TSTP Solution File: GEO208+2 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO208+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n004.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 15:18:25 EDT 2022
% Result : Theorem 45.32s 9.55s
% Output : Proof 45.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GEO208+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.11 % Command : goeland -dmt -presko -proof %s
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Aug 31 06:52:19 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 [DMT] DMT loaded with preskolemization
% 0.11/0.33 [EQ] equality loaded.
% 0.11/0.33 [0.000039s][1][MAIN] Problem : theBenchmark.p
% 0.11/0.33 Conjecture not found
% 0.11/0.33 Conjecture not found
% 0.11/0.33 Start search
% 0.11/0.33 nb_step : 1 - limit : 16
% 0.11/0.33 Launch Gotab with destructive = true
% 45.32/9.53 % SZS output start Proof for theBenchmark.p
% 45.32/9.54 [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] : (~convergent_lines(parallel_through_point(Y36_36, X35_35), Y36_36)) & ! [X37_37, Y38_38] : (~apart_point_and_line(X37_37, parallel_through_point(Y38_38, X37_37))) & ! [X39_39, Y40_40, Z41_41] : ((distinct_lines(Y40_40, Z41_41) => ((apart_point_and_line(X39_39, Y40_40) | apart_point_and_line(X39_39, Z41_41)) | convergent_lines(Y40_40, Z41_41))))) & ~! [X42_42, Y43_43, Z44_44] : ((((~apart_point_and_line(X42_42, Y43_43) & ~apart_point_and_line(X42_42, Z44_44)) & ~convergent_lines(Y43_43, Z44_44)) => ~distinct_lines(Y43_43, Z44_44))))
% 45.32/9.54 -> [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] : (~convergent_lines(parallel_through_point(Y36_36, X35_35), Y36_36)) & ! [X37_37, Y38_38] : (~apart_point_and_line(X37_37, parallel_through_point(Y38_38, X37_37))) & ! [X39_39, Y40_40, Z41_41] : ((distinct_lines(Y40_40, Z41_41) => ((apart_point_and_line(X39_39, Y40_40) | apart_point_and_line(X39_39, Z41_41)) | convergent_lines(Y40_40, Z41_41))))), ~! [X42_42, Y43_43, Z44_44] : ((((~apart_point_and_line(X42_42, Y43_43) & ~apart_point_and_line(X42_42, Z44_44)) & ~convergent_lines(Y43_43, Z44_44)) => ~distinct_lines(Y43_43, Z44_44)))
% 45.32/9.54
% 45.32/9.54 [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))))
% 45.32/9.54 -> [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)))
% 45.32/9.54
% 45.32/9.54 [2] ALPHA_AND : (! [X35_35, Y36_36] : (~convergent_lines(parallel_through_point(Y36_36, X35_35), Y36_36)) & ! [X37_37, Y38_38] : (~apart_point_and_line(X37_37, parallel_through_point(Y38_38, X37_37))) & ! [X39_39, Y40_40, Z41_41] : ((distinct_lines(Y40_40, Z41_41) => ((apart_point_and_line(X39_39, Y40_40) | apart_point_and_line(X39_39, Z41_41)) | convergent_lines(Y40_40, Z41_41)))))
% 45.32/9.54 -> [3] ! [X35_35, Y36_36] : (~convergent_lines(parallel_through_point(Y36_36, X35_35), Y36_36)), ! [X37_37, Y38_38] : (~apart_point_and_line(X37_37, parallel_through_point(Y38_38, X37_37))), ! [X39_39, Y40_40, Z41_41] : ((distinct_lines(Y40_40, Z41_41) => ((apart_point_and_line(X39_39, Y40_40) | apart_point_and_line(X39_39, Z41_41)) | convergent_lines(Y40_40, Z41_41))))
% 45.32/9.54
% 45.32/9.54 [3] DELTA_NOT_FORALL : ~! [X42_42, Y43_43, Z44_44] : ((((~apart_point_and_line(X42_42, Y43_43) & ~apart_point_and_line(X42_42, Z44_44)) & ~convergent_lines(Y43_43, Z44_44)) => ~distinct_lines(Y43_43, Z44_44)))
% 45.32/9.54 -> [4] ~(((~apart_point_and_line(skolem_X4242, skolem_Y4343) & ~apart_point_and_line(skolem_X4242, skolem_Z4444)) & ~convergent_lines(skolem_Y4343, skolem_Z4444)) => ~distinct_lines(skolem_Y4343, skolem_Z4444))
% 45.32/9.54
% 45.32/9.54 [4] ALPHA_NOT_IMPLY : ~(((~apart_point_and_line(skolem_X4242, skolem_Y4343) & ~apart_point_and_line(skolem_X4242, skolem_Z4444)) & ~convergent_lines(skolem_Y4343, skolem_Z4444)) => ~distinct_lines(skolem_Y4343, skolem_Z4444))
% 45.32/9.54 -> [5] ((~apart_point_and_line(skolem_X4242, skolem_Y4343) & ~apart_point_and_line(skolem_X4242, skolem_Z4444)) & ~convergent_lines(skolem_Y4343, skolem_Z4444)), ~~distinct_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.54
% 45.32/9.54 [5] ALPHA_AND : ((~apart_point_and_line(skolem_X4242, skolem_Y4343) & ~apart_point_and_line(skolem_X4242, skolem_Z4444)) & ~convergent_lines(skolem_Y4343, skolem_Z4444))
% 45.32/9.54 -> [6] (~apart_point_and_line(skolem_X4242, skolem_Y4343) & ~apart_point_and_line(skolem_X4242, skolem_Z4444)), ~convergent_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.54
% 45.32/9.54 [6] ALPHA_NOT_NOT : ~~distinct_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.54 -> [7] distinct_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.54
% 45.32/9.54 [7] ALPHA_AND : (~apart_point_and_line(skolem_X4242, skolem_Y4343) & ~apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.54 -> [8] ~apart_point_and_line(skolem_X4242, skolem_Y4343), ~apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.54
% 45.32/9.54 [8] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 45.32/9.54 -> [9] ~distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444))
% 45.32/9.54
% 45.32/9.54 [9] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 45.32/9.54 -> [10] ~distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.54
% 45.32/9.54 [10] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 45.32/9.54 -> [11] ~convergent_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.54
% 45.32/9.54 [11] 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))))
% 45.32/9.54 -> [12] (distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)) => (distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)) | distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444))))
% 45.32/9.54
% 45.32/9.54 [12] BETA_IMPLY : (distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)) => (distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)) | distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444))))
% 45.32/9.54 -> [13] ~distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444))
% 45.32/9.54 -> [14] (distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)) | distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)))
% 45.32/9.54
% 45.32/9.54 [14] BETA_OR : (distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)) | distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)))
% 45.32/9.54 -> [18] distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444))
% 45.32/9.54 -> [19] distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444))
% 45.32/9.54
% 45.32/9.54 [19] CLOSURE : distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444))
% 45.32/9.54
% 45.32/9.54 [18] CLOSURE : distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444))
% 45.32/9.54
% 45.32/9.54 [15] BETA_IMPLY : (distinct_lines(skolem_Z4444, skolem_Z4444) => (distinct_lines(skolem_Z4444, skolem_Z4444) | distinct_lines(skolem_Z4444, skolem_Z4444)))
% 45.32/9.54 -> [3636] ~distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.54 -> [3637] (distinct_lines(skolem_Z4444, skolem_Z4444) | distinct_lines(skolem_Z4444, skolem_Z4444))
% 45.32/9.54
% 45.32/9.54 [3637] BETA_OR : (distinct_lines(skolem_Z4444, skolem_Z4444) | distinct_lines(skolem_Z4444, skolem_Z4444))
% 45.32/9.54 -> [3638] distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.54 -> [3639] distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.54
% 45.32/9.54 [3638] CLOSURE : distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.54
% 45.32/9.54 [3639] CLOSURE : distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.54
% 45.32/9.54 [3636] 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))))
% 45.32/9.54 -> [3640] (convergent_lines(skolem_Y4343, skolem_Z4444) => (convergent_lines(skolem_Y4343, skolem_Z4444) | convergent_lines(skolem_Z4444, skolem_Z4444)))
% 45.32/9.54
% 45.32/9.54 [3640] BETA_IMPLY : (convergent_lines(skolem_Y4343, skolem_Z4444) => (convergent_lines(skolem_Y4343, skolem_Z4444) | convergent_lines(skolem_Z4444, skolem_Z4444)))
% 45.32/9.54 -> [3641] ~convergent_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.54 -> [3642] (convergent_lines(skolem_Y4343, skolem_Z4444) | convergent_lines(skolem_Z4444, skolem_Z4444))
% 45.32/9.54
% 45.32/9.54 [3642] BETA_OR : (convergent_lines(skolem_Y4343, skolem_Z4444) | convergent_lines(skolem_Z4444, skolem_Z4444))
% 45.32/9.54 -> [3643] convergent_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.54 -> [3644] convergent_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.54
% 45.32/9.54 [3644] CLOSURE : convergent_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.54
% 45.32/9.54 [3643] CLOSURE : convergent_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.54
% 45.32/9.54 [3645] BETA_IMPLY : (distinct_points(intersection_point(X20_9_7, skolem_Z4444), skolem_X4242) => (apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), line_connecting(intersection_point(X20_9_7, skolem_Z4444), skolem_X4242)) => (distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)) & distinct_points(intersection_point(X20_9_7, skolem_Z4444), skolem_X4242))))
% 45.32/9.54 -> [5172] ~distinct_points(intersection_point(X20_9_7, skolem_Z4444), skolem_X4242)
% 45.32/9.54 -> [5173] (apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), line_connecting(intersection_point(X20_9_7, skolem_Z4444), skolem_X4242)) => (distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)) & distinct_points(intersection_point(X20_9_7, skolem_Z4444), skolem_X4242)))
% 45.32/9.54
% 45.32/9.54 [5172] 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)))))
% 45.32/9.54 -> [5176] (convergent_lines(X20_9_7, skolem_Z4444) => ((apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), X20_9_7) | apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), skolem_Z4444)) => distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444))))
% 45.32/9.54
% 45.32/9.54 [5176] BETA_IMPLY : (convergent_lines(X20_9_7, skolem_Z4444) => ((apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), X20_9_7) | apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), skolem_Z4444)) => distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444))))
% 45.32/9.54 -> [5178] ~convergent_lines(X20_9_7, skolem_Z4444)
% 45.32/9.54 -> [5179] ((apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), X20_9_7) | apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), skolem_Z4444)) => distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)))
% 45.32/9.54
% 45.32/9.54 [5179] BETA_IMPLY : ((apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), X20_9_7) | apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), skolem_Z4444)) => distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)))
% 45.32/9.54 -> [5181] ~(apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), X20_9_7) | apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), skolem_Z4444))
% 45.32/9.54 -> [5182] distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444))
% 45.32/9.54
% 45.32/9.54 [5182] CLOSURE : distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444))
% 45.32/9.54
% 45.32/9.54 [5192] BETA_IMPLY : ((distinct_points(skolem_X4242, skolem_X4242) & distinct_lines(skolem_Y4343, skolem_Z4444)) => (((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Y4343)) | apart_point_and_line(skolem_X4242, skolem_Z4444)))
% 45.32/9.54 -> [5893] ~(distinct_points(skolem_X4242, skolem_X4242) & distinct_lines(skolem_Y4343, skolem_Z4444))
% 45.32/9.54 -> [5894] (((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Y4343)) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.54
% 45.32/9.54 [5893] BETA_NOT_AND : ~(distinct_points(skolem_X4242, skolem_X4242) & distinct_lines(skolem_Y4343, skolem_Z4444))
% 45.32/9.54 -> [5900] ~distinct_points(skolem_X4242, skolem_X4242)
% 45.32/9.54 -> [5901] ~distinct_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [5901] CLOSURE : ~distinct_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [5907] BETA_IMPLY : (apart_point_and_line(intersection_point(X20_9_7, Z32_131_10), Z32_131_10) => (distinct_points(intersection_point(X20_9_7, Z32_131_10), intersection_point(X20_9_7, Z32_131_10)) | apart_point_and_line(intersection_point(X20_9_7, Z32_131_10), Z32_131_10)))
% 45.32/9.55 -> [6071] ~apart_point_and_line(intersection_point(X20_9_7, Z32_131_10), Z32_131_10)
% 45.32/9.55 -> [6072] (distinct_points(intersection_point(X20_9_7, Z32_131_10), intersection_point(X20_9_7, Z32_131_10)) | apart_point_and_line(intersection_point(X20_9_7, Z32_131_10), Z32_131_10))
% 45.32/9.55
% 45.32/9.55 [6072] BETA_OR : (distinct_points(intersection_point(X20_9_7, Z32_131_10), intersection_point(X20_9_7, Z32_131_10)) | apart_point_and_line(intersection_point(X20_9_7, Z32_131_10), Z32_131_10))
% 45.32/9.55 -> [6073] distinct_points(intersection_point(X20_9_7, Z32_131_10), intersection_point(X20_9_7, Z32_131_10))
% 45.32/9.55 -> [6074] apart_point_and_line(intersection_point(X20_9_7, Z32_131_10), Z32_131_10)
% 45.32/9.55
% 45.32/9.55 [6074] CLOSURE : apart_point_and_line(intersection_point(X20_9_7, Z32_131_10), Z32_131_10)
% 45.32/9.55
% 45.32/9.55 [6073] CLOSURE : distinct_points(intersection_point(X20_9_7, Z32_131_10), intersection_point(X20_9_7, Z32_131_10))
% 45.32/9.55
% 45.32/9.55 [6077] BETA_IMPLY : (apart_point_and_line(intersection_point(X20_9_7, Z32_131_10), Z32_131_10) => (distinct_lines(Z32_131_10, Z32_131_10) | apart_point_and_line(intersection_point(X20_9_7, Z32_131_10), Z32_131_10)))
% 45.32/9.55 -> [6128] ~apart_point_and_line(intersection_point(X20_9_7, Z32_131_10), Z32_131_10)
% 45.32/9.55 -> [6129] (distinct_lines(Z32_131_10, Z32_131_10) | apart_point_and_line(intersection_point(X20_9_7, Z32_131_10), Z32_131_10))
% 45.32/9.55
% 45.32/9.55 [6129] BETA_OR : (distinct_lines(Z32_131_10, Z32_131_10) | apart_point_and_line(intersection_point(X20_9_7, Z32_131_10), Z32_131_10))
% 45.32/9.55 -> [6130] distinct_lines(Z32_131_10, Z32_131_10)
% 45.32/9.55 -> [6131] apart_point_and_line(intersection_point(X20_9_7, Z32_131_10), Z32_131_10)
% 45.32/9.55
% 45.32/9.55 [6131] CLOSURE : apart_point_and_line(intersection_point(X20_9_7, Z32_131_10), Z32_131_10)
% 45.32/9.55
% 45.32/9.55 [6130] CLOSURE : distinct_lines(Z32_131_10, Z32_131_10)
% 45.32/9.55
% 45.32/9.55 [6128] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 45.32/9.55 -> [6132] (convergent_lines(Y34_217_11, Y34_217_11) => distinct_lines(Y34_217_11, Y34_217_11))
% 45.32/9.55
% 45.32/9.55 [6132] BETA_IMPLY : (convergent_lines(Y34_217_11, Y34_217_11) => distinct_lines(Y34_217_11, Y34_217_11))
% 45.32/9.55 -> [6133] ~convergent_lines(Y34_217_11, Y34_217_11)
% 45.32/9.55 -> [6134] distinct_lines(Y34_217_11, Y34_217_11)
% 45.32/9.55
% 45.32/9.55 [6134] CLOSURE : distinct_lines(Y34_217_11, Y34_217_11)
% 45.32/9.55
% 45.32/9.55 [6133] GAMMA_FORALL : ! [X35_35, Y36_36] : (~convergent_lines(parallel_through_point(Y36_36, X35_35), Y36_36))
% 45.32/9.55 -> [6135] ~convergent_lines(parallel_through_point(Y36_218_12, X35_218_12), Y36_218_12)
% 45.32/9.55
% 45.32/9.55 [6135] GAMMA_FORALL : ! [X37_37, Y38_38] : (~apart_point_and_line(X37_37, parallel_through_point(Y38_38, X37_37)))
% 45.32/9.55 -> [6136] ~apart_point_and_line(X37_218_13, parallel_through_point(Y38_218_13, X37_218_13))
% 45.32/9.55
% 45.32/9.55 [6136] GAMMA_FORALL : ! [X39_39, Y40_40, Z41_41] : ((distinct_lines(Y40_40, Z41_41) => ((apart_point_and_line(X39_39, Y40_40) | apart_point_and_line(X39_39, Z41_41)) | convergent_lines(Y40_40, Z41_41))))
% 45.32/9.55 -> [6137] (distinct_lines(skolem_Y4343, skolem_Z4444) => ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444)))
% 45.32/9.55
% 45.32/9.55 [6137] BETA_IMPLY : (distinct_lines(skolem_Y4343, skolem_Z4444) => ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444)))
% 45.32/9.55 -> [6138] ~distinct_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55 -> [6139] ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [6138] CLOSURE : ~distinct_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6139] BETA_OR : ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444))
% 45.32/9.55 -> [6146] (apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [6147] convergent_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6147] CLOSURE : convergent_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6146] BETA_OR : (apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [6148] apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55 -> [6149] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6149] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6148] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55
% 45.32/9.55 [5894] BETA_OR : (((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Y4343)) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [6150] ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Y4343))
% 45.32/9.55 -> [6151] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6150] BETA_OR : ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Y4343))
% 45.32/9.55 -> [6152] (apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [6153] apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55
% 45.32/9.55 [6152] BETA_OR : (apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [6154] apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55 -> [6155] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6154] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55
% 45.32/9.55 [6155] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6153] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55
% 45.32/9.55 [6151] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [5185] BETA_IMPLY : ((distinct_points(skolem_X4242, skolem_X4242) & distinct_lines(skolem_Z4444, skolem_Z4444)) => (((apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Z4444)))
% 45.32/9.55 -> [6156] ~(distinct_points(skolem_X4242, skolem_X4242) & distinct_lines(skolem_Z4444, skolem_Z4444))
% 45.32/9.55 -> [6157] (((apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [6157] BETA_OR : (((apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [6160] ((apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [6161] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6161] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6160] BETA_OR : ((apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [6190] (apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [6191] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6191] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6190] BETA_OR : (apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [6194] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55 -> [6195] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6194] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6195] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6156] BETA_NOT_AND : ~(distinct_points(skolem_X4242, skolem_X4242) & distinct_lines(skolem_Z4444, skolem_Z4444))
% 45.32/9.55 -> [6267] ~distinct_points(skolem_X4242, skolem_X4242)
% 45.32/9.55 -> [6268] ~distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6268] 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))))
% 45.32/9.55 -> [6270] (apart_point_and_line(X27_101_9, skolem_Z4444) => (distinct_points(X27_101_9, skolem_X4242) | apart_point_and_line(skolem_X4242, skolem_Z4444)))
% 45.32/9.55
% 45.32/9.55 [6270] BETA_IMPLY : (apart_point_and_line(X27_101_9, skolem_Z4444) => (distinct_points(X27_101_9, skolem_X4242) | apart_point_and_line(skolem_X4242, skolem_Z4444)))
% 45.32/9.55 -> [6273] ~apart_point_and_line(X27_101_9, skolem_Z4444)
% 45.32/9.55 -> [6274] (distinct_points(X27_101_9, skolem_X4242) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [6273] 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))))
% 45.32/9.55 -> [6279] (apart_point_and_line(skolem_X4242, skolem_Z4444) => (distinct_lines(skolem_Z4444, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444)))
% 45.32/9.55
% 45.32/9.55 [6279] BETA_IMPLY : (apart_point_and_line(skolem_X4242, skolem_Z4444) => (distinct_lines(skolem_Z4444, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444)))
% 45.32/9.55 -> [6281] ~apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55 -> [6282] (distinct_lines(skolem_Z4444, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [6282] BETA_OR : (distinct_lines(skolem_Z4444, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [6288] distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55 -> [6289] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6289] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6288] CLOSURE : distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6281] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 45.32/9.55 -> [6285] (convergent_lines(skolem_Z4444, skolem_Z4444) => distinct_lines(skolem_Z4444, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [6285] BETA_IMPLY : (convergent_lines(skolem_Z4444, skolem_Z4444) => distinct_lines(skolem_Z4444, skolem_Z4444))
% 45.32/9.55 -> [6290] ~convergent_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55 -> [6291] distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6291] CLOSURE : distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6290] GAMMA_FORALL : ! [X35_35, Y36_36] : (~convergent_lines(parallel_through_point(Y36_36, X35_35), Y36_36))
% 45.32/9.55 -> [6296] ~convergent_lines(parallel_through_point(Y36_224_12, X35_224_12), Y36_224_12)
% 45.32/9.55
% 45.32/9.55 [6296] GAMMA_FORALL : ! [X37_37, Y38_38] : (~apart_point_and_line(X37_37, parallel_through_point(Y38_38, X37_37)))
% 45.32/9.55 -> [6300] ~apart_point_and_line(X37_223_13, parallel_through_point(Y38_223_13, X37_223_13))
% 45.32/9.55
% 45.32/9.55 [6300] GAMMA_FORALL : ! [X39_39, Y40_40, Z41_41] : ((distinct_lines(Y40_40, Z41_41) => ((apart_point_and_line(X39_39, Y40_40) | apart_point_and_line(X39_39, Z41_41)) | convergent_lines(Y40_40, Z41_41))))
% 45.32/9.55 -> [6304] (distinct_lines(skolem_Y4343, skolem_Z4444) => ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444)))
% 45.32/9.55
% 45.32/9.55 [6304] BETA_IMPLY : (distinct_lines(skolem_Y4343, skolem_Z4444) => ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444)))
% 45.32/9.55 -> [6308] ~distinct_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55 -> [6309] ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [6308] CLOSURE : ~distinct_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6309] BETA_OR : ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444))
% 45.32/9.55 -> [6325] (apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [6326] convergent_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6326] CLOSURE : convergent_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6325] BETA_OR : (apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [6327] apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55 -> [6328] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6328] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6327] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55
% 45.32/9.55 [6274] BETA_OR : (distinct_points(X27_101_9, skolem_X4242) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [6333] distinct_points(X27_101_9, skolem_X4242)
% 45.32/9.55 -> [6334] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6334] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6333] CLOSURE : distinct_points(X27_101_9, skolem_X4242)
% 45.32/9.55
% 45.32/9.55 [6269] BETA_IMPLY : (apart_point_and_line(X27_100_9, skolem_Z4444) => (distinct_points(X27_100_9, skolem_X4242) | apart_point_and_line(skolem_X4242, skolem_Z4444)))
% 45.32/9.55 -> [6373] ~apart_point_and_line(X27_100_9, skolem_Z4444)
% 45.32/9.55 -> [6374] (distinct_points(X27_100_9, skolem_X4242) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [6373] 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))))
% 45.32/9.55 -> [6377] (apart_point_and_line(X30_137_10, skolem_Z4444) => (distinct_lines(skolem_Z4444, skolem_Z4444) | apart_point_and_line(X30_137_10, skolem_Z4444)))
% 45.32/9.55
% 45.32/9.55 [6377] BETA_IMPLY : (apart_point_and_line(X30_137_10, skolem_Z4444) => (distinct_lines(skolem_Z4444, skolem_Z4444) | apart_point_and_line(X30_137_10, skolem_Z4444)))
% 45.32/9.55 -> [6378] ~apart_point_and_line(X30_137_10, skolem_Z4444)
% 45.32/9.55 -> [6379] (distinct_lines(skolem_Z4444, skolem_Z4444) | apart_point_and_line(X30_137_10, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [6379] BETA_OR : (distinct_lines(skolem_Z4444, skolem_Z4444) | apart_point_and_line(X30_137_10, skolem_Z4444))
% 45.32/9.55 -> [6380] distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55 -> [6381] apart_point_and_line(X30_137_10, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6380] CLOSURE : distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6381] CLOSURE : apart_point_and_line(X30_137_10, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6378] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 45.32/9.55 -> [6382] (convergent_lines(skolem_Z4444, skolem_Z4444) => distinct_lines(skolem_Z4444, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [6382] BETA_IMPLY : (convergent_lines(skolem_Z4444, skolem_Z4444) => distinct_lines(skolem_Z4444, skolem_Z4444))
% 45.32/9.55 -> [6383] ~convergent_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55 -> [6384] distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6384] CLOSURE : distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6383] GAMMA_FORALL : ! [X35_35, Y36_36] : (~convergent_lines(parallel_through_point(Y36_36, X35_35), Y36_36))
% 45.32/9.55 -> [6385] ~convergent_lines(parallel_through_point(Y36_228_12, X35_228_12), Y36_228_12)
% 45.32/9.55
% 45.32/9.55 [6385] GAMMA_FORALL : ! [X37_37, Y38_38] : (~apart_point_and_line(X37_37, parallel_through_point(Y38_38, X37_37)))
% 45.32/9.55 -> [6387] ~apart_point_and_line(X37_228_13, parallel_through_point(Y38_228_13, X37_228_13))
% 45.32/9.55
% 45.32/9.55 [6387] GAMMA_FORALL : ! [X39_39, Y40_40, Z41_41] : ((distinct_lines(Y40_40, Z41_41) => ((apart_point_and_line(X39_39, Y40_40) | apart_point_and_line(X39_39, Z41_41)) | convergent_lines(Y40_40, Z41_41))))
% 45.32/9.55 -> [6390] (distinct_lines(skolem_Y4343, skolem_Z4444) => ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444)))
% 45.32/9.55
% 45.32/9.55 [6390] BETA_IMPLY : (distinct_lines(skolem_Y4343, skolem_Z4444) => ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444)))
% 45.32/9.55 -> [6393] ~distinct_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55 -> [6394] ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [6393] CLOSURE : ~distinct_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6394] BETA_OR : ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444))
% 45.32/9.55 -> [6412] (apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [6413] convergent_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6413] CLOSURE : convergent_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6412] BETA_OR : (apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [6414] apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55 -> [6415] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6414] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55
% 45.32/9.55 [6415] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6374] BETA_OR : (distinct_points(X27_100_9, skolem_X4242) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [6417] distinct_points(X27_100_9, skolem_X4242)
% 45.32/9.55 -> [6418] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6417] CLOSURE : distinct_points(X27_100_9, skolem_X4242)
% 45.32/9.55
% 45.32/9.55 [6418] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [5173] BETA_IMPLY : (apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), line_connecting(intersection_point(X20_9_7, skolem_Z4444), skolem_X4242)) => (distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)) & distinct_points(intersection_point(X20_9_7, skolem_Z4444), skolem_X4242)))
% 45.32/9.55 -> [6419] ~apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), line_connecting(intersection_point(X20_9_7, skolem_Z4444), skolem_X4242))
% 45.32/9.55 -> [6420] (distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)) & distinct_points(intersection_point(X20_9_7, skolem_Z4444), skolem_X4242))
% 45.32/9.55
% 45.32/9.55 [6420] ALPHA_AND : (distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)) & distinct_points(intersection_point(X20_9_7, skolem_Z4444), skolem_X4242))
% 45.32/9.55 -> [6421] distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)), distinct_points(intersection_point(X20_9_7, skolem_Z4444), skolem_X4242)
% 45.32/9.55
% 45.32/9.55 [6421] CLOSURE : distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [6422] BETA_IMPLY : (convergent_lines(X20_9_7, skolem_Z4444) => ((apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), X20_9_7) | apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), skolem_Z4444)) => distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444))))
% 45.32/9.55 -> [6967] ~convergent_lines(X20_9_7, skolem_Z4444)
% 45.32/9.55 -> [6968] ((apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), X20_9_7) | apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), skolem_Z4444)) => distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)))
% 45.32/9.55
% 45.32/9.55 [6967] 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))))
% 45.32/9.55 -> [6972] ((distinct_points(skolem_X4242, skolem_X4242) & distinct_lines(skolem_Z4444, skolem_Y4343)) => (((apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Y4343)) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Y4343)))
% 45.32/9.55
% 45.32/9.55 [6972] BETA_IMPLY : ((distinct_points(skolem_X4242, skolem_X4242) & distinct_lines(skolem_Z4444, skolem_Y4343)) => (((apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Y4343)) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Y4343)))
% 45.32/9.55 -> [6973] ~(distinct_points(skolem_X4242, skolem_X4242) & distinct_lines(skolem_Z4444, skolem_Y4343))
% 45.32/9.55 -> [6974] (((apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Y4343)) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Y4343))
% 45.32/9.55
% 45.32/9.55 [6974] BETA_OR : (((apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Y4343)) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Y4343))
% 45.32/9.55 -> [6980] ((apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Y4343)) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [6981] apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55
% 45.32/9.55 [6981] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55
% 45.32/9.55 [6980] BETA_OR : ((apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Y4343)) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [7062] (apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Y4343))
% 45.32/9.55 -> [7063] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7062] BETA_OR : (apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Y4343))
% 45.32/9.55 -> [7068] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55 -> [7069] apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55
% 45.32/9.55 [7068] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7069] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55
% 45.32/9.55 [7063] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6973] BETA_NOT_AND : ~(distinct_points(skolem_X4242, skolem_X4242) & distinct_lines(skolem_Z4444, skolem_Y4343))
% 45.32/9.55 -> [7090] ~distinct_points(skolem_X4242, skolem_X4242)
% 45.32/9.55 -> [7091] ~distinct_lines(skolem_Z4444, skolem_Y4343)
% 45.32/9.55
% 45.32/9.55 [7091] 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))))
% 45.32/9.55 -> [7093] (apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), line_connecting(intersection_point(X20_9_7, skolem_Z4444), skolem_X4242)) => (distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)) | apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), line_connecting(intersection_point(X20_9_7, skolem_Z4444), skolem_X4242))))
% 45.32/9.55
% 45.32/9.55 [7093] BETA_IMPLY : (apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), line_connecting(intersection_point(X20_9_7, skolem_Z4444), skolem_X4242)) => (distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)) | apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), line_connecting(intersection_point(X20_9_7, skolem_Z4444), skolem_X4242))))
% 45.32/9.55 -> [7096] ~apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), line_connecting(intersection_point(X20_9_7, skolem_Z4444), skolem_X4242))
% 45.32/9.55 -> [7097] (distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)) | apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), line_connecting(intersection_point(X20_9_7, skolem_Z4444), skolem_X4242)))
% 45.32/9.55
% 45.32/9.55 [7097] BETA_OR : (distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)) | apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), line_connecting(intersection_point(X20_9_7, skolem_Z4444), skolem_X4242)))
% 45.32/9.55 -> [7100] distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444))
% 45.32/9.55 -> [7101] apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), line_connecting(intersection_point(X20_9_7, skolem_Z4444), skolem_X4242))
% 45.32/9.55
% 45.32/9.55 [7100] CLOSURE : distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [7101] CLOSURE : apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), line_connecting(intersection_point(X20_9_7, skolem_Z4444), skolem_X4242))
% 45.32/9.55
% 45.32/9.55 [7096] 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))))
% 45.32/9.55 -> [7103] (apart_point_and_line(skolem_X4242, skolem_Z4444) => (distinct_lines(skolem_Z4444, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444)))
% 45.32/9.55
% 45.32/9.55 [7103] BETA_IMPLY : (apart_point_and_line(skolem_X4242, skolem_Z4444) => (distinct_lines(skolem_Z4444, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444)))
% 45.32/9.55 -> [7106] ~apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55 -> [7107] (distinct_lines(skolem_Z4444, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [7107] BETA_OR : (distinct_lines(skolem_Z4444, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [7112] distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55 -> [7113] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7113] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7112] CLOSURE : distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7106] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 45.32/9.55 -> [7115] (convergent_lines(skolem_Z4444, skolem_Y4343) => distinct_lines(skolem_Z4444, skolem_Y4343))
% 45.32/9.55
% 45.32/9.55 [7115] BETA_IMPLY : (convergent_lines(skolem_Z4444, skolem_Y4343) => distinct_lines(skolem_Z4444, skolem_Y4343))
% 45.32/9.55 -> [7118] ~convergent_lines(skolem_Z4444, skolem_Y4343)
% 45.32/9.55 -> [7119] distinct_lines(skolem_Z4444, skolem_Y4343)
% 45.32/9.55
% 45.32/9.55 [7119] CLOSURE : distinct_lines(skolem_Z4444, skolem_Y4343)
% 45.32/9.55
% 45.32/9.55 [7118] GAMMA_FORALL : ! [X35_35, Y36_36] : (~convergent_lines(parallel_through_point(Y36_36, X35_35), Y36_36))
% 45.32/9.55 -> [7129] ~convergent_lines(parallel_through_point(Y36_257_12, X35_257_12), Y36_257_12)
% 45.32/9.55
% 45.32/9.55 [7129] GAMMA_FORALL : ! [X37_37, Y38_38] : (~apart_point_and_line(X37_37, parallel_through_point(Y38_38, X37_37)))
% 45.32/9.55 -> [7133] ~apart_point_and_line(X37_257_13, parallel_through_point(Y38_257_13, X37_257_13))
% 45.32/9.55
% 45.32/9.55 [7133] GAMMA_FORALL : ! [X39_39, Y40_40, Z41_41] : ((distinct_lines(Y40_40, Z41_41) => ((apart_point_and_line(X39_39, Y40_40) | apart_point_and_line(X39_39, Z41_41)) | convergent_lines(Y40_40, Z41_41))))
% 45.32/9.55 -> [7135] (distinct_lines(skolem_Y4343, skolem_Z4444) => ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444)))
% 45.32/9.55
% 45.32/9.55 [7135] BETA_IMPLY : (distinct_lines(skolem_Y4343, skolem_Z4444) => ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444)))
% 45.32/9.55 -> [7137] ~distinct_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55 -> [7138] ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [7137] CLOSURE : ~distinct_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7138] BETA_OR : ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444))
% 45.32/9.55 -> [7179] (apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [7180] convergent_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7180] CLOSURE : convergent_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7179] BETA_OR : (apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [7181] apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55 -> [7182] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7181] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55
% 45.32/9.55 [7182] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7090] 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))))
% 45.32/9.55 -> [7092] (apart_point_and_line(skolem_X4242, skolem_Y4343) => (distinct_points(skolem_X4242, skolem_X4242) | apart_point_and_line(skolem_X4242, skolem_Y4343)))
% 45.32/9.55
% 45.32/9.55 [7092] BETA_IMPLY : (apart_point_and_line(skolem_X4242, skolem_Y4343) => (distinct_points(skolem_X4242, skolem_X4242) | apart_point_and_line(skolem_X4242, skolem_Y4343)))
% 45.32/9.55 -> [7094] ~apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55 -> [7095] (distinct_points(skolem_X4242, skolem_X4242) | apart_point_and_line(skolem_X4242, skolem_Y4343))
% 45.32/9.55
% 45.32/9.55 [7095] BETA_OR : (distinct_points(skolem_X4242, skolem_X4242) | apart_point_and_line(skolem_X4242, skolem_Y4343))
% 45.32/9.55 -> [7098] distinct_points(skolem_X4242, skolem_X4242)
% 45.32/9.55 -> [7099] apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55
% 45.32/9.55 [7099] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55
% 45.32/9.55 [7098] CLOSURE : distinct_points(skolem_X4242, skolem_X4242)
% 45.32/9.55
% 45.32/9.55 [7102] BETA_IMPLY : (apart_point_and_line(skolem_X4242, skolem_Z4444) => (distinct_lines(skolem_Z4444, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444)))
% 45.32/9.55 -> [7187] ~apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55 -> [7188] (distinct_lines(skolem_Z4444, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [7188] BETA_OR : (distinct_lines(skolem_Z4444, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [7189] distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55 -> [7190] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7190] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7189] CLOSURE : distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7187] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 45.32/9.55 -> [7191] (convergent_lines(skolem_Z4444, skolem_Z4444) => distinct_lines(skolem_Z4444, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [7191] BETA_IMPLY : (convergent_lines(skolem_Z4444, skolem_Z4444) => distinct_lines(skolem_Z4444, skolem_Z4444))
% 45.32/9.55 -> [7192] ~convergent_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55 -> [7193] distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7193] CLOSURE : distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7192] GAMMA_FORALL : ! [X35_35, Y36_36] : (~convergent_lines(parallel_through_point(Y36_36, X35_35), Y36_36))
% 45.32/9.55 -> [7194] ~convergent_lines(parallel_through_point(Y36_260_12, X35_260_12), Y36_260_12)
% 45.32/9.55
% 45.32/9.55 [7194] GAMMA_FORALL : ! [X37_37, Y38_38] : (~apart_point_and_line(X37_37, parallel_through_point(Y38_38, X37_37)))
% 45.32/9.55 -> [7195] ~apart_point_and_line(X37_260_13, parallel_through_point(Y38_260_13, X37_260_13))
% 45.32/9.55
% 45.32/9.55 [7195] GAMMA_FORALL : ! [X39_39, Y40_40, Z41_41] : ((distinct_lines(Y40_40, Z41_41) => ((apart_point_and_line(X39_39, Y40_40) | apart_point_and_line(X39_39, Z41_41)) | convergent_lines(Y40_40, Z41_41))))
% 45.32/9.55 -> [7196] (distinct_lines(skolem_Y4343, skolem_Z4444) => ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444)))
% 45.32/9.55
% 45.32/9.55 [7196] BETA_IMPLY : (distinct_lines(skolem_Y4343, skolem_Z4444) => ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444)))
% 45.32/9.55 -> [7197] ~distinct_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55 -> [7198] ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [7197] CLOSURE : ~distinct_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7198] BETA_OR : ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444))
% 45.32/9.55 -> [7261] (apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [7262] convergent_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7262] CLOSURE : convergent_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7261] BETA_OR : (apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [7263] apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55 -> [7264] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7264] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7263] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55
% 45.32/9.55 [6968] BETA_IMPLY : ((apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), X20_9_7) | apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), skolem_Z4444)) => distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)))
% 45.32/9.55 -> [6969] ~(apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), X20_9_7) | apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), skolem_Z4444))
% 45.32/9.55 -> [6970] distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [6969] ALPHA_NOT_OR : ~(apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), X20_9_7) | apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), skolem_Z4444))
% 45.32/9.55 -> [6971] ~apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), X20_9_7), ~apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6971] 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))))
% 45.32/9.55 -> [6975] ((distinct_points(skolem_X4242, skolem_X4242) & distinct_lines(skolem_Z4444, skolem_Z4444)) => (((apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Z4444)))
% 45.32/9.55
% 45.32/9.55 [6975] BETA_IMPLY : ((distinct_points(skolem_X4242, skolem_X4242) & distinct_lines(skolem_Z4444, skolem_Z4444)) => (((apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Z4444)))
% 45.32/9.55 -> [6976] ~(distinct_points(skolem_X4242, skolem_X4242) & distinct_lines(skolem_Z4444, skolem_Z4444))
% 45.32/9.55 -> [6977] (((apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [6977] BETA_OR : (((apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [6986] ((apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [6987] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6986] BETA_OR : ((apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [6993] (apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [6994] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6994] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6993] BETA_OR : (apart_point_and_line(skolem_X4242, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [7055] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55 -> [7056] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7055] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7056] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6987] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6976] BETA_NOT_AND : ~(distinct_points(skolem_X4242, skolem_X4242) & distinct_lines(skolem_Z4444, skolem_Z4444))
% 45.32/9.55 -> [7203] ~distinct_points(skolem_X4242, skolem_X4242)
% 45.32/9.55 -> [7204] ~distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7203] 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))))
% 45.32/9.55 -> [7206] (apart_point_and_line(skolem_X4242, skolem_Z4444) => (distinct_points(skolem_X4242, skolem_X4242) | apart_point_and_line(skolem_X4242, skolem_Z4444)))
% 45.32/9.55
% 45.32/9.55 [7206] BETA_IMPLY : (apart_point_and_line(skolem_X4242, skolem_Z4444) => (distinct_points(skolem_X4242, skolem_X4242) | apart_point_and_line(skolem_X4242, skolem_Z4444)))
% 45.32/9.55 -> [7209] ~apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55 -> [7210] (distinct_points(skolem_X4242, skolem_X4242) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [7210] BETA_OR : (distinct_points(skolem_X4242, skolem_X4242) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [7213] distinct_points(skolem_X4242, skolem_X4242)
% 45.32/9.55 -> [7214] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7214] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7213] CLOSURE : distinct_points(skolem_X4242, skolem_X4242)
% 45.32/9.55
% 45.32/9.55 [7216] BETA_IMPLY : (apart_point_and_line(skolem_X4242, skolem_Z4444) => (distinct_lines(skolem_Z4444, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444)))
% 45.32/9.55 -> [7275] ~apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55 -> [7276] (distinct_lines(skolem_Z4444, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [7276] BETA_OR : (distinct_lines(skolem_Z4444, skolem_Z4444) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [7277] distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55 -> [7278] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7278] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7277] CLOSURE : distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7275] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 45.32/9.55 -> [7279] (convergent_lines(skolem_Z4444, skolem_Z4444) => distinct_lines(skolem_Z4444, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [7279] BETA_IMPLY : (convergent_lines(skolem_Z4444, skolem_Z4444) => distinct_lines(skolem_Z4444, skolem_Z4444))
% 45.32/9.55 -> [7280] ~convergent_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55 -> [7281] distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7281] CLOSURE : distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7280] GAMMA_FORALL : ! [X35_35, Y36_36] : (~convergent_lines(parallel_through_point(Y36_36, X35_35), Y36_36))
% 45.32/9.55 -> [7282] ~convergent_lines(parallel_through_point(Y36_264_12, X35_264_12), Y36_264_12)
% 45.32/9.55
% 45.32/9.55 [7282] GAMMA_FORALL : ! [X37_37, Y38_38] : (~apart_point_and_line(X37_37, parallel_through_point(Y38_38, X37_37)))
% 45.32/9.55 -> [7283] ~apart_point_and_line(X37_264_13, parallel_through_point(Y38_264_13, X37_264_13))
% 45.32/9.55
% 45.32/9.55 [7283] GAMMA_FORALL : ! [X39_39, Y40_40, Z41_41] : ((distinct_lines(Y40_40, Z41_41) => ((apart_point_and_line(X39_39, Y40_40) | apart_point_and_line(X39_39, Z41_41)) | convergent_lines(Y40_40, Z41_41))))
% 45.32/9.55 -> [7284] (distinct_lines(skolem_Y4343, skolem_Z4444) => ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444)))
% 45.32/9.55
% 45.32/9.55 [7284] BETA_IMPLY : (distinct_lines(skolem_Y4343, skolem_Z4444) => ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444)))
% 45.32/9.55 -> [7285] ~distinct_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55 -> [7286] ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [7285] CLOSURE : ~distinct_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7286] BETA_OR : ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444))
% 45.32/9.55 -> [7293] (apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [7294] convergent_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7294] CLOSURE : convergent_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7293] BETA_OR : (apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [7295] apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55 -> [7296] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7295] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55
% 45.32/9.55 [7296] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7204] 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))))
% 45.32/9.55 -> [7205] (apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), Y28_113_9) => (distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)) | apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), Y28_113_9)))
% 45.32/9.55
% 45.32/9.55 [7205] BETA_IMPLY : (apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), Y28_113_9) => (distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)) | apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), Y28_113_9)))
% 45.32/9.55 -> [7207] ~apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), Y28_113_9)
% 45.32/9.55 -> [7208] (distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)) | apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), Y28_113_9))
% 45.32/9.55
% 45.32/9.55 [7208] BETA_OR : (distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444)) | apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), Y28_113_9))
% 45.32/9.55 -> [7211] distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444))
% 45.32/9.55 -> [7212] apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), Y28_113_9)
% 45.32/9.55
% 45.32/9.55 [7212] CLOSURE : apart_point_and_line(intersection_point(X20_9_7, skolem_Z4444), Y28_113_9)
% 45.32/9.55
% 45.32/9.55 [7211] CLOSURE : distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [7207] 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))))
% 45.32/9.55 -> [7215] (apart_point_and_line(skolem_X4242, Y31_156_10) => (distinct_lines(Y31_156_10, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Y4343)))
% 45.32/9.55
% 45.32/9.55 [7215] BETA_IMPLY : (apart_point_and_line(skolem_X4242, Y31_156_10) => (distinct_lines(Y31_156_10, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Y4343)))
% 45.32/9.55 -> [7217] ~apart_point_and_line(skolem_X4242, Y31_156_10)
% 45.32/9.55 -> [7218] (distinct_lines(Y31_156_10, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Y4343))
% 45.32/9.55
% 45.32/9.55 [7217] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 45.32/9.55 -> [7225] (convergent_lines(skolem_Z4444, skolem_Z4444) => distinct_lines(skolem_Z4444, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [7225] BETA_IMPLY : (convergent_lines(skolem_Z4444, skolem_Z4444) => distinct_lines(skolem_Z4444, skolem_Z4444))
% 45.32/9.55 -> [7227] ~convergent_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55 -> [7228] distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7228] CLOSURE : distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7227] GAMMA_FORALL : ! [X35_35, Y36_36] : (~convergent_lines(parallel_through_point(Y36_36, X35_35), Y36_36))
% 45.32/9.55 -> [7232] ~convergent_lines(parallel_through_point(Y36_262_12, X35_262_12), Y36_262_12)
% 45.32/9.55
% 45.32/9.55 [7232] GAMMA_FORALL : ! [X37_37, Y38_38] : (~apart_point_and_line(X37_37, parallel_through_point(Y38_38, X37_37)))
% 45.32/9.55 -> [7233] ~apart_point_and_line(X37_261_13, parallel_through_point(Y38_261_13, X37_261_13))
% 45.32/9.55
% 45.32/9.55 [7233] GAMMA_FORALL : ! [X39_39, Y40_40, Z41_41] : ((distinct_lines(Y40_40, Z41_41) => ((apart_point_and_line(X39_39, Y40_40) | apart_point_and_line(X39_39, Z41_41)) | convergent_lines(Y40_40, Z41_41))))
% 45.32/9.55 -> [7235] (distinct_lines(skolem_Y4343, skolem_Z4444) => ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444)))
% 45.32/9.55
% 45.32/9.55 [7235] BETA_IMPLY : (distinct_lines(skolem_Y4343, skolem_Z4444) => ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444)))
% 45.32/9.55 -> [7236] ~distinct_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55 -> [7237] ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [7236] CLOSURE : ~distinct_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7237] BETA_OR : ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444))
% 45.32/9.55 -> [7271] (apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [7272] convergent_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7272] CLOSURE : convergent_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7271] BETA_OR : (apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [7273] apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55 -> [7274] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7273] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55
% 45.32/9.55 [7274] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7218] BETA_OR : (distinct_lines(Y31_156_10, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Y4343))
% 45.32/9.55 -> [7221] distinct_lines(Y31_156_10, skolem_Y4343)
% 45.32/9.55 -> [7222] apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55
% 45.32/9.55 [7222] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55
% 45.32/9.55 [7221] GAMMA_FORALL : ! [X33_33, Y34_34] : ((convergent_lines(X33_33, Y34_34) => distinct_lines(X33_33, Y34_34)))
% 45.32/9.55 -> [7241] (convergent_lines(skolem_Z4444, skolem_Z4444) => distinct_lines(skolem_Z4444, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [7241] BETA_IMPLY : (convergent_lines(skolem_Z4444, skolem_Z4444) => distinct_lines(skolem_Z4444, skolem_Z4444))
% 45.32/9.55 -> [7242] ~convergent_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55 -> [7243] distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7243] CLOSURE : distinct_lines(skolem_Z4444, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7242] GAMMA_FORALL : ! [X35_35, Y36_36] : (~convergent_lines(parallel_through_point(Y36_36, X35_35), Y36_36))
% 45.32/9.55 -> [7248] ~convergent_lines(parallel_through_point(Y36_263_12, X35_263_12), Y36_263_12)
% 45.32/9.55
% 45.32/9.55 [7248] GAMMA_FORALL : ! [X37_37, Y38_38] : (~apart_point_and_line(X37_37, parallel_through_point(Y38_38, X37_37)))
% 45.32/9.55 -> [7253] ~apart_point_and_line(X37_263_13, parallel_through_point(Y38_263_13, X37_263_13))
% 45.32/9.55
% 45.32/9.55 [7253] GAMMA_FORALL : ! [X39_39, Y40_40, Z41_41] : ((distinct_lines(Y40_40, Z41_41) => ((apart_point_and_line(X39_39, Y40_40) | apart_point_and_line(X39_39, Z41_41)) | convergent_lines(Y40_40, Z41_41))))
% 45.32/9.55 -> [7254] (distinct_lines(skolem_Y4343, skolem_Z4444) => ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444)))
% 45.32/9.55
% 45.32/9.55 [7254] BETA_IMPLY : (distinct_lines(skolem_Y4343, skolem_Z4444) => ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444)))
% 45.32/9.55 -> [7255] ~distinct_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55 -> [7256] ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 [7255] CLOSURE : ~distinct_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7256] BETA_OR : ((apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444)) | convergent_lines(skolem_Y4343, skolem_Z4444))
% 45.32/9.55 -> [7297] (apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [7298] convergent_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7298] CLOSURE : convergent_lines(skolem_Y4343, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7297] BETA_OR : (apart_point_and_line(skolem_X4242, skolem_Y4343) | apart_point_and_line(skolem_X4242, skolem_Z4444))
% 45.32/9.55 -> [7299] apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55 -> [7300] apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [7299] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Y4343)
% 45.32/9.55
% 45.32/9.55 [7300] CLOSURE : apart_point_and_line(skolem_X4242, skolem_Z4444)
% 45.32/9.55
% 45.32/9.55 [6970] CLOSURE : distinct_points(intersection_point(X20_9_7, skolem_Z4444), intersection_point(X20_9_7, skolem_Z4444))
% 45.32/9.55
% 45.32/9.55 % SZS output end Proof for theBenchmark.p
% 45.32/9.55 [9.215524s][1][Res] 68033 goroutines created
% 45.32/9.55 ==== Result ====
% 45.32/9.55 [9.215563s][1][Res] VALID
% 45.32/9.55 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------