TSTP Solution File: GEO176+2 by Goeland---1.0.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO176+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 15:18:14 EDT 2022
% Result : Theorem 16.98s 4.91s
% Output : Proof 16.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO176+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 06:45:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 [DMT] DMT loaded with preskolemization
% 0.13/0.35 [EQ] equality loaded.
% 0.13/0.35 [0.000051s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.36 Conjecture not found
% 0.13/0.36 Start search
% 0.13/0.36 nb_step : 1 - limit : 13
% 0.13/0.36 Launch Gotab with destructive = true
% 16.98/4.90 % SZS output start Proof for theBenchmark.p
% 16.98/4.90 [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, Z19_19] : ((distinct_points(X17_17, Y18_18) => (apart_point_and_line(Z19_19, line_connecting(X17_17, Y18_18)) => (distinct_points(Z19_19, X17_17) & distinct_points(Z19_19, Y18_18))))) & ! [X20_20, Y21_21, Z22_22] : ((convergent_lines(X20_20, Y21_21) => ((apart_point_and_line(Z22_22, X20_20) | apart_point_and_line(Z22_22, Y21_21)) => distinct_points(Z22_22, intersection_point(X20_20, Y21_21))))) & ! [X23_23, Y24_24, U25_25, V26_26] : (((distinct_points(X23_23, Y24_24) & distinct_lines(U25_25, V26_26)) => (((apart_point_and_line(X23_23, U25_25) | apart_point_and_line(X23_23, V26_26)) | apart_point_and_line(Y24_24, U25_25)) | apart_point_and_line(Y24_24, V26_26)))) & ! [X27_27, Y28_28, Z29_29] : ((apart_point_and_line(X27_27, Y28_28) => (distinct_points(X27_27, Z29_29) | apart_point_and_line(Z29_29, Y28_28)))) & ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_lines(Y31_31, Z32_32) | apart_point_and_line(X30_30, Z32_32)))) & ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))) & ~! [X35_35, Y36_36, U37_37, V38_38] : ((((distinct_points(X35_35, Y36_36) & convergent_lines(U37_37, V38_38)) & (apart_point_and_line(X35_35, U37_37) | apart_point_and_line(X35_35, V38_38))) => distinct_points(X35_35, intersection_point(U37_37, V38_38)))))
% 16.98/4.90 -> [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, Z19_19] : ((distinct_points(X17_17, Y18_18) => (apart_point_and_line(Z19_19, line_connecting(X17_17, Y18_18)) => (distinct_points(Z19_19, X17_17) & distinct_points(Z19_19, Y18_18))))) & ! [X20_20, Y21_21, Z22_22] : ((convergent_lines(X20_20, Y21_21) => ((apart_point_and_line(Z22_22, X20_20) | apart_point_and_line(Z22_22, Y21_21)) => distinct_points(Z22_22, intersection_point(X20_20, Y21_21))))) & ! [X23_23, Y24_24, U25_25, V26_26] : (((distinct_points(X23_23, Y24_24) & distinct_lines(U25_25, V26_26)) => (((apart_point_and_line(X23_23, U25_25) | apart_point_and_line(X23_23, V26_26)) | apart_point_and_line(Y24_24, U25_25)) | apart_point_and_line(Y24_24, V26_26)))) & ! [X27_27, Y28_28, Z29_29] : ((apart_point_and_line(X27_27, Y28_28) => (distinct_points(X27_27, Z29_29) | apart_point_and_line(Z29_29, Y28_28)))) & ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_lines(Y31_31, Z32_32) | apart_point_and_line(X30_30, Z32_32)))) & ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))), ~! [X35_35, Y36_36, U37_37, V38_38] : ((((distinct_points(X35_35, Y36_36) & convergent_lines(U37_37, V38_38)) & (apart_point_and_line(X35_35, U37_37) | apart_point_and_line(X35_35, V38_38))) => distinct_points(X35_35, intersection_point(U37_37, V38_38))))
% 16.98/4.90
% 16.98/4.90 [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, Z19_19] : ((distinct_points(X17_17, Y18_18) => (apart_point_and_line(Z19_19, line_connecting(X17_17, Y18_18)) => (distinct_points(Z19_19, X17_17) & distinct_points(Z19_19, Y18_18))))) & ! [X20_20, Y21_21, Z22_22] : ((convergent_lines(X20_20, Y21_21) => ((apart_point_and_line(Z22_22, X20_20) | apart_point_and_line(Z22_22, Y21_21)) => distinct_points(Z22_22, intersection_point(X20_20, Y21_21))))) & ! [X23_23, Y24_24, U25_25, V26_26] : (((distinct_points(X23_23, Y24_24) & distinct_lines(U25_25, V26_26)) => (((apart_point_and_line(X23_23, U25_25) | apart_point_and_line(X23_23, V26_26)) | apart_point_and_line(Y24_24, U25_25)) | apart_point_and_line(Y24_24, V26_26)))) & ! [X27_27, Y28_28, Z29_29] : ((apart_point_and_line(X27_27, Y28_28) => (distinct_points(X27_27, Z29_29) | apart_point_and_line(Z29_29, Y28_28)))) & ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_lines(Y31_31, Z32_32) | apart_point_and_line(X30_30, Z32_32)))) & ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34))))
% 16.98/4.90 -> [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, Z19_19] : ((distinct_points(X17_17, Y18_18) => (apart_point_and_line(Z19_19, line_connecting(X17_17, Y18_18)) => (distinct_points(Z19_19, X17_17) & distinct_points(Z19_19, Y18_18))))), ! [X20_20, Y21_21, Z22_22] : ((convergent_lines(X20_20, Y21_21) => ((apart_point_and_line(Z22_22, X20_20) | apart_point_and_line(Z22_22, Y21_21)) => distinct_points(Z22_22, intersection_point(X20_20, Y21_21))))), ! [X23_23, Y24_24, U25_25, V26_26] : (((distinct_points(X23_23, Y24_24) & distinct_lines(U25_25, V26_26)) => (((apart_point_and_line(X23_23, U25_25) | apart_point_and_line(X23_23, V26_26)) | apart_point_and_line(Y24_24, U25_25)) | apart_point_and_line(Y24_24, V26_26)))), ! [X27_27, Y28_28, Z29_29] : ((apart_point_and_line(X27_27, Y28_28) => (distinct_points(X27_27, Z29_29) | apart_point_and_line(Z29_29, Y28_28)))), ! [X30_30, Y31_31, Z32_32] : ((apart_point_and_line(X30_30, Y31_31) => (distinct_lines(Y31_31, Z32_32) | apart_point_and_line(X30_30, Z32_32)))), ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 16.98/4.90
% 16.98/4.90 [2] DELTA_NOT_FORALL : ~! [X35_35, Y36_36, U37_37, V38_38] : ((((distinct_points(X35_35, Y36_36) & convergent_lines(U37_37, V38_38)) & (apart_point_and_line(X35_35, U37_37) | apart_point_and_line(X35_35, V38_38))) => distinct_points(X35_35, intersection_point(U37_37, V38_38))))
% 16.98/4.90 -> [3] ~(((distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)) & (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))) => distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)))
% 16.98/4.90
% 16.98/4.90 [3] ALPHA_NOT_IMPLY : ~(((distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)) & (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))) => distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)))
% 16.98/4.90 -> [4] ((distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)) & (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))), ~distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 16.98/4.90
% 16.98/4.90 [4] ALPHA_AND : ((distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)) & (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)))
% 16.98/4.90 -> [5] (distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)), (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 16.98/4.90
% 16.98/4.90 [5] ALPHA_AND : (distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838))
% 16.98/4.90 -> [6] distinct_points(skolem_X3535, skolem_Y3636), convergent_lines(skolem_U3737, skolem_V3838)
% 16.98/4.90
% 16.98/4.90 [6] BETA_OR : (apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 16.98/4.90 -> [7] apart_point_and_line(skolem_X3535, skolem_U3737)
% 16.98/4.90 -> [8] apart_point_and_line(skolem_X3535, skolem_V3838)
% 16.98/4.90
% 16.98/4.90 [7] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 16.98/4.90 -> [9] ~distinct_points(skolem_Y3636, skolem_Y3636)
% 16.98/4.90
% 16.98/4.90 [9] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 16.98/4.90 -> [11] ~distinct_lines(X6_0_1, X6_0_1)
% 16.98/4.90
% 16.98/4.90 [11] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 16.98/4.90 -> [13] ~convergent_lines(skolem_U3737, skolem_U3737)
% 16.98/4.90
% 16.98/4.90 [13] GAMMA_FORALL : ! [X8_8, Y9_9, Z10_10] : ((distinct_points(X8_8, Y9_9) => (distinct_points(X8_8, Z10_10) | distinct_points(Y9_9, Z10_10))))
% 16.98/4.90 -> [15] (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636)))
% 16.98/4.90
% 16.98/4.90 [15] BETA_IMPLY : (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636)))
% 16.98/4.90 -> [17] ~distinct_points(skolem_X3535, skolem_Y3636)
% 16.98/4.90 -> [18] (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636))
% 16.98/4.90
% 16.98/4.90 [17] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 16.98/4.90
% 16.98/4.90 [18] BETA_OR : (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636))
% 16.98/4.90 -> [25] distinct_points(skolem_X3535, skolem_Y3636)
% 16.98/4.90 -> [26] distinct_points(skolem_Y3636, skolem_Y3636)
% 16.98/4.90
% 16.98/4.90 [26] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 16.98/4.90
% 16.98/4.90 [25] 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))))
% 16.98/4.90 -> [29] (distinct_lines(Z13_0_4, Z13_0_4) => (distinct_lines(Z13_0_4, Z13_0_4) | distinct_lines(Z13_0_4, Z13_0_4)))
% 16.98/4.90
% 16.98/4.90 [29] BETA_IMPLY : (distinct_lines(Z13_0_4, Z13_0_4) => (distinct_lines(Z13_0_4, Z13_0_4) | distinct_lines(Z13_0_4, Z13_0_4)))
% 16.98/4.90 -> [30] ~distinct_lines(Z13_0_4, Z13_0_4)
% 16.98/4.90 -> [31] (distinct_lines(Z13_0_4, Z13_0_4) | distinct_lines(Z13_0_4, Z13_0_4))
% 16.98/4.90
% 16.98/4.90 [30] GAMMA_FORALL : ! [X14_14, Y15_15, Z16_16] : ((convergent_lines(X14_14, Y15_15) => (convergent_lines(X14_14, Z16_16) | convergent_lines(Y15_15, Z16_16))))
% 16.98/4.90 -> [37] (convergent_lines(skolem_U3737, skolem_V3838) => (convergent_lines(skolem_U3737, skolem_U3737) | convergent_lines(skolem_V3838, skolem_U3737)))
% 16.98/4.90
% 16.98/4.90 [37] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => (convergent_lines(skolem_U3737, skolem_U3737) | convergent_lines(skolem_V3838, skolem_U3737)))
% 16.98/4.90 -> [40] ~convergent_lines(skolem_U3737, skolem_V3838)
% 16.98/4.90 -> [41] (convergent_lines(skolem_U3737, skolem_U3737) | convergent_lines(skolem_V3838, skolem_U3737))
% 16.98/4.90
% 16.98/4.90 [40] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 16.98/4.90
% 16.98/4.90 [41] BETA_OR : (convergent_lines(skolem_U3737, skolem_U3737) | convergent_lines(skolem_V3838, skolem_U3737))
% 16.98/4.90 -> [49] convergent_lines(skolem_U3737, skolem_U3737)
% 16.98/4.90 -> [50] convergent_lines(skolem_V3838, skolem_U3737)
% 16.98/4.90
% 16.98/4.90 [49] CLOSURE : convergent_lines(skolem_U3737, skolem_U3737)
% 16.98/4.90
% 16.98/4.90 [50] GAMMA_FORALL : ! [X17_17, Y18_18, Z19_19] : ((distinct_points(X17_17, Y18_18) => (apart_point_and_line(Z19_19, line_connecting(X17_17, Y18_18)) => (distinct_points(Z19_19, X17_17) & distinct_points(Z19_19, Y18_18)))))
% 16.98/4.90 -> [53] (distinct_points(skolem_X3535, skolem_Y3636) => (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636))))
% 16.98/4.90
% 16.98/4.90 [53] BETA_IMPLY : (distinct_points(skolem_X3535, skolem_Y3636) => (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636))))
% 16.98/4.90 -> [54] ~distinct_points(skolem_X3535, skolem_Y3636)
% 16.98/4.90 -> [55] (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636)))
% 16.98/4.90
% 16.98/4.90 [54] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 16.98/4.90
% 16.98/4.90 [55] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636)))
% 16.98/4.90 -> [367] ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 16.98/4.90 -> [368] (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636))
% 16.98/4.90
% 16.98/4.90 [368] ALPHA_AND : (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636))
% 16.98/4.90 -> [369] distinct_points(skolem_Y3636, skolem_X3535), distinct_points(skolem_Y3636, skolem_Y3636)
% 16.98/4.90
% 16.98/4.90 [369] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 16.98/4.90
% 16.98/4.90 [367] GAMMA_FORALL : ! [X20_20, Y21_21, Z22_22] : ((convergent_lines(X20_20, Y21_21) => ((apart_point_and_line(Z22_22, X20_20) | apart_point_and_line(Z22_22, Y21_21)) => distinct_points(Z22_22, intersection_point(X20_20, Y21_21)))))
% 16.98/4.90 -> [370] (convergent_lines(skolem_U3737, skolem_V3838) => ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) => distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))))
% 16.98/4.90
% 16.98/4.90 [370] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) => distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))))
% 16.98/4.90 -> [371] ~convergent_lines(skolem_U3737, skolem_V3838)
% 16.98/4.90 -> [372] ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) => distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)))
% 16.98/4.90
% 16.98/4.90 [371] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 16.98/4.90
% 16.98/4.90 [372] BETA_IMPLY : ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) => distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)))
% 16.98/4.90 -> [390] ~(apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 16.98/4.90 -> [391] distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 16.98/4.90
% 16.98/4.90 [391] CLOSURE : distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 16.98/4.90
% 16.98/4.90 [390] ALPHA_NOT_OR : ~(apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 16.98/4.90 -> [392] ~apart_point_and_line(skolem_X3535, skolem_U3737), ~apart_point_and_line(skolem_X3535, skolem_V3838)
% 16.98/4.90
% 16.98/4.90 [392] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 16.98/4.90
% 16.98/4.90 [31] BETA_OR : (distinct_lines(Z13_0_4, Z13_0_4) | distinct_lines(Z13_0_4, Z13_0_4))
% 16.98/4.90 -> [402] distinct_lines(Z13_0_4, Z13_0_4)
% 16.98/4.90 -> [403] distinct_lines(Z13_0_4, Z13_0_4)
% 16.98/4.90
% 16.98/4.90 [403] CLOSURE : distinct_lines(Z13_0_4, Z13_0_4)
% 16.98/4.90
% 16.98/4.90 [402] CLOSURE : distinct_lines(Z13_0_4, Z13_0_4)
% 16.98/4.90
% 16.98/4.90 [8] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 16.98/4.90 -> [10] ~distinct_points(skolem_Y3636, skolem_Y3636)
% 16.98/4.90
% 16.98/4.90 [10] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 16.98/4.90 -> [12] ~distinct_lines(X6_1_1, X6_1_1)
% 16.98/4.90
% 16.98/4.90 [12] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 16.98/4.90 -> [14] ~convergent_lines(X7_1_2, X7_1_2)
% 16.98/4.90
% 16.98/4.90 [14] 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))))
% 16.98/4.90 -> [16] (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636)))
% 16.98/4.90
% 16.98/4.90 [16] BETA_IMPLY : (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636)))
% 16.98/4.90 -> [19] ~distinct_points(skolem_X3535, skolem_Y3636)
% 16.98/4.90 -> [20] (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636))
% 16.98/4.90
% 16.98/4.90 [19] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 16.98/4.90
% 16.98/4.90 [20] BETA_OR : (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636))
% 16.98/4.90 -> [27] distinct_points(skolem_X3535, skolem_Y3636)
% 16.98/4.90 -> [28] distinct_points(skolem_Y3636, skolem_Y3636)
% 16.98/4.90
% 16.98/4.90 [28] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 16.98/4.90
% 16.98/4.90 [27] GAMMA_FORALL : ! [X11_11, Y12_12, Z13_13] : ((distinct_lines(X11_11, Y12_12) => (distinct_lines(X11_11, Z13_13) | distinct_lines(Y12_12, Z13_13))))
% 16.98/4.90 -> [34] (distinct_lines(Z13_1_4, Z13_1_4) => (distinct_lines(Z13_1_4, Z13_1_4) | distinct_lines(Z13_1_4, Z13_1_4)))
% 16.98/4.90
% 16.98/4.90 [34] BETA_IMPLY : (distinct_lines(Z13_1_4, Z13_1_4) => (distinct_lines(Z13_1_4, Z13_1_4) | distinct_lines(Z13_1_4, Z13_1_4)))
% 16.98/4.90 -> [35] ~distinct_lines(Z13_1_4, Z13_1_4)
% 16.98/4.90 -> [36] (distinct_lines(Z13_1_4, Z13_1_4) | distinct_lines(Z13_1_4, Z13_1_4))
% 16.98/4.91
% 16.98/4.91 [36] BETA_OR : (distinct_lines(Z13_1_4, Z13_1_4) | distinct_lines(Z13_1_4, Z13_1_4))
% 16.98/4.91 -> [38] distinct_lines(Z13_1_4, Z13_1_4)
% 16.98/4.91 -> [39] distinct_lines(Z13_1_4, Z13_1_4)
% 16.98/4.91
% 16.98/4.91 [38] CLOSURE : distinct_lines(Z13_1_4, Z13_1_4)
% 16.98/4.91
% 16.98/4.91 [39] CLOSURE : distinct_lines(Z13_1_4, Z13_1_4)
% 16.98/4.91
% 16.98/4.91 [44] BETA_IMPLY : (convergent_lines(Z16_1_5, Z16_1_5) => (convergent_lines(Z16_1_5, Z16_1_5) | convergent_lines(Z16_1_5, Z16_1_5)))
% 16.98/4.91 -> [1195] ~convergent_lines(Z16_1_5, Z16_1_5)
% 16.98/4.91 -> [1196] (convergent_lines(Z16_1_5, Z16_1_5) | convergent_lines(Z16_1_5, Z16_1_5))
% 16.98/4.91
% 16.98/4.91 [1196] BETA_OR : (convergent_lines(Z16_1_5, Z16_1_5) | convergent_lines(Z16_1_5, Z16_1_5))
% 16.98/4.91 -> [1197] convergent_lines(Z16_1_5, Z16_1_5)
% 16.98/4.91 -> [1198] convergent_lines(Z16_1_5, Z16_1_5)
% 16.98/4.91
% 16.98/4.91 [1197] CLOSURE : convergent_lines(Z16_1_5, Z16_1_5)
% 16.98/4.91
% 16.98/4.91 [1198] CLOSURE : convergent_lines(Z16_1_5, Z16_1_5)
% 16.98/4.91
% 16.98/4.91 [1195] GAMMA_FORALL : ! [X17_17, Y18_18, Z19_19] : ((distinct_points(X17_17, Y18_18) => (apart_point_and_line(Z19_19, line_connecting(X17_17, Y18_18)) => (distinct_points(Z19_19, X17_17) & distinct_points(Z19_19, Y18_18)))))
% 16.98/4.91 -> [1199] (distinct_points(skolem_X3535, skolem_Y3636) => (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636))))
% 16.98/4.91
% 16.98/4.91 [1199] BETA_IMPLY : (distinct_points(skolem_X3535, skolem_Y3636) => (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636))))
% 16.98/4.91 -> [1200] ~distinct_points(skolem_X3535, skolem_Y3636)
% 16.98/4.91 -> [1201] (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636)))
% 16.98/4.91
% 16.98/4.91 [1200] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 16.98/4.91
% 16.98/4.91 [1201] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636)))
% 16.98/4.91 -> [1942] ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 16.98/4.91 -> [1943] (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636))
% 16.98/4.91
% 16.98/4.91 [1943] ALPHA_AND : (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636))
% 16.98/4.91 -> [1944] distinct_points(skolem_Y3636, skolem_X3535), distinct_points(skolem_Y3636, skolem_Y3636)
% 16.98/4.91
% 16.98/4.91 [1944] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 16.98/4.91
% 16.98/4.91 [1942] GAMMA_FORALL : ! [X20_20, Y21_21, Z22_22] : ((convergent_lines(X20_20, Y21_21) => ((apart_point_and_line(Z22_22, X20_20) | apart_point_and_line(Z22_22, Y21_21)) => distinct_points(Z22_22, intersection_point(X20_20, Y21_21)))))
% 16.98/4.91 -> [1945] (convergent_lines(skolem_U3737, skolem_V3838) => ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) => distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))))
% 16.98/4.91
% 16.98/4.91 [1945] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) => distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))))
% 16.98/4.91 -> [1946] ~convergent_lines(skolem_U3737, skolem_V3838)
% 16.98/4.91 -> [1947] ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) => distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)))
% 16.98/4.91
% 16.98/4.91 [1946] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 16.98/4.91
% 16.98/4.91 [1947] BETA_IMPLY : ((apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838)) => distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838)))
% 16.98/4.91 -> [1951] ~(apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 16.98/4.91 -> [1952] distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 16.98/4.91
% 16.98/4.91 [1952] CLOSURE : distinct_points(skolem_X3535, intersection_point(skolem_U3737, skolem_V3838))
% 16.98/4.91
% 16.98/4.91 [1951] ALPHA_NOT_OR : ~(apart_point_and_line(skolem_X3535, skolem_U3737) | apart_point_and_line(skolem_X3535, skolem_V3838))
% 16.98/4.91 -> [1953] ~apart_point_and_line(skolem_X3535, skolem_U3737), ~apart_point_and_line(skolem_X3535, skolem_V3838)
% 16.98/4.91
% 16.98/4.91 [1953] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_V3838)
% 16.98/4.91
% 16.98/4.91 % SZS output end Proof for theBenchmark.p
% 16.98/4.91 [4.551817s][1][Res] 48547 goroutines created
% 16.98/4.91 ==== Result ====
% 16.98/4.91 [4.551852s][1][Res] VALID
% 16.98/4.91 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------