => distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50
% 133.09/29.50 [14381] BETA_IMPLY : (convergent_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) => distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50 -> [14384] ~convergent_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50 -> [14385] distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [14385] CLOSURE : distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 133.09/29.50
% 133.09/29.50 [14384] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50 -> [14432] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50
% 133.09/29.50 [14432] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50 -> [14437] ~distinct_points(X5_1892_0, X5_1892_0)
% 133.09/29.50
% 133.09/29.50 [14437] CLOSURE : ~distinct_points(X5_1892_0, X5_1892_0)
% 133.09/29.50
% 133.09/29.50 [14280] 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))))
% 133.09/29.50 -> [14296] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50
% 133.09/29.50 [14296] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50 -> [14298] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [14299] (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14298] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14299] BETA_OR : (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50 -> [14382] distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50 -> [14383] apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14382] CLOSURE : distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14383] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 133.09/29.50 -> [14394] (convergent_lines(skolem_U3737, skolem_U3737) => distinct_lines(skolem_U3737, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14394] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_U3737) => distinct_lines(skolem_U3737, skolem_U3737))
% 133.09/29.50 -> [14396] ~convergent_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50 -> [14397] distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14397] CLOSURE : distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14396] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50 -> [14428] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50
% 133.09/29.50 [14428] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50 -> [14429] ~distinct_points(X5_1891_0, X5_1891_0)
% 133.09/29.50
% 133.09/29.50 [14429] CLOSURE : ~distinct_points(X5_1891_0, X5_1891_0)
% 133.09/29.50
% 133.09/29.50 [14111] 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))))
% 133.09/29.50 -> [14121] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, Z29_227_9) | apart_point_and_line(Z29_227_9, skolem_U3737)))
% 133.09/29.50
% 133.09/29.50 [14121] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, Z29_227_9) | apart_point_and_line(Z29_227_9, skolem_U3737)))
% 133.09/29.50 -> [14125] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [14126] (distinct_points(skolem_X3535, Z29_227_9) | apart_point_and_line(Z29_227_9, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14125] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14126] BETA_OR : (distinct_points(skolem_X3535, Z29_227_9) | apart_point_and_line(Z29_227_9, skolem_U3737))
% 133.09/29.50 -> [14324] distinct_points(skolem_X3535, Z29_227_9)
% 133.09/29.50 -> [14325] apart_point_and_line(Z29_227_9, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14324] 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))))
% 133.09/29.50 -> [14348] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50
% 133.09/29.50 [14348] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50 -> [14352] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [14353] (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14352] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14353] BETA_OR : (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50 -> [14412] distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50 -> [14413] apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14412] CLOSURE : distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14413] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 133.09/29.50 -> [14419] (convergent_lines(skolem_V3838, skolem_U3737) => distinct_lines(skolem_V3838, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14419] BETA_IMPLY : (convergent_lines(skolem_V3838, skolem_U3737) => distinct_lines(skolem_V3838, skolem_U3737))
% 133.09/29.50 -> [14420] ~convergent_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50 -> [14421] distinct_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14420] CLOSURE : ~convergent_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14421] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50 -> [14442] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50
% 133.09/29.50 [14442] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50 -> [14443] ~distinct_points(X5_1895_0, X5_1895_0)
% 133.09/29.50
% 133.09/29.50 [14443] CLOSURE : ~distinct_points(X5_1895_0, X5_1895_0)
% 133.09/29.50
% 133.09/29.50 [14325] 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))))
% 133.09/29.50 -> [14340] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50
% 133.09/29.50 [14340] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50 -> [14343] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [14344] (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14343] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14344] BETA_OR : (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50 -> [14426] distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50 -> [14427] apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14426] CLOSURE : distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14427] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 133.09/29.50 -> [14431] (convergent_lines(skolem_U3737, skolem_U3737) => distinct_lines(skolem_U3737, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14431] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_U3737) => distinct_lines(skolem_U3737, skolem_U3737))
% 133.09/29.50 -> [14435] ~convergent_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50 -> [14436] distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14436] CLOSURE : distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14435] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50 -> [14449] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50
% 133.09/29.50 [14449] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50 -> [14450] ~distinct_points(X5_1896_0, X5_1896_0)
% 133.09/29.50
% 133.09/29.50 [14450] CLOSURE : ~distinct_points(X5_1896_0, X5_1896_0)
% 133.09/29.50
% 133.09/29.50 [14110] 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))))
% 133.09/29.50 -> [14124] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, Z29_228_9) | apart_point_and_line(Z29_228_9, skolem_U3737)))
% 133.09/29.50
% 133.09/29.50 [14124] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, Z29_228_9) | apart_point_and_line(Z29_228_9, skolem_U3737)))
% 133.09/29.50 -> [14128] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [14129] (distinct_points(skolem_X3535, Z29_228_9) | apart_point_and_line(Z29_228_9, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14128] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14129] BETA_OR : (distinct_points(skolem_X3535, Z29_228_9) | apart_point_and_line(Z29_228_9, skolem_U3737))
% 133.09/29.50 -> [14322] distinct_points(skolem_X3535, Z29_228_9)
% 133.09/29.50 -> [14323] apart_point_and_line(Z29_228_9, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14322] 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))))
% 133.09/29.50 -> [14326] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50
% 133.09/29.50 [14326] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50 -> [14328] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [14329] (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14328] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14329] BETA_OR : (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50 -> [14410] distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50 -> [14411] apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14410] CLOSURE : distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14411] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 133.09/29.50 -> [14416] (convergent_lines(skolem_U3737, skolem_U3737) => distinct_lines(skolem_U3737, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14416] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_U3737) => distinct_lines(skolem_U3737, skolem_U3737))
% 133.09/29.50 -> [14417] ~convergent_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50 -> [14418] distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14418] CLOSURE : distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14417] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50 -> [14440] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50
% 133.09/29.50 [14440] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50 -> [14441] ~distinct_points(X5_1894_0, X5_1894_0)
% 133.09/29.50
% 133.09/29.50 [14441] CLOSURE : ~distinct_points(X5_1894_0, X5_1894_0)
% 133.09/29.50
% 133.09/29.50 [14323] 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))))
% 133.09/29.50 -> [14327] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50
% 133.09/29.50 [14327] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50 -> [14330] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [14331] (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14330] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14331] BETA_OR : (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50 -> [14424] distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50 -> [14425] apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14424] CLOSURE : distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14425] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 133.09/29.50 -> [14430] (convergent_lines(skolem_V3838, skolem_U3737) => distinct_lines(skolem_V3838, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14430] BETA_IMPLY : (convergent_lines(skolem_V3838, skolem_U3737) => distinct_lines(skolem_V3838, skolem_U3737))
% 133.09/29.50 -> [14433] ~convergent_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50 -> [14434] distinct_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14433] CLOSURE : ~convergent_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14434] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50 -> [14453] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50
% 133.09/29.50 [14453] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 133.09/29.50 -> [14454] ~distinct_points(X5_1897_0, X5_1897_0)
% 133.09/29.50
% 133.09/29.50 [14454] CLOSURE : ~distinct_points(X5_1897_0, X5_1897_0)
% 133.09/29.50
% 133.09/29.50 [14103] BETA_NOT_AND : ~(distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(skolem_V3838, skolem_U3737))
% 133.09/29.50 -> [14526] ~distinct_points(skolem_X3535, skolem_X3535)
% 133.09/29.50 -> [14527] ~distinct_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14527] 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))))
% 133.09/29.50 -> [14528] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, Z29_230_9) | apart_point_and_line(Z29_230_9, skolem_U3737)))
% 133.09/29.50
% 133.09/29.50 [14528] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, Z29_230_9) | apart_point_and_line(Z29_230_9, skolem_U3737)))
% 133.09/29.50 -> [14529] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [14530] (distinct_points(skolem_X3535, Z29_230_9) | apart_point_and_line(Z29_230_9, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14529] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14530] BETA_OR : (distinct_points(skolem_X3535, Z29_230_9) | apart_point_and_line(Z29_230_9, skolem_U3737))
% 133.09/29.50 -> [14550] distinct_points(skolem_X3535, Z29_230_9)
% 133.09/29.50 -> [14551] apart_point_and_line(Z29_230_9, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14550] 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))))
% 133.09/29.50 -> [14552] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50
% 133.09/29.50 [14552] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 133.09/29.50 -> [14554] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50 -> [14555] (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14554] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14555] BETA_OR : (distinct_lines(skolem_U3737, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 133.09/29.50 -> [14576] distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50 -> [14577] apart_point_and_line(skolem_X3535, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14577] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 133.09/29.50 -> [14580] (convergent_lines(skolem_V3838, skolem_U3737) => distinct_lines(skolem_V3838, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14580] BETA_IMPLY : (convergent_lines(skolem_V3838, skolem_U3737) => distinct_lines(skolem_V3838, skolem_U3737))
% 133.09/29.50 -> [14581] ~convergent_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50 -> [14582] distinct_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14581] CLOSURE : ~convergent_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14582] CLOSURE : distinct_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14576] CLOSURE : distinct_lines(skolem_U3737, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14553] BETA_IMPLY : (apart_point_and_line(X30_558_10, skolem_U3737) => (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(X30_558_10, line_connecting(skolem_X3535, skolem_Y3636))))
% 133.09/29.50 -> [14588] ~apart_point_and_line(X30_558_10, skolem_U3737)
% 133.09/29.50 -> [14589] (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(X30_558_10, line_connecting(skolem_X3535, skolem_Y3636)))
% 133.09/29.50
% 133.09/29.50 [14589] BETA_OR : (distinct_lines(skolem_V3838, skolem_U3737) | apart_point_and_line(X30_558_10, skolem_U3737))
% 133.09/29.50 -> [14590] distinct_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50 -> [14591] apart_point_and_line(X30_558_10, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14590] CLOSURE : distinct_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14591] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 133.09/29.50 -> [14592] (convergent_lines(skolem_V3838, skolem_U3737) => distinct_lines(skolem_V3838, skolem_U3737))
% 133.09/29.50
% 133.09/29.50 [14592] BETA_IMPLY : (convergent_lines(skolem_V3838, skolem_U3737) => distinct_lines(skolem_V3838, skolem_U3737))
% 133.09/29.50 -> [14593] ~convergent_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50 -> [14594] distinct_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14593] CLOSURE : ~convergent_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14594] CLOSURE : distinct_lines(skolem_V3838, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14588] CLOSURE : ~apart_point_and_line(X30_558_10, skolem_U3737)
% 133.09/29.50
% 133.09/29.50 [14526] CLOSURE : ~distinct_points(skolem_X3535, skolem_X3535)
% 133.09/29.50
% 133.09/29.50 % SZS output end Proof for theBenchmark.p
% 133.09/29.50 [29.147820s][1][Res] 379460 goroutines created
% 133.09/29.50 ==== Result ====
% 133.09/29.50 [29.147879s][1][Res] VALID
% 133.09/29.50 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------