TSTP Solution File: GEO176+1 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO176+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n011.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 180.35s 83.37s
% Output : Proof 180.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GEO176+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.11 % Command : goeland -dmt -presko -proof %s
% 0.11/0.32 % Computer : n011.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Aug 31 06:43:11 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 [DMT] DMT loaded with preskolemization
% 0.11/0.32 [EQ] equality loaded.
% 0.11/0.32 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.11/0.33 Conjecture not found
% 0.11/0.33 Start search
% 0.11/0.33 nb_step : 1 - limit : 15
% 0.11/0.33 Launch Gotab with destructive = true
% 180.35/83.36 % SZS output start Proof for theBenchmark.p
% 180.35/83.37 [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)) & (apart_point_and_line(X38_38, U40_40) | apart_point_and_line(X38_38, V41_41))) => distinct_points(X38_38, intersection_point(U40_40, V41_41)))))
% 180.35/83.37 -> [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)) & (apart_point_and_line(X38_38, U40_40) | apart_point_and_line(X38_38, V41_41))) => distinct_points(X38_38, intersection_point(U40_40, V41_41))))
% 180.35/83.37
% 180.35/83.37 [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)))))
% 180.35/83.37 -> [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))))
% 180.35/83.37
% 180.35/83.37 [2] DELTA_NOT_FORALL : ~! [X38_38, Y39_39, U40_40, V41_41] : ((((distinct_points(X38_38, Y39_39) & convergent_lines(U40_40, V41_41)) & (apart_point_and_line(X38_38, U40_40) | apart_point_and_line(X38_38, V41_41))) => distinct_points(X38_38, intersection_point(U40_40, V41_41))))
% 180.35/83.37 -> [3] ~(((distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)) & (apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_V4141))) => distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)))
% 180.35/83.37
% 180.35/83.37 [3] ALPHA_NOT_IMPLY : ~(((distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)) & (apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_V4141))) => distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)))
% 180.35/83.37 -> [4] ((distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)) & (apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_V4141))), ~distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 180.35/83.37
% 180.35/83.37 [4] ALPHA_AND : ((distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)) & (apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_V4141)))
% 180.35/83.37 -> [5] (distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)), (apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_V4141))
% 180.35/83.37
% 180.35/83.37 [5] ALPHA_AND : (distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141))
% 180.35/83.37 -> [6] distinct_points(skolem_X3838, skolem_Y3939), convergent_lines(skolem_U4040, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [6] BETA_OR : (apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_V4141))
% 180.35/83.37 -> [7] apart_point_and_line(skolem_X3838, skolem_U4040)
% 180.35/83.37 -> [8] apart_point_and_line(skolem_X3838, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [7] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 180.35/83.37 -> [9] ~distinct_points(skolem_Y3939, skolem_Y3939)
% 180.35/83.37
% 180.35/83.37 [9] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 180.35/83.37 -> [11] ~distinct_lines(X6_0_1, X6_0_1)
% 180.35/83.37
% 180.35/83.37 [11] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 180.35/83.37 -> [13] ~convergent_lines(skolem_U4040, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [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))))
% 180.35/83.37 -> [15] (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939)))
% 180.35/83.37
% 180.35/83.37 [15] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939)))
% 180.35/83.37 -> [17] ~distinct_points(skolem_X3838, skolem_Y3939)
% 180.35/83.37 -> [18] (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939))
% 180.35/83.37
% 180.35/83.37 [17] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 180.35/83.37
% 180.35/83.37 [18] BETA_OR : (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939))
% 180.35/83.37 -> [27] distinct_points(skolem_X3838, skolem_Y3939)
% 180.35/83.37 -> [28] distinct_points(skolem_Y3939, skolem_Y3939)
% 180.35/83.37
% 180.35/83.37 [28] CLOSURE : distinct_points(skolem_Y3939, skolem_Y3939)
% 180.35/83.37
% 180.35/83.37 [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))))
% 180.35/83.37 -> [30] (distinct_lines(Z13_1_4, Z13_1_4) => (distinct_lines(Z13_1_4, Z13_1_4) | distinct_lines(Z13_1_4, Z13_1_4)))
% 180.35/83.37
% 180.35/83.37 [30] BETA_IMPLY : (distinct_lines(Z13_1_4, Z13_1_4) => (distinct_lines(Z13_1_4, Z13_1_4) | distinct_lines(Z13_1_4, Z13_1_4)))
% 180.35/83.37 -> [33] ~distinct_lines(Z13_1_4, Z13_1_4)
% 180.35/83.37 -> [34] (distinct_lines(Z13_1_4, Z13_1_4) | distinct_lines(Z13_1_4, Z13_1_4))
% 180.35/83.37
% 180.35/83.37 [33] GAMMA_FORALL : ! [X14_14, Y15_15, Z16_16] : ((convergent_lines(X14_14, Y15_15) => (convergent_lines(X14_14, Z16_16) | convergent_lines(Y15_15, Z16_16))))
% 180.35/83.37 -> [39] (convergent_lines(skolem_U4040, skolem_V4141) => (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040)))
% 180.35/83.37
% 180.35/83.37 [39] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040)))
% 180.35/83.37 -> [40] ~convergent_lines(skolem_U4040, skolem_V4141)
% 180.35/83.37 -> [41] (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040))
% 180.35/83.37
% 180.35/83.37 [40] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [41] BETA_OR : (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040))
% 180.35/83.37 -> [49] convergent_lines(skolem_U4040, skolem_U4040)
% 180.35/83.37 -> [50] convergent_lines(skolem_V4141, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [49] CLOSURE : convergent_lines(skolem_U4040, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [50] GAMMA_FORALL : ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18))))
% 180.35/83.37 -> [53] (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 180.35/83.37
% 180.35/83.37 [53] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 180.35/83.37 -> [54] ~distinct_points(skolem_X3838, skolem_Y3939)
% 180.35/83.37 -> [55] ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 180.35/83.37
% 180.35/83.37 [54] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 180.35/83.37
% 180.35/83.37 [59] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 180.35/83.37 -> [1192] ~distinct_points(skolem_X3838, skolem_Y3939)
% 180.35/83.37 -> [1193] ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 180.35/83.37
% 180.35/83.37 [1192] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 180.35/83.37
% 180.35/83.37 [1193] GAMMA_FORALL : ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21)))
% 180.35/83.37 -> [1194] (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 180.35/83.37
% 180.35/83.37 [1194] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 180.35/83.37 -> [1195] ~convergent_lines(skolem_U4040, skolem_V4141)
% 180.35/83.37 -> [1196] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [1195] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [1196] GAMMA_FORALL : ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24)))
% 180.35/83.37 -> [1197] (convergent_lines(skolem_V4141, skolem_U4040) => ~apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040))
% 180.35/83.37
% 180.35/83.37 [1197] BETA_IMPLY : (convergent_lines(skolem_V4141, skolem_U4040) => ~apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040))
% 180.35/83.37 -> [1198] ~convergent_lines(skolem_V4141, skolem_U4040)
% 180.35/83.37 -> [1199] ~apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [1198] CLOSURE : ~convergent_lines(skolem_V4141, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [1200] BETA_IMPLY : ((distinct_points(intersection_point(skolem_V4141, skolem_U4040), intersection_point(skolem_V4141, skolem_U4040)) & distinct_lines(skolem_U4040, skolem_U4040)) => (((apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040) | apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040)) | apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040)) | apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040)))
% 180.35/83.37 -> [1312] ~(distinct_points(intersection_point(skolem_V4141, skolem_U4040), intersection_point(skolem_V4141, skolem_U4040)) & distinct_lines(skolem_U4040, skolem_U4040))
% 180.35/83.37 -> [1313] (((apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040) | apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040)) | apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040)) | apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040))
% 180.35/83.37
% 180.35/83.37 [1313] BETA_OR : (((apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040) | apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040)) | apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040)) | apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040))
% 180.35/83.37 -> [1316] ((apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040) | apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040)) | apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040))
% 180.35/83.37 -> [1317] apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [1317] CLOSURE : apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [1316] BETA_OR : ((apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040) | apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040)) | apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040))
% 180.35/83.37 -> [1339] (apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040) | apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040))
% 180.35/83.37 -> [1340] apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [1340] CLOSURE : apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [1339] BETA_OR : (apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040) | apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040))
% 180.35/83.37 -> [1389] apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040)
% 180.35/83.37 -> [1390] apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [1389] CLOSURE : apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [1390] CLOSURE : apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [1312] BETA_NOT_AND : ~(distinct_points(intersection_point(skolem_V4141, skolem_U4040), intersection_point(skolem_V4141, skolem_U4040)) & distinct_lines(skolem_U4040, skolem_U4040))
% 180.35/83.37 -> [1428] ~distinct_points(intersection_point(skolem_V4141, skolem_U4040), intersection_point(skolem_V4141, skolem_U4040))
% 180.35/83.37 -> [1429] ~distinct_lines(skolem_U4040, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [1428] 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))))
% 180.35/83.37 -> [1430] (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)))
% 180.35/83.37
% 180.35/83.37 [1430] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)))
% 180.35/83.37 -> [1432] ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 180.35/83.37 -> [1433] (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 180.35/83.37
% 180.35/83.37 [1432] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [1433] BETA_OR : (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 180.35/83.37 -> [1446] distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 180.35/83.37 -> [1447] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [1447] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [1446] CLOSURE : distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 180.35/83.37
% 180.35/83.37 [1429] 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))))
% 180.35/83.37 -> [1431] (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)))
% 180.35/83.37
% 180.35/83.37 [1431] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)))
% 180.35/83.37 -> [1434] ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 180.35/83.37 -> [1435] (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 180.35/83.37
% 180.35/83.37 [1434] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [1435] BETA_OR : (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 180.35/83.37 -> [1448] distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 180.35/83.37 -> [1449] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [1448] CLOSURE : distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 180.35/83.37
% 180.35/83.37 [1449] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [34] BETA_OR : (distinct_lines(Z13_1_4, Z13_1_4) | distinct_lines(Z13_1_4, Z13_1_4))
% 180.35/83.37 -> [1461] distinct_lines(Z13_1_4, Z13_1_4)
% 180.35/83.37 -> [1462] distinct_lines(Z13_1_4, Z13_1_4)
% 180.35/83.37
% 180.35/83.37 [1461] CLOSURE : distinct_lines(Z13_1_4, Z13_1_4)
% 180.35/83.37
% 180.35/83.37 [1462] CLOSURE : distinct_lines(Z13_1_4, Z13_1_4)
% 180.35/83.37
% 180.35/83.37 [8] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 180.35/83.37 -> [10] ~distinct_points(skolem_X3838, skolem_X3838)
% 180.35/83.37
% 180.35/83.37 [10] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 180.35/83.37 -> [12] ~distinct_lines(skolem_V4141, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [12] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 180.35/83.37 -> [14] ~convergent_lines(skolem_U4040, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [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))))
% 180.35/83.37 -> [16] (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_X3838) | distinct_points(skolem_Y3939, skolem_X3838)))
% 180.35/83.37
% 180.35/83.37 [16] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_X3838) | distinct_points(skolem_Y3939, skolem_X3838)))
% 180.35/83.37 -> [19] ~distinct_points(skolem_X3838, skolem_Y3939)
% 180.35/83.37 -> [20] (distinct_points(skolem_X3838, skolem_X3838) | distinct_points(skolem_Y3939, skolem_X3838))
% 180.35/83.37
% 180.35/83.37 [19] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 180.35/83.37
% 180.35/83.37 [20] BETA_OR : (distinct_points(skolem_X3838, skolem_X3838) | distinct_points(skolem_Y3939, skolem_X3838))
% 180.35/83.37 -> [25] distinct_points(skolem_X3838, skolem_X3838)
% 180.35/83.37 -> [26] distinct_points(skolem_Y3939, skolem_X3838)
% 180.35/83.37
% 180.35/83.37 [25] CLOSURE : distinct_points(skolem_X3838, skolem_X3838)
% 180.35/83.37
% 180.35/83.37 [26] 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))))
% 180.35/83.37 -> [29] (distinct_lines(skolem_V4141, skolem_U4040) => (distinct_lines(skolem_V4141, skolem_V4141) | distinct_lines(skolem_U4040, skolem_V4141)))
% 180.35/83.37
% 180.35/83.37 [29] BETA_IMPLY : (distinct_lines(skolem_V4141, skolem_U4040) => (distinct_lines(skolem_V4141, skolem_V4141) | distinct_lines(skolem_U4040, skolem_V4141)))
% 180.35/83.37 -> [31] ~distinct_lines(skolem_V4141, skolem_U4040)
% 180.35/83.37 -> [32] (distinct_lines(skolem_V4141, skolem_V4141) | distinct_lines(skolem_U4040, skolem_V4141))
% 180.35/83.37
% 180.35/83.37 [31] GAMMA_FORALL : ! [X14_14, Y15_15, Z16_16] : ((convergent_lines(X14_14, Y15_15) => (convergent_lines(X14_14, Z16_16) | convergent_lines(Y15_15, Z16_16))))
% 180.35/83.37 -> [42] (convergent_lines(skolem_U4040, skolem_V4141) => (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040)))
% 180.35/83.37
% 180.35/83.37 [42] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040)))
% 180.35/83.37 -> [43] ~convergent_lines(skolem_U4040, skolem_V4141)
% 180.35/83.37 -> [44] (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040))
% 180.35/83.37
% 180.35/83.37 [43] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [44] BETA_OR : (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040))
% 180.35/83.37 -> [51] convergent_lines(skolem_U4040, skolem_U4040)
% 180.35/83.37 -> [52] convergent_lines(skolem_V4141, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [51] CLOSURE : convergent_lines(skolem_U4040, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [52] GAMMA_FORALL : ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18))))
% 180.35/83.37 -> [56] (distinct_points(skolem_Y3939, skolem_X3838) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_Y3939, skolem_X3838)))
% 180.35/83.37
% 180.35/83.37 [56] BETA_IMPLY : (distinct_points(skolem_Y3939, skolem_X3838) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_Y3939, skolem_X3838)))
% 180.35/83.37 -> [57] ~distinct_points(skolem_Y3939, skolem_X3838)
% 180.35/83.37 -> [58] ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_Y3939, skolem_X3838))
% 180.35/83.37
% 180.35/83.37 [57] CLOSURE : ~distinct_points(skolem_Y3939, skolem_X3838)
% 180.35/83.37
% 180.35/83.37 [62] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 180.35/83.37 -> [1918] ~distinct_points(skolem_X3838, skolem_Y3939)
% 180.35/83.37 -> [1919] ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 180.35/83.37
% 180.35/83.37 [1918] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 180.35/83.37
% 180.35/83.37 [1920] BETA_IMPLY : (convergent_lines(skolem_V4141, skolem_U4040) => ~apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_V4141))
% 180.35/83.37 -> [2340] ~convergent_lines(skolem_V4141, skolem_U4040)
% 180.35/83.37 -> [2341] ~apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [2340] CLOSURE : ~convergent_lines(skolem_V4141, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [2342] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 180.35/83.37 -> [2807] ~convergent_lines(skolem_U4040, skolem_V4141)
% 180.35/83.37 -> [2808] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [2808] 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))))
% 180.35/83.37 -> [2809] ((distinct_points(skolem_Y3939, skolem_X3838) & distinct_lines(skolem_V4141, skolem_U4040)) => (((apart_point_and_line(skolem_Y3939, skolem_V4141) | apart_point_and_line(skolem_Y3939, skolem_U4040)) | apart_point_and_line(skolem_X3838, skolem_V4141)) | apart_point_and_line(skolem_X3838, skolem_U4040)))
% 180.35/83.37
% 180.35/83.37 [2809] BETA_IMPLY : ((distinct_points(skolem_Y3939, skolem_X3838) & distinct_lines(skolem_V4141, skolem_U4040)) => (((apart_point_and_line(skolem_Y3939, skolem_V4141) | apart_point_and_line(skolem_Y3939, skolem_U4040)) | apart_point_and_line(skolem_X3838, skolem_V4141)) | apart_point_and_line(skolem_X3838, skolem_U4040)))
% 180.35/83.37 -> [2810] ~(distinct_points(skolem_Y3939, skolem_X3838) & distinct_lines(skolem_V4141, skolem_U4040))
% 180.35/83.37 -> [2811] (((apart_point_and_line(skolem_Y3939, skolem_V4141) | apart_point_and_line(skolem_Y3939, skolem_U4040)) | apart_point_and_line(skolem_X3838, skolem_V4141)) | apart_point_and_line(skolem_X3838, skolem_U4040))
% 180.35/83.37
% 180.35/83.37 [2810] BETA_NOT_AND : ~(distinct_points(skolem_Y3939, skolem_X3838) & distinct_lines(skolem_V4141, skolem_U4040))
% 180.35/83.37 -> [2812] ~distinct_points(skolem_Y3939, skolem_X3838)
% 180.35/83.37 -> [2813] ~distinct_lines(skolem_V4141, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [2812] CLOSURE : ~distinct_points(skolem_Y3939, skolem_X3838)
% 180.35/83.37
% 180.35/83.37 [2818] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_V4141) => (distinct_points(skolem_X3838, skolem_X3838) | apart_point_and_line(skolem_X3838, skolem_V4141)))
% 180.35/83.37 -> [2918] ~apart_point_and_line(skolem_X3838, skolem_V4141)
% 180.35/83.37 -> [2919] (distinct_points(skolem_X3838, skolem_X3838) | apart_point_and_line(skolem_X3838, skolem_V4141))
% 180.35/83.37
% 180.35/83.37 [2919] BETA_OR : (distinct_points(skolem_X3838, skolem_X3838) | apart_point_and_line(skolem_X3838, skolem_V4141))
% 180.35/83.37 -> [2920] distinct_points(skolem_X3838, skolem_X3838)
% 180.35/83.37 -> [2921] apart_point_and_line(skolem_X3838, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [2920] CLOSURE : distinct_points(skolem_X3838, skolem_X3838)
% 180.35/83.37
% 180.35/83.37 [2921] 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))))
% 180.35/83.37 -> [2926] (apart_point_and_line(skolem_X3838, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_U4040)))
% 180.35/83.37
% 180.35/83.37 [2926] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_U4040)))
% 180.35/83.37 -> [2927] ~apart_point_and_line(skolem_X3838, skolem_V4141)
% 180.35/83.37 -> [2928] (distinct_lines(skolem_V4141, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_U4040))
% 180.35/83.37
% 180.35/83.37 [2927] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [2928] BETA_OR : (distinct_lines(skolem_V4141, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_U4040))
% 180.35/83.37 -> [2931] distinct_lines(skolem_V4141, skolem_U4040)
% 180.35/83.37 -> [2932] apart_point_and_line(skolem_X3838, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [2931] CLOSURE : distinct_lines(skolem_V4141, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [2933] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040)))
% 180.35/83.37 -> [2940] ~convergent_lines(skolem_U4040, skolem_V4141)
% 180.35/83.37 -> [2941] (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 180.35/83.37
% 180.35/83.37 [2940] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [2941] BETA_OR : (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 180.35/83.37 -> [2944] distinct_lines(skolem_V4141, skolem_U4040)
% 180.35/83.37 -> [2945] convergent_lines(skolem_U4040, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [2945] CLOSURE : convergent_lines(skolem_U4040, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [2944] CLOSURE : distinct_lines(skolem_V4141, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [2918] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [2811] BETA_OR : (((apart_point_and_line(skolem_Y3939, skolem_V4141) | apart_point_and_line(skolem_Y3939, skolem_U4040)) | apart_point_and_line(skolem_X3838, skolem_V4141)) | apart_point_and_line(skolem_X3838, skolem_U4040))
% 180.35/83.37 -> [2946] ((apart_point_and_line(skolem_Y3939, skolem_V4141) | apart_point_and_line(skolem_Y3939, skolem_U4040)) | apart_point_and_line(skolem_X3838, skolem_V4141))
% 180.35/83.37 -> [2947] apart_point_and_line(skolem_X3838, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [2947] 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))))
% 180.35/83.37 -> [2952] (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, skolem_X3838) | apart_point_and_line(skolem_X3838, skolem_U4040)))
% 180.35/83.37
% 180.35/83.37 [2952] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, skolem_X3838) | apart_point_and_line(skolem_X3838, skolem_U4040)))
% 180.35/83.37 -> [2953] ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 180.35/83.37 -> [2954] (distinct_points(skolem_X3838, skolem_X3838) | apart_point_and_line(skolem_X3838, skolem_U4040))
% 180.35/83.37
% 180.35/83.37 [2953] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [2954] BETA_OR : (distinct_points(skolem_X3838, skolem_X3838) | apart_point_and_line(skolem_X3838, skolem_U4040))
% 180.35/83.37 -> [3070] distinct_points(skolem_X3838, skolem_X3838)
% 180.35/83.37 -> [3071] apart_point_and_line(skolem_X3838, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [3070] CLOSURE : distinct_points(skolem_X3838, skolem_X3838)
% 180.35/83.37
% 180.35/83.37 [3071] 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))))
% 180.35/83.37 -> [3074] (apart_point_and_line(skolem_X3838, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_V4141) | apart_point_and_line(skolem_X3838, skolem_V4141)))
% 180.35/83.37
% 180.35/83.37 [3074] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_V4141) | apart_point_and_line(skolem_X3838, skolem_V4141)))
% 180.35/83.37 -> [3075] ~apart_point_and_line(skolem_X3838, skolem_V4141)
% 180.35/83.37 -> [3076] (distinct_lines(skolem_V4141, skolem_V4141) | apart_point_and_line(skolem_X3838, skolem_V4141))
% 180.35/83.37
% 180.35/83.37 [3075] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [3076] BETA_OR : (distinct_lines(skolem_V4141, skolem_V4141) | apart_point_and_line(skolem_X3838, skolem_V4141))
% 180.35/83.37 -> [3085] distinct_lines(skolem_V4141, skolem_V4141)
% 180.35/83.37 -> [3086] apart_point_and_line(skolem_X3838, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [3085] CLOSURE : distinct_lines(skolem_V4141, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [3087] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040)))
% 180.35/83.37 -> [3106] ~convergent_lines(skolem_U4040, skolem_V4141)
% 180.35/83.37 -> [3107] (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 180.35/83.37
% 180.35/83.37 [3106] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [3107] BETA_OR : (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 180.35/83.37 -> [3114] distinct_lines(skolem_V4141, skolem_U4040)
% 180.35/83.37 -> [3115] convergent_lines(skolem_U4040, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [3114] CLOSURE : distinct_lines(skolem_V4141, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [3115] CLOSURE : convergent_lines(skolem_U4040, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [2946] BETA_OR : ((apart_point_and_line(skolem_Y3939, skolem_V4141) | apart_point_and_line(skolem_Y3939, skolem_U4040)) | apart_point_and_line(skolem_X3838, skolem_V4141))
% 180.35/83.37 -> [3216] (apart_point_and_line(skolem_Y3939, skolem_V4141) | apart_point_and_line(skolem_Y3939, skolem_U4040))
% 180.35/83.37 -> [3217] apart_point_and_line(skolem_X3838, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [3217] 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))))
% 180.35/83.37 -> [3220] (apart_point_and_line(skolem_X3838, skolem_V4141) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)))
% 180.35/83.37
% 180.35/83.37 [3220] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_V4141) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)))
% 180.35/83.37 -> [3224] ~apart_point_and_line(skolem_X3838, skolem_V4141)
% 180.35/83.37 -> [3225] (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 180.35/83.37
% 180.35/83.37 [3224] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [3225] BETA_OR : (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 180.35/83.37 -> [3299] distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 180.35/83.37 -> [3300] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [3300] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [3299] CLOSURE : distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 180.35/83.37
% 180.35/83.37 [3216] BETA_OR : (apart_point_and_line(skolem_Y3939, skolem_V4141) | apart_point_and_line(skolem_Y3939, skolem_U4040))
% 180.35/83.37 -> [3218] apart_point_and_line(skolem_Y3939, skolem_V4141)
% 180.35/83.37 -> [3219] apart_point_and_line(skolem_Y3939, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [3218] 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))))
% 180.35/83.37 -> [3221] (apart_point_and_line(skolem_Y3939, skolem_V4141) => (distinct_points(skolem_Y3939, intersection_point(skolem_V4141, skolem_U4040)) | apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_V4141)))
% 180.35/83.37
% 180.35/83.37 [3221] BETA_IMPLY : (apart_point_and_line(skolem_Y3939, skolem_V4141) => (distinct_points(skolem_Y3939, intersection_point(skolem_V4141, skolem_U4040)) | apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_V4141)))
% 180.35/83.37 -> [3222] ~apart_point_and_line(skolem_Y3939, skolem_V4141)
% 180.35/83.37 -> [3223] (distinct_points(skolem_Y3939, intersection_point(skolem_V4141, skolem_U4040)) | apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_V4141))
% 180.35/83.37
% 180.35/83.37 [3222] CLOSURE : ~apart_point_and_line(skolem_Y3939, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [3223] BETA_OR : (distinct_points(skolem_Y3939, intersection_point(skolem_V4141, skolem_U4040)) | apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_V4141))
% 180.35/83.37 -> [3242] distinct_points(skolem_Y3939, intersection_point(skolem_V4141, skolem_U4040))
% 180.35/83.37 -> [3243] apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [3243] CLOSURE : apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [3242] 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))))
% 180.35/83.37 -> [3244] (apart_point_and_line(skolem_X3838, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_U4040)))
% 180.35/83.37
% 180.35/83.37 [3244] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_U4040)))
% 180.35/83.37 -> [3246] ~apart_point_and_line(skolem_X3838, skolem_V4141)
% 180.35/83.37 -> [3247] (distinct_lines(skolem_V4141, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_U4040))
% 180.35/83.37
% 180.35/83.37 [3246] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [3247] BETA_OR : (distinct_lines(skolem_V4141, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_U4040))
% 180.35/83.37 -> [3263] distinct_lines(skolem_V4141, skolem_U4040)
% 180.35/83.37 -> [3264] apart_point_and_line(skolem_X3838, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [3263] CLOSURE : distinct_lines(skolem_V4141, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [3272] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040)))
% 180.35/83.37 -> [3295] ~convergent_lines(skolem_U4040, skolem_V4141)
% 180.35/83.37 -> [3296] (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 180.35/83.37
% 180.35/83.37 [3296] BETA_OR : (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 180.35/83.37 -> [3297] distinct_lines(skolem_V4141, skolem_U4040)
% 180.35/83.37 -> [3298] convergent_lines(skolem_U4040, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [3298] CLOSURE : convergent_lines(skolem_U4040, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [3297] CLOSURE : distinct_lines(skolem_V4141, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [3295] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [3226] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_V4141) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)))
% 180.35/83.37 -> [3301] ~apart_point_and_line(skolem_X3838, skolem_V4141)
% 180.35/83.37 -> [3302] (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 180.35/83.37
% 180.35/83.37 [3302] BETA_OR : (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 180.35/83.37 -> [3303] distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 180.35/83.37 -> [3304] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [3303] CLOSURE : distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 180.35/83.37
% 180.35/83.37 [3304] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [3301] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [2807] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [32] BETA_OR : (distinct_lines(skolem_V4141, skolem_V4141) | distinct_lines(skolem_U4040, skolem_V4141))
% 180.35/83.37 -> [3305] distinct_lines(skolem_V4141, skolem_V4141)
% 180.35/83.37 -> [3306] distinct_lines(skolem_U4040, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [3305] CLOSURE : distinct_lines(skolem_V4141, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [3306] GAMMA_FORALL : ! [X14_14, Y15_15, Z16_16] : ((convergent_lines(X14_14, Y15_15) => (convergent_lines(X14_14, Z16_16) | convergent_lines(Y15_15, Z16_16))))
% 180.35/83.37 -> [3307] (convergent_lines(skolem_U4040, skolem_V4141) => (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040)))
% 180.35/83.37
% 180.35/83.37 [3307] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040)))
% 180.35/83.37 -> [3308] ~convergent_lines(skolem_U4040, skolem_V4141)
% 180.35/83.37 -> [3309] (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040))
% 180.35/83.37
% 180.35/83.37 [3308] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [3309] BETA_OR : (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040))
% 180.35/83.37 -> [3312] convergent_lines(skolem_U4040, skolem_U4040)
% 180.35/83.37 -> [3313] convergent_lines(skolem_V4141, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [3312] CLOSURE : convergent_lines(skolem_U4040, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [3314] BETA_IMPLY : (distinct_points(skolem_Y3939, skolem_X3838) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_Y3939, skolem_X3838)))
% 180.35/83.37 -> [7145] ~distinct_points(skolem_Y3939, skolem_X3838)
% 180.35/83.37 -> [7146] ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_Y3939, skolem_X3838))
% 180.35/83.37
% 180.35/83.37 [7145] CLOSURE : ~distinct_points(skolem_Y3939, skolem_X3838)
% 180.35/83.37
% 180.35/83.37 [7147] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 180.35/83.37 -> [14245] ~distinct_points(skolem_X3838, skolem_Y3939)
% 180.35/83.37 -> [14246] ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 180.35/83.37
% 180.35/83.37 [14245] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 180.35/83.37
% 180.35/83.37 [14247] BETA_IMPLY : (convergent_lines(skolem_V4141, skolem_U4040) => ~apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_V4141))
% 180.35/83.37 -> [16992] ~convergent_lines(skolem_V4141, skolem_U4040)
% 180.35/83.37 -> [16993] ~apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [16992] CLOSURE : ~convergent_lines(skolem_V4141, skolem_U4040)
% 180.35/83.37
% 180.35/83.37 [16993] GAMMA_FORALL : ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24)))
% 180.35/83.37 -> [16994] (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 180.35/83.37
% 180.35/83.37 [16994] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 180.35/83.37 -> [16995] ~convergent_lines(skolem_U4040, skolem_V4141)
% 180.35/83.37 -> [16996] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [16995] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [16997] BETA_IMPLY : ((distinct_points(skolem_Y3939, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), 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))) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 180.35/83.37 -> [18090] ~(distinct_points(skolem_Y3939, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 180.35/83.37 -> [18091] (((apart_point_and_line(skolem_Y3939, 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))) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 180.35/83.37
% 180.35/83.37 [18091] BETA_OR : (((apart_point_and_line(skolem_Y3939, 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))) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 180.35/83.37 -> [18094] ((apart_point_and_line(skolem_Y3939, 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)))
% 180.35/83.37 -> [18095] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 180.35/83.37
% 180.35/83.37 [18094] BETA_OR : ((apart_point_and_line(skolem_Y3939, 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)))
% 180.35/83.37 -> [18096] (apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 180.35/83.37 -> [18097] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 180.35/83.37
% 180.35/83.37 [18097] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 180.35/83.37
% 180.35/83.37 [18096] BETA_OR : (apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 180.35/83.37 -> [18100] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 180.35/83.37 -> [18101] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 180.35/83.37
% 180.35/83.37 [18101] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 180.35/83.37
% 180.35/83.37 [18100] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 180.35/83.37
% 180.35/83.37 [18095] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 180.35/83.37
% 180.35/83.37 [18090] BETA_NOT_AND : ~(distinct_points(skolem_Y3939, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 180.35/83.37 -> [18102] ~distinct_points(skolem_Y3939, skolem_Y3939)
% 180.35/83.37 -> [18103] ~distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))
% 180.35/83.37
% 180.35/83.37 [18102] 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))))
% 180.35/83.37 -> [18104] (apart_point_and_line(skolem_X3838, skolem_V4141) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)))
% 180.35/83.37
% 180.35/83.37 [18104] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_V4141) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)))
% 180.35/83.37 -> [18106] ~apart_point_and_line(skolem_X3838, skolem_V4141)
% 180.35/83.37 -> [18107] (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 180.35/83.37
% 180.35/83.37 [18106] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [18107] BETA_OR : (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 180.35/83.37 -> [18114] distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 180.35/83.37 -> [18115] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [18114] CLOSURE : distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 180.35/83.37
% 180.35/83.37 [18115] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [18103] 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))))
% 180.35/83.37 -> [18105] (apart_point_and_line(skolem_X3838, skolem_V4141) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)))
% 180.35/83.37
% 180.35/83.37 [18105] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_V4141) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)))
% 180.35/83.37 -> [18108] ~apart_point_and_line(skolem_X3838, skolem_V4141)
% 180.35/83.37 -> [18109] (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 180.35/83.37
% 180.35/83.37 [18108] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [18109] BETA_OR : (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 180.35/83.37 -> [18116] distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 180.35/83.37 -> [18117] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 180.35/83.37
% 180.35/83.37 [18116] CLOSURE : distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 180.35/83.37
% 180.35/83.37 [18117] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 180.35/83.37
% 180.35/83.37 % SZS output end Proof for theBenchmark.p
% 180.35/83.37 [83.043658s][1][Res] 712800 goroutines created
% 180.35/83.37 ==== Result ====
% 180.35/83.37 [83.043696s][1][Res] VALID
% 180.35/83.37 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------