TSTP Solution File: GEO178+2 by Goeland---1.0.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO178+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n028.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 14.34s 3.86s
% Output : Proof 14.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : GEO178+2 : TPTP v8.1.0. Released v3.3.0.
% 0.09/0.11 % Command : goeland -dmt -presko -proof %s
% 0.11/0.31 % Computer : n028.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Wed Aug 31 06:55:34 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.11/0.32 [DMT] DMT loaded with preskolemization
% 0.11/0.32 [EQ] equality loaded.
% 0.11/0.32 [0.000032s][1][MAIN] Problem : theBenchmark.p
% 0.11/0.32 Conjecture not found
% 0.11/0.32 Start search
% 0.11/0.32 nb_step : 1 - limit : 13
% 0.11/0.32 Launch Gotab with destructive = true
% 14.34/3.86 % SZS output start Proof for theBenchmark.p
% 14.34/3.86 [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, Z37_37] : (((distinct_points(X35_35, Y36_36) & apart_point_and_line(Z37_37, line_connecting(X35_35, Y36_36))) => (distinct_points(Z37_37, X35_35) & distinct_points(Z37_37, Y36_36)))))
% 14.34/3.86 -> [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, Z37_37] : (((distinct_points(X35_35, Y36_36) & apart_point_and_line(Z37_37, line_connecting(X35_35, Y36_36))) => (distinct_points(Z37_37, X35_35) & distinct_points(Z37_37, Y36_36))))
% 14.34/3.86
% 14.34/3.86 [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))))
% 14.34/3.86 -> [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)))
% 14.34/3.86
% 14.34/3.86 [2] DELTA_NOT_FORALL : ~! [X35_35, Y36_36, Z37_37] : (((distinct_points(X35_35, Y36_36) & apart_point_and_line(Z37_37, line_connecting(X35_35, Y36_36))) => (distinct_points(Z37_37, X35_35) & distinct_points(Z37_37, Y36_36))))
% 14.34/3.86 -> [3] ~((distinct_points(skolem_X3535, skolem_Y3636) & apart_point_and_line(skolem_Z3737, line_connecting(skolem_X3535, skolem_Y3636))) => (distinct_points(skolem_Z3737, skolem_X3535) & distinct_points(skolem_Z3737, skolem_Y3636)))
% 14.34/3.86
% 14.34/3.86 [3] ALPHA_NOT_IMPLY : ~((distinct_points(skolem_X3535, skolem_Y3636) & apart_point_and_line(skolem_Z3737, line_connecting(skolem_X3535, skolem_Y3636))) => (distinct_points(skolem_Z3737, skolem_X3535) & distinct_points(skolem_Z3737, skolem_Y3636)))
% 14.34/3.86 -> [4] (distinct_points(skolem_X3535, skolem_Y3636) & apart_point_and_line(skolem_Z3737, line_connecting(skolem_X3535, skolem_Y3636))), ~(distinct_points(skolem_Z3737, skolem_X3535) & distinct_points(skolem_Z3737, skolem_Y3636))
% 14.34/3.86
% 14.34/3.86 [4] ALPHA_AND : (distinct_points(skolem_X3535, skolem_Y3636) & apart_point_and_line(skolem_Z3737, line_connecting(skolem_X3535, skolem_Y3636)))
% 14.34/3.86 -> [5] distinct_points(skolem_X3535, skolem_Y3636), apart_point_and_line(skolem_Z3737, line_connecting(skolem_X3535, skolem_Y3636))
% 14.34/3.86
% 14.34/3.86 [5] BETA_NOT_AND : ~(distinct_points(skolem_Z3737, skolem_X3535) & distinct_points(skolem_Z3737, skolem_Y3636))
% 14.34/3.86 -> [6] ~distinct_points(skolem_Z3737, skolem_X3535)
% 14.34/3.86 -> [7] ~distinct_points(skolem_Z3737, skolem_Y3636)
% 14.34/3.86
% 14.34/3.86 [7] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 14.34/3.86 -> [9] ~distinct_points(skolem_Y3636, skolem_Y3636)
% 14.34/3.86
% 14.34/3.86 [9] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 14.34/3.86 -> [11] ~distinct_lines(X6_1_1, X6_1_1)
% 14.34/3.86
% 14.34/3.86 [11] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 14.34/3.86 -> [13] ~convergent_lines(X7_1_2, X7_1_2)
% 14.34/3.86
% 14.34/3.86 [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))))
% 14.34/3.86 -> [15] (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636)))
% 14.34/3.86
% 14.34/3.86 [15] BETA_IMPLY : (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636)))
% 14.34/3.86 -> [16] ~distinct_points(skolem_X3535, skolem_Y3636)
% 14.34/3.86 -> [17] (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636))
% 14.34/3.86
% 14.34/3.86 [16] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 14.34/3.86
% 14.34/3.86 [17] BETA_OR : (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636))
% 14.34/3.86 -> [24] distinct_points(skolem_X3535, skolem_Y3636)
% 14.34/3.86 -> [25] distinct_points(skolem_Y3636, skolem_Y3636)
% 14.34/3.86
% 14.34/3.86 [25] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 14.34/3.86
% 14.34/3.86 [24] GAMMA_FORALL : ! [X11_11, Y12_12, Z13_13] : ((distinct_lines(X11_11, Y12_12) => (distinct_lines(X11_11, Z13_13) | distinct_lines(Y12_12, Z13_13))))
% 14.34/3.86 -> [28] (distinct_lines(Z13_0_4, Z13_0_4) => (distinct_lines(Z13_0_4, Z13_0_4) | distinct_lines(Z13_0_4, Z13_0_4)))
% 14.34/3.86
% 14.34/3.86 [28] BETA_IMPLY : (distinct_lines(Z13_0_4, Z13_0_4) => (distinct_lines(Z13_0_4, Z13_0_4) | distinct_lines(Z13_0_4, Z13_0_4)))
% 14.34/3.86 -> [30] ~distinct_lines(Z13_0_4, Z13_0_4)
% 14.34/3.86 -> [31] (distinct_lines(Z13_0_4, Z13_0_4) | distinct_lines(Z13_0_4, Z13_0_4))
% 14.34/3.86
% 14.34/3.86 [31] BETA_OR : (distinct_lines(Z13_0_4, Z13_0_4) | distinct_lines(Z13_0_4, Z13_0_4))
% 14.34/3.86 -> [34] distinct_lines(Z13_0_4, Z13_0_4)
% 14.34/3.86 -> [35] distinct_lines(Z13_0_4, Z13_0_4)
% 14.34/3.86
% 14.34/3.86 [35] CLOSURE : distinct_lines(Z13_0_4, Z13_0_4)
% 14.34/3.86
% 14.34/3.86 [34] CLOSURE : distinct_lines(Z13_0_4, Z13_0_4)
% 14.34/3.86
% 14.34/3.86 [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))))
% 14.34/3.86 -> [41] (convergent_lines(Z16_1_5, Z16_1_5) => (convergent_lines(Z16_1_5, Z16_1_5) | convergent_lines(Z16_1_5, Z16_1_5)))
% 14.34/3.86
% 14.34/3.86 [41] BETA_IMPLY : (convergent_lines(Z16_1_5, Z16_1_5) => (convergent_lines(Z16_1_5, Z16_1_5) | convergent_lines(Z16_1_5, Z16_1_5)))
% 14.34/3.86 -> [42] ~convergent_lines(Z16_1_5, Z16_1_5)
% 14.34/3.86 -> [43] (convergent_lines(Z16_1_5, Z16_1_5) | convergent_lines(Z16_1_5, Z16_1_5))
% 14.34/3.86
% 14.34/3.86 [43] BETA_OR : (convergent_lines(Z16_1_5, Z16_1_5) | convergent_lines(Z16_1_5, Z16_1_5))
% 14.34/3.86 -> [46] convergent_lines(Z16_1_5, Z16_1_5)
% 14.34/3.86 -> [47] convergent_lines(Z16_1_5, Z16_1_5)
% 14.34/3.86
% 14.34/3.86 [46] CLOSURE : convergent_lines(Z16_1_5, Z16_1_5)
% 14.34/3.86
% 14.34/3.86 [47] CLOSURE : convergent_lines(Z16_1_5, Z16_1_5)
% 14.34/3.86
% 14.34/3.86 [42] 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)))))
% 14.34/3.86 -> [49] (distinct_points(skolem_X3535, skolem_Y3636) => (apart_point_and_line(skolem_Z3737, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Z3737, skolem_X3535) & distinct_points(skolem_Z3737, skolem_Y3636))))
% 14.34/3.86
% 14.34/3.86 [49] BETA_IMPLY : (distinct_points(skolem_X3535, skolem_Y3636) => (apart_point_and_line(skolem_Z3737, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Z3737, skolem_X3535) & distinct_points(skolem_Z3737, skolem_Y3636))))
% 14.34/3.86 -> [52] ~distinct_points(skolem_X3535, skolem_Y3636)
% 14.34/3.86 -> [53] (apart_point_and_line(skolem_Z3737, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Z3737, skolem_X3535) & distinct_points(skolem_Z3737, skolem_Y3636)))
% 14.34/3.86
% 14.34/3.86 [52] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 14.34/3.86
% 14.34/3.86 [53] BETA_IMPLY : (apart_point_and_line(skolem_Z3737, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Z3737, skolem_X3535) & distinct_points(skolem_Z3737, skolem_Y3636)))
% 14.34/3.86 -> [972] ~apart_point_and_line(skolem_Z3737, line_connecting(skolem_X3535, skolem_Y3636))
% 14.34/3.86 -> [973] (distinct_points(skolem_Z3737, skolem_X3535) & distinct_points(skolem_Z3737, skolem_Y3636))
% 14.34/3.86
% 14.34/3.86 [972] CLOSURE : ~apart_point_and_line(skolem_Z3737, line_connecting(skolem_X3535, skolem_Y3636))
% 14.34/3.86
% 14.34/3.86 [973] ALPHA_AND : (distinct_points(skolem_Z3737, skolem_X3535) & distinct_points(skolem_Z3737, skolem_Y3636))
% 14.34/3.86 -> [978] distinct_points(skolem_Z3737, skolem_X3535), distinct_points(skolem_Z3737, skolem_Y3636)
% 14.34/3.86
% 14.34/3.86 [978] CLOSURE : distinct_points(skolem_Z3737, skolem_Y3636)
% 14.34/3.86
% 14.34/3.86 [6] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 14.34/3.86 -> [8] ~distinct_points(skolem_X3535, skolem_X3535)
% 14.34/3.86
% 14.34/3.86 [8] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 14.34/3.86 -> [10] ~distinct_lines(X6_0_1, X6_0_1)
% 14.34/3.86
% 14.34/3.86 [10] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 14.34/3.86 -> [12] ~convergent_lines(X7_0_2, X7_0_2)
% 14.34/3.86
% 14.34/3.86 [12] GAMMA_FORALL : ! [X8_8, Y9_9, Z10_10] : ((distinct_points(X8_8, Y9_9) => (distinct_points(X8_8, Z10_10) | distinct_points(Y9_9, Z10_10))))
% 14.34/3.86 -> [14] (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_X3535) | distinct_points(skolem_Y3636, skolem_X3535)))
% 14.34/3.86
% 14.34/3.86 [14] BETA_IMPLY : (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_X3535) | distinct_points(skolem_Y3636, skolem_X3535)))
% 14.34/3.86 -> [18] ~distinct_points(skolem_X3535, skolem_Y3636)
% 14.34/3.86 -> [19] (distinct_points(skolem_X3535, skolem_X3535) | distinct_points(skolem_Y3636, skolem_X3535))
% 14.34/3.86
% 14.34/3.86 [18] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 14.34/3.86
% 14.34/3.86 [19] BETA_OR : (distinct_points(skolem_X3535, skolem_X3535) | distinct_points(skolem_Y3636, skolem_X3535))
% 14.34/3.86 -> [26] distinct_points(skolem_X3535, skolem_X3535)
% 14.34/3.86 -> [27] distinct_points(skolem_Y3636, skolem_X3535)
% 14.34/3.86
% 14.34/3.86 [26] CLOSURE : distinct_points(skolem_X3535, skolem_X3535)
% 14.34/3.86
% 14.34/3.86 [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))))
% 14.34/3.86 -> [29] (distinct_lines(Z13_1_4, Z13_1_4) => (distinct_lines(Z13_1_4, Z13_1_4) | distinct_lines(Z13_1_4, Z13_1_4)))
% 14.34/3.86
% 14.34/3.86 [29] BETA_IMPLY : (distinct_lines(Z13_1_4, Z13_1_4) => (distinct_lines(Z13_1_4, Z13_1_4) | distinct_lines(Z13_1_4, Z13_1_4)))
% 14.34/3.86 -> [32] ~distinct_lines(Z13_1_4, Z13_1_4)
% 14.34/3.86 -> [33] (distinct_lines(Z13_1_4, Z13_1_4) | distinct_lines(Z13_1_4, Z13_1_4))
% 14.34/3.86
% 14.34/3.86 [33] BETA_OR : (distinct_lines(Z13_1_4, Z13_1_4) | distinct_lines(Z13_1_4, Z13_1_4))
% 14.34/3.86 -> [36] distinct_lines(Z13_1_4, Z13_1_4)
% 14.34/3.86 -> [37] distinct_lines(Z13_1_4, Z13_1_4)
% 14.34/3.86
% 14.34/3.86 [36] CLOSURE : distinct_lines(Z13_1_4, Z13_1_4)
% 14.34/3.86
% 14.34/3.86 [37] CLOSURE : distinct_lines(Z13_1_4, Z13_1_4)
% 14.34/3.86
% 14.34/3.86 [32] GAMMA_FORALL : ! [X14_14, Y15_15, Z16_16] : ((convergent_lines(X14_14, Y15_15) => (convergent_lines(X14_14, Z16_16) | convergent_lines(Y15_15, Z16_16))))
% 14.34/3.86 -> [38] (convergent_lines(Z16_0_5, Z16_0_5) => (convergent_lines(Z16_0_5, Z16_0_5) | convergent_lines(Z16_0_5, Z16_0_5)))
% 14.34/3.86
% 14.34/3.86 [38] 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)))
% 14.34/3.86 -> [39] ~convergent_lines(Z16_0_5, Z16_0_5)
% 14.34/3.86 -> [40] (convergent_lines(Z16_0_5, Z16_0_5) | convergent_lines(Z16_0_5, Z16_0_5))
% 14.34/3.86
% 14.34/3.86 [40] BETA_OR : (convergent_lines(Z16_0_5, Z16_0_5) | convergent_lines(Z16_0_5, Z16_0_5))
% 14.34/3.86 -> [44] convergent_lines(Z16_0_5, Z16_0_5)
% 14.34/3.86 -> [45] convergent_lines(Z16_0_5, Z16_0_5)
% 14.34/3.86
% 14.34/3.86 [45] CLOSURE : convergent_lines(Z16_0_5, Z16_0_5)
% 14.34/3.86
% 14.34/3.86 [44] CLOSURE : convergent_lines(Z16_0_5, Z16_0_5)
% 14.34/3.86
% 14.34/3.86 [48] BETA_IMPLY : (distinct_points(skolem_X3535, skolem_Y3636) => (apart_point_and_line(skolem_Z3737, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Z3737, skolem_X3535) & distinct_points(skolem_Z3737, skolem_Y3636))))
% 14.34/3.86 -> [1217] ~distinct_points(skolem_X3535, skolem_Y3636)
% 14.34/3.86 -> [1218] (apart_point_and_line(skolem_Z3737, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Z3737, skolem_X3535) & distinct_points(skolem_Z3737, skolem_Y3636)))
% 14.34/3.86
% 14.34/3.86 [1217] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 14.34/3.86
% 14.34/3.86 [1218] BETA_IMPLY : (apart_point_and_line(skolem_Z3737, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Z3737, skolem_X3535) & distinct_points(skolem_Z3737, skolem_Y3636)))
% 14.34/3.86 -> [1432] ~apart_point_and_line(skolem_Z3737, line_connecting(skolem_X3535, skolem_Y3636))
% 14.34/3.86 -> [1433] (distinct_points(skolem_Z3737, skolem_X3535) & distinct_points(skolem_Z3737, skolem_Y3636))
% 14.34/3.86
% 14.34/3.86 [1432] CLOSURE : ~apart_point_and_line(skolem_Z3737, line_connecting(skolem_X3535, skolem_Y3636))
% 14.34/3.86
% 14.34/3.86 [1433] ALPHA_AND : (distinct_points(skolem_Z3737, skolem_X3535) & distinct_points(skolem_Z3737, skolem_Y3636))
% 14.34/3.86 -> [1434] distinct_points(skolem_Z3737, skolem_X3535), distinct_points(skolem_Z3737, skolem_Y3636)
% 14.34/3.86
% 14.34/3.86 [1434] CLOSURE : distinct_points(skolem_Z3737, skolem_X3535)
% 14.34/3.86
% 14.34/3.86 % SZS output end Proof for theBenchmark.p
% 14.34/3.86 [3.542000s][1][Res] 31318 goroutines created
% 14.34/3.86 ==== Result ====
% 14.34/3.86 [3.542047s][1][Res] VALID
% 14.34/3.86 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------