TSTP Solution File: RNG125+4 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : RNG125+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n024.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 : Tue Sep 20 03:07:48 EDT 2022
% Result : Theorem 23.18s 9.19s
% Output : Proof 23.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : RNG125+4 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : goeland -dmt -presko -proof %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 22:50:18 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 [DMT] DMT loaded with preskolemization
% 0.12/0.35 [EQ] equality loaded.
% 0.12/0.35 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.19/0.36 Start search
% 0.19/0.37 nb_step : 1 - limit : 90
% 0.19/0.37 Launch Gotab with destructive = true
% 22.97/9.18 % SZS output start Proof for theBenchmark.p
% 23.18/9.19 [0] ALPHA_AND : (! [W06_6] : ((aElement0(W06_6) => $true)) & aElement0(sz00) & aElement0(sz10) & ! [W07_7] : ((aElement0(W07_7) => aElement0(smndt0(W07_7)))) & ! [W08_8, W19_9] : (((aElement0(W08_8) & aElement0(W19_9)) => aElement0(sdtpldt0(W08_8, W19_9)))) & ! [W010_10, W111_11] : (((aElement0(W010_10) & aElement0(W111_11)) => aElement0(sdtasdt0(W010_10, W111_11)))) & ! [W012_12, W113_13] : (((aElement0(W012_12) & aElement0(W113_13)) => =(sdtpldt0(W012_12, W113_13), sdtpldt0(W113_13, W012_12)))) & ! [W014_14, W115_15, W216_16] : ((((aElement0(W014_14) & aElement0(W115_15)) & aElement0(W216_16)) => =(sdtpldt0(sdtpldt0(W014_14, W115_15), W216_16), sdtpldt0(W014_14, sdtpldt0(W115_15, W216_16))))) & ! [W017_17] : ((aElement0(W017_17) => (=(sdtpldt0(W017_17, sz00), W017_17) & =(W017_17, sdtpldt0(sz00, W017_17))))) & ! [W018_18] : ((aElement0(W018_18) => (=(sdtpldt0(W018_18, smndt0(W018_18)), sz00) & =(sz00, sdtpldt0(smndt0(W018_18), W018_18))))) & ! [W019_19, W120_20] : (((aElement0(W019_19) & aElement0(W120_20)) => =(sdtasdt0(W019_19, W120_20), sdtasdt0(W120_20, W019_19)))) & ! [W021_21, W122_22, W223_23] : ((((aElement0(W021_21) & aElement0(W122_22)) & aElement0(W223_23)) => =(sdtasdt0(sdtasdt0(W021_21, W122_22), W223_23), sdtasdt0(W021_21, sdtasdt0(W122_22, W223_23))))) & ! [W024_24] : ((aElement0(W024_24) => (=(sdtasdt0(W024_24, sz10), W024_24) & =(W024_24, sdtasdt0(sz10, W024_24))))) & ! [W025_25, W126_26, W227_27] : ((((aElement0(W025_25) & aElement0(W126_26)) & aElement0(W227_27)) => (=(sdtasdt0(W025_25, sdtpldt0(W126_26, W227_27)), sdtpldt0(sdtasdt0(W025_25, W126_26), sdtasdt0(W025_25, W227_27))) & =(sdtasdt0(sdtpldt0(W126_26, W227_27), W025_25), sdtpldt0(sdtasdt0(W126_26, W025_25), sdtasdt0(W227_27, W025_25)))))) & ! [W028_28] : ((aElement0(W028_28) => (=(sdtasdt0(smndt0(sz10), W028_28), smndt0(W028_28)) & =(smndt0(W028_28), sdtasdt0(W028_28, smndt0(sz10)))))) & ! [W029_29] : ((aElement0(W029_29) => (=(sdtasdt0(W029_29, sz00), sz00) & =(sz00, sdtasdt0(sz00, W029_29))))) & ! [W030_30, W131_31] : (((aElement0(W030_30) & aElement0(W131_31)) => (=(sdtasdt0(W030_30, W131_31), sz00) => (=(W030_30, sz00) | =(W131_31, sz00))))) & ~=(sz10, sz00) & ! [W032_32] : ((aSet0(W032_32) => $true)) & ! [W033_33] : ((aSet0(W033_33) => ! [W134_34] : ((aElementOf0(W134_34, W033_33) => aElement0(W134_34))))) & ! [W035_35, W136_36] : (((aSet0(W035_35) & aSet0(W136_36)) => ((! [W237_37] : ((aElementOf0(W237_37, W035_35) => aElementOf0(W237_37, W136_36))) & ! [W238_38] : ((aElementOf0(W238_38, W136_36) => aElementOf0(W238_38, W035_35)))) => =(W035_35, W136_36)))) & ! [W039_39, W140_40] : (((aSet0(W039_39) & aSet0(W140_40)) => ! [W241_41] : ((=(W241_41, sdtpldt1(W039_39, W140_40)) <=> (aSet0(W241_41) & ! [W342_42] : ((aElementOf0(W342_42, W241_41) <=> ? [W443_43, W544_44] : (((aElementOf0(W443_43, W039_39) & aElementOf0(W544_44, W140_40)) & =(sdtpldt0(W443_43, W544_44), W342_42)))))))))) & ! [W045_45, W146_46] : (((aSet0(W045_45) & aSet0(W146_46)) => ! [W247_47] : ((=(W247_47, sdtasasdt0(W045_45, W146_46)) <=> (aSet0(W247_47) & ! [W348_48] : ((aElementOf0(W348_48, W247_47) <=> (aElementOf0(W348_48, W045_45) & aElementOf0(W348_48, W146_46))))))))) & ! [W053_53, W154_54] : (((aIdeal0(W053_53) & aIdeal0(W154_54)) => aIdeal0(sdtpldt1(W053_53, W154_54)))) & ! [W055_55, W156_56] : (((aIdeal0(W055_55) & aIdeal0(W156_56)) => aIdeal0(sdtasasdt0(W055_55, W156_56)))) & ! [W057_57, W158_58, W259_59] : ((((aElement0(W057_57) & aElement0(W158_58)) & aIdeal0(W259_59)) => (sdteqdtlpzmzozddtrp0(W057_57, W158_58, W259_59) <=> aElementOf0(sdtpldt0(W057_57, smndt0(W158_58)), W259_59)))) & ! [W060_60, W161_61] : (((aIdeal0(W060_60) & aIdeal0(W161_61)) => (! [W262_62] : ((aElement0(W262_62) => aElementOf0(W262_62, sdtpldt1(W060_60, W161_61)))) => ! [W263_63, W364_64] : (((aElement0(W263_63) & aElement0(W364_64)) => ? [W465_65] : (((aElement0(W465_65) & sdteqdtlpzmzozddtrp0(W465_65, W263_63, W060_60)) & sdteqdtlpzmzozddtrp0(W465_65, W364_64, W161_61)))))))) & ! [W066_66] : ((aNaturalNumber0(W066_66) => $true)) & ! [W067_67] : (((aElement0(W067_67) & ~=(W067_67, sz00)) => aNaturalNumber0(sbrdtbr0(W067_67)))) & ! [W068_68, W169_69] : (((aNaturalNumber0(W068_68) & aNaturalNumber0(W169_69)) => (iLess0(W068_68, W169_69) => $true))) & ! [W070_70, W171_71] : ((((aElement0(W070_70) & aElement0(W171_71)) & ~=(W171_71, sz00)) => ? [W272_72, W373_73] : ((((aElement0(W272_72) & aElement0(W373_73)) & =(W070_70, sdtpldt0(sdtasdt0(W272_72, W171_71), W373_73))) & (~=(W373_73, sz00) => iLess0(sbrdtbr0(W373_73), sbrdtbr0(W171_71))))))) & ! [W074_74, W175_75] : (((aElement0(W074_74) & aElement0(W175_75)) => (doDivides0(W074_74, W175_75) <=> ? [W276_76] : ((aElement0(W276_76) & =(sdtasdt0(W074_74, W276_76), W175_75)))))) & ! [W077_77] : ((aElement0(W077_77) => ! [W178_78] : ((aDivisorOf0(W178_78, W077_77) <=> (aElement0(W178_78) & doDivides0(W178_78, W077_77)))))) & ! [W079_79, W180_80] : (((aElement0(W079_79) & aElement0(W180_80)) => ! [W281_81] : ((aGcdOfAnd0(W281_81, W079_79, W180_80) <=> ((aDivisorOf0(W281_81, W079_79) & aDivisorOf0(W281_81, W180_80)) & ! [W382_82] : (((aDivisorOf0(W382_82, W079_79) & aDivisorOf0(W382_82, W180_80)) => doDivides0(W382_82, W281_81)))))))) & ! [W083_83, W184_84] : (((aElement0(W083_83) & aElement0(W184_84)) => (misRelativelyPrime0(W083_83, W184_84) <=> aGcdOfAnd0(sz10, W083_83, W184_84)))) & ! [W085_85] : ((aElement0(W085_85) => ! [W186_86] : ((=(W186_86, slsdtgt0(W085_85)) <=> (aSet0(W186_86) & ! [W287_87] : ((aElementOf0(W287_87, W186_86) <=> ? [W388_88] : ((aElement0(W388_88) & =(sdtasdt0(W085_85, W388_88), W287_87)))))))))) & ! [W089_89] : ((aElement0(W089_89) => aIdeal0(slsdtgt0(W089_89)))) & (aElement0(xa) & aElement0(xb)) & (~=(xa, sz00) | ~=(xb, sz00)) & (((((((((aElement0(xc) & ? [W090_90] : ((aElement0(W090_90) & =(sdtasdt0(xc, W090_90), xa)))) & doDivides0(xc, xa)) & aDivisorOf0(xc, xa)) & aElement0(xc)) & ? [W091_91] : ((aElement0(W091_91) & =(sdtasdt0(xc, W091_91), xb)))) & doDivides0(xc, xb)) & aDivisorOf0(xc, xb)) & ! [W092_92] : (((((aElement0(W092_92) & (? [W193_93] : ((aElement0(W193_93) & =(sdtasdt0(W092_92, W193_93), xa))) | doDivides0(W092_92, xa))) | aDivisorOf0(W092_92, xa)) & ((? [W194_94] : ((aElement0(W194_94) & =(sdtasdt0(W092_92, W194_94), xb))) | doDivides0(W092_92, xb)) | aDivisorOf0(W092_92, xb))) => (? [W195_95] : ((aElement0(W195_95) & =(sdtasdt0(W092_92, W195_95), xc))) & doDivides0(W092_92, xc))))) & aGcdOfAnd0(xc, xa, xb)) & ((((((aSet0(xI) & ! [W096_96] : ((aElementOf0(W096_96, xI) => (! [W197_97] : ((aElementOf0(W197_97, xI) => aElementOf0(sdtpldt0(W096_96, W197_97), xI))) & ! [W198_98] : ((aElement0(W198_98) => aElementOf0(sdtasdt0(W198_98, W096_96), xI))))))) & aIdeal0(xI)) & ! [W099_99] : ((aElementOf0(W099_99, slsdtgt0(xa)) <=> ? [W1100_100] : ((aElement0(W1100_100) & =(sdtasdt0(xa, W1100_100), W099_99)))))) & ! [W0101_101] : ((aElementOf0(W0101_101, slsdtgt0(xb)) <=> ? [W1102_102] : ((aElement0(W1102_102) & =(sdtasdt0(xb, W1102_102), W0101_101)))))) & ! [W0103_103] : ((aElementOf0(W0103_103, xI) <=> ? [W1104_104, W2105_105] : (((aElementOf0(W1104_104, slsdtgt0(xa)) & aElementOf0(W2105_105, slsdtgt0(xb))) & =(sdtpldt0(W1104_104, W2105_105), W0103_103)))))) & =(xI, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & (((((((? [W0106_106] : ((aElement0(W0106_106) & =(sdtasdt0(xa, W0106_106), sz00))) & aElementOf0(sz00, slsdtgt0(xa))) & ? [W0107_107] : ((aElement0(W0107_107) & =(sdtasdt0(xa, W0107_107), xa)))) & aElementOf0(xa, slsdtgt0(xa))) & ? [W0108_108] : ((aElement0(W0108_108) & =(sdtasdt0(xb, W0108_108), sz00)))) & aElementOf0(sz00, slsdtgt0(xb))) & ? [W0109_109] : ((aElement0(W0109_109) & =(sdtasdt0(xb, W0109_109), xb)))) & aElementOf0(xb, slsdtgt0(xb))) & ? [W0110_110] : (((((! [W1111_111] : ((aElementOf0(W1111_111, slsdtgt0(xa)) <=> ? [W2112_112] : ((aElement0(W2112_112) & =(sdtasdt0(xa, W2112_112), W1111_111))))) & ! [W1113_113] : ((aElementOf0(W1113_113, slsdtgt0(xb)) <=> ? [W2114_114] : ((aElement0(W2114_114) & =(sdtasdt0(xb, W2114_114), W1113_113)))))) & ? [W1115_115, W2116_116] : (((aElementOf0(W1115_115, slsdtgt0(xa)) & aElementOf0(W2116_116, slsdtgt0(xb))) & =(sdtpldt0(W1115_115, W2116_116), W0110_110)))) & aElementOf0(W0110_110, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ~=(W0110_110, sz00))) & (((? [W0117_117, W1118_118] : (((aElementOf0(W0117_117, slsdtgt0(xa)) & aElementOf0(W1118_118, slsdtgt0(xb))) & =(sdtpldt0(W0117_117, W1118_118), xu))) & aElementOf0(xu, xI)) & ~=(xu, sz00)) & ! [W0119_119] : ((((? [W1120_120, W2121_121] : (((aElementOf0(W1120_120, slsdtgt0(xa)) & aElementOf0(W2121_121, slsdtgt0(xb))) & =(sdtpldt0(W1120_120, W2121_121), W0119_119))) | aElementOf0(W0119_119, xI)) & ~=(W0119_119, sz00)) => ~iLess0(sbrdtbr0(W0119_119), sbrdtbr0(xu))))) & ~(((? [W0122_122] : ((aElement0(W0122_122) & =(sdtasdt0(xu, W0122_122), xa))) | doDivides0(xu, xa)) | aDivisorOf0(xu, xa)) & ((? [W0123_123] : ((aElement0(W0123_123) & =(sdtasdt0(xu, W0123_123), xb))) | doDivides0(xu, xb)) | aDivisorOf0(xu, xb))) & ? [W0124_124, W1125_125] : (((aElement0(W0124_124) & aElement0(W1125_125)) & =(xu, sdtpldt0(sdtasdt0(xa, W0124_124), sdtasdt0(xb, W1125_125))))) & ~~(? [W0126_126] : ((aElement0(W0126_126) & =(sdtasdt0(xu, W0126_126), xa))) & doDivides0(xu, xa)) & ~~(? [W0127_127] : ((aElement0(W0127_127) & =(sdtasdt0(xu, W0127_127), xb))) & doDivides0(xu, xb)) & ~$false)
% 23.18/9.19 -> [1] ! [W06_6] : ((aElement0(W06_6) => $true)), aElement0(sz00), aElement0(sz10), ! [W07_7] : ((aElement0(W07_7) => aElement0(smndt0(W07_7)))), ! [W08_8, W19_9] : (((aElement0(W08_8) & aElement0(W19_9)) => aElement0(sdtpldt0(W08_8, W19_9)))), ! [W010_10, W111_11] : (((aElement0(W010_10) & aElement0(W111_11)) => aElement0(sdtasdt0(W010_10, W111_11)))), ! [W012_12, W113_13] : (((aElement0(W012_12) & aElement0(W113_13)) => =(sdtpldt0(W012_12, W113_13), sdtpldt0(W113_13, W012_12)))), ! [W014_14, W115_15, W216_16] : ((((aElement0(W014_14) & aElement0(W115_15)) & aElement0(W216_16)) => =(sdtpldt0(sdtpldt0(W014_14, W115_15), W216_16), sdtpldt0(W014_14, sdtpldt0(W115_15, W216_16))))), ! [W017_17] : ((aElement0(W017_17) => (=(sdtpldt0(W017_17, sz00), W017_17) & =(W017_17, sdtpldt0(sz00, W017_17))))), ! [W018_18] : ((aElement0(W018_18) => (=(sdtpldt0(W018_18, smndt0(W018_18)), sz00) & =(sz00, sdtpldt0(smndt0(W018_18), W018_18))))), ! [W019_19, W120_20] : (((aElement0(W019_19) & aElement0(W120_20)) => =(sdtasdt0(W019_19, W120_20), sdtasdt0(W120_20, W019_19)))), ! [W021_21, W122_22, W223_23] : ((((aElement0(W021_21) & aElement0(W122_22)) & aElement0(W223_23)) => =(sdtasdt0(sdtasdt0(W021_21, W122_22), W223_23), sdtasdt0(W021_21, sdtasdt0(W122_22, W223_23))))), ! [W024_24] : ((aElement0(W024_24) => (=(sdtasdt0(W024_24, sz10), W024_24) & =(W024_24, sdtasdt0(sz10, W024_24))))), ! [W025_25, W126_26, W227_27] : ((((aElement0(W025_25) & aElement0(W126_26)) & aElement0(W227_27)) => (=(sdtasdt0(W025_25, sdtpldt0(W126_26, W227_27)), sdtpldt0(sdtasdt0(W025_25, W126_26), sdtasdt0(W025_25, W227_27))) & =(sdtasdt0(sdtpldt0(W126_26, W227_27), W025_25), sdtpldt0(sdtasdt0(W126_26, W025_25), sdtasdt0(W227_27, W025_25)))))), ! [W028_28] : ((aElement0(W028_28) => (=(sdtasdt0(smndt0(sz10), W028_28), smndt0(W028_28)) & =(smndt0(W028_28), sdtasdt0(W028_28, smndt0(sz10)))))), ! [W029_29] : ((aElement0(W029_29) => (=(sdtasdt0(W029_29, sz00), sz00) & =(sz00, sdtasdt0(sz00, W029_29))))), ! [W030_30, W131_31] : (((aElement0(W030_30) & aElement0(W131_31)) => (=(sdtasdt0(W030_30, W131_31), sz00) => (=(W030_30, sz00) | =(W131_31, sz00))))), ~=(sz10, sz00), ! [W032_32] : ((aSet0(W032_32) => $true)), ! [W033_33] : ((aSet0(W033_33) => ! [W134_34] : ((aElementOf0(W134_34, W033_33) => aElement0(W134_34))))), ! [W035_35, W136_36] : (((aSet0(W035_35) & aSet0(W136_36)) => ((! [W237_37] : ((aElementOf0(W237_37, W035_35) => aElementOf0(W237_37, W136_36))) & ! [W238_38] : ((aElementOf0(W238_38, W136_36) => aElementOf0(W238_38, W035_35)))) => =(W035_35, W136_36)))), ! [W039_39, W140_40] : (((aSet0(W039_39) & aSet0(W140_40)) => ! [W241_41] : ((=(W241_41, sdtpldt1(W039_39, W140_40)) <=> (aSet0(W241_41) & ! [W342_42] : ((aElementOf0(W342_42, W241_41) <=> ? [W443_43, W544_44] : (((aElementOf0(W443_43, W039_39) & aElementOf0(W544_44, W140_40)) & =(sdtpldt0(W443_43, W544_44), W342_42)))))))))), ! [W045_45, W146_46] : (((aSet0(W045_45) & aSet0(W146_46)) => ! [W247_47] : ((=(W247_47, sdtasasdt0(W045_45, W146_46)) <=> (aSet0(W247_47) & ! [W348_48] : ((aElementOf0(W348_48, W247_47) <=> (aElementOf0(W348_48, W045_45) & aElementOf0(W348_48, W146_46))))))))), ! [W053_53, W154_54] : (((aIdeal0(W053_53) & aIdeal0(W154_54)) => aIdeal0(sdtpldt1(W053_53, W154_54)))), ! [W055_55, W156_56] : (((aIdeal0(W055_55) & aIdeal0(W156_56)) => aIdeal0(sdtasasdt0(W055_55, W156_56)))), ! [W057_57, W158_58, W259_59] : ((((aElement0(W057_57) & aElement0(W158_58)) & aIdeal0(W259_59)) => (sdteqdtlpzmzozddtrp0(W057_57, W158_58, W259_59) <=> aElementOf0(sdtpldt0(W057_57, smndt0(W158_58)), W259_59)))), ! [W060_60, W161_61] : (((aIdeal0(W060_60) & aIdeal0(W161_61)) => (! [W262_62] : ((aElement0(W262_62) => aElementOf0(W262_62, sdtpldt1(W060_60, W161_61)))) => ! [W263_63, W364_64] : (((aElement0(W263_63) & aElement0(W364_64)) => ? [W465_65] : (((aElement0(W465_65) & sdteqdtlpzmzozddtrp0(W465_65, W263_63, W060_60)) & sdteqdtlpzmzozddtrp0(W465_65, W364_64, W161_61)))))))), ! [W066_66] : ((aNaturalNumber0(W066_66) => $true)), ! [W067_67] : (((aElement0(W067_67) & ~=(W067_67, sz00)) => aNaturalNumber0(sbrdtbr0(W067_67)))), ! [W068_68, W169_69] : (((aNaturalNumber0(W068_68) & aNaturalNumber0(W169_69)) => (iLess0(W068_68, W169_69) => $true))), ! [W070_70, W171_71] : ((((aElement0(W070_70) & aElement0(W171_71)) & ~=(W171_71, sz00)) => ? [W272_72, W373_73] : ((((aElement0(W272_72) & aElement0(W373_73)) & =(W070_70, sdtpldt0(sdtasdt0(W272_72, W171_71), W373_73))) & (~=(W373_73, sz00) => iLess0(sbrdtbr0(W373_73), sbrdtbr0(W171_71))))))), ! [W074_74, W175_75] : (((aElement0(W074_74) & aElement0(W175_75)) => (doDivides0(W074_74, W175_75) <=> ? [W276_76] : ((aElement0(W276_76) & =(sdtasdt0(W074_74, W276_76), W175_75)))))), ! [W077_77] : ((aElement0(W077_77) => ! [W178_78] : ((aDivisorOf0(W178_78, W077_77) <=> (aElement0(W178_78) & doDivides0(W178_78, W077_77)))))), ! [W079_79, W180_80] : (((aElement0(W079_79) & aElement0(W180_80)) => ! [W281_81] : ((aGcdOfAnd0(W281_81, W079_79, W180_80) <=> ((aDivisorOf0(W281_81, W079_79) & aDivisorOf0(W281_81, W180_80)) & ! [W382_82] : (((aDivisorOf0(W382_82, W079_79) & aDivisorOf0(W382_82, W180_80)) => doDivides0(W382_82, W281_81)))))))), ! [W083_83, W184_84] : (((aElement0(W083_83) & aElement0(W184_84)) => (misRelativelyPrime0(W083_83, W184_84) <=> aGcdOfAnd0(sz10, W083_83, W184_84)))), ! [W085_85] : ((aElement0(W085_85) => ! [W186_86] : ((=(W186_86, slsdtgt0(W085_85)) <=> (aSet0(W186_86) & ! [W287_87] : ((aElementOf0(W287_87, W186_86) <=> ? [W388_88] : ((aElement0(W388_88) & =(sdtasdt0(W085_85, W388_88), W287_87)))))))))), ! [W089_89] : ((aElement0(W089_89) => aIdeal0(slsdtgt0(W089_89)))), (aElement0(xa) & aElement0(xb)), (~=(xa, sz00) | ~=(xb, sz00)), (((((((((aElement0(xc) & ? [W090_90] : ((aElement0(W090_90) & =(sdtasdt0(xc, W090_90), xa)))) & doDivides0(xc, xa)) & aDivisorOf0(xc, xa)) & aElement0(xc)) & ? [W091_91] : ((aElement0(W091_91) & =(sdtasdt0(xc, W091_91), xb)))) & doDivides0(xc, xb)) & aDivisorOf0(xc, xb)) & ! [W092_92] : (((((aElement0(W092_92) & (? [W193_93] : ((aElement0(W193_93) & =(sdtasdt0(W092_92, W193_93), xa))) | doDivides0(W092_92, xa))) | aDivisorOf0(W092_92, xa)) & ((? [W194_94] : ((aElement0(W194_94) & =(sdtasdt0(W092_92, W194_94), xb))) | doDivides0(W092_92, xb)) | aDivisorOf0(W092_92, xb))) => (? [W195_95] : ((aElement0(W195_95) & =(sdtasdt0(W092_92, W195_95), xc))) & doDivides0(W092_92, xc))))) & aGcdOfAnd0(xc, xa, xb)), ((((((aSet0(xI) & ! [W096_96] : ((aElementOf0(W096_96, xI) => (! [W197_97] : ((aElementOf0(W197_97, xI) => aElementOf0(sdtpldt0(W096_96, W197_97), xI))) & ! [W198_98] : ((aElement0(W198_98) => aElementOf0(sdtasdt0(W198_98, W096_96), xI))))))) & aIdeal0(xI)) & ! [W099_99] : ((aElementOf0(W099_99, slsdtgt0(xa)) <=> ? [W1100_100] : ((aElement0(W1100_100) & =(sdtasdt0(xa, W1100_100), W099_99)))))) & ! [W0101_101] : ((aElementOf0(W0101_101, slsdtgt0(xb)) <=> ? [W1102_102] : ((aElement0(W1102_102) & =(sdtasdt0(xb, W1102_102), W0101_101)))))) & ! [W0103_103] : ((aElementOf0(W0103_103, xI) <=> ? [W1104_104, W2105_105] : (((aElementOf0(W1104_104, slsdtgt0(xa)) & aElementOf0(W2105_105, slsdtgt0(xb))) & =(sdtpldt0(W1104_104, W2105_105), W0103_103)))))) & =(xI, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))), (((((((? [W0106_106] : ((aElement0(W0106_106) & =(sdtasdt0(xa, W0106_106), sz00))) & aElementOf0(sz00, slsdtgt0(xa))) & ? [W0107_107] : ((aElement0(W0107_107) & =(sdtasdt0(xa, W0107_107), xa)))) & aElementOf0(xa, slsdtgt0(xa))) & ? [W0108_108] : ((aElement0(W0108_108) & =(sdtasdt0(xb, W0108_108), sz00)))) & aElementOf0(sz00, slsdtgt0(xb))) & ? [W0109_109] : ((aElement0(W0109_109) & =(sdtasdt0(xb, W0109_109), xb)))) & aElementOf0(xb, slsdtgt0(xb))), ? [W0110_110] : (((((! [W1111_111] : ((aElementOf0(W1111_111, slsdtgt0(xa)) <=> ? [W2112_112] : ((aElement0(W2112_112) & =(sdtasdt0(xa, W2112_112), W1111_111))))) & ! [W1113_113] : ((aElementOf0(W1113_113, slsdtgt0(xb)) <=> ? [W2114_114] : ((aElement0(W2114_114) & =(sdtasdt0(xb, W2114_114), W1113_113)))))) & ? [W1115_115, W2116_116] : (((aElementOf0(W1115_115, slsdtgt0(xa)) & aElementOf0(W2116_116, slsdtgt0(xb))) & =(sdtpldt0(W1115_115, W2116_116), W0110_110)))) & aElementOf0(W0110_110, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ~=(W0110_110, sz00))), (((? [W0117_117, W1118_118] : (((aElementOf0(W0117_117, slsdtgt0(xa)) & aElementOf0(W1118_118, slsdtgt0(xb))) & =(sdtpldt0(W0117_117, W1118_118), xu))) & aElementOf0(xu, xI)) & ~=(xu, sz00)) & ! [W0119_119] : ((((? [W1120_120, W2121_121] : (((aElementOf0(W1120_120, slsdtgt0(xa)) & aElementOf0(W2121_121, slsdtgt0(xb))) & =(sdtpldt0(W1120_120, W2121_121), W0119_119))) | aElementOf0(W0119_119, xI)) & ~=(W0119_119, sz00)) => ~iLess0(sbrdtbr0(W0119_119), sbrdtbr0(xu))))), ~(((? [W0122_122] : ((aElement0(W0122_122) & =(sdtasdt0(xu, W0122_122), xa))) | doDivides0(xu, xa)) | aDivisorOf0(xu, xa)) & ((? [W0123_123] : ((aElement0(W0123_123) & =(sdtasdt0(xu, W0123_123), xb))) | doDivides0(xu, xb)) | aDivisorOf0(xu, xb))), ? [W0124_124, W1125_125] : (((aElement0(W0124_124) & aElement0(W1125_125)) & =(xu, sdtpldt0(sdtasdt0(xa, W0124_124), sdtasdt0(xb, W1125_125))))), ~~(? [W0126_126] : ((aElement0(W0126_126) & =(sdtasdt0(xu, W0126_126), xa))) & doDivides0(xu, xa)), ~~(? [W0127_127] : ((aElement0(W0127_127) & =(sdtasdt0(xu, W0127_127), xb))) & doDivides0(xu, xb)), ~$false
% 23.18/9.19
% 23.18/9.19 [1] ALPHA_AND : (aElement0(xa) & aElement0(xb))
% 23.18/9.19 -> [2] aElement0(xa), aElement0(xb)
% 23.18/9.19
% 23.18/9.19 [2] ALPHA_AND : (((((((((aElement0(xc) & ? [W090_90] : ((aElement0(W090_90) & =(sdtasdt0(xc, W090_90), xa)))) & doDivides0(xc, xa)) & aDivisorOf0(xc, xa)) & aElement0(xc)) & ? [W091_91] : ((aElement0(W091_91) & =(sdtasdt0(xc, W091_91), xb)))) & doDivides0(xc, xb)) & aDivisorOf0(xc, xb)) & ! [W092_92] : (((((aElement0(W092_92) & (? [W193_93] : ((aElement0(W193_93) & =(sdtasdt0(W092_92, W193_93), xa))) | doDivides0(W092_92, xa))) | aDivisorOf0(W092_92, xa)) & ((? [W194_94] : ((aElement0(W194_94) & =(sdtasdt0(W092_92, W194_94), xb))) | doDivides0(W092_92, xb)) | aDivisorOf0(W092_92, xb))) => (? [W195_95] : ((aElement0(W195_95) & =(sdtasdt0(W092_92, W195_95), xc))) & doDivides0(W092_92, xc))))) & aGcdOfAnd0(xc, xa, xb))
% 23.18/9.19 -> [3] ((((((((aElement0(xc) & ? [W090_90] : ((aElement0(W090_90) & =(sdtasdt0(xc, W090_90), xa)))) & doDivides0(xc, xa)) & aDivisorOf0(xc, xa)) & aElement0(xc)) & ? [W091_91] : ((aElement0(W091_91) & =(sdtasdt0(xc, W091_91), xb)))) & doDivides0(xc, xb)) & aDivisorOf0(xc, xb)) & ! [W092_92] : (((((aElement0(W092_92) & (? [W193_93] : ((aElement0(W193_93) & =(sdtasdt0(W092_92, W193_93), xa))) | doDivides0(W092_92, xa))) | aDivisorOf0(W092_92, xa)) & ((? [W194_94] : ((aElement0(W194_94) & =(sdtasdt0(W092_92, W194_94), xb))) | doDivides0(W092_92, xb)) | aDivisorOf0(W092_92, xb))) => (? [W195_95] : ((aElement0(W195_95) & =(sdtasdt0(W092_92, W195_95), xc))) & doDivides0(W092_92, xc))))), aGcdOfAnd0(xc, xa, xb)
% 23.18/9.19
% 23.18/9.19 [3] ALPHA_AND : ((((((aSet0(xI) & ! [W096_96] : ((aElementOf0(W096_96, xI) => (! [W197_97] : ((aElementOf0(W197_97, xI) => aElementOf0(sdtpldt0(W096_96, W197_97), xI))) & ! [W198_98] : ((aElement0(W198_98) => aElementOf0(sdtasdt0(W198_98, W096_96), xI))))))) & aIdeal0(xI)) & ! [W099_99] : ((aElementOf0(W099_99, slsdtgt0(xa)) <=> ? [W1100_100] : ((aElement0(W1100_100) & =(sdtasdt0(xa, W1100_100), W099_99)))))) & ! [W0101_101] : ((aElementOf0(W0101_101, slsdtgt0(xb)) <=> ? [W1102_102] : ((aElement0(W1102_102) & =(sdtasdt0(xb, W1102_102), W0101_101)))))) & ! [W0103_103] : ((aElementOf0(W0103_103, xI) <=> ? [W1104_104, W2105_105] : (((aElementOf0(W1104_104, slsdtgt0(xa)) & aElementOf0(W2105_105, slsdtgt0(xb))) & =(sdtpldt0(W1104_104, W2105_105), W0103_103)))))) & =(xI, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))
% 23.18/9.19 -> [4] (((((aSet0(xI) & ! [W096_96] : ((aElementOf0(W096_96, xI) => (! [W197_97] : ((aElementOf0(W197_97, xI) => aElementOf0(sdtpldt0(W096_96, W197_97), xI))) & ! [W198_98] : ((aElement0(W198_98) => aElementOf0(sdtasdt0(W198_98, W096_96), xI))))))) & aIdeal0(xI)) & ! [W099_99] : ((aElementOf0(W099_99, slsdtgt0(xa)) <=> ? [W1100_100] : ((aElement0(W1100_100) & =(sdtasdt0(xa, W1100_100), W099_99)))))) & ! [W0101_101] : ((aElementOf0(W0101_101, slsdtgt0(xb)) <=> ? [W1102_102] : ((aElement0(W1102_102) & =(sdtasdt0(xb, W1102_102), W0101_101)))))) & ! [W0103_103] : ((aElementOf0(W0103_103, xI) <=> ? [W1104_104, W2105_105] : (((aElementOf0(W1104_104, slsdtgt0(xa)) & aElementOf0(W2105_105, slsdtgt0(xb))) & =(sdtpldt0(W1104_104, W2105_105), W0103_103)))))), =(xI, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))
% 23.18/9.19
% 23.18/9.19 [4] ALPHA_AND : (((((((? [W0106_106] : ((aElement0(W0106_106) & =(sdtasdt0(xa, W0106_106), sz00))) & aElementOf0(sz00, slsdtgt0(xa))) & ? [W0107_107] : ((aElement0(W0107_107) & =(sdtasdt0(xa, W0107_107), xa)))) & aElementOf0(xa, slsdtgt0(xa))) & ? [W0108_108] : ((aElement0(W0108_108) & =(sdtasdt0(xb, W0108_108), sz00)))) & aElementOf0(sz00, slsdtgt0(xb))) & ? [W0109_109] : ((aElement0(W0109_109) & =(sdtasdt0(xb, W0109_109), xb)))) & aElementOf0(xb, slsdtgt0(xb)))
% 23.18/9.19 -> [5] ((((((? [W0106_106] : ((aElement0(W0106_106) & =(sdtasdt0(xa, W0106_106), sz00))) & aElementOf0(sz00, slsdtgt0(xa))) & ? [W0107_107] : ((aElement0(W0107_107) & =(sdtasdt0(xa, W0107_107), xa)))) & aElementOf0(xa, slsdtgt0(xa))) & ? [W0108_108] : ((aElement0(W0108_108) & =(sdtasdt0(xb, W0108_108), sz00)))) & aElementOf0(sz00, slsdtgt0(xb))) & ? [W0109_109] : ((aElement0(W0109_109) & =(sdtasdt0(xb, W0109_109), xb)))), aElementOf0(xb, slsdtgt0(xb))
% 23.18/9.19
% 23.18/9.19 [5] ALPHA_AND : (((? [W0117_117, W1118_118] : (((aElementOf0(W0117_117, slsdtgt0(xa)) & aElementOf0(W1118_118, slsdtgt0(xb))) & =(sdtpldt0(W0117_117, W1118_118), xu))) & aElementOf0(xu, xI)) & ~=(xu, sz00)) & ! [W0119_119] : ((((? [W1120_120, W2121_121] : (((aElementOf0(W1120_120, slsdtgt0(xa)) & aElementOf0(W2121_121, slsdtgt0(xb))) & =(sdtpldt0(W1120_120, W2121_121), W0119_119))) | aElementOf0(W0119_119, xI)) & ~=(W0119_119, sz00)) => ~iLess0(sbrdtbr0(W0119_119), sbrdtbr0(xu)))))
% 23.18/9.19 -> [6] ((? [W0117_117, W1118_118] : (((aElementOf0(W0117_117, slsdtgt0(xa)) & aElementOf0(W1118_118, slsdtgt0(xb))) & =(sdtpldt0(W0117_117, W1118_118), xu))) & aElementOf0(xu, xI)) & ~=(xu, sz00)), ! [W0119_119] : ((((? [W1120_120, W2121_121] : (((aElementOf0(W1120_120, slsdtgt0(xa)) & aElementOf0(W2121_121, slsdtgt0(xb))) & =(sdtpldt0(W1120_120, W2121_121), W0119_119))) | aElementOf0(W0119_119, xI)) & ~=(W0119_119, sz00)) => ~iLess0(sbrdtbr0(W0119_119), sbrdtbr0(xu))))
% 23.18/9.19
% 23.18/9.19 [6] ALPHA_NOT_NOT : ~~(? [W0126_126] : ((aElement0(W0126_126) & =(sdtasdt0(xu, W0126_126), xa))) & doDivides0(xu, xa))
% 23.18/9.19 -> [7] (? [W0126_126] : ((aElement0(W0126_126) & =(sdtasdt0(xu, W0126_126), xa))) & doDivides0(xu, xa))
% 23.18/9.19
% 23.18/9.19 [7] ALPHA_NOT_NOT : ~~(? [W0127_127] : ((aElement0(W0127_127) & =(sdtasdt0(xu, W0127_127), xb))) & doDivides0(xu, xb))
% 23.18/9.19 -> [8] (? [W0127_127] : ((aElement0(W0127_127) & =(sdtasdt0(xu, W0127_127), xb))) & doDivides0(xu, xb))
% 23.18/9.19
% 23.18/9.19 [8] ALPHA_AND : ((((((((aElement0(xc) & ? [W090_90] : ((aElement0(W090_90) & =(sdtasdt0(xc, W090_90), xa)))) & doDivides0(xc, xa)) & aDivisorOf0(xc, xa)) & aElement0(xc)) & ? [W091_91] : ((aElement0(W091_91) & =(sdtasdt0(xc, W091_91), xb)))) & doDivides0(xc, xb)) & aDivisorOf0(xc, xb)) & ! [W092_92] : (((((aElement0(W092_92) & (? [W193_93] : ((aElement0(W193_93) & =(sdtasdt0(W092_92, W193_93), xa))) | doDivides0(W092_92, xa))) | aDivisorOf0(W092_92, xa)) & ((? [W194_94] : ((aElement0(W194_94) & =(sdtasdt0(W092_92, W194_94), xb))) | doDivides0(W092_92, xb)) | aDivisorOf0(W092_92, xb))) => (? [W195_95] : ((aElement0(W195_95) & =(sdtasdt0(W092_92, W195_95), xc))) & doDivides0(W092_92, xc)))))
% 23.18/9.19 -> [9] (((((((aElement0(xc) & ? [W090_90] : ((aElement0(W090_90) & =(sdtasdt0(xc, W090_90), xa)))) & doDivides0(xc, xa)) & aDivisorOf0(xc, xa)) & aElement0(xc)) & ? [W091_91] : ((aElement0(W091_91) & =(sdtasdt0(xc, W091_91), xb)))) & doDivides0(xc, xb)) & aDivisorOf0(xc, xb)), ! [W092_92] : (((((aElement0(W092_92) & (? [W193_93] : ((aElement0(W193_93) & =(sdtasdt0(W092_92, W193_93), xa))) | doDivides0(W092_92, xa))) | aDivisorOf0(W092_92, xa)) & ((? [W194_94] : ((aElement0(W194_94) & =(sdtasdt0(W092_92, W194_94), xb))) | doDivides0(W092_92, xb)) | aDivisorOf0(W092_92, xb))) => (? [W195_95] : ((aElement0(W195_95) & =(sdtasdt0(W092_92, W195_95), xc))) & doDivides0(W092_92, xc))))
% 23.18/9.19
% 23.18/9.19 [9] ALPHA_AND : (((((aSet0(xI) & ! [W096_96] : ((aElementOf0(W096_96, xI) => (! [W197_97] : ((aElementOf0(W197_97, xI) => aElementOf0(sdtpldt0(W096_96, W197_97), xI))) & ! [W198_98] : ((aElement0(W198_98) => aElementOf0(sdtasdt0(W198_98, W096_96), xI))))))) & aIdeal0(xI)) & ! [W099_99] : ((aElementOf0(W099_99, slsdtgt0(xa)) <=> ? [W1100_100] : ((aElement0(W1100_100) & =(sdtasdt0(xa, W1100_100), W099_99)))))) & ! [W0101_101] : ((aElementOf0(W0101_101, slsdtgt0(xb)) <=> ? [W1102_102] : ((aElement0(W1102_102) & =(sdtasdt0(xb, W1102_102), W0101_101)))))) & ! [W0103_103] : ((aElementOf0(W0103_103, xI) <=> ? [W1104_104, W2105_105] : (((aElementOf0(W1104_104, slsdtgt0(xa)) & aElementOf0(W2105_105, slsdtgt0(xb))) & =(sdtpldt0(W1104_104, W2105_105), W0103_103))))))
% 23.18/9.19 -> [10] ((((aSet0(xI) & ! [W096_96] : ((aElementOf0(W096_96, xI) => (! [W197_97] : ((aElementOf0(W197_97, xI) => aElementOf0(sdtpldt0(W096_96, W197_97), xI))) & ! [W198_98] : ((aElement0(W198_98) => aElementOf0(sdtasdt0(W198_98, W096_96), xI))))))) & aIdeal0(xI)) & ! [W099_99] : ((aElementOf0(W099_99, slsdtgt0(xa)) <=> ? [W1100_100] : ((aElement0(W1100_100) & =(sdtasdt0(xa, W1100_100), W099_99)))))) & ! [W0101_101] : ((aElementOf0(W0101_101, slsdtgt0(xb)) <=> ? [W1102_102] : ((aElement0(W1102_102) & =(sdtasdt0(xb, W1102_102), W0101_101)))))), ! [W0103_103] : ((aElementOf0(W0103_103, xI) <=> ? [W1104_104, W2105_105] : (((aElementOf0(W1104_104, slsdtgt0(xa)) & aElementOf0(W2105_105, slsdtgt0(xb))) & =(sdtpldt0(W1104_104, W2105_105), W0103_103)))))
% 23.18/9.19
% 23.18/9.19 [10] ALPHA_AND : ((((((? [W0106_106] : ((aElement0(W0106_106) & =(sdtasdt0(xa, W0106_106), sz00))) & aElementOf0(sz00, slsdtgt0(xa))) & ? [W0107_107] : ((aElement0(W0107_107) & =(sdtasdt0(xa, W0107_107), xa)))) & aElementOf0(xa, slsdtgt0(xa))) & ? [W0108_108] : ((aElement0(W0108_108) & =(sdtasdt0(xb, W0108_108), sz00)))) & aElementOf0(sz00, slsdtgt0(xb))) & ? [W0109_109] : ((aElement0(W0109_109) & =(sdtasdt0(xb, W0109_109), xb))))
% 23.18/9.19 -> [11] (((((? [W0106_106] : ((aElement0(W0106_106) & =(sdtasdt0(xa, W0106_106), sz00))) & aElementOf0(sz00, slsdtgt0(xa))) & ? [W0107_107] : ((aElement0(W0107_107) & =(sdtasdt0(xa, W0107_107), xa)))) & aElementOf0(xa, slsdtgt0(xa))) & ? [W0108_108] : ((aElement0(W0108_108) & =(sdtasdt0(xb, W0108_108), sz00)))) & aElementOf0(sz00, slsdtgt0(xb))), ? [W0109_109] : ((aElement0(W0109_109) & =(sdtasdt0(xb, W0109_109), xb)))
% 23.18/9.19
% 23.18/9.19 [11] ALPHA_AND : ((? [W0117_117, W1118_118] : (((aElementOf0(W0117_117, slsdtgt0(xa)) & aElementOf0(W1118_118, slsdtgt0(xb))) & =(sdtpldt0(W0117_117, W1118_118), xu))) & aElementOf0(xu, xI)) & ~=(xu, sz00))
% 23.18/9.19 -> [12] (? [W0117_117, W1118_118] : (((aElementOf0(W0117_117, slsdtgt0(xa)) & aElementOf0(W1118_118, slsdtgt0(xb))) & =(sdtpldt0(W0117_117, W1118_118), xu))) & aElementOf0(xu, xI)), ~=(xu, sz00)
% 23.18/9.19
% 23.18/9.19 [12] ALPHA_AND : (? [W0126_126] : ((aElement0(W0126_126) & =(sdtasdt0(xu, W0126_126), xa))) & doDivides0(xu, xa))
% 23.18/9.19 -> [13] ? [W0126_126] : ((aElement0(W0126_126) & =(sdtasdt0(xu, W0126_126), xa))), doDivides0(xu, xa)
% 23.18/9.19
% 23.18/9.19 [13] ALPHA_AND : (? [W0127_127] : ((aElement0(W0127_127) & =(sdtasdt0(xu, W0127_127), xb))) & doDivides0(xu, xb))
% 23.18/9.19 -> [14] ? [W0127_127] : ((aElement0(W0127_127) & =(sdtasdt0(xu, W0127_127), xb))), doDivides0(xu, xb)
% 23.18/9.19
% 23.18/9.19 [14] ALPHA_AND : (((((((aElement0(xc) & ? [W090_90] : ((aElement0(W090_90) & =(sdtasdt0(xc, W090_90), xa)))) & doDivides0(xc, xa)) & aDivisorOf0(xc, xa)) & aElement0(xc)) & ? [W091_91] : ((aElement0(W091_91) & =(sdtasdt0(xc, W091_91), xb)))) & doDivides0(xc, xb)) & aDivisorOf0(xc, xb))
% 23.18/9.19 -> [15] ((((((aElement0(xc) & ? [W090_90] : ((aElement0(W090_90) & =(sdtasdt0(xc, W090_90), xa)))) & doDivides0(xc, xa)) & aDivisorOf0(xc, xa)) & aElement0(xc)) & ? [W091_91] : ((aElement0(W091_91) & =(sdtasdt0(xc, W091_91), xb)))) & doDivides0(xc, xb)), aDivisorOf0(xc, xb)
% 23.18/9.19
% 23.18/9.19 [15] ALPHA_AND : ((((aSet0(xI) & ! [W096_96] : ((aElementOf0(W096_96, xI) => (! [W197_97] : ((aElementOf0(W197_97, xI) => aElementOf0(sdtpldt0(W096_96, W197_97), xI))) & ! [W198_98] : ((aElement0(W198_98) => aElementOf0(sdtasdt0(W198_98, W096_96), xI))))))) & aIdeal0(xI)) & ! [W099_99] : ((aElementOf0(W099_99, slsdtgt0(xa)) <=> ? [W1100_100] : ((aElement0(W1100_100) & =(sdtasdt0(xa, W1100_100), W099_99)))))) & ! [W0101_101] : ((aElementOf0(W0101_101, slsdtgt0(xb)) <=> ? [W1102_102] : ((aElement0(W1102_102) & =(sdtasdt0(xb, W1102_102), W0101_101))))))
% 23.18/9.19 -> [16] (((aSet0(xI) & ! [W096_96] : ((aElementOf0(W096_96, xI) => (! [W197_97] : ((aElementOf0(W197_97, xI) => aElementOf0(sdtpldt0(W096_96, W197_97), xI))) & ! [W198_98] : ((aElement0(W198_98) => aElementOf0(sdtasdt0(W198_98, W096_96), xI))))))) & aIdeal0(xI)) & ! [W099_99] : ((aElementOf0(W099_99, slsdtgt0(xa)) <=> ? [W1100_100] : ((aElement0(W1100_100) & =(sdtasdt0(xa, W1100_100), W099_99)))))), ! [W0101_101] : ((aElementOf0(W0101_101, slsdtgt0(xb)) <=> ? [W1102_102] : ((aElement0(W1102_102) & =(sdtasdt0(xb, W1102_102), W0101_101)))))
% 23.18/9.19
% 23.18/9.19 [16] ALPHA_AND : (((((? [W0106_106] : ((aElement0(W0106_106) & =(sdtasdt0(xa, W0106_106), sz00))) & aElementOf0(sz00, slsdtgt0(xa))) & ? [W0107_107] : ((aElement0(W0107_107) & =(sdtasdt0(xa, W0107_107), xa)))) & aElementOf0(xa, slsdtgt0(xa))) & ? [W0108_108] : ((aElement0(W0108_108) & =(sdtasdt0(xb, W0108_108), sz00)))) & aElementOf0(sz00, slsdtgt0(xb)))
% 23.18/9.19 -> [17] ((((? [W0106_106] : ((aElement0(W0106_106) & =(sdtasdt0(xa, W0106_106), sz00))) & aElementOf0(sz00, slsdtgt0(xa))) & ? [W0107_107] : ((aElement0(W0107_107) & =(sdtasdt0(xa, W0107_107), xa)))) & aElementOf0(xa, slsdtgt0(xa))) & ? [W0108_108] : ((aElement0(W0108_108) & =(sdtasdt0(xb, W0108_108), sz00)))), aElementOf0(sz00, slsdtgt0(xb))
% 23.18/9.19
% 23.18/9.19 [17] ALPHA_AND : (? [W0117_117, W1118_118] : (((aElementOf0(W0117_117, slsdtgt0(xa)) & aElementOf0(W1118_118, slsdtgt0(xb))) & =(sdtpldt0(W0117_117, W1118_118), xu))) & aElementOf0(xu, xI))
% 23.18/9.19 -> [18] ? [W0117_117, W1118_118] : (((aElementOf0(W0117_117, slsdtgt0(xa)) & aElementOf0(W1118_118, slsdtgt0(xb))) & =(sdtpldt0(W0117_117, W1118_118), xu))), aElementOf0(xu, xI)
% 23.18/9.19
% 23.18/9.19 [18] ALPHA_AND : ((((((aElement0(xc) & ? [W090_90] : ((aElement0(W090_90) & =(sdtasdt0(xc, W090_90), xa)))) & doDivides0(xc, xa)) & aDivisorOf0(xc, xa)) & aElement0(xc)) & ? [W091_91] : ((aElement0(W091_91) & =(sdtasdt0(xc, W091_91), xb)))) & doDivides0(xc, xb))
% 23.18/9.19 -> [19] (((((aElement0(xc) & ? [W090_90] : ((aElement0(W090_90) & =(sdtasdt0(xc, W090_90), xa)))) & doDivides0(xc, xa)) & aDivisorOf0(xc, xa)) & aElement0(xc)) & ? [W091_91] : ((aElement0(W091_91) & =(sdtasdt0(xc, W091_91), xb)))), doDivides0(xc, xb)
% 23.18/9.19
% 23.18/9.19 [19] ALPHA_AND : (((aSet0(xI) & ! [W096_96] : ((aElementOf0(W096_96, xI) => (! [W197_97] : ((aElementOf0(W197_97, xI) => aElementOf0(sdtpldt0(W096_96, W197_97), xI))) & ! [W198_98] : ((aElement0(W198_98) => aElementOf0(sdtasdt0(W198_98, W096_96), xI))))))) & aIdeal0(xI)) & ! [W099_99] : ((aElementOf0(W099_99, slsdtgt0(xa)) <=> ? [W1100_100] : ((aElement0(W1100_100) & =(sdtasdt0(xa, W1100_100), W099_99))))))
% 23.18/9.19 -> [20] ((aSet0(xI) & ! [W096_96] : ((aElementOf0(W096_96, xI) => (! [W197_97] : ((aElementOf0(W197_97, xI) => aElementOf0(sdtpldt0(W096_96, W197_97), xI))) & ! [W198_98] : ((aElement0(W198_98) => aElementOf0(sdtasdt0(W198_98, W096_96), xI))))))) & aIdeal0(xI)), ! [W099_99] : ((aElementOf0(W099_99, slsdtgt0(xa)) <=> ? [W1100_100] : ((aElement0(W1100_100) & =(sdtasdt0(xa, W1100_100), W099_99)))))
% 23.18/9.19
% 23.18/9.19 [20] ALPHA_AND : ((((? [W0106_106] : ((aElement0(W0106_106) & =(sdtasdt0(xa, W0106_106), sz00))) & aElementOf0(sz00, slsdtgt0(xa))) & ? [W0107_107] : ((aElement0(W0107_107) & =(sdtasdt0(xa, W0107_107), xa)))) & aElementOf0(xa, slsdtgt0(xa))) & ? [W0108_108] : ((aElement0(W0108_108) & =(sdtasdt0(xb, W0108_108), sz00))))
% 23.18/9.19 -> [21] (((? [W0106_106] : ((aElement0(W0106_106) & =(sdtasdt0(xa, W0106_106), sz00))) & aElementOf0(sz00, slsdtgt0(xa))) & ? [W0107_107] : ((aElement0(W0107_107) & =(sdtasdt0(xa, W0107_107), xa)))) & aElementOf0(xa, slsdtgt0(xa))), ? [W0108_108] : ((aElement0(W0108_108) & =(sdtasdt0(xb, W0108_108), sz00)))
% 23.18/9.19
% 23.18/9.19 [21] ALPHA_AND : (((((aElement0(xc) & ? [W090_90] : ((aElement0(W090_90) & =(sdtasdt0(xc, W090_90), xa)))) & doDivides0(xc, xa)) & aDivisorOf0(xc, xa)) & aElement0(xc)) & ? [W091_91] : ((aElement0(W091_91) & =(sdtasdt0(xc, W091_91), xb))))
% 23.18/9.19 -> [22] ((((aElement0(xc) & ? [W090_90] : ((aElement0(W090_90) & =(sdtasdt0(xc, W090_90), xa)))) & doDivides0(xc, xa)) & aDivisorOf0(xc, xa)) & aElement0(xc)), ? [W091_91] : ((aElement0(W091_91) & =(sdtasdt0(xc, W091_91), xb)))
% 23.18/9.19
% 23.18/9.19 [22] ALPHA_AND : ((aSet0(xI) & ! [W096_96] : ((aElementOf0(W096_96, xI) => (! [W197_97] : ((aElementOf0(W197_97, xI) => aElementOf0(sdtpldt0(W096_96, W197_97), xI))) & ! [W198_98] : ((aElement0(W198_98) => aElementOf0(sdtasdt0(W198_98, W096_96), xI))))))) & aIdeal0(xI))
% 23.18/9.19 -> [23] (aSet0(xI) & ! [W096_96] : ((aElementOf0(W096_96, xI) => (! [W197_97] : ((aElementOf0(W197_97, xI) => aElementOf0(sdtpldt0(W096_96, W197_97), xI))) & ! [W198_98] : ((aElement0(W198_98) => aElementOf0(sdtasdt0(W198_98, W096_96), xI))))))), aIdeal0(xI)
% 23.18/9.19
% 23.18/9.19 [23] Rewrite : aIdeal0(xI)
% 23.18/9.19 -> [24] (aSet0(xI) & ! [W150_50] : ((aElementOf0(W150_50, xI) => (! [W251_51] : ((aElementOf0(W251_51, xI) => aElementOf0(sdtpldt0(W150_50, W251_51), xI))) & ! [W252_52] : ((aElement0(W252_52) => aElementOf0(sdtasdt0(W252_52, W150_50), xI)))))))
% 23.18/9.19
% 23.18/9.19 [24] ALPHA_AND : (((? [W0106_106] : ((aElement0(W0106_106) & =(sdtasdt0(xa, W0106_106), sz00))) & aElementOf0(sz00, slsdtgt0(xa))) & ? [W0107_107] : ((aElement0(W0107_107) & =(sdtasdt0(xa, W0107_107), xa)))) & aElementOf0(xa, slsdtgt0(xa)))
% 23.18/9.19 -> [25] ((? [W0106_106] : ((aElement0(W0106_106) & =(sdtasdt0(xa, W0106_106), sz00))) & aElementOf0(sz00, slsdtgt0(xa))) & ? [W0107_107] : ((aElement0(W0107_107) & =(sdtasdt0(xa, W0107_107), xa)))), aElementOf0(xa, slsdtgt0(xa))
% 23.18/9.19
% 23.18/9.19 [25] ALPHA_AND : ((((aElement0(xc) & ? [W090_90] : ((aElement0(W090_90) & =(sdtasdt0(xc, W090_90), xa)))) & doDivides0(xc, xa)) & aDivisorOf0(xc, xa)) & aElement0(xc))
% 23.18/9.19 -> [26] (((aElement0(xc) & ? [W090_90] : ((aElement0(W090_90) & =(sdtasdt0(xc, W090_90), xa)))) & doDivides0(xc, xa)) & aDivisorOf0(xc, xa)), aElement0(xc)
% 23.18/9.19
% 23.18/9.19 [26] ALPHA_AND : (aSet0(xI) & ! [W096_96] : ((aElementOf0(W096_96, xI) => (! [W197_97] : ((aElementOf0(W197_97, xI) => aElementOf0(sdtpldt0(W096_96, W197_97), xI))) & ! [W198_98] : ((aElement0(W198_98) => aElementOf0(sdtasdt0(W198_98, W096_96), xI)))))))
% 23.18/9.19 -> [27] aSet0(xI), ! [W096_96] : ((aElementOf0(W096_96, xI) => (! [W197_97] : ((aElementOf0(W197_97, xI) => aElementOf0(sdtpldt0(W096_96, W197_97), xI))) & ! [W198_98] : ((aElement0(W198_98) => aElementOf0(sdtasdt0(W198_98, W096_96), xI))))))
% 23.18/9.19
% 23.18/9.19 [27] ALPHA_AND : (aSet0(xI) & ! [W150_50] : ((aElementOf0(W150_50, xI) => (! [W251_51] : ((aElementOf0(W251_51, xI) => aElementOf0(sdtpldt0(W150_50, W251_51), xI))) & ! [W252_52] : ((aElement0(W252_52) => aElementOf0(sdtasdt0(W252_52, W150_50), xI)))))))
% 23.18/9.19 -> [28] aSet0(xI), ! [W150_50] : ((aElementOf0(W150_50, xI) => (! [W251_51] : ((aElementOf0(W251_51, xI) => aElementOf0(sdtpldt0(W150_50, W251_51), xI))) & ! [W252_52] : ((aElement0(W252_52) => aElementOf0(sdtasdt0(W252_52, W150_50), xI))))))
% 23.18/9.19
% 23.18/9.19 [28] ALPHA_AND : ((? [W0106_106] : ((aElement0(W0106_106) & =(sdtasdt0(xa, W0106_106), sz00))) & aElementOf0(sz00, slsdtgt0(xa))) & ? [W0107_107] : ((aElement0(W0107_107) & =(sdtasdt0(xa, W0107_107), xa))))
% 23.18/9.19 -> [29] (? [W0106_106] : ((aElement0(W0106_106) & =(sdtasdt0(xa, W0106_106), sz00))) & aElementOf0(sz00, slsdtgt0(xa))), ? [W0107_107] : ((aElement0(W0107_107) & =(sdtasdt0(xa, W0107_107), xa)))
% 23.18/9.19
% 23.18/9.19 [29] ALPHA_AND : (((aElement0(xc) & ? [W090_90] : ((aElement0(W090_90) & =(sdtasdt0(xc, W090_90), xa)))) & doDivides0(xc, xa)) & aDivisorOf0(xc, xa))
% 23.18/9.19 -> [30] ((aElement0(xc) & ? [W090_90] : ((aElement0(W090_90) & =(sdtasdt0(xc, W090_90), xa)))) & doDivides0(xc, xa)), aDivisorOf0(xc, xa)
% 23.18/9.19
% 23.18/9.19 [30] ALPHA_AND : (? [W0106_106] : ((aElement0(W0106_106) & =(sdtasdt0(xa, W0106_106), sz00))) & aElementOf0(sz00, slsdtgt0(xa)))
% 23.18/9.19 -> [31] ? [W0106_106] : ((aElement0(W0106_106) & =(sdtasdt0(xa, W0106_106), sz00))), aElementOf0(sz00, slsdtgt0(xa))
% 23.18/9.19
% 23.18/9.19 [31] ALPHA_AND : ((aElement0(xc) & ? [W090_90] : ((aElement0(W090_90) & =(sdtasdt0(xc, W090_90), xa)))) & doDivides0(xc, xa))
% 23.18/9.19 -> [32] (aElement0(xc) & ? [W090_90] : ((aElement0(W090_90) & =(sdtasdt0(xc, W090_90), xa)))), doDivides0(xc, xa)
% 23.18/9.19
% 23.18/9.19 [32] ALPHA_AND : (aElement0(xc) & ? [W090_90] : ((aElement0(W090_90) & =(sdtasdt0(xc, W090_90), xa))))
% 23.18/9.19 -> [33] aElement0(xc), ? [W090_90] : ((aElement0(W090_90) & =(sdtasdt0(xc, W090_90), xa)))
% 23.18/9.19
% 23.18/9.19 [33] DELTA_EXISTS : ? [W0110_110] : (((((! [W1111_111] : ((aElementOf0(W1111_111, slsdtgt0(xa)) <=> ? [W2112_112] : ((aElement0(W2112_112) & =(sdtasdt0(xa, W2112_112), W1111_111))))) & ! [W1113_113] : ((aElementOf0(W1113_113, slsdtgt0(xb)) <=> ? [W2114_114] : ((aElement0(W2114_114) & =(sdtasdt0(xb, W2114_114), W1113_113)))))) & ? [W1115_115, W2116_116] : (((aElementOf0(W1115_115, slsdtgt0(xa)) & aElementOf0(W2116_116, slsdtgt0(xb))) & =(sdtpldt0(W1115_115, W2116_116), W0110_110)))) & aElementOf0(W0110_110, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ~=(W0110_110, sz00)))
% 23.18/9.19 -> [34] ((((! [W1111_111] : ((aElementOf0(W1111_111, slsdtgt0(xa)) <=> ? [W2112_112] : ((aElement0(W2112_112) & =(sdtasdt0(xa, W2112_112), W1111_111))))) & ! [W1113_113] : ((aElementOf0(W1113_113, slsdtgt0(xb)) <=> ? [W2114_114] : ((aElement0(W2114_114) & =(sdtasdt0(xb, W2114_114), W1113_113)))))) & ? [W1115_115, W2116_116] : (((aElementOf0(W1115_115, slsdtgt0(xa)) & aElementOf0(W2116_116, slsdtgt0(xb))) & =(sdtpldt0(W1115_115, W2116_116), skolem_W0110110)))) & aElementOf0(skolem_W0110110, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ~=(skolem_W0110110, sz00))
% 23.18/9.19
% 23.18/9.19 [34] ALPHA_AND : ((((! [W1111_111] : ((aElementOf0(W1111_111, slsdtgt0(xa)) <=> ? [W2112_112] : ((aElement0(W2112_112) & =(sdtasdt0(xa, W2112_112), W1111_111))))) & ! [W1113_113] : ((aElementOf0(W1113_113, slsdtgt0(xb)) <=> ? [W2114_114] : ((aElement0(W2114_114) & =(sdtasdt0(xb, W2114_114), W1113_113)))))) & ? [W1115_115, W2116_116] : (((aElementOf0(W1115_115, slsdtgt0(xa)) & aElementOf0(W2116_116, slsdtgt0(xb))) & =(sdtpldt0(W1115_115, W2116_116), skolem_W0110110)))) & aElementOf0(skolem_W0110110, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ~=(skolem_W0110110, sz00))
% 23.18/9.19 -> [35] (((! [W1111_111] : ((aElementOf0(W1111_111, slsdtgt0(xa)) <=> ? [W2112_112] : ((aElement0(W2112_112) & =(sdtasdt0(xa, W2112_112), W1111_111))))) & ! [W1113_113] : ((aElementOf0(W1113_113, slsdtgt0(xb)) <=> ? [W2114_114] : ((aElement0(W2114_114) & =(sdtasdt0(xb, W2114_114), W1113_113)))))) & ? [W1115_115, W2116_116] : (((aElementOf0(W1115_115, slsdtgt0(xa)) & aElementOf0(W2116_116, slsdtgt0(xb))) & =(sdtpldt0(W1115_115, W2116_116), skolem_W0110110)))) & aElementOf0(skolem_W0110110, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))), ~=(skolem_W0110110, sz00)
% 23.18/9.19
% 23.18/9.19 [35] ALPHA_AND : (((! [W1111_111] : ((aElementOf0(W1111_111, slsdtgt0(xa)) <=> ? [W2112_112] : ((aElement0(W2112_112) & =(sdtasdt0(xa, W2112_112), W1111_111))))) & ! [W1113_113] : ((aElementOf0(W1113_113, slsdtgt0(xb)) <=> ? [W2114_114] : ((aElement0(W2114_114) & =(sdtasdt0(xb, W2114_114), W1113_113)))))) & ? [W1115_115, W2116_116] : (((aElementOf0(W1115_115, slsdtgt0(xa)) & aElementOf0(W2116_116, slsdtgt0(xb))) & =(sdtpldt0(W1115_115, W2116_116), skolem_W0110110)))) & aElementOf0(skolem_W0110110, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))
% 23.18/9.19 -> [36] ((! [W1111_111] : ((aElementOf0(W1111_111, slsdtgt0(xa)) <=> ? [W2112_112] : ((aElement0(W2112_112) & =(sdtasdt0(xa, W2112_112), W1111_111))))) & ! [W1113_113] : ((aElementOf0(W1113_113, slsdtgt0(xb)) <=> ? [W2114_114] : ((aElement0(W2114_114) & =(sdtasdt0(xb, W2114_114), W1113_113)))))) & ? [W1115_115, W2116_116] : (((aElementOf0(W1115_115, slsdtgt0(xa)) & aElementOf0(W2116_116, slsdtgt0(xb))) & =(sdtpldt0(W1115_115, W2116_116), skolem_W0110110)))), aElementOf0(skolem_W0110110, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))
% 23.18/9.19
% 23.18/9.19 [36] ALPHA_AND : ((! [W1111_111] : ((aElementOf0(W1111_111, slsdtgt0(xa)) <=> ? [W2112_112] : ((aElement0(W2112_112) & =(sdtasdt0(xa, W2112_112), W1111_111))))) & ! [W1113_113] : ((aElementOf0(W1113_113, slsdtgt0(xb)) <=> ? [W2114_114] : ((aElement0(W2114_114) & =(sdtasdt0(xb, W2114_114), W1113_113)))))) & ? [W1115_115, W2116_116] : (((aElementOf0(W1115_115, slsdtgt0(xa)) & aElementOf0(W2116_116, slsdtgt0(xb))) & =(sdtpldt0(W1115_115, W2116_116), skolem_W0110110))))
% 23.18/9.19 -> [37] (! [W1111_111] : ((aElementOf0(W1111_111, slsdtgt0(xa)) <=> ? [W2112_112] : ((aElement0(W2112_112) & =(sdtasdt0(xa, W2112_112), W1111_111))))) & ! [W1113_113] : ((aElementOf0(W1113_113, slsdtgt0(xb)) <=> ? [W2114_114] : ((aElement0(W2114_114) & =(sdtasdt0(xb, W2114_114), W1113_113)))))), ? [W1115_115, W2116_116] : (((aElementOf0(W1115_115, slsdtgt0(xa)) & aElementOf0(W2116_116, slsdtgt0(xb))) & =(sdtpldt0(W1115_115, W2116_116), skolem_W0110110)))
% 23.18/9.19
% 23.18/9.19 [37] ALPHA_AND : (! [W1111_111] : ((aElementOf0(W1111_111, slsdtgt0(xa)) <=> ? [W2112_112] : ((aElement0(W2112_112) & =(sdtasdt0(xa, W2112_112), W1111_111))))) & ! [W1113_113] : ((aElementOf0(W1113_113, slsdtgt0(xb)) <=> ? [W2114_114] : ((aElement0(W2114_114) & =(sdtasdt0(xb, W2114_114), W1113_113))))))
% 23.18/9.19 -> [38] ! [W1111_111] : ((aElementOf0(W1111_111, slsdtgt0(xa)) <=> ? [W2112_112] : ((aElement0(W2112_112) & =(sdtasdt0(xa, W2112_112), W1111_111))))), ! [W1113_113] : ((aElementOf0(W1113_113, slsdtgt0(xb)) <=> ? [W2114_114] : ((aElement0(W2114_114) & =(sdtasdt0(xb, W2114_114), W1113_113)))))
% 23.18/9.19
% 23.18/9.19 [38] DELTA_EXISTS : ? [W0124_124, W1125_125] : (((aElement0(W0124_124) & aElement0(W1125_125)) & =(xu, sdtpldt0(sdtasdt0(xa, W0124_124), sdtasdt0(xb, W1125_125)))))
% 23.18/9.19 -> [39] ((aElement0(skolem_W0124124) & aElement0(skolem_W1125125)) & =(xu, sdtpldt0(sdtasdt0(xa, skolem_W0124124), sdtasdt0(xb, skolem_W1125125))))
% 23.18/9.19
% 23.18/9.19 [39] ALPHA_AND : ((aElement0(skolem_W0124124) & aElement0(skolem_W1125125)) & =(xu, sdtpldt0(sdtasdt0(xa, skolem_W0124124), sdtasdt0(xb, skolem_W1125125))))
% 23.18/9.19 -> [40] (aElement0(skolem_W0124124) & aElement0(skolem_W1125125)), =(xu, sdtpldt0(sdtasdt0(xa, skolem_W0124124), sdtasdt0(xb, skolem_W1125125)))
% 23.18/9.19
% 23.18/9.19 [40] ALPHA_AND : (aElement0(skolem_W0124124) & aElement0(skolem_W1125125))
% 23.18/9.19 -> [41] aElement0(skolem_W0124124), aElement0(skolem_W1125125)
% 23.18/9.19
% 23.18/9.19 [41] DELTA_EXISTS : ? [W0109_109] : ((aElement0(W0109_109) & =(sdtasdt0(xb, W0109_109), xb)))
% 23.18/9.19 -> [42] (aElement0(skolem_W0109109) & =(sdtasdt0(xb, skolem_W0109109), xb))
% 23.18/9.19
% 23.18/9.19 [42] ALPHA_AND : (aElement0(skolem_W0109109) & =(sdtasdt0(xb, skolem_W0109109), xb))
% 23.18/9.19 -> [43] aElement0(skolem_W0109109), =(sdtasdt0(xb, skolem_W0109109), xb)
% 23.18/9.19
% 23.18/9.19 [43] DELTA_EXISTS : ? [W0126_126] : ((aElement0(W0126_126) & =(sdtasdt0(xu, W0126_126), xa)))
% 23.18/9.19 -> [44] (aElement0(skolem_W0126126) & =(sdtasdt0(xu, skolem_W0126126), xa))
% 23.18/9.19
% 23.18/9.19 [44] ALPHA_AND : (aElement0(skolem_W0126126) & =(sdtasdt0(xu, skolem_W0126126), xa))
% 23.18/9.19 -> [45] aElement0(skolem_W0126126), =(sdtasdt0(xu, skolem_W0126126), xa)
% 23.18/9.19
% 23.18/9.19 [45] DELTA_EXISTS : ? [W0127_127] : ((aElement0(W0127_127) & =(sdtasdt0(xu, W0127_127), xb)))
% 23.18/9.19 -> [46] (aElement0(skolem_W0127127) & =(sdtasdt0(xu, skolem_W0127127), xb))
% 23.18/9.19
% 23.18/9.19 [46] ALPHA_AND : (aElement0(skolem_W0127127) & =(sdtasdt0(xu, skolem_W0127127), xb))
% 23.18/9.19 -> [47] aElement0(skolem_W0127127), =(sdtasdt0(xu, skolem_W0127127), xb)
% 23.18/9.19
% 23.18/9.19 [47] DELTA_EXISTS : ? [W0117_117, W1118_118] : (((aElementOf0(W0117_117, slsdtgt0(xa)) & aElementOf0(W1118_118, slsdtgt0(xb))) & =(sdtpldt0(W0117_117, W1118_118), xu)))
% 23.18/9.19 -> [48] ((aElementOf0(skolem_W0117117, slsdtgt0(xa)) & aElementOf0(skolem_W1118118, slsdtgt0(xb))) & =(sdtpldt0(skolem_W0117117, skolem_W1118118), xu))
% 23.18/9.19
% 23.18/9.19 [48] ALPHA_AND : ((aElementOf0(skolem_W0117117, slsdtgt0(xa)) & aElementOf0(skolem_W1118118, slsdtgt0(xb))) & =(sdtpldt0(skolem_W0117117, skolem_W1118118), xu))
% 23.18/9.19 -> [49] (aElementOf0(skolem_W0117117, slsdtgt0(xa)) & aElementOf0(skolem_W1118118, slsdtgt0(xb))), =(sdtpldt0(skolem_W0117117, skolem_W1118118), xu)
% 23.18/9.19
% 23.18/9.19 [49] ALPHA_AND : (aElementOf0(skolem_W0117117, slsdtgt0(xa)) & aElementOf0(skolem_W1118118, slsdtgt0(xb)))
% 23.18/9.19 -> [50] aElementOf0(skolem_W0117117, slsdtgt0(xa)), aElementOf0(skolem_W1118118, slsdtgt0(xb))
% 23.18/9.19
% 23.18/9.19 [50] DELTA_EXISTS : ? [W0108_108] : ((aElement0(W0108_108) & =(sdtasdt0(xb, W0108_108), sz00)))
% 23.18/9.19 -> [51] (aElement0(skolem_W0108108) & =(sdtasdt0(xb, skolem_W0108108), sz00))
% 23.18/9.19
% 23.18/9.19 [51] ALPHA_AND : (aElement0(skolem_W0108108) & =(sdtasdt0(xb, skolem_W0108108), sz00))
% 23.18/9.19 -> [52] aElement0(skolem_W0108108), =(sdtasdt0(xb, skolem_W0108108), sz00)
% 23.18/9.19
% 23.18/9.19 [52] DELTA_EXISTS : ? [W091_91] : ((aElement0(W091_91) & =(sdtasdt0(xc, W091_91), xb)))
% 23.18/9.19 -> [53] (aElement0(skolem_W09191) & =(sdtasdt0(xc, skolem_W09191), xb))
% 23.18/9.19
% 23.18/9.19 [53] ALPHA_AND : (aElement0(skolem_W09191) & =(sdtasdt0(xc, skolem_W09191), xb))
% 23.18/9.19 -> [54] aElement0(skolem_W09191), =(sdtasdt0(xc, skolem_W09191), xb)
% 23.18/9.19
% 23.18/9.19 [54] DELTA_EXISTS : ? [W0107_107] : ((aElement0(W0107_107) & =(sdtasdt0(xa, W0107_107), xa)))
% 23.18/9.19 -> [55] (aElement0(skolem_W0107107) & =(sdtasdt0(xa, skolem_W0107107), xa))
% 23.18/9.19
% 23.18/9.19 [55] ALPHA_AND : (aElement0(skolem_W0107107) & =(sdtasdt0(xa, skolem_W0107107), xa))
% 23.18/9.19 -> [56] aElement0(skolem_W0107107), =(sdtasdt0(xa, skolem_W0107107), xa)
% 23.18/9.19
% 23.18/9.19 [56] DELTA_EXISTS : ? [W0106_106] : ((aElement0(W0106_106) & =(sdtasdt0(xa, W0106_106), sz00)))
% 23.18/9.19 -> [57] (aElement0(skolem_W0106106) & =(sdtasdt0(xa, skolem_W0106106), sz00))
% 23.18/9.19
% 23.18/9.19 [57] ALPHA_AND : (aElement0(skolem_W0106106) & =(sdtasdt0(xa, skolem_W0106106), sz00))
% 23.18/9.19 -> [58] aElement0(skolem_W0106106), =(sdtasdt0(xa, skolem_W0106106), sz00)
% 23.18/9.19
% 23.18/9.19 [58] DELTA_EXISTS : ? [W090_90] : ((aElement0(W090_90) & =(sdtasdt0(xc, W090_90), xa)))
% 23.18/9.19 -> [59] (aElement0(skolem_W09090) & =(sdtasdt0(xc, skolem_W09090), xa))
% 23.18/9.19
% 23.18/9.19 [59] ALPHA_AND : (aElement0(skolem_W09090) & =(sdtasdt0(xc, skolem_W09090), xa))
% 23.18/9.19 -> [60] aElement0(skolem_W09090), =(sdtasdt0(xc, skolem_W09090), xa)
% 23.18/9.19
% 23.18/9.19 [60] DELTA_EXISTS : ? [W1115_115, W2116_116] : (((aElementOf0(W1115_115, slsdtgt0(xa)) & aElementOf0(W2116_116, slsdtgt0(xb))) & =(sdtpldt0(W1115_115, W2116_116), skolem_W0110110)))
% 23.18/9.19 -> [61] ((aElementOf0(skolem_W1115115, slsdtgt0(xa)) & aElementOf0(skolem_W2116116, slsdtgt0(xb))) & =(sdtpldt0(skolem_W1115115, skolem_W2116116), skolem_W0110110))
% 23.18/9.19
% 23.18/9.19 [61] ALPHA_AND : ((aElementOf0(skolem_W1115115, slsdtgt0(xa)) & aElementOf0(skolem_W2116116, slsdtgt0(xb))) & =(sdtpldt0(skolem_W1115115, skolem_W2116116), skolem_W0110110))
% 23.18/9.19 -> [62] (aElementOf0(skolem_W1115115, slsdtgt0(xa)) & aElementOf0(skolem_W2116116, slsdtgt0(xb))), =(sdtpldt0(skolem_W1115115, skolem_W2116116), skolem_W0110110)
% 23.18/9.19
% 23.18/9.19 [62] ALPHA_AND : (aElementOf0(skolem_W1115115, slsdtgt0(xa)) & aElementOf0(skolem_W2116116, slsdtgt0(xb)))
% 23.18/9.19 -> [63] aElementOf0(skolem_W1115115, slsdtgt0(xa)), aElementOf0(skolem_W2116116, slsdtgt0(xb))
% 23.18/9.19
% 23.18/9.19 [63] BETA_OR : (~=(xa, sz00) | ~=(xb, sz00))
% 23.18/9.19 -> [64] ~=(xa, sz00)
% 23.18/9.19 -> [65] ~=(xb, sz00)
% 23.18/9.19
% 23.18/9.19 [65] BETA_NOT_AND : ~(((? [W0122_122] : ((aElement0(W0122_122) & =(sdtasdt0(xu, W0122_122), xa))) | doDivides0(xu, xa)) | aDivisorOf0(xu, xa)) & ((? [W0123_123] : ((aElement0(W0123_123) & =(sdtasdt0(xu, W0123_123), xb))) | doDivides0(xu, xb)) | aDivisorOf0(xu, xb)))
% 23.18/9.19 -> [68] ~((? [W0122_122] : ((aElement0(W0122_122) & =(sdtasdt0(xu, W0122_122), xa))) | doDivides0(xu, xa)) | aDivisorOf0(xu, xa))
% 23.18/9.19 -> [69] ~((? [W0123_123] : ((aElement0(W0123_123) & =(sdtasdt0(xu, W0123_123), xb))) | doDivides0(xu, xb)) | aDivisorOf0(xu, xb))
% 23.18/9.19
% 23.18/9.19 [69] ALPHA_NOT_OR : ~((? [W0123_123] : ((aElement0(W0123_123) & =(sdtasdt0(xu, W0123_123), xb))) | doDivides0(xu, xb)) | aDivisorOf0(xu, xb))
% 23.18/9.19 -> [73] ~(? [W0123_123] : ((aElement0(W0123_123) & =(sdtasdt0(xu, W0123_123), xb))) | doDivides0(xu, xb)), ~aDivisorOf0(xu, xb)
% 23.18/9.19
% 23.18/9.19 [73] ALPHA_NOT_OR : ~(? [W0123_123] : ((aElement0(W0123_123) & =(sdtasdt0(xu, W0123_123), xb))) | doDivides0(xu, xb))
% 23.18/9.19 -> [75] ~? [W0123_123] : ((aElement0(W0123_123) & =(sdtasdt0(xu, W0123_123), xb))), ~doDivides0(xu, xb)
% 23.18/9.19
% 23.18/9.19 [75] CLOSURE : ~doDivides0(xu, xb)
% 23.18/9.19
% 23.18/9.19 [68] ALPHA_NOT_OR : ~((? [W0122_122] : ((aElement0(W0122_122) & =(sdtasdt0(xu, W0122_122), xa))) | doDivides0(xu, xa)) | aDivisorOf0(xu, xa))
% 23.18/9.19 -> [72] ~(? [W0122_122] : ((aElement0(W0122_122) & =(sdtasdt0(xu, W0122_122), xa))) | doDivides0(xu, xa)), ~aDivisorOf0(xu, xa)
% 23.18/9.19
% 23.18/9.19 [72] ALPHA_NOT_OR : ~(? [W0122_122] : ((aElement0(W0122_122) & =(sdtasdt0(xu, W0122_122), xa))) | doDivides0(xu, xa))
% 23.18/9.19 -> [76] ~? [W0122_122] : ((aElement0(W0122_122) & =(sdtasdt0(xu, W0122_122), xa))), ~doDivides0(xu, xa)
% 23.18/9.19
% 23.18/9.19 [76] CLOSURE : ~doDivides0(xu, xa)
% 23.18/9.19
% 23.18/9.19 [64] BETA_NOT_AND : ~(((? [W0122_122] : ((aElement0(W0122_122) & =(sdtasdt0(xu, W0122_122), xa))) | doDivides0(xu, xa)) | aDivisorOf0(xu, xa)) & ((? [W0123_123] : ((aElement0(W0123_123) & =(sdtasdt0(xu, W0123_123), xb))) | doDivides0(xu, xb)) | aDivisorOf0(xu, xb)))
% 23.18/9.19 -> [66] ~((? [W0122_122] : ((aElement0(W0122_122) & =(sdtasdt0(xu, W0122_122), xa))) | doDivides0(xu, xa)) | aDivisorOf0(xu, xa))
% 23.18/9.19 -> [67] ~((? [W0123_123] : ((aElement0(W0123_123) & =(sdtasdt0(xu, W0123_123), xb))) | doDivides0(xu, xb)) | aDivisorOf0(xu, xb))
% 23.18/9.19
% 23.18/9.19 [66] ALPHA_NOT_OR : ~((? [W0122_122] : ((aElement0(W0122_122) & =(sdtasdt0(xu, W0122_122), xa))) | doDivides0(xu, xa)) | aDivisorOf0(xu, xa))
% 23.18/9.19 -> [70] ~(? [W0122_122] : ((aElement0(W0122_122) & =(sdtasdt0(xu, W0122_122), xa))) | doDivides0(xu, xa)), ~aDivisorOf0(xu, xa)
% 23.18/9.19
% 23.18/9.19 [70] ALPHA_NOT_OR : ~(? [W0122_122] : ((aElement0(W0122_122) & =(sdtasdt0(xu, W0122_122), xa))) | doDivides0(xu, xa))
% 23.18/9.19 -> [74] ~? [W0122_122] : ((aElement0(W0122_122) & =(sdtasdt0(xu, W0122_122), xa))), ~doDivides0(xu, xa)
% 23.18/9.19
% 23.18/9.19 [74] CLOSURE : ~doDivides0(xu, xa)
% 23.18/9.19
% 23.18/9.19 [67] ALPHA_NOT_OR : ~((? [W0123_123] : ((aElement0(W0123_123) & =(sdtasdt0(xu, W0123_123), xb))) | doDivides0(xu, xb)) | aDivisorOf0(xu, xb))
% 23.18/9.19 -> [71] ~(? [W0123_123] : ((aElement0(W0123_123) & =(sdtasdt0(xu, W0123_123), xb))) | doDivides0(xu, xb)), ~aDivisorOf0(xu, xb)
% 23.18/9.19
% 23.18/9.19 [71] ALPHA_NOT_OR : ~(? [W0123_123] : ((aElement0(W0123_123) & =(sdtasdt0(xu, W0123_123), xb))) | doDivides0(xu, xb))
% 23.18/9.19 -> [77] ~? [W0123_123] : ((aElement0(W0123_123) & =(sdtasdt0(xu, W0123_123), xb))), ~doDivides0(xu, xb)
% 23.18/9.19
% 23.18/9.19 [77] CLOSURE : ~doDivides0(xu, xb)
% 23.18/9.19
% 23.18/9.19 % SZS output end Proof for theBenchmark.p
% 23.18/9.19 [8.840735s][1][Res] 65323 goroutines created
% 23.18/9.19 ==== Result ====
% 23.18/9.19 [8.840750s][1][Res] VALID
% 23.18/9.19 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------