TSTP Solution File: GEO172+2 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO172+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n009.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 22.93s 7.52s
% Output : Proof 22.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO172+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : goeland -dmt -presko -proof %s
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Aug 31 06:41:35 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.18/0.33 [DMT] DMT loaded with preskolemization
% 0.18/0.33 [EQ] equality loaded.
% 0.18/0.33 [0.000044s][1][MAIN] Problem : theBenchmark.p
% 0.18/0.33 Conjecture not found
% 0.18/0.33 Start search
% 0.18/0.33 nb_step : 1 - limit : 13
% 0.18/0.33 Launch Gotab with destructive = true
% 22.93/7.52 % SZS output start Proof for theBenchmark.p
% 22.93/7.52 [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] : ((((convergent_lines(X35_35, Y36_36) & ~apart_point_and_line(Z37_37, X35_35)) & ~apart_point_and_line(Z37_37, Y36_36)) => ~distinct_points(Z37_37, intersection_point(X35_35, Y36_36)))))
% 22.93/7.52 -> [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] : ((((convergent_lines(X35_35, Y36_36) & ~apart_point_and_line(Z37_37, X35_35)) & ~apart_point_and_line(Z37_37, Y36_36)) => ~distinct_points(Z37_37, intersection_point(X35_35, Y36_36))))
% 22.93/7.52
% 22.93/7.52 [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))))
% 22.93/7.52 -> [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)))
% 22.93/7.52
% 22.93/7.52 [2] DELTA_NOT_FORALL : ~! [X35_35, Y36_36, Z37_37] : ((((convergent_lines(X35_35, Y36_36) & ~apart_point_and_line(Z37_37, X35_35)) & ~apart_point_and_line(Z37_37, Y36_36)) => ~distinct_points(Z37_37, intersection_point(X35_35, Y36_36))))
% 22.93/7.52 -> [3] ~(((convergent_lines(skolem_X3535, skolem_Y3636) & ~apart_point_and_line(skolem_Z3737, skolem_X3535)) & ~apart_point_and_line(skolem_Z3737, skolem_Y3636)) => ~distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)))
% 22.93/7.52
% 22.93/7.52 [3] ALPHA_NOT_IMPLY : ~(((convergent_lines(skolem_X3535, skolem_Y3636) & ~apart_point_and_line(skolem_Z3737, skolem_X3535)) & ~apart_point_and_line(skolem_Z3737, skolem_Y3636)) => ~distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)))
% 22.93/7.52 -> [4] ((convergent_lines(skolem_X3535, skolem_Y3636) & ~apart_point_and_line(skolem_Z3737, skolem_X3535)) & ~apart_point_and_line(skolem_Z3737, skolem_Y3636)), ~~distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52
% 22.93/7.52 [4] ALPHA_AND : ((convergent_lines(skolem_X3535, skolem_Y3636) & ~apart_point_and_line(skolem_Z3737, skolem_X3535)) & ~apart_point_and_line(skolem_Z3737, skolem_Y3636))
% 22.93/7.52 -> [5] (convergent_lines(skolem_X3535, skolem_Y3636) & ~apart_point_and_line(skolem_Z3737, skolem_X3535)), ~apart_point_and_line(skolem_Z3737, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [5] ALPHA_NOT_NOT : ~~distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52 -> [6] distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52
% 22.93/7.52 [6] ALPHA_AND : (convergent_lines(skolem_X3535, skolem_Y3636) & ~apart_point_and_line(skolem_Z3737, skolem_X3535))
% 22.93/7.52 -> [7] convergent_lines(skolem_X3535, skolem_Y3636), ~apart_point_and_line(skolem_Z3737, skolem_X3535)
% 22.93/7.52
% 22.93/7.52 [7] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 22.93/7.52 -> [8] ~distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52
% 22.93/7.52 [8] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 22.93/7.52 -> [9] ~distinct_lines(skolem_Y3636, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [9] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 22.93/7.52 -> [10] ~convergent_lines(skolem_Y3636, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [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))))
% 22.93/7.52 -> [11] (distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)) | distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636))))
% 22.93/7.52
% 22.93/7.52 [11] BETA_IMPLY : (distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)) | distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636))))
% 22.93/7.52 -> [12] ~distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52 -> [13] (distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)) | distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636)))
% 22.93/7.52
% 22.93/7.52 [12] CLOSURE : ~distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52
% 22.93/7.52 [13] BETA_OR : (distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)) | distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636)))
% 22.93/7.52 -> [16] distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52 -> [17] distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52
% 22.93/7.52 [17] CLOSURE : distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52
% 22.93/7.52 [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))))
% 22.93/7.52 -> [18] (distinct_lines(skolem_X3535, skolem_Y3636) => (distinct_lines(skolem_X3535, skolem_Y3636) | distinct_lines(skolem_Y3636, skolem_Y3636)))
% 22.93/7.52
% 22.93/7.52 [18] BETA_IMPLY : (distinct_lines(skolem_X3535, skolem_Y3636) => (distinct_lines(skolem_X3535, skolem_Y3636) | distinct_lines(skolem_Y3636, skolem_Y3636)))
% 22.93/7.52 -> [19] ~distinct_lines(skolem_X3535, skolem_Y3636)
% 22.93/7.52 -> [20] (distinct_lines(skolem_X3535, skolem_Y3636) | distinct_lines(skolem_Y3636, skolem_Y3636))
% 22.93/7.52
% 22.93/7.52 [19] 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))))
% 22.93/7.52 -> [23] (convergent_lines(skolem_X3535, skolem_Y3636) => (convergent_lines(skolem_X3535, skolem_Y3636) | convergent_lines(skolem_Y3636, skolem_Y3636)))
% 22.93/7.52
% 22.93/7.52 [23] BETA_IMPLY : (convergent_lines(skolem_X3535, skolem_Y3636) => (convergent_lines(skolem_X3535, skolem_Y3636) | convergent_lines(skolem_Y3636, skolem_Y3636)))
% 22.93/7.52 -> [24] ~convergent_lines(skolem_X3535, skolem_Y3636)
% 22.93/7.52 -> [25] (convergent_lines(skolem_X3535, skolem_Y3636) | convergent_lines(skolem_Y3636, skolem_Y3636))
% 22.93/7.52
% 22.93/7.52 [24] CLOSURE : ~convergent_lines(skolem_X3535, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [25] BETA_OR : (convergent_lines(skolem_X3535, skolem_Y3636) | convergent_lines(skolem_Y3636, skolem_Y3636))
% 22.93/7.52 -> [28] convergent_lines(skolem_X3535, skolem_Y3636)
% 22.93/7.52 -> [29] convergent_lines(skolem_Y3636, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [29] CLOSURE : convergent_lines(skolem_Y3636, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [28] 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)))))
% 22.93/7.52 -> [30] (distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)) => (apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), line_connecting(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))) => (distinct_points(intersection_point(skolem_X3535, skolem_Y3636), skolem_Z3737) & distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636)))))
% 22.93/7.52
% 22.93/7.52 [30] BETA_IMPLY : (distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)) => (apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), line_connecting(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))) => (distinct_points(intersection_point(skolem_X3535, skolem_Y3636), skolem_Z3737) & distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636)))))
% 22.93/7.52 -> [31] ~distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52 -> [32] (apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), line_connecting(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))) => (distinct_points(intersection_point(skolem_X3535, skolem_Y3636), skolem_Z3737) & distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636))))
% 22.93/7.52
% 22.93/7.52 [31] CLOSURE : ~distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52
% 22.93/7.52 [32] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), line_connecting(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))) => (distinct_points(intersection_point(skolem_X3535, skolem_Y3636), skolem_Z3737) & distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636))))
% 22.93/7.52 -> [718] ~apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), line_connecting(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)))
% 22.93/7.52 -> [719] (distinct_points(intersection_point(skolem_X3535, skolem_Y3636), skolem_Z3737) & distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636)))
% 22.93/7.52
% 22.93/7.52 [718] 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)))))
% 22.93/7.52 -> [721] (convergent_lines(skolem_X3535, skolem_Y3636) => ((apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_Y3636)) => distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636))))
% 22.93/7.52
% 22.93/7.52 [721] BETA_IMPLY : (convergent_lines(skolem_X3535, skolem_Y3636) => ((apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_Y3636)) => distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636))))
% 22.93/7.52 -> [722] ~convergent_lines(skolem_X3535, skolem_Y3636)
% 22.93/7.52 -> [723] ((apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_Y3636)) => distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636)))
% 22.93/7.52
% 22.93/7.52 [722] CLOSURE : ~convergent_lines(skolem_X3535, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [723] BETA_IMPLY : ((apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_Y3636)) => distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636)))
% 22.93/7.52 -> [1656] ~(apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_Y3636))
% 22.93/7.52 -> [1657] distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52
% 22.93/7.52 [1656] ALPHA_NOT_OR : ~(apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_Y3636))
% 22.93/7.52 -> [1658] ~apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535), ~apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [1658] GAMMA_FORALL : ! [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))))
% 22.93/7.52 -> [1659] ((distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)) & distinct_lines(skolem_X3535, skolem_X3535)) => (((apart_point_and_line(skolem_Z3737, skolem_X3535) | apart_point_and_line(skolem_Z3737, skolem_X3535)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535)))
% 22.93/7.52
% 22.93/7.52 [1659] BETA_IMPLY : ((distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)) & distinct_lines(skolem_X3535, skolem_X3535)) => (((apart_point_and_line(skolem_Z3737, skolem_X3535) | apart_point_and_line(skolem_Z3737, skolem_X3535)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535)))
% 22.93/7.52 -> [1660] ~(distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)) & distinct_lines(skolem_X3535, skolem_X3535))
% 22.93/7.52 -> [1661] (((apart_point_and_line(skolem_Z3737, skolem_X3535) | apart_point_and_line(skolem_Z3737, skolem_X3535)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535))
% 22.93/7.52
% 22.93/7.52 [1660] BETA_NOT_AND : ~(distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)) & distinct_lines(skolem_X3535, skolem_X3535))
% 22.93/7.52 -> [1662] ~distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52 -> [1663] ~distinct_lines(skolem_X3535, skolem_X3535)
% 22.93/7.52
% 22.93/7.52 [1663] GAMMA_FORALL : ! [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))))
% 22.93/7.52 -> [1668] (apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535) => (distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535)))
% 22.93/7.52
% 22.93/7.52 [1668] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535) => (distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535)))
% 22.93/7.52 -> [1671] ~apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535)
% 22.93/7.52 -> [1672] (distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535))
% 22.93/7.52
% 22.93/7.52 [1671] GAMMA_FORALL : ! [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))))
% 22.93/7.52 -> [1675] (apart_point_and_line(skolem_Z3737, Y31_65_10) => (distinct_lines(Y31_65_10, skolem_X3535) | apart_point_and_line(skolem_Z3737, skolem_X3535)))
% 22.93/7.52
% 22.93/7.52 [1675] BETA_IMPLY : (apart_point_and_line(skolem_Z3737, Y31_65_10) => (distinct_lines(Y31_65_10, skolem_X3535) | apart_point_and_line(skolem_Z3737, skolem_X3535)))
% 22.93/7.52 -> [1676] ~apart_point_and_line(skolem_Z3737, Y31_65_10)
% 22.93/7.52 -> [1677] (distinct_lines(Y31_65_10, skolem_X3535) | apart_point_and_line(skolem_Z3737, skolem_X3535))
% 22.93/7.52
% 22.93/7.52 [1677] BETA_OR : (distinct_lines(Y31_65_10, skolem_Y3636) | apart_point_and_line(skolem_Z3737, skolem_Y3636))
% 22.93/7.52 -> [1678] distinct_lines(Y31_65_10, skolem_Y3636)
% 22.93/7.52 -> [1679] apart_point_and_line(skolem_Z3737, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [1678] CLOSURE : distinct_lines(Y31_65_10, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [1679] CLOSURE : apart_point_and_line(skolem_Z3737, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [1680] BETA_IMPLY : (convergent_lines(skolem_X3535, skolem_Y3636) => distinct_lines(skolem_X3535, skolem_Y3636))
% 22.93/7.52 -> [1685] ~convergent_lines(skolem_X3535, skolem_Y3636)
% 22.93/7.52 -> [1686] distinct_lines(skolem_X3535, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [1686] CLOSURE : distinct_lines(skolem_X3535, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [1685] CLOSURE : ~convergent_lines(skolem_X3535, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [1672] BETA_OR : (distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535))
% 22.93/7.52 -> [1689] distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52 -> [1690] apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535)
% 22.93/7.52
% 22.93/7.52 [1690] CLOSURE : apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535)
% 22.93/7.52
% 22.93/7.52 [1689] CLOSURE : distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52
% 22.93/7.52 [1662] CLOSURE : ~distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52
% 22.93/7.52 [1661] BETA_OR : (((apart_point_and_line(skolem_Z3737, skolem_X3535) | apart_point_and_line(skolem_Z3737, skolem_X3535)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535))
% 22.93/7.52 -> [1691] ((apart_point_and_line(skolem_Z3737, skolem_X3535) | apart_point_and_line(skolem_Z3737, skolem_X3535)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535))
% 22.93/7.52 -> [1692] apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535)
% 22.93/7.52
% 22.93/7.52 [1692] CLOSURE : apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535)
% 22.93/7.52
% 22.93/7.52 [1691] BETA_OR : ((apart_point_and_line(skolem_Z3737, skolem_X3535) | apart_point_and_line(skolem_Z3737, skolem_X3535)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535))
% 22.93/7.52 -> [1693] (apart_point_and_line(skolem_Z3737, skolem_X3535) | apart_point_and_line(skolem_Z3737, skolem_X3535))
% 22.93/7.52 -> [1694] apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535)
% 22.93/7.52
% 22.93/7.52 [1694] CLOSURE : apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535)
% 22.93/7.52
% 22.93/7.52 [1693] BETA_OR : (apart_point_and_line(skolem_Z3737, line_connecting(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_Z3737, skolem_X3535))
% 22.93/7.52 -> [1695] apart_point_and_line(skolem_Z3737, line_connecting(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)))
% 22.93/7.52 -> [1696] apart_point_and_line(skolem_Z3737, skolem_X3535)
% 22.93/7.52
% 22.93/7.52 [1696] CLOSURE : apart_point_and_line(skolem_Z3737, skolem_X3535)
% 22.93/7.52
% 22.93/7.52 [1695] CLOSURE : apart_point_and_line(skolem_Z3737, line_connecting(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)))
% 22.93/7.52
% 22.93/7.52 [1657] CLOSURE : distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52
% 22.93/7.52 [720] CLOSURE : distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52
% 22.93/7.52 [20] BETA_OR : (distinct_lines(skolem_X3535, skolem_Y3636) | distinct_lines(skolem_Y3636, skolem_Y3636))
% 22.93/7.52 -> [1697] distinct_lines(skolem_X3535, skolem_Y3636)
% 22.93/7.52 -> [1698] distinct_lines(skolem_Y3636, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [1698] CLOSURE : distinct_lines(skolem_Y3636, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [1697] 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))))
% 22.93/7.52 -> [1699] (convergent_lines(skolem_X3535, skolem_Y3636) => (convergent_lines(skolem_X3535, skolem_Y3636) | convergent_lines(skolem_Y3636, skolem_Y3636)))
% 22.93/7.52
% 22.93/7.52 [1699] BETA_IMPLY : (convergent_lines(skolem_X3535, skolem_Y3636) => (convergent_lines(skolem_X3535, skolem_Y3636) | convergent_lines(skolem_Y3636, skolem_Y3636)))
% 22.93/7.52 -> [1700] ~convergent_lines(skolem_X3535, skolem_Y3636)
% 22.93/7.52 -> [1701] (convergent_lines(skolem_X3535, skolem_Y3636) | convergent_lines(skolem_Y3636, skolem_Y3636))
% 22.93/7.52
% 22.93/7.52 [1700] CLOSURE : ~convergent_lines(skolem_X3535, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [1701] BETA_OR : (convergent_lines(skolem_X3535, skolem_Y3636) | convergent_lines(skolem_Y3636, skolem_Y3636))
% 22.93/7.52 -> [1704] convergent_lines(skolem_X3535, skolem_Y3636)
% 22.93/7.52 -> [1705] convergent_lines(skolem_Y3636, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [1705] CLOSURE : convergent_lines(skolem_Y3636, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [1704] 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)))))
% 22.93/7.52 -> [1706] (distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)) => (apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), line_connecting(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))) => (distinct_points(intersection_point(skolem_X3535, skolem_Y3636), skolem_Z3737) & distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636)))))
% 22.93/7.52
% 22.93/7.52 [1706] BETA_IMPLY : (distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)) => (apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), line_connecting(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))) => (distinct_points(intersection_point(skolem_X3535, skolem_Y3636), skolem_Z3737) & distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636)))))
% 22.93/7.52 -> [1707] ~distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52 -> [1708] (apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), line_connecting(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))) => (distinct_points(intersection_point(skolem_X3535, skolem_Y3636), skolem_Z3737) & distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636))))
% 22.93/7.52
% 22.93/7.52 [1707] CLOSURE : ~distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52
% 22.93/7.52 [1708] BETA_IMPLY : (apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), line_connecting(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))) => (distinct_points(intersection_point(skolem_X3535, skolem_Y3636), skolem_Z3737) & distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636))))
% 22.93/7.52 -> [2327] ~apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), line_connecting(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)))
% 22.93/7.52 -> [2328] (distinct_points(intersection_point(skolem_X3535, skolem_Y3636), skolem_Z3737) & distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636)))
% 22.93/7.52
% 22.93/7.52 [2328] ALPHA_AND : (distinct_points(intersection_point(skolem_X3535, skolem_Y3636), skolem_Z3737) & distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636)))
% 22.93/7.52 -> [2329] distinct_points(intersection_point(skolem_X3535, skolem_Y3636), skolem_Z3737), distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52
% 22.93/7.52 [2329] CLOSURE : distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52
% 22.93/7.52 [2327] 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)))))
% 22.93/7.52 -> [2330] (convergent_lines(skolem_X3535, skolem_Y3636) => ((apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_Y3636)) => distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636))))
% 22.93/7.52
% 22.93/7.52 [2330] BETA_IMPLY : (convergent_lines(skolem_X3535, skolem_Y3636) => ((apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_Y3636)) => distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636))))
% 22.93/7.52 -> [2331] ~convergent_lines(skolem_X3535, skolem_Y3636)
% 22.93/7.52 -> [2332] ((apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_Y3636)) => distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636)))
% 22.93/7.52
% 22.93/7.52 [2331] CLOSURE : ~convergent_lines(skolem_X3535, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [2332] BETA_IMPLY : ((apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_Y3636)) => distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636)))
% 22.93/7.52 -> [2361] ~(apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_Y3636))
% 22.93/7.52 -> [2362] distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52
% 22.93/7.52 [2362] CLOSURE : distinct_points(intersection_point(skolem_X3535, skolem_Y3636), intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52
% 22.93/7.52 [2361] ALPHA_NOT_OR : ~(apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_Y3636))
% 22.93/7.52 -> [2363] ~apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535), ~apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [2363] GAMMA_FORALL : ! [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))))
% 22.93/7.52 -> [2364] ((distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)) & distinct_lines(skolem_X3535, skolem_Y3636)) => (((apart_point_and_line(skolem_Z3737, skolem_X3535) | apart_point_and_line(skolem_Z3737, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_Y3636)))
% 22.93/7.52
% 22.93/7.52 [2364] BETA_IMPLY : ((distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)) & distinct_lines(skolem_X3535, skolem_Y3636)) => (((apart_point_and_line(skolem_Z3737, skolem_X3535) | apart_point_and_line(skolem_Z3737, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_Y3636)))
% 22.93/7.52 -> [2365] ~(distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)) & distinct_lines(skolem_X3535, skolem_Y3636))
% 22.93/7.52 -> [2366] (((apart_point_and_line(skolem_Z3737, skolem_X3535) | apart_point_and_line(skolem_Z3737, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_Y3636))
% 22.93/7.52
% 22.93/7.52 [2365] BETA_NOT_AND : ~(distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636)) & distinct_lines(skolem_X3535, skolem_Y3636))
% 22.93/7.52 -> [2367] ~distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52 -> [2368] ~distinct_lines(skolem_X3535, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [2368] CLOSURE : ~distinct_lines(skolem_X3535, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [2367] CLOSURE : ~distinct_points(skolem_Z3737, intersection_point(skolem_X3535, skolem_Y3636))
% 22.93/7.52
% 22.93/7.52 [2366] BETA_OR : (((apart_point_and_line(skolem_Z3737, skolem_X3535) | apart_point_and_line(skolem_Z3737, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_Y3636))
% 22.93/7.52 -> [2381] ((apart_point_and_line(skolem_Z3737, skolem_X3535) | apart_point_and_line(skolem_Z3737, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535))
% 22.93/7.52 -> [2382] apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [2382] CLOSURE : apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [2381] BETA_OR : ((apart_point_and_line(skolem_Z3737, skolem_X3535) | apart_point_and_line(skolem_Z3737, skolem_Y3636)) | apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535))
% 22.93/7.52 -> [2383] (apart_point_and_line(skolem_Z3737, skolem_X3535) | apart_point_and_line(skolem_Z3737, skolem_Y3636))
% 22.93/7.52 -> [2384] apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535)
% 22.93/7.52
% 22.93/7.52 [2384] CLOSURE : apart_point_and_line(intersection_point(skolem_X3535, skolem_Y3636), skolem_X3535)
% 22.93/7.52
% 22.93/7.52 [2383] BETA_OR : (apart_point_and_line(skolem_Z3737, skolem_X3535) | apart_point_and_line(skolem_Z3737, skolem_Y3636))
% 22.93/7.52 -> [2385] apart_point_and_line(skolem_Z3737, skolem_X3535)
% 22.93/7.52 -> [2386] apart_point_and_line(skolem_Z3737, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 [2385] CLOSURE : apart_point_and_line(skolem_Z3737, skolem_X3535)
% 22.93/7.52
% 22.93/7.52 [2386] CLOSURE : apart_point_and_line(skolem_Z3737, skolem_Y3636)
% 22.93/7.52
% 22.93/7.52 % SZS output end Proof for theBenchmark.p
% 22.93/7.52 [7.189271s][1][Res] 60798 goroutines created
% 22.93/7.52 ==== Result ====
% 22.93/7.52 [7.189308s][1][Res] VALID
% 22.93/7.52 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------