TSTP Solution File: GEO185+1 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO185+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n014.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 60.75s 20.19s
% Output : Proof 60.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GEO185+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : goeland -dmt -presko -proof %s
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Aug 31 06:49:32 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.34 [DMT] DMT loaded with preskolemization
% 0.11/0.34 [EQ] equality loaded.
% 0.11/0.34 [0.000039s][1][MAIN] Problem : theBenchmark.p
% 0.11/0.34 Conjecture not found
% 0.11/0.34 Start search
% 0.11/0.34 nb_step : 1 - limit : 15
% 0.11/0.34 Launch Gotab with destructive = true
% 60.63/20.19 % SZS output start Proof for theBenchmark.p
% 60.75/20.19 [0] ALPHA_AND : ((! [X5_5] : (~distinct_points(X5_5, X5_5)) & ! [X6_6] : (~distinct_lines(X6_6, X6_6)) & ! [X7_7] : (~convergent_lines(X7_7, X7_7)) & ! [X8_8, Y9_9, Z10_10] : ((distinct_points(X8_8, Y9_9) => (distinct_points(X8_8, Z10_10) | distinct_points(Y9_9, Z10_10)))) & ! [X11_11, Y12_12, Z13_13] : ((distinct_lines(X11_11, Y12_12) => (distinct_lines(X11_11, Z13_13) | distinct_lines(Y12_12, Z13_13)))) & ! [X14_14, Y15_15, Z16_16] : ((convergent_lines(X14_14, Y15_15) => (convergent_lines(X14_14, Z16_16) | convergent_lines(Y15_15, Z16_16)))) & ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18)))) & ! [X19_19, Y20_20] : ((distinct_points(X19_19, Y20_20) => ~apart_point_and_line(Y20_20, line_connecting(X19_19, Y20_20)))) & ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21))) & ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24))) & ! [X25_25, Y26_26, U27_27, V28_28] : (((distinct_points(X25_25, Y26_26) & distinct_lines(U27_27, V28_28)) => (((apart_point_and_line(X25_25, U27_27) | apart_point_and_line(X25_25, V28_28)) | apart_point_and_line(Y26_26, U27_27)) | apart_point_and_line(Y26_26, V28_28)))) & ! [X29_29, Y30_30, Z31_31] : ((apart_point_and_line(X29_29, Y30_30) => (distinct_points(X29_29, Z31_31) | apart_point_and_line(Z31_31, Y30_30)))) & ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34)))) & ! [X35_35, Y36_36, Z37_37] : ((convergent_lines(X35_35, Y36_36) => (distinct_lines(Y36_36, Z37_37) | convergent_lines(X35_35, Z37_37))))) & ~! [X38_38, Y39_39, U40_40, V41_41] : ((((distinct_points(X38_38, Y39_39) & convergent_lines(U40_40, V41_41)) & ~distinct_points(X38_38, intersection_point(U40_40, V41_41))) => (~apart_point_and_line(X38_38, U40_40) & ~apart_point_and_line(X38_38, V41_41)))))
% 60.75/20.19 -> [1] (! [X5_5] : (~distinct_points(X5_5, X5_5)) & ! [X6_6] : (~distinct_lines(X6_6, X6_6)) & ! [X7_7] : (~convergent_lines(X7_7, X7_7)) & ! [X8_8, Y9_9, Z10_10] : ((distinct_points(X8_8, Y9_9) => (distinct_points(X8_8, Z10_10) | distinct_points(Y9_9, Z10_10)))) & ! [X11_11, Y12_12, Z13_13] : ((distinct_lines(X11_11, Y12_12) => (distinct_lines(X11_11, Z13_13) | distinct_lines(Y12_12, Z13_13)))) & ! [X14_14, Y15_15, Z16_16] : ((convergent_lines(X14_14, Y15_15) => (convergent_lines(X14_14, Z16_16) | convergent_lines(Y15_15, Z16_16)))) & ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18)))) & ! [X19_19, Y20_20] : ((distinct_points(X19_19, Y20_20) => ~apart_point_and_line(Y20_20, line_connecting(X19_19, Y20_20)))) & ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21))) & ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24))) & ! [X25_25, Y26_26, U27_27, V28_28] : (((distinct_points(X25_25, Y26_26) & distinct_lines(U27_27, V28_28)) => (((apart_point_and_line(X25_25, U27_27) | apart_point_and_line(X25_25, V28_28)) | apart_point_and_line(Y26_26, U27_27)) | apart_point_and_line(Y26_26, V28_28)))) & ! [X29_29, Y30_30, Z31_31] : ((apart_point_and_line(X29_29, Y30_30) => (distinct_points(X29_29, Z31_31) | apart_point_and_line(Z31_31, Y30_30)))) & ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34)))) & ! [X35_35, Y36_36, Z37_37] : ((convergent_lines(X35_35, Y36_36) => (distinct_lines(Y36_36, Z37_37) | convergent_lines(X35_35, Z37_37))))), ~! [X38_38, Y39_39, U40_40, V41_41] : ((((distinct_points(X38_38, Y39_39) & convergent_lines(U40_40, V41_41)) & ~distinct_points(X38_38, intersection_point(U40_40, V41_41))) => (~apart_point_and_line(X38_38, U40_40) & ~apart_point_and_line(X38_38, V41_41))))
% 60.75/20.19
% 60.75/20.19 [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)))))
% 60.75/20.19 -> [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))))
% 60.75/20.19
% 60.75/20.19 [2] DELTA_NOT_FORALL : ~! [X38_38, Y39_39, U40_40, V41_41] : ((((distinct_points(X38_38, Y39_39) & convergent_lines(U40_40, V41_41)) & ~distinct_points(X38_38, intersection_point(U40_40, V41_41))) => (~apart_point_and_line(X38_38, U40_40) & ~apart_point_and_line(X38_38, V41_41))))
% 60.75/20.19 -> [3] ~(((distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)) & ~distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))) => (~apart_point_and_line(skolem_X3838, skolem_U4040) & ~apart_point_and_line(skolem_X3838, skolem_V4141)))
% 60.75/20.19
% 60.75/20.19 [3] ALPHA_NOT_IMPLY : ~(((distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)) & ~distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))) => (~apart_point_and_line(skolem_X3838, skolem_U4040) & ~apart_point_and_line(skolem_X3838, skolem_V4141)))
% 60.75/20.19 -> [4] ((distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)) & ~distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))), ~(~apart_point_and_line(skolem_X3838, skolem_U4040) & ~apart_point_and_line(skolem_X3838, skolem_V4141))
% 60.75/20.19
% 60.75/20.19 [4] ALPHA_AND : ((distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)) & ~distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)))
% 60.75/20.19 -> [5] (distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)), ~distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 60.75/20.19
% 60.75/20.19 [5] ALPHA_AND : (distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141))
% 60.75/20.19 -> [6] distinct_points(skolem_X3838, skolem_Y3939), convergent_lines(skolem_U4040, skolem_V4141)
% 60.75/20.19
% 60.75/20.19 [6] BETA_NOT_AND : ~(~apart_point_and_line(skolem_X3838, skolem_U4040) & ~apart_point_and_line(skolem_X3838, skolem_V4141))
% 60.75/20.19 -> [7] ~~apart_point_and_line(skolem_X3838, skolem_U4040)
% 60.75/20.19 -> [8] ~~apart_point_and_line(skolem_X3838, skolem_V4141)
% 60.75/20.19
% 60.75/20.19 [7] ALPHA_NOT_NOT : ~~apart_point_and_line(skolem_X3838, skolem_U4040)
% 60.75/20.19 -> [9] apart_point_and_line(skolem_X3838, skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [9] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 60.75/20.19 -> [11] ~distinct_points(skolem_Y3939, skolem_Y3939)
% 60.75/20.19
% 60.75/20.19 [11] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 60.75/20.19 -> [13] ~distinct_lines(X6_0_1, X6_0_1)
% 60.75/20.19
% 60.75/20.19 [13] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 60.75/20.19 -> [15] ~convergent_lines(X7_0_2, X7_0_2)
% 60.75/20.19
% 60.75/20.19 [15] GAMMA_FORALL : ! [X8_8, Y9_9, Z10_10] : ((distinct_points(X8_8, Y9_9) => (distinct_points(X8_8, Z10_10) | distinct_points(Y9_9, Z10_10))))
% 60.75/20.19 -> [17] (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939)))
% 60.75/20.19
% 60.75/20.19 [17] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939)))
% 60.75/20.19 -> [19] ~distinct_points(skolem_X3838, skolem_Y3939)
% 60.75/20.19 -> [20] (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939))
% 60.75/20.19
% 60.75/20.19 [19] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 60.75/20.19
% 60.75/20.19 [20] BETA_OR : (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939))
% 60.75/20.19 -> [27] distinct_points(skolem_X3838, skolem_Y3939)
% 60.75/20.19 -> [28] distinct_points(skolem_Y3939, skolem_Y3939)
% 60.75/20.19
% 60.75/20.19 [28] CLOSURE : distinct_points(skolem_Y3939, skolem_Y3939)
% 60.75/20.19
% 60.75/20.19 [27] GAMMA_FORALL : ! [X11_11, Y12_12, Z13_13] : ((distinct_lines(X11_11, Y12_12) => (distinct_lines(X11_11, Z13_13) | distinct_lines(Y12_12, Z13_13))))
% 60.75/20.19 -> [31] (distinct_lines(Z13_0_4, Z13_0_4) => (distinct_lines(Z13_0_4, Z13_0_4) | distinct_lines(Z13_0_4, Z13_0_4)))
% 60.75/20.19
% 60.75/20.19 [31] BETA_IMPLY : (distinct_lines(Z13_0_4, Z13_0_4) => (distinct_lines(Z13_0_4, Z13_0_4) | distinct_lines(Z13_0_4, Z13_0_4)))
% 60.75/20.19 -> [32] ~distinct_lines(Z13_0_4, Z13_0_4)
% 60.75/20.19 -> [33] (distinct_lines(Z13_0_4, Z13_0_4) | distinct_lines(Z13_0_4, Z13_0_4))
% 60.75/20.19
% 60.75/20.19 [33] BETA_OR : (distinct_lines(Z13_0_4, Z13_0_4) | distinct_lines(Z13_0_4, Z13_0_4))
% 60.75/20.19 -> [35] distinct_lines(Z13_0_4, Z13_0_4)
% 60.75/20.19 -> [36] distinct_lines(Z13_0_4, Z13_0_4)
% 60.75/20.19
% 60.75/20.19 [35] CLOSURE : distinct_lines(Z13_0_4, Z13_0_4)
% 60.75/20.19
% 60.75/20.19 [36] CLOSURE : distinct_lines(Z13_0_4, Z13_0_4)
% 60.75/20.19
% 60.75/20.19 [39] BETA_IMPLY : (convergent_lines(Z16_0_5, Z16_0_5) => (convergent_lines(Z16_0_5, Z16_0_5) | convergent_lines(Z16_0_5, Z16_0_5)))
% 60.75/20.19 -> [1981] ~convergent_lines(Z16_0_5, Z16_0_5)
% 60.75/20.19 -> [1982] (convergent_lines(Z16_0_5, Z16_0_5) | convergent_lines(Z16_0_5, Z16_0_5))
% 60.75/20.19
% 60.75/20.19 [1982] BETA_OR : (convergent_lines(Z16_0_5, Z16_0_5) | convergent_lines(Z16_0_5, Z16_0_5))
% 60.75/20.19 -> [1983] convergent_lines(Z16_0_5, Z16_0_5)
% 60.75/20.19 -> [1984] convergent_lines(Z16_0_5, Z16_0_5)
% 60.75/20.19
% 60.75/20.19 [1983] CLOSURE : convergent_lines(Z16_0_5, Z16_0_5)
% 60.75/20.19
% 60.75/20.19 [1984] CLOSURE : convergent_lines(Z16_0_5, Z16_0_5)
% 60.75/20.19
% 60.75/20.19 [1981] GAMMA_FORALL : ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18))))
% 60.75/20.19 -> [1987] (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 60.75/20.19
% 60.75/20.19 [1987] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 60.75/20.19 -> [1988] ~distinct_points(skolem_X3838, skolem_Y3939)
% 60.75/20.19 -> [1989] ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 60.75/20.19
% 60.75/20.19 [1988] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 60.75/20.19
% 60.75/20.19 [1992] BETA_IMPLY : (distinct_points(X19_2_7, skolem_X3838) => ~apart_point_and_line(skolem_X3838, line_connecting(X19_2_7, skolem_X3838)))
% 60.75/20.19 -> [3265] ~distinct_points(X19_2_7, skolem_X3838)
% 60.75/20.19 -> [3266] ~apart_point_and_line(skolem_X3838, line_connecting(X19_2_7, skolem_X3838))
% 60.75/20.19
% 60.75/20.19 [3266] GAMMA_FORALL : ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21)))
% 60.75/20.19 -> [3267] (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 60.75/20.19
% 60.75/20.19 [3267] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 60.75/20.19 -> [3268] ~convergent_lines(skolem_U4040, skolem_V4141)
% 60.75/20.19 -> [3269] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [3268] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 60.75/20.19
% 60.75/20.19 [3270] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 60.75/20.19 -> [3428] ~convergent_lines(skolem_U4040, skolem_V4141)
% 60.75/20.19 -> [3429] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 60.75/20.19
% 60.75/20.19 [3428] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 60.75/20.19
% 60.75/20.19 [3430] BETA_IMPLY : ((distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(X19_2_7, skolem_X3838), line_connecting(X19_2_7, skolem_X3838))) => (((apart_point_and_line(skolem_X3838, line_connecting(X19_2_7, skolem_X3838)) | apart_point_and_line(skolem_X3838, line_connecting(X19_2_7, skolem_X3838))) | apart_point_and_line(skolem_Y3939, line_connecting(X19_2_7, skolem_X3838))) | apart_point_and_line(skolem_Y3939, line_connecting(X19_2_7, skolem_X3838))))
% 60.75/20.19 -> [4161] ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(X19_2_7, skolem_X3838), line_connecting(X19_2_7, skolem_X3838)))
% 60.75/20.19 -> [4162] (((apart_point_and_line(skolem_X3838, line_connecting(X19_2_7, skolem_X3838)) | apart_point_and_line(skolem_X3838, line_connecting(X19_2_7, skolem_X3838))) | apart_point_and_line(skolem_Y3939, line_connecting(X19_2_7, skolem_X3838))) | apart_point_and_line(skolem_Y3939, line_connecting(X19_2_7, skolem_X3838)))
% 60.75/20.19
% 60.75/20.19 [4161] BETA_NOT_AND : ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(X19_2_7, skolem_X3838), line_connecting(X19_2_7, skolem_X3838)))
% 60.75/20.19 -> [4165] ~distinct_points(skolem_X3838, skolem_Y3939)
% 60.75/20.19 -> [4166] ~distinct_lines(line_connecting(X19_2_7, skolem_X3838), line_connecting(X19_2_7, skolem_X3838))
% 60.75/20.19
% 60.75/20.19 [4165] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 60.75/20.19
% 60.75/20.19 [4166] 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))))
% 60.75/20.19 -> [4175] (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)))
% 60.75/20.19
% 60.75/20.19 [4175] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)))
% 60.75/20.19 -> [4176] ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 60.75/20.19 -> [4177] (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 60.75/20.19
% 60.75/20.19 [4176] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [4177] BETA_OR : (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 60.75/20.19 -> [4180] distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 60.75/20.19 -> [4181] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [4180] CLOSURE : distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 60.75/20.19
% 60.75/20.19 [4181] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [4162] BETA_OR : (((apart_point_and_line(skolem_X3838, line_connecting(X19_2_7, skolem_X3838)) | apart_point_and_line(skolem_X3838, line_connecting(X19_2_7, skolem_X3838))) | apart_point_and_line(skolem_Y3939, line_connecting(X19_2_7, skolem_X3838))) | apart_point_and_line(skolem_Y3939, line_connecting(X19_2_7, skolem_X3838)))
% 60.75/20.19 -> [4200] ((apart_point_and_line(skolem_X3838, line_connecting(X19_2_7, skolem_X3838)) | apart_point_and_line(skolem_X3838, line_connecting(X19_2_7, skolem_X3838))) | apart_point_and_line(skolem_Y3939, line_connecting(X19_2_7, skolem_X3838)))
% 60.75/20.19 -> [4201] apart_point_and_line(skolem_Y3939, line_connecting(X19_2_7, skolem_X3838))
% 60.75/20.19
% 60.75/20.19 [4200] BETA_OR : ((apart_point_and_line(skolem_X3838, line_connecting(X19_2_7, skolem_X3838)) | apart_point_and_line(skolem_X3838, line_connecting(X19_2_7, skolem_X3838))) | apart_point_and_line(skolem_Y3939, line_connecting(X19_2_7, skolem_X3838)))
% 60.75/20.19 -> [4202] (apart_point_and_line(skolem_X3838, line_connecting(X19_2_7, skolem_X3838)) | apart_point_and_line(skolem_X3838, line_connecting(X19_2_7, skolem_X3838)))
% 60.75/20.19 -> [4203] apart_point_and_line(skolem_Y3939, line_connecting(X19_2_7, skolem_X3838))
% 60.75/20.19
% 60.75/20.19 [4202] BETA_OR : (apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(X19_2_7, skolem_X3838)))
% 60.75/20.19 -> [4206] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 60.75/20.19 -> [4207] apart_point_and_line(skolem_X3838, line_connecting(X19_2_7, skolem_X3838))
% 60.75/20.19
% 60.75/20.19 [4207] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(X19_2_7, skolem_X3838))
% 60.75/20.19
% 60.75/20.19 [4206] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 60.75/20.19
% 60.75/20.19 [4203] 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))))
% 60.75/20.19 -> [4210] (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)))
% 60.75/20.19
% 60.75/20.19 [4210] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)))
% 60.75/20.19 -> [4211] ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 60.75/20.19 -> [4212] (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 60.75/20.19
% 60.75/20.19 [4211] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [4212] BETA_OR : (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 60.75/20.19 -> [4727] distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 60.75/20.19 -> [4728] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [4727] CLOSURE : distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 60.75/20.19
% 60.75/20.19 [4728] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [4201] 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))))
% 60.75/20.19 -> [4731] (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)))
% 60.75/20.19
% 60.75/20.19 [4731] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)))
% 60.75/20.19 -> [4732] ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 60.75/20.19 -> [4733] (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 60.75/20.19
% 60.75/20.19 [4732] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [4733] BETA_OR : (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 60.75/20.19 -> [4740] distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 60.75/20.19 -> [4741] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [4740] CLOSURE : distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 60.75/20.19
% 60.75/20.19 [4741] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [3265] GAMMA_FORALL : ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21)))
% 60.75/20.19 -> [4749] (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 60.75/20.19
% 60.75/20.19 [4749] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 60.75/20.19 -> [4750] ~convergent_lines(skolem_U4040, skolem_V4141)
% 60.75/20.19 -> [4751] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [4750] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 60.75/20.19
% 60.75/20.19 [4751] GAMMA_FORALL : ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24)))
% 60.75/20.19 -> [4754] (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 60.75/20.19
% 60.75/20.19 [4754] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 60.75/20.19 -> [4755] ~convergent_lines(skolem_U4040, skolem_V4141)
% 60.75/20.19 -> [4756] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 60.75/20.19
% 60.75/20.19 [4755] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 60.75/20.19
% 60.75/20.19 [4757] BETA_IMPLY : ((distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))) => (((apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 60.75/20.19 -> [4851] ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 60.75/20.19 -> [4852] (((apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 60.75/20.19
% 60.75/20.19 [4851] BETA_NOT_AND : ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 60.75/20.19 -> [4853] ~distinct_points(skolem_X3838, skolem_Y3939)
% 60.75/20.19 -> [4854] ~distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))
% 60.75/20.19
% 60.75/20.19 [4853] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 60.75/20.19
% 60.75/20.19 [4863] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)))
% 60.75/20.19 -> [4901] ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 60.75/20.19 -> [4902] (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 60.75/20.19
% 60.75/20.19 [4901] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [4902] BETA_OR : (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 60.75/20.19 -> [4907] distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 60.75/20.19 -> [4908] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [4908] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [4907] CLOSURE : distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 60.75/20.19
% 60.75/20.19 [4852] BETA_OR : (((apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 60.75/20.19 -> [4916] ((apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 60.75/20.19 -> [4917] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 60.75/20.19
% 60.75/20.19 [4916] BETA_OR : ((apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 60.75/20.19 -> [4918] (apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 60.75/20.19 -> [4919] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 60.75/20.19
% 60.75/20.19 [4918] BETA_OR : (apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 60.75/20.19 -> [4920] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 60.75/20.19 -> [4921] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 60.75/20.19
% 60.75/20.19 [4920] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 60.75/20.19
% 60.75/20.19 [4921] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 60.75/20.19
% 60.75/20.19 [4919] 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))))
% 60.75/20.19 -> [4923] (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)))
% 60.75/20.19
% 60.75/20.19 [4923] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)))
% 60.75/20.19 -> [4926] ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 60.75/20.19 -> [4927] (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 60.75/20.19
% 60.75/20.19 [4926] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [4927] BETA_OR : (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 60.75/20.19 -> [4936] distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 60.75/20.19 -> [4937] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [4936] CLOSURE : distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 60.75/20.19
% 60.75/20.19 [4937] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [4917] 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))))
% 60.75/20.19 -> [4922] (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)))
% 60.75/20.19
% 60.75/20.19 [4922] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_U4040) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)))
% 60.75/20.19 -> [4924] ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 60.75/20.19 -> [4925] (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 60.75/20.19
% 60.75/20.19 [4924] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [4925] BETA_OR : (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 60.75/20.19 -> [4938] distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 60.75/20.19 -> [4939] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [4938] CLOSURE : distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 60.75/20.19
% 60.75/20.19 [4939] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [8] ALPHA_NOT_NOT : ~~apart_point_and_line(skolem_X3838, skolem_V4141)
% 60.75/20.19 -> [10] apart_point_and_line(skolem_X3838, skolem_V4141)
% 60.75/20.19
% 60.75/20.19 [10] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 60.75/20.19 -> [12] ~distinct_points(skolem_Y3939, skolem_Y3939)
% 60.75/20.19
% 60.75/20.19 [12] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 60.75/20.19 -> [14] ~distinct_lines(X6_1_1, X6_1_1)
% 60.75/20.19
% 60.75/20.19 [14] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 60.75/20.19 -> [16] ~convergent_lines(X7_1_2, X7_1_2)
% 60.75/20.19
% 60.75/20.19 [16] GAMMA_FORALL : ! [X8_8, Y9_9, Z10_10] : ((distinct_points(X8_8, Y9_9) => (distinct_points(X8_8, Z10_10) | distinct_points(Y9_9, Z10_10))))
% 60.75/20.19 -> [18] (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939)))
% 60.75/20.19
% 60.75/20.19 [18] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939)))
% 60.75/20.19 -> [21] ~distinct_points(skolem_X3838, skolem_Y3939)
% 60.75/20.19 -> [22] (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939))
% 60.75/20.19
% 60.75/20.19 [21] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 60.75/20.19
% 60.75/20.19 [22] BETA_OR : (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939))
% 60.75/20.19 -> [29] distinct_points(skolem_X3838, skolem_Y3939)
% 60.75/20.19 -> [30] distinct_points(skolem_Y3939, skolem_Y3939)
% 60.75/20.19
% 60.75/20.19 [30] CLOSURE : distinct_points(skolem_Y3939, skolem_Y3939)
% 60.75/20.19
% 60.75/20.19 [29] GAMMA_FORALL : ! [X11_11, Y12_12, Z13_13] : ((distinct_lines(X11_11, Y12_12) => (distinct_lines(X11_11, Z13_13) | distinct_lines(Y12_12, Z13_13))))
% 60.75/20.19 -> [34] (distinct_lines(Z13_1_4, Z13_1_4) => (distinct_lines(Z13_1_4, Z13_1_4) | distinct_lines(Z13_1_4, Z13_1_4)))
% 60.75/20.19
% 60.75/20.19 [34] BETA_IMPLY : (distinct_lines(Z13_1_4, Z13_1_4) => (distinct_lines(Z13_1_4, Z13_1_4) | distinct_lines(Z13_1_4, Z13_1_4)))
% 60.75/20.19 -> [37] ~distinct_lines(Z13_1_4, Z13_1_4)
% 60.75/20.19 -> [38] (distinct_lines(Z13_1_4, Z13_1_4) | distinct_lines(Z13_1_4, Z13_1_4))
% 60.75/20.19
% 60.75/20.19 [38] BETA_OR : (distinct_lines(Z13_1_4, Z13_1_4) | distinct_lines(Z13_1_4, Z13_1_4))
% 60.75/20.19 -> [42] distinct_lines(Z13_1_4, Z13_1_4)
% 60.75/20.19 -> [43] distinct_lines(Z13_1_4, Z13_1_4)
% 60.75/20.19
% 60.75/20.19 [42] CLOSURE : distinct_lines(Z13_1_4, Z13_1_4)
% 60.75/20.19
% 60.75/20.19 [43] CLOSURE : distinct_lines(Z13_1_4, Z13_1_4)
% 60.75/20.19
% 60.75/20.19 [44] BETA_IMPLY : (convergent_lines(Z16_1_5, Z16_1_5) => (convergent_lines(Z16_1_5, Z16_1_5) | convergent_lines(Z16_1_5, Z16_1_5)))
% 60.75/20.19 -> [5685] ~convergent_lines(Z16_1_5, Z16_1_5)
% 60.75/20.19 -> [5686] (convergent_lines(Z16_1_5, Z16_1_5) | convergent_lines(Z16_1_5, Z16_1_5))
% 60.75/20.19
% 60.75/20.19 [5686] BETA_OR : (convergent_lines(Z16_1_5, Z16_1_5) | convergent_lines(Z16_1_5, Z16_1_5))
% 60.75/20.19 -> [5687] convergent_lines(Z16_1_5, Z16_1_5)
% 60.75/20.19 -> [5688] convergent_lines(Z16_1_5, Z16_1_5)
% 60.75/20.19
% 60.75/20.19 [5687] CLOSURE : convergent_lines(Z16_1_5, Z16_1_5)
% 60.75/20.19
% 60.75/20.19 [5688] CLOSURE : convergent_lines(Z16_1_5, Z16_1_5)
% 60.75/20.19
% 60.75/20.19 [5685] GAMMA_FORALL : ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18))))
% 60.75/20.19 -> [5689] (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 60.75/20.19
% 60.75/20.19 [5689] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 60.75/20.19 -> [5690] ~distinct_points(skolem_X3838, skolem_Y3939)
% 60.75/20.19 -> [5691] ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 60.75/20.19
% 60.75/20.19 [5690] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 60.75/20.19
% 60.75/20.19 [5691] GAMMA_FORALL : ! [X19_19, Y20_20] : ((distinct_points(X19_19, Y20_20) => ~apart_point_and_line(Y20_20, line_connecting(X19_19, Y20_20))))
% 60.75/20.19 -> [5692] (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 60.75/20.19
% 60.75/20.19 [5692] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 60.75/20.19 -> [5693] ~distinct_points(skolem_X3838, skolem_Y3939)
% 60.75/20.19 -> [5694] ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 60.75/20.19
% 60.75/20.19 [5693] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 60.75/20.19
% 60.75/20.19 [5694] GAMMA_FORALL : ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21)))
% 60.75/20.19 -> [5695] (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 60.75/20.19
% 60.75/20.19 [5695] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 60.75/20.19 -> [5696] ~convergent_lines(skolem_U4040, skolem_V4141)
% 60.75/20.19 -> [5697] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [5696] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 60.75/20.19
% 60.75/20.19 [5698] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 60.75/20.19 -> [5780] ~convergent_lines(skolem_U4040, skolem_V4141)
% 60.75/20.19 -> [5781] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 60.75/20.19
% 60.75/20.19 [5780] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 60.75/20.19
% 60.75/20.19 [5782] BETA_IMPLY : ((distinct_points(intersection_point(skolem_U4040, skolem_V4141), intersection_point(skolem_U4040, skolem_V4141)) & distinct_lines(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)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)))
% 60.75/20.19 -> [6271] ~(distinct_points(intersection_point(skolem_U4040, skolem_V4141), intersection_point(skolem_U4040, skolem_V4141)) & distinct_lines(skolem_V4141, skolem_U4040))
% 60.75/20.19 -> [6272] (((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)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 60.75/20.19
% 60.75/20.19 [6272] BETA_OR : (((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)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 60.75/20.19 -> [6275] ((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))
% 60.75/20.19 -> [6276] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [6276] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [6275] BETA_OR : ((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))
% 60.75/20.19 -> [6288] (apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 60.75/20.19 -> [6289] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 60.75/20.19
% 60.75/20.19 [6289] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 60.75/20.19
% 60.75/20.19 [6288] BETA_OR : (apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 60.75/20.19 -> [6292] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 60.75/20.19 -> [6293] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [6292] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 60.75/20.19
% 60.75/20.19 [6293] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [6271] BETA_NOT_AND : ~(distinct_points(intersection_point(skolem_U4040, skolem_V4141), intersection_point(skolem_U4040, skolem_V4141)) & distinct_lines(skolem_V4141, skolem_U4040))
% 60.75/20.19 -> [6294] ~distinct_points(intersection_point(skolem_U4040, skolem_V4141), intersection_point(skolem_U4040, skolem_V4141))
% 60.75/20.19 -> [6295] ~distinct_lines(skolem_V4141, skolem_U4040)
% 60.75/20.19
% 60.75/20.19 [6295] 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))))
% 60.75/20.19 -> [6297] (apart_point_and_line(skolem_X3838, skolem_V4141) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)))
% 60.75/20.19
% 60.75/20.19 [6297] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_V4141) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)))
% 60.75/20.19 -> [6300] ~apart_point_and_line(skolem_X3838, skolem_V4141)
% 60.75/20.19 -> [6301] (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 60.75/20.19
% 60.75/20.19 [6300] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_V4141)
% 60.75/20.19
% 60.75/20.19 [6301] BETA_OR : (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 60.75/20.19 -> [6306] distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 60.75/20.19 -> [6307] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 60.75/20.19
% 60.75/20.19 [6306] CLOSURE : distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 60.75/20.19
% 60.75/20.19 [6307] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 60.75/20.19
% 60.75/20.19 [6294] 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))))
% 60.75/20.19 -> [6296] (apart_point_and_line(skolem_X3838, skolem_V4141) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)))
% 60.75/20.19
% 60.75/20.19 [6296] BETA_IMPLY : (apart_point_and_line(skolem_X3838, skolem_V4141) => (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)))
% 60.75/20.19 -> [6298] ~apart_point_and_line(skolem_X3838, skolem_V4141)
% 60.75/20.19 -> [6299] (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 60.75/20.19
% 60.75/20.19 [6298] CLOSURE : ~apart_point_and_line(skolem_X3838, skolem_V4141)
% 60.75/20.19
% 60.75/20.19 [6299] BETA_OR : (distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141)) | apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141))
% 60.75/20.19 -> [6308] distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 60.75/20.19 -> [6309] apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 60.75/20.19
% 60.75/20.19 [6308] CLOSURE : distinct_points(skolem_X3838, intersection_point(skolem_U4040, skolem_V4141))
% 60.75/20.19
% 60.75/20.19 [6309] CLOSURE : apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_V4141)
% 60.75/20.19
% 60.75/20.19 % SZS output end Proof for theBenchmark.p
% 60.75/20.19 [19.856254s][1][Res] 217693 goroutines created
% 60.75/20.19 ==== Result ====
% 60.75/20.19 [19.856292s][1][Res] VALID
% 60.75/20.19 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------