TSTP Solution File: GEO178+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO178+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n009.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 15:18:14 EDT 2022
% Result : Theorem 56.26s 8.82s
% Output : Proof 56.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO178+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 06:43:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 [DMT] DMT loaded with preskolemization
% 0.13/0.34 [EQ] equality loaded.
% 0.13/0.34 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.35 Conjecture not found
% 0.13/0.35 Start search
% 0.13/0.35 nb_step : 1 - limit : 15
% 0.13/0.35 Launch Gotab with destructive = true
% 56.26/8.81 % SZS output start Proof for theBenchmark.p
% 56.26/8.82 [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] : (((distinct_points(X38_38, Y39_39) & apart_point_and_line(Z40_40, line_connecting(X38_38, Y39_39))) => (distinct_points(Z40_40, X38_38) & distinct_points(Z40_40, Y39_39)))))
% 56.26/8.82 -> [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] : (((distinct_points(X38_38, Y39_39) & apart_point_and_line(Z40_40, line_connecting(X38_38, Y39_39))) => (distinct_points(Z40_40, X38_38) & distinct_points(Z40_40, Y39_39))))
% 56.26/8.82
% 56.26/8.82 [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)))))
% 56.26/8.82 -> [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))))
% 56.26/8.82
% 56.26/8.82 [2] DELTA_NOT_FORALL : ~! [X38_38, Y39_39, Z40_40] : (((distinct_points(X38_38, Y39_39) & apart_point_and_line(Z40_40, line_connecting(X38_38, Y39_39))) => (distinct_points(Z40_40, X38_38) & distinct_points(Z40_40, Y39_39))))
% 56.26/8.82 -> [3] ~((distinct_points(skolem_X3838, skolem_Y3939) & apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))) => (distinct_points(skolem_Z4040, skolem_X3838) & distinct_points(skolem_Z4040, skolem_Y3939)))
% 56.26/8.82
% 56.26/8.82 [3] ALPHA_NOT_IMPLY : ~((distinct_points(skolem_X3838, skolem_Y3939) & apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))) => (distinct_points(skolem_Z4040, skolem_X3838) & distinct_points(skolem_Z4040, skolem_Y3939)))
% 56.26/8.82 -> [4] (distinct_points(skolem_X3838, skolem_Y3939) & apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))), ~(distinct_points(skolem_Z4040, skolem_X3838) & distinct_points(skolem_Z4040, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4] ALPHA_AND : (distinct_points(skolem_X3838, skolem_Y3939) & apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5] distinct_points(skolem_X3838, skolem_Y3939), apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5] BETA_NOT_AND : ~(distinct_points(skolem_Z4040, skolem_X3838) & distinct_points(skolem_Z4040, skolem_Y3939))
% 56.26/8.82 -> [6] ~distinct_points(skolem_Z4040, skolem_X3838)
% 56.26/8.82 -> [7] ~distinct_points(skolem_Z4040, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [6] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 56.26/8.82 -> [8] ~distinct_points(skolem_Y3939, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [8] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 56.26/8.82 -> [10] ~distinct_lines(X6_0_1, X6_0_1)
% 56.26/8.82
% 56.26/8.82 [10] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 56.26/8.82 -> [12] ~convergent_lines(X7_0_2, X7_0_2)
% 56.26/8.82
% 56.26/8.82 [12] 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))))
% 56.26/8.82 -> [14] (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939)))
% 56.26/8.82
% 56.26/8.82 [14] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939)))
% 56.26/8.82 -> [16] ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82 -> [17] (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [16] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [17] BETA_OR : (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939))
% 56.26/8.82 -> [24] distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82 -> [25] distinct_points(skolem_Y3939, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [25] CLOSURE : distinct_points(skolem_Y3939, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [24] 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))))
% 56.26/8.82 -> [29] (distinct_lines(Z13_1_4, Z13_1_4) => (distinct_lines(Z13_1_4, Z13_1_4) | distinct_lines(Z13_1_4, Z13_1_4)))
% 56.26/8.82
% 56.26/8.82 [29] 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)))
% 56.26/8.82 -> [32] ~distinct_lines(Z13_1_4, Z13_1_4)
% 56.26/8.82 -> [33] (distinct_lines(Z13_1_4, Z13_1_4) | distinct_lines(Z13_1_4, Z13_1_4))
% 56.26/8.82
% 56.26/8.82 [33] BETA_OR : (distinct_lines(Z13_1_4, Z13_1_4) | distinct_lines(Z13_1_4, Z13_1_4))
% 56.26/8.82 -> [36] distinct_lines(Z13_1_4, Z13_1_4)
% 56.26/8.82 -> [37] distinct_lines(Z13_1_4, Z13_1_4)
% 56.26/8.82
% 56.26/8.82 [36] CLOSURE : distinct_lines(Z13_1_4, Z13_1_4)
% 56.26/8.82
% 56.26/8.82 [37] CLOSURE : distinct_lines(Z13_1_4, Z13_1_4)
% 56.26/8.82
% 56.26/8.82 [32] 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))))
% 56.26/8.82 -> [41] (convergent_lines(Z16_1_5, Z16_1_5) => (convergent_lines(Z16_1_5, Z16_1_5) | convergent_lines(Z16_1_5, Z16_1_5)))
% 56.26/8.82
% 56.26/8.82 [41] 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)))
% 56.26/8.82 -> [42] ~convergent_lines(Z16_1_5, Z16_1_5)
% 56.26/8.82 -> [43] (convergent_lines(Z16_1_5, Z16_1_5) | convergent_lines(Z16_1_5, Z16_1_5))
% 56.26/8.82
% 56.26/8.82 [43] BETA_OR : (convergent_lines(Z16_1_5, Z16_1_5) | convergent_lines(Z16_1_5, Z16_1_5))
% 56.26/8.82 -> [46] convergent_lines(Z16_1_5, Z16_1_5)
% 56.26/8.82 -> [47] convergent_lines(Z16_1_5, Z16_1_5)
% 56.26/8.82
% 56.26/8.82 [46] CLOSURE : convergent_lines(Z16_1_5, Z16_1_5)
% 56.26/8.82
% 56.26/8.82 [47] CLOSURE : convergent_lines(Z16_1_5, Z16_1_5)
% 56.26/8.82
% 56.26/8.82 [42] GAMMA_FORALL : ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18))))
% 56.26/8.82 -> [48] (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82
% 56.26/8.82 [48] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [49] ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82 -> [50] ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [49] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [54] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [4658] ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82 -> [4659] ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4658] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [4659] GAMMA_FORALL : ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21)))
% 56.26/8.82 -> [4664] (convergent_lines(X21_2_8, Y22_2_8) => ~apart_point_and_line(intersection_point(X21_2_8, Y22_2_8), X21_2_8))
% 56.26/8.82
% 56.26/8.82 [4664] BETA_IMPLY : (convergent_lines(X21_2_8, Y22_2_8) => ~apart_point_and_line(intersection_point(X21_2_8, Y22_2_8), X21_2_8))
% 56.26/8.82 -> [4665] ~convergent_lines(X21_2_8, Y22_2_8)
% 56.26/8.82 -> [4666] ~apart_point_and_line(intersection_point(X21_2_8, Y22_2_8), X21_2_8)
% 56.26/8.82
% 56.26/8.82 [4665] GAMMA_FORALL : ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24)))
% 56.26/8.82 -> [4667] (convergent_lines(X23_8_9, Y24_8_9) => ~apart_point_and_line(intersection_point(X23_8_9, Y24_8_9), Y24_8_9))
% 56.26/8.82
% 56.26/8.82 [4667] BETA_IMPLY : (convergent_lines(X23_8_9, Y24_8_9) => ~apart_point_and_line(intersection_point(X23_8_9, Y24_8_9), Y24_8_9))
% 56.26/8.82 -> [4668] ~convergent_lines(X23_8_9, Y24_8_9)
% 56.26/8.82 -> [4669] ~apart_point_and_line(intersection_point(X23_8_9, Y24_8_9), Y24_8_9)
% 56.26/8.82
% 56.26/8.82 [4669] 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))))
% 56.26/8.82 -> [4676] ((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))))
% 56.26/8.82
% 56.26/8.82 [4676] 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))))
% 56.26/8.82 -> [4678] ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [4679] (((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)))
% 56.26/8.82
% 56.26/8.82 [4678] BETA_NOT_AND : ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [4695] ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82 -> [4696] ~distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4695] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [4696] 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))))
% 56.26/8.82 -> [4718] (apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 56.26/8.82
% 56.26/8.82 [4718] BETA_IMPLY : (apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 56.26/8.82 -> [4721] ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82 -> [4722] (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82
% 56.26/8.82 [4721] CLOSURE : ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4722] BETA_OR : (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [4763] distinct_points(skolem_Z4040, skolem_X3838)
% 56.26/8.82 -> [4764] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4764] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4763] CLOSURE : distinct_points(skolem_Z4040, skolem_X3838)
% 56.26/8.82
% 56.26/8.82 [4679] 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)))
% 56.26/8.82 -> [4848] ((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)))
% 56.26/8.82 -> [4849] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4849] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4848] 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)))
% 56.26/8.82 -> [4887] (apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [4888] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4888] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4887] 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)))
% 56.26/8.82 -> [4926] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82 -> [4927] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4927] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4926] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4668] 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))))
% 56.26/8.82 -> [4673] ((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))))
% 56.26/8.82
% 56.26/8.82 [4673] 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))))
% 56.26/8.82 -> [4674] ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [4675] (((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)))
% 56.26/8.82
% 56.26/8.82 [4674] BETA_NOT_AND : ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [4683] ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82 -> [4684] ~distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4683] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [4684] 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))))
% 56.26/8.82 -> [4703] (apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 56.26/8.82
% 56.26/8.82 [4703] BETA_IMPLY : (apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 56.26/8.82 -> [4706] ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82 -> [4707] (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82
% 56.26/8.82 [4706] CLOSURE : ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4707] BETA_OR : (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [4767] distinct_points(skolem_Z4040, skolem_X3838)
% 56.26/8.82 -> [4768] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4768] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4767] CLOSURE : distinct_points(skolem_Z4040, skolem_X3838)
% 56.26/8.82
% 56.26/8.82 [4675] 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)))
% 56.26/8.82 -> [4830] ((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)))
% 56.26/8.82 -> [4831] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4831] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4830] 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)))
% 56.26/8.82 -> [5353] (apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5354] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5354] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5353] 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)))
% 56.26/8.82 -> [5364] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82 -> [5365] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5364] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5365] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4666] GAMMA_FORALL : ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24)))
% 56.26/8.82 -> [4670] (convergent_lines(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939)) => ~apart_point_and_line(intersection_point(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939)), line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82
% 56.26/8.82 [4670] BETA_IMPLY : (convergent_lines(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939)) => ~apart_point_and_line(intersection_point(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939)), line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [4671] ~convergent_lines(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82 -> [4672] ~apart_point_and_line(intersection_point(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939)), line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4672] 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))))
% 56.26/8.82 -> [4680] ((distinct_points(skolem_X3838, intersection_point(X23_9_9, line_connecting(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(intersection_point(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939)), line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(intersection_point(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939)), line_connecting(skolem_X3838, skolem_Y3939))))
% 56.26/8.82
% 56.26/8.82 [4680] BETA_IMPLY : ((distinct_points(skolem_X3838, intersection_point(X23_9_9, line_connecting(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(intersection_point(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939)), line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(intersection_point(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939)), line_connecting(skolem_X3838, skolem_Y3939))))
% 56.26/8.82 -> [4685] ~(distinct_points(skolem_X3838, intersection_point(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939))) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [4686] (((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(intersection_point(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939)), line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(intersection_point(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939)), line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82
% 56.26/8.82 [4686] 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(intersection_point(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939)), line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(intersection_point(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939)), line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [4693] ((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(intersection_point(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939)), line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [4694] apart_point_and_line(intersection_point(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939)), line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4694] CLOSURE : apart_point_and_line(intersection_point(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939)), line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4693] 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(intersection_point(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939)), line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [4805] (apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [4806] apart_point_and_line(intersection_point(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939)), line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4805] BETA_OR : (apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_X3838)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [4807] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_X3838))
% 56.26/8.82 -> [4808] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4808] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4807] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_X3838))
% 56.26/8.82
% 56.26/8.82 [4806] CLOSURE : apart_point_and_line(intersection_point(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939)), line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4685] BETA_NOT_AND : ~(distinct_points(skolem_X3838, intersection_point(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939))) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [4861] ~distinct_points(skolem_X3838, intersection_point(X23_9_9, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [4862] ~distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4861] 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))))
% 56.26/8.82 -> [4870] (apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 56.26/8.82
% 56.26/8.82 [4870] BETA_IMPLY : (apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 56.26/8.82 -> [4872] ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82 -> [4873] (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82
% 56.26/8.82 [4872] CLOSURE : ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4873] BETA_OR : (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [4912] distinct_points(skolem_Z4040, skolem_X3838)
% 56.26/8.82 -> [4913] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4912] CLOSURE : distinct_points(skolem_Z4040, skolem_X3838)
% 56.26/8.82
% 56.26/8.82 [4913] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4862] 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))))
% 56.26/8.82 -> [4871] (apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 56.26/8.82
% 56.26/8.82 [4871] BETA_IMPLY : (apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 56.26/8.82 -> [4874] ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82 -> [4875] (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82
% 56.26/8.82 [4874] CLOSURE : ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [4875] BETA_OR : (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5045] distinct_points(skolem_Z4040, skolem_X3838)
% 56.26/8.82 -> [5046] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5046] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5045] CLOSURE : distinct_points(skolem_Z4040, skolem_X3838)
% 56.26/8.82
% 56.26/8.82 [4677] BETA_IMPLY : ((distinct_points(skolem_Y3939, skolem_X3838) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))) => (((apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 56.26/8.82 -> [5738] ~(distinct_points(skolem_Y3939, skolem_X3838) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5739] (((apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82
% 56.26/8.82 [5739] BETA_OR : (((apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5742] ((apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5743] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5743] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5742] BETA_OR : ((apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5785] (apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5786] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5786] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5785] BETA_OR : (apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5798] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82 -> [5799] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5798] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5799] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5738] BETA_NOT_AND : ~(distinct_points(skolem_Y3939, skolem_X3838) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5802] ~distinct_points(skolem_Y3939, skolem_X3838)
% 56.26/8.82 -> [5803] ~distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5802] 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))))
% 56.26/8.82 -> [5807] (apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 56.26/8.82
% 56.26/8.82 [5807] BETA_IMPLY : (apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 56.26/8.82 -> [5811] ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82 -> [5812] (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82
% 56.26/8.82 [5811] CLOSURE : ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5812] BETA_OR : (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5829] distinct_points(skolem_Z4040, skolem_X3838)
% 56.26/8.82 -> [5830] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5829] CLOSURE : distinct_points(skolem_Z4040, skolem_X3838)
% 56.26/8.82
% 56.26/8.82 [5830] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5803] 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))))
% 56.26/8.82 -> [5810] (apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 56.26/8.82
% 56.26/8.82 [5810] BETA_IMPLY : (apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))))
% 56.26/8.82 -> [5814] ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82 -> [5815] (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82
% 56.26/8.82 [5814] CLOSURE : ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5815] BETA_OR : (distinct_points(skolem_Z4040, skolem_X3838) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5832] distinct_points(skolem_Z4040, skolem_X3838)
% 56.26/8.82 -> [5833] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5832] CLOSURE : distinct_points(skolem_Z4040, skolem_X3838)
% 56.26/8.82
% 56.26/8.82 [5833] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [7] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 56.26/8.82 -> [9] ~distinct_points(skolem_Y3939, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [9] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 56.26/8.82 -> [11] ~distinct_lines(X6_1_1, X6_1_1)
% 56.26/8.82
% 56.26/8.82 [11] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 56.26/8.82 -> [13] ~convergent_lines(X7_1_2, X7_1_2)
% 56.26/8.82
% 56.26/8.82 [13] GAMMA_FORALL : ! [X8_8, Y9_9, Z10_10] : ((distinct_points(X8_8, Y9_9) => (distinct_points(X8_8, Z10_10) | distinct_points(Y9_9, Z10_10))))
% 56.26/8.82 -> [15] (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939)))
% 56.26/8.82
% 56.26/8.82 [15] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939)))
% 56.26/8.82 -> [18] ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82 -> [19] (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [18] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [19] BETA_OR : (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939))
% 56.26/8.82 -> [26] distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82 -> [27] distinct_points(skolem_Y3939, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [27] CLOSURE : distinct_points(skolem_Y3939, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [26] GAMMA_FORALL : ! [X11_11, Y12_12, Z13_13] : ((distinct_lines(X11_11, Y12_12) => (distinct_lines(X11_11, Z13_13) | distinct_lines(Y12_12, Z13_13))))
% 56.26/8.82 -> [28] (distinct_lines(Z13_0_4, Z13_0_4) => (distinct_lines(Z13_0_4, Z13_0_4) | distinct_lines(Z13_0_4, Z13_0_4)))
% 56.26/8.82
% 56.26/8.82 [28] 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)))
% 56.26/8.82 -> [30] ~distinct_lines(Z13_0_4, Z13_0_4)
% 56.26/8.82 -> [31] (distinct_lines(Z13_0_4, Z13_0_4) | distinct_lines(Z13_0_4, Z13_0_4))
% 56.26/8.82
% 56.26/8.82 [31] BETA_OR : (distinct_lines(Z13_0_4, Z13_0_4) | distinct_lines(Z13_0_4, Z13_0_4))
% 56.26/8.82 -> [34] distinct_lines(Z13_0_4, Z13_0_4)
% 56.26/8.82 -> [35] distinct_lines(Z13_0_4, Z13_0_4)
% 56.26/8.82
% 56.26/8.82 [35] CLOSURE : distinct_lines(Z13_0_4, Z13_0_4)
% 56.26/8.82
% 56.26/8.82 [34] CLOSURE : distinct_lines(Z13_0_4, Z13_0_4)
% 56.26/8.82
% 56.26/8.82 [30] 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))))
% 56.26/8.82 -> [38] (convergent_lines(X14_0_5, X14_0_5) => (convergent_lines(X14_0_5, X14_0_5) | convergent_lines(X14_0_5, X14_0_5)))
% 56.26/8.82
% 56.26/8.82 [38] BETA_IMPLY : (convergent_lines(X14_0_5, X14_0_5) => (convergent_lines(X14_0_5, X14_0_5) | convergent_lines(X14_0_5, X14_0_5)))
% 56.26/8.82 -> [39] ~convergent_lines(X14_0_5, X14_0_5)
% 56.26/8.82 -> [40] (convergent_lines(X14_0_5, X14_0_5) | convergent_lines(X14_0_5, X14_0_5))
% 56.26/8.82
% 56.26/8.82 [40] BETA_OR : (convergent_lines(X14_0_5, X14_0_5) | convergent_lines(X14_0_5, X14_0_5))
% 56.26/8.82 -> [44] convergent_lines(X14_0_5, X14_0_5)
% 56.26/8.82 -> [45] convergent_lines(X14_0_5, X14_0_5)
% 56.26/8.82
% 56.26/8.82 [45] CLOSURE : convergent_lines(X14_0_5, X14_0_5)
% 56.26/8.82
% 56.26/8.82 [44] CLOSURE : convergent_lines(X14_0_5, X14_0_5)
% 56.26/8.82
% 56.26/8.82 [39] GAMMA_FORALL : ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18))))
% 56.26/8.82 -> [51] (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82
% 56.26/8.82 [51] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [52] ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82 -> [53] ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [52] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [57] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5855] ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82 -> [5856] ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5855] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [5856] GAMMA_FORALL : ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21)))
% 56.26/8.82 -> [5857] (convergent_lines(X21_3_8, Y22_3_8) => ~apart_point_and_line(intersection_point(X21_3_8, Y22_3_8), X21_3_8))
% 56.26/8.82
% 56.26/8.82 [5857] BETA_IMPLY : (convergent_lines(X21_3_8, Y22_3_8) => ~apart_point_and_line(intersection_point(X21_3_8, Y22_3_8), X21_3_8))
% 56.26/8.82 -> [5858] ~convergent_lines(X21_3_8, Y22_3_8)
% 56.26/8.82 -> [5859] ~apart_point_and_line(intersection_point(X21_3_8, Y22_3_8), X21_3_8)
% 56.26/8.82
% 56.26/8.82 [5859] GAMMA_FORALL : ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24)))
% 56.26/8.82 -> [5861] (convergent_lines(X23_11_9, Y24_11_9) => ~apart_point_and_line(intersection_point(X23_11_9, Y24_11_9), Y24_11_9))
% 56.26/8.82
% 56.26/8.82 [5861] BETA_IMPLY : (convergent_lines(X23_11_9, Y24_11_9) => ~apart_point_and_line(intersection_point(X23_11_9, Y24_11_9), Y24_11_9))
% 56.26/8.82 -> [5864] ~convergent_lines(X23_11_9, Y24_11_9)
% 56.26/8.82 -> [5865] ~apart_point_and_line(intersection_point(X23_11_9, Y24_11_9), Y24_11_9)
% 56.26/8.82
% 56.26/8.82 [5864] 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))))
% 56.26/8.82 -> [5868] ((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))))
% 56.26/8.82
% 56.26/8.82 [5868] 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))))
% 56.26/8.82 -> [5873] ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5874] (((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)))
% 56.26/8.82
% 56.26/8.82 [5873] BETA_NOT_AND : ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5880] ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82 -> [5881] ~distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5881] 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))))
% 56.26/8.82 -> [5906] (apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_points(skolem_Z4040, skolem_Y3939) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 56.26/8.82
% 56.26/8.82 [5906] BETA_IMPLY : (apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_points(skolem_Z4040, skolem_Y3939) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 56.26/8.82 -> [5909] ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82 -> [5910] (distinct_points(skolem_Z4040, skolem_Y3939) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82
% 56.26/8.82 [5909] CLOSURE : ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5910] BETA_OR : (distinct_points(skolem_Z4040, skolem_Y3939) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5982] distinct_points(skolem_Z4040, skolem_Y3939)
% 56.26/8.82 -> [5983] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5983] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5982] CLOSURE : distinct_points(skolem_Z4040, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [5880] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [5874] 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)))
% 56.26/8.82 -> [6003] ((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)))
% 56.26/8.82 -> [6004] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6003] 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)))
% 56.26/8.82 -> [6008] (apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [6009] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6009] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6008] 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)))
% 56.26/8.82 -> [6018] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82 -> [6019] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6018] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6019] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6004] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5865] 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))))
% 56.26/8.82 -> [5875] ((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))))
% 56.26/8.82
% 56.26/8.82 [5875] 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))))
% 56.26/8.82 -> [5884] ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5885] (((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)))
% 56.26/8.82
% 56.26/8.82 [5884] BETA_NOT_AND : ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5894] ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82 -> [5895] ~distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5894] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [5917] BETA_IMPLY : (apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_points(skolem_Z4040, skolem_Y3939) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 56.26/8.82 -> [6000] ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82 -> [6001] (distinct_points(skolem_Z4040, skolem_Y3939) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82
% 56.26/8.82 [6000] CLOSURE : ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6001] BETA_OR : (distinct_points(skolem_Z4040, skolem_Y3939) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [6021] distinct_points(skolem_Z4040, skolem_Y3939)
% 56.26/8.82 -> [6022] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6022] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6021] CLOSURE : distinct_points(skolem_Z4040, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [5885] 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)))
% 56.26/8.82 -> [6035] ((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)))
% 56.26/8.82 -> [6036] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6036] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6035] 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)))
% 56.26/8.82 -> [6049] (apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [6050] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6050] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6049] 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)))
% 56.26/8.82 -> [6051] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82 -> [6052] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6052] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6051] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5858] GAMMA_FORALL : ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24)))
% 56.26/8.82 -> [5860] (convergent_lines(X23_10_9, Y24_10_9) => ~apart_point_and_line(intersection_point(X23_10_9, Y24_10_9), Y24_10_9))
% 56.26/8.82
% 56.26/8.82 [5860] BETA_IMPLY : (convergent_lines(X23_10_9, Y24_10_9) => ~apart_point_and_line(intersection_point(X23_10_9, Y24_10_9), Y24_10_9))
% 56.26/8.82 -> [5862] ~convergent_lines(X23_10_9, Y24_10_9)
% 56.26/8.82 -> [5863] ~apart_point_and_line(intersection_point(X23_10_9, Y24_10_9), Y24_10_9)
% 56.26/8.82
% 56.26/8.82 [5862] 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))))
% 56.26/8.82 -> [5866] ((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))))
% 56.26/8.82
% 56.26/8.82 [5866] 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))))
% 56.26/8.82 -> [5869] ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5870] (((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)))
% 56.26/8.82
% 56.26/8.82 [5869] BETA_NOT_AND : ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5876] ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82 -> [5877] ~distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5876] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [5896] BETA_IMPLY : (apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_points(skolem_Z4040, skolem_Y3939) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 56.26/8.82 -> [5954] ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82 -> [5955] (distinct_points(skolem_Z4040, skolem_Y3939) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82
% 56.26/8.82 [5955] BETA_OR : (distinct_points(skolem_Y3939, skolem_Y3939) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5958] distinct_points(skolem_Y3939, skolem_Y3939)
% 56.26/8.82 -> [5959] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5959] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5958] CLOSURE : distinct_points(skolem_Y3939, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [5954] CLOSURE : ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5870] 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)))
% 56.26/8.82 -> [6041] ((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)))
% 56.26/8.82 -> [6042] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6041] 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)))
% 56.26/8.82 -> [6043] (apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [6044] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6044] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6043] 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)))
% 56.26/8.82 -> [6053] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82 -> [6054] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6053] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6054] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6042] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5863] 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))))
% 56.26/8.82 -> [5867] ((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))))
% 56.26/8.82
% 56.26/8.82 [5867] 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))))
% 56.26/8.82 -> [5871] ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5872] (((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)))
% 56.26/8.82
% 56.26/8.82 [5872] 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)))
% 56.26/8.82 -> [5886] ((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)))
% 56.26/8.82 -> [5887] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5886] BETA_OR : ((apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_X3838)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_X3838)))
% 56.26/8.82 -> [5890] (apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_X3838)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5891] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_X3838))
% 56.26/8.82
% 56.26/8.82 [5891] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_X3838))
% 56.26/8.82
% 56.26/8.82 [5890] BETA_OR : (apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_X3838)) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [5937] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_X3838))
% 56.26/8.82 -> [5938] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5938] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5937] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_X3838))
% 56.26/8.82
% 56.26/8.82 [5887] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [5871] BETA_NOT_AND : ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [6055] ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82 -> [6056] ~distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6055] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [6056] 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))))
% 56.26/8.82 -> [6057] (apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_points(skolem_Z4040, skolem_Y3939) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 56.26/8.82
% 56.26/8.82 [6057] BETA_IMPLY : (apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_points(skolem_Z4040, skolem_Y3939) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 56.26/8.82 -> [6058] ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82 -> [6059] (distinct_points(skolem_Z4040, skolem_Y3939) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82
% 56.26/8.82 [6058] CLOSURE : ~apart_point_and_line(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6059] BETA_OR : (distinct_points(skolem_Z4040, skolem_Y3939) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 56.26/8.82 -> [6062] distinct_points(skolem_Z4040, skolem_Y3939)
% 56.26/8.82 -> [6063] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 [6062] CLOSURE : distinct_points(skolem_Z4040, skolem_Y3939)
% 56.26/8.82
% 56.26/8.82 [6063] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 56.26/8.82
% 56.26/8.82 % SZS output end Proof for theBenchmark.p
% 56.26/8.82 [8.474568s][1][Res] 134498 goroutines created
% 56.26/8.82 ==== Result ====
% 56.26/8.82 [8.474584s][1][Res] VALID
% 56.26/8.82 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------