TSTP Solution File: GEO183+2 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO183+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n006.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 15:18:16 EDT 2022
% Result : Theorem 121.82s 27.55s
% Output : Proof 121.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO183+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n006.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 06:47:09 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 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.35 Conjecture not found
% 0.13/0.35 Start search
% 0.13/0.35 nb_step : 1 - limit : 13
% 0.13/0.35 Launch Gotab with destructive = true
% 121.82/27.54 % SZS output start Proof for theBenchmark.p
% 121.82/27.55 [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)) & ~distinct_lines(U37_37, line_connecting(X35_35, Y36_36))) => (~apart_point_and_line(X35_35, U37_37) & ~apart_point_and_line(Y36_36, U37_37)))))
% 121.82/27.55 -> [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)) & ~distinct_lines(U37_37, line_connecting(X35_35, Y36_36))) => (~apart_point_and_line(X35_35, U37_37) & ~apart_point_and_line(Y36_36, U37_37))))
% 121.82/27.55
% 121.82/27.55 [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))))
% 121.82/27.55 -> [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)))
% 121.82/27.55
% 121.82/27.55 [2] DELTA_NOT_FORALL : ~! [X35_35, Y36_36, U37_37, V38_38] : ((((distinct_points(X35_35, Y36_36) & convergent_lines(U37_37, V38_38)) & ~distinct_lines(U37_37, line_connecting(X35_35, Y36_36))) => (~apart_point_and_line(X35_35, U37_37) & ~apart_point_and_line(Y36_36, U37_37))))
% 121.82/27.55 -> [3] ~(((distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)) & ~distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))) => (~apart_point_and_line(skolem_X3535, skolem_U3737) & ~apart_point_and_line(skolem_Y3636, skolem_U3737)))
% 121.82/27.55
% 121.82/27.55 [3] ALPHA_NOT_IMPLY : ~(((distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)) & ~distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))) => (~apart_point_and_line(skolem_X3535, skolem_U3737) & ~apart_point_and_line(skolem_Y3636, skolem_U3737)))
% 121.82/27.55 -> [4] ((distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)) & ~distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))), ~(~apart_point_and_line(skolem_X3535, skolem_U3737) & ~apart_point_and_line(skolem_Y3636, skolem_U3737))
% 121.82/27.55
% 121.82/27.55 [4] ALPHA_AND : ((distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)) & ~distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [5] (distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838)), ~distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [5] ALPHA_AND : (distinct_points(skolem_X3535, skolem_Y3636) & convergent_lines(skolem_U3737, skolem_V3838))
% 121.82/27.55 -> [6] distinct_points(skolem_X3535, skolem_Y3636), convergent_lines(skolem_U3737, skolem_V3838)
% 121.82/27.55
% 121.82/27.55 [6] BETA_NOT_AND : ~(~apart_point_and_line(skolem_X3535, skolem_U3737) & ~apart_point_and_line(skolem_Y3636, skolem_U3737))
% 121.82/27.55 -> [7] ~~apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55 -> [8] ~~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [8] ALPHA_NOT_NOT : ~~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 121.82/27.55 -> [10] apart_point_and_line(skolem_Y3636, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [10] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 121.82/27.55 -> [11] ~distinct_points(skolem_Y3636, skolem_Y3636)
% 121.82/27.55
% 121.82/27.55 [11] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 121.82/27.55 -> [13] ~distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [13] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 121.82/27.55 -> [14] ~convergent_lines(X7_0_2, X7_0_2)
% 121.82/27.55
% 121.82/27.55 [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))))
% 121.82/27.55 -> [16] (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636)))
% 121.82/27.55
% 121.82/27.55 [16] BETA_IMPLY : (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636)))
% 121.82/27.55 -> [17] ~distinct_points(skolem_X3535, skolem_Y3636)
% 121.82/27.55 -> [18] (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [17] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 121.82/27.55
% 121.82/27.55 [18] BETA_OR : (distinct_points(skolem_X3535, skolem_Y3636) | distinct_points(skolem_Y3636, skolem_Y3636))
% 121.82/27.55 -> [25] distinct_points(skolem_X3535, skolem_Y3636)
% 121.82/27.55 -> [26] distinct_points(skolem_Y3636, skolem_Y3636)
% 121.82/27.55
% 121.82/27.55 [26] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 121.82/27.55
% 121.82/27.55 [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))))
% 121.82/27.55 -> [29] (distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), skolem_U3737) => (distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)) | distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))))
% 121.82/27.55
% 121.82/27.55 [29] BETA_IMPLY : (distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), skolem_U3737) => (distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)) | distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))))
% 121.82/27.55 -> [30] ~distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), skolem_U3737)
% 121.82/27.55 -> [31] (distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)) | distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55
% 121.82/27.55 [31] BETA_OR : (distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)) | distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [32] distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55 -> [33] distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [32] CLOSURE : distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [33] CLOSURE : distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [34] 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)))
% 121.82/27.55 -> [3310] ~convergent_lines(Z16_0_5, Z16_0_5)
% 121.82/27.55 -> [3311] (convergent_lines(Z16_0_5, Z16_0_5) | convergent_lines(Z16_0_5, Z16_0_5))
% 121.82/27.55
% 121.82/27.55 [3311] BETA_OR : (convergent_lines(Z16_0_5, Z16_0_5) | convergent_lines(Z16_0_5, Z16_0_5))
% 121.82/27.55 -> [3312] convergent_lines(Z16_0_5, Z16_0_5)
% 121.82/27.55 -> [3313] convergent_lines(Z16_0_5, Z16_0_5)
% 121.82/27.55
% 121.82/27.55 [3313] CLOSURE : convergent_lines(Z16_0_5, Z16_0_5)
% 121.82/27.55
% 121.82/27.55 [3312] CLOSURE : convergent_lines(Z16_0_5, Z16_0_5)
% 121.82/27.55
% 121.82/27.55 [3310] 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)))))
% 121.82/27.55 -> [3322] (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))))
% 121.82/27.55
% 121.82/27.55 [3322] 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))))
% 121.82/27.55 -> [3323] ~distinct_points(skolem_X3535, skolem_Y3636)
% 121.82/27.55 -> [3324] (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636)))
% 121.82/27.55
% 121.82/27.55 [3323] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 121.82/27.55
% 121.82/27.55 [3324] 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)))
% 121.82/27.55 -> [6195] ~apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55 -> [6196] (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [6196] ALPHA_AND : (distinct_points(skolem_Y3636, skolem_X3535) & distinct_points(skolem_Y3636, skolem_Y3636))
% 121.82/27.55 -> [6197] distinct_points(skolem_Y3636, skolem_X3535), distinct_points(skolem_Y3636, skolem_Y3636)
% 121.82/27.55
% 121.82/27.55 [6197] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 121.82/27.55
% 121.82/27.55 [6195] 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)))))
% 121.82/27.55 -> [6198] (convergent_lines(skolem_U3737, skolem_V3838) => ((apart_point_and_line(skolem_Y3636, skolem_U3737) | apart_point_and_line(skolem_Y3636, skolem_V3838)) => distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))))
% 121.82/27.55
% 121.82/27.55 [6198] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => ((apart_point_and_line(skolem_Y3636, skolem_U3737) | apart_point_and_line(skolem_Y3636, skolem_V3838)) => distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))))
% 121.82/27.55 -> [6201] ~convergent_lines(skolem_U3737, skolem_V3838)
% 121.82/27.55 -> [6202] ((apart_point_and_line(skolem_Y3636, skolem_U3737) | apart_point_and_line(skolem_Y3636, skolem_V3838)) => distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 121.82/27.55
% 121.82/27.55 [6201] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 121.82/27.55
% 121.82/27.55 [6202] BETA_IMPLY : ((apart_point_and_line(skolem_Y3636, skolem_U3737) | apart_point_and_line(skolem_Y3636, skolem_V3838)) => distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838)))
% 121.82/27.55 -> [6647] ~(apart_point_and_line(skolem_Y3636, skolem_U3737) | apart_point_and_line(skolem_Y3636, skolem_V3838))
% 121.82/27.55 -> [6648] distinct_points(skolem_Y3636, intersection_point(skolem_U3737, skolem_V3838))
% 121.82/27.55
% 121.82/27.55 [6647] ALPHA_NOT_OR : ~(apart_point_and_line(skolem_Y3636, skolem_U3737) | apart_point_and_line(skolem_Y3636, skolem_V3838))
% 121.82/27.55 -> [6649] ~apart_point_and_line(skolem_Y3636, skolem_U3737), ~apart_point_and_line(skolem_Y3636, skolem_V3838)
% 121.82/27.55
% 121.82/27.55 [6649] CLOSURE : ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [6650] BETA_IMPLY : ((distinct_points(skolem_Y3636, skolem_Y3636) & distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))) => (((apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))))
% 121.82/27.55 -> [7944] ~(distinct_points(skolem_Y3636, skolem_Y3636) & distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [7945] (((apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55
% 121.82/27.55 [7945] BETA_OR : (((apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [7948] ((apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [7949] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [7949] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [7948] BETA_OR : ((apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [7994] (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [7995] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [7994] BETA_OR : (apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [7996] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55 -> [7997] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [7996] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [7997] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [7995] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [7944] BETA_NOT_AND : ~(distinct_points(skolem_Y3636, skolem_Y3636) & distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [8046] ~distinct_points(skolem_Y3636, skolem_Y3636)
% 121.82/27.55 -> [8047] ~distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8046] 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))))
% 121.82/27.55 -> [8053] (apart_point_and_line(skolem_Y3636, skolem_U3737) => (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, skolem_U3737)))
% 121.82/27.55
% 121.82/27.55 [8053] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, skolem_U3737) => (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, skolem_U3737)))
% 121.82/27.55 -> [8056] ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 121.82/27.55 -> [8057] (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, skolem_U3737))
% 121.82/27.55
% 121.82/27.55 [8056] CLOSURE : ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [8057] BETA_OR : (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, skolem_U3737))
% 121.82/27.55 -> [8074] distinct_points(skolem_Y3636, skolem_Y3636)
% 121.82/27.55 -> [8075] apart_point_and_line(skolem_Y3636, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [8075] 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))))
% 121.82/27.55 -> [8076] (apart_point_and_line(skolem_Y3636, skolem_U3737) => (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))))
% 121.82/27.55
% 121.82/27.55 [8076] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, skolem_U3737) => (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))))
% 121.82/27.55 -> [8077] ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 121.82/27.55 -> [8078] (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55
% 121.82/27.55 [8077] CLOSURE : ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [8078] BETA_OR : (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [8085] distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55 -> [8086] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8086] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8085] CLOSURE : distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8074] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 121.82/27.55
% 121.82/27.55 [8047] 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))))
% 121.82/27.55 -> [8052] (apart_point_and_line(skolem_Y3636, skolem_U3737) => (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, skolem_U3737)))
% 121.82/27.55
% 121.82/27.55 [8052] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, skolem_U3737) => (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, skolem_U3737)))
% 121.82/27.55 -> [8054] ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 121.82/27.55 -> [8055] (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, skolem_U3737))
% 121.82/27.55
% 121.82/27.55 [8054] CLOSURE : ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [8055] BETA_OR : (distinct_points(skolem_Y3636, skolem_Y3636) | apart_point_and_line(skolem_Y3636, skolem_U3737))
% 121.82/27.55 -> [8065] distinct_points(skolem_Y3636, skolem_Y3636)
% 121.82/27.55 -> [8066] apart_point_and_line(skolem_Y3636, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [8065] CLOSURE : distinct_points(skolem_Y3636, skolem_Y3636)
% 121.82/27.55
% 121.82/27.55 [8069] BETA_IMPLY : (apart_point_and_line(skolem_Y3636, skolem_U3737) => (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))))
% 121.82/27.55 -> [8087] ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 121.82/27.55 -> [8088] (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55
% 121.82/27.55 [8087] CLOSURE : ~apart_point_and_line(skolem_Y3636, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [8088] BETA_OR : (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [8095] distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55 -> [8096] apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8096] CLOSURE : apart_point_and_line(skolem_Y3636, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8095] CLOSURE : distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [7] ALPHA_NOT_NOT : ~~apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55 -> [9] apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [9] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 121.82/27.55 -> [12] ~distinct_points(skolem_X3535, skolem_X3535)
% 121.82/27.55
% 121.82/27.55 [12] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 121.82/27.55 -> [15] ~distinct_lines(X6_1_1, X6_1_1)
% 121.82/27.55
% 121.82/27.55 [15] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 121.82/27.55 -> [21] ~convergent_lines(skolem_V3838, skolem_V3838)
% 121.82/27.55
% 121.82/27.55 [21] 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))))
% 121.82/27.55 -> [22] (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_X3535) | distinct_points(skolem_Y3636, skolem_X3535)))
% 121.82/27.55
% 121.82/27.55 [22] BETA_IMPLY : (distinct_points(skolem_X3535, skolem_Y3636) => (distinct_points(skolem_X3535, skolem_X3535) | distinct_points(skolem_Y3636, skolem_X3535)))
% 121.82/27.55 -> [23] ~distinct_points(skolem_X3535, skolem_Y3636)
% 121.82/27.55 -> [24] (distinct_points(skolem_X3535, skolem_X3535) | distinct_points(skolem_Y3636, skolem_X3535))
% 121.82/27.55
% 121.82/27.55 [23] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 121.82/27.55
% 121.82/27.55 [24] BETA_OR : (distinct_points(skolem_X3535, skolem_X3535) | distinct_points(skolem_Y3636, skolem_X3535))
% 121.82/27.55 -> [37] distinct_points(skolem_X3535, skolem_X3535)
% 121.82/27.55 -> [38] distinct_points(skolem_Y3636, skolem_X3535)
% 121.82/27.55
% 121.82/27.55 [37] CLOSURE : distinct_points(skolem_X3535, skolem_X3535)
% 121.82/27.55
% 121.82/27.55 [38] 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))))
% 121.82/27.55 -> [41] (distinct_lines(skolem_U3737, skolem_U3737) => (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))))
% 121.82/27.55
% 121.82/27.55 [41] BETA_IMPLY : (distinct_lines(skolem_U3737, skolem_U3737) => (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))))
% 121.82/27.55 -> [42] ~distinct_lines(skolem_U3737, skolem_U3737)
% 121.82/27.55 -> [43] (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55
% 121.82/27.55 [43] BETA_OR : (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [44] distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55 -> [45] distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [45] CLOSURE : distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [44] CLOSURE : distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [48] BETA_IMPLY : (convergent_lines(skolem_U3737, skolem_V3838) => (convergent_lines(skolem_U3737, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838)))
% 121.82/27.55 -> [6135] ~convergent_lines(skolem_U3737, skolem_V3838)
% 121.82/27.55 -> [6136] (convergent_lines(skolem_U3737, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838))
% 121.82/27.55
% 121.82/27.55 [6135] CLOSURE : ~convergent_lines(skolem_U3737, skolem_V3838)
% 121.82/27.55
% 121.82/27.55 [6136] BETA_OR : (convergent_lines(skolem_U3737, skolem_V3838) | convergent_lines(skolem_V3838, skolem_V3838))
% 121.82/27.55 -> [6142] convergent_lines(skolem_U3737, skolem_V3838)
% 121.82/27.55 -> [6143] convergent_lines(skolem_V3838, skolem_V3838)
% 121.82/27.55
% 121.82/27.55 [6143] CLOSURE : convergent_lines(skolem_V3838, skolem_V3838)
% 121.82/27.55
% 121.82/27.55 [6142] 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)))))
% 121.82/27.55 -> [6144] (distinct_points(skolem_X3535, skolem_Y3636) => (apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_X3535, skolem_X3535) & distinct_points(skolem_X3535, skolem_Y3636))))
% 121.82/27.55
% 121.82/27.55 [6144] BETA_IMPLY : (distinct_points(skolem_X3535, skolem_Y3636) => (apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_X3535, skolem_X3535) & distinct_points(skolem_X3535, skolem_Y3636))))
% 121.82/27.55 -> [6145] ~distinct_points(skolem_X3535, skolem_Y3636)
% 121.82/27.55 -> [6146] (apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_X3535, skolem_X3535) & distinct_points(skolem_X3535, skolem_Y3636)))
% 121.82/27.55
% 121.82/27.55 [6146] BETA_IMPLY : (apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) => (distinct_points(skolem_X3535, skolem_X3535) & distinct_points(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [6148] ~apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55 -> [6149] (distinct_points(skolem_X3535, skolem_X3535) & distinct_points(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [6149] ALPHA_AND : (distinct_points(skolem_X3535, skolem_X3535) & distinct_points(skolem_X3535, skolem_Y3636))
% 121.82/27.55 -> [6151] distinct_points(skolem_X3535, skolem_X3535), distinct_points(skolem_X3535, skolem_Y3636)
% 121.82/27.55
% 121.82/27.55 [6151] CLOSURE : distinct_points(skolem_X3535, skolem_Y3636)
% 121.82/27.55
% 121.82/27.55 [6152] BETA_IMPLY : (convergent_lines(X20_6_7, skolem_U3737) => ((apart_point_and_line(skolem_X3535, X20_6_7) | apart_point_and_line(skolem_X3535, skolem_U3737)) => distinct_points(skolem_X3535, intersection_point(X20_6_7, skolem_U3737))))
% 121.82/27.55 -> [7719] ~convergent_lines(X20_6_7, skolem_U3737)
% 121.82/27.55 -> [7720] ((apart_point_and_line(skolem_X3535, X20_6_7) | apart_point_and_line(skolem_X3535, skolem_U3737)) => distinct_points(skolem_X3535, intersection_point(X20_6_7, skolem_U3737)))
% 121.82/27.55
% 121.82/27.55 [7720] BETA_IMPLY : ((apart_point_and_line(skolem_X3535, X20_6_7) | apart_point_and_line(skolem_X3535, skolem_U3737)) => distinct_points(skolem_X3535, intersection_point(X20_6_7, skolem_U3737)))
% 121.82/27.55 -> [7721] ~(apart_point_and_line(skolem_X3535, X20_6_7) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 121.82/27.55 -> [7722] distinct_points(skolem_X3535, intersection_point(X20_6_7, skolem_U3737))
% 121.82/27.55
% 121.82/27.55 [7721] ALPHA_NOT_OR : ~(apart_point_and_line(skolem_X3535, X20_6_7) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 121.82/27.55 -> [7723] ~apart_point_and_line(skolem_X3535, X20_6_7), ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [7723] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [7724] BETA_IMPLY : ((distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))) => (((apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))))
% 121.82/27.55 -> [8091] ~(distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [8092] (((apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55
% 121.82/27.55 [8092] BETA_OR : (((apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [8097] ((apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [8098] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8098] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8097] BETA_OR : ((apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [8115] (apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [8116] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8116] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8115] BETA_OR : (apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [8119] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55 -> [8120] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8119] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8120] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8091] BETA_NOT_AND : ~(distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [8149] ~distinct_points(skolem_X3535, skolem_X3535)
% 121.82/27.55 -> [8150] ~distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8150] 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))))
% 121.82/27.55 -> [8154] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 121.82/27.55
% 121.82/27.55 [8154] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 121.82/27.55 -> [8157] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55 -> [8158] (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 121.82/27.55
% 121.82/27.55 [8157] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [8158] BETA_OR : (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 121.82/27.55 -> [8168] distinct_points(skolem_X3535, skolem_X3535)
% 121.82/27.55 -> [8169] apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [8168] CLOSURE : distinct_points(skolem_X3535, skolem_X3535)
% 121.82/27.55
% 121.82/27.55 [8170] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))))
% 121.82/27.55 -> [8184] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55 -> [8185] (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55
% 121.82/27.55 [8184] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [8185] BETA_OR : (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [8216] distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55 -> [8217] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8216] CLOSURE : distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8217] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8149] 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))))
% 121.82/27.55 -> [8151] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 121.82/27.55
% 121.82/27.55 [8151] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 121.82/27.55 -> [8152] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55 -> [8153] (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 121.82/27.55
% 121.82/27.55 [8152] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [8153] BETA_OR : (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 121.82/27.55 -> [8161] distinct_points(skolem_X3535, skolem_X3535)
% 121.82/27.55 -> [8162] apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [8161] CLOSURE : distinct_points(skolem_X3535, skolem_X3535)
% 121.82/27.55
% 121.82/27.55 [8163] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))))
% 121.82/27.55 -> [8218] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55 -> [8219] (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55
% 121.82/27.55 [8218] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [8219] BETA_OR : (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [8222] distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55 -> [8223] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8223] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8222] CLOSURE : distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [7719] 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))))
% 121.82/27.55 -> [8224] ((distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))) => (((apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))))
% 121.82/27.55
% 121.82/27.55 [8224] BETA_IMPLY : ((distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))) => (((apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))))
% 121.82/27.55 -> [8225] ~(distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [8226] (((apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55
% 121.82/27.55 [8226] BETA_OR : (((apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [8229] ((apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [8230] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8229] BETA_OR : ((apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [8231] (apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [8232] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8232] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8231] BETA_OR : (apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [8242] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55 -> [8243] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8243] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8242] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8230] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8225] BETA_NOT_AND : ~(distinct_points(skolem_X3535, skolem_X3535) & distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [8251] ~distinct_points(skolem_X3535, skolem_X3535)
% 121.82/27.55 -> [8252] ~distinct_lines(line_connecting(skolem_X3535, skolem_Y3636), line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8252] 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))))
% 121.82/27.55 -> [8256] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 121.82/27.55
% 121.82/27.55 [8256] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 121.82/27.55 -> [8257] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55 -> [8258] (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 121.82/27.55
% 121.82/27.55 [8257] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [8258] BETA_OR : (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 121.82/27.55 -> [8263] distinct_points(skolem_X3535, skolem_X3535)
% 121.82/27.55 -> [8264] apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [8263] CLOSURE : distinct_points(skolem_X3535, skolem_X3535)
% 121.82/27.55
% 121.82/27.55 [8264] 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))))
% 121.82/27.55 -> [8265] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))))
% 121.82/27.55
% 121.82/27.55 [8265] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))))
% 121.82/27.55 -> [8268] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55 -> [8269] (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55
% 121.82/27.55 [8268] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [8269] BETA_OR : (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [8280] distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55 -> [8281] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8281] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8280] CLOSURE : distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8251] 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))))
% 121.82/27.55 -> [8253] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 121.82/27.55
% 121.82/27.55 [8253] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737)))
% 121.82/27.55 -> [8254] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55 -> [8255] (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 121.82/27.55
% 121.82/27.55 [8254] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [8255] BETA_OR : (distinct_points(skolem_X3535, skolem_X3535) | apart_point_and_line(skolem_X3535, skolem_U3737))
% 121.82/27.55 -> [8266] distinct_points(skolem_X3535, skolem_X3535)
% 121.82/27.55 -> [8267] apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [8266] CLOSURE : distinct_points(skolem_X3535, skolem_X3535)
% 121.82/27.55
% 121.82/27.55 [8267] 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))))
% 121.82/27.55 -> [8272] (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))))
% 121.82/27.55
% 121.82/27.55 [8272] BETA_IMPLY : (apart_point_and_line(skolem_X3535, skolem_U3737) => (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))))
% 121.82/27.55 -> [8273] ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55 -> [8274] (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55
% 121.82/27.55 [8273] CLOSURE : ~apart_point_and_line(skolem_X3535, skolem_U3737)
% 121.82/27.55
% 121.82/27.55 [8274] BETA_OR : (distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636)) | apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636)))
% 121.82/27.55 -> [8290] distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55 -> [8291] apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8290] CLOSURE : distinct_lines(skolem_U3737, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [8291] CLOSURE : apart_point_and_line(skolem_X3535, line_connecting(skolem_X3535, skolem_Y3636))
% 121.82/27.55
% 121.82/27.55 [6145] CLOSURE : ~distinct_points(skolem_X3535, skolem_Y3636)
% 121.82/27.55
% 121.82/27.55 % SZS output end Proof for theBenchmark.p
% 121.82/27.55 [27.198163s][1][Res] 341742 goroutines created
% 121.82/27.55 ==== Result ====
% 121.82/27.55 [27.198210s][1][Res] VALID
% 121.82/27.55 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------