TSTP Solution File: GEO183+1 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO183+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n001.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 15:18:16 EDT 2022
% Result : Theorem 64.12s 21.43s
% Output : Proof 64.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO183+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n001.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 07:09:33 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 [0.000040s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.35 Conjecture not found
% 0.13/0.35 Start search
% 0.13/0.35 nb_step : 1 - limit : 15
% 0.13/0.35 Launch Gotab with destructive = true
% 64.12/21.42 % SZS output start Proof for theBenchmark.p
% 64.12/21.43 [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] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18)))) & ! [X19_19, Y20_20] : ((distinct_points(X19_19, Y20_20) => ~apart_point_and_line(Y20_20, line_connecting(X19_19, Y20_20)))) & ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21))) & ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24))) & ! [X25_25, Y26_26, U27_27, V28_28] : (((distinct_points(X25_25, Y26_26) & distinct_lines(U27_27, V28_28)) => (((apart_point_and_line(X25_25, U27_27) | apart_point_and_line(X25_25, V28_28)) | apart_point_and_line(Y26_26, U27_27)) | apart_point_and_line(Y26_26, V28_28)))) & ! [X29_29, Y30_30, Z31_31] : ((apart_point_and_line(X29_29, Y30_30) => (distinct_points(X29_29, Z31_31) | apart_point_and_line(Z31_31, Y30_30)))) & ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34)))) & ! [X35_35, Y36_36, Z37_37] : ((convergent_lines(X35_35, Y36_36) => (distinct_lines(Y36_36, Z37_37) | convergent_lines(X35_35, Z37_37))))) & ~! [X38_38, Y39_39, U40_40, V41_41] : ((((distinct_points(X38_38, Y39_39) & convergent_lines(U40_40, V41_41)) & ~distinct_lines(U40_40, line_connecting(X38_38, Y39_39))) => (~apart_point_and_line(X38_38, U40_40) & ~apart_point_and_line(Y39_39, U40_40)))))
% 64.12/21.43 -> [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] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18)))) & ! [X19_19, Y20_20] : ((distinct_points(X19_19, Y20_20) => ~apart_point_and_line(Y20_20, line_connecting(X19_19, Y20_20)))) & ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21))) & ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24))) & ! [X25_25, Y26_26, U27_27, V28_28] : (((distinct_points(X25_25, Y26_26) & distinct_lines(U27_27, V28_28)) => (((apart_point_and_line(X25_25, U27_27) | apart_point_and_line(X25_25, V28_28)) | apart_point_and_line(Y26_26, U27_27)) | apart_point_and_line(Y26_26, V28_28)))) & ! [X29_29, Y30_30, Z31_31] : ((apart_point_and_line(X29_29, Y30_30) => (distinct_points(X29_29, Z31_31) | apart_point_and_line(Z31_31, Y30_30)))) & ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34)))) & ! [X35_35, Y36_36, Z37_37] : ((convergent_lines(X35_35, Y36_36) => (distinct_lines(Y36_36, Z37_37) | convergent_lines(X35_35, Z37_37))))), ~! [X38_38, Y39_39, U40_40, V41_41] : ((((distinct_points(X38_38, Y39_39) & convergent_lines(U40_40, V41_41)) & ~distinct_lines(U40_40, line_connecting(X38_38, Y39_39))) => (~apart_point_and_line(X38_38, U40_40) & ~apart_point_and_line(Y39_39, U40_40))))
% 64.12/21.43
% 64.12/21.43 [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] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18)))) & ! [X19_19, Y20_20] : ((distinct_points(X19_19, Y20_20) => ~apart_point_and_line(Y20_20, line_connecting(X19_19, Y20_20)))) & ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21))) & ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24))) & ! [X25_25, Y26_26, U27_27, V28_28] : (((distinct_points(X25_25, Y26_26) & distinct_lines(U27_27, V28_28)) => (((apart_point_and_line(X25_25, U27_27) | apart_point_and_line(X25_25, V28_28)) | apart_point_and_line(Y26_26, U27_27)) | apart_point_and_line(Y26_26, V28_28)))) & ! [X29_29, Y30_30, Z31_31] : ((apart_point_and_line(X29_29, Y30_30) => (distinct_points(X29_29, Z31_31) | apart_point_and_line(Z31_31, Y30_30)))) & ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34)))) & ! [X35_35, Y36_36, Z37_37] : ((convergent_lines(X35_35, Y36_36) => (distinct_lines(Y36_36, Z37_37) | convergent_lines(X35_35, Z37_37)))))
% 64.12/21.43 -> [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] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18)))), ! [X19_19, Y20_20] : ((distinct_points(X19_19, Y20_20) => ~apart_point_and_line(Y20_20, line_connecting(X19_19, Y20_20)))), ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21))), ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24))), ! [X25_25, Y26_26, U27_27, V28_28] : (((distinct_points(X25_25, Y26_26) & distinct_lines(U27_27, V28_28)) => (((apart_point_and_line(X25_25, U27_27) | apart_point_and_line(X25_25, V28_28)) | apart_point_and_line(Y26_26, U27_27)) | apart_point_and_line(Y26_26, V28_28)))), ! [X29_29, Y30_30, Z31_31] : ((apart_point_and_line(X29_29, Y30_30) => (distinct_points(X29_29, Z31_31) | apart_point_and_line(Z31_31, Y30_30)))), ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34)))), ! [X35_35, Y36_36, Z37_37] : ((convergent_lines(X35_35, Y36_36) => (distinct_lines(Y36_36, Z37_37) | convergent_lines(X35_35, Z37_37))))
% 64.12/21.43
% 64.12/21.43 [2] DELTA_NOT_FORALL : ~! [X38_38, Y39_39, U40_40, V41_41] : ((((distinct_points(X38_38, Y39_39) & convergent_lines(U40_40, V41_41)) & ~distinct_lines(U40_40, line_connecting(X38_38, Y39_39))) => (~apart_point_and_line(X38_38, U40_40) & ~apart_point_and_line(Y39_39, U40_40))))
% 64.12/21.43 -> [3] ~(((distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)) & ~distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))) => (~apart_point_and_line(skolem_X3838, skolem_U4040) & ~apart_point_and_line(skolem_Y3939, skolem_U4040)))
% 64.12/21.43
% 64.12/21.43 [3] ALPHA_NOT_IMPLY : ~(((distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)) & ~distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))) => (~apart_point_and_line(skolem_X3838, skolem_U4040) & ~apart_point_and_line(skolem_Y3939, skolem_U4040)))
% 64.12/21.43 -> [4] ((distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)) & ~distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))), ~(~apart_point_and_line(skolem_X3838, skolem_U4040) & ~apart_point_and_line(skolem_Y3939, skolem_U4040))
% 64.12/21.43
% 64.12/21.43 [4] ALPHA_AND : ((distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)) & ~distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [5] (distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)), ~distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [5] ALPHA_AND : (distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141))
% 64.12/21.43 -> [6] distinct_points(skolem_X3838, skolem_Y3939), convergent_lines(skolem_U4040, skolem_V4141)
% 64.12/21.43
% 64.12/21.43 [6] BETA_NOT_AND : ~(~apart_point_and_line(skolem_X3838, skolem_U4040) & ~apart_point_and_line(skolem_Y3939, skolem_U4040))
% 64.12/21.43 -> [7] ~~apart_point_and_line(skolem_X3838, skolem_U4040)
% 64.12/21.43 -> [8] ~~apart_point_and_line(skolem_Y3939, skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [8] ALPHA_NOT_NOT : ~~apart_point_and_line(skolem_Y3939, skolem_U4040)
% 64.12/21.43 -> [10] apart_point_and_line(skolem_Y3939, skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [10] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 64.12/21.43 -> [12] ~distinct_points(skolem_Y3939, skolem_Y3939)
% 64.12/21.43
% 64.12/21.43 [12] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 64.12/21.43 -> [14] ~distinct_lines(X6_1_1, X6_1_1)
% 64.12/21.43
% 64.12/21.43 [14] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 64.12/21.43 -> [16] ~convergent_lines(skolem_V4141, skolem_V4141)
% 64.12/21.43
% 64.12/21.43 [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))))
% 64.12/21.43 -> [18] (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939)))
% 64.12/21.43
% 64.12/21.43 [18] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939)))
% 64.12/21.43 -> [21] ~distinct_points(skolem_X3838, skolem_Y3939)
% 64.12/21.43 -> [22] (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [21] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 64.12/21.43
% 64.12/21.43 [22] BETA_OR : (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939))
% 64.12/21.43 -> [29] distinct_points(skolem_X3838, skolem_Y3939)
% 64.12/21.43 -> [30] distinct_points(skolem_Y3939, skolem_Y3939)
% 64.12/21.43
% 64.12/21.43 [30] CLOSURE : distinct_points(skolem_Y3939, skolem_Y3939)
% 64.12/21.43
% 64.12/21.43 [29] 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))))
% 64.12/21.43 -> [34] (distinct_lines(skolem_U4040, skolem_U4040) => (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))))
% 64.12/21.43
% 64.12/21.43 [34] BETA_IMPLY : (distinct_lines(skolem_U4040, skolem_U4040) => (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))))
% 64.12/21.43 -> [35] ~distinct_lines(skolem_U4040, skolem_U4040)
% 64.12/21.43 -> [36] (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43
% 64.12/21.43 [36] BETA_OR : (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [39] distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43 -> [40] distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [40] CLOSURE : distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [39] CLOSURE : distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [44] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => (convergent_lines(skolem_U4040, skolem_V4141) | convergent_lines(skolem_V4141, skolem_V4141)))
% 64.12/21.43 -> [2434] ~convergent_lines(skolem_U4040, skolem_V4141)
% 64.12/21.43 -> [2435] (convergent_lines(skolem_U4040, skolem_V4141) | convergent_lines(skolem_V4141, skolem_V4141))
% 64.12/21.43
% 64.12/21.43 [2434] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 64.12/21.43
% 64.12/21.43 [2435] BETA_OR : (convergent_lines(skolem_U4040, skolem_V4141) | convergent_lines(skolem_V4141, skolem_V4141))
% 64.12/21.43 -> [2445] convergent_lines(skolem_U4040, skolem_V4141)
% 64.12/21.43 -> [2446] convergent_lines(skolem_V4141, skolem_V4141)
% 64.12/21.43
% 64.12/21.43 [2446] CLOSURE : convergent_lines(skolem_V4141, skolem_V4141)
% 64.12/21.43
% 64.12/21.43 [2445] GAMMA_FORALL : ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18))))
% 64.12/21.43 -> [2447] (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43
% 64.12/21.43 [2447] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [2448] ~distinct_points(skolem_X3838, skolem_Y3939)
% 64.12/21.43 -> [2449] ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [2448] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 64.12/21.43
% 64.12/21.43 [2449] GAMMA_FORALL : ! [X19_19, Y20_20] : ((distinct_points(X19_19, Y20_20) => ~apart_point_and_line(Y20_20, line_connecting(X19_19, Y20_20))))
% 64.12/21.43 -> [2450] (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43
% 64.12/21.43 [2450] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [2451] ~distinct_points(skolem_X3838, skolem_Y3939)
% 64.12/21.43 -> [2452] ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [2451] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 64.12/21.43
% 64.12/21.43 [2452] GAMMA_FORALL : ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21)))
% 64.12/21.43 -> [2453] (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 64.12/21.43
% 64.12/21.43 [2453] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 64.12/21.43 -> [2454] ~convergent_lines(skolem_U4040, skolem_V4141)
% 64.12/21.43 -> [2455] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [2454] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 64.12/21.43
% 64.12/21.43 [2456] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 64.12/21.43 -> [2996] ~convergent_lines(skolem_U4040, skolem_V4141)
% 64.12/21.43 -> [2997] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 64.12/21.43
% 64.12/21.43 [2997] GAMMA_FORALL : ! [X25_25, Y26_26, U27_27, V28_28] : (((distinct_points(X25_25, Y26_26) & distinct_lines(U27_27, V28_28)) => (((apart_point_and_line(X25_25, U27_27) | apart_point_and_line(X25_25, V28_28)) | apart_point_and_line(Y26_26, U27_27)) | apart_point_and_line(Y26_26, V28_28))))
% 64.12/21.43 -> [2998] ((distinct_points(intersection_point(skolem_U4040, skolem_V4141), intersection_point(skolem_U4040, skolem_V4141)) & distinct_lines(skolem_U4040, skolem_V4141)) => (((apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)))
% 64.12/21.43
% 64.12/21.43 [2998] BETA_IMPLY : ((distinct_points(intersection_point(skolem_U4040, skolem_V4141), intersection_point(skolem_U4040, skolem_V4141)) & distinct_lines(skolem_U4040, skolem_V4141)) => (((apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)))
% 64.12/21.43 -> [2999] ~(distinct_points(intersection_point(skolem_U4040, skolem_V4141), intersection_point(skolem_U4040, skolem_V4141)) & distinct_lines(skolem_U4040, skolem_V4141))
% 64.12/21.43 -> [3000] (((apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 64.12/21.43
% 64.12/21.43 [3000] BETA_OR : (((apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 64.12/21.43 -> [3003] ((apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 64.12/21.43 -> [3004] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 64.12/21.43
% 64.12/21.43 [3004] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 64.12/21.43
% 64.12/21.43 [3003] BETA_OR : ((apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 64.12/21.43 -> [3036] (apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 64.12/21.43 -> [3037] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [3037] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [3036] BETA_OR : (apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 64.12/21.43 -> [3053] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 64.12/21.43 -> [3054] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 64.12/21.43
% 64.12/21.43 [3054] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 64.12/21.43
% 64.12/21.43 [3053] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [2999] BETA_NOT_AND : ~(distinct_points(intersection_point(skolem_U4040, skolem_V4141), intersection_point(skolem_U4040, skolem_V4141)) & distinct_lines(skolem_U4040, skolem_V4141))
% 64.12/21.43 -> [3080] ~distinct_points(intersection_point(skolem_U4040, skolem_V4141), intersection_point(skolem_U4040, skolem_V4141))
% 64.12/21.43 -> [3081] ~distinct_lines(skolem_U4040, skolem_V4141)
% 64.12/21.43
% 64.12/21.43 [3080] GAMMA_FORALL : ! [X29_29, Y30_30, Z31_31] : ((apart_point_and_line(X29_29, Y30_30) => (distinct_points(X29_29, Z31_31) | apart_point_and_line(Z31_31, Y30_30))))
% 64.12/21.43 -> [3082] (apart_point_and_line(skolem_Y3939, skolem_U4040) => (distinct_points(skolem_Y3939, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)))
% 64.12/21.43
% 64.12/21.43 [3082] BETA_IMPLY : (apart_point_and_line(skolem_Y3939, skolem_U4040) => (distinct_points(skolem_Y3939, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)))
% 64.12/21.43 -> [3084] ~apart_point_and_line(skolem_Y3939, skolem_U4040)
% 64.12/21.43 -> [3085] (distinct_points(skolem_Y3939, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 64.12/21.43
% 64.12/21.43 [3084] CLOSURE : ~apart_point_and_line(skolem_Y3939, skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [3085] BETA_OR : (distinct_points(skolem_Y3939, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 64.12/21.43 -> [3099] distinct_points(skolem_Y3939, intersection_point(skolem_U4040, skolem_V4141))
% 64.12/21.43 -> [3100] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [3100] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [3099] GAMMA_FORALL : ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34))))
% 64.12/21.43 -> [3103] (apart_point_and_line(skolem_Y3939, skolem_U4040) => (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 64.12/21.43
% 64.12/21.43 [3103] BETA_IMPLY : (apart_point_and_line(skolem_Y3939, skolem_U4040) => (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 64.12/21.43 -> [3104] ~apart_point_and_line(skolem_Y3939, skolem_U4040)
% 64.12/21.43 -> [3105] (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43
% 64.12/21.43 [3104] CLOSURE : ~apart_point_and_line(skolem_Y3939, skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [3105] BETA_OR : (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [3119] distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43 -> [3120] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [3119] CLOSURE : distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [3120] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [3081] GAMMA_FORALL : ! [X29_29, Y30_30, Z31_31] : ((apart_point_and_line(X29_29, Y30_30) => (distinct_points(X29_29, Z31_31) | apart_point_and_line(Z31_31, Y30_30))))
% 64.12/21.43 -> [3083] (apart_point_and_line(skolem_Y3939, skolem_U4040) => (distinct_points(skolem_Y3939, skolem_Y3939) | apart_point_and_line(skolem_Y3939, skolem_U4040)))
% 64.12/21.43
% 64.12/21.43 [3083] BETA_IMPLY : (apart_point_and_line(skolem_Y3939, skolem_U4040) => (distinct_points(skolem_Y3939, skolem_Y3939) | apart_point_and_line(skolem_Y3939, skolem_U4040)))
% 64.12/21.43 -> [3086] ~apart_point_and_line(skolem_Y3939, skolem_U4040)
% 64.12/21.43 -> [3087] (distinct_points(skolem_Y3939, skolem_Y3939) | apart_point_and_line(skolem_Y3939, skolem_U4040))
% 64.12/21.43
% 64.12/21.43 [3086] CLOSURE : ~apart_point_and_line(skolem_Y3939, skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [3087] BETA_OR : (distinct_points(skolem_Y3939, skolem_Y3939) | apart_point_and_line(skolem_Y3939, skolem_U4040))
% 64.12/21.43 -> [3151] distinct_points(skolem_Y3939, skolem_Y3939)
% 64.12/21.43 -> [3152] apart_point_and_line(skolem_Y3939, skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [3151] CLOSURE : distinct_points(skolem_Y3939, skolem_Y3939)
% 64.12/21.43
% 64.12/21.43 [3152] GAMMA_FORALL : ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34))))
% 64.12/21.43 -> [3164] (apart_point_and_line(skolem_Y3939, skolem_U4040) => (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 64.12/21.43
% 64.12/21.43 [3164] BETA_IMPLY : (apart_point_and_line(skolem_Y3939, skolem_U4040) => (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 64.12/21.43 -> [3165] ~apart_point_and_line(skolem_Y3939, skolem_U4040)
% 64.12/21.43 -> [3166] (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43
% 64.12/21.43 [3165] CLOSURE : ~apart_point_and_line(skolem_Y3939, skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [3166] BETA_OR : (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [3178] distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43 -> [3179] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [3179] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [3178] CLOSURE : distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [2996] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 64.12/21.43
% 64.12/21.43 [7] ALPHA_NOT_NOT : ~~apart_point_and_line(skolem_X3838, skolem_U4040)
% 64.12/21.43 -> [9] apart_point_and_line(skolem_X3838, skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [9] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 64.12/21.43 -> [11] ~distinct_points(skolem_Y3939, skolem_Y3939)
% 64.12/21.43
% 64.12/21.43 [11] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 64.12/21.43 -> [13] ~distinct_lines(X6_0_1, X6_0_1)
% 64.12/21.43
% 64.12/21.43 [13] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 64.12/21.43 -> [15] ~convergent_lines(X7_0_2, X7_0_2)
% 64.12/21.43
% 64.12/21.43 [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))))
% 64.12/21.43 -> [17] (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939)))
% 64.12/21.43
% 64.12/21.43 [17] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939)))
% 64.12/21.43 -> [19] ~distinct_points(skolem_X3838, skolem_Y3939)
% 64.12/21.43 -> [20] (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [19] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 64.12/21.43
% 64.12/21.43 [20] BETA_OR : (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939))
% 64.12/21.43 -> [27] distinct_points(skolem_X3838, skolem_Y3939)
% 64.12/21.43 -> [28] distinct_points(skolem_Y3939, skolem_Y3939)
% 64.12/21.43
% 64.12/21.43 [28] CLOSURE : distinct_points(skolem_Y3939, skolem_Y3939)
% 64.12/21.43
% 64.12/21.43 [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))))
% 64.12/21.43 -> [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)))
% 64.12/21.43
% 64.12/21.43 [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)))
% 64.12/21.43 -> [32] ~distinct_lines(Z13_0_4, Z13_0_4)
% 64.12/21.43 -> [33] (distinct_lines(Z13_0_4, Z13_0_4) | distinct_lines(Z13_0_4, Z13_0_4))
% 64.12/21.43
% 64.12/21.43 [33] BETA_OR : (distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)) | distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [37] distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43 -> [38] distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [37] CLOSURE : distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [38] CLOSURE : distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [41] BETA_IMPLY : (convergent_lines(Z16_0_5, Z16_0_5) => (convergent_lines(Z16_0_5, Z16_0_5) | convergent_lines(Z16_0_5, Z16_0_5)))
% 64.12/21.43 -> [2854] ~convergent_lines(Z16_0_5, Z16_0_5)
% 64.12/21.43 -> [2855] (convergent_lines(Z16_0_5, Z16_0_5) | convergent_lines(Z16_0_5, Z16_0_5))
% 64.12/21.43
% 64.12/21.43 [2855] BETA_OR : (convergent_lines(Z16_0_5, Z16_0_5) | convergent_lines(Z16_0_5, Z16_0_5))
% 64.12/21.43 -> [2858] convergent_lines(Z16_0_5, Z16_0_5)
% 64.12/21.43 -> [2859] convergent_lines(Z16_0_5, Z16_0_5)
% 64.12/21.43
% 64.12/21.43 [2859] CLOSURE : convergent_lines(Z16_0_5, Z16_0_5)
% 64.12/21.43
% 64.12/21.43 [2858] CLOSURE : convergent_lines(Z16_0_5, Z16_0_5)
% 64.12/21.43
% 64.12/21.43 [2854] GAMMA_FORALL : ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18))))
% 64.12/21.43 -> [2870] (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43
% 64.12/21.43 [2870] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [2871] ~distinct_points(skolem_X3838, skolem_Y3939)
% 64.12/21.43 -> [2872] ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [2871] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 64.12/21.43
% 64.12/21.43 [2873] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [5934] ~distinct_points(skolem_X3838, skolem_Y3939)
% 64.12/21.43 -> [5935] ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [5934] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 64.12/21.43
% 64.12/21.43 [5936] BETA_IMPLY : (convergent_lines(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8) => ~apart_point_and_line(intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8), line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [6269] ~convergent_lines(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8)
% 64.12/21.43 -> [6270] ~apart_point_and_line(intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8), line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6270] GAMMA_FORALL : ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24)))
% 64.12/21.43 -> [6271] (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 64.12/21.43
% 64.12/21.43 [6271] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 64.12/21.43 -> [6272] ~convergent_lines(skolem_U4040, skolem_V4141)
% 64.12/21.43 -> [6273] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 64.12/21.43
% 64.12/21.43 [6272] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 64.12/21.43
% 64.12/21.43 [6274] BETA_IMPLY : ((distinct_points(skolem_X3838, intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8)) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))) => (((apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8), line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8), line_connecting(skolem_X3838, skolem_Y3939))))
% 64.12/21.43 -> [6337] ~(distinct_points(skolem_X3838, intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8)) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [6338] (((apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8), line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8), line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43
% 64.12/21.43 [6338] BETA_OR : (((apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8), line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8), line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [6341] ((apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8), line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [6342] apart_point_and_line(intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8), line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6341] BETA_OR : ((apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8), line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [6343] (apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [6344] apart_point_and_line(intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8), line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6344] CLOSURE : apart_point_and_line(intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8), line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6343] BETA_OR : (apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [6352] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43 -> [6353] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6352] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6353] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6342] CLOSURE : apart_point_and_line(intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8), line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6337] BETA_NOT_AND : ~(distinct_points(skolem_X3838, intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8)) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [6383] ~distinct_points(skolem_X3838, intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8))
% 64.12/21.43 -> [6384] ~distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6384] GAMMA_FORALL : ! [X29_29, Y30_30, Z31_31] : ((apart_point_and_line(X29_29, Y30_30) => (distinct_points(X29_29, Z31_31) | apart_point_and_line(Z31_31, Y30_30))))
% 64.12/21.43 -> [6386] (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, Z31_113_11) | apart_point_and_line(Z31_113_11, skolem_U4040)))
% 64.12/21.43
% 64.12/21.43 [6386] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, Z31_113_11) | apart_point_and_line(Z31_113_11, skolem_U4040)))
% 64.12/21.43 -> [6389] ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 64.12/21.43 -> [6390] (distinct_points(skolem_X3838, Z31_113_11) | apart_point_and_line(Z31_113_11, skolem_U4040))
% 64.12/21.43
% 64.12/21.43 [6389] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [6390] BETA_OR : (distinct_points(skolem_X3838, Z31_113_11) | apart_point_and_line(Z31_113_11, skolem_U4040))
% 64.12/21.43 -> [6395] distinct_points(skolem_X3838, Z31_113_11)
% 64.12/21.43 -> [6396] apart_point_and_line(Z31_113_11, skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [6395] GAMMA_FORALL : ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34))))
% 64.12/21.43 -> [6399] (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 64.12/21.43
% 64.12/21.43 [6399] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 64.12/21.43 -> [6400] ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 64.12/21.43 -> [6401] (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43
% 64.12/21.43 [6400] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [6401] BETA_OR : (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [6414] distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43 -> [6415] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6414] CLOSURE : distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6415] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6396] GAMMA_FORALL : ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34))))
% 64.12/21.43 -> [6402] (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 64.12/21.43
% 64.12/21.43 [6402] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 64.12/21.43 -> [6404] ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 64.12/21.43 -> [6405] (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43
% 64.12/21.43 [6404] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [6405] BETA_OR : (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [6416] distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43 -> [6417] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6416] CLOSURE : distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6417] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6383] GAMMA_FORALL : ! [X29_29, Y30_30, Z31_31] : ((apart_point_and_line(X29_29, Y30_30) => (distinct_points(X29_29, Z31_31) | apart_point_and_line(Z31_31, Y30_30))))
% 64.12/21.43 -> [6385] (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8)) | apart_point_and_line(intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8), skolem_U4040)))
% 64.12/21.43
% 64.12/21.43 [6385] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8)) | apart_point_and_line(intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8), skolem_U4040)))
% 64.12/21.43 -> [6387] ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 64.12/21.43 -> [6388] (distinct_points(skolem_X3838, intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8)) | apart_point_and_line(intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8), skolem_U4040))
% 64.12/21.43
% 64.12/21.43 [6387] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [6388] BETA_OR : (distinct_points(skolem_X3838, intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8)) | apart_point_and_line(intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8), skolem_U4040))
% 64.12/21.43 -> [6397] distinct_points(skolem_X3838, intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8))
% 64.12/21.43 -> [6398] apart_point_and_line(intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8), skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [6397] CLOSURE : distinct_points(skolem_X3838, intersection_point(line_connecting(skolem_X3838, skolem_Y3939), Y22_6_8))
% 64.12/21.43
% 64.12/21.43 [6398] GAMMA_FORALL : ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34))))
% 64.12/21.43 -> [6403] (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 64.12/21.43
% 64.12/21.43 [6403] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 64.12/21.43 -> [6406] ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 64.12/21.43 -> [6407] (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43
% 64.12/21.43 [6406] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [6407] BETA_OR : (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [6418] distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43 -> [6419] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6418] CLOSURE : distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6419] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6269] GAMMA_FORALL : ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24)))
% 64.12/21.43 -> [6420] (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 64.12/21.43
% 64.12/21.43 [6420] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 64.12/21.43 -> [6421] ~convergent_lines(skolem_U4040, skolem_V4141)
% 64.12/21.43 -> [6422] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 64.12/21.43
% 64.12/21.43 [6421] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 64.12/21.43
% 64.12/21.43 [6423] BETA_IMPLY : ((distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))) => (((apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 64.12/21.43 -> [6469] ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [6470] (((apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43
% 64.12/21.43 [6470] BETA_OR : (((apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [6473] ((apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [6474] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6474] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6473] BETA_OR : ((apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [6489] (apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [6490] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6489] BETA_OR : (apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [6491] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43 -> [6492] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6491] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6492] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6490] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6469] BETA_NOT_AND : ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [6511] ~distinct_points(skolem_X3838, skolem_Y3939)
% 64.12/21.43 -> [6512] ~distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6511] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 64.12/21.43
% 64.12/21.43 [6512] GAMMA_FORALL : ! [X29_29, Y30_30, Z31_31] : ((apart_point_and_line(X29_29, Y30_30) => (distinct_points(X29_29, Z31_31) | apart_point_and_line(Z31_31, Y30_30))))
% 64.12/21.43 -> [6513] (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, Z31_116_11) | apart_point_and_line(Z31_116_11, skolem_U4040)))
% 64.12/21.43
% 64.12/21.43 [6513] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, Z31_116_11) | apart_point_and_line(Z31_116_11, skolem_U4040)))
% 64.12/21.43 -> [6514] ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 64.12/21.43 -> [6515] (distinct_points(skolem_X3838, Z31_116_11) | apart_point_and_line(Z31_116_11, skolem_U4040))
% 64.12/21.43
% 64.12/21.43 [6514] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [6515] BETA_OR : (distinct_points(skolem_X3838, Z31_116_11) | apart_point_and_line(Z31_116_11, skolem_U4040))
% 64.12/21.43 -> [6518] distinct_points(skolem_X3838, Z31_116_11)
% 64.12/21.43 -> [6519] apart_point_and_line(Z31_116_11, skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [6518] GAMMA_FORALL : ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34))))
% 64.12/21.43 -> [6520] (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 64.12/21.43
% 64.12/21.43 [6520] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 64.12/21.43 -> [6522] ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 64.12/21.43 -> [6523] (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43
% 64.12/21.43 [6522] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [6523] BETA_OR : (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [6530] distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43 -> [6531] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6530] CLOSURE : distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6531] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6519] GAMMA_FORALL : ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34))))
% 64.12/21.43 -> [6521] (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 64.12/21.43
% 64.12/21.43 [6521] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 64.12/21.43 -> [6524] ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 64.12/21.43 -> [6525] (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43
% 64.12/21.43 [6524] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 64.12/21.43
% 64.12/21.43 [6525] BETA_OR : (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 64.12/21.43 -> [6532] distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43 -> [6533] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6532] CLOSURE : distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 [6533] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 64.12/21.43
% 64.12/21.43 % SZS output end Proof for theBenchmark.p
% 64.12/21.43 [21.084332s][1][Res] 209205 goroutines created
% 64.12/21.43 ==== Result ====
% 64.12/21.43 [21.084373s][1][Res] VALID
% 64.12/21.43 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------