TSTP Solution File: GEO170+1 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO170+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 15:18:11 EDT 2022
% Result : Theorem 4.06s 1.68s
% Output : Proof 4.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO170+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 06:52:57 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 [DMT] DMT loaded with preskolemization
% 0.12/0.34 [EQ] equality loaded.
% 0.12/0.34 [0.000037s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.34 Conjecture not found
% 0.12/0.34 Start search
% 0.12/0.34 nb_step : 1 - limit : 15
% 0.12/0.34 Launch Gotab with destructive = true
% 4.06/1.67 % SZS output start Proof for theBenchmark.p
% 4.06/1.68 [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(X38_38, Z40_40)) & ~apart_point_and_line(Y39_39, Z40_40)) => ~distinct_lines(Z40_40, line_connecting(X38_38, Y39_39)))))
% 4.06/1.68 -> [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(X38_38, Z40_40)) & ~apart_point_and_line(Y39_39, Z40_40)) => ~distinct_lines(Z40_40, line_connecting(X38_38, Y39_39))))
% 4.06/1.68
% 4.06/1.68 [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)))))
% 4.06/1.68 -> [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))))
% 4.06/1.68
% 4.06/1.68 [2] DELTA_NOT_FORALL : ~! [X38_38, Y39_39, Z40_40] : ((((distinct_points(X38_38, Y39_39) & ~apart_point_and_line(X38_38, Z40_40)) & ~apart_point_and_line(Y39_39, Z40_40)) => ~distinct_lines(Z40_40, line_connecting(X38_38, Y39_39))))
% 4.06/1.68 -> [3] ~(((distinct_points(skolem_X3838, skolem_Y3939) & ~apart_point_and_line(skolem_X3838, skolem_Z4040)) & ~apart_point_and_line(skolem_Y3939, skolem_Z4040)) => ~distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68
% 4.06/1.68 [3] ALPHA_NOT_IMPLY : ~(((distinct_points(skolem_X3838, skolem_Y3939) & ~apart_point_and_line(skolem_X3838, skolem_Z4040)) & ~apart_point_and_line(skolem_Y3939, skolem_Z4040)) => ~distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [4] ((distinct_points(skolem_X3838, skolem_Y3939) & ~apart_point_and_line(skolem_X3838, skolem_Z4040)) & ~apart_point_and_line(skolem_Y3939, skolem_Z4040)), ~~distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [4] ALPHA_AND : ((distinct_points(skolem_X3838, skolem_Y3939) & ~apart_point_and_line(skolem_X3838, skolem_Z4040)) & ~apart_point_and_line(skolem_Y3939, skolem_Z4040))
% 4.06/1.68 -> [5] (distinct_points(skolem_X3838, skolem_Y3939) & ~apart_point_and_line(skolem_X3838, skolem_Z4040)), ~apart_point_and_line(skolem_Y3939, skolem_Z4040)
% 4.06/1.68
% 4.06/1.68 [5] ALPHA_NOT_NOT : ~~distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68 -> [6] distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [6] ALPHA_AND : (distinct_points(skolem_X3838, skolem_Y3939) & ~apart_point_and_line(skolem_X3838, skolem_Z4040))
% 4.06/1.68 -> [7] distinct_points(skolem_X3838, skolem_Y3939), ~apart_point_and_line(skolem_X3838, skolem_Z4040)
% 4.06/1.68
% 4.06/1.68 [7] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 4.06/1.68 -> [8] ~distinct_points(skolem_Y3939, skolem_Y3939)
% 4.06/1.68
% 4.06/1.68 [8] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 4.06/1.68 -> [9] ~distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [9] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 4.06/1.68 -> [10] ~convergent_lines(X7_0_2, X7_0_2)
% 4.06/1.68
% 4.06/1.68 [10] GAMMA_FORALL : ! [X8_8, Y9_9, Z10_10] : ((distinct_points(X8_8, Y9_9) => (distinct_points(X8_8, Z10_10) | distinct_points(Y9_9, Z10_10))))
% 4.06/1.68 -> [11] (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939)))
% 4.06/1.68
% 4.06/1.68 [11] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939)))
% 4.06/1.68 -> [12] ~distinct_points(skolem_X3838, skolem_Y3939)
% 4.06/1.68 -> [13] (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [12] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 4.06/1.68
% 4.06/1.68 [13] BETA_OR : (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939))
% 4.06/1.68 -> [16] distinct_points(skolem_X3838, skolem_Y3939)
% 4.06/1.68 -> [17] distinct_points(skolem_Y3939, skolem_Y3939)
% 4.06/1.68
% 4.06/1.68 [17] CLOSURE : distinct_points(skolem_Y3939, skolem_Y3939)
% 4.06/1.68
% 4.06/1.68 [16] GAMMA_FORALL : ! [X11_11, Y12_12, Z13_13] : ((distinct_lines(X11_11, Y12_12) => (distinct_lines(X11_11, Z13_13) | distinct_lines(Y12_12, Z13_13))))
% 4.06/1.68 -> [18] (distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) | distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))))
% 4.06/1.68
% 4.06/1.68 [18] BETA_IMPLY : (distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) | distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))))
% 4.06/1.68 -> [19] ~distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68 -> [20] (distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) | distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68
% 4.06/1.68 [19] CLOSURE : ~distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [20] BETA_OR : (distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)) | distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [23] distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68 -> [24] distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [24] CLOSURE : distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [23] 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))))
% 4.06/1.68 -> [25] (convergent_lines(Z16_0_5, Z16_0_5) => (convergent_lines(Z16_0_5, Z16_0_5) | convergent_lines(Z16_0_5, Z16_0_5)))
% 4.06/1.68
% 4.06/1.68 [25] BETA_IMPLY : (convergent_lines(Z16_0_5, Z16_0_5) => (convergent_lines(Z16_0_5, Z16_0_5) | convergent_lines(Z16_0_5, Z16_0_5)))
% 4.06/1.68 -> [26] ~convergent_lines(Z16_0_5, Z16_0_5)
% 4.06/1.68 -> [27] (convergent_lines(Z16_0_5, Z16_0_5) | convergent_lines(Z16_0_5, Z16_0_5))
% 4.06/1.68
% 4.06/1.68 [27] BETA_OR : (convergent_lines(Z16_0_5, Z16_0_5) | convergent_lines(Z16_0_5, Z16_0_5))
% 4.06/1.68 -> [28] convergent_lines(Z16_0_5, Z16_0_5)
% 4.06/1.68 -> [29] convergent_lines(Z16_0_5, Z16_0_5)
% 4.06/1.68
% 4.06/1.68 [29] CLOSURE : convergent_lines(Z16_0_5, Z16_0_5)
% 4.06/1.68
% 4.06/1.68 [28] CLOSURE : convergent_lines(Z16_0_5, Z16_0_5)
% 4.06/1.68
% 4.06/1.68 [26] GAMMA_FORALL : ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18))))
% 4.06/1.68 -> [30] (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68
% 4.06/1.68 [30] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [31] ~distinct_points(skolem_X3838, skolem_Y3939)
% 4.06/1.68 -> [32] ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [31] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 4.06/1.68
% 4.06/1.68 [32] GAMMA_FORALL : ! [X19_19, Y20_20] : ((distinct_points(X19_19, Y20_20) => ~apart_point_and_line(Y20_20, line_connecting(X19_19, Y20_20))))
% 4.06/1.68 -> [33] (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68
% 4.06/1.68 [33] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [34] ~distinct_points(skolem_X3838, skolem_Y3939)
% 4.06/1.68 -> [35] ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [34] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 4.06/1.68
% 4.06/1.68 [36] BETA_IMPLY : (convergent_lines(X21_0_8, Y22_0_8) => ~apart_point_and_line(intersection_point(X21_0_8, Y22_0_8), X21_0_8))
% 4.06/1.68 -> [145] ~convergent_lines(X21_0_8, Y22_0_8)
% 4.06/1.68 -> [146] ~apart_point_and_line(intersection_point(X21_0_8, Y22_0_8), X21_0_8)
% 4.06/1.68
% 4.06/1.68 [146] GAMMA_FORALL : ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24)))
% 4.06/1.68 -> [147] (convergent_lines(X23_2_9, Y24_2_9) => ~apart_point_and_line(intersection_point(X23_2_9, Y24_2_9), Y24_2_9))
% 4.06/1.68
% 4.06/1.68 [147] BETA_IMPLY : (convergent_lines(X23_2_9, Y24_2_9) => ~apart_point_and_line(intersection_point(X23_2_9, Y24_2_9), Y24_2_9))
% 4.06/1.68 -> [149] ~convergent_lines(X23_2_9, Y24_2_9)
% 4.06/1.68 -> [150] ~apart_point_and_line(intersection_point(X23_2_9, Y24_2_9), Y24_2_9)
% 4.06/1.68
% 4.06/1.68 [149] 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))))
% 4.06/1.68 -> [153] ((distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))) => (((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 4.06/1.68
% 4.06/1.68 [153] BETA_IMPLY : ((distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))) => (((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 4.06/1.68 -> [155] ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [156] (((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68
% 4.06/1.68 [155] BETA_NOT_AND : ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [163] ~distinct_points(skolem_X3838, skolem_Y3939)
% 4.06/1.68 -> [164] ~distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [163] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 4.06/1.68
% 4.06/1.68 [164] CLOSURE : ~distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [156] BETA_OR : (((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [230] ((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040))
% 4.06/1.68 -> [231] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [231] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [230] BETA_OR : ((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040))
% 4.06/1.68 -> [232] (apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [233] apart_point_and_line(skolem_Y3939, skolem_Z4040)
% 4.06/1.68
% 4.06/1.68 [233] CLOSURE : apart_point_and_line(skolem_Y3939, skolem_Z4040)
% 4.06/1.68
% 4.06/1.68 [232] BETA_OR : (apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [234] apart_point_and_line(skolem_X3838, skolem_Z4040)
% 4.06/1.68 -> [235] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [234] CLOSURE : apart_point_and_line(skolem_X3838, skolem_Z4040)
% 4.06/1.68
% 4.06/1.68 [235] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [150] 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))))
% 4.06/1.68 -> [154] ((distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))) => (((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 4.06/1.68
% 4.06/1.68 [154] BETA_IMPLY : ((distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))) => (((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 4.06/1.68 -> [159] ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [160] (((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68
% 4.06/1.68 [159] BETA_NOT_AND : ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [169] ~distinct_points(skolem_X3838, skolem_Y3939)
% 4.06/1.68 -> [170] ~distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [169] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 4.06/1.68
% 4.06/1.68 [170] CLOSURE : ~distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [160] BETA_OR : (((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [246] ((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040))
% 4.06/1.68 -> [247] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [247] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [246] BETA_OR : ((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040))
% 4.06/1.68 -> [250] (apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [251] apart_point_and_line(skolem_Y3939, skolem_Z4040)
% 4.06/1.68
% 4.06/1.68 [251] CLOSURE : apart_point_and_line(skolem_Y3939, skolem_Z4040)
% 4.06/1.68
% 4.06/1.68 [250] BETA_OR : (apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [254] apart_point_and_line(skolem_X3838, skolem_Z4040)
% 4.06/1.68 -> [255] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [254] CLOSURE : apart_point_and_line(skolem_X3838, skolem_Z4040)
% 4.06/1.68
% 4.06/1.68 [255] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [145] GAMMA_FORALL : ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24)))
% 4.06/1.68 -> [148] (convergent_lines(X23_3_9, Y24_3_9) => ~apart_point_and_line(intersection_point(X23_3_9, Y24_3_9), Y24_3_9))
% 4.06/1.68
% 4.06/1.68 [148] BETA_IMPLY : (convergent_lines(X23_3_9, Y24_3_9) => ~apart_point_and_line(intersection_point(X23_3_9, Y24_3_9), Y24_3_9))
% 4.06/1.68 -> [151] ~convergent_lines(X23_3_9, Y24_3_9)
% 4.06/1.68 -> [152] ~apart_point_and_line(intersection_point(X23_3_9, Y24_3_9), Y24_3_9)
% 4.06/1.68
% 4.06/1.68 [151] 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))))
% 4.06/1.68 -> [158] ((distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))) => (((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 4.06/1.68
% 4.06/1.68 [158] BETA_IMPLY : ((distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))) => (((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 4.06/1.68 -> [165] ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [166] (((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68
% 4.06/1.68 [165] BETA_NOT_AND : ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [175] ~distinct_points(skolem_X3838, skolem_Y3939)
% 4.06/1.68 -> [176] ~distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [176] CLOSURE : ~distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [175] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 4.06/1.68
% 4.06/1.68 [166] BETA_OR : (((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [215] ((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040))
% 4.06/1.68 -> [216] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [216] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [215] BETA_OR : ((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040))
% 4.06/1.68 -> [219] (apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [220] apart_point_and_line(skolem_Y3939, skolem_Z4040)
% 4.06/1.68
% 4.06/1.68 [220] CLOSURE : apart_point_and_line(skolem_Y3939, skolem_Z4040)
% 4.06/1.68
% 4.06/1.68 [219] BETA_OR : (apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [223] apart_point_and_line(skolem_X3838, skolem_Z4040)
% 4.06/1.68 -> [224] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [223] CLOSURE : apart_point_and_line(skolem_X3838, skolem_Z4040)
% 4.06/1.68
% 4.06/1.68 [224] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [152] 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))))
% 4.06/1.68 -> [157] ((distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))) => (((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 4.06/1.68
% 4.06/1.68 [157] BETA_IMPLY : ((distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))) => (((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 4.06/1.68 -> [161] ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [162] (((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68
% 4.06/1.68 [161] BETA_NOT_AND : ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [171] ~distinct_points(skolem_X3838, skolem_Y3939)
% 4.06/1.68 -> [172] ~distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [171] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 4.06/1.68
% 4.06/1.68 [172] CLOSURE : ~distinct_lines(skolem_Z4040, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [162] BETA_OR : (((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [351] ((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040))
% 4.06/1.68 -> [352] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [352] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [351] BETA_OR : ((apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_Z4040))
% 4.06/1.68 -> [353] (apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [354] apart_point_and_line(skolem_Y3939, skolem_Z4040)
% 4.06/1.68
% 4.06/1.68 [354] CLOSURE : apart_point_and_line(skolem_Y3939, skolem_Z4040)
% 4.06/1.68
% 4.06/1.68 [353] BETA_OR : (apart_point_and_line(skolem_X3838, skolem_Z4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 4.06/1.68 -> [355] apart_point_and_line(skolem_X3838, skolem_Z4040)
% 4.06/1.68 -> [356] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 [355] CLOSURE : apart_point_and_line(skolem_X3838, skolem_Z4040)
% 4.06/1.68
% 4.06/1.68 [356] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 4.06/1.68
% 4.06/1.68 % SZS output end Proof for theBenchmark.p
% 4.06/1.68 [1.336065s][1][Res] 7145 goroutines created
% 4.06/1.68 ==== Result ====
% 4.06/1.68 [1.336106s][1][Res] VALID
% 4.06/1.68 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------