TSTP Solution File: NUM530+3 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : NUM530+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n023.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 10:19:24 EDT 2022
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM530+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : goeland -dmt -presko -proof %s
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Sep 2 11:52:48 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 [DMT] DMT loaded with preskolemization
% 0.14/0.34 [EQ] equality loaded.
% 0.14/0.34 [0.000041s][1][MAIN] Problem : theBenchmark.p
% 0.14/0.36 Start search
% 0.14/0.36 nb_step : 1 - limit : 54
% 0.14/0.36 Launch Gotab with destructive = true
% 0.20/0.45 % SZS output start Proof for theBenchmark.p
% 0.20/0.46 [0] ALPHA_AND : (! [W05_5] : ((aNaturalNumber0(W05_5) => $true)) & aNaturalNumber0(sz00) & (aNaturalNumber0(sz10) & ~=(sz10, sz00)) & ! [W06_6, W17_7] : (((aNaturalNumber0(W06_6) & aNaturalNumber0(W17_7)) => aNaturalNumber0(sdtpldt0(W06_6, W17_7)))) & ! [W08_8, W19_9] : (((aNaturalNumber0(W08_8) & aNaturalNumber0(W19_9)) => aNaturalNumber0(sdtasdt0(W08_8, W19_9)))) & ! [W010_10, W111_11] : (((aNaturalNumber0(W010_10) & aNaturalNumber0(W111_11)) => =(sdtpldt0(W010_10, W111_11), sdtpldt0(W111_11, W010_10)))) & ! [W012_12, W113_13, W214_14] : ((((aNaturalNumber0(W012_12) & aNaturalNumber0(W113_13)) & aNaturalNumber0(W214_14)) => =(sdtpldt0(sdtpldt0(W012_12, W113_13), W214_14), sdtpldt0(W012_12, sdtpldt0(W113_13, W214_14))))) & ! [W015_15] : ((aNaturalNumber0(W015_15) => (=(sdtpldt0(W015_15, sz00), W015_15) & =(W015_15, sdtpldt0(sz00, W015_15))))) & ! [W016_16, W117_17] : (((aNaturalNumber0(W016_16) & aNaturalNumber0(W117_17)) => =(sdtasdt0(W016_16, W117_17), sdtasdt0(W117_17, W016_16)))) & ! [W018_18, W119_19, W220_20] : ((((aNaturalNumber0(W018_18) & aNaturalNumber0(W119_19)) & aNaturalNumber0(W220_20)) => =(sdtasdt0(sdtasdt0(W018_18, W119_19), W220_20), sdtasdt0(W018_18, sdtasdt0(W119_19, W220_20))))) & ! [W021_21] : ((aNaturalNumber0(W021_21) => (=(sdtasdt0(W021_21, sz10), W021_21) & =(W021_21, sdtasdt0(sz10, W021_21))))) & ! [W022_22] : ((aNaturalNumber0(W022_22) => (=(sdtasdt0(W022_22, sz00), sz00) & =(sz00, sdtasdt0(sz00, W022_22))))) & ! [W023_23, W124_24, W225_25] : ((((aNaturalNumber0(W023_23) & aNaturalNumber0(W124_24)) & aNaturalNumber0(W225_25)) => (=(sdtasdt0(W023_23, sdtpldt0(W124_24, W225_25)), sdtpldt0(sdtasdt0(W023_23, W124_24), sdtasdt0(W023_23, W225_25))) & =(sdtasdt0(sdtpldt0(W124_24, W225_25), W023_23), sdtpldt0(sdtasdt0(W124_24, W023_23), sdtasdt0(W225_25, W023_23)))))) & ! [W026_26, W127_27, W228_28] : ((((aNaturalNumber0(W026_26) & aNaturalNumber0(W127_27)) & aNaturalNumber0(W228_28)) => ((=(sdtpldt0(W026_26, W127_27), sdtpldt0(W026_26, W228_28)) | =(sdtpldt0(W127_27, W026_26), sdtpldt0(W228_28, W026_26))) => =(W127_27, W228_28)))) & ! [W029_29] : ((aNaturalNumber0(W029_29) => (~=(W029_29, sz00) => ! [W130_30, W231_31] : (((aNaturalNumber0(W130_30) & aNaturalNumber0(W231_31)) => ((=(sdtasdt0(W029_29, W130_30), sdtasdt0(W029_29, W231_31)) | =(sdtasdt0(W130_30, W029_29), sdtasdt0(W231_31, W029_29))) => =(W130_30, W231_31))))))) & ! [W032_32, W133_33] : (((aNaturalNumber0(W032_32) & aNaturalNumber0(W133_33)) => (=(sdtpldt0(W032_32, W133_33), sz00) => (=(W032_32, sz00) & =(W133_33, sz00))))) & ! [W034_34, W135_35] : (((aNaturalNumber0(W034_34) & aNaturalNumber0(W135_35)) => (=(sdtasdt0(W034_34, W135_35), sz00) => (=(W034_34, sz00) | =(W135_35, sz00))))) & ! [W036_36, W137_37] : (((aNaturalNumber0(W036_36) & aNaturalNumber0(W137_37)) => (sdtlseqdt0(W036_36, W137_37) <=> ? [W238_38] : ((aNaturalNumber0(W238_38) & =(sdtpldt0(W036_36, W238_38), W137_37)))))) & ! [W039_39, W140_40] : (((aNaturalNumber0(W039_39) & aNaturalNumber0(W140_40)) => (sdtlseqdt0(W039_39, W140_40) => ! [W241_41] : ((=(W241_41, sdtmndt0(W140_40, W039_39)) <=> (aNaturalNumber0(W241_41) & =(sdtpldt0(W039_39, W241_41), W140_40))))))) & ! [W042_42] : ((aNaturalNumber0(W042_42) => sdtlseqdt0(W042_42, W042_42))) & ! [W043_43, W144_44] : (((aNaturalNumber0(W043_43) & aNaturalNumber0(W144_44)) => ((sdtlseqdt0(W043_43, W144_44) & sdtlseqdt0(W144_44, W043_43)) => =(W043_43, W144_44)))) & ! [W045_45, W146_46, W247_47] : ((((aNaturalNumber0(W045_45) & aNaturalNumber0(W146_46)) & aNaturalNumber0(W247_47)) => ((sdtlseqdt0(W045_45, W146_46) & sdtlseqdt0(W146_46, W247_47)) => sdtlseqdt0(W045_45, W247_47)))) & ! [W048_48, W149_49] : (((aNaturalNumber0(W048_48) & aNaturalNumber0(W149_49)) => (sdtlseqdt0(W048_48, W149_49) | (~=(W149_49, W048_48) & sdtlseqdt0(W149_49, W048_48))))) & ! [W050_50, W151_51] : (((aNaturalNumber0(W050_50) & aNaturalNumber0(W151_51)) => ((~=(W050_50, W151_51) & sdtlseqdt0(W050_50, W151_51)) => ! [W252_52] : ((aNaturalNumber0(W252_52) => (((~=(sdtpldt0(W252_52, W050_50), sdtpldt0(W252_52, W151_51)) & sdtlseqdt0(sdtpldt0(W252_52, W050_50), sdtpldt0(W252_52, W151_51))) & ~=(sdtpldt0(W050_50, W252_52), sdtpldt0(W151_51, W252_52))) & sdtlseqdt0(sdtpldt0(W050_50, W252_52), sdtpldt0(W151_51, W252_52)))))))) & ! [W053_53, W154_54, W255_55] : ((((aNaturalNumber0(W053_53) & aNaturalNumber0(W154_54)) & aNaturalNumber0(W255_55)) => (((~=(W053_53, sz00) & ~=(W154_54, W255_55)) & sdtlseqdt0(W154_54, W255_55)) => (((~=(sdtasdt0(W053_53, W154_54), sdtasdt0(W053_53, W255_55)) & sdtlseqdt0(sdtasdt0(W053_53, W154_54), sdtasdt0(W053_53, W255_55))) & ~=(sdtasdt0(W154_54, W053_53), sdtasdt0(W255_55, W053_53))) & sdtlseqdt0(sdtasdt0(W154_54, W053_53), sdtasdt0(W255_55, W053_53)))))) & ! [W056_56] : ((aNaturalNumber0(W056_56) => ((=(W056_56, sz00) | =(W056_56, sz10)) | (~=(sz10, W056_56) & sdtlseqdt0(sz10, W056_56))))) & ! [W057_57, W158_58] : (((aNaturalNumber0(W057_57) & aNaturalNumber0(W158_58)) => (~=(W057_57, sz00) => sdtlseqdt0(W158_58, sdtasdt0(W158_58, W057_57))))) & ! [W059_59, W160_60] : (((aNaturalNumber0(W059_59) & aNaturalNumber0(W160_60)) => (iLess0(W059_59, W160_60) => $true))) & ! [W061_61, W162_62] : (((aNaturalNumber0(W061_61) & aNaturalNumber0(W162_62)) => ((~=(W061_61, W162_62) & sdtlseqdt0(W061_61, W162_62)) => iLess0(W061_61, W162_62)))) & ! [W063_63, W164_64] : (((aNaturalNumber0(W063_63) & aNaturalNumber0(W164_64)) => (doDivides0(W063_63, W164_64) <=> ? [W265_65] : ((aNaturalNumber0(W265_65) & =(W164_64, sdtasdt0(W063_63, W265_65))))))) & ! [W066_66, W167_67] : (((aNaturalNumber0(W066_66) & aNaturalNumber0(W167_67)) => ((~=(W066_66, sz00) & doDivides0(W066_66, W167_67)) => ! [W268_68] : ((=(W268_68, sdtsldt0(W167_67, W066_66)) <=> (aNaturalNumber0(W268_68) & =(W167_67, sdtasdt0(W066_66, W268_68)))))))) & ! [W069_69, W170_70, W271_71] : ((((aNaturalNumber0(W069_69) & aNaturalNumber0(W170_70)) & aNaturalNumber0(W271_71)) => ((doDivides0(W069_69, W170_70) & doDivides0(W170_70, W271_71)) => doDivides0(W069_69, W271_71)))) & ! [W072_72, W173_73, W274_74] : ((((aNaturalNumber0(W072_72) & aNaturalNumber0(W173_73)) & aNaturalNumber0(W274_74)) => ((doDivides0(W072_72, W173_73) & doDivides0(W072_72, W274_74)) => doDivides0(W072_72, sdtpldt0(W173_73, W274_74))))) & ! [W075_75, W176_76, W277_77] : ((((aNaturalNumber0(W075_75) & aNaturalNumber0(W176_76)) & aNaturalNumber0(W277_77)) => ((doDivides0(W075_75, W176_76) & doDivides0(W075_75, sdtpldt0(W176_76, W277_77))) => doDivides0(W075_75, W277_77)))) & ! [W078_78, W179_79] : (((aNaturalNumber0(W078_78) & aNaturalNumber0(W179_79)) => ((doDivides0(W078_78, W179_79) & ~=(W179_79, sz00)) => sdtlseqdt0(W078_78, W179_79)))) & ! [W080_80, W181_81] : (((aNaturalNumber0(W080_80) & aNaturalNumber0(W181_81)) => ((~=(W080_80, sz00) & doDivides0(W080_80, W181_81)) => ! [W282_82] : ((aNaturalNumber0(W282_82) => =(sdtasdt0(W282_82, sdtsldt0(W181_81, W080_80)), sdtsldt0(sdtasdt0(W282_82, W181_81), W080_80))))))) & ! [W083_83] : ((aNaturalNumber0(W083_83) => (isPrime0(W083_83) <=> ((~=(W083_83, sz00) & ~=(W083_83, sz10)) & ! [W184_84] : (((aNaturalNumber0(W184_84) & doDivides0(W184_84, W083_83)) => (=(W184_84, sz10) | =(W184_84, W083_83)))))))) & ! [W085_85] : ((((aNaturalNumber0(W085_85) & ~=(W085_85, sz00)) & ~=(W085_85, sz10)) => ? [W186_86] : (((aNaturalNumber0(W186_86) & doDivides0(W186_86, W085_85)) & isPrime0(W186_86))))) & ! [W087_87, W188_88, W289_89] : ((((aNaturalNumber0(W087_87) & aNaturalNumber0(W188_88)) & aNaturalNumber0(W289_89)) => ((isPrime0(W289_89) & doDivides0(W289_89, sdtasdt0(W087_87, W188_88))) => (doDivides0(W289_89, W087_87) | doDivides0(W289_89, W188_88))))) & (((((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)) & ~=(xn, sz00)) & ~=(xm, sz00)) & ~=(xp, sz00)) & ! [W090_90, W191_91, W292_92] : (((((((aNaturalNumber0(W090_90) & aNaturalNumber0(W191_91)) & aNaturalNumber0(W292_92)) & ~=(W090_90, sz00)) & ~=(W191_91, sz00)) & ~=(W292_92, sz00)) => (=(sdtasdt0(W292_92, sdtasdt0(W191_91, W191_91)), sdtasdt0(W090_90, W090_90)) => (iLess0(W090_90, xn) => ~((~=(W292_92, sz10) & ! [W393_93] : ((((aNaturalNumber0(W393_93) & ? [W494_94] : ((aNaturalNumber0(W494_94) & =(W292_92, sdtasdt0(W393_93, W494_94))))) & doDivides0(W393_93, W292_92)) => (=(W393_93, sz10) | =(W393_93, W292_92))))) | isPrime0(W292_92)))))) & =(sdtasdt0(xp, sdtasdt0(xm, xm)), sdtasdt0(xn, xn)) & ((~=(xp, sz10) & ! [W095_95] : (((aNaturalNumber0(W095_95) & (? [W196_96] : ((aNaturalNumber0(W196_96) & =(xp, sdtasdt0(W095_95, W196_96)))) | doDivides0(W095_95, xp))) => (=(W095_95, sz10) | =(W095_95, xp))))) & isPrime0(xp)) & (((? [W097_97] : ((aNaturalNumber0(W097_97) & =(sdtasdt0(xn, xn), sdtasdt0(xp, W097_97)))) & doDivides0(xp, sdtasdt0(xn, xn))) & ? [W098_98] : ((aNaturalNumber0(W098_98) & =(xn, sdtasdt0(xp, W098_98))))) & doDivides0(xp, xn)) & ((aNaturalNumber0(xq) & =(xn, sdtasdt0(xp, xq))) & =(xq, sdtsldt0(xn, xp))) & =(sdtasdt0(xm, xm), sdtasdt0(xp, sdtasdt0(xq, xq))) & ((~=(xm, xn) & ? [W099_99] : ((aNaturalNumber0(W099_99) & =(sdtpldt0(xm, W099_99), xn)))) & sdtlseqdt0(xm, xn)) & ~$true & ~$false)
% 0.20/0.46 -> [1] ! [W05_5] : ((aNaturalNumber0(W05_5) => $true)), aNaturalNumber0(sz00), (aNaturalNumber0(sz10) & ~=(sz10, sz00)), ! [W06_6, W17_7] : (((aNaturalNumber0(W06_6) & aNaturalNumber0(W17_7)) => aNaturalNumber0(sdtpldt0(W06_6, W17_7)))), ! [W08_8, W19_9] : (((aNaturalNumber0(W08_8) & aNaturalNumber0(W19_9)) => aNaturalNumber0(sdtasdt0(W08_8, W19_9)))), ! [W010_10, W111_11] : (((aNaturalNumber0(W010_10) & aNaturalNumber0(W111_11)) => =(sdtpldt0(W010_10, W111_11), sdtpldt0(W111_11, W010_10)))), ! [W012_12, W113_13, W214_14] : ((((aNaturalNumber0(W012_12) & aNaturalNumber0(W113_13)) & aNaturalNumber0(W214_14)) => =(sdtpldt0(sdtpldt0(W012_12, W113_13), W214_14), sdtpldt0(W012_12, sdtpldt0(W113_13, W214_14))))), ! [W015_15] : ((aNaturalNumber0(W015_15) => (=(sdtpldt0(W015_15, sz00), W015_15) & =(W015_15, sdtpldt0(sz00, W015_15))))), ! [W016_16, W117_17] : (((aNaturalNumber0(W016_16) & aNaturalNumber0(W117_17)) => =(sdtasdt0(W016_16, W117_17), sdtasdt0(W117_17, W016_16)))), ! [W018_18, W119_19, W220_20] : ((((aNaturalNumber0(W018_18) & aNaturalNumber0(W119_19)) & aNaturalNumber0(W220_20)) => =(sdtasdt0(sdtasdt0(W018_18, W119_19), W220_20), sdtasdt0(W018_18, sdtasdt0(W119_19, W220_20))))), ! [W021_21] : ((aNaturalNumber0(W021_21) => (=(sdtasdt0(W021_21, sz10), W021_21) & =(W021_21, sdtasdt0(sz10, W021_21))))), ! [W022_22] : ((aNaturalNumber0(W022_22) => (=(sdtasdt0(W022_22, sz00), sz00) & =(sz00, sdtasdt0(sz00, W022_22))))), ! [W023_23, W124_24, W225_25] : ((((aNaturalNumber0(W023_23) & aNaturalNumber0(W124_24)) & aNaturalNumber0(W225_25)) => (=(sdtasdt0(W023_23, sdtpldt0(W124_24, W225_25)), sdtpldt0(sdtasdt0(W023_23, W124_24), sdtasdt0(W023_23, W225_25))) & =(sdtasdt0(sdtpldt0(W124_24, W225_25), W023_23), sdtpldt0(sdtasdt0(W124_24, W023_23), sdtasdt0(W225_25, W023_23)))))), ! [W026_26, W127_27, W228_28] : ((((aNaturalNumber0(W026_26) & aNaturalNumber0(W127_27)) & aNaturalNumber0(W228_28)) => ((=(sdtpldt0(W026_26, W127_27), sdtpldt0(W026_26, W228_28)) | =(sdtpldt0(W127_27, W026_26), sdtpldt0(W228_28, W026_26))) => =(W127_27, W228_28)))), ! [W029_29] : ((aNaturalNumber0(W029_29) => (~=(W029_29, sz00) => ! [W130_30, W231_31] : (((aNaturalNumber0(W130_30) & aNaturalNumber0(W231_31)) => ((=(sdtasdt0(W029_29, W130_30), sdtasdt0(W029_29, W231_31)) | =(sdtasdt0(W130_30, W029_29), sdtasdt0(W231_31, W029_29))) => =(W130_30, W231_31))))))), ! [W032_32, W133_33] : (((aNaturalNumber0(W032_32) & aNaturalNumber0(W133_33)) => (=(sdtpldt0(W032_32, W133_33), sz00) => (=(W032_32, sz00) & =(W133_33, sz00))))), ! [W034_34, W135_35] : (((aNaturalNumber0(W034_34) & aNaturalNumber0(W135_35)) => (=(sdtasdt0(W034_34, W135_35), sz00) => (=(W034_34, sz00) | =(W135_35, sz00))))), ! [W036_36, W137_37] : (((aNaturalNumber0(W036_36) & aNaturalNumber0(W137_37)) => (sdtlseqdt0(W036_36, W137_37) <=> ? [W238_38] : ((aNaturalNumber0(W238_38) & =(sdtpldt0(W036_36, W238_38), W137_37)))))), ! [W039_39, W140_40] : (((aNaturalNumber0(W039_39) & aNaturalNumber0(W140_40)) => (sdtlseqdt0(W039_39, W140_40) => ! [W241_41] : ((=(W241_41, sdtmndt0(W140_40, W039_39)) <=> (aNaturalNumber0(W241_41) & =(sdtpldt0(W039_39, W241_41), W140_40))))))), ! [W042_42] : ((aNaturalNumber0(W042_42) => sdtlseqdt0(W042_42, W042_42))), ! [W043_43, W144_44] : (((aNaturalNumber0(W043_43) & aNaturalNumber0(W144_44)) => ((sdtlseqdt0(W043_43, W144_44) & sdtlseqdt0(W144_44, W043_43)) => =(W043_43, W144_44)))), ! [W045_45, W146_46, W247_47] : ((((aNaturalNumber0(W045_45) & aNaturalNumber0(W146_46)) & aNaturalNumber0(W247_47)) => ((sdtlseqdt0(W045_45, W146_46) & sdtlseqdt0(W146_46, W247_47)) => sdtlseqdt0(W045_45, W247_47)))), ! [W048_48, W149_49] : (((aNaturalNumber0(W048_48) & aNaturalNumber0(W149_49)) => (sdtlseqdt0(W048_48, W149_49) | (~=(W149_49, W048_48) & sdtlseqdt0(W149_49, W048_48))))), ! [W050_50, W151_51] : (((aNaturalNumber0(W050_50) & aNaturalNumber0(W151_51)) => ((~=(W050_50, W151_51) & sdtlseqdt0(W050_50, W151_51)) => ! [W252_52] : ((aNaturalNumber0(W252_52) => (((~=(sdtpldt0(W252_52, W050_50), sdtpldt0(W252_52, W151_51)) & sdtlseqdt0(sdtpldt0(W252_52, W050_50), sdtpldt0(W252_52, W151_51))) & ~=(sdtpldt0(W050_50, W252_52), sdtpldt0(W151_51, W252_52))) & sdtlseqdt0(sdtpldt0(W050_50, W252_52), sdtpldt0(W151_51, W252_52)))))))), ! [W053_53, W154_54, W255_55] : ((((aNaturalNumber0(W053_53) & aNaturalNumber0(W154_54)) & aNaturalNumber0(W255_55)) => (((~=(W053_53, sz00) & ~=(W154_54, W255_55)) & sdtlseqdt0(W154_54, W255_55)) => (((~=(sdtasdt0(W053_53, W154_54), sdtasdt0(W053_53, W255_55)) & sdtlseqdt0(sdtasdt0(W053_53, W154_54), sdtasdt0(W053_53, W255_55))) & ~=(sdtasdt0(W154_54, W053_53), sdtasdt0(W255_55, W053_53))) & sdtlseqdt0(sdtasdt0(W154_54, W053_53), sdtasdt0(W255_55, W053_53)))))), ! [W056_56] : ((aNaturalNumber0(W056_56) => ((=(W056_56, sz00) | =(W056_56, sz10)) | (~=(sz10, W056_56) & sdtlseqdt0(sz10, W056_56))))), ! [W057_57, W158_58] : (((aNaturalNumber0(W057_57) & aNaturalNumber0(W158_58)) => (~=(W057_57, sz00) => sdtlseqdt0(W158_58, sdtasdt0(W158_58, W057_57))))), ! [W059_59, W160_60] : (((aNaturalNumber0(W059_59) & aNaturalNumber0(W160_60)) => (iLess0(W059_59, W160_60) => $true))), ! [W061_61, W162_62] : (((aNaturalNumber0(W061_61) & aNaturalNumber0(W162_62)) => ((~=(W061_61, W162_62) & sdtlseqdt0(W061_61, W162_62)) => iLess0(W061_61, W162_62)))), ! [W063_63, W164_64] : (((aNaturalNumber0(W063_63) & aNaturalNumber0(W164_64)) => (doDivides0(W063_63, W164_64) <=> ? [W265_65] : ((aNaturalNumber0(W265_65) & =(W164_64, sdtasdt0(W063_63, W265_65))))))), ! [W066_66, W167_67] : (((aNaturalNumber0(W066_66) & aNaturalNumber0(W167_67)) => ((~=(W066_66, sz00) & doDivides0(W066_66, W167_67)) => ! [W268_68] : ((=(W268_68, sdtsldt0(W167_67, W066_66)) <=> (aNaturalNumber0(W268_68) & =(W167_67, sdtasdt0(W066_66, W268_68)))))))), ! [W069_69, W170_70, W271_71] : ((((aNaturalNumber0(W069_69) & aNaturalNumber0(W170_70)) & aNaturalNumber0(W271_71)) => ((doDivides0(W069_69, W170_70) & doDivides0(W170_70, W271_71)) => doDivides0(W069_69, W271_71)))), ! [W072_72, W173_73, W274_74] : ((((aNaturalNumber0(W072_72) & aNaturalNumber0(W173_73)) & aNaturalNumber0(W274_74)) => ((doDivides0(W072_72, W173_73) & doDivides0(W072_72, W274_74)) => doDivides0(W072_72, sdtpldt0(W173_73, W274_74))))), ! [W075_75, W176_76, W277_77] : ((((aNaturalNumber0(W075_75) & aNaturalNumber0(W176_76)) & aNaturalNumber0(W277_77)) => ((doDivides0(W075_75, W176_76) & doDivides0(W075_75, sdtpldt0(W176_76, W277_77))) => doDivides0(W075_75, W277_77)))), ! [W078_78, W179_79] : (((aNaturalNumber0(W078_78) & aNaturalNumber0(W179_79)) => ((doDivides0(W078_78, W179_79) & ~=(W179_79, sz00)) => sdtlseqdt0(W078_78, W179_79)))), ! [W080_80, W181_81] : (((aNaturalNumber0(W080_80) & aNaturalNumber0(W181_81)) => ((~=(W080_80, sz00) & doDivides0(W080_80, W181_81)) => ! [W282_82] : ((aNaturalNumber0(W282_82) => =(sdtasdt0(W282_82, sdtsldt0(W181_81, W080_80)), sdtsldt0(sdtasdt0(W282_82, W181_81), W080_80))))))), ! [W083_83] : ((aNaturalNumber0(W083_83) => (isPrime0(W083_83) <=> ((~=(W083_83, sz00) & ~=(W083_83, sz10)) & ! [W184_84] : (((aNaturalNumber0(W184_84) & doDivides0(W184_84, W083_83)) => (=(W184_84, sz10) | =(W184_84, W083_83)))))))), ! [W085_85] : ((((aNaturalNumber0(W085_85) & ~=(W085_85, sz00)) & ~=(W085_85, sz10)) => ? [W186_86] : (((aNaturalNumber0(W186_86) & doDivides0(W186_86, W085_85)) & isPrime0(W186_86))))), ! [W087_87, W188_88, W289_89] : ((((aNaturalNumber0(W087_87) & aNaturalNumber0(W188_88)) & aNaturalNumber0(W289_89)) => ((isPrime0(W289_89) & doDivides0(W289_89, sdtasdt0(W087_87, W188_88))) => (doDivides0(W289_89, W087_87) | doDivides0(W289_89, W188_88))))), (((((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)) & ~=(xn, sz00)) & ~=(xm, sz00)) & ~=(xp, sz00)), ! [W090_90, W191_91, W292_92] : (((((((aNaturalNumber0(W090_90) & aNaturalNumber0(W191_91)) & aNaturalNumber0(W292_92)) & ~=(W090_90, sz00)) & ~=(W191_91, sz00)) & ~=(W292_92, sz00)) => (=(sdtasdt0(W292_92, sdtasdt0(W191_91, W191_91)), sdtasdt0(W090_90, W090_90)) => (iLess0(W090_90, xn) => ~((~=(W292_92, sz10) & ! [W393_93] : ((((aNaturalNumber0(W393_93) & ? [W494_94] : ((aNaturalNumber0(W494_94) & =(W292_92, sdtasdt0(W393_93, W494_94))))) & doDivides0(W393_93, W292_92)) => (=(W393_93, sz10) | =(W393_93, W292_92))))) | isPrime0(W292_92)))))), =(sdtasdt0(xp, sdtasdt0(xm, xm)), sdtasdt0(xn, xn)), ((~=(xp, sz10) & ! [W095_95] : (((aNaturalNumber0(W095_95) & (? [W196_96] : ((aNaturalNumber0(W196_96) & =(xp, sdtasdt0(W095_95, W196_96)))) | doDivides0(W095_95, xp))) => (=(W095_95, sz10) | =(W095_95, xp))))) & isPrime0(xp)), (((? [W097_97] : ((aNaturalNumber0(W097_97) & =(sdtasdt0(xn, xn), sdtasdt0(xp, W097_97)))) & doDivides0(xp, sdtasdt0(xn, xn))) & ? [W098_98] : ((aNaturalNumber0(W098_98) & =(xn, sdtasdt0(xp, W098_98))))) & doDivides0(xp, xn)), ((aNaturalNumber0(xq) & =(xn, sdtasdt0(xp, xq))) & =(xq, sdtsldt0(xn, xp))), =(sdtasdt0(xm, xm), sdtasdt0(xp, sdtasdt0(xq, xq))), ((~=(xm, xn) & ? [W099_99] : ((aNaturalNumber0(W099_99) & =(sdtpldt0(xm, W099_99), xn)))) & sdtlseqdt0(xm, xn)), ~$true, ~$false
% 0.20/0.46
% 0.20/0.46 [1] CLOSURE : ~$true
% 0.20/0.46
% 0.20/0.46 % SZS output end Proof for theBenchmark.p
% 0.20/0.46 [0.112851s][1][Res] 1 goroutines created
% 0.20/0.46 ==== Result ====
% 0.20/0.46 [0.112898s][1][Res] VALID
% 0.20/0.46 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------