TSTP Solution File: GEO186+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO186+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 15:18:17 EDT 2022
% Result : Theorem 119.12s 42.38s
% Output : Proof 119.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO186+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.11 % Command : goeland -dmt -presko -proof %s
% 0.10/0.31 % Computer : n001.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Aug 31 07:10:18 EDT 2022
% 0.10/0.32 % CPUTime :
% 0.10/0.32 [DMT] DMT loaded with preskolemization
% 0.10/0.32 [EQ] equality loaded.
% 0.10/0.32 [0.000037s][1][MAIN] Problem : theBenchmark.p
% 0.10/0.32 Conjecture not found
% 0.10/0.32 Start search
% 0.10/0.32 nb_step : 1 - limit : 15
% 0.10/0.32 Launch Gotab with destructive = true
% 119.02/42.37 % SZS output start Proof for theBenchmark.p
% 119.12/42.37 [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)))))
% 119.12/42.37 -> [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))))
% 119.12/42.37
% 119.12/42.37 [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)))))
% 119.12/42.37 -> [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))))
% 119.12/42.37
% 119.12/42.37 [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))))
% 119.12/42.37 -> [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)))
% 119.12/42.37
% 119.12/42.37 [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)))
% 119.12/42.37 -> [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))
% 119.12/42.37
% 119.12/42.37 [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))
% 119.12/42.37 -> [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)
% 119.12/42.37
% 119.12/42.37 [5] ALPHA_NOT_NOT : ~~distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 119.12/42.37 -> [6] distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 119.12/42.37
% 119.12/42.37 [6] ALPHA_AND : ((distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)) & ~apart_point_and_line(skolem_X3838, skolem_U4040))
% 119.12/42.37 -> [7] (distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)), ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 119.12/42.37
% 119.12/42.37 [7] ALPHA_AND : (distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141))
% 119.12/42.37 -> [8] distinct_points(skolem_X3838, skolem_Y3939), convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.37
% 119.12/42.37 [8] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 119.12/42.37 -> [9] ~distinct_points(skolem_Y3939, skolem_Y3939)
% 119.12/42.37
% 119.12/42.37 [9] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 119.12/42.37 -> [10] ~distinct_lines(line_connecting(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)), line_connecting(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)))
% 119.12/42.37
% 119.12/42.37 [10] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 119.12/42.37 -> [11] ~convergent_lines(skolem_U4040, skolem_U4040)
% 119.12/42.37
% 119.12/42.37 [11] 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))))
% 119.12/42.37 -> [12] (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939)))
% 119.12/42.37
% 119.12/42.37 [12] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939)))
% 119.12/42.37 -> [13] ~distinct_points(skolem_X3838, skolem_Y3939)
% 119.12/42.37 -> [14] (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939))
% 119.12/42.37
% 119.12/42.37 [13] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 119.12/42.37
% 119.12/42.37 [14] BETA_OR : (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939))
% 119.12/42.37 -> [17] distinct_points(skolem_X3838, skolem_Y3939)
% 119.12/42.37 -> [18] distinct_points(skolem_Y3939, skolem_Y3939)
% 119.12/42.37
% 119.12/42.37 [18] CLOSURE : distinct_points(skolem_Y3939, skolem_Y3939)
% 119.12/42.37
% 119.12/42.37 [17] 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))))
% 119.12/42.37 -> [19] (distinct_lines(skolem_V4141, skolem_U4040) => (distinct_lines(skolem_V4141, skolem_V4141) | distinct_lines(skolem_U4040, skolem_V4141)))
% 119.12/42.37
% 119.12/42.37 [19] BETA_IMPLY : (distinct_lines(skolem_V4141, skolem_U4040) => (distinct_lines(skolem_V4141, skolem_V4141) | distinct_lines(skolem_U4040, skolem_V4141)))
% 119.12/42.37 -> [20] ~distinct_lines(skolem_V4141, skolem_U4040)
% 119.12/42.37 -> [21] (distinct_lines(skolem_V4141, skolem_V4141) | distinct_lines(skolem_U4040, skolem_V4141))
% 119.12/42.37
% 119.12/42.37 [20] 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))))
% 119.12/42.37 -> [24] (convergent_lines(skolem_U4040, skolem_V4141) => (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040)))
% 119.12/42.37
% 119.12/42.37 [24] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040)))
% 119.12/42.37 -> [25] ~convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.37 -> [26] (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040))
% 119.12/42.37
% 119.12/42.37 [25] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.37
% 119.12/42.37 [26] BETA_OR : (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040))
% 119.12/42.37 -> [29] convergent_lines(skolem_U4040, skolem_U4040)
% 119.12/42.37 -> [30] convergent_lines(skolem_V4141, skolem_U4040)
% 119.12/42.37
% 119.12/42.37 [29] CLOSURE : convergent_lines(skolem_U4040, skolem_U4040)
% 119.12/42.37
% 119.12/42.37 [30] GAMMA_FORALL : ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18))))
% 119.12/42.37 -> [99] (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 119.12/42.37
% 119.12/42.37 [99] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 119.12/42.37 -> [100] ~distinct_points(skolem_X3838, skolem_Y3939)
% 119.12/42.37 -> [101] ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 119.12/42.37
% 119.12/42.37 [100] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 119.12/42.37
% 119.12/42.37 [102] BETA_IMPLY : (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), line_connecting(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))))
% 119.12/42.37 -> [2204] ~distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 119.12/42.37 -> [2205] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), line_connecting(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)))
% 119.12/42.37
% 119.12/42.37 [2204] CLOSURE : ~distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 119.12/42.37
% 119.12/42.37 [2206] BETA_IMPLY : (convergent_lines(skolem_V4141, skolem_U4040) => ~apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_V4141))
% 119.12/42.37 -> [3048] ~convergent_lines(skolem_V4141, skolem_U4040)
% 119.12/42.37 -> [3049] ~apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_V4141)
% 119.12/42.37
% 119.12/42.37 [3048] CLOSURE : ~convergent_lines(skolem_V4141, skolem_U4040)
% 119.12/42.37
% 119.12/42.37 [3050] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 119.12/42.37 -> [4240] ~convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.37 -> [4241] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 119.12/42.37
% 119.12/42.37 [4240] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.37
% 119.12/42.37 [4242] BETA_IMPLY : ((distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), skolem_V4141)) => (((apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, skolem_V4141)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_V4141)))
% 119.12/42.37 -> [4461] ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), skolem_V4141))
% 119.12/42.37 -> [4462] (((apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, skolem_V4141)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_V4141))
% 119.12/42.37
% 119.12/42.37 [4461] BETA_NOT_AND : ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), skolem_V4141))
% 119.12/42.37 -> [4463] ~distinct_points(skolem_X3838, skolem_Y3939)
% 119.12/42.37 -> [4464] ~distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), skolem_V4141)
% 119.12/42.37
% 119.12/42.37 [4464] 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))))
% 119.12/42.37 -> [4471] (apart_point_and_line(skolem_Y3939, Y30_43_11) => (distinct_points(skolem_Y3939, skolem_Y3939) | apart_point_and_line(skolem_Y3939, Y30_43_11)))
% 119.12/42.37
% 119.12/42.37 [4471] BETA_IMPLY : (apart_point_and_line(skolem_Y3939, Y30_43_11) => (distinct_points(skolem_Y3939, skolem_Y3939) | apart_point_and_line(skolem_Y3939, Y30_43_11)))
% 119.12/42.37 -> [4472] ~apart_point_and_line(skolem_Y3939, Y30_43_11)
% 119.12/42.37 -> [4473] (distinct_points(skolem_Y3939, skolem_Y3939) | apart_point_and_line(skolem_Y3939, Y30_43_11))
% 119.12/42.37
% 119.12/42.37 [4473] BETA_OR : (distinct_points(skolem_Y3939, skolem_Y3939) | apart_point_and_line(skolem_Y3939, Y30_43_11))
% 119.12/42.37 -> [4474] distinct_points(skolem_Y3939, skolem_Y3939)
% 119.12/42.37 -> [4475] apart_point_and_line(skolem_Y3939, Y30_43_11)
% 119.12/42.37
% 119.12/42.37 [4474] CLOSURE : distinct_points(skolem_Y3939, skolem_Y3939)
% 119.12/42.37
% 119.12/42.37 [4475] 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))))
% 119.12/42.37 -> [4486] (apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), Y33_122_12) => (distinct_lines(Y33_122_12, skolem_V4141) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)))
% 119.12/42.37
% 119.12/42.37 [4486] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), Y33_122_12) => (distinct_lines(Y33_122_12, skolem_V4141) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)))
% 119.12/42.37 -> [4487] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), Y33_122_12)
% 119.12/42.37 -> [4488] (distinct_lines(Y33_122_12, skolem_V4141) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 119.12/42.37
% 119.12/42.37 [4488] BETA_OR : (distinct_lines(Y33_122_12, skolem_V4141) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 119.12/42.37 -> [4489] distinct_lines(Y33_122_12, skolem_V4141)
% 119.12/42.37 -> [4490] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 119.12/42.37
% 119.12/42.37 [4490] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 119.12/42.37
% 119.12/42.37 [4489] CLOSURE : distinct_lines(Y33_122_12, skolem_V4141)
% 119.12/42.37
% 119.12/42.37 [4487] 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))))
% 119.12/42.37 -> [4499] (convergent_lines(skolem_U4040, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040)))
% 119.12/42.37
% 119.12/42.37 [4499] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040)))
% 119.12/42.37 -> [4500] ~convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.37 -> [4501] (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 119.12/42.37
% 119.12/42.37 [4500] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.37
% 119.12/42.37 [4501] BETA_OR : (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 119.12/42.37 -> [4526] distinct_lines(skolem_V4141, skolem_U4040)
% 119.12/42.37 -> [4527] convergent_lines(skolem_U4040, skolem_U4040)
% 119.12/42.37
% 119.12/42.37 [4527] CLOSURE : convergent_lines(skolem_U4040, skolem_U4040)
% 119.12/42.37
% 119.12/42.37 [4526] CLOSURE : distinct_lines(skolem_V4141, skolem_U4040)
% 119.12/42.37
% 119.12/42.37 [4476] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), line_connecting(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))) => (distinct_lines(line_connecting(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)), line_connecting(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), line_connecting(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)))))
% 119.12/42.38 -> [4539] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), line_connecting(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)))
% 119.12/42.38 -> [4540] (distinct_lines(line_connecting(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)), line_connecting(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), line_connecting(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))))
% 119.12/42.38
% 119.12/42.38 [4540] BETA_OR : (distinct_lines(line_connecting(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)), line_connecting(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), line_connecting(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))))
% 119.12/42.38 -> [4541] distinct_lines(line_connecting(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)), line_connecting(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)))
% 119.12/42.38 -> [4542] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), line_connecting(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)))
% 119.12/42.38
% 119.12/42.38 [4542] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), line_connecting(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)))
% 119.12/42.38
% 119.12/42.38 [4541] CLOSURE : distinct_lines(line_connecting(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)), line_connecting(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)))
% 119.12/42.38
% 119.12/42.38 [4539] 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))))
% 119.12/42.38 -> [4543] (convergent_lines(skolem_U4040, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040)))
% 119.12/42.38
% 119.12/42.38 [4543] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040)))
% 119.12/42.38 -> [4544] ~convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.38 -> [4545] (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 119.12/42.38
% 119.12/42.38 [4544] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [4545] BETA_OR : (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 119.12/42.38 -> [4561] distinct_lines(skolem_V4141, skolem_U4040)
% 119.12/42.38 -> [4562] convergent_lines(skolem_U4040, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [4562] CLOSURE : convergent_lines(skolem_U4040, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [4561] CLOSURE : distinct_lines(skolem_V4141, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [4463] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 119.12/42.38
% 119.12/42.38 [4462] BETA_OR : (((apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, skolem_V4141)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_V4141))
% 119.12/42.38 -> [4710] ((apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, skolem_V4141)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 119.12/42.38 -> [4711] apart_point_and_line(skolem_Y3939, skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [4711] 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))))
% 119.12/42.38 -> [4716] (apart_point_and_line(skolem_Y3939, skolem_V4141) => (distinct_points(skolem_Y3939, skolem_X3838) | apart_point_and_line(skolem_X3838, skolem_V4141)))
% 119.12/42.38
% 119.12/42.38 [4716] BETA_IMPLY : (apart_point_and_line(skolem_Y3939, skolem_V4141) => (distinct_points(skolem_Y3939, skolem_X3838) | apart_point_and_line(skolem_X3838, skolem_V4141)))
% 119.12/42.38 -> [4717] ~apart_point_and_line(skolem_Y3939, skolem_V4141)
% 119.12/42.38 -> [4718] (distinct_points(skolem_Y3939, skolem_X3838) | apart_point_and_line(skolem_X3838, skolem_V4141))
% 119.12/42.38
% 119.12/42.38 [4717] CLOSURE : ~apart_point_and_line(skolem_Y3939, skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [4718] BETA_OR : (distinct_points(skolem_Y3939, skolem_X3838) | apart_point_and_line(skolem_X3838, skolem_V4141))
% 119.12/42.38 -> [4782] distinct_points(skolem_Y3939, skolem_X3838)
% 119.12/42.38 -> [4783] apart_point_and_line(skolem_X3838, skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [4783] CLOSURE : apart_point_and_line(skolem_X3838, skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [4782] 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))))
% 119.12/42.38 -> [4785] (apart_point_and_line(skolem_Y3939, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | apart_point_and_line(skolem_Y3939, skolem_U4040)))
% 119.12/42.38
% 119.12/42.38 [4785] BETA_IMPLY : (apart_point_and_line(skolem_Y3939, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | apart_point_and_line(skolem_Y3939, skolem_U4040)))
% 119.12/42.38 -> [4786] ~apart_point_and_line(skolem_Y3939, skolem_V4141)
% 119.12/42.38 -> [4787] (distinct_lines(skolem_V4141, skolem_U4040) | apart_point_and_line(skolem_Y3939, skolem_U4040))
% 119.12/42.38
% 119.12/42.38 [4786] CLOSURE : ~apart_point_and_line(skolem_Y3939, skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [4787] BETA_OR : (distinct_lines(skolem_V4141, skolem_U4040) | apart_point_and_line(skolem_Y3939, skolem_U4040))
% 119.12/42.38 -> [4794] distinct_lines(skolem_V4141, skolem_U4040)
% 119.12/42.38 -> [4795] apart_point_and_line(skolem_Y3939, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [4794] CLOSURE : distinct_lines(skolem_V4141, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [4795] 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))))
% 119.12/42.38 -> [4796] (convergent_lines(skolem_U4040, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040)))
% 119.12/42.38
% 119.12/42.38 [4796] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040)))
% 119.12/42.38 -> [4797] ~convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.38 -> [4798] (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 119.12/42.38
% 119.12/42.38 [4798] BETA_OR : (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 119.12/42.38 -> [4799] distinct_lines(skolem_V4141, skolem_U4040)
% 119.12/42.38 -> [4800] convergent_lines(skolem_U4040, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [4799] CLOSURE : distinct_lines(skolem_V4141, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [4800] CLOSURE : convergent_lines(skolem_U4040, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [4797] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [4710] BETA_OR : ((apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, skolem_V4141)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 119.12/42.38 -> [4712] (apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, skolem_V4141))
% 119.12/42.38 -> [4713] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 119.12/42.38
% 119.12/42.38 [4712] BETA_OR : (apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, skolem_V4141))
% 119.12/42.38 -> [4714] apart_point_and_line(skolem_X3838, skolem_U4040)
% 119.12/42.38 -> [4715] apart_point_and_line(skolem_X3838, skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [4715] CLOSURE : apart_point_and_line(skolem_X3838, skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [4714] CLOSURE : apart_point_and_line(skolem_X3838, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [4719] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141) => (distinct_points(intersection_point(skolem_U4040, skolem_V4141), intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)))
% 119.12/42.38 -> [4820] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 119.12/42.38 -> [4821] (distinct_points(intersection_point(skolem_U4040, skolem_V4141), intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 119.12/42.38
% 119.12/42.38 [4821] BETA_OR : (distinct_points(intersection_point(skolem_U4040, skolem_V4141), intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 119.12/42.38 -> [4822] distinct_points(intersection_point(skolem_U4040, skolem_V4141), intersection_point(skolem_U4040, skolem_V4141))
% 119.12/42.38 -> [4823] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [4823] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [4822] 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))))
% 119.12/42.38 -> [4824] (apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), Z34_130_12) | apart_point_and_line(skolem_Y3939, Z34_130_12)))
% 119.12/42.38
% 119.12/42.38 [4824] BETA_IMPLY : (apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), Z34_130_12) | apart_point_and_line(skolem_Y3939, Z34_130_12)))
% 119.12/42.38 -> [4825] ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 119.12/42.38 -> [4826] (distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), Z34_130_12) | apart_point_and_line(skolem_Y3939, Z34_130_12))
% 119.12/42.38
% 119.12/42.38 [4825] CLOSURE : ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 119.12/42.38
% 119.12/42.38 [4826] BETA_OR : (distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), Z34_130_12) | apart_point_and_line(skolem_Y3939, Z34_130_12))
% 119.12/42.38 -> [4840] distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), Z34_130_12)
% 119.12/42.38 -> [4841] apart_point_and_line(skolem_Y3939, Z34_130_12)
% 119.12/42.38
% 119.12/42.38 [4841] 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))))
% 119.12/42.38 -> [4843] (convergent_lines(skolem_V4141, skolem_U4040) => (distinct_lines(skolem_U4040, Z37_222_13) | convergent_lines(skolem_V4141, Z37_222_13)))
% 119.12/42.38
% 119.12/42.38 [4843] BETA_IMPLY : (convergent_lines(skolem_V4141, skolem_U4040) => (distinct_lines(skolem_U4040, Z37_222_13) | convergent_lines(skolem_V4141, Z37_222_13)))
% 119.12/42.38 -> [4844] ~convergent_lines(skolem_V4141, skolem_U4040)
% 119.12/42.38 -> [4845] (distinct_lines(skolem_U4040, Z37_222_13) | convergent_lines(skolem_V4141, Z37_222_13))
% 119.12/42.38
% 119.12/42.38 [4844] CLOSURE : ~convergent_lines(skolem_V4141, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [4845] BETA_OR : (distinct_lines(skolem_U4040, Z37_222_13) | convergent_lines(skolem_V4141, Z37_222_13))
% 119.12/42.38 -> [4852] distinct_lines(skolem_U4040, Z37_222_13)
% 119.12/42.38 -> [4853] convergent_lines(skolem_V4141, Z37_222_13)
% 119.12/42.38
% 119.12/42.38 [4853] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 119.12/42.38 -> [4857] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 119.12/42.38
% 119.12/42.38 [4857] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 119.12/42.38 -> [4858] ~distinct_points(X5_550_0, X5_550_0)
% 119.12/42.38
% 119.12/42.38 [4858] CLOSURE : ~distinct_points(X5_550_0, X5_550_0)
% 119.12/42.38
% 119.12/42.38 [4852] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 119.12/42.38 -> [4856] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 119.12/42.38
% 119.12/42.38 [4856] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 119.12/42.38 -> [4859] ~distinct_points(X5_551_0, X5_551_0)
% 119.12/42.38
% 119.12/42.38 [4859] CLOSURE : ~distinct_points(X5_551_0, X5_551_0)
% 119.12/42.38
% 119.12/42.38 [4840] 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))))
% 119.12/42.38 -> [4842] (convergent_lines(skolem_V4141, skolem_U4040) => (distinct_lines(skolem_U4040, Z37_221_13) | convergent_lines(skolem_V4141, Z37_221_13)))
% 119.12/42.38
% 119.12/42.38 [4842] BETA_IMPLY : (convergent_lines(skolem_V4141, skolem_U4040) => (distinct_lines(skolem_U4040, Z37_221_13) | convergent_lines(skolem_V4141, Z37_221_13)))
% 119.12/42.38 -> [4846] ~convergent_lines(skolem_V4141, skolem_U4040)
% 119.12/42.38 -> [4847] (distinct_lines(skolem_U4040, Z37_221_13) | convergent_lines(skolem_V4141, Z37_221_13))
% 119.12/42.38
% 119.12/42.38 [4846] CLOSURE : ~convergent_lines(skolem_V4141, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [4847] BETA_OR : (distinct_lines(skolem_U4040, Z37_221_13) | convergent_lines(skolem_V4141, Z37_221_13))
% 119.12/42.38 -> [4854] distinct_lines(skolem_U4040, Z37_221_13)
% 119.12/42.38 -> [4855] convergent_lines(skolem_V4141, Z37_221_13)
% 119.12/42.38
% 119.12/42.38 [4854] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 119.12/42.38 -> [4860] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 119.12/42.38
% 119.12/42.38 [4860] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 119.12/42.38 -> [4861] ~distinct_points(X5_552_0, X5_552_0)
% 119.12/42.38
% 119.12/42.38 [4861] CLOSURE : ~distinct_points(X5_552_0, X5_552_0)
% 119.12/42.38
% 119.12/42.38 [4855] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 119.12/42.38 -> [4862] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 119.12/42.38
% 119.12/42.38 [4862] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 119.12/42.38 -> [4863] ~distinct_points(X5_553_0, X5_553_0)
% 119.12/42.38
% 119.12/42.38 [4863] CLOSURE : ~distinct_points(X5_553_0, X5_553_0)
% 119.12/42.38
% 119.12/42.38 [4820] 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))))
% 119.12/42.38 -> [4864] (apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), Z34_131_12) | apart_point_and_line(skolem_Y3939, Z34_131_12)))
% 119.12/42.38
% 119.12/42.38 [4864] BETA_IMPLY : (apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), Z34_131_12) | apart_point_and_line(skolem_Y3939, Z34_131_12)))
% 119.12/42.38 -> [4865] ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 119.12/42.38 -> [4866] (distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), Z34_131_12) | apart_point_and_line(skolem_Y3939, Z34_131_12))
% 119.12/42.38
% 119.12/42.38 [4865] CLOSURE : ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 119.12/42.38
% 119.12/42.38 [4866] BETA_OR : (distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), Z34_131_12) | apart_point_and_line(skolem_Y3939, Z34_131_12))
% 119.12/42.38 -> [4880] distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), Z34_131_12)
% 119.12/42.38 -> [4881] apart_point_and_line(skolem_Y3939, Z34_131_12)
% 119.12/42.38
% 119.12/42.38 [4880] 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))))
% 119.12/42.38 -> [4883] (convergent_lines(skolem_U4040, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040)))
% 119.12/42.38
% 119.12/42.38 [4883] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040)))
% 119.12/42.38 -> [4886] ~convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.38 -> [4887] (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 119.12/42.38
% 119.12/42.38 [4887] BETA_OR : (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 119.12/42.38 -> [4890] distinct_lines(skolem_V4141, skolem_U4040)
% 119.12/42.38 -> [4891] convergent_lines(skolem_U4040, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [4891] CLOSURE : convergent_lines(skolem_U4040, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [4890] CLOSURE : distinct_lines(skolem_V4141, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [4886] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [4881] 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))))
% 119.12/42.38 -> [4882] (convergent_lines(skolem_U4040, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040)))
% 119.12/42.38
% 119.12/42.38 [4882] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040)))
% 119.12/42.38 -> [4884] ~convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.38 -> [4885] (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 119.12/42.38
% 119.12/42.38 [4885] BETA_OR : (distinct_lines(skolem_V4141, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 119.12/42.38 -> [4888] distinct_lines(skolem_V4141, skolem_U4040)
% 119.12/42.38 -> [4889] convergent_lines(skolem_U4040, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [4889] CLOSURE : convergent_lines(skolem_U4040, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [4888] CLOSURE : distinct_lines(skolem_V4141, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [4884] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [21] BETA_OR : (distinct_lines(skolem_V4141, skolem_V4141) | distinct_lines(skolem_U4040, skolem_V4141))
% 119.12/42.38 -> [7594] distinct_lines(skolem_V4141, skolem_V4141)
% 119.12/42.38 -> [7595] distinct_lines(skolem_U4040, skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [7594] 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))))
% 119.12/42.38 -> [7596] (convergent_lines(skolem_U4040, skolem_V4141) => (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040)))
% 119.12/42.38
% 119.12/42.38 [7596] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040)))
% 119.12/42.38 -> [7597] ~convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.38 -> [7598] (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040))
% 119.12/42.38
% 119.12/42.38 [7597] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [7598] BETA_OR : (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040))
% 119.12/42.38 -> [7606] convergent_lines(skolem_U4040, skolem_U4040)
% 119.12/42.38 -> [7607] convergent_lines(skolem_V4141, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [7607] GAMMA_FORALL : ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18))))
% 119.12/42.38 -> [7608] (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 119.12/42.38
% 119.12/42.38 [7608] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 119.12/42.38 -> [7611] ~distinct_points(skolem_X3838, skolem_Y3939)
% 119.12/42.38 -> [7612] ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 119.12/42.38
% 119.12/42.38 [7612] GAMMA_FORALL : ! [X19_19, Y20_20] : ((distinct_points(X19_19, Y20_20) => ~apart_point_and_line(Y20_20, line_connecting(X19_19, Y20_20))))
% 119.12/42.38 -> [7614] (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 119.12/42.38
% 119.12/42.38 [7614] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 119.12/42.38 -> [7617] ~distinct_points(skolem_X3838, skolem_Y3939)
% 119.12/42.38 -> [7618] ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 119.12/42.38
% 119.12/42.38 [7618] GAMMA_FORALL : ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21)))
% 119.12/42.38 -> [7620] (convergent_lines(skolem_V4141, Y22_6_8) => ~apart_point_and_line(intersection_point(skolem_V4141, Y22_6_8), skolem_V4141))
% 119.12/42.38
% 119.12/42.38 [7620] BETA_IMPLY : (convergent_lines(skolem_V4141, Y22_6_8) => ~apart_point_and_line(intersection_point(skolem_V4141, Y22_6_8), skolem_V4141))
% 119.12/42.38 -> [7623] ~convergent_lines(skolem_V4141, Y22_6_8)
% 119.12/42.38 -> [7624] ~apart_point_and_line(intersection_point(skolem_V4141, Y22_6_8), skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [7624] GAMMA_FORALL : ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24)))
% 119.12/42.38 -> [7626] (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 119.12/42.38
% 119.12/42.38 [7626] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 119.12/42.38 -> [7629] ~convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.38 -> [7630] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [7629] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [7634] BETA_IMPLY : ((distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) & distinct_lines(skolem_V4141, skolem_V4141)) => (((apart_point_and_line(skolem_X3838, skolem_V4141) | apart_point_and_line(skolem_X3838, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)))
% 119.12/42.38 -> [7750] ~(distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) & distinct_lines(skolem_V4141, skolem_V4141))
% 119.12/42.38 -> [7751] (((apart_point_and_line(skolem_X3838, skolem_V4141) | apart_point_and_line(skolem_X3838, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 119.12/42.38
% 119.12/42.38 [7750] BETA_NOT_AND : ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(skolem_V4141, skolem_V4141))
% 119.12/42.38 -> [7754] ~distinct_points(skolem_X3838, skolem_Y3939)
% 119.12/42.38 -> [7755] ~distinct_lines(skolem_V4141, skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [7755] CLOSURE : ~distinct_lines(skolem_V4141, skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [7754] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 119.12/42.38
% 119.12/42.38 [7751] BETA_OR : (((apart_point_and_line(skolem_X3838, skolem_V4141) | apart_point_and_line(skolem_X3838, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 119.12/42.38 -> [8407] ((apart_point_and_line(skolem_X3838, skolem_V4141) | apart_point_and_line(skolem_X3838, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 119.12/42.38 -> [8408] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [8408] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [8407] 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))
% 119.12/42.38 -> [8409] (apart_point_and_line(skolem_X3838, skolem_V4141) | apart_point_and_line(skolem_X3838, skolem_U4040))
% 119.12/42.38 -> [8410] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [8410] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [8409] BETA_OR : (apart_point_and_line(skolem_X3838, skolem_V4141) | apart_point_and_line(skolem_X3838, skolem_U4040))
% 119.12/42.38 -> [8413] apart_point_and_line(skolem_X3838, skolem_V4141)
% 119.12/42.38 -> [8414] apart_point_and_line(skolem_X3838, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [8413] CLOSURE : apart_point_and_line(skolem_X3838, skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [8414] CLOSURE : apart_point_and_line(skolem_X3838, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [7623] CLOSURE : ~convergent_lines(skolem_V4141, Y22_6_8)
% 119.12/42.38
% 119.12/42.38 [7617] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 119.12/42.38
% 119.12/42.38 [7611] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 119.12/42.38
% 119.12/42.38 [7606] CLOSURE : convergent_lines(skolem_U4040, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [7599] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_U4040) => (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040)))
% 119.12/42.38 -> [10914] ~convergent_lines(skolem_U4040, skolem_U4040)
% 119.12/42.38 -> [10915] (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 119.12/42.38
% 119.12/42.38 [10915] BETA_OR : (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_U4040, skolem_U4040))
% 119.12/42.38 -> [10916] convergent_lines(skolem_U4040, skolem_U4040)
% 119.12/42.38 -> [10917] convergent_lines(skolem_U4040, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [10917] CLOSURE : convergent_lines(skolem_U4040, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [10916] CLOSURE : convergent_lines(skolem_U4040, skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [10914] GAMMA_FORALL : ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18))))
% 119.12/42.38 -> [11372] (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 119.12/42.38
% 119.12/42.38 [11372] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 119.12/42.38 -> [11373] ~distinct_points(skolem_X3838, skolem_Y3939)
% 119.12/42.38 -> [11374] ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 119.12/42.38
% 119.12/42.38 [11373] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 119.12/42.38
% 119.12/42.38 [11374] GAMMA_FORALL : ! [X19_19, Y20_20] : ((distinct_points(X19_19, Y20_20) => ~apart_point_and_line(Y20_20, line_connecting(X19_19, Y20_20))))
% 119.12/42.38 -> [11375] (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 119.12/42.38
% 119.12/42.38 [11375] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 119.12/42.38 -> [11376] ~distinct_points(skolem_X3838, skolem_Y3939)
% 119.12/42.38 -> [11377] ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 119.12/42.38
% 119.12/42.38 [11376] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 119.12/42.38
% 119.12/42.38 [11377] GAMMA_FORALL : ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21)))
% 119.12/42.38 -> [11378] (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 119.12/42.38
% 119.12/42.38 [11378] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 119.12/42.38 -> [11379] ~convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.38 -> [11380] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [11379] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [11380] GAMMA_FORALL : ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24)))
% 119.12/42.38 -> [11381] (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 119.12/42.38
% 119.12/42.38 [11381] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 119.12/42.38 -> [11382] ~convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.38 -> [11383] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [11382] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [11384] 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)))
% 119.12/42.38 -> [11411] ~(distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) & distinct_lines(skolem_U4040, skolem_V4141))
% 119.12/42.38 -> [11412] (((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))
% 119.12/42.38
% 119.12/42.38 [11412] BETA_OR : (((apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 119.12/42.38 -> [11413] ((apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 119.12/42.38 -> [11414] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [11414] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [11413] BETA_OR : ((apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 119.12/42.38 -> [11423] (apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 119.12/42.38 -> [11424] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [11424] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [11423] BETA_OR : (apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 119.12/42.38 -> [11427] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 119.12/42.38 -> [11428] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [11428] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [11427] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 119.12/42.38
% 119.12/42.38 [11411] BETA_NOT_AND : ~(distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) & distinct_lines(skolem_U4040, skolem_V4141))
% 119.12/42.38 -> [11457] ~distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 119.12/42.38 -> [11458] ~distinct_lines(skolem_U4040, skolem_V4141)
% 119.12/42.38
% 119.12/42.38 [11457] CLOSURE : ~distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 119.12/42.38
% 119.12/42.38 [11458] CLOSURE : ~distinct_lines(skolem_U4040, skolem_V4141)
% 119.12/42.38
% 119.12/42.38 % SZS output end Proof for theBenchmark.p
% 119.12/42.38 [42.054335s][1][Res] 339782 goroutines created
% 119.12/42.38 ==== Result ====
% 119.12/42.38 [42.054376s][1][Res] VALID
% 119.12/42.38 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------