TSTP Solution File: GEO207+3 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO207+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n027.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 0.22s 0.45s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GEO207+3 : TPTP v8.1.0. Released v4.0.0.
% 0.14/0.14 % Command : goeland -dmt -presko -proof %s
% 0.14/0.36 % Computer : n027.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 31 07:10:32 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 [DMT] DMT loaded with preskolemization
% 0.14/0.36 [EQ] equality loaded.
% 0.14/0.36 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.14/0.37 Conjecture not found
% 0.14/0.37 Conjecture not found
% 0.14/0.37 Conjecture not found
% 0.14/0.37 Conjecture not found
% 0.14/0.37 Conjecture not found
% 0.14/0.37 Conjecture not found
% 0.14/0.37 Conjecture not found
% 0.14/0.37 Start search
% 0.14/0.37 nb_step : 1 - limit : 36
% 0.14/0.37 Launch Gotab with destructive = true
% 0.22/0.44 % SZS output start Proof for theBenchmark.p
% 0.22/0.45 [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] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18)))) & ! [X19_19, Y20_20] : ((distinct_points(X19_19, Y20_20) => ~apart_point_and_line(Y20_20, line_connecting(X19_19, Y20_20)))) & ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21))) & ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24))) & ! [X25_25, Y26_26, U27_27, V28_28] : (((distinct_points(X25_25, Y26_26) & distinct_lines(U27_27, V28_28)) => (((apart_point_and_line(X25_25, U27_27) | apart_point_and_line(X25_25, V28_28)) | apart_point_and_line(Y26_26, U27_27)) | apart_point_and_line(Y26_26, V28_28)))) & ! [X29_29, Y30_30, Z31_31] : ((apart_point_and_line(X29_29, Y30_30) => (distinct_points(X29_29, Z31_31) | apart_point_and_line(Z31_31, Y30_30)))) & ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34)))) & ! [X35_35, Y36_36, Z37_37] : ((convergent_lines(X35_35, Y36_36) => (distinct_lines(Y36_36, Z37_37) | convergent_lines(X35_35, Z37_37))))) & (! [X38_38, Y39_39] : ((distinct_lines(X38_38, Y39_39) => convergent_lines(X38_38, Y39_39)))) & (! [X40_40, Y41_41] : (~convergent_lines(parallel_through_point(Y41_41, X40_40), Y41_41)) & ! [X42_42, Y43_43] : (~apart_point_and_line(X42_42, parallel_through_point(Y43_43, X42_42))) & ! [X44_44, Y45_45, Z46_46] : ((distinct_lines(Y45_45, Z46_46) => ((apart_point_and_line(X44_44, Y45_45) | apart_point_and_line(X44_44, Z46_46)) | convergent_lines(Y45_45, Z46_46))))) & (! [L51_51, M52_52] : ((convergent_lines(L51_51, M52_52) | unorthogonal_lines(L51_51, M52_52))) & ! [L53_53, M54_54, N55_55] : (((convergent_lines(L53_53, M54_54) & unorthogonal_lines(L53_53, M54_54)) => ((convergent_lines(L53_53, N55_55) & unorthogonal_lines(L53_53, N55_55)) | (convergent_lines(M54_54, N55_55) & unorthogonal_lines(M54_54, N55_55))))) & ! [A56_56, L57_57] : (~unorthogonal_lines(orthogonal_through_point(L57_57, A56_56), L57_57)) & ! [A58_58, L59_59] : (~apart_point_and_line(A58_58, orthogonal_through_point(L59_59, A58_58))) & ! [A60_60, L61_61, M62_62, N63_63] : ((distinct_lines(L61_61, M62_62) => (((apart_point_and_line(A60_60, L61_61) | apart_point_and_line(A60_60, M62_62)) | unorthogonal_lines(L61_61, N63_63)) | unorthogonal_lines(M62_62, N63_63))))) & (! [L64_64, M65_65] : (~(~convergent_lines(L64_64, M65_65) & ~unorthogonal_lines(L64_64, M65_65))) & ! [L66_66, M67_67, N68_68] : ((((~convergent_lines(L66_66, M67_67) | ~unorthogonal_lines(L66_66, M67_67)) & (~convergent_lines(L66_66, N68_68) | ~unorthogonal_lines(L66_66, N68_68))) => (~convergent_lines(M67_67, N68_68) | ~unorthogonal_lines(M67_67, N68_68)))) & ! [L69_69, M70_70, N71_71] : (((~unorthogonal_lines(L69_69, M70_70) & ~unorthogonal_lines(L69_69, N71_71)) => ~convergent_lines(M70_70, N71_71)))) & (! [A73_73, B74_74] : ((((point(A73_73) & point(B74_74)) & distinct_points(A73_73, B74_74)) => line(line_connecting(A73_73, B74_74)))) & ! [L75_75, M76_76] : ((((line(L75_75) & line(M76_76)) & convergent_lines(L75_75, M76_76)) => point(intersection_point(L75_75, M76_76)))) & ! [L77_77, A78_78] : (((line(L77_77) & point(A78_78)) => line(parallel_through_point(L77_77, A78_78)))) & ! [L79_79, A80_80] : (((line(L79_79) & point(A80_80)) => line(orthogonal_through_point(L79_79, A80_80))))) & (! [X81_81, Y82_82] : ((equal_points(X81_81, Y82_82) <=> ~distinct_points(X81_81, Y82_82))) & ! [X83_83, Y84_84] : ((equal_lines(X83_83, Y84_84) <=> ~distinct_lines(X83_83, Y84_84))) & ! [X85_85, Y86_86] : ((parallel_lines(X85_85, Y86_86) <=> ~convergent_lines(X85_85, Y86_86))) & ! [X87_87, Y88_88] : ((incident_point_and_line(X87_87, Y88_88) <=> ~apart_point_and_line(X87_87, Y88_88))) & ! [X89_89, Y90_90] : ((orthogonal_lines(X89_89, Y90_90) <=> ~unorthogonal_lines(X89_89, Y90_90)))) & ~! [X91_91] : (~convergent_lines(X91_91, X91_91)))
% 0.22/0.45 -> [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] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18)))) & ! [X19_19, Y20_20] : ((distinct_points(X19_19, Y20_20) => ~apart_point_and_line(Y20_20, line_connecting(X19_19, Y20_20)))) & ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21))) & ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24))) & ! [X25_25, Y26_26, U27_27, V28_28] : (((distinct_points(X25_25, Y26_26) & distinct_lines(U27_27, V28_28)) => (((apart_point_and_line(X25_25, U27_27) | apart_point_and_line(X25_25, V28_28)) | apart_point_and_line(Y26_26, U27_27)) | apart_point_and_line(Y26_26, V28_28)))) & ! [X29_29, Y30_30, Z31_31] : ((apart_point_and_line(X29_29, Y30_30) => (distinct_points(X29_29, Z31_31) | apart_point_and_line(Z31_31, Y30_30)))) & ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34)))) & ! [X35_35, Y36_36, Z37_37] : ((convergent_lines(X35_35, Y36_36) => (distinct_lines(Y36_36, Z37_37) | convergent_lines(X35_35, Z37_37))))), (! [X38_38, Y39_39] : ((distinct_lines(X38_38, Y39_39) => convergent_lines(X38_38, Y39_39)))), (! [X40_40, Y41_41] : (~convergent_lines(parallel_through_point(Y41_41, X40_40), Y41_41)) & ! [X42_42, Y43_43] : (~apart_point_and_line(X42_42, parallel_through_point(Y43_43, X42_42))) & ! [X44_44, Y45_45, Z46_46] : ((distinct_lines(Y45_45, Z46_46) => ((apart_point_and_line(X44_44, Y45_45) | apart_point_and_line(X44_44, Z46_46)) | convergent_lines(Y45_45, Z46_46))))), (! [L51_51, M52_52] : ((convergent_lines(L51_51, M52_52) | unorthogonal_lines(L51_51, M52_52))) & ! [L53_53, M54_54, N55_55] : (((convergent_lines(L53_53, M54_54) & unorthogonal_lines(L53_53, M54_54)) => ((convergent_lines(L53_53, N55_55) & unorthogonal_lines(L53_53, N55_55)) | (convergent_lines(M54_54, N55_55) & unorthogonal_lines(M54_54, N55_55))))) & ! [A56_56, L57_57] : (~unorthogonal_lines(orthogonal_through_point(L57_57, A56_56), L57_57)) & ! [A58_58, L59_59] : (~apart_point_and_line(A58_58, orthogonal_through_point(L59_59, A58_58))) & ! [A60_60, L61_61, M62_62, N63_63] : ((distinct_lines(L61_61, M62_62) => (((apart_point_and_line(A60_60, L61_61) | apart_point_and_line(A60_60, M62_62)) | unorthogonal_lines(L61_61, N63_63)) | unorthogonal_lines(M62_62, N63_63))))), (! [L64_64, M65_65] : (~(~convergent_lines(L64_64, M65_65) & ~unorthogonal_lines(L64_64, M65_65))) & ! [L66_66, M67_67, N68_68] : ((((~convergent_lines(L66_66, M67_67) | ~unorthogonal_lines(L66_66, M67_67)) & (~convergent_lines(L66_66, N68_68) | ~unorthogonal_lines(L66_66, N68_68))) => (~convergent_lines(M67_67, N68_68) | ~unorthogonal_lines(M67_67, N68_68)))) & ! [L69_69, M70_70, N71_71] : (((~unorthogonal_lines(L69_69, M70_70) & ~unorthogonal_lines(L69_69, N71_71)) => ~convergent_lines(M70_70, N71_71)))), (! [A73_73, B74_74] : ((((point(A73_73) & point(B74_74)) & distinct_points(A73_73, B74_74)) => line(line_connecting(A73_73, B74_74)))) & ! [L75_75, M76_76] : ((((line(L75_75) & line(M76_76)) & convergent_lines(L75_75, M76_76)) => point(intersection_point(L75_75, M76_76)))) & ! [L77_77, A78_78] : (((line(L77_77) & point(A78_78)) => line(parallel_through_point(L77_77, A78_78)))) & ! [L79_79, A80_80] : (((line(L79_79) & point(A80_80)) => line(orthogonal_through_point(L79_79, A80_80))))), (! [X81_81, Y82_82] : ((equal_points(X81_81, Y82_82) <=> ~distinct_points(X81_81, Y82_82))) & ! [X83_83, Y84_84] : ((equal_lines(X83_83, Y84_84) <=> ~distinct_lines(X83_83, Y84_84))) & ! [X85_85, Y86_86] : ((parallel_lines(X85_85, Y86_86) <=> ~convergent_lines(X85_85, Y86_86))) & ! [X87_87, Y88_88] : ((incident_point_and_line(X87_87, Y88_88) <=> ~apart_point_and_line(X87_87, Y88_88))) & ! [X89_89, Y90_90] : ((orthogonal_lines(X89_89, Y90_90) <=> ~unorthogonal_lines(X89_89, Y90_90)))), ~! [X91_91] : (~convergent_lines(X91_91, X91_91))
% 0.22/0.45
% 0.22/0.45 [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] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18)))) & ! [X19_19, Y20_20] : ((distinct_points(X19_19, Y20_20) => ~apart_point_and_line(Y20_20, line_connecting(X19_19, Y20_20)))) & ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21))) & ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24))) & ! [X25_25, Y26_26, U27_27, V28_28] : (((distinct_points(X25_25, Y26_26) & distinct_lines(U27_27, V28_28)) => (((apart_point_and_line(X25_25, U27_27) | apart_point_and_line(X25_25, V28_28)) | apart_point_and_line(Y26_26, U27_27)) | apart_point_and_line(Y26_26, V28_28)))) & ! [X29_29, Y30_30, Z31_31] : ((apart_point_and_line(X29_29, Y30_30) => (distinct_points(X29_29, Z31_31) | apart_point_and_line(Z31_31, Y30_30)))) & ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34)))) & ! [X35_35, Y36_36, Z37_37] : ((convergent_lines(X35_35, Y36_36) => (distinct_lines(Y36_36, Z37_37) | convergent_lines(X35_35, Z37_37)))))
% 0.22/0.45 -> [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] : ((distinct_points(X17_17, Y18_18) => ~apart_point_and_line(X17_17, line_connecting(X17_17, Y18_18)))), ! [X19_19, Y20_20] : ((distinct_points(X19_19, Y20_20) => ~apart_point_and_line(Y20_20, line_connecting(X19_19, Y20_20)))), ! [X21_21, Y22_22] : ((convergent_lines(X21_21, Y22_22) => ~apart_point_and_line(intersection_point(X21_21, Y22_22), X21_21))), ! [X23_23, Y24_24] : ((convergent_lines(X23_23, Y24_24) => ~apart_point_and_line(intersection_point(X23_23, Y24_24), Y24_24))), ! [X25_25, Y26_26, U27_27, V28_28] : (((distinct_points(X25_25, Y26_26) & distinct_lines(U27_27, V28_28)) => (((apart_point_and_line(X25_25, U27_27) | apart_point_and_line(X25_25, V28_28)) | apart_point_and_line(Y26_26, U27_27)) | apart_point_and_line(Y26_26, V28_28)))), ! [X29_29, Y30_30, Z31_31] : ((apart_point_and_line(X29_29, Y30_30) => (distinct_points(X29_29, Z31_31) | apart_point_and_line(Z31_31, Y30_30)))), ! [X32_32, Y33_33, Z34_34] : ((apart_point_and_line(X32_32, Y33_33) => (distinct_lines(Y33_33, Z34_34) | apart_point_and_line(X32_32, Z34_34)))), ! [X35_35, Y36_36, Z37_37] : ((convergent_lines(X35_35, Y36_36) => (distinct_lines(Y36_36, Z37_37) | convergent_lines(X35_35, Z37_37))))
% 0.22/0.45
% 0.22/0.45 [2] ALPHA_AND : (! [X38_38, Y39_39] : ((distinct_lines(X38_38, Y39_39) => convergent_lines(X38_38, Y39_39))))
% 0.22/0.45 -> [3] ! [X38_38, Y39_39] : ((distinct_lines(X38_38, Y39_39) => convergent_lines(X38_38, Y39_39)))
% 0.22/0.45
% 0.22/0.45 [3] ALPHA_AND : (! [X40_40, Y41_41] : (~convergent_lines(parallel_through_point(Y41_41, X40_40), Y41_41)) & ! [X42_42, Y43_43] : (~apart_point_and_line(X42_42, parallel_through_point(Y43_43, X42_42))) & ! [X44_44, Y45_45, Z46_46] : ((distinct_lines(Y45_45, Z46_46) => ((apart_point_and_line(X44_44, Y45_45) | apart_point_and_line(X44_44, Z46_46)) | convergent_lines(Y45_45, Z46_46)))))
% 0.22/0.45 -> [4] ! [X40_40, Y41_41] : (~convergent_lines(parallel_through_point(Y41_41, X40_40), Y41_41)), ! [X42_42, Y43_43] : (~apart_point_and_line(X42_42, parallel_through_point(Y43_43, X42_42))), ! [X44_44, Y45_45, Z46_46] : ((distinct_lines(Y45_45, Z46_46) => ((apart_point_and_line(X44_44, Y45_45) | apart_point_and_line(X44_44, Z46_46)) | convergent_lines(Y45_45, Z46_46))))
% 0.22/0.45
% 0.22/0.45 [4] ALPHA_AND : (! [L51_51, M52_52] : ((convergent_lines(L51_51, M52_52) | unorthogonal_lines(L51_51, M52_52))) & ! [L53_53, M54_54, N55_55] : (((convergent_lines(L53_53, M54_54) & unorthogonal_lines(L53_53, M54_54)) => ((convergent_lines(L53_53, N55_55) & unorthogonal_lines(L53_53, N55_55)) | (convergent_lines(M54_54, N55_55) & unorthogonal_lines(M54_54, N55_55))))) & ! [A56_56, L57_57] : (~unorthogonal_lines(orthogonal_through_point(L57_57, A56_56), L57_57)) & ! [A58_58, L59_59] : (~apart_point_and_line(A58_58, orthogonal_through_point(L59_59, A58_58))) & ! [A60_60, L61_61, M62_62, N63_63] : ((distinct_lines(L61_61, M62_62) => (((apart_point_and_line(A60_60, L61_61) | apart_point_and_line(A60_60, M62_62)) | unorthogonal_lines(L61_61, N63_63)) | unorthogonal_lines(M62_62, N63_63)))))
% 0.22/0.45 -> [5] ! [L51_51, M52_52] : ((convergent_lines(L51_51, M52_52) | unorthogonal_lines(L51_51, M52_52))), ! [L53_53, M54_54, N55_55] : (((convergent_lines(L53_53, M54_54) & unorthogonal_lines(L53_53, M54_54)) => ((convergent_lines(L53_53, N55_55) & unorthogonal_lines(L53_53, N55_55)) | (convergent_lines(M54_54, N55_55) & unorthogonal_lines(M54_54, N55_55))))), ! [A56_56, L57_57] : (~unorthogonal_lines(orthogonal_through_point(L57_57, A56_56), L57_57)), ! [A58_58, L59_59] : (~apart_point_and_line(A58_58, orthogonal_through_point(L59_59, A58_58))), ! [A60_60, L61_61, M62_62, N63_63] : ((distinct_lines(L61_61, M62_62) => (((apart_point_and_line(A60_60, L61_61) | apart_point_and_line(A60_60, M62_62)) | unorthogonal_lines(L61_61, N63_63)) | unorthogonal_lines(M62_62, N63_63))))
% 0.22/0.45
% 0.22/0.45 [5] ALPHA_AND : (! [L64_64, M65_65] : (~(~convergent_lines(L64_64, M65_65) & ~unorthogonal_lines(L64_64, M65_65))) & ! [L66_66, M67_67, N68_68] : ((((~convergent_lines(L66_66, M67_67) | ~unorthogonal_lines(L66_66, M67_67)) & (~convergent_lines(L66_66, N68_68) | ~unorthogonal_lines(L66_66, N68_68))) => (~convergent_lines(M67_67, N68_68) | ~unorthogonal_lines(M67_67, N68_68)))) & ! [L69_69, M70_70, N71_71] : (((~unorthogonal_lines(L69_69, M70_70) & ~unorthogonal_lines(L69_69, N71_71)) => ~convergent_lines(M70_70, N71_71))))
% 0.22/0.45 -> [6] ! [L64_64, M65_65] : (~(~convergent_lines(L64_64, M65_65) & ~unorthogonal_lines(L64_64, M65_65))), ! [L66_66, M67_67, N68_68] : ((((~convergent_lines(L66_66, M67_67) | ~unorthogonal_lines(L66_66, M67_67)) & (~convergent_lines(L66_66, N68_68) | ~unorthogonal_lines(L66_66, N68_68))) => (~convergent_lines(M67_67, N68_68) | ~unorthogonal_lines(M67_67, N68_68)))), ! [L69_69, M70_70, N71_71] : (((~unorthogonal_lines(L69_69, M70_70) & ~unorthogonal_lines(L69_69, N71_71)) => ~convergent_lines(M70_70, N71_71)))
% 0.22/0.45
% 0.22/0.45 [6] ALPHA_AND : (! [A73_73, B74_74] : ((((point(A73_73) & point(B74_74)) & distinct_points(A73_73, B74_74)) => line(line_connecting(A73_73, B74_74)))) & ! [L75_75, M76_76] : ((((line(L75_75) & line(M76_76)) & convergent_lines(L75_75, M76_76)) => point(intersection_point(L75_75, M76_76)))) & ! [L77_77, A78_78] : (((line(L77_77) & point(A78_78)) => line(parallel_through_point(L77_77, A78_78)))) & ! [L79_79, A80_80] : (((line(L79_79) & point(A80_80)) => line(orthogonal_through_point(L79_79, A80_80)))))
% 0.22/0.45 -> [7] ! [A73_73, B74_74] : ((((point(A73_73) & point(B74_74)) & distinct_points(A73_73, B74_74)) => line(line_connecting(A73_73, B74_74)))), ! [L75_75, M76_76] : ((((line(L75_75) & line(M76_76)) & convergent_lines(L75_75, M76_76)) => point(intersection_point(L75_75, M76_76)))), ! [L77_77, A78_78] : (((line(L77_77) & point(A78_78)) => line(parallel_through_point(L77_77, A78_78)))), ! [L79_79, A80_80] : (((line(L79_79) & point(A80_80)) => line(orthogonal_through_point(L79_79, A80_80))))
% 0.22/0.45
% 0.22/0.45 [7] ALPHA_AND : (! [X81_81, Y82_82] : ((equal_points(X81_81, Y82_82) <=> ~distinct_points(X81_81, Y82_82))) & ! [X83_83, Y84_84] : ((equal_lines(X83_83, Y84_84) <=> ~distinct_lines(X83_83, Y84_84))) & ! [X85_85, Y86_86] : ((parallel_lines(X85_85, Y86_86) <=> ~convergent_lines(X85_85, Y86_86))) & ! [X87_87, Y88_88] : ((incident_point_and_line(X87_87, Y88_88) <=> ~apart_point_and_line(X87_87, Y88_88))) & ! [X89_89, Y90_90] : ((orthogonal_lines(X89_89, Y90_90) <=> ~unorthogonal_lines(X89_89, Y90_90))))
% 0.22/0.45 -> [8] ! [X81_81, Y82_82] : ((equal_points(X81_81, Y82_82) <=> ~distinct_points(X81_81, Y82_82))), ! [X83_83, Y84_84] : ((equal_lines(X83_83, Y84_84) <=> ~distinct_lines(X83_83, Y84_84))), ! [X85_85, Y86_86] : ((parallel_lines(X85_85, Y86_86) <=> ~convergent_lines(X85_85, Y86_86))), ! [X87_87, Y88_88] : ((incident_point_and_line(X87_87, Y88_88) <=> ~apart_point_and_line(X87_87, Y88_88))), ! [X89_89, Y90_90] : ((orthogonal_lines(X89_89, Y90_90) <=> ~unorthogonal_lines(X89_89, Y90_90)))
% 0.22/0.45
% 0.22/0.45 [8] DELTA_NOT_FORALL : ~! [X91_91] : (~convergent_lines(X91_91, X91_91))
% 0.22/0.45 -> [9] ~~convergent_lines(skolem_X9191, skolem_X9191)
% 0.22/0.45
% 0.22/0.45 [9] ALPHA_NOT_NOT : ~~convergent_lines(skolem_X9191, skolem_X9191)
% 0.22/0.45 -> [10] convergent_lines(skolem_X9191, skolem_X9191)
% 0.22/0.45
% 0.22/0.45 [10] GAMMA_FORALL : ! [X5_5] : (~distinct_points(X5_5, X5_5))
% 0.22/0.45 -> [11] ~distinct_points(X5_0_0, X5_0_0)
% 0.22/0.45
% 0.22/0.45 [11] GAMMA_FORALL : ! [X6_6] : (~distinct_lines(X6_6, X6_6))
% 0.22/0.45 -> [12] ~distinct_lines(X6_0_1, X6_0_1)
% 0.22/0.45
% 0.22/0.45 [12] GAMMA_FORALL : ! [X7_7] : (~convergent_lines(X7_7, X7_7))
% 0.22/0.45 -> [13] ~convergent_lines(X7_0_2, X7_0_2)
% 0.22/0.45
% 0.22/0.45 [13] CLOSURE : ~convergent_lines(X7_0_2, X7_0_2)
% 0.22/0.45
% 0.22/0.45 % SZS output end Proof for theBenchmark.p
% 0.22/0.45 [0.083633s][1][Res] 1 goroutines created
% 0.22/0.45 ==== Result ====
% 0.22/0.45 [0.083689s][1][Res] VALID
% 0.22/0.45 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------