TSTP Solution File: GEO172+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO172+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n016.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 15:18:11 EDT 2022
% Result : Theorem 46.38s 17.74s
% Output : Proof 46.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO172+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14 % Command : goeland -dmt -presko -proof %s
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 31 07:06:32 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 [DMT] DMT loaded with preskolemization
% 0.14/0.36 [EQ] equality loaded.
% 0.14/0.36 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.14/0.36 Conjecture not found
% 0.14/0.36 Start search
% 0.14/0.36 nb_step : 1 - limit : 15
% 0.14/0.36 Launch Gotab with destructive = true
% 46.38/17.73 % SZS output start Proof for theBenchmark.p
% 46.38/17.74 [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, Z40_40] : ((((convergent_lines(X38_38, Y39_39) & ~apart_point_and_line(Z40_40, X38_38)) & ~apart_point_and_line(Z40_40, Y39_39)) => ~distinct_points(Z40_40, intersection_point(X38_38, Y39_39)))))
% 46.38/17.74 -> [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, Z40_40] : ((((convergent_lines(X38_38, Y39_39) & ~apart_point_and_line(Z40_40, X38_38)) & ~apart_point_and_line(Z40_40, Y39_39)) => ~distinct_points(Z40_40, intersection_point(X38_38, Y39_39))))
% 46.38/17.74
% 46.38/17.74 [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)))))
% 46.38/17.74 -> [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))))
% 46.38/17.74
% 46.38/17.74 [2] DELTA_NOT_FORALL : ~! [X38_38, Y39_39, Z40_40] : ((((convergent_lines(X38_38, Y39_39) & ~apart_point_and_line(Z40_40, X38_38)) & ~apart_point_and_line(Z40_40, Y39_39)) => ~distinct_points(Z40_40, intersection_point(X38_38, Y39_39))))
% 46.38/17.74 -> [3] ~(((convergent_lines(skolem_X3838, skolem_Y3939) & ~apart_point_and_line(skolem_Z4040, skolem_X3838)) & ~apart_point_and_line(skolem_Z4040, skolem_Y3939)) => ~distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))
% 46.38/17.74
% 46.38/17.74 [3] ALPHA_NOT_IMPLY : ~(((convergent_lines(skolem_X3838, skolem_Y3939) & ~apart_point_and_line(skolem_Z4040, skolem_X3838)) & ~apart_point_and_line(skolem_Z4040, skolem_Y3939)) => ~distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))
% 46.38/17.74 -> [4] ((convergent_lines(skolem_X3838, skolem_Y3939) & ~apart_point_and_line(skolem_Z4040, skolem_X3838)) & ~apart_point_and_line(skolem_Z4040, skolem_Y3939)), ~~distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))
% 46.38/17.74
% 46.38/17.74 [4] ALPHA_AND : ((convergent_lines(skolem_X3838, skolem_Y3939) & ~apart_point_and_line(skolem_Z4040, skolem_X3838)) & ~apart_point_and_line(skolem_Z4040, skolem_Y3939))
% 46.38/17.74 -> [5] (convergent_lines(skolem_X3838, skolem_Y3939) & ~apart_point_and_line(skolem_Z4040, skolem_X3838)), ~apart_point_and_line(skolem_Z4040, skolem_Y3939)
% 46.38/17.74
% 46.38/17.74 [5] ALPHA_NOT_NOT : ~~distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))
% 46.38/17.74 -> [6] distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))
% 46.38/17.74
% 46.38/17.74 [6] ALPHA_AND : (convergent_lines(skolem_X3838, skolem_Y3939) & ~apart_point_and_line(skolem_Z4040, skolem_X3838))
% 46.38/17.74 -> [7] convergent_lines(skolem_X3838, skolem_Y3939), ~apart_point_and_line(skolem_Z4040, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [7] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 46.38/17.74 -> [8] ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_X3838, skolem_Y3939))
% 46.38/17.74
% 46.38/17.74 [8] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 46.38/17.74 -> [9] ~distinct_lines(skolem_X3838, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [9] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 46.38/17.74 -> [10] ~convergent_lines(skolem_X3838, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [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))))
% 46.38/17.74 -> [11] (distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)) => (distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)) | distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_X3838, skolem_Y3939))))
% 46.38/17.74
% 46.38/17.74 [11] BETA_IMPLY : (distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)) => (distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)) | distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_X3838, skolem_Y3939))))
% 46.38/17.74 -> [12] ~distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))
% 46.38/17.74 -> [13] (distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)) | distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_X3838, skolem_Y3939)))
% 46.38/17.74
% 46.38/17.74 [12] CLOSURE : ~distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))
% 46.38/17.74
% 46.38/17.74 [13] BETA_OR : (distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)) | distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_X3838, skolem_Y3939)))
% 46.38/17.74 -> [16] distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))
% 46.38/17.74 -> [17] distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_X3838, skolem_Y3939))
% 46.38/17.74
% 46.38/17.74 [17] CLOSURE : distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_X3838, skolem_Y3939))
% 46.38/17.74
% 46.38/17.74 [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))))
% 46.38/17.74 -> [18] (distinct_lines(skolem_Y3939, skolem_X3838) => (distinct_lines(skolem_Y3939, skolem_X3838) | distinct_lines(skolem_X3838, skolem_X3838)))
% 46.38/17.74
% 46.38/17.74 [18] BETA_IMPLY : (distinct_lines(skolem_Y3939, skolem_X3838) => (distinct_lines(skolem_Y3939, skolem_X3838) | distinct_lines(skolem_X3838, skolem_X3838)))
% 46.38/17.74 -> [19] ~distinct_lines(skolem_Y3939, skolem_X3838)
% 46.38/17.74 -> [20] (distinct_lines(skolem_Y3939, skolem_X3838) | distinct_lines(skolem_X3838, skolem_X3838))
% 46.38/17.74
% 46.38/17.74 [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))))
% 46.38/17.74 -> [23] (convergent_lines(skolem_X3838, skolem_Y3939) => (convergent_lines(skolem_X3838, skolem_X3838) | convergent_lines(skolem_Y3939, skolem_X3838)))
% 46.38/17.74
% 46.38/17.74 [23] BETA_IMPLY : (convergent_lines(skolem_X3838, skolem_Y3939) => (convergent_lines(skolem_X3838, skolem_X3838) | convergent_lines(skolem_Y3939, skolem_X3838)))
% 46.38/17.74 -> [24] ~convergent_lines(skolem_X3838, skolem_Y3939)
% 46.38/17.74 -> [25] (convergent_lines(skolem_X3838, skolem_X3838) | convergent_lines(skolem_Y3939, skolem_X3838))
% 46.38/17.74
% 46.38/17.74 [24] CLOSURE : ~convergent_lines(skolem_X3838, skolem_Y3939)
% 46.38/17.74
% 46.38/17.74 [25] BETA_OR : (convergent_lines(skolem_X3838, skolem_X3838) | convergent_lines(skolem_Y3939, skolem_X3838))
% 46.38/17.74 -> [28] convergent_lines(skolem_X3838, skolem_X3838)
% 46.38/17.74 -> [29] convergent_lines(skolem_Y3939, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [28] CLOSURE : convergent_lines(skolem_X3838, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [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))))
% 46.38/17.74 -> [88] (distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)) => ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))))
% 46.38/17.74
% 46.38/17.74 [88] BETA_IMPLY : (distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)) => ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))))
% 46.38/17.74 -> [89] ~distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))
% 46.38/17.74 -> [90] ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))
% 46.38/17.74
% 46.38/17.74 [89] CLOSURE : ~distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))
% 46.38/17.74
% 46.38/17.74 [91] BETA_IMPLY : (distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)) => ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))))
% 46.38/17.74 -> [1930] ~distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))
% 46.38/17.74 -> [1931] ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))
% 46.38/17.74
% 46.38/17.74 [1930] CLOSURE : ~distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))
% 46.38/17.74
% 46.38/17.74 [1932] BETA_IMPLY : (convergent_lines(skolem_Y3939, skolem_X3838) => ~apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939))
% 46.38/17.74 -> [2627] ~convergent_lines(skolem_Y3939, skolem_X3838)
% 46.38/17.74 -> [2628] ~apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939)
% 46.38/17.74
% 46.38/17.74 [2628] GAMMA_FORALL : ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24)))
% 46.38/17.74 -> [2629] (convergent_lines(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939))
% 46.38/17.74
% 46.38/17.74 [2629] BETA_IMPLY : (convergent_lines(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939))
% 46.38/17.74 -> [2630] ~convergent_lines(skolem_X3838, skolem_Y3939)
% 46.38/17.74 -> [2631] ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)
% 46.38/17.74
% 46.38/17.74 [2630] CLOSURE : ~convergent_lines(skolem_X3838, skolem_Y3939)
% 46.38/17.74
% 46.38/17.74 [2632] BETA_IMPLY : ((distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)) & distinct_lines(line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)), line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))) => (((apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))))
% 46.38/17.74 -> [2717] ~(distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)) & distinct_lines(line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)), line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))))
% 46.38/17.74 -> [2718] (((apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))))
% 46.38/17.74
% 46.38/17.74 [2717] BETA_NOT_AND : ~(distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)) & distinct_lines(line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)), line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))))
% 46.38/17.74 -> [2719] ~distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))
% 46.38/17.74 -> [2720] ~distinct_lines(line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)), line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))
% 46.38/17.74
% 46.38/17.74 [2719] CLOSURE : ~distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))
% 46.38/17.74
% 46.38/17.74 [2727] BETA_IMPLY : (apart_point_and_line(X29_31_11, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))) => (distinct_points(X29_31_11, skolem_Z4040) | apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))))
% 46.38/17.74 -> [2782] ~apart_point_and_line(X29_31_11, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))
% 46.38/17.74 -> [2783] (distinct_points(X29_31_11, skolem_Z4040) | apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))))
% 46.38/17.74
% 46.38/17.74 [2782] 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))))
% 46.38/17.74 -> [2786] (apart_point_and_line(X32_72_12, Z34_72_12) => (distinct_lines(Z34_72_12, Z34_72_12) | apart_point_and_line(X32_72_12, Z34_72_12)))
% 46.38/17.74
% 46.38/17.74 [2786] BETA_IMPLY : (apart_point_and_line(X32_72_12, Z34_72_12) => (distinct_lines(Z34_72_12, Z34_72_12) | apart_point_and_line(X32_72_12, Z34_72_12)))
% 46.38/17.74 -> [2787] ~apart_point_and_line(X32_72_12, Z34_72_12)
% 46.38/17.74 -> [2788] (distinct_lines(Z34_72_12, Z34_72_12) | apart_point_and_line(X32_72_12, Z34_72_12))
% 46.38/17.74
% 46.38/17.74 [2787] 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))))
% 46.38/17.74 -> [2791] (convergent_lines(skolem_X3838, skolem_Y3939) => (distinct_lines(skolem_Y3939, skolem_X3838) | convergent_lines(skolem_X3838, skolem_X3838)))
% 46.38/17.74
% 46.38/17.74 [2791] BETA_IMPLY : (convergent_lines(skolem_X3838, skolem_Y3939) => (distinct_lines(skolem_Y3939, skolem_X3838) | convergent_lines(skolem_X3838, skolem_X3838)))
% 46.38/17.74 -> [2792] ~convergent_lines(skolem_X3838, skolem_Y3939)
% 46.38/17.74 -> [2793] (distinct_lines(skolem_Y3939, skolem_X3838) | convergent_lines(skolem_X3838, skolem_X3838))
% 46.38/17.74
% 46.38/17.74 [2792] CLOSURE : ~convergent_lines(skolem_X3838, skolem_Y3939)
% 46.38/17.74
% 46.38/17.74 [2793] BETA_OR : (distinct_lines(skolem_Y3939, skolem_X3838) | convergent_lines(skolem_X3838, skolem_X3838))
% 46.38/17.74 -> [2814] distinct_lines(skolem_Y3939, skolem_X3838)
% 46.38/17.74 -> [2815] convergent_lines(skolem_X3838, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [2814] CLOSURE : distinct_lines(skolem_Y3939, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [2815] CLOSURE : convergent_lines(skolem_X3838, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [2788] BETA_OR : (distinct_lines(Z34_72_12, Z34_72_12) | apart_point_and_line(X32_72_12, Z34_72_12))
% 46.38/17.74 -> [2820] distinct_lines(Z34_72_12, Z34_72_12)
% 46.38/17.74 -> [2821] apart_point_and_line(X32_72_12, Z34_72_12)
% 46.38/17.74
% 46.38/17.74 [2820] CLOSURE : distinct_lines(Z34_72_12, Z34_72_12)
% 46.38/17.74
% 46.38/17.74 [2821] CLOSURE : apart_point_and_line(X32_72_12, Z34_72_12)
% 46.38/17.74
% 46.38/17.74 [2783] BETA_OR : (distinct_points(X29_31_11, skolem_Z4040) | apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))))
% 46.38/17.74 -> [2824] distinct_points(X29_31_11, skolem_Z4040)
% 46.38/17.74 -> [2825] apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))
% 46.38/17.74
% 46.38/17.74 [2825] CLOSURE : apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))
% 46.38/17.74
% 46.38/17.74 [2824] 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))))
% 46.38/17.74 -> [2826] (apart_point_and_line(skolem_Z4040, skolem_Y3939) => (distinct_lines(skolem_Y3939, skolem_X3838) | apart_point_and_line(skolem_Z4040, skolem_X3838)))
% 46.38/17.74
% 46.38/17.74 [2826] BETA_IMPLY : (apart_point_and_line(skolem_Z4040, skolem_Y3939) => (distinct_lines(skolem_Y3939, skolem_X3838) | apart_point_and_line(skolem_Z4040, skolem_X3838)))
% 46.38/17.74 -> [2827] ~apart_point_and_line(skolem_Z4040, skolem_Y3939)
% 46.38/17.74 -> [2828] (distinct_lines(skolem_Y3939, skolem_X3838) | apart_point_and_line(skolem_Z4040, skolem_X3838))
% 46.38/17.74
% 46.38/17.74 [2828] BETA_OR : (distinct_lines(skolem_Y3939, skolem_X3838) | apart_point_and_line(skolem_Z4040, skolem_X3838))
% 46.38/17.74 -> [2829] distinct_lines(skolem_Y3939, skolem_X3838)
% 46.38/17.74 -> [2830] apart_point_and_line(skolem_Z4040, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [2830] CLOSURE : apart_point_and_line(skolem_Z4040, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [2829] CLOSURE : distinct_lines(skolem_Y3939, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [2831] BETA_IMPLY : (convergent_lines(skolem_X3838, skolem_Y3939) => (distinct_lines(skolem_Y3939, skolem_X3838) | convergent_lines(skolem_X3838, skolem_X3838)))
% 46.38/17.74 -> [2840] ~convergent_lines(skolem_X3838, skolem_Y3939)
% 46.38/17.74 -> [2841] (distinct_lines(skolem_Y3939, skolem_X3838) | convergent_lines(skolem_X3838, skolem_X3838))
% 46.38/17.74
% 46.38/17.74 [2841] BETA_OR : (distinct_lines(skolem_Y3939, skolem_X3838) | convergent_lines(skolem_X3838, skolem_X3838))
% 46.38/17.74 -> [2842] distinct_lines(skolem_Y3939, skolem_X3838)
% 46.38/17.74 -> [2843] convergent_lines(skolem_X3838, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [2842] CLOSURE : distinct_lines(skolem_Y3939, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [2843] CLOSURE : convergent_lines(skolem_X3838, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [2840] CLOSURE : ~convergent_lines(skolem_X3838, skolem_Y3939)
% 46.38/17.74
% 46.38/17.74 [2718] BETA_OR : (((apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))))
% 46.38/17.74 -> [2844] ((apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))))
% 46.38/17.74 -> [2845] apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))
% 46.38/17.74
% 46.38/17.74 [2844] BETA_OR : ((apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Z4040, skolem_X3838)) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))))
% 46.38/17.74 -> [2846] (apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Z4040, skolem_X3838))
% 46.38/17.74 -> [2847] apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))
% 46.38/17.74
% 46.38/17.74 [2847] CLOSURE : apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))
% 46.38/17.74
% 46.38/17.74 [2846] BETA_OR : (apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Z4040, skolem_X3838))
% 46.38/17.74 -> [2850] apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))
% 46.38/17.74 -> [2851] apart_point_and_line(skolem_Z4040, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [2850] CLOSURE : apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))
% 46.38/17.74
% 46.38/17.74 [2851] CLOSURE : apart_point_and_line(skolem_Z4040, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [2845] CLOSURE : apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))
% 46.38/17.74
% 46.38/17.74 [2627] CLOSURE : ~convergent_lines(skolem_Y3939, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [20] BETA_OR : (distinct_lines(skolem_Y3939, skolem_X3838) | distinct_lines(skolem_X3838, skolem_X3838))
% 46.38/17.74 -> [2852] distinct_lines(skolem_Y3939, skolem_X3838)
% 46.38/17.74 -> [2853] distinct_lines(skolem_X3838, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [2853] CLOSURE : distinct_lines(skolem_X3838, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [2852] 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))))
% 46.38/17.74 -> [2854] (convergent_lines(skolem_X3838, skolem_Y3939) => (convergent_lines(skolem_X3838, skolem_X3838) | convergent_lines(skolem_Y3939, skolem_X3838)))
% 46.38/17.74
% 46.38/17.74 [2854] BETA_IMPLY : (convergent_lines(skolem_X3838, skolem_Y3939) => (convergent_lines(skolem_X3838, skolem_X3838) | convergent_lines(skolem_Y3939, skolem_X3838)))
% 46.38/17.74 -> [2855] ~convergent_lines(skolem_X3838, skolem_Y3939)
% 46.38/17.74 -> [2856] (convergent_lines(skolem_X3838, skolem_X3838) | convergent_lines(skolem_Y3939, skolem_X3838))
% 46.38/17.74
% 46.38/17.74 [2855] CLOSURE : ~convergent_lines(skolem_X3838, skolem_Y3939)
% 46.38/17.74
% 46.38/17.74 [2856] BETA_OR : (convergent_lines(skolem_X3838, skolem_X3838) | convergent_lines(skolem_Y3939, skolem_X3838))
% 46.38/17.74 -> [2859] convergent_lines(skolem_X3838, skolem_X3838)
% 46.38/17.74 -> [2860] convergent_lines(skolem_Y3939, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [2860] GAMMA_FORALL : ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18))))
% 46.38/17.74 -> [2861] (distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)) => ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))))
% 46.38/17.74
% 46.38/17.74 [2861] BETA_IMPLY : (distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)) => ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))))
% 46.38/17.74 -> [2862] ~distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))
% 46.38/17.74 -> [2863] ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))
% 46.38/17.74
% 46.38/17.74 [2862] CLOSURE : ~distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))
% 46.38/17.74
% 46.38/17.74 [2864] BETA_IMPLY : (distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)) => ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))))
% 46.38/17.74 -> [3876] ~distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))
% 46.38/17.74 -> [3877] ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)))
% 46.38/17.74
% 46.38/17.74 [3877] GAMMA_FORALL : ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21)))
% 46.38/17.74 -> [3878] (convergent_lines(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838))
% 46.38/17.74
% 46.38/17.74 [3878] BETA_IMPLY : (convergent_lines(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838))
% 46.38/17.74 -> [3879] ~convergent_lines(skolem_X3838, skolem_Y3939)
% 46.38/17.74 -> [3880] ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [3879] CLOSURE : ~convergent_lines(skolem_X3838, skolem_Y3939)
% 46.38/17.74
% 46.38/17.74 [3881] BETA_IMPLY : (convergent_lines(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939))
% 46.38/17.74 -> [4017] ~convergent_lines(skolem_X3838, skolem_Y3939)
% 46.38/17.74 -> [4018] ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)
% 46.38/17.74
% 46.38/17.74 [4018] 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))))
% 46.38/17.74 -> [4019] ((distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)) & distinct_lines(skolem_Y3939, skolem_X3838)) => (((apart_point_and_line(skolem_Z4040, skolem_Y3939) | apart_point_and_line(skolem_Z4040, skolem_X3838)) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)))
% 46.38/17.74
% 46.38/17.74 [4019] BETA_IMPLY : ((distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)) & distinct_lines(skolem_Y3939, skolem_X3838)) => (((apart_point_and_line(skolem_Z4040, skolem_Y3939) | apart_point_and_line(skolem_Z4040, skolem_X3838)) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)))
% 46.38/17.74 -> [4020] ~(distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)) & distinct_lines(skolem_Y3939, skolem_X3838))
% 46.38/17.74 -> [4021] (((apart_point_and_line(skolem_Z4040, skolem_Y3939) | apart_point_and_line(skolem_Z4040, skolem_X3838)) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838))
% 46.38/17.74
% 46.38/17.74 [4020] BETA_NOT_AND : ~(distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939)) & distinct_lines(skolem_Y3939, skolem_X3838))
% 46.38/17.74 -> [4022] ~distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))
% 46.38/17.74 -> [4023] ~distinct_lines(skolem_Y3939, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [4023] CLOSURE : ~distinct_lines(skolem_Y3939, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [4022] CLOSURE : ~distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))
% 46.38/17.74
% 46.38/17.74 [4021] BETA_OR : (((apart_point_and_line(skolem_Z4040, skolem_Y3939) | apart_point_and_line(skolem_Z4040, skolem_X3838)) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838))
% 46.38/17.74 -> [4083] ((apart_point_and_line(skolem_Z4040, skolem_Y3939) | apart_point_and_line(skolem_Z4040, skolem_X3838)) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939))
% 46.38/17.74 -> [4084] apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [4084] CLOSURE : apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [4083] BETA_OR : ((apart_point_and_line(skolem_Z4040, skolem_Y3939) | apart_point_and_line(skolem_Z4040, skolem_X3838)) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939))
% 46.38/17.74 -> [4089] (apart_point_and_line(skolem_Z4040, skolem_Y3939) | apart_point_and_line(skolem_Z4040, skolem_X3838))
% 46.38/17.74 -> [4090] apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)
% 46.38/17.74
% 46.38/17.74 [4090] CLOSURE : apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)
% 46.38/17.74
% 46.38/17.74 [4089] BETA_OR : (apart_point_and_line(skolem_Z4040, skolem_Y3939) | apart_point_and_line(skolem_Z4040, skolem_X3838))
% 46.38/17.74 -> [4091] apart_point_and_line(skolem_Z4040, skolem_Y3939)
% 46.38/17.74 -> [4092] apart_point_and_line(skolem_Z4040, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [4092] CLOSURE : apart_point_and_line(skolem_Z4040, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 [4091] CLOSURE : apart_point_and_line(skolem_Z4040, skolem_Y3939)
% 46.38/17.74
% 46.38/17.74 [4017] CLOSURE : ~convergent_lines(skolem_X3838, skolem_Y3939)
% 46.38/17.74
% 46.38/17.74 [3876] CLOSURE : ~distinct_points(skolem_Z4040, intersection_point(skolem_X3838, skolem_Y3939))
% 46.38/17.74
% 46.38/17.74 [2859] CLOSURE : convergent_lines(skolem_X3838, skolem_X3838)
% 46.38/17.74
% 46.38/17.74 % SZS output end Proof for theBenchmark.p
% 46.38/17.74 [17.380487s][1][Res] 106204 goroutines created
% 46.38/17.74 ==== Result ====
% 46.38/17.74 [17.380532s][1][Res] VALID
% 46.38/17.74 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------