TSTP Solution File: GEO201+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO201+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n023.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 15:18:22 EDT 2022
% Result : Theorem 237.55s 113.02s
% Output : Proof 237.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO201+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n023.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 07:15:04 EDT 2022
% 0.20/0.34 % CPUTime :
% 0.20/0.35 [DMT] DMT loaded with preskolemization
% 0.20/0.35 [EQ] equality loaded.
% 0.20/0.35 [0.000040s][1][MAIN] Problem : theBenchmark.p
% 0.20/0.35 Conjecture not found
% 0.20/0.35 Start search
% 0.20/0.35 nb_step : 1 - limit : 15
% 0.20/0.35 Launch Gotab with destructive = true
% 237.55/113.00 % SZS output start Proof for theBenchmark.p
% 237.55/113.01 [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] : ((convergent_lines(X38_38, Y39_39) => ~distinct_points(intersection_point(X38_38, Y39_39), intersection_point(Y39_39, X38_38)))))
% 237.55/113.01 -> [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] : ((convergent_lines(X38_38, Y39_39) => ~distinct_points(intersection_point(X38_38, Y39_39), intersection_point(Y39_39, X38_38))))
% 237.55/113.01
% 237.55/113.01 [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)))))
% 237.55/113.01 -> [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))))
% 237.55/113.01
% 237.55/113.01 [2] DELTA_NOT_FORALL : ~! [X38_38, Y39_39] : ((convergent_lines(X38_38, Y39_39) => ~distinct_points(intersection_point(X38_38, Y39_39), intersection_point(Y39_39, X38_38))))
% 237.55/113.01 -> [3] ~(convergent_lines(skolem_X3838, skolem_Y3939) => ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.01
% 237.55/113.01 [3] ALPHA_NOT_IMPLY : ~(convergent_lines(skolem_X3838, skolem_Y3939) => ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.01 -> [4] convergent_lines(skolem_X3838, skolem_Y3939), ~~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [4] ALPHA_NOT_NOT : ~~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01 -> [5] distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [5] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 237.55/113.01 -> [6] ~distinct_points(intersection_point(skolem_Y3939, skolem_X3838), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [6] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 237.55/113.01 -> [7] ~distinct_lines(skolem_X3838, skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [7] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 237.55/113.01 -> [8] ~convergent_lines(skolem_X3838, skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [8] 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))))
% 237.55/113.01 -> [9] (distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) => (distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) | distinct_points(intersection_point(skolem_Y3939, skolem_X3838), intersection_point(skolem_Y3939, skolem_X3838))))
% 237.55/113.01
% 237.55/113.01 [9] BETA_IMPLY : (distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) => (distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) | distinct_points(intersection_point(skolem_Y3939, skolem_X3838), intersection_point(skolem_Y3939, skolem_X3838))))
% 237.55/113.01 -> [10] ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01 -> [11] (distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) | distinct_points(intersection_point(skolem_Y3939, skolem_X3838), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.01
% 237.55/113.01 [10] CLOSURE : ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [11] BETA_OR : (distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) | distinct_points(intersection_point(skolem_Y3939, skolem_X3838), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.01 -> [14] distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01 -> [15] distinct_points(intersection_point(skolem_Y3939, skolem_X3838), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [15] CLOSURE : distinct_points(intersection_point(skolem_Y3939, skolem_X3838), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [14] 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))))
% 237.55/113.01 -> [8248] (distinct_lines(skolem_X3838, skolem_Y3939) => (distinct_lines(skolem_X3838, line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))) | distinct_lines(skolem_Y3939, line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))))
% 237.55/113.01
% 237.55/113.01 [8248] BETA_IMPLY : (distinct_lines(skolem_X3838, skolem_Y3939) => (distinct_lines(skolem_X3838, line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))) | distinct_lines(skolem_Y3939, line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))))
% 237.55/113.01 -> [8249] ~distinct_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01 -> [8250] (distinct_lines(skolem_X3838, line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))) | distinct_lines(skolem_Y3939, line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))))
% 237.55/113.01
% 237.55/113.01 [8249] 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))))
% 237.55/113.01 -> [8253] (convergent_lines(skolem_X3838, skolem_Y3939) => (convergent_lines(skolem_X3838, skolem_X3838) | convergent_lines(skolem_Y3939, skolem_X3838)))
% 237.55/113.01
% 237.55/113.01 [8253] BETA_IMPLY : (convergent_lines(skolem_X3838, skolem_Y3939) => (convergent_lines(skolem_X3838, skolem_X3838) | convergent_lines(skolem_Y3939, skolem_X3838)))
% 237.55/113.01 -> [8254] ~convergent_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01 -> [8255] (convergent_lines(skolem_X3838, skolem_X3838) | convergent_lines(skolem_Y3939, skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [8254] CLOSURE : ~convergent_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [8255] BETA_OR : (convergent_lines(skolem_X3838, skolem_X3838) | convergent_lines(skolem_Y3939, skolem_X3838))
% 237.55/113.01 -> [8258] convergent_lines(skolem_X3838, skolem_X3838)
% 237.55/113.01 -> [8259] convergent_lines(skolem_Y3939, skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [8258] CLOSURE : convergent_lines(skolem_X3838, skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [8259] GAMMA_FORALL : ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18))))
% 237.55/113.01 -> [8306] (distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) => ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))))
% 237.55/113.01
% 237.55/113.01 [8306] BETA_IMPLY : (distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) => ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))))
% 237.55/113.01 -> [8307] ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01 -> [8308] ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.01
% 237.55/113.01 [8307] CLOSURE : ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [8309] BETA_IMPLY : (distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) => ~apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))))
% 237.55/113.01 -> [10663] ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01 -> [10664] ~apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.01
% 237.55/113.01 [10664] GAMMA_FORALL : ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21)))
% 237.55/113.01 -> [10665] (convergent_lines(skolem_Y3939, skolem_X3838) => ~apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939))
% 237.55/113.01
% 237.55/113.01 [10665] BETA_IMPLY : (convergent_lines(skolem_Y3939, skolem_X3838) => ~apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939))
% 237.55/113.01 -> [10666] ~convergent_lines(skolem_Y3939, skolem_X3838)
% 237.55/113.01 -> [10667] ~apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [10666] CLOSURE : ~convergent_lines(skolem_Y3939, skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [10668] BETA_IMPLY : (convergent_lines(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939))
% 237.55/113.01 -> [10958] ~convergent_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01 -> [10959] ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [10958] CLOSURE : ~convergent_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [10960] BETA_IMPLY : ((distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) & distinct_lines(skolem_Y3939, skolem_X3838)) => (((apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838)))
% 237.55/113.01 -> [11567] ~(distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) & distinct_lines(skolem_Y3939, skolem_X3838))
% 237.55/113.01 -> [11568] (((apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [11567] BETA_NOT_AND : ~(distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) & distinct_lines(skolem_Y3939, skolem_X3838))
% 237.55/113.01 -> [11569] ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01 -> [11570] ~distinct_lines(skolem_Y3939, skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [11569] CLOSURE : ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [11577] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))) => (distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_X3838, skolem_Y3939)) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))))
% 237.55/113.01 -> [11627] ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.01 -> [11628] (distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_X3838, skolem_Y3939)) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))))
% 237.55/113.01
% 237.55/113.01 [11628] BETA_OR : (distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_X3838, skolem_Y3939)) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))))
% 237.55/113.01 -> [11629] distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_X3838, skolem_Y3939))
% 237.55/113.01 -> [11630] apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.01
% 237.55/113.01 [11630] CLOSURE : apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.01
% 237.55/113.01 [11629] GAMMA_FORALL : ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34))))
% 237.55/113.01 -> [11641] (apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), Y33_237_12) => (distinct_lines(Y33_237_12, skolem_Y3939) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)))
% 237.55/113.01
% 237.55/113.01 [11641] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), Y33_237_12) => (distinct_lines(Y33_237_12, skolem_Y3939) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)))
% 237.55/113.01 -> [11642] ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), Y33_237_12)
% 237.55/113.01 -> [11643] (distinct_lines(Y33_237_12, skolem_Y3939) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939))
% 237.55/113.01
% 237.55/113.01 [11642] GAMMA_FORALL : ! [X35_35, Y36_36, Z37_37] : ((convergent_lines(X35_35, Y36_36) => (distinct_lines(Y36_36, Z37_37) | convergent_lines(X35_35, Z37_37))))
% 237.55/113.01 -> [11646] (convergent_lines(skolem_Y3939, skolem_X3838) => (distinct_lines(skolem_X3838, Z37_621_13) | convergent_lines(skolem_Y3939, Z37_621_13)))
% 237.55/113.01
% 237.55/113.01 [11646] BETA_IMPLY : (convergent_lines(skolem_Y3939, skolem_X3838) => (distinct_lines(skolem_X3838, Z37_621_13) | convergent_lines(skolem_Y3939, Z37_621_13)))
% 237.55/113.01 -> [11647] ~convergent_lines(skolem_Y3939, skolem_X3838)
% 237.55/113.01 -> [11648] (distinct_lines(skolem_X3838, Z37_621_13) | convergent_lines(skolem_Y3939, Z37_621_13))
% 237.55/113.01
% 237.55/113.01 [11647] CLOSURE : ~convergent_lines(skolem_Y3939, skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [11648] BETA_OR : (distinct_lines(skolem_X3838, Z37_621_13) | convergent_lines(skolem_Y3939, Z37_621_13))
% 237.55/113.01 -> [11655] distinct_lines(skolem_X3838, Z37_621_13)
% 237.55/113.01 -> [11656] convergent_lines(skolem_Y3939, Z37_621_13)
% 237.55/113.01
% 237.55/113.01 [11656] : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 237.55/113.01 -> [11659] ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 237.55/113.01
% 237.55/113.01 [11659] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 237.55/113.01 -> [11660] ~distinct_points(X5_1669_0, X5_1669_0)
% 237.55/113.01
% 237.55/113.01 [11660] CLOSURE : ~distinct_points(X5_1669_0, X5_1669_0)
% 237.55/113.01
% 237.55/113.01 [11655] CLOSURE : distinct_lines(skolem_X3838, Z37_621_13)
% 237.55/113.01
% 237.55/113.01 [11643] BETA_OR : (distinct_lines(Y33_237_12, skolem_Y3939) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939))
% 237.55/113.01 -> [11663] distinct_lines(Y33_237_12, skolem_Y3939)
% 237.55/113.01 -> [11664] apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [11664] CLOSURE : apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [11663] CLOSURE : distinct_lines(Y33_237_12, skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [11631] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), Y33_236_12) => (distinct_lines(Y33_236_12, line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))))
% 237.55/113.01 -> [11667] ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), Y33_236_12)
% 237.55/113.01 -> [11668] (distinct_lines(Y33_236_12, line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))))
% 237.55/113.01
% 237.55/113.01 [11667] GAMMA_FORALL : ! [X35_35, Y36_36, Z37_37] : ((convergent_lines(X35_35, Y36_36) => (distinct_lines(Y36_36, Z37_37) | convergent_lines(X35_35, Z37_37))))
% 237.55/113.01 -> [11671] (convergent_lines(skolem_X3838, skolem_Y3939) => (distinct_lines(skolem_Y3939, skolem_X3838) | convergent_lines(skolem_X3838, skolem_X3838)))
% 237.55/113.01
% 237.55/113.01 [11671] BETA_IMPLY : (convergent_lines(skolem_X3838, skolem_Y3939) => (distinct_lines(skolem_Y3939, skolem_X3838) | convergent_lines(skolem_X3838, skolem_X3838)))
% 237.55/113.01 -> [11672] ~convergent_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01 -> [11673] (distinct_lines(skolem_Y3939, skolem_X3838) | convergent_lines(skolem_X3838, skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [11672] CLOSURE : ~convergent_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [11673] BETA_OR : (distinct_lines(skolem_Y3939, skolem_X3838) | convergent_lines(skolem_X3838, skolem_X3838))
% 237.55/113.01 -> [11680] distinct_lines(skolem_Y3939, skolem_X3838)
% 237.55/113.01 -> [11681] convergent_lines(skolem_X3838, skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [11681] CLOSURE : convergent_lines(skolem_X3838, skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [11680] CLOSURE : distinct_lines(skolem_Y3939, skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [11668] BETA_OR : (distinct_lines(Y33_236_12, line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))))
% 237.55/113.01 -> [11682] distinct_lines(Y33_236_12, line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.01 -> [11683] apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.01
% 237.55/113.01 [11683] CLOSURE : apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.01
% 237.55/113.01 [11682] GAMMA_FORALL : ! [X35_35, Y36_36, Z37_37] : ((convergent_lines(X35_35, Y36_36) => (distinct_lines(Y36_36, Z37_37) | convergent_lines(X35_35, Z37_37))))
% 237.55/113.01 -> [11684] (convergent_lines(skolem_X3838, skolem_Y3939) => (distinct_lines(skolem_Y3939, skolem_X3838) | convergent_lines(skolem_X3838, skolem_X3838)))
% 237.55/113.01
% 237.55/113.01 [11684] BETA_IMPLY : (convergent_lines(skolem_X3838, skolem_Y3939) => (distinct_lines(skolem_Y3939, skolem_X3838) | convergent_lines(skolem_X3838, skolem_X3838)))
% 237.55/113.01 -> [11685] ~convergent_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01 -> [11686] (distinct_lines(skolem_Y3939, skolem_X3838) | convergent_lines(skolem_X3838, skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [11686] BETA_OR : (distinct_lines(skolem_Y3939, skolem_X3838) | convergent_lines(skolem_X3838, skolem_X3838))
% 237.55/113.01 -> [11687] distinct_lines(skolem_Y3939, skolem_X3838)
% 237.55/113.01 -> [11688] convergent_lines(skolem_X3838, skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [11687] CLOSURE : distinct_lines(skolem_Y3939, skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [11688] CLOSURE : convergent_lines(skolem_X3838, skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [11685] CLOSURE : ~convergent_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [11568] BETA_OR : (((apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838))
% 237.55/113.01 -> [11693] ((apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939))
% 237.55/113.01 -> [11694] apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [11694] 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))))
% 237.55/113.01 -> [11699] (apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838) => (distinct_points(intersection_point(skolem_Y3939, skolem_X3838), intersection_point(skolem_Y3939, skolem_X3838)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838)))
% 237.55/113.01
% 237.55/113.01 [11699] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838) => (distinct_points(intersection_point(skolem_Y3939, skolem_X3838), intersection_point(skolem_Y3939, skolem_X3838)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838)))
% 237.55/113.01 -> [11700] ~apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838)
% 237.55/113.01 -> [11701] (distinct_points(intersection_point(skolem_Y3939, skolem_X3838), intersection_point(skolem_Y3939, skolem_X3838)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [11700] CLOSURE : ~apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [11701] BETA_OR : (distinct_points(intersection_point(skolem_Y3939, skolem_X3838), intersection_point(skolem_Y3939, skolem_X3838)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838))
% 237.55/113.01 -> [11709] distinct_points(intersection_point(skolem_Y3939, skolem_X3838), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01 -> [11710] apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [11710] GAMMA_FORALL : ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34))))
% 237.55/113.01 -> [11713] (apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838) => (distinct_lines(skolem_X3838, skolem_Y3939) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939)))
% 237.55/113.01
% 237.55/113.01 [11713] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838) => (distinct_lines(skolem_X3838, skolem_Y3939) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939)))
% 237.55/113.01 -> [11714] ~apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838)
% 237.55/113.01 -> [11715] (distinct_lines(skolem_X3838, skolem_Y3939) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939))
% 237.55/113.01
% 237.55/113.01 [11714] CLOSURE : ~apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [11715] BETA_OR : (distinct_lines(skolem_X3838, skolem_Y3939) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939))
% 237.55/113.01 -> [11809] distinct_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01 -> [11810] apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [11809] CLOSURE : distinct_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [11810] CLOSURE : apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [11709] CLOSURE : distinct_points(intersection_point(skolem_Y3939, skolem_X3838), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [11693] BETA_OR : ((apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939))
% 237.55/113.01 -> [11695] (apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838))
% 237.55/113.01 -> [11696] apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [11696] CLOSURE : apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [11695] BETA_OR : (apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838))
% 237.55/113.01 -> [11697] apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)
% 237.55/113.01 -> [11698] apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [11697] CLOSURE : apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [11698] 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))))
% 237.55/113.01 -> [11704] (apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838) => (distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_X3838, skolem_Y3939)) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)))
% 237.55/113.01
% 237.55/113.01 [11704] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838) => (distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_X3838, skolem_Y3939)) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)))
% 237.55/113.01 -> [11705] ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)
% 237.55/113.01 -> [11706] (distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_X3838, skolem_Y3939)) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [11705] CLOSURE : ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [11706] BETA_OR : (distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_X3838, skolem_Y3939)) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838))
% 237.55/113.01 -> [11711] distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_X3838, skolem_Y3939))
% 237.55/113.01 -> [11712] apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [11711] GAMMA_FORALL : ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34))))
% 237.55/113.01 -> [11718] (apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838) => (distinct_lines(skolem_X3838, skolem_X3838) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)))
% 237.55/113.01
% 237.55/113.01 [11718] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838) => (distinct_lines(skolem_X3838, skolem_X3838) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)))
% 237.55/113.01 -> [11719] ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)
% 237.55/113.01 -> [11720] (distinct_lines(skolem_X3838, skolem_X3838) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [11719] CLOSURE : ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [11720] BETA_OR : (distinct_lines(skolem_X3838, skolem_X3838) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838))
% 237.55/113.01 -> [11738] distinct_lines(skolem_X3838, skolem_X3838)
% 237.55/113.01 -> [11739] apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [11738] CLOSURE : distinct_lines(skolem_X3838, skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [11739] GAMMA_FORALL : ! [X35_35, Y36_36, Z37_37] : ((convergent_lines(X35_35, Y36_36) => (distinct_lines(Y36_36, Z37_37) | convergent_lines(X35_35, Z37_37))))
% 237.55/113.01 -> [11740] (convergent_lines(skolem_Y3939, skolem_X3838) => (distinct_lines(skolem_X3838, skolem_Y3939) | convergent_lines(skolem_Y3939, skolem_Y3939)))
% 237.55/113.01
% 237.55/113.01 [11740] BETA_IMPLY : (convergent_lines(skolem_Y3939, skolem_X3838) => (distinct_lines(skolem_X3838, skolem_Y3939) | convergent_lines(skolem_Y3939, skolem_Y3939)))
% 237.55/113.01 -> [11743] ~convergent_lines(skolem_Y3939, skolem_X3838)
% 237.55/113.01 -> [11744] (distinct_lines(skolem_X3838, skolem_Y3939) | convergent_lines(skolem_Y3939, skolem_Y3939))
% 237.55/113.01
% 237.55/113.01 [11743] CLOSURE : ~convergent_lines(skolem_Y3939, skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [11744] BETA_OR : (distinct_lines(skolem_X3838, skolem_Y3939) | convergent_lines(skolem_Y3939, skolem_Y3939))
% 237.55/113.01 -> [11753] distinct_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01 -> [11754] convergent_lines(skolem_Y3939, skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [11753] CLOSURE : distinct_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [11756] CLOSURE : ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_X3838, skolem_Y3939))
% 237.55/113.01
% 237.55/113.01 [11721] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838) => (distinct_lines(skolem_X3838, skolem_Y3939) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)))
% 237.55/113.01 -> [11811] ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)
% 237.55/113.01 -> [11812] (distinct_lines(skolem_X3838, skolem_Y3939) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939))
% 237.55/113.01
% 237.55/113.01 [11811] CLOSURE : ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [11812] BETA_OR : (distinct_lines(skolem_X3838, skolem_Y3939) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939))
% 237.55/113.01 -> [11815] distinct_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01 -> [11816] apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [11815] CLOSURE : distinct_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [11816] CLOSURE : apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [10663] CLOSURE : ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [8250] BETA_OR : (distinct_lines(skolem_X3838, line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))) | distinct_lines(skolem_Y3939, line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))))
% 237.55/113.01 -> [11817] distinct_lines(skolem_X3838, line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.01 -> [11818] distinct_lines(skolem_Y3939, line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.01
% 237.55/113.01 [11818] 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))))
% 237.55/113.01 -> [11819] (convergent_lines(skolem_X3838, skolem_Y3939) => (convergent_lines(skolem_X3838, skolem_X3838) | convergent_lines(skolem_Y3939, skolem_X3838)))
% 237.55/113.01
% 237.55/113.01 [11819] BETA_IMPLY : (convergent_lines(skolem_X3838, skolem_Y3939) => (convergent_lines(skolem_X3838, skolem_X3838) | convergent_lines(skolem_Y3939, skolem_X3838)))
% 237.55/113.01 -> [11820] ~convergent_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01 -> [11821] (convergent_lines(skolem_X3838, skolem_X3838) | convergent_lines(skolem_Y3939, skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [11820] CLOSURE : ~convergent_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [11821] BETA_OR : (convergent_lines(skolem_X3838, skolem_X3838) | convergent_lines(skolem_Y3939, skolem_X3838))
% 237.55/113.01 -> [11824] convergent_lines(skolem_X3838, skolem_X3838)
% 237.55/113.01 -> [11825] convergent_lines(skolem_Y3939, skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [11824] CLOSURE : convergent_lines(skolem_X3838, skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [11826] BETA_IMPLY : (distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) => ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))))
% 237.55/113.01 -> [14713] ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01 -> [14714] ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.01
% 237.55/113.01 [14713] CLOSURE : ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [14715] BETA_IMPLY : (distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) => ~apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))))
% 237.55/113.01 -> [16460] ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01 -> [16461] ~apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.01
% 237.55/113.01 [16460] CLOSURE : ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [16462] BETA_IMPLY : (convergent_lines(skolem_Y3939, skolem_X3838) => ~apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939))
% 237.55/113.01 -> [16921] ~convergent_lines(skolem_Y3939, skolem_X3838)
% 237.55/113.01 -> [16922] ~apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [16921] CLOSURE : ~convergent_lines(skolem_Y3939, skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [16923] BETA_IMPLY : (convergent_lines(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939))
% 237.55/113.01 -> [17271] ~convergent_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01 -> [17272] ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [17271] CLOSURE : ~convergent_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [17273] BETA_IMPLY : ((distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) & distinct_lines(skolem_Y3939, skolem_Y3939)) => (((apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939)))
% 237.55/113.01 -> [17714] ~(distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) & distinct_lines(skolem_Y3939, skolem_Y3939))
% 237.55/113.01 -> [17715] (((apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939))
% 237.55/113.01
% 237.55/113.01 [17714] BETA_NOT_AND : ~(distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) & distinct_lines(skolem_Y3939, skolem_Y3939))
% 237.55/113.01 -> [17716] ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01 -> [17717] ~distinct_lines(skolem_Y3939, skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [17717] CLOSURE : ~distinct_lines(skolem_Y3939, skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [17716] CLOSURE : ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [17715] BETA_OR : (((apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939))
% 237.55/113.01 -> [17831] ((apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939))
% 237.55/113.01 -> [17832] apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [17832] CLOSURE : apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [17831] BETA_OR : ((apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939))
% 237.55/113.01 -> [17833] (apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939))
% 237.55/113.01 -> [17834] apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [17834] CLOSURE : apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [17833] BETA_OR : (apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939))
% 237.55/113.01 -> [17835] apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)
% 237.55/113.01 -> [17836] apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [17835] CLOSURE : apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [17836] CLOSURE : apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [11817] 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))))
% 237.55/113.01 -> [18837] (convergent_lines(skolem_X3838, skolem_Y3939) => (convergent_lines(skolem_X3838, skolem_X3838) | convergent_lines(skolem_Y3939, skolem_X3838)))
% 237.55/113.01
% 237.55/113.01 [18837] BETA_IMPLY : (convergent_lines(skolem_X3838, skolem_Y3939) => (convergent_lines(skolem_X3838, skolem_X3838) | convergent_lines(skolem_Y3939, skolem_X3838)))
% 237.55/113.01 -> [18838] ~convergent_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01 -> [18839] (convergent_lines(skolem_X3838, skolem_X3838) | convergent_lines(skolem_Y3939, skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [18838] CLOSURE : ~convergent_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [18839] BETA_OR : (convergent_lines(skolem_X3838, skolem_X3838) | convergent_lines(skolem_Y3939, skolem_X3838))
% 237.55/113.01 -> [18842] convergent_lines(skolem_X3838, skolem_X3838)
% 237.55/113.01 -> [18843] convergent_lines(skolem_Y3939, skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [18842] CLOSURE : convergent_lines(skolem_X3838, skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [18843] GAMMA_FORALL : ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18))))
% 237.55/113.01 -> [18844] (distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) => ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))))
% 237.55/113.01
% 237.55/113.01 [18844] BETA_IMPLY : (distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) => ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))))
% 237.55/113.01 -> [18845] ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01 -> [18846] ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.01
% 237.55/113.01 [18845] CLOSURE : ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [18847] BETA_IMPLY : (distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) => ~apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))))
% 237.55/113.01 -> [20057] ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.01 -> [20058] ~apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.01
% 237.55/113.01 [20058] GAMMA_FORALL : ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21)))
% 237.55/113.01 -> [20059] (convergent_lines(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838))
% 237.55/113.01
% 237.55/113.01 [20059] BETA_IMPLY : (convergent_lines(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838))
% 237.55/113.01 -> [20060] ~convergent_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01 -> [20061] ~apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [20060] CLOSURE : ~convergent_lines(skolem_X3838, skolem_Y3939)
% 237.55/113.01
% 237.55/113.01 [20062] BETA_IMPLY : (convergent_lines(skolem_Y3939, skolem_X3838) => ~apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838))
% 237.55/113.01 -> [20486] ~convergent_lines(skolem_Y3939, skolem_X3838)
% 237.55/113.01 -> [20487] ~apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [20486] CLOSURE : ~convergent_lines(skolem_Y3939, skolem_X3838)
% 237.55/113.01
% 237.55/113.01 [20488] BETA_IMPLY : ((distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) & distinct_lines(skolem_X3838, line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))) => (((apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))))
% 237.55/113.02 -> [20511] ~(distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) & distinct_lines(skolem_X3838, line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))))
% 237.55/113.02 -> [20512] (((apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))))
% 237.55/113.02
% 237.55/113.02 [20511] BETA_NOT_AND : ~(distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)) & distinct_lines(skolem_X3838, line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))))
% 237.55/113.02 -> [20515] ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.02 -> [20516] ~distinct_lines(skolem_X3838, line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.02
% 237.55/113.02 [20515] CLOSURE : ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.02
% 237.55/113.02 [20516] CLOSURE : ~distinct_lines(skolem_X3838, line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.02
% 237.55/113.02 [20512] BETA_OR : (((apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838)) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))))
% 237.55/113.02 -> [20593] ((apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838))
% 237.55/113.02 -> [20594] apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.02
% 237.55/113.02 [20593] BETA_OR : ((apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))) | apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838))
% 237.55/113.02 -> [20595] (apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))))
% 237.55/113.02 -> [20596] apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838)
% 237.55/113.02
% 237.55/113.02 [20596] CLOSURE : apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), skolem_X3838)
% 237.55/113.02
% 237.55/113.02 [20595] BETA_OR : (apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838) | apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))))
% 237.55/113.02 -> [20597] apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)
% 237.55/113.02 -> [20598] apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.02
% 237.55/113.02 [20597] CLOSURE : apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), skolem_X3838)
% 237.55/113.02
% 237.55/113.02 [20598] CLOSURE : apart_point_and_line(intersection_point(skolem_X3838, skolem_Y3939), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.02
% 237.55/113.02 [20594] CLOSURE : apart_point_and_line(intersection_point(skolem_Y3939, skolem_X3838), line_connecting(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838)))
% 237.55/113.02
% 237.55/113.02 [20057] CLOSURE : ~distinct_points(intersection_point(skolem_X3838, skolem_Y3939), intersection_point(skolem_Y3939, skolem_X3838))
% 237.55/113.02
% 237.55/113.02 % SZS output end Proof for theBenchmark.p
% 237.55/113.02 [112.665904s][1][Res] 585153 goroutines created
% 237.55/113.02 ==== Result ====
% 237.55/113.02 [112.665949s][1][Res] VALID
% 237.55/113.02 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------