TSTP Solution File: NUM484+3 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : NUM484+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n010.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 : Sun Sep 18 10:19:11 EDT 2022
% Result : Theorem 0.18s 0.46s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM484+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : goeland -dmt -presko -proof %s
% 0.11/0.32 % Computer : n010.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
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Sep 2 10:51:58 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 [DMT] DMT loaded with preskolemization
% 0.11/0.33 [EQ] equality loaded.
% 0.11/0.33 [0.000036s][1][MAIN] Problem : theBenchmark.p
% 0.11/0.34 Start search
% 0.11/0.35 nb_step : 1 - limit : 54
% 0.11/0.35 Launch Gotab with destructive = true
% 0.18/0.45 % SZS output start Proof for theBenchmark.p
% 0.18/0.46 [0] ALPHA_AND : (! [W04_4] : ((aNaturalNumber0(W04_4) => $true)) & aNaturalNumber0(sz00) & (aNaturalNumber0(sz10) & ~=(sz10, sz00)) & ! [W05_5, W16_6] : (((aNaturalNumber0(W05_5) & aNaturalNumber0(W16_6)) => aNaturalNumber0(sdtpldt0(W05_5, W16_6)))) & ! [W07_7, W18_8] : (((aNaturalNumber0(W07_7) & aNaturalNumber0(W18_8)) => aNaturalNumber0(sdtasdt0(W07_7, W18_8)))) & ! [W09_9, W110_10] : (((aNaturalNumber0(W09_9) & aNaturalNumber0(W110_10)) => =(sdtpldt0(W09_9, W110_10), sdtpldt0(W110_10, W09_9)))) & ! [W011_11, W112_12, W213_13] : ((((aNaturalNumber0(W011_11) & aNaturalNumber0(W112_12)) & aNaturalNumber0(W213_13)) => =(sdtpldt0(sdtpldt0(W011_11, W112_12), W213_13), sdtpldt0(W011_11, sdtpldt0(W112_12, W213_13))))) & ! [W014_14] : ((aNaturalNumber0(W014_14) => (=(sdtpldt0(W014_14, sz00), W014_14) & =(W014_14, sdtpldt0(sz00, W014_14))))) & ! [W015_15, W116_16] : (((aNaturalNumber0(W015_15) & aNaturalNumber0(W116_16)) => =(sdtasdt0(W015_15, W116_16), sdtasdt0(W116_16, W015_15)))) & ! [W017_17, W118_18, W219_19] : ((((aNaturalNumber0(W017_17) & aNaturalNumber0(W118_18)) & aNaturalNumber0(W219_19)) => =(sdtasdt0(sdtasdt0(W017_17, W118_18), W219_19), sdtasdt0(W017_17, sdtasdt0(W118_18, W219_19))))) & ! [W020_20] : ((aNaturalNumber0(W020_20) => (=(sdtasdt0(W020_20, sz10), W020_20) & =(W020_20, sdtasdt0(sz10, W020_20))))) & ! [W021_21] : ((aNaturalNumber0(W021_21) => (=(sdtasdt0(W021_21, sz00), sz00) & =(sz00, sdtasdt0(sz00, W021_21))))) & ! [W022_22, W123_23, W224_24] : ((((aNaturalNumber0(W022_22) & aNaturalNumber0(W123_23)) & aNaturalNumber0(W224_24)) => (=(sdtasdt0(W022_22, sdtpldt0(W123_23, W224_24)), sdtpldt0(sdtasdt0(W022_22, W123_23), sdtasdt0(W022_22, W224_24))) & =(sdtasdt0(sdtpldt0(W123_23, W224_24), W022_22), sdtpldt0(sdtasdt0(W123_23, W022_22), sdtasdt0(W224_24, W022_22)))))) & ! [W025_25, W126_26, W227_27] : ((((aNaturalNumber0(W025_25) & aNaturalNumber0(W126_26)) & aNaturalNumber0(W227_27)) => ((=(sdtpldt0(W025_25, W126_26), sdtpldt0(W025_25, W227_27)) | =(sdtpldt0(W126_26, W025_25), sdtpldt0(W227_27, W025_25))) => =(W126_26, W227_27)))) & ! [W028_28] : ((aNaturalNumber0(W028_28) => (~=(W028_28, sz00) => ! [W129_29, W230_30] : (((aNaturalNumber0(W129_29) & aNaturalNumber0(W230_30)) => ((=(sdtasdt0(W028_28, W129_29), sdtasdt0(W028_28, W230_30)) | =(sdtasdt0(W129_29, W028_28), sdtasdt0(W230_30, W028_28))) => =(W129_29, W230_30))))))) & ! [W031_31, W132_32] : (((aNaturalNumber0(W031_31) & aNaturalNumber0(W132_32)) => (=(sdtpldt0(W031_31, W132_32), sz00) => (=(W031_31, sz00) & =(W132_32, sz00))))) & ! [W033_33, W134_34] : (((aNaturalNumber0(W033_33) & aNaturalNumber0(W134_34)) => (=(sdtasdt0(W033_33, W134_34), sz00) => (=(W033_33, sz00) | =(W134_34, sz00))))) & ! [W035_35, W136_36] : (((aNaturalNumber0(W035_35) & aNaturalNumber0(W136_36)) => (sdtlseqdt0(W035_35, W136_36) <=> ? [W237_37] : ((aNaturalNumber0(W237_37) & =(sdtpldt0(W035_35, W237_37), W136_36)))))) & ! [W038_38, W139_39] : (((aNaturalNumber0(W038_38) & aNaturalNumber0(W139_39)) => (sdtlseqdt0(W038_38, W139_39) => ! [W240_40] : ((=(W240_40, sdtmndt0(W139_39, W038_38)) <=> (aNaturalNumber0(W240_40) & =(sdtpldt0(W038_38, W240_40), W139_39))))))) & ! [W041_41] : ((aNaturalNumber0(W041_41) => sdtlseqdt0(W041_41, W041_41))) & ! [W042_42, W143_43] : (((aNaturalNumber0(W042_42) & aNaturalNumber0(W143_43)) => ((sdtlseqdt0(W042_42, W143_43) & sdtlseqdt0(W143_43, W042_42)) => =(W042_42, W143_43)))) & ! [W044_44, W145_45, W246_46] : ((((aNaturalNumber0(W044_44) & aNaturalNumber0(W145_45)) & aNaturalNumber0(W246_46)) => ((sdtlseqdt0(W044_44, W145_45) & sdtlseqdt0(W145_45, W246_46)) => sdtlseqdt0(W044_44, W246_46)))) & ! [W047_47, W148_48] : (((aNaturalNumber0(W047_47) & aNaturalNumber0(W148_48)) => (sdtlseqdt0(W047_47, W148_48) | (~=(W148_48, W047_47) & sdtlseqdt0(W148_48, W047_47))))) & ! [W049_49, W150_50] : (((aNaturalNumber0(W049_49) & aNaturalNumber0(W150_50)) => ((~=(W049_49, W150_50) & sdtlseqdt0(W049_49, W150_50)) => ! [W251_51] : ((aNaturalNumber0(W251_51) => (((~=(sdtpldt0(W251_51, W049_49), sdtpldt0(W251_51, W150_50)) & sdtlseqdt0(sdtpldt0(W251_51, W049_49), sdtpldt0(W251_51, W150_50))) & ~=(sdtpldt0(W049_49, W251_51), sdtpldt0(W150_50, W251_51))) & sdtlseqdt0(sdtpldt0(W049_49, W251_51), sdtpldt0(W150_50, W251_51)))))))) & ! [W052_52, W153_53, W254_54] : ((((aNaturalNumber0(W052_52) & aNaturalNumber0(W153_53)) & aNaturalNumber0(W254_54)) => (((~=(W052_52, sz00) & ~=(W153_53, W254_54)) & sdtlseqdt0(W153_53, W254_54)) => (((~=(sdtasdt0(W052_52, W153_53), sdtasdt0(W052_52, W254_54)) & sdtlseqdt0(sdtasdt0(W052_52, W153_53), sdtasdt0(W052_52, W254_54))) & ~=(sdtasdt0(W153_53, W052_52), sdtasdt0(W254_54, W052_52))) & sdtlseqdt0(sdtasdt0(W153_53, W052_52), sdtasdt0(W254_54, W052_52)))))) & ! [W055_55] : ((aNaturalNumber0(W055_55) => ((=(W055_55, sz00) | =(W055_55, sz10)) | (~=(sz10, W055_55) & sdtlseqdt0(sz10, W055_55))))) & ! [W056_56, W157_57] : (((aNaturalNumber0(W056_56) & aNaturalNumber0(W157_57)) => (~=(W056_56, sz00) => sdtlseqdt0(W157_57, sdtasdt0(W157_57, W056_56))))) & ! [W058_58, W159_59] : (((aNaturalNumber0(W058_58) & aNaturalNumber0(W159_59)) => (iLess0(W058_58, W159_59) => $true))) & ! [W060_60, W161_61] : (((aNaturalNumber0(W060_60) & aNaturalNumber0(W161_61)) => ((~=(W060_60, W161_61) & sdtlseqdt0(W060_60, W161_61)) => iLess0(W060_60, W161_61)))) & ! [W062_62, W163_63] : (((aNaturalNumber0(W062_62) & aNaturalNumber0(W163_63)) => (doDivides0(W062_62, W163_63) <=> ? [W264_64] : ((aNaturalNumber0(W264_64) & =(W163_63, sdtasdt0(W062_62, W264_64))))))) & ! [W065_65, W166_66] : (((aNaturalNumber0(W065_65) & aNaturalNumber0(W166_66)) => ((~=(W065_65, sz00) & doDivides0(W065_65, W166_66)) => ! [W267_67] : ((=(W267_67, sdtsldt0(W166_66, W065_65)) <=> (aNaturalNumber0(W267_67) & =(W166_66, sdtasdt0(W065_65, W267_67)))))))) & ! [W068_68, W169_69, W270_70] : ((((aNaturalNumber0(W068_68) & aNaturalNumber0(W169_69)) & aNaturalNumber0(W270_70)) => ((doDivides0(W068_68, W169_69) & doDivides0(W169_69, W270_70)) => doDivides0(W068_68, W270_70)))) & ! [W071_71, W172_72, W273_73] : ((((aNaturalNumber0(W071_71) & aNaturalNumber0(W172_72)) & aNaturalNumber0(W273_73)) => ((doDivides0(W071_71, W172_72) & doDivides0(W071_71, W273_73)) => doDivides0(W071_71, sdtpldt0(W172_72, W273_73))))) & ! [W074_74, W175_75, W276_76] : ((((aNaturalNumber0(W074_74) & aNaturalNumber0(W175_75)) & aNaturalNumber0(W276_76)) => ((doDivides0(W074_74, W175_75) & doDivides0(W074_74, sdtpldt0(W175_75, W276_76))) => doDivides0(W074_74, W276_76)))) & ! [W077_77, W178_78] : (((aNaturalNumber0(W077_77) & aNaturalNumber0(W178_78)) => ((doDivides0(W077_77, W178_78) & ~=(W178_78, sz00)) => sdtlseqdt0(W077_77, W178_78)))) & ! [W079_79, W180_80] : (((aNaturalNumber0(W079_79) & aNaturalNumber0(W180_80)) => ((~=(W079_79, sz00) & doDivides0(W079_79, W180_80)) => ! [W281_81] : ((aNaturalNumber0(W281_81) => =(sdtasdt0(W281_81, sdtsldt0(W180_80, W079_79)), sdtsldt0(sdtasdt0(W281_81, W180_80), W079_79))))))) & ! [W082_82] : ((aNaturalNumber0(W082_82) => (isPrime0(W082_82) <=> ((~=(W082_82, sz00) & ~=(W082_82, sz10)) & ! [W183_83] : (((aNaturalNumber0(W183_83) & doDivides0(W183_83, W082_82)) => (=(W183_83, sz10) | =(W183_83, W082_82)))))))) & aNaturalNumber0(xk) & ! [W084_84] : ((((aNaturalNumber0(W084_84) & ~=(W084_84, sz00)) & ~=(W084_84, sz10)) => (iLess0(W084_84, xk) => ? [W185_85] : (((((((aNaturalNumber0(W185_85) & ? [W286_86] : ((aNaturalNumber0(W286_86) & =(W084_84, sdtasdt0(W185_85, W286_86))))) & doDivides0(W185_85, W084_84)) & ~=(W185_85, sz00)) & ~=(W185_85, sz10)) & ! [W287_87] : (((aNaturalNumber0(W287_87) & (? [W388_88] : ((aNaturalNumber0(W388_88) & =(W185_85, sdtasdt0(W287_87, W388_88)))) | doDivides0(W287_87, W185_85))) => (=(W287_87, sz10) | =(W287_87, W185_85))))) & isPrime0(W185_85)))))) & (~=(xk, sz00) & ~=(xk, sz10)) & ~(! [W089_89] : ((((aNaturalNumber0(W089_89) & ? [W190_90] : ((aNaturalNumber0(W190_90) & =(xk, sdtasdt0(W089_89, W190_90))))) & doDivides0(W089_89, xk)) => (=(W089_89, sz10) | =(W089_89, xk)))) | isPrime0(xk)) & ~~$false & ~? [W091_91] : (((aNaturalNumber0(W091_91) & (? [W192_92] : ((aNaturalNumber0(W192_92) & =(xk, sdtasdt0(W091_91, W192_92)))) | doDivides0(W091_91, xk))) & (((~=(W091_91, sz00) & ~=(W091_91, sz10)) & ! [W193_93] : ((((aNaturalNumber0(W193_93) & ? [W294_94] : ((aNaturalNumber0(W294_94) & =(W091_91, sdtasdt0(W193_93, W294_94))))) & doDivides0(W193_93, W091_91)) => (=(W193_93, sz10) | =(W193_93, W091_91))))) | isPrime0(W091_91)))))
% 0.18/0.46 -> [1] ! [W04_4] : ((aNaturalNumber0(W04_4) => $true)), aNaturalNumber0(sz00), (aNaturalNumber0(sz10) & ~=(sz10, sz00)), ! [W05_5, W16_6] : (((aNaturalNumber0(W05_5) & aNaturalNumber0(W16_6)) => aNaturalNumber0(sdtpldt0(W05_5, W16_6)))), ! [W07_7, W18_8] : (((aNaturalNumber0(W07_7) & aNaturalNumber0(W18_8)) => aNaturalNumber0(sdtasdt0(W07_7, W18_8)))), ! [W09_9, W110_10] : (((aNaturalNumber0(W09_9) & aNaturalNumber0(W110_10)) => =(sdtpldt0(W09_9, W110_10), sdtpldt0(W110_10, W09_9)))), ! [W011_11, W112_12, W213_13] : ((((aNaturalNumber0(W011_11) & aNaturalNumber0(W112_12)) & aNaturalNumber0(W213_13)) => =(sdtpldt0(sdtpldt0(W011_11, W112_12), W213_13), sdtpldt0(W011_11, sdtpldt0(W112_12, W213_13))))), ! [W014_14] : ((aNaturalNumber0(W014_14) => (=(sdtpldt0(W014_14, sz00), W014_14) & =(W014_14, sdtpldt0(sz00, W014_14))))), ! [W015_15, W116_16] : (((aNaturalNumber0(W015_15) & aNaturalNumber0(W116_16)) => =(sdtasdt0(W015_15, W116_16), sdtasdt0(W116_16, W015_15)))), ! [W017_17, W118_18, W219_19] : ((((aNaturalNumber0(W017_17) & aNaturalNumber0(W118_18)) & aNaturalNumber0(W219_19)) => =(sdtasdt0(sdtasdt0(W017_17, W118_18), W219_19), sdtasdt0(W017_17, sdtasdt0(W118_18, W219_19))))), ! [W020_20] : ((aNaturalNumber0(W020_20) => (=(sdtasdt0(W020_20, sz10), W020_20) & =(W020_20, sdtasdt0(sz10, W020_20))))), ! [W021_21] : ((aNaturalNumber0(W021_21) => (=(sdtasdt0(W021_21, sz00), sz00) & =(sz00, sdtasdt0(sz00, W021_21))))), ! [W022_22, W123_23, W224_24] : ((((aNaturalNumber0(W022_22) & aNaturalNumber0(W123_23)) & aNaturalNumber0(W224_24)) => (=(sdtasdt0(W022_22, sdtpldt0(W123_23, W224_24)), sdtpldt0(sdtasdt0(W022_22, W123_23), sdtasdt0(W022_22, W224_24))) & =(sdtasdt0(sdtpldt0(W123_23, W224_24), W022_22), sdtpldt0(sdtasdt0(W123_23, W022_22), sdtasdt0(W224_24, W022_22)))))), ! [W025_25, W126_26, W227_27] : ((((aNaturalNumber0(W025_25) & aNaturalNumber0(W126_26)) & aNaturalNumber0(W227_27)) => ((=(sdtpldt0(W025_25, W126_26), sdtpldt0(W025_25, W227_27)) | =(sdtpldt0(W126_26, W025_25), sdtpldt0(W227_27, W025_25))) => =(W126_26, W227_27)))), ! [W028_28] : ((aNaturalNumber0(W028_28) => (~=(W028_28, sz00) => ! [W129_29, W230_30] : (((aNaturalNumber0(W129_29) & aNaturalNumber0(W230_30)) => ((=(sdtasdt0(W028_28, W129_29), sdtasdt0(W028_28, W230_30)) | =(sdtasdt0(W129_29, W028_28), sdtasdt0(W230_30, W028_28))) => =(W129_29, W230_30))))))), ! [W031_31, W132_32] : (((aNaturalNumber0(W031_31) & aNaturalNumber0(W132_32)) => (=(sdtpldt0(W031_31, W132_32), sz00) => (=(W031_31, sz00) & =(W132_32, sz00))))), ! [W033_33, W134_34] : (((aNaturalNumber0(W033_33) & aNaturalNumber0(W134_34)) => (=(sdtasdt0(W033_33, W134_34), sz00) => (=(W033_33, sz00) | =(W134_34, sz00))))), ! [W035_35, W136_36] : (((aNaturalNumber0(W035_35) & aNaturalNumber0(W136_36)) => (sdtlseqdt0(W035_35, W136_36) <=> ? [W237_37] : ((aNaturalNumber0(W237_37) & =(sdtpldt0(W035_35, W237_37), W136_36)))))), ! [W038_38, W139_39] : (((aNaturalNumber0(W038_38) & aNaturalNumber0(W139_39)) => (sdtlseqdt0(W038_38, W139_39) => ! [W240_40] : ((=(W240_40, sdtmndt0(W139_39, W038_38)) <=> (aNaturalNumber0(W240_40) & =(sdtpldt0(W038_38, W240_40), W139_39))))))), ! [W041_41] : ((aNaturalNumber0(W041_41) => sdtlseqdt0(W041_41, W041_41))), ! [W042_42, W143_43] : (((aNaturalNumber0(W042_42) & aNaturalNumber0(W143_43)) => ((sdtlseqdt0(W042_42, W143_43) & sdtlseqdt0(W143_43, W042_42)) => =(W042_42, W143_43)))), ! [W044_44, W145_45, W246_46] : ((((aNaturalNumber0(W044_44) & aNaturalNumber0(W145_45)) & aNaturalNumber0(W246_46)) => ((sdtlseqdt0(W044_44, W145_45) & sdtlseqdt0(W145_45, W246_46)) => sdtlseqdt0(W044_44, W246_46)))), ! [W047_47, W148_48] : (((aNaturalNumber0(W047_47) & aNaturalNumber0(W148_48)) => (sdtlseqdt0(W047_47, W148_48) | (~=(W148_48, W047_47) & sdtlseqdt0(W148_48, W047_47))))), ! [W049_49, W150_50] : (((aNaturalNumber0(W049_49) & aNaturalNumber0(W150_50)) => ((~=(W049_49, W150_50) & sdtlseqdt0(W049_49, W150_50)) => ! [W251_51] : ((aNaturalNumber0(W251_51) => (((~=(sdtpldt0(W251_51, W049_49), sdtpldt0(W251_51, W150_50)) & sdtlseqdt0(sdtpldt0(W251_51, W049_49), sdtpldt0(W251_51, W150_50))) & ~=(sdtpldt0(W049_49, W251_51), sdtpldt0(W150_50, W251_51))) & sdtlseqdt0(sdtpldt0(W049_49, W251_51), sdtpldt0(W150_50, W251_51)))))))), ! [W052_52, W153_53, W254_54] : ((((aNaturalNumber0(W052_52) & aNaturalNumber0(W153_53)) & aNaturalNumber0(W254_54)) => (((~=(W052_52, sz00) & ~=(W153_53, W254_54)) & sdtlseqdt0(W153_53, W254_54)) => (((~=(sdtasdt0(W052_52, W153_53), sdtasdt0(W052_52, W254_54)) & sdtlseqdt0(sdtasdt0(W052_52, W153_53), sdtasdt0(W052_52, W254_54))) & ~=(sdtasdt0(W153_53, W052_52), sdtasdt0(W254_54, W052_52))) & sdtlseqdt0(sdtasdt0(W153_53, W052_52), sdtasdt0(W254_54, W052_52)))))), ! [W055_55] : ((aNaturalNumber0(W055_55) => ((=(W055_55, sz00) | =(W055_55, sz10)) | (~=(sz10, W055_55) & sdtlseqdt0(sz10, W055_55))))), ! [W056_56, W157_57] : (((aNaturalNumber0(W056_56) & aNaturalNumber0(W157_57)) => (~=(W056_56, sz00) => sdtlseqdt0(W157_57, sdtasdt0(W157_57, W056_56))))), ! [W058_58, W159_59] : (((aNaturalNumber0(W058_58) & aNaturalNumber0(W159_59)) => (iLess0(W058_58, W159_59) => $true))), ! [W060_60, W161_61] : (((aNaturalNumber0(W060_60) & aNaturalNumber0(W161_61)) => ((~=(W060_60, W161_61) & sdtlseqdt0(W060_60, W161_61)) => iLess0(W060_60, W161_61)))), ! [W062_62, W163_63] : (((aNaturalNumber0(W062_62) & aNaturalNumber0(W163_63)) => (doDivides0(W062_62, W163_63) <=> ? [W264_64] : ((aNaturalNumber0(W264_64) & =(W163_63, sdtasdt0(W062_62, W264_64))))))), ! [W065_65, W166_66] : (((aNaturalNumber0(W065_65) & aNaturalNumber0(W166_66)) => ((~=(W065_65, sz00) & doDivides0(W065_65, W166_66)) => ! [W267_67] : ((=(W267_67, sdtsldt0(W166_66, W065_65)) <=> (aNaturalNumber0(W267_67) & =(W166_66, sdtasdt0(W065_65, W267_67)))))))), ! [W068_68, W169_69, W270_70] : ((((aNaturalNumber0(W068_68) & aNaturalNumber0(W169_69)) & aNaturalNumber0(W270_70)) => ((doDivides0(W068_68, W169_69) & doDivides0(W169_69, W270_70)) => doDivides0(W068_68, W270_70)))), ! [W071_71, W172_72, W273_73] : ((((aNaturalNumber0(W071_71) & aNaturalNumber0(W172_72)) & aNaturalNumber0(W273_73)) => ((doDivides0(W071_71, W172_72) & doDivides0(W071_71, W273_73)) => doDivides0(W071_71, sdtpldt0(W172_72, W273_73))))), ! [W074_74, W175_75, W276_76] : ((((aNaturalNumber0(W074_74) & aNaturalNumber0(W175_75)) & aNaturalNumber0(W276_76)) => ((doDivides0(W074_74, W175_75) & doDivides0(W074_74, sdtpldt0(W175_75, W276_76))) => doDivides0(W074_74, W276_76)))), ! [W077_77, W178_78] : (((aNaturalNumber0(W077_77) & aNaturalNumber0(W178_78)) => ((doDivides0(W077_77, W178_78) & ~=(W178_78, sz00)) => sdtlseqdt0(W077_77, W178_78)))), ! [W079_79, W180_80] : (((aNaturalNumber0(W079_79) & aNaturalNumber0(W180_80)) => ((~=(W079_79, sz00) & doDivides0(W079_79, W180_80)) => ! [W281_81] : ((aNaturalNumber0(W281_81) => =(sdtasdt0(W281_81, sdtsldt0(W180_80, W079_79)), sdtsldt0(sdtasdt0(W281_81, W180_80), W079_79))))))), ! [W082_82] : ((aNaturalNumber0(W082_82) => (isPrime0(W082_82) <=> ((~=(W082_82, sz00) & ~=(W082_82, sz10)) & ! [W183_83] : (((aNaturalNumber0(W183_83) & doDivides0(W183_83, W082_82)) => (=(W183_83, sz10) | =(W183_83, W082_82)))))))), aNaturalNumber0(xk), ! [W084_84] : ((((aNaturalNumber0(W084_84) & ~=(W084_84, sz00)) & ~=(W084_84, sz10)) => (iLess0(W084_84, xk) => ? [W185_85] : (((((((aNaturalNumber0(W185_85) & ? [W286_86] : ((aNaturalNumber0(W286_86) & =(W084_84, sdtasdt0(W185_85, W286_86))))) & doDivides0(W185_85, W084_84)) & ~=(W185_85, sz00)) & ~=(W185_85, sz10)) & ! [W287_87] : (((aNaturalNumber0(W287_87) & (? [W388_88] : ((aNaturalNumber0(W388_88) & =(W185_85, sdtasdt0(W287_87, W388_88)))) | doDivides0(W287_87, W185_85))) => (=(W287_87, sz10) | =(W287_87, W185_85))))) & isPrime0(W185_85)))))), (~=(xk, sz00) & ~=(xk, sz10)), ~(! [W089_89] : ((((aNaturalNumber0(W089_89) & ? [W190_90] : ((aNaturalNumber0(W190_90) & =(xk, sdtasdt0(W089_89, W190_90))))) & doDivides0(W089_89, xk)) => (=(W089_89, sz10) | =(W089_89, xk)))) | isPrime0(xk)), ~~$false, ~? [W091_91] : (((aNaturalNumber0(W091_91) & (? [W192_92] : ((aNaturalNumber0(W192_92) & =(xk, sdtasdt0(W091_91, W192_92)))) | doDivides0(W091_91, xk))) & (((~=(W091_91, sz00) & ~=(W091_91, sz10)) & ! [W193_93] : ((((aNaturalNumber0(W193_93) & ? [W294_94] : ((aNaturalNumber0(W294_94) & =(W091_91, sdtasdt0(W193_93, W294_94))))) & doDivides0(W193_93, W091_91)) => (=(W193_93, sz10) | =(W193_93, W091_91))))) | isPrime0(W091_91))))
% 0.18/0.46
% 0.18/0.46 [1] ALPHA_AND : (aNaturalNumber0(sz10) & ~=(sz10, sz00))
% 0.18/0.46 -> [2] aNaturalNumber0(sz10), ~=(sz10, sz00)
% 0.18/0.46
% 0.18/0.46 [2] ALPHA_AND : (~=(xk, sz00) & ~=(xk, sz10))
% 0.18/0.46 -> [3] ~=(xk, sz00), ~=(xk, sz10)
% 0.18/0.46
% 0.18/0.46 [3] ALPHA_NOT_OR : ~(! [W089_89] : ((((aNaturalNumber0(W089_89) & ? [W190_90] : ((aNaturalNumber0(W190_90) & =(xk, sdtasdt0(W089_89, W190_90))))) & doDivides0(W089_89, xk)) => (=(W089_89, sz10) | =(W089_89, xk)))) | isPrime0(xk))
% 0.18/0.46 -> [4] ~! [W089_89] : ((((aNaturalNumber0(W089_89) & ? [W190_90] : ((aNaturalNumber0(W190_90) & =(xk, sdtasdt0(W089_89, W190_90))))) & doDivides0(W089_89, xk)) => (=(W089_89, sz10) | =(W089_89, xk)))), ~isPrime0(xk)
% 0.18/0.46
% 0.18/0.46 [4] ALPHA_NOT_NOT : ~~$false
% 0.18/0.46 -> [5] $false
% 0.18/0.46
% 0.18/0.46 [5] CLOSURE : $false
% 0.18/0.46
% 0.18/0.46 % SZS output end Proof for theBenchmark.p
% 0.18/0.46 [0.124197s][1][Res] 1 goroutines created
% 0.18/0.46 ==== Result ====
% 0.18/0.46 [0.124246s][1][Res] VALID
% 0.18/0.46 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------