TSTP Solution File: GEO173+1 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO173+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 15:18:12 EDT 2022
% Result : Theorem 2.99s 1.82s
% Output : Proof 2.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : GEO173+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.10 % Command : goeland -dmt -presko -proof %s
% 0.09/0.30 % Computer : n014.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Wed Aug 31 06:45:17 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30 [DMT] DMT loaded with preskolemization
% 0.09/0.30 [EQ] equality loaded.
% 0.09/0.30 [0.000036s][1][MAIN] Problem : theBenchmark.p
% 0.09/0.30 Conjecture not found
% 0.09/0.30 Start search
% 0.09/0.31 nb_step : 1 - limit : 15
% 0.09/0.31 Launch Gotab with destructive = true
% 2.99/1.82 % SZS output start Proof for theBenchmark.p
% 2.99/1.82 [0] ALPHA_AND : ((! [X5_5] : (~distinct_points(X5_5, X5_5)) & ! [X6_6] : (~distinct_lines(X6_6, X6_6)) & ! [X7_7] : (~convergent_lines(X7_7, X7_7)) & ! [X8_8, Y9_9, Z10_10] : ((distinct_points(X8_8, Y9_9) => (distinct_points(X8_8, Z10_10) | distinct_points(Y9_9, Z10_10)))) & ! [X11_11, Y12_12, Z13_13] : ((distinct_lines(X11_11, Y12_12) => (distinct_lines(X11_11, Z13_13) | distinct_lines(Y12_12, Z13_13)))) & ! [X14_14, Y15_15, Z16_16] : ((convergent_lines(X14_14, Y15_15) => (convergent_lines(X14_14, Z16_16) | convergent_lines(Y15_15, Z16_16)))) & ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18)))) & ! [X19_19, Y20_20] : ((distinct_points(X19_19, Y20_20) => ~apart_point_and_line(Y20_20, line_connecting(X19_19, Y20_20)))) & ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21))) & ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24))) & ! [X25_25, Y26_26, U27_27, V28_28] : (((distinct_points(X25_25, Y26_26) & distinct_lines(U27_27, V28_28)) => (((apart_point_and_line(X25_25, U27_27) | apart_point_and_line(X25_25, V28_28)) | apart_point_and_line(Y26_26, U27_27)) | apart_point_and_line(Y26_26, V28_28)))) & ! [X29_29, Y30_30, Z31_31] : ((apart_point_and_line(X29_29, Y30_30) => (distinct_points(X29_29, Z31_31) | apart_point_and_line(Z31_31, Y30_30)))) & ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34)))) & ! [X35_35, Y36_36, Z37_37] : ((convergent_lines(X35_35, Y36_36) => (distinct_lines(Y36_36, Z37_37) | convergent_lines(X35_35, Z37_37))))) & ~! [X38_38, Y39_39, U40_40, V41_41] : ((((distinct_points(X38_38, Y39_39) & convergent_lines(U40_40, V41_41)) & distinct_lines(U40_40, line_connecting(X38_38, Y39_39))) => (apart_point_and_line(X38_38, U40_40) | apart_point_and_line(Y39_39, U40_40)))))
% 2.99/1.82 -> [1] (! [X5_5] : (~distinct_points(X5_5, X5_5)) & ! [X6_6] : (~distinct_lines(X6_6, X6_6)) & ! [X7_7] : (~convergent_lines(X7_7, X7_7)) & ! [X8_8, Y9_9, Z10_10] : ((distinct_points(X8_8, Y9_9) => (distinct_points(X8_8, Z10_10) | distinct_points(Y9_9, Z10_10)))) & ! [X11_11, Y12_12, Z13_13] : ((distinct_lines(X11_11, Y12_12) => (distinct_lines(X11_11, Z13_13) | distinct_lines(Y12_12, Z13_13)))) & ! [X14_14, Y15_15, Z16_16] : ((convergent_lines(X14_14, Y15_15) => (convergent_lines(X14_14, Z16_16) | convergent_lines(Y15_15, Z16_16)))) & ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18)))) & ! [X19_19, Y20_20] : ((distinct_points(X19_19, Y20_20) => ~apart_point_and_line(Y20_20, line_connecting(X19_19, Y20_20)))) & ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21))) & ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24))) & ! [X25_25, Y26_26, U27_27, V28_28] : (((distinct_points(X25_25, Y26_26) & distinct_lines(U27_27, V28_28)) => (((apart_point_and_line(X25_25, U27_27) | apart_point_and_line(X25_25, V28_28)) | apart_point_and_line(Y26_26, U27_27)) | apart_point_and_line(Y26_26, V28_28)))) & ! [X29_29, Y30_30, Z31_31] : ((apart_point_and_line(X29_29, Y30_30) => (distinct_points(X29_29, Z31_31) | apart_point_and_line(Z31_31, Y30_30)))) & ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34)))) & ! [X35_35, Y36_36, Z37_37] : ((convergent_lines(X35_35, Y36_36) => (distinct_lines(Y36_36, Z37_37) | convergent_lines(X35_35, Z37_37))))), ~! [X38_38, Y39_39, U40_40, V41_41] : ((((distinct_points(X38_38, Y39_39) & convergent_lines(U40_40, V41_41)) & distinct_lines(U40_40, line_connecting(X38_38, Y39_39))) => (apart_point_and_line(X38_38, U40_40) | apart_point_and_line(Y39_39, U40_40))))
% 2.99/1.82
% 2.99/1.82 [1] ALPHA_AND : (! [X5_5] : (~distinct_points(X5_5, X5_5)) & ! [X6_6] : (~distinct_lines(X6_6, X6_6)) & ! [X7_7] : (~convergent_lines(X7_7, X7_7)) & ! [X8_8, Y9_9, Z10_10] : ((distinct_points(X8_8, Y9_9) => (distinct_points(X8_8, Z10_10) | distinct_points(Y9_9, Z10_10)))) & ! [X11_11, Y12_12, Z13_13] : ((distinct_lines(X11_11, Y12_12) => (distinct_lines(X11_11, Z13_13) | distinct_lines(Y12_12, Z13_13)))) & ! [X14_14, Y15_15, Z16_16] : ((convergent_lines(X14_14, Y15_15) => (convergent_lines(X14_14, Z16_16) | convergent_lines(Y15_15, Z16_16)))) & ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18)))) & ! [X19_19, Y20_20] : ((distinct_points(X19_19, Y20_20) => ~apart_point_and_line(Y20_20, line_connecting(X19_19, Y20_20)))) & ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21))) & ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24))) & ! [X25_25, Y26_26, U27_27, V28_28] : (((distinct_points(X25_25, Y26_26) & distinct_lines(U27_27, V28_28)) => (((apart_point_and_line(X25_25, U27_27) | apart_point_and_line(X25_25, V28_28)) | apart_point_and_line(Y26_26, U27_27)) | apart_point_and_line(Y26_26, V28_28)))) & ! [X29_29, Y30_30, Z31_31] : ((apart_point_and_line(X29_29, Y30_30) => (distinct_points(X29_29, Z31_31) | apart_point_and_line(Z31_31, Y30_30)))) & ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34)))) & ! [X35_35, Y36_36, Z37_37] : ((convergent_lines(X35_35, Y36_36) => (distinct_lines(Y36_36, Z37_37) | convergent_lines(X35_35, Z37_37)))))
% 2.99/1.82 -> [2] ! [X5_5] : (~distinct_points(X5_5, X5_5)), ! [X6_6] : (~distinct_lines(X6_6, X6_6)), ! [X7_7] : (~convergent_lines(X7_7, X7_7)), ! [X8_8, Y9_9, Z10_10] : ((distinct_points(X8_8, Y9_9) => (distinct_points(X8_8, Z10_10) | distinct_points(Y9_9, Z10_10)))), ! [X11_11, Y12_12, Z13_13] : ((distinct_lines(X11_11, Y12_12) => (distinct_lines(X11_11, Z13_13) | distinct_lines(Y12_12, Z13_13)))), ! [X14_14, Y15_15, Z16_16] : ((convergent_lines(X14_14, Y15_15) => (convergent_lines(X14_14, Z16_16) | convergent_lines(Y15_15, Z16_16)))), ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18)))), ! [X19_19, Y20_20] : ((distinct_points(X19_19, Y20_20) => ~apart_point_and_line(Y20_20, line_connecting(X19_19, Y20_20)))), ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21))), ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24))), ! [X25_25, Y26_26, U27_27, V28_28] : (((distinct_points(X25_25, Y26_26) & distinct_lines(U27_27, V28_28)) => (((apart_point_and_line(X25_25, U27_27) | apart_point_and_line(X25_25, V28_28)) | apart_point_and_line(Y26_26, U27_27)) | apart_point_and_line(Y26_26, V28_28)))), ! [X29_29, Y30_30, Z31_31] : ((apart_point_and_line(X29_29, Y30_30) => (distinct_points(X29_29, Z31_31) | apart_point_and_line(Z31_31, Y30_30)))), ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34)))), ! [X35_35, Y36_36, Z37_37] : ((convergent_lines(X35_35, Y36_36) => (distinct_lines(Y36_36, Z37_37) | convergent_lines(X35_35, Z37_37))))
% 2.99/1.82
% 2.99/1.82 [2] DELTA_NOT_FORALL : ~! [X38_38, Y39_39, U40_40, V41_41] : ((((distinct_points(X38_38, Y39_39) & convergent_lines(U40_40, V41_41)) & distinct_lines(U40_40, line_connecting(X38_38, Y39_39))) => (apart_point_and_line(X38_38, U40_40) | apart_point_and_line(Y39_39, U40_40))))
% 2.99/1.82 -> [3] ~(((distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)) & distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))) => (apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_Y3939, skolem_U4040)))
% 2.99/1.82
% 2.99/1.82 [3] ALPHA_NOT_IMPLY : ~(((distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)) & distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))) => (apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_Y3939, skolem_U4040)))
% 2.99/1.82 -> [4] ((distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)) & distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))), ~(apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_Y3939, skolem_U4040))
% 2.99/1.82
% 2.99/1.82 [4] ALPHA_AND : ((distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)) & distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)))
% 2.99/1.82 -> [5] (distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141)), distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 2.99/1.82
% 2.99/1.82 [5] ALPHA_NOT_OR : ~(apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_Y3939, skolem_U4040))
% 2.99/1.82 -> [6] ~apart_point_and_line(skolem_X3838, skolem_U4040), ~apart_point_and_line(skolem_Y3939, skolem_U4040)
% 2.99/1.82
% 2.99/1.82 [6] ALPHA_AND : (distinct_points(skolem_X3838, skolem_Y3939) & convergent_lines(skolem_U4040, skolem_V4141))
% 2.99/1.82 -> [7] distinct_points(skolem_X3838, skolem_Y3939), convergent_lines(skolem_U4040, skolem_V4141)
% 2.99/1.82
% 2.99/1.82 [7] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 2.99/1.82 -> [8] ~distinct_points(skolem_Y3939, skolem_Y3939)
% 2.99/1.82
% 2.99/1.82 [8] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 2.99/1.82 -> [9] ~distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))
% 2.99/1.82
% 2.99/1.82 [9] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 2.99/1.82 -> [10] ~convergent_lines(skolem_U4040, skolem_U4040)
% 2.99/1.82
% 2.99/1.82 [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))))
% 2.99/1.82 -> [11] (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939)))
% 2.99/1.82
% 2.99/1.82 [11] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939)))
% 2.99/1.82 -> [12] ~distinct_points(skolem_X3838, skolem_Y3939)
% 2.99/1.82 -> [13] (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939))
% 2.99/1.82
% 2.99/1.82 [12] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 2.99/1.82
% 2.99/1.82 [13] BETA_OR : (distinct_points(skolem_X3838, skolem_Y3939) | distinct_points(skolem_Y3939, skolem_Y3939))
% 2.99/1.82 -> [16] distinct_points(skolem_X3838, skolem_Y3939)
% 2.99/1.82 -> [17] distinct_points(skolem_Y3939, skolem_Y3939)
% 2.99/1.82
% 2.99/1.82 [17] CLOSURE : distinct_points(skolem_Y3939, skolem_Y3939)
% 2.99/1.82
% 2.99/1.82 [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))))
% 2.99/1.82 -> [18] (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))))
% 2.99/1.82
% 2.99/1.82 [18] BETA_IMPLY : (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) => (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))))
% 2.99/1.82 -> [19] ~distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 2.99/1.82 -> [20] (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 2.99/1.82
% 2.99/1.82 [19] CLOSURE : ~distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 2.99/1.82
% 2.99/1.82 [20] BETA_OR : (distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)) | distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939)))
% 2.99/1.82 -> [23] distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 2.99/1.82 -> [24] distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))
% 2.99/1.82
% 2.99/1.82 [24] CLOSURE : distinct_lines(line_connecting(skolem_X3838, skolem_Y3939), line_connecting(skolem_X3838, skolem_Y3939))
% 2.99/1.82
% 2.99/1.82 [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))))
% 2.99/1.82 -> [25] (convergent_lines(skolem_U4040, skolem_V4141) => (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040)))
% 2.99/1.82
% 2.99/1.82 [25] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040)))
% 2.99/1.82 -> [26] ~convergent_lines(skolem_U4040, skolem_V4141)
% 2.99/1.82 -> [27] (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040))
% 2.99/1.82
% 2.99/1.82 [26] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 2.99/1.82
% 2.99/1.82 [27] BETA_OR : (convergent_lines(skolem_U4040, skolem_U4040) | convergent_lines(skolem_V4141, skolem_U4040))
% 2.99/1.82 -> [30] convergent_lines(skolem_U4040, skolem_U4040)
% 2.99/1.82 -> [31] convergent_lines(skolem_V4141, skolem_U4040)
% 2.99/1.82
% 2.99/1.82 [30] CLOSURE : convergent_lines(skolem_U4040, skolem_U4040)
% 2.99/1.82
% 2.99/1.82 [31] GAMMA_FORALL : ! [X17_17, Y18_18] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18))))
% 2.99/1.82 -> [32] (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 2.99/1.82
% 2.99/1.82 [32] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 2.99/1.82 -> [33] ~distinct_points(skolem_X3838, skolem_Y3939)
% 2.99/1.82 -> [34] ~apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 2.99/1.82
% 2.99/1.82 [33] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 2.99/1.82
% 2.99/1.82 [34] GAMMA_FORALL : ! [X19_19, Y20_20] : ((distinct_points(X19_19, Y20_20) => ~apart_point_and_line(Y20_20, line_connecting(X19_19, Y20_20))))
% 2.99/1.82 -> [35] (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 2.99/1.82
% 2.99/1.82 [35] BETA_IMPLY : (distinct_points(skolem_X3838, skolem_Y3939) => ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 2.99/1.82 -> [36] ~distinct_points(skolem_X3838, skolem_Y3939)
% 2.99/1.82 -> [37] ~apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 2.99/1.82
% 2.99/1.82 [36] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 2.99/1.82
% 2.99/1.82 [38] BETA_IMPLY : (convergent_lines(skolem_U4040, skolem_V4141) => ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040))
% 2.99/1.82 -> [193] ~convergent_lines(skolem_U4040, skolem_V4141)
% 2.99/1.82 -> [194] ~apart_point_and_line(intersection_point(skolem_U4040, skolem_V4141), skolem_U4040)
% 2.99/1.82
% 2.99/1.82 [193] CLOSURE : ~convergent_lines(skolem_U4040, skolem_V4141)
% 2.99/1.82
% 2.99/1.82 [195] BETA_IMPLY : (convergent_lines(skolem_V4141, skolem_U4040) => ~apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040))
% 2.99/1.82 -> [231] ~convergent_lines(skolem_V4141, skolem_U4040)
% 2.99/1.82 -> [232] ~apart_point_and_line(intersection_point(skolem_V4141, skolem_U4040), skolem_U4040)
% 2.99/1.82
% 2.99/1.82 [232] 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))))
% 2.99/1.82 -> [233] ((distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))) => (((apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_U4040)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 2.99/1.82
% 2.99/1.82 [233] BETA_IMPLY : ((distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))) => (((apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_U4040)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))))
% 2.99/1.82 -> [234] ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)))
% 2.99/1.82 -> [235] (((apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_U4040)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 2.99/1.82
% 2.99/1.82 [234] BETA_NOT_AND : ~(distinct_points(skolem_X3838, skolem_Y3939) & distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939)))
% 2.99/1.82 -> [236] ~distinct_points(skolem_X3838, skolem_Y3939)
% 2.99/1.82 -> [237] ~distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 2.99/1.82
% 2.99/1.82 [237] CLOSURE : ~distinct_lines(skolem_U4040, line_connecting(skolem_X3838, skolem_Y3939))
% 2.99/1.82
% 2.99/1.82 [236] CLOSURE : ~distinct_points(skolem_X3838, skolem_Y3939)
% 2.99/1.82
% 2.99/1.82 [235] BETA_OR : (((apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_U4040)) | apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939)))
% 2.99/1.82 -> [250] ((apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_U4040))
% 2.99/1.82 -> [251] apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 2.99/1.82
% 2.99/1.82 [251] CLOSURE : apart_point_and_line(skolem_Y3939, line_connecting(skolem_X3838, skolem_Y3939))
% 2.99/1.82
% 2.99/1.82 [250] BETA_OR : ((apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))) | apart_point_and_line(skolem_Y3939, skolem_U4040))
% 2.99/1.82 -> [252] (apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 2.99/1.82 -> [253] apart_point_and_line(skolem_Y3939, skolem_U4040)
% 2.99/1.82
% 2.99/1.82 [253] CLOSURE : apart_point_and_line(skolem_Y3939, skolem_U4040)
% 2.99/1.82
% 2.99/1.82 [252] BETA_OR : (apart_point_and_line(skolem_X3838, skolem_U4040) | apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939)))
% 2.99/1.82 -> [254] apart_point_and_line(skolem_X3838, skolem_U4040)
% 2.99/1.82 -> [255] apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 2.99/1.82
% 2.99/1.82 [254] CLOSURE : apart_point_and_line(skolem_X3838, skolem_U4040)
% 2.99/1.82
% 2.99/1.82 [255] CLOSURE : apart_point_and_line(skolem_X3838, line_connecting(skolem_X3838, skolem_Y3939))
% 2.99/1.82
% 2.99/1.82 [231] CLOSURE : ~convergent_lines(skolem_V4141, skolem_U4040)
% 2.99/1.82
% 2.99/1.82 % SZS output end Proof for theBenchmark.p
% 2.99/1.82 [1.522189s][1][Res] 6208 goroutines created
% 2.99/1.82 ==== Result ====
% 2.99/1.82 [1.522245s][1][Res] VALID
% 2.99/1.82 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------