TSTP Solution File: GEO175+1 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO175+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 15:18:13 EDT 2022
% Result : Theorem 128.32s 48.80s
% Output : Proof 128.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GEO175+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.11 % Command : goeland -dmt -presko -proof %s
% 0.11/0.31 % Computer : n002.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Wed Aug 31 06:57:44 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 [0.000092s][1][MAIN] Problem : theBenchmark.p
% 0.11/0.32 Conjecture not found
% 0.11/0.32 Start search
% 0.11/0.32 nb_step : 1 - limit : 15
% 0.11/0.32 Launch Gotab with destructive = true
% 128.32/48.79 % SZS output start Proof for theBenchmark.p
% 128.32/48.80 [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_points(X38_38, intersection_point(U40_40, V41_41))) => (apart_point_and_line(X38_38, U40_40) | apart_point_and_line(X38_38, V41_41)))))
% 128.32/48.80 -> [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_points(X38_38, intersection_point(U40_40, V41_41))) => (apart_point_and_line(X38_38, U40_40) | apart_point_and_line(X38_38, V41_41))))
% 128.32/48.80
% 128.32/48.80 [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)))))
% 128.32/48.80 -> [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))))
% 128.32/48.80
% 128.32/48.80 [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_points(X38_38, intersection_point(U40_40, V41_41))) => (apart_point_and_line(X38_38, U40_40) | apart_point_and_line(X38_38, V41_41))))
% 128.32/48.80 -> [3] ~(((distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)) & distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))) => (apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_V4141)))
% 128.32/48.80
% 128.32/48.80 [3] ALPHA_NOT_IMPLY : ~(((distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)) & distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))) => (apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_V4141)))
% 128.32/48.80 -> [4] ((distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)) & distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))), ~(apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_V4141))
% 128.32/48.80
% 128.32/48.80 [4] ALPHA_AND : ((distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)) & distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)))
% 128.32/48.80 -> [5] (distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)), distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 128.32/48.80
% 128.32/48.80 [5] ALPHA_NOT_OR : ~(apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_V4141))
% 128.32/48.80 -> [6] ~apart_point_and_line(skolem_X3838, skolem_U4040), ~apart_point_and_line(skolem_X3838, skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [6] ALPHA_AND : (distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141))
% 128.32/48.80 -> [7] distinct_points(skolem_X3838, skolem_Y3939), convergent_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [7] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 128.32/48.80 -> [8] ~distinct_points(skolem_Y3939, skolem_Y3939)
% 128.32/48.80
% 128.32/48.80 [8] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 128.32/48.80 -> [9] ~distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))
% 128.32/48.80
% 128.32/48.80 [9] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 128.32/48.80 -> [10] ~convergent_lines(skolem_U4040, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [10] GAMMA_FORALL : ! [X8_8, Y9_9, Z10_10] : ((distinct_points(X8_8, Y9_9) => (distinct_points(X8_8, Z10_10) | distinct_points(Y9_9, Z10_10))))
% 128.32/48.80 -> [11] (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939)))
% 128.32/48.80
% 128.32/48.80 [11] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939)))
% 128.32/48.80 -> [12] ~distinct_points(skolem_X3838, skolem_Y3939)
% 128.32/48.80 -> [13] (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939))
% 128.32/48.80
% 128.32/48.80 [12] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 128.32/48.80
% 128.32/48.80 [13] BETA_OR : (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939))
% 128.32/48.80 -> [16] distinct_points(skolem_X3838, skolem_Y3939)
% 128.32/48.80 -> [17] distinct_points(skolem_Y3939, skolem_Y3939)
% 128.32/48.80
% 128.32/48.80 [17] CLOSURE : distinct_points(skolem_Y3939, skolem_Y3939)
% 128.32/48.80
% 128.32/48.80 [16] GAMMA_FORALL : ! [X11_11, Y12_12, Z13_13] : ((distinct_lines(X11_11, Y12_12) => (distinct_lines(X11_11, Z13_13) | distinct_lines(Y12_12, Z13_13))))
% 128.32/48.80 -> [18] (distinct_lines(skolem_V4141, skolem_U4040) => (distinct_lines(skolem_V4141, skolem_V4141) | distinct_lines(skolem_U4040, skolem_V4141)))
% 128.32/48.80
% 128.32/48.80 [18] BETA_IMPLY : (distinct_lines(skolem_V4141, skolem_U4040) => (distinct_lines(skolem_V4141, skolem_V4141) | distinct_lines(skolem_U4040, skolem_V4141)))
% 128.32/48.80 -> [19] ~distinct_lines(skolem_V4141, skolem_U4040)
% 128.32/48.80 -> [20] (distinct_lines(skolem_V4141, skolem_V4141) | distinct_lines(skolem_U4040, skolem_V4141))
% 128.32/48.80
% 128.32/48.80 [19] GAMMA_FORALL : ! [X14_14, Y15_15, Z16_16] : ((convergent_lines(X14_14, Y15_15) => (convergent_lines(X14_14, Z16_16) | convergent_lines(Y15_15, Z16_16))))
% 128.32/48.80 -> [23] (convergent_lines(skolem_U4040, skolem_V4141) => (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040)))
% 128.32/48.80
% 128.32/48.80 [23] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040)))
% 128.32/48.80 -> [24] ~convergent_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80 -> [25] (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040))
% 128.32/48.80
% 128.32/48.80 [24] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [25] BETA_OR : (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040))
% 128.32/48.80 -> [28] convergent_lines(skolem_U4040, skolem_U4040)
% 128.32/48.80 -> [29] convergent_lines(skolem_V4141, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [28] CLOSURE : convergent_lines(skolem_U4040, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [29] GAMMA_FORALL : ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18))))
% 128.32/48.80 -> [88] (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 128.32/48.80
% 128.32/48.80 [88] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 128.32/48.80 -> [89] ~distinct_points(skolem_X3838, skolem_Y3939)
% 128.32/48.80 -> [90] ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 128.32/48.80
% 128.32/48.80 [89] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 128.32/48.80
% 128.32/48.80 [91] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 128.32/48.80 -> [1901] ~distinct_points(skolem_X3838, skolem_Y3939)
% 128.32/48.80 -> [1902] ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 128.32/48.80
% 128.32/48.80 [1902] GAMMA_FORALL : ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21)))
% 128.32/48.80 -> [1903] (convergent_lines(skolem_V4141, skolem_U4040) => ~apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_V4141))
% 128.32/48.80
% 128.32/48.80 [1903] BETA_IMPLY : (convergent_lines(skolem_V4141, skolem_U4040) => ~apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_V4141))
% 128.32/48.80 -> [1904] ~convergent_lines(skolem_V4141, skolem_U4040)
% 128.32/48.80 -> [1905] ~apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [1904] CLOSURE : ~convergent_lines(skolem_V4141, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [1906] BETA_IMPLY : (convergent_lines(skolem_V4141, skolem_U4040) => ~apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040))
% 128.32/48.80 -> [2508] ~convergent_lines(skolem_V4141, skolem_U4040)
% 128.32/48.80 -> [2509] ~apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [2509] 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))))
% 128.32/48.80 -> [2510] ((distinct_points(skolem_X3838, skolem_X3838) & 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_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 128.32/48.80
% 128.32/48.80 [2510] BETA_IMPLY : ((distinct_points(skolem_X3838, skolem_X3838) & 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_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 128.32/48.80 -> [2511] ~(distinct_points(skolem_X3838, skolem_X3838) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 128.32/48.80 -> [2512] (((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_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 128.32/48.80
% 128.32/48.80 [2512] 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_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 128.32/48.80 -> [2515] ((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_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 128.32/48.80 -> [2516] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 128.32/48.80
% 128.32/48.80 [2516] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 128.32/48.80
% 128.32/48.80 [2515] 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_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 128.32/48.80 -> [2556] (apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 128.32/48.80 -> [2557] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 128.32/48.80
% 128.32/48.80 [2557] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 128.32/48.80
% 128.32/48.80 [2556] 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)))
% 128.32/48.80 -> [2599] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 128.32/48.80 -> [2600] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 128.32/48.80
% 128.32/48.80 [2599] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 128.32/48.80
% 128.32/48.80 [2600] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 128.32/48.80
% 128.32/48.80 [2511] BETA_NOT_AND : ~(distinct_points(skolem_X3838, skolem_X3838) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 128.32/48.80 -> [2601] ~distinct_points(skolem_X3838, skolem_X3838)
% 128.32/48.80 -> [2602] ~distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))
% 128.32/48.80
% 128.32/48.80 [2602] 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))))
% 128.32/48.80 -> [2604] (apart_point_and_line(skolem_Y3939, skolem_U4040) => (distinct_points(skolem_Y3939, skolem_Y3939) | apart_point_and_line(skolem_Y3939, skolem_U4040)))
% 128.32/48.80
% 128.32/48.80 [2604] BETA_IMPLY : (apart_point_and_line(skolem_Y3939, skolem_U4040) => (distinct_points(skolem_Y3939, skolem_Y3939) | apart_point_and_line(skolem_Y3939, skolem_U4040)))
% 128.32/48.80 -> [2607] ~apart_point_and_line(skolem_Y3939, skolem_U4040)
% 128.32/48.80 -> [2608] (distinct_points(skolem_Y3939, skolem_Y3939) | apart_point_and_line(skolem_Y3939, skolem_U4040))
% 128.32/48.80
% 128.32/48.80 [2607] 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))))
% 128.32/48.80 -> [2613] (apart_point_and_line(X32_77_12, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | apart_point_and_line(X32_77_12, skolem_U4040)))
% 128.32/48.80
% 128.32/48.80 [2613] BETA_IMPLY : (apart_point_and_line(X32_77_12, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | apart_point_and_line(X32_77_12, skolem_U4040)))
% 128.32/48.80 -> [2614] ~apart_point_and_line(X32_77_12, skolem_V4141)
% 128.32/48.80 -> [2615] (distinct_lines(skolem_V4141, skolem_U4040) | apart_point_and_line(X32_77_12, skolem_U4040))
% 128.32/48.80
% 128.32/48.80 [2614] GAMMA_FORALL : ! [X35_35, Y36_36, Z37_37] : ((convergent_lines(X35_35, Y36_36) => (distinct_lines(Y36_36, Z37_37) | convergent_lines(X35_35, Z37_37))))
% 128.32/48.80 -> [2623] (convergent_lines(skolem_U4040, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040)))
% 128.32/48.80
% 128.32/48.80 [2623] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040)))
% 128.32/48.80 -> [2625] ~convergent_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80 -> [2626] (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 128.32/48.80
% 128.32/48.80 [2625] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [2626] BETA_OR : (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 128.32/48.80 -> [2663] distinct_lines(skolem_V4141, skolem_U4040)
% 128.32/48.80 -> [2664] convergent_lines(skolem_U4040, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [2663] CLOSURE : distinct_lines(skolem_V4141, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [2664] CLOSURE : convergent_lines(skolem_U4040, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [2615] BETA_OR : (distinct_lines(skolem_V4141, skolem_U4040) | apart_point_and_line(X32_77_12, skolem_U4040))
% 128.32/48.80 -> [2718] distinct_lines(skolem_V4141, skolem_U4040)
% 128.32/48.80 -> [2719] apart_point_and_line(X32_77_12, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [2718] CLOSURE : distinct_lines(skolem_V4141, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [2719] CLOSURE : apart_point_and_line(X32_77_12, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [2608] BETA_OR : (distinct_points(skolem_Y3939, skolem_Y3939) | apart_point_and_line(skolem_Y3939, skolem_U4040))
% 128.32/48.80 -> [2726] distinct_points(skolem_Y3939, skolem_Y3939)
% 128.32/48.80 -> [2727] apart_point_and_line(skolem_Y3939, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [2726] CLOSURE : distinct_points(skolem_Y3939, skolem_Y3939)
% 128.32/48.80
% 128.32/48.80 [2727] 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))))
% 128.32/48.80 -> [2732] (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))))
% 128.32/48.80
% 128.32/48.80 [2732] 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))))
% 128.32/48.80 -> [2733] ~apart_point_and_line(skolem_Y3939, skolem_U4040)
% 128.32/48.80 -> [2734] (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 128.32/48.80
% 128.32/48.80 [2733] CLOSURE : ~apart_point_and_line(skolem_Y3939, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [2734] BETA_OR : (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 128.32/48.80 -> [2743] distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 128.32/48.80 -> [2744] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 128.32/48.80
% 128.32/48.80 [2744] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 128.32/48.80
% 128.32/48.80 [2743] GAMMA_FORALL : ! [X35_35, Y36_36, Z37_37] : ((convergent_lines(X35_35, Y36_36) => (distinct_lines(Y36_36, Z37_37) | convergent_lines(X35_35, Z37_37))))
% 128.32/48.80 -> [2747] (convergent_lines(skolem_U4040, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040)))
% 128.32/48.80
% 128.32/48.80 [2747] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040)))
% 128.32/48.80 -> [2749] ~convergent_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80 -> [2750] (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 128.32/48.80
% 128.32/48.80 [2749] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [2750] BETA_OR : (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 128.32/48.80 -> [2766] distinct_lines(skolem_V4141, skolem_U4040)
% 128.32/48.80 -> [2767] convergent_lines(skolem_U4040, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [2767] CLOSURE : convergent_lines(skolem_U4040, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [2766] CLOSURE : distinct_lines(skolem_V4141, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [2603] BETA_IMPLY : (apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_points(skolem_Y3939, skolem_Y3939) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 128.32/48.80 -> [2768] ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 128.32/48.80 -> [2769] (distinct_points(skolem_Y3939, skolem_Y3939) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 128.32/48.80
% 128.32/48.80 [2768] 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))))
% 128.32/48.80 -> [2772] (apart_point_and_line(X32_81_12, Z34_81_12) => (distinct_lines(Z34_81_12, Z34_81_12) | apart_point_and_line(X32_81_12, Z34_81_12)))
% 128.32/48.80
% 128.32/48.80 [2772] BETA_IMPLY : (apart_point_and_line(X32_81_12, Z34_81_12) => (distinct_lines(Z34_81_12, Z34_81_12) | apart_point_and_line(X32_81_12, Z34_81_12)))
% 128.32/48.80 -> [2773] ~apart_point_and_line(X32_81_12, Z34_81_12)
% 128.32/48.80 -> [2774] (distinct_lines(Z34_81_12, Z34_81_12) | apart_point_and_line(X32_81_12, Z34_81_12))
% 128.32/48.80
% 128.32/48.80 [2774] BETA_OR : (distinct_lines(Z34_81_12, Z34_81_12) | apart_point_and_line(X32_81_12, Z34_81_12))
% 128.32/48.80 -> [2775] distinct_lines(Z34_81_12, Z34_81_12)
% 128.32/48.80 -> [2776] apart_point_and_line(X32_81_12, Z34_81_12)
% 128.32/48.80
% 128.32/48.80 [2775] CLOSURE : distinct_lines(Z34_81_12, Z34_81_12)
% 128.32/48.80
% 128.32/48.80 [2776] CLOSURE : apart_point_and_line(X32_81_12, Z34_81_12)
% 128.32/48.80
% 128.32/48.80 [2773] GAMMA_FORALL : ! [X35_35, Y36_36, Z37_37] : ((convergent_lines(X35_35, Y36_36) => (distinct_lines(Y36_36, Z37_37) | convergent_lines(X35_35, Z37_37))))
% 128.32/48.80 -> [2777] (convergent_lines(skolem_U4040, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040)))
% 128.32/48.80
% 128.32/48.80 [2777] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040)))
% 128.32/48.80 -> [2778] ~convergent_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80 -> [2779] (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 128.32/48.80
% 128.32/48.80 [2778] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [2779] BETA_OR : (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 128.32/48.80 -> [2786] distinct_lines(skolem_V4141, skolem_U4040)
% 128.32/48.80 -> [2787] convergent_lines(skolem_U4040, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [2786] CLOSURE : distinct_lines(skolem_V4141, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [2787] CLOSURE : convergent_lines(skolem_U4040, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [2769] BETA_OR : (distinct_points(skolem_Y3939, skolem_Y3939) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 128.32/48.80 -> [2788] distinct_points(skolem_Y3939, skolem_Y3939)
% 128.32/48.80 -> [2789] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 128.32/48.80
% 128.32/48.80 [2788] CLOSURE : distinct_points(skolem_Y3939, skolem_Y3939)
% 128.32/48.80
% 128.32/48.80 [2789] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 128.32/48.80
% 128.32/48.80 [2508] CLOSURE : ~convergent_lines(skolem_V4141, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [1901] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 128.32/48.80
% 128.32/48.80 [20] BETA_OR : (distinct_lines(skolem_V4141, skolem_V4141) | distinct_lines(skolem_U4040, skolem_V4141))
% 128.32/48.80 -> [2790] distinct_lines(skolem_V4141, skolem_V4141)
% 128.32/48.80 -> [2791] distinct_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [2790] 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))))
% 128.32/48.80 -> [2792] (convergent_lines(skolem_U4040, skolem_V4141) => (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040)))
% 128.32/48.80
% 128.32/48.80 [2792] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040)))
% 128.32/48.80 -> [2794] ~convergent_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80 -> [2795] (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040))
% 128.32/48.80
% 128.32/48.80 [2794] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [2795] BETA_OR : (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040))
% 128.32/48.80 -> [2802] convergent_lines(skolem_U4040, skolem_U4040)
% 128.32/48.80 -> [2803] convergent_lines(skolem_V4141, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [2803] GAMMA_FORALL : ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18))))
% 128.32/48.80 -> [2806] (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 128.32/48.80
% 128.32/48.80 [2806] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 128.32/48.80 -> [2807] ~distinct_points(skolem_X3838, skolem_Y3939)
% 128.32/48.80 -> [2808] ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 128.32/48.80
% 128.32/48.80 [2807] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 128.32/48.80
% 128.32/48.80 [2812] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 128.32/48.80 -> [4481] ~distinct_points(skolem_X3838, skolem_Y3939)
% 128.32/48.80 -> [4482] ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 128.32/48.80
% 128.32/48.80 [4482] GAMMA_FORALL : ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21)))
% 128.32/48.80 -> [4484] (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 128.32/48.80
% 128.32/48.80 [4484] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 128.32/48.80 -> [4486] ~convergent_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80 -> [4487] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [4486] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [4488] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 128.32/48.80 -> [6266] ~convergent_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80 -> [6267] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [6266] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [6268] BETA_IMPLY : ((distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) & distinct_lines(skolem_V4141, skolem_U4040)) => (((apart_point_and_line(skolem_X3838, skolem_V4141) | apart_point_and_line(skolem_X3838, 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)))
% 128.32/48.80 -> [6409] ~(distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) & distinct_lines(skolem_V4141, skolem_U4040))
% 128.32/48.80 -> [6410] (((apart_point_and_line(skolem_X3838, skolem_V4141) | apart_point_and_line(skolem_X3838, 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))
% 128.32/48.80
% 128.32/48.80 [6409] BETA_NOT_AND : ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(skolem_V4141, skolem_U4040))
% 128.32/48.80 -> [6411] ~distinct_points(skolem_X3838, skolem_Y3939)
% 128.32/48.80 -> [6412] ~distinct_lines(skolem_V4141, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [6412] CLOSURE : ~distinct_lines(skolem_V4141, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [6411] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 128.32/48.80
% 128.32/48.80 [6410] BETA_OR : (((apart_point_and_line(skolem_X3838, skolem_V4141) | apart_point_and_line(skolem_X3838, 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))
% 128.32/48.80 -> [6802] ((apart_point_and_line(skolem_X3838, skolem_V4141) | apart_point_and_line(skolem_X3838, skolem_U4040)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 128.32/48.80 -> [6803] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [6803] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [6802] BETA_OR : ((apart_point_and_line(skolem_X3838, skolem_V4141) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_X3838))) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 128.32/48.80 -> [6806] (apart_point_and_line(skolem_X3838, skolem_V4141) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_X3838)))
% 128.32/48.80 -> [6807] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [6807] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [6806] BETA_OR : (apart_point_and_line(skolem_X3838, skolem_V4141) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_X3838)))
% 128.32/48.80 -> [6808] apart_point_and_line(skolem_X3838, skolem_V4141)
% 128.32/48.80 -> [6809] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_X3838))
% 128.32/48.80
% 128.32/48.80 [6808] CLOSURE : apart_point_and_line(skolem_X3838, skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [6809] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_X3838))
% 128.32/48.80
% 128.32/48.80 [4481] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 128.32/48.80
% 128.32/48.80 [2802] CLOSURE : convergent_lines(skolem_U4040, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [2793] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040)))
% 128.32/48.80 -> [11615] ~convergent_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80 -> [11616] (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040))
% 128.32/48.80
% 128.32/48.80 [11615] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [11616] BETA_OR : (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040))
% 128.32/48.80 -> [11619] convergent_lines(skolem_U4040, skolem_U4040)
% 128.32/48.80 -> [11620] convergent_lines(skolem_V4141, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [11619] CLOSURE : convergent_lines(skolem_U4040, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [11620] GAMMA_FORALL : ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18))))
% 128.32/48.80 -> [11621] (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 128.32/48.80
% 128.32/48.80 [11621] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 128.32/48.80 -> [11622] ~distinct_points(skolem_X3838, skolem_Y3939)
% 128.32/48.80 -> [11623] ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 128.32/48.80
% 128.32/48.80 [11622] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 128.32/48.80
% 128.32/48.80 [11623] GAMMA_FORALL : ! [X19_19, Y20_20] : ((distinct_points(X19_19, Y20_20) => ~apart_point_and_line(Y20_20, line_connecting(X19_19, Y20_20))))
% 128.32/48.80 -> [11624] (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 128.32/48.80
% 128.32/48.80 [11624] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 128.32/48.80 -> [11625] ~distinct_points(skolem_X3838, skolem_Y3939)
% 128.32/48.80 -> [11626] ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 128.32/48.80
% 128.32/48.80 [11625] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 128.32/48.80
% 128.32/48.80 [11626] GAMMA_FORALL : ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21)))
% 128.32/48.80 -> [11627] (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 128.32/48.80
% 128.32/48.80 [11627] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 128.32/48.80 -> [11628] ~convergent_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80 -> [11629] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [11628] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [11629] GAMMA_FORALL : ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24)))
% 128.32/48.80 -> [11630] (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 128.32/48.80
% 128.32/48.80 [11630] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 128.32/48.80 -> [11631] ~convergent_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80 -> [11632] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [11632] 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))))
% 128.32/48.80 -> [11633] ((distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) & distinct_lines(skolem_U4040, skolem_V4141)) => (((apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, 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)))
% 128.32/48.80
% 128.32/48.80 [11633] BETA_IMPLY : ((distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) & distinct_lines(skolem_U4040, skolem_V4141)) => (((apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, 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)))
% 128.32/48.80 -> [11634] ~(distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) & distinct_lines(skolem_U4040, skolem_V4141))
% 128.32/48.80 -> [11635] (((apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, 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))
% 128.32/48.80
% 128.32/48.80 [11634] BETA_NOT_AND : ~(distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) & distinct_lines(skolem_U4040, skolem_V4141))
% 128.32/48.80 -> [11636] ~distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 128.32/48.80 -> [11637] ~distinct_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [11636] CLOSURE : ~distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 128.32/48.80
% 128.32/48.80 [11637] CLOSURE : ~distinct_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [11635] BETA_OR : (((apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, 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))
% 128.32/48.80 -> [11644] ((apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 128.32/48.80 -> [11645] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [11644] BETA_OR : ((apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 128.32/48.80 -> [11646] (apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_V4141))
% 128.32/48.80 -> [11647] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [11647] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [11646] BETA_OR : (apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_V4141))
% 128.32/48.80 -> [11648] apart_point_and_line(skolem_X3838, skolem_U4040)
% 128.32/48.80 -> [11649] apart_point_and_line(skolem_X3838, skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [11648] CLOSURE : apart_point_and_line(skolem_X3838, skolem_U4040)
% 128.32/48.80
% 128.32/48.80 [11649] CLOSURE : apart_point_and_line(skolem_X3838, skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [11645] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 128.32/48.80
% 128.32/48.80 [11631] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 128.32/48.80
% 128.32/48.80 % SZS output end Proof for theBenchmark.p
% 128.32/48.80 [48.477810s][1][Res] 365053 goroutines created
% 128.32/48.80 ==== Result ====
% 128.32/48.80 [48.477848s][1][Res] VALID
% 128.32/48.80 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------