TSTP Solution File: GEO237+3 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : GEO237+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n021.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 15:18:37 EDT 2022
% Result : Theorem 0.10s 0.39s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : GEO237+3 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.07 % Command : goeland -dmt -presko -proof %s
% 0.07/0.26 % Computer : n021.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Wed Aug 31 07:04:41 EDT 2022
% 0.07/0.26 % CPUTime :
% 0.07/0.26 [DMT] DMT loaded with preskolemization
% 0.07/0.26 [EQ] equality loaded.
% 0.07/0.26 [0.000018s][1][MAIN] Problem : theBenchmark.p
% 0.07/0.26 Conjecture not found
% 0.07/0.26 Start search
% 0.07/0.27 nb_step : 1 - limit : 37
% 0.07/0.27 Launch Gotab with destructive = true
% 0.10/0.38 % SZS output start Proof for theBenchmark.p
% 0.10/0.39 [0] ALPHA_AND : ((! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9)))) & ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11)))) & ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13)))) & ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15))) & ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17))) & ! [A32_32] : (~distinct_points(A32_32, A32_32)) & ! [A33_33, B34_34, C35_35] : ((distinct_points(A33_33, B34_34) => (distinct_points(A33_33, C35_35) | distinct_points(B34_34, C35_35)))) & ! [L36_36] : (~distinct_lines(L36_36, L36_36)) & ! [L37_37, M38_38, N39_39] : ((distinct_lines(L37_37, M38_38) => (distinct_lines(L37_37, N39_39) | distinct_lines(M38_38, N39_39)))) & ! [L40_40] : (equally_directed_lines(L40_40, L40_40)) & ! [L41_41, M42_42, N43_43] : ((unequally_directed_lines(L41_41, M42_42) => (unequally_directed_lines(L41_41, N43_43) | unequally_directed_lines(M42_42, N43_43)))) & ! [L44_44, M45_45, N46_46] : (((unequally_directed_lines(L44_44, M45_45) & unequally_directed_lines(L44_44, reverse_line(M45_45))) => ((unequally_directed_lines(L44_44, N46_46) & unequally_directed_lines(L44_44, reverse_line(N46_46))) | (unequally_directed_lines(M45_45, N46_46) & unequally_directed_lines(M45_45, reverse_line(N46_46)))))) & ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48)))) & ! [L49_49, M50_50] : (((unequally_directed_lines(L49_49, M50_50) & unequally_directed_lines(L49_49, reverse_line(M50_50))) => (left_convergent_lines(L49_49, M50_50) | left_convergent_lines(L49_49, reverse_line(M50_50))))) & ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52)))) & ! [L53_53, M54_54] : (~(left_convergent_lines(L53_53, M54_54) | left_convergent_lines(L53_53, reverse_line(M54_54)))) & ! [A55_55, B56_56] : ((((point(A55_55) & point(B56_56)) & distinct_points(A55_55, B56_56)) => line(line_connecting(A55_55, B56_56)))) & ! [L57_57, M58_58] : (((((line(L57_57) & line(M58_58)) & unequally_directed_lines(L57_57, M58_58)) & unequally_directed_lines(L57_57, reverse_line(M58_58))) => point(intersection_point(L57_57, M58_58)))) & ! [L59_59, A60_60] : (((point(A60_60) & line(L59_59)) => line(parallel_through_point(L59_59, A60_60)))) & ! [L61_61] : ((line(L61_61) => line(reverse_line(L61_61)))) & ! [A62_62, B63_63] : ((distinct_points(A62_62, B63_63) => (~apart_point_and_line(A62_62, line_connecting(A62_62, B63_63)) & ~apart_point_and_line(B63_63, line_connecting(A62_62, B63_63))))) & ! [L64_64, M65_65] : (((unequally_directed_lines(L64_64, M65_65) & unequally_directed_lines(L64_64, reverse_line(M65_65))) => (~apart_point_and_line(intersection_point(L64_64, M65_65), L64_64) & ~apart_point_and_line(intersection_point(L64_64, M65_65), M65_65)))) & ! [A66_66, L67_67] : (~apart_point_and_line(A66_66, parallel_through_point(L67_67, A66_66))) & ! [L68_68] : (~distinct_lines(L68_68, reverse_line(L68_68))) & ! [A69_69, B70_70] : ((distinct_points(A69_69, B70_70) => equally_directed_lines(line_connecting(A69_69, B70_70), reverse_line(line_connecting(B70_70, A69_69))))) & ! [A71_71, L72_72] : (equally_directed_lines(parallel_through_point(L72_72, A71_71), L72_72)) & ! [A73_73, B74_74, L75_75, M76_76] : (((distinct_points(A73_73, B74_74) & distinct_lines(L75_75, M76_76)) => (((((((left_apart_point(A73_73, L75_75) | left_apart_point(B74_74, L75_75)) | left_apart_point(A73_73, M76_76)) | left_apart_point(B74_74, M76_76)) | left_apart_point(A73_73, reverse_line(L75_75))) | left_apart_point(B74_74, reverse_line(L75_75))) | left_apart_point(A73_73, reverse_line(M76_76))) | left_apart_point(B74_74, reverse_line(M76_76))))) & ! [A77_77, B78_78, L79_79] : (((distinct_points(A77_77, B78_78) & left_apart_point(A77_77, L79_79)) => (left_apart_point(B78_78, L79_79) | left_convergent_lines(line_connecting(A77_77, B78_78), L79_79)))) & ! [A80_80, B81_81, L82_82] : ((left_apart_point(A80_80, L82_82) => (distinct_points(A80_80, B81_81) | left_apart_point(B81_81, L82_82)))) & ! [A83_83, L84_84, M85_85] : (((left_apart_point(A83_83, L84_84) & unequally_directed_lines(L84_84, M85_85)) => (distinct_lines(L84_84, M85_85) | left_apart_point(A83_83, reverse_line(M85_85))))) & ! [L86_86, M87_87, N88_88] : ((left_convergent_lines(L86_86, M87_87) => (unequally_directed_lines(M87_87, N88_88) | left_convergent_lines(L86_86, N88_88))))) & ~! [A89_89, B90_90, C91_91, L92_92] : ((apart_point_and_line(C91_91, L92_92) => (divides_points(L92_92, A89_89, B90_90) => (divides_points(L92_92, A89_89, C91_91) | divides_points(L92_92, B90_90, C91_91))))))
% 0.10/0.39 -> [1] (! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9)))) & ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11)))) & ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13)))) & ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15))) & ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17))) & ! [A32_32] : (~distinct_points(A32_32, A32_32)) & ! [A33_33, B34_34, C35_35] : ((distinct_points(A33_33, B34_34) => (distinct_points(A33_33, C35_35) | distinct_points(B34_34, C35_35)))) & ! [L36_36] : (~distinct_lines(L36_36, L36_36)) & ! [L37_37, M38_38, N39_39] : ((distinct_lines(L37_37, M38_38) => (distinct_lines(L37_37, N39_39) | distinct_lines(M38_38, N39_39)))) & ! [L40_40] : (equally_directed_lines(L40_40, L40_40)) & ! [L41_41, M42_42, N43_43] : ((unequally_directed_lines(L41_41, M42_42) => (unequally_directed_lines(L41_41, N43_43) | unequally_directed_lines(M42_42, N43_43)))) & ! [L44_44, M45_45, N46_46] : (((unequally_directed_lines(L44_44, M45_45) & unequally_directed_lines(L44_44, reverse_line(M45_45))) => ((unequally_directed_lines(L44_44, N46_46) & unequally_directed_lines(L44_44, reverse_line(N46_46))) | (unequally_directed_lines(M45_45, N46_46) & unequally_directed_lines(M45_45, reverse_line(N46_46)))))) & ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48)))) & ! [L49_49, M50_50] : (((unequally_directed_lines(L49_49, M50_50) & unequally_directed_lines(L49_49, reverse_line(M50_50))) => (left_convergent_lines(L49_49, M50_50) | left_convergent_lines(L49_49, reverse_line(M50_50))))) & ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52)))) & ! [L53_53, M54_54] : (~(left_convergent_lines(L53_53, M54_54) | left_convergent_lines(L53_53, reverse_line(M54_54)))) & ! [A55_55, B56_56] : ((((point(A55_55) & point(B56_56)) & distinct_points(A55_55, B56_56)) => line(line_connecting(A55_55, B56_56)))) & ! [L57_57, M58_58] : (((((line(L57_57) & line(M58_58)) & unequally_directed_lines(L57_57, M58_58)) & unequally_directed_lines(L57_57, reverse_line(M58_58))) => point(intersection_point(L57_57, M58_58)))) & ! [L59_59, A60_60] : (((point(A60_60) & line(L59_59)) => line(parallel_through_point(L59_59, A60_60)))) & ! [L61_61] : ((line(L61_61) => line(reverse_line(L61_61)))) & ! [A62_62, B63_63] : ((distinct_points(A62_62, B63_63) => (~apart_point_and_line(A62_62, line_connecting(A62_62, B63_63)) & ~apart_point_and_line(B63_63, line_connecting(A62_62, B63_63))))) & ! [L64_64, M65_65] : (((unequally_directed_lines(L64_64, M65_65) & unequally_directed_lines(L64_64, reverse_line(M65_65))) => (~apart_point_and_line(intersection_point(L64_64, M65_65), L64_64) & ~apart_point_and_line(intersection_point(L64_64, M65_65), M65_65)))) & ! [A66_66, L67_67] : (~apart_point_and_line(A66_66, parallel_through_point(L67_67, A66_66))) & ! [L68_68] : (~distinct_lines(L68_68, reverse_line(L68_68))) & ! [A69_69, B70_70] : ((distinct_points(A69_69, B70_70) => equally_directed_lines(line_connecting(A69_69, B70_70), reverse_line(line_connecting(B70_70, A69_69))))) & ! [A71_71, L72_72] : (equally_directed_lines(parallel_through_point(L72_72, A71_71), L72_72)) & ! [A73_73, B74_74, L75_75, M76_76] : (((distinct_points(A73_73, B74_74) & distinct_lines(L75_75, M76_76)) => (((((((left_apart_point(A73_73, L75_75) | left_apart_point(B74_74, L75_75)) | left_apart_point(A73_73, M76_76)) | left_apart_point(B74_74, M76_76)) | left_apart_point(A73_73, reverse_line(L75_75))) | left_apart_point(B74_74, reverse_line(L75_75))) | left_apart_point(A73_73, reverse_line(M76_76))) | left_apart_point(B74_74, reverse_line(M76_76))))) & ! [A77_77, B78_78, L79_79] : (((distinct_points(A77_77, B78_78) & left_apart_point(A77_77, L79_79)) => (left_apart_point(B78_78, L79_79) | left_convergent_lines(line_connecting(A77_77, B78_78), L79_79)))) & ! [A80_80, B81_81, L82_82] : ((left_apart_point(A80_80, L82_82) => (distinct_points(A80_80, B81_81) | left_apart_point(B81_81, L82_82)))) & ! [A83_83, L84_84, M85_85] : (((left_apart_point(A83_83, L84_84) & unequally_directed_lines(L84_84, M85_85)) => (distinct_lines(L84_84, M85_85) | left_apart_point(A83_83, reverse_line(M85_85))))) & ! [L86_86, M87_87, N88_88] : ((left_convergent_lines(L86_86, M87_87) => (unequally_directed_lines(M87_87, N88_88) | left_convergent_lines(L86_86, N88_88))))), ~! [A89_89, B90_90, C91_91, L92_92] : ((apart_point_and_line(C91_91, L92_92) => (divides_points(L92_92, A89_89, B90_90) => (divides_points(L92_92, A89_89, C91_91) | divides_points(L92_92, B90_90, C91_91)))))
% 0.10/0.39
% 0.10/0.39 [1] ALPHA_AND : (! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9)))) & ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11)))) & ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13)))) & ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15))) & ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17))) & ! [A32_32] : (~distinct_points(A32_32, A32_32)) & ! [A33_33, B34_34, C35_35] : ((distinct_points(A33_33, B34_34) => (distinct_points(A33_33, C35_35) | distinct_points(B34_34, C35_35)))) & ! [L36_36] : (~distinct_lines(L36_36, L36_36)) & ! [L37_37, M38_38, N39_39] : ((distinct_lines(L37_37, M38_38) => (distinct_lines(L37_37, N39_39) | distinct_lines(M38_38, N39_39)))) & ! [L40_40] : (equally_directed_lines(L40_40, L40_40)) & ! [L41_41, M42_42, N43_43] : ((unequally_directed_lines(L41_41, M42_42) => (unequally_directed_lines(L41_41, N43_43) | unequally_directed_lines(M42_42, N43_43)))) & ! [L44_44, M45_45, N46_46] : (((unequally_directed_lines(L44_44, M45_45) & unequally_directed_lines(L44_44, reverse_line(M45_45))) => ((unequally_directed_lines(L44_44, N46_46) & unequally_directed_lines(L44_44, reverse_line(N46_46))) | (unequally_directed_lines(M45_45, N46_46) & unequally_directed_lines(M45_45, reverse_line(N46_46)))))) & ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48)))) & ! [L49_49, M50_50] : (((unequally_directed_lines(L49_49, M50_50) & unequally_directed_lines(L49_49, reverse_line(M50_50))) => (left_convergent_lines(L49_49, M50_50) | left_convergent_lines(L49_49, reverse_line(M50_50))))) & ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52)))) & ! [L53_53, M54_54] : (~(left_convergent_lines(L53_53, M54_54) | left_convergent_lines(L53_53, reverse_line(M54_54)))) & ! [A55_55, B56_56] : ((((point(A55_55) & point(B56_56)) & distinct_points(A55_55, B56_56)) => line(line_connecting(A55_55, B56_56)))) & ! [L57_57, M58_58] : (((((line(L57_57) & line(M58_58)) & unequally_directed_lines(L57_57, M58_58)) & unequally_directed_lines(L57_57, reverse_line(M58_58))) => point(intersection_point(L57_57, M58_58)))) & ! [L59_59, A60_60] : (((point(A60_60) & line(L59_59)) => line(parallel_through_point(L59_59, A60_60)))) & ! [L61_61] : ((line(L61_61) => line(reverse_line(L61_61)))) & ! [A62_62, B63_63] : ((distinct_points(A62_62, B63_63) => (~apart_point_and_line(A62_62, line_connecting(A62_62, B63_63)) & ~apart_point_and_line(B63_63, line_connecting(A62_62, B63_63))))) & ! [L64_64, M65_65] : (((unequally_directed_lines(L64_64, M65_65) & unequally_directed_lines(L64_64, reverse_line(M65_65))) => (~apart_point_and_line(intersection_point(L64_64, M65_65), L64_64) & ~apart_point_and_line(intersection_point(L64_64, M65_65), M65_65)))) & ! [A66_66, L67_67] : (~apart_point_and_line(A66_66, parallel_through_point(L67_67, A66_66))) & ! [L68_68] : (~distinct_lines(L68_68, reverse_line(L68_68))) & ! [A69_69, B70_70] : ((distinct_points(A69_69, B70_70) => equally_directed_lines(line_connecting(A69_69, B70_70), reverse_line(line_connecting(B70_70, A69_69))))) & ! [A71_71, L72_72] : (equally_directed_lines(parallel_through_point(L72_72, A71_71), L72_72)) & ! [A73_73, B74_74, L75_75, M76_76] : (((distinct_points(A73_73, B74_74) & distinct_lines(L75_75, M76_76)) => (((((((left_apart_point(A73_73, L75_75) | left_apart_point(B74_74, L75_75)) | left_apart_point(A73_73, M76_76)) | left_apart_point(B74_74, M76_76)) | left_apart_point(A73_73, reverse_line(L75_75))) | left_apart_point(B74_74, reverse_line(L75_75))) | left_apart_point(A73_73, reverse_line(M76_76))) | left_apart_point(B74_74, reverse_line(M76_76))))) & ! [A77_77, B78_78, L79_79] : (((distinct_points(A77_77, B78_78) & left_apart_point(A77_77, L79_79)) => (left_apart_point(B78_78, L79_79) | left_convergent_lines(line_connecting(A77_77, B78_78), L79_79)))) & ! [A80_80, B81_81, L82_82] : ((left_apart_point(A80_80, L82_82) => (distinct_points(A80_80, B81_81) | left_apart_point(B81_81, L82_82)))) & ! [A83_83, L84_84, M85_85] : (((left_apart_point(A83_83, L84_84) & unequally_directed_lines(L84_84, M85_85)) => (distinct_lines(L84_84, M85_85) | left_apart_point(A83_83, reverse_line(M85_85))))) & ! [L86_86, M87_87, N88_88] : ((left_convergent_lines(L86_86, M87_87) => (unequally_directed_lines(M87_87, N88_88) | left_convergent_lines(L86_86, N88_88)))))
% 0.10/0.39 -> [2] ! [X8_8, Y9_9] : ((unequally_directed_opposite_lines(X8_8, Y9_9) <=> unequally_directed_lines(X8_8, reverse_line(Y9_9)))), ! [X10_10, Y11_11] : ((right_apart_point(X10_10, Y11_11) <=> left_apart_point(X10_10, reverse_line(Y11_11)))), ! [X12_12, Y13_13] : ((right_convergent_lines(X12_12, Y13_13) <=> left_convergent_lines(X12_12, reverse_line(Y13_13)))), ! [X14_14, Y15_15] : ((equally_directed_lines(X14_14, Y15_15) <=> ~unequally_directed_lines(X14_14, Y15_15))), ! [X16_16, Y17_17] : ((equally_directed_opposite_lines(X16_16, Y17_17) <=> ~unequally_directed_opposite_lines(X16_16, Y17_17))), ! [A32_32] : (~distinct_points(A32_32, A32_32)), ! [A33_33, B34_34, C35_35] : ((distinct_points(A33_33, B34_34) => (distinct_points(A33_33, C35_35) | distinct_points(B34_34, C35_35)))), ! [L36_36] : (~distinct_lines(L36_36, L36_36)), ! [L37_37, M38_38, N39_39] : ((distinct_lines(L37_37, M38_38) => (distinct_lines(L37_37, N39_39) | distinct_lines(M38_38, N39_39)))), ! [L40_40] : (equally_directed_lines(L40_40, L40_40)), ! [L41_41, M42_42, N43_43] : ((unequally_directed_lines(L41_41, M42_42) => (unequally_directed_lines(L41_41, N43_43) | unequally_directed_lines(M42_42, N43_43)))), ! [L44_44, M45_45, N46_46] : (((unequally_directed_lines(L44_44, M45_45) & unequally_directed_lines(L44_44, reverse_line(M45_45))) => ((unequally_directed_lines(L44_44, N46_46) & unequally_directed_lines(L44_44, reverse_line(N46_46))) | (unequally_directed_lines(M45_45, N46_46) & unequally_directed_lines(M45_45, reverse_line(N46_46)))))), ! [L47_47, M48_48] : ((unequally_directed_lines(L47_47, M48_48) | unequally_directed_lines(L47_47, reverse_line(M48_48)))), ! [L49_49, M50_50] : (((unequally_directed_lines(L49_49, M50_50) & unequally_directed_lines(L49_49, reverse_line(M50_50))) => (left_convergent_lines(L49_49, M50_50) | left_convergent_lines(L49_49, reverse_line(M50_50))))), ! [A51_51, L52_52] : (~(left_apart_point(A51_51, L52_52) | left_apart_point(A51_51, reverse_line(L52_52)))), ! [L53_53, M54_54] : (~(left_convergent_lines(L53_53, M54_54) | left_convergent_lines(L53_53, reverse_line(M54_54)))), ! [A55_55, B56_56] : ((((point(A55_55) & point(B56_56)) & distinct_points(A55_55, B56_56)) => line(line_connecting(A55_55, B56_56)))), ! [L57_57, M58_58] : (((((line(L57_57) & line(M58_58)) & unequally_directed_lines(L57_57, M58_58)) & unequally_directed_lines(L57_57, reverse_line(M58_58))) => point(intersection_point(L57_57, M58_58)))), ! [L59_59, A60_60] : (((point(A60_60) & line(L59_59)) => line(parallel_through_point(L59_59, A60_60)))), ! [L61_61] : ((line(L61_61) => line(reverse_line(L61_61)))), ! [A62_62, B63_63] : ((distinct_points(A62_62, B63_63) => (~apart_point_and_line(A62_62, line_connecting(A62_62, B63_63)) & ~apart_point_and_line(B63_63, line_connecting(A62_62, B63_63))))), ! [L64_64, M65_65] : (((unequally_directed_lines(L64_64, M65_65) & unequally_directed_lines(L64_64, reverse_line(M65_65))) => (~apart_point_and_line(intersection_point(L64_64, M65_65), L64_64) & ~apart_point_and_line(intersection_point(L64_64, M65_65), M65_65)))), ! [A66_66, L67_67] : (~apart_point_and_line(A66_66, parallel_through_point(L67_67, A66_66))), ! [L68_68] : (~distinct_lines(L68_68, reverse_line(L68_68))), ! [A69_69, B70_70] : ((distinct_points(A69_69, B70_70) => equally_directed_lines(line_connecting(A69_69, B70_70), reverse_line(line_connecting(B70_70, A69_69))))), ! [A71_71, L72_72] : (equally_directed_lines(parallel_through_point(L72_72, A71_71), L72_72)), ! [A73_73, B74_74, L75_75, M76_76] : (((distinct_points(A73_73, B74_74) & distinct_lines(L75_75, M76_76)) => (((((((left_apart_point(A73_73, L75_75) | left_apart_point(B74_74, L75_75)) | left_apart_point(A73_73, M76_76)) | left_apart_point(B74_74, M76_76)) | left_apart_point(A73_73, reverse_line(L75_75))) | left_apart_point(B74_74, reverse_line(L75_75))) | left_apart_point(A73_73, reverse_line(M76_76))) | left_apart_point(B74_74, reverse_line(M76_76))))), ! [A77_77, B78_78, L79_79] : (((distinct_points(A77_77, B78_78) & left_apart_point(A77_77, L79_79)) => (left_apart_point(B78_78, L79_79) | left_convergent_lines(line_connecting(A77_77, B78_78), L79_79)))), ! [A80_80, B81_81, L82_82] : ((left_apart_point(A80_80, L82_82) => (distinct_points(A80_80, B81_81) | left_apart_point(B81_81, L82_82)))), ! [A83_83, L84_84, M85_85] : (((left_apart_point(A83_83, L84_84) & unequally_directed_lines(L84_84, M85_85)) => (distinct_lines(L84_84, M85_85) | left_apart_point(A83_83, reverse_line(M85_85))))), ! [L86_86, M87_87, N88_88] : ((left_convergent_lines(L86_86, M87_87) => (unequally_directed_lines(M87_87, N88_88) | left_convergent_lines(L86_86, N88_88))))
% 0.10/0.39
% 0.10/0.39 [2] DELTA_NOT_FORALL : ~! [A89_89, B90_90, C91_91, L92_92] : ((apart_point_and_line(C91_91, L92_92) => (divides_points(L92_92, A89_89, B90_90) => (divides_points(L92_92, A89_89, C91_91) | divides_points(L92_92, B90_90, C91_91)))))
% 0.10/0.39 -> [3] ~(apart_point_and_line(skolem_C9191, skolem_L9292) => (divides_points(skolem_L9292, skolem_A8989, skolem_B9090) => (divides_points(skolem_L9292, skolem_A8989, skolem_C9191) | divides_points(skolem_L9292, skolem_B9090, skolem_C9191))))
% 0.10/0.39
% 0.10/0.39 [3] ALPHA_NOT_IMPLY : ~(apart_point_and_line(skolem_C9191, skolem_L9292) => (divides_points(skolem_L9292, skolem_A8989, skolem_B9090) => (divides_points(skolem_L9292, skolem_A8989, skolem_C9191) | divides_points(skolem_L9292, skolem_B9090, skolem_C9191))))
% 0.10/0.39 -> [4] apart_point_and_line(skolem_C9191, skolem_L9292), ~(divides_points(skolem_L9292, skolem_A8989, skolem_B9090) => (divides_points(skolem_L9292, skolem_A8989, skolem_C9191) | divides_points(skolem_L9292, skolem_B9090, skolem_C9191)))
% 0.10/0.39
% 0.10/0.39 [4] Rewrite : apart_point_and_line(skolem_C9191, skolem_L9292)
% 0.10/0.39 -> [5] (left_apart_point(skolem_C9191, skolem_L9292) | right_apart_point(skolem_C9191, skolem_L9292))
% 0.10/0.39
% 0.10/0.39 [5] ALPHA_NOT_IMPLY : ~(divides_points(skolem_L9292, skolem_A8989, skolem_B9090) => (divides_points(skolem_L9292, skolem_A8989, skolem_C9191) | divides_points(skolem_L9292, skolem_B9090, skolem_C9191)))
% 0.10/0.39 -> [6] divides_points(skolem_L9292, skolem_A8989, skolem_B9090), ~(divides_points(skolem_L9292, skolem_A8989, skolem_C9191) | divides_points(skolem_L9292, skolem_B9090, skolem_C9191))
% 0.10/0.39
% 0.10/0.39 [6] Rewrite : divides_points(skolem_L9292, skolem_A8989, skolem_B9090)
% 0.10/0.39 -> [7] ((left_apart_point(skolem_A8989, skolem_L9292) & right_apart_point(skolem_B9090, skolem_L9292)) | (right_apart_point(skolem_A8989, skolem_L9292) & left_apart_point(skolem_B9090, skolem_L9292)))
% 0.10/0.39
% 0.10/0.39 [7] ALPHA_NOT_OR : ~(divides_points(skolem_L9292, skolem_A8989, skolem_C9191) | divides_points(skolem_L9292, skolem_B9090, skolem_C9191))
% 0.10/0.39 -> [8] ~divides_points(skolem_L9292, skolem_A8989, skolem_C9191), ~divides_points(skolem_L9292, skolem_B9090, skolem_C9191)
% 0.10/0.39
% 0.10/0.39 [8] Rewrite : ~divides_points(skolem_L9292, skolem_A8989, skolem_C9191)
% 0.10/0.39 -> [9] ~((left_apart_point(skolem_A8989, skolem_L9292) & right_apart_point(skolem_C9191, skolem_L9292)) | (right_apart_point(skolem_A8989, skolem_L9292) & left_apart_point(skolem_C9191, skolem_L9292)))
% 0.10/0.39
% 0.10/0.39 [9] Rewrite : ~divides_points(skolem_L9292, skolem_B9090, skolem_C9191)
% 0.10/0.39 -> [10] ~((left_apart_point(skolem_B9090, skolem_L9292) & right_apart_point(skolem_C9191, skolem_L9292)) | (right_apart_point(skolem_B9090, skolem_L9292) & left_apart_point(skolem_C9191, skolem_L9292)))
% 0.10/0.39
% 0.10/0.39 [10] ALPHA_NOT_OR : ~((left_apart_point(skolem_A8989, skolem_L9292) & right_apart_point(skolem_C9191, skolem_L9292)) | (right_apart_point(skolem_A8989, skolem_L9292) & left_apart_point(skolem_C9191, skolem_L9292)))
% 0.10/0.39 -> [11] ~(left_apart_point(skolem_A8989, skolem_L9292) & right_apart_point(skolem_C9191, skolem_L9292)), ~(right_apart_point(skolem_A8989, skolem_L9292) & left_apart_point(skolem_C9191, skolem_L9292))
% 0.10/0.39
% 0.10/0.39 [11] ALPHA_NOT_OR : ~((left_apart_point(skolem_B9090, skolem_L9292) & right_apart_point(skolem_C9191, skolem_L9292)) | (right_apart_point(skolem_B9090, skolem_L9292) & left_apart_point(skolem_C9191, skolem_L9292)))
% 0.10/0.39 -> [12] ~(left_apart_point(skolem_B9090, skolem_L9292) & right_apart_point(skolem_C9191, skolem_L9292)), ~(right_apart_point(skolem_B9090, skolem_L9292) & left_apart_point(skolem_C9191, skolem_L9292))
% 0.10/0.39
% 0.10/0.39 [12] BETA_OR : (left_apart_point(skolem_C9191, skolem_L9292) | right_apart_point(skolem_C9191, skolem_L9292))
% 0.10/0.39 -> [13] left_apart_point(skolem_C9191, skolem_L9292)
% 0.10/0.39 -> [14] right_apart_point(skolem_C9191, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [14] BETA_OR : ((left_apart_point(skolem_A8989, skolem_L9292) & right_apart_point(skolem_B9090, skolem_L9292)) | (right_apart_point(skolem_A8989, skolem_L9292) & left_apart_point(skolem_B9090, skolem_L9292)))
% 0.10/0.39 -> [17] (left_apart_point(skolem_A8989, skolem_L9292) & right_apart_point(skolem_B9090, skolem_L9292))
% 0.10/0.39 -> [18] (right_apart_point(skolem_A8989, skolem_L9292) & left_apart_point(skolem_B9090, skolem_L9292))
% 0.10/0.39
% 0.10/0.39 [17] ALPHA_AND : (left_apart_point(skolem_A8989, skolem_L9292) & right_apart_point(skolem_B9090, skolem_L9292))
% 0.10/0.39 -> [21] left_apart_point(skolem_A8989, skolem_L9292), right_apart_point(skolem_B9090, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [21] BETA_NOT_AND : ~(left_apart_point(skolem_A8989, skolem_L9292) & right_apart_point(skolem_C9191, skolem_L9292))
% 0.10/0.39 -> [27] ~left_apart_point(skolem_A8989, skolem_L9292)
% 0.10/0.39 -> [28] ~right_apart_point(skolem_C9191, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [27] CLOSURE : ~left_apart_point(skolem_A8989, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [28] CLOSURE : ~right_apart_point(skolem_C9191, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [18] ALPHA_AND : (right_apart_point(skolem_A8989, skolem_L9292) & left_apart_point(skolem_B9090, skolem_L9292))
% 0.10/0.39 -> [22] right_apart_point(skolem_A8989, skolem_L9292), left_apart_point(skolem_B9090, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [22] BETA_NOT_AND : ~(left_apart_point(skolem_A8989, skolem_L9292) & right_apart_point(skolem_C9191, skolem_L9292))
% 0.10/0.39 -> [29] ~left_apart_point(skolem_A8989, skolem_L9292)
% 0.10/0.39 -> [30] ~right_apart_point(skolem_C9191, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [30] CLOSURE : ~right_apart_point(skolem_C9191, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [29] BETA_NOT_AND : ~(right_apart_point(skolem_A8989, skolem_L9292) & left_apart_point(skolem_C9191, skolem_L9292))
% 0.10/0.39 -> [37] ~right_apart_point(skolem_A8989, skolem_L9292)
% 0.10/0.39 -> [38] ~left_apart_point(skolem_C9191, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [37] CLOSURE : ~right_apart_point(skolem_A8989, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [38] BETA_NOT_AND : ~(left_apart_point(skolem_B9090, skolem_L9292) & right_apart_point(skolem_C9191, skolem_L9292))
% 0.10/0.39 -> [43] ~left_apart_point(skolem_B9090, skolem_L9292)
% 0.10/0.39 -> [44] ~right_apart_point(skolem_C9191, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [43] CLOSURE : ~left_apart_point(skolem_B9090, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [44] CLOSURE : ~right_apart_point(skolem_C9191, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [13] BETA_OR : ((left_apart_point(skolem_A8989, skolem_L9292) & right_apart_point(skolem_B9090, skolem_L9292)) | (right_apart_point(skolem_A8989, skolem_L9292) & left_apart_point(skolem_B9090, skolem_L9292)))
% 0.10/0.39 -> [15] (left_apart_point(skolem_A8989, skolem_L9292) & right_apart_point(skolem_B9090, skolem_L9292))
% 0.10/0.39 -> [16] (right_apart_point(skolem_A8989, skolem_L9292) & left_apart_point(skolem_B9090, skolem_L9292))
% 0.10/0.39
% 0.10/0.39 [16] ALPHA_AND : (right_apart_point(skolem_A8989, skolem_L9292) & left_apart_point(skolem_B9090, skolem_L9292))
% 0.10/0.39 -> [20] right_apart_point(skolem_A8989, skolem_L9292), left_apart_point(skolem_B9090, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [20] BETA_NOT_AND : ~(left_apart_point(skolem_A8989, skolem_L9292) & right_apart_point(skolem_C9191, skolem_L9292))
% 0.10/0.39 -> [23] ~left_apart_point(skolem_A8989, skolem_L9292)
% 0.10/0.39 -> [24] ~right_apart_point(skolem_C9191, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [23] BETA_NOT_AND : ~(right_apart_point(skolem_A8989, skolem_L9292) & left_apart_point(skolem_C9191, skolem_L9292))
% 0.10/0.39 -> [31] ~right_apart_point(skolem_A8989, skolem_L9292)
% 0.10/0.39 -> [32] ~left_apart_point(skolem_C9191, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [31] CLOSURE : ~right_apart_point(skolem_A8989, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [32] CLOSURE : ~left_apart_point(skolem_C9191, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [24] BETA_NOT_AND : ~(right_apart_point(skolem_A8989, skolem_L9292) & left_apart_point(skolem_C9191, skolem_L9292))
% 0.10/0.39 -> [33] ~right_apart_point(skolem_A8989, skolem_L9292)
% 0.10/0.39 -> [34] ~left_apart_point(skolem_C9191, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [33] CLOSURE : ~right_apart_point(skolem_A8989, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [34] CLOSURE : ~left_apart_point(skolem_C9191, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [15] ALPHA_AND : (left_apart_point(skolem_A8989, skolem_L9292) & right_apart_point(skolem_B9090, skolem_L9292))
% 0.10/0.39 -> [19] left_apart_point(skolem_A8989, skolem_L9292), right_apart_point(skolem_B9090, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [19] BETA_NOT_AND : ~(left_apart_point(skolem_A8989, skolem_L9292) & right_apart_point(skolem_C9191, skolem_L9292))
% 0.10/0.39 -> [25] ~left_apart_point(skolem_A8989, skolem_L9292)
% 0.10/0.39 -> [26] ~right_apart_point(skolem_C9191, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [25] CLOSURE : ~left_apart_point(skolem_A8989, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [26] BETA_NOT_AND : ~(right_apart_point(skolem_A8989, skolem_L9292) & left_apart_point(skolem_C9191, skolem_L9292))
% 0.10/0.39 -> [35] ~right_apart_point(skolem_A8989, skolem_L9292)
% 0.10/0.39 -> [36] ~left_apart_point(skolem_C9191, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [36] CLOSURE : ~left_apart_point(skolem_C9191, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [35] BETA_NOT_AND : ~(left_apart_point(skolem_B9090, skolem_L9292) & right_apart_point(skolem_C9191, skolem_L9292))
% 0.10/0.39 -> [39] ~left_apart_point(skolem_B9090, skolem_L9292)
% 0.10/0.39 -> [40] ~right_apart_point(skolem_C9191, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [40] BETA_NOT_AND : ~(right_apart_point(skolem_B9090, skolem_L9292) & left_apart_point(skolem_C9191, skolem_L9292))
% 0.10/0.39 -> [41] ~right_apart_point(skolem_B9090, skolem_L9292)
% 0.10/0.39 -> [42] ~left_apart_point(skolem_C9191, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [41] CLOSURE : ~right_apart_point(skolem_B9090, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [42] CLOSURE : ~left_apart_point(skolem_C9191, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [39] BETA_NOT_AND : ~(right_apart_point(skolem_B9090, skolem_L9292) & left_apart_point(skolem_C9191, skolem_L9292))
% 0.10/0.39 -> [45] ~right_apart_point(skolem_B9090, skolem_L9292)
% 0.10/0.39 -> [46] ~left_apart_point(skolem_C9191, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [45] CLOSURE : ~right_apart_point(skolem_B9090, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 [46] CLOSURE : ~left_apart_point(skolem_C9191, skolem_L9292)
% 0.10/0.39
% 0.10/0.39 % SZS output end Proof for theBenchmark.p
% 0.10/0.39 [0.128532s][1][Res] 260 goroutines created
% 0.10/0.39 ==== Result ====
% 0.10/0.39 [0.128567s][1][Res] VALID
% 0.10/0.39 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------