TSTP Solution File: NUM557+3 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : NUM557+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n019.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 10:19:31 EDT 2022
% Result : Theorem 11.08s 8.89s
% Output : Proof 11.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM557+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : goeland -dmt -presko -proof %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Sep 2 11:47:50 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 [DMT] DMT loaded with preskolemization
% 0.13/0.36 [EQ] equality loaded.
% 0.13/0.36 [0.000040s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.37 Start search
% 0.13/0.39 nb_step : 1 - limit : 104
% 0.13/0.39 Launch Gotab with destructive = true
% 11.00/8.86 % SZS output start Proof for theBenchmark.p
% 11.08/8.89 [0] ALPHA_AND : (! [W04_4] : ((aSet0(W04_4) => $true)) & ! [W05_5] : ((aElement0(W05_5) => $true)) & ! [W06_6] : ((aSet0(W06_6) => ! [W17_7] : ((aElementOf0(W17_7, W06_6) => aElement0(W17_7))))) & ! [W08_8] : ((aSet0(W08_8) => (isFinite0(W08_8) => $true))) & ! [W09_9] : ((=(W09_9, slcrc0) <=> (aSet0(W09_9) & ~? [W110_10] : (aElementOf0(W110_10, W09_9))))) & isFinite0(slcrc0) & ! [W011_11] : ((aSet0(W011_11) => (isCountable0(W011_11) => $true))) & ! [W012_12] : (((aSet0(W012_12) & isCountable0(W012_12)) => ~isFinite0(W012_12))) & ! [W013_13] : (((aSet0(W013_13) & isCountable0(W013_13)) => ~=(W013_13, slcrc0))) & ! [W014_14] : ((aSet0(W014_14) => ! [W115_15] : ((aSubsetOf0(W115_15, W014_14) <=> (aSet0(W115_15) & ! [W216_16] : ((aElementOf0(W216_16, W115_15) => aElementOf0(W216_16, W014_14)))))))) & ! [W017_17] : (((aSet0(W017_17) & isFinite0(W017_17)) => ! [W118_18] : ((aSubsetOf0(W118_18, W017_17) => isFinite0(W118_18))))) & ! [W019_19] : ((aSet0(W019_19) => aSubsetOf0(W019_19, W019_19))) & ! [W020_20, W121_21] : (((aSet0(W020_20) & aSet0(W121_21)) => ((aSubsetOf0(W020_20, W121_21) & aSubsetOf0(W121_21, W020_20)) => =(W020_20, W121_21)))) & ! [W022_22, W123_23, W224_24] : ((((aSet0(W022_22) & aSet0(W123_23)) & aSet0(W224_24)) => ((aSubsetOf0(W022_22, W123_23) & aSubsetOf0(W123_23, W224_24)) => aSubsetOf0(W022_22, W224_24)))) & ! [W025_25, W126_26] : (((aSet0(W025_25) & aElement0(W126_26)) => ! [W227_27] : ((=(W227_27, sdtpldt0(W025_25, W126_26)) <=> (aSet0(W227_27) & ! [W328_28] : ((aElementOf0(W328_28, W227_27) <=> (aElement0(W328_28) & (aElementOf0(W328_28, W025_25) | =(W328_28, W126_26)))))))))) & ! [W029_29, W130_30] : (((aSet0(W029_29) & aElement0(W130_30)) => ! [W231_31] : ((=(W231_31, sdtmndt0(W029_29, W130_30)) <=> (aSet0(W231_31) & ! [W332_32] : ((aElementOf0(W332_32, W231_31) <=> ((aElement0(W332_32) & aElementOf0(W332_32, W029_29)) & ~=(W332_32, W130_30))))))))) & ! [W033_33] : ((aSet0(W033_33) => ! [W134_34] : ((aElementOf0(W134_34, W033_33) => =(sdtpldt0(sdtmndt0(W033_33, W134_34), W134_34), W033_33))))) & ! [W035_35, W136_36] : (((aElement0(W035_35) & aSet0(W136_36)) => (~aElementOf0(W035_35, W136_36) => =(sdtmndt0(sdtpldt0(W136_36, W035_35), W035_35), W136_36)))) & ! [W037_37] : ((aElement0(W037_37) => ! [W138_38] : (((aSet0(W138_38) & isCountable0(W138_38)) => isCountable0(sdtpldt0(W138_38, W037_37)))))) & ! [W039_39] : ((aElement0(W039_39) => ! [W140_40] : (((aSet0(W140_40) & isCountable0(W140_40)) => isCountable0(sdtmndt0(W140_40, W039_39)))))) & ! [W041_41] : ((aElement0(W041_41) => ! [W142_42] : (((aSet0(W142_42) & isFinite0(W142_42)) => isFinite0(sdtpldt0(W142_42, W041_41)))))) & ! [W043_43] : ((aElement0(W043_43) => ! [W144_44] : (((aSet0(W144_44) & isFinite0(W144_44)) => isFinite0(sdtmndt0(W144_44, W043_43)))))) & (aSet0(szNzAzT0) & isCountable0(szNzAzT0)) & aElementOf0(sz00, szNzAzT0) & ! [W045_45] : ((aElementOf0(W045_45, szNzAzT0) => (aElementOf0(szszuzczcdt0(W045_45), szNzAzT0) & ~=(szszuzczcdt0(W045_45), sz00)))) & ! [W046_46, W147_47] : (((aElementOf0(W046_46, szNzAzT0) & aElementOf0(W147_47, szNzAzT0)) => (=(szszuzczcdt0(W046_46), szszuzczcdt0(W147_47)) => =(W046_46, W147_47)))) & ! [W048_48] : ((aElementOf0(W048_48, szNzAzT0) => (=(W048_48, sz00) | ? [W149_49] : ((aElementOf0(W149_49, szNzAzT0) & =(W048_48, szszuzczcdt0(W149_49))))))) & ! [W050_50] : ((aElementOf0(W050_50, szNzAzT0) => ~=(W050_50, szszuzczcdt0(W050_50)))) & ! [W051_51, W152_52] : (((aElementOf0(W051_51, szNzAzT0) & aElementOf0(W152_52, szNzAzT0)) => (sdtlseqdt0(W051_51, W152_52) => $true))) & ! [W053_53] : ((aElementOf0(W053_53, szNzAzT0) => sdtlseqdt0(sz00, W053_53))) & ! [W054_54] : ((aElementOf0(W054_54, szNzAzT0) => ~sdtlseqdt0(szszuzczcdt0(W054_54), sz00))) & ! [W055_55, W156_56] : (((aElementOf0(W055_55, szNzAzT0) & aElementOf0(W156_56, szNzAzT0)) => (sdtlseqdt0(W055_55, W156_56) <=> sdtlseqdt0(szszuzczcdt0(W055_55), szszuzczcdt0(W156_56))))) & ! [W057_57] : ((aElementOf0(W057_57, szNzAzT0) => sdtlseqdt0(W057_57, szszuzczcdt0(W057_57)))) & ! [W058_58] : ((aElementOf0(W058_58, szNzAzT0) => sdtlseqdt0(W058_58, W058_58))) & ! [W059_59, W160_60] : (((aElementOf0(W059_59, szNzAzT0) & aElementOf0(W160_60, szNzAzT0)) => ((sdtlseqdt0(W059_59, W160_60) & sdtlseqdt0(W160_60, W059_59)) => =(W059_59, W160_60)))) & ! [W061_61, W162_62, W263_63] : ((((aElementOf0(W061_61, szNzAzT0) & aElementOf0(W162_62, szNzAzT0)) & aElementOf0(W263_63, szNzAzT0)) => ((sdtlseqdt0(W061_61, W162_62) & sdtlseqdt0(W162_62, W263_63)) => sdtlseqdt0(W061_61, W263_63)))) & ! [W064_64, W165_65] : (((aElementOf0(W064_64, szNzAzT0) & aElementOf0(W165_65, szNzAzT0)) => (sdtlseqdt0(W064_64, W165_65) | sdtlseqdt0(szszuzczcdt0(W165_65), W064_64)))) & ! [W066_66, W167_67] : (((aElementOf0(W066_66, szNzAzT0) & aElementOf0(W167_67, szNzAzT0)) => (iLess0(W066_66, W167_67) => $true))) & ! [W068_68] : ((aElementOf0(W068_68, szNzAzT0) => iLess0(W068_68, szszuzczcdt0(W068_68)))) & ! [W069_69] : ((aSet0(W069_69) => aElement0(sbrdtbr0(W069_69)))) & ! [W070_70] : ((aSet0(W070_70) => (aElementOf0(sbrdtbr0(W070_70), szNzAzT0) <=> isFinite0(W070_70)))) & ! [W071_71] : ((aSet0(W071_71) => (=(sbrdtbr0(W071_71), sz00) <=> =(W071_71, slcrc0)))) & ! [W072_72] : (((aSet0(W072_72) & isFinite0(W072_72)) => ! [W173_73] : ((aElement0(W173_73) => (~aElementOf0(W173_73, W072_72) => =(sbrdtbr0(sdtpldt0(W072_72, W173_73)), szszuzczcdt0(sbrdtbr0(W072_72)))))))) & ! [W074_74] : ((aSet0(W074_74) => ! [W175_75] : (((isFinite0(W074_74) & aElementOf0(W175_75, W074_74)) => =(szszuzczcdt0(sbrdtbr0(sdtmndt0(W074_74, W175_75))), sbrdtbr0(W074_74)))))) & ! [W076_76] : ((aSet0(W076_76) => ! [W177_77] : (((isFinite0(W076_76) & aSubsetOf0(W177_77, W076_76)) => sdtlseqdt0(sbrdtbr0(W177_77), sbrdtbr0(W076_76)))))) & ! [W078_78, W179_79] : (((aSet0(W078_78) & aElementOf0(W179_79, szNzAzT0)) => ((isFinite0(W078_78) & sdtlseqdt0(W179_79, sbrdtbr0(W078_78))) => ? [W280_80] : ((aSubsetOf0(W280_80, W078_78) & =(sbrdtbr0(W280_80), W179_79)))))) & ! [W081_81] : (((aSubsetOf0(W081_81, szNzAzT0) & ~=(W081_81, slcrc0)) => ! [W182_82] : ((=(W182_82, szmzizndt0(W081_81)) <=> (aElementOf0(W182_82, W081_81) & ! [W283_83] : ((aElementOf0(W283_83, W081_81) => sdtlseqdt0(W182_82, W283_83)))))))) & ! [W084_84] : ((((aSubsetOf0(W084_84, szNzAzT0) & isFinite0(W084_84)) & ~=(W084_84, slcrc0)) => ! [W185_85] : ((=(W185_85, szmzazxdt0(W084_84)) <=> (aElementOf0(W185_85, W084_84) & ! [W286_86] : ((aElementOf0(W286_86, W084_84) => sdtlseqdt0(W286_86, W185_85)))))))) & ! [W087_87, W188_88] : (((((aSubsetOf0(W087_87, szNzAzT0) & aSubsetOf0(W188_88, szNzAzT0)) & ~=(W087_87, slcrc0)) & ~=(W188_88, slcrc0)) => ((aElementOf0(szmzizndt0(W087_87), W188_88) & aElementOf0(szmzizndt0(W188_88), W087_87)) => =(szmzizndt0(W087_87), szmzizndt0(W188_88))))) & ! [W089_89] : ((aElementOf0(W089_89, szNzAzT0) => ! [W190_90] : ((=(W190_90, slbdtrb0(W089_89)) <=> (aSet0(W190_90) & ! [W291_91] : ((aElementOf0(W291_91, W190_90) <=> (aElementOf0(W291_91, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W291_91), W089_89))))))))) & ! [W092_92] : ((aElementOf0(W092_92, szNzAzT0) => isFinite0(slbdtrb0(W092_92)))) & =(slbdtrb0(sz00), slcrc0) & ! [W093_93, W194_94] : (((aElementOf0(W093_93, szNzAzT0) & aElementOf0(W194_94, szNzAzT0)) => (aElementOf0(W093_93, slbdtrb0(szszuzczcdt0(W194_94))) <=> (aElementOf0(W093_93, slbdtrb0(W194_94)) | =(W093_93, W194_94))))) & ! [W095_95, W196_96] : (((aElementOf0(W095_95, szNzAzT0) & aElementOf0(W196_96, szNzAzT0)) => (sdtlseqdt0(W095_95, W196_96) <=> aSubsetOf0(slbdtrb0(W095_95), slbdtrb0(W196_96))))) & ! [W097_97] : (((aSubsetOf0(W097_97, szNzAzT0) & isFinite0(W097_97)) => ? [W198_98] : ((aElementOf0(W198_98, szNzAzT0) & aSubsetOf0(W097_97, slbdtrb0(W198_98)))))) & ! [W099_99] : ((aElementOf0(W099_99, szNzAzT0) => =(sbrdtbr0(slbdtrb0(W099_99)), W099_99))) & ! [W0100_100, W1101_101] : (((aSet0(W0100_100) & aElementOf0(W1101_101, szNzAzT0)) => ! [W2102_102] : ((=(W2102_102, slbdtsldtrb0(W0100_100, W1101_101)) <=> (aSet0(W2102_102) & ! [W3103_103] : ((aElementOf0(W3103_103, W2102_102) <=> (aSubsetOf0(W3103_103, W0100_100) & =(sbrdtbr0(W3103_103), W1101_101))))))))) & ! [W0104_104] : (((aSet0(W0104_104) & isFinite0(W0104_104)) => ! [W1105_105] : ((aElementOf0(W1105_105, szNzAzT0) => isFinite0(slbdtsldtrb0(W0104_104, W1105_105)))))) & ! [W0106_106] : (((aSet0(W0106_106) & ~isFinite0(W0106_106)) => ! [W1107_107] : ((aElementOf0(W1107_107, szNzAzT0) => ~=(slbdtsldtrb0(W0106_106, W1107_107), slcrc0))))) & ! [W0108_108] : (((aSet0(W0108_108) & isCountable0(W0108_108)) => ! [W1109_109] : (((aElementOf0(W1109_109, szNzAzT0) & ~=(W1109_109, sz00)) => isCountable0(slbdtsldtrb0(W0108_108, W1109_109)))))) & aElementOf0(xk, szNzAzT0) & ((aSet0(xS) & aSet0(xT)) & ~=(xk, sz00)) & ((((((aSet0(slbdtsldtrb0(xS, xk)) & ! [W0110_110] : (((aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)) => (((aSet0(W0110_110) & ! [W1111_111] : ((aElementOf0(W1111_111, W0110_110) => aElementOf0(W1111_111, xS)))) & aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk))) & ((((aSet0(W0110_110) & ! [W1112_112] : ((aElementOf0(W1112_112, W0110_110) => aElementOf0(W1112_112, xS)))) | aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk)) => aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)))))) & aSet0(slbdtsldtrb0(xT, xk))) & ! [W0113_113] : (((aElementOf0(W0113_113, slbdtsldtrb0(xT, xk)) => (((aSet0(W0113_113) & ! [W1114_114] : ((aElementOf0(W1114_114, W0113_113) => aElementOf0(W1114_114, xT)))) & aSubsetOf0(W0113_113, xT)) & =(sbrdtbr0(W0113_113), xk))) & ((((aSet0(W0113_113) & ! [W1115_115] : ((aElementOf0(W1115_115, W0113_113) => aElementOf0(W1115_115, xT)))) | aSubsetOf0(W0113_113, xT)) & =(sbrdtbr0(W0113_113), xk)) => aElementOf0(W0113_113, slbdtsldtrb0(xT, xk)))))) & ! [W0116_116] : ((aElementOf0(W0116_116, slbdtsldtrb0(xS, xk)) => aElementOf0(W0116_116, slbdtsldtrb0(xT, xk))))) & aSubsetOf0(slbdtsldtrb0(xS, xk), slbdtsldtrb0(xT, xk))) & ~(! [W0117_117] : (((aElementOf0(W0117_117, slbdtsldtrb0(xS, xk)) => (((aSet0(W0117_117) & ! [W1118_118] : ((aElementOf0(W1118_118, W0117_117) => aElementOf0(W1118_118, xS)))) & aSubsetOf0(W0117_117, xS)) & =(sbrdtbr0(W0117_117), xk))) & ((((aSet0(W0117_117) & ! [W1119_119] : ((aElementOf0(W1119_119, W0117_117) => aElementOf0(W1119_119, xS)))) | aSubsetOf0(W0117_117, xS)) & =(sbrdtbr0(W0117_117), xk)) => aElementOf0(W0117_117, slbdtsldtrb0(xS, xk))))) => (~? [W0120_120] : (aElementOf0(W0120_120, slbdtsldtrb0(xS, xk))) | =(slbdtsldtrb0(xS, xk), slcrc0)))) & aElementOf0(xx, xS) & ((((aSet0(xQ) & ! [W0121_121] : ((aElementOf0(W0121_121, xQ) => aElementOf0(W0121_121, xS)))) & aSubsetOf0(xQ, xS)) & =(sbrdtbr0(xQ), xk)) & aElementOf0(xQ, slbdtsldtrb0(xS, xk))) & ((aSet0(xQ) & isFinite0(xQ)) & =(sbrdtbr0(xQ), xk)) & (aElement0(xy) & aElementOf0(xy, xQ)) & ~aElementOf0(xx, xQ) & ~aElementOf0(xx, xQ) & ((((aSet0(sdtmndt0(xQ, xy)) & ! [W0122_122] : ((aElementOf0(W0122_122, sdtmndt0(xQ, xy)) <=> ((aElement0(W0122_122) & aElementOf0(W0122_122, xQ)) & ~=(W0122_122, xy))))) & aSet0(xP)) & ! [W0123_123] : ((aElementOf0(W0123_123, xP) <=> (aElement0(W0123_123) & (aElementOf0(W0123_123, sdtmndt0(xQ, xy)) | =(W0123_123, xx)))))) & =(xP, sdtpldt0(sdtmndt0(xQ, xy), xx))) & ((~aElementOf0(xx, sdtmndt0(xQ, xy)) & aSet0(sdtmndt0(xQ, xy))) & ! [W0124_124] : ((aElementOf0(W0124_124, sdtmndt0(xQ, xy)) <=> ((aElement0(W0124_124) & aElementOf0(W0124_124, xQ)) & ~=(W0124_124, xy))))) & ((! [W0125_125] : ((aElementOf0(W0125_125, xP) => aElementOf0(W0125_125, xS))) & aSubsetOf0(xP, xS)) & =(sbrdtbr0(xP), xk)) & ~(((! [W0126_126] : ((aElementOf0(W0126_126, xP) => aElementOf0(W0126_126, xS))) | aSubsetOf0(xP, xS)) & =(sbrdtbr0(xP), xk)) | aElementOf0(xP, slbdtsldtrb0(xS, xk))))
% 11.08/8.89 -> [1] ! [W04_4] : ((aSet0(W04_4) => $true)), ! [W05_5] : ((aElement0(W05_5) => $true)), ! [W06_6] : ((aSet0(W06_6) => ! [W17_7] : ((aElementOf0(W17_7, W06_6) => aElement0(W17_7))))), ! [W08_8] : ((aSet0(W08_8) => (isFinite0(W08_8) => $true))), ! [W09_9] : ((=(W09_9, slcrc0) <=> (aSet0(W09_9) & ~? [W110_10] : (aElementOf0(W110_10, W09_9))))), isFinite0(slcrc0), ! [W011_11] : ((aSet0(W011_11) => (isCountable0(W011_11) => $true))), ! [W012_12] : (((aSet0(W012_12) & isCountable0(W012_12)) => ~isFinite0(W012_12))), ! [W013_13] : (((aSet0(W013_13) & isCountable0(W013_13)) => ~=(W013_13, slcrc0))), ! [W014_14] : ((aSet0(W014_14) => ! [W115_15] : ((aSubsetOf0(W115_15, W014_14) <=> (aSet0(W115_15) & ! [W216_16] : ((aElementOf0(W216_16, W115_15) => aElementOf0(W216_16, W014_14)))))))), ! [W017_17] : (((aSet0(W017_17) & isFinite0(W017_17)) => ! [W118_18] : ((aSubsetOf0(W118_18, W017_17) => isFinite0(W118_18))))), ! [W019_19] : ((aSet0(W019_19) => aSubsetOf0(W019_19, W019_19))), ! [W020_20, W121_21] : (((aSet0(W020_20) & aSet0(W121_21)) => ((aSubsetOf0(W020_20, W121_21) & aSubsetOf0(W121_21, W020_20)) => =(W020_20, W121_21)))), ! [W022_22, W123_23, W224_24] : ((((aSet0(W022_22) & aSet0(W123_23)) & aSet0(W224_24)) => ((aSubsetOf0(W022_22, W123_23) & aSubsetOf0(W123_23, W224_24)) => aSubsetOf0(W022_22, W224_24)))), ! [W025_25, W126_26] : (((aSet0(W025_25) & aElement0(W126_26)) => ! [W227_27] : ((=(W227_27, sdtpldt0(W025_25, W126_26)) <=> (aSet0(W227_27) & ! [W328_28] : ((aElementOf0(W328_28, W227_27) <=> (aElement0(W328_28) & (aElementOf0(W328_28, W025_25) | =(W328_28, W126_26)))))))))), ! [W029_29, W130_30] : (((aSet0(W029_29) & aElement0(W130_30)) => ! [W231_31] : ((=(W231_31, sdtmndt0(W029_29, W130_30)) <=> (aSet0(W231_31) & ! [W332_32] : ((aElementOf0(W332_32, W231_31) <=> ((aElement0(W332_32) & aElementOf0(W332_32, W029_29)) & ~=(W332_32, W130_30))))))))), ! [W033_33] : ((aSet0(W033_33) => ! [W134_34] : ((aElementOf0(W134_34, W033_33) => =(sdtpldt0(sdtmndt0(W033_33, W134_34), W134_34), W033_33))))), ! [W035_35, W136_36] : (((aElement0(W035_35) & aSet0(W136_36)) => (~aElementOf0(W035_35, W136_36) => =(sdtmndt0(sdtpldt0(W136_36, W035_35), W035_35), W136_36)))), ! [W037_37] : ((aElement0(W037_37) => ! [W138_38] : (((aSet0(W138_38) & isCountable0(W138_38)) => isCountable0(sdtpldt0(W138_38, W037_37)))))), ! [W039_39] : ((aElement0(W039_39) => ! [W140_40] : (((aSet0(W140_40) & isCountable0(W140_40)) => isCountable0(sdtmndt0(W140_40, W039_39)))))), ! [W041_41] : ((aElement0(W041_41) => ! [W142_42] : (((aSet0(W142_42) & isFinite0(W142_42)) => isFinite0(sdtpldt0(W142_42, W041_41)))))), ! [W043_43] : ((aElement0(W043_43) => ! [W144_44] : (((aSet0(W144_44) & isFinite0(W144_44)) => isFinite0(sdtmndt0(W144_44, W043_43)))))), (aSet0(szNzAzT0) & isCountable0(szNzAzT0)), aElementOf0(sz00, szNzAzT0), ! [W045_45] : ((aElementOf0(W045_45, szNzAzT0) => (aElementOf0(szszuzczcdt0(W045_45), szNzAzT0) & ~=(szszuzczcdt0(W045_45), sz00)))), ! [W046_46, W147_47] : (((aElementOf0(W046_46, szNzAzT0) & aElementOf0(W147_47, szNzAzT0)) => (=(szszuzczcdt0(W046_46), szszuzczcdt0(W147_47)) => =(W046_46, W147_47)))), ! [W048_48] : ((aElementOf0(W048_48, szNzAzT0) => (=(W048_48, sz00) | ? [W149_49] : ((aElementOf0(W149_49, szNzAzT0) & =(W048_48, szszuzczcdt0(W149_49))))))), ! [W050_50] : ((aElementOf0(W050_50, szNzAzT0) => ~=(W050_50, szszuzczcdt0(W050_50)))), ! [W051_51, W152_52] : (((aElementOf0(W051_51, szNzAzT0) & aElementOf0(W152_52, szNzAzT0)) => (sdtlseqdt0(W051_51, W152_52) => $true))), ! [W053_53] : ((aElementOf0(W053_53, szNzAzT0) => sdtlseqdt0(sz00, W053_53))), ! [W054_54] : ((aElementOf0(W054_54, szNzAzT0) => ~sdtlseqdt0(szszuzczcdt0(W054_54), sz00))), ! [W055_55, W156_56] : (((aElementOf0(W055_55, szNzAzT0) & aElementOf0(W156_56, szNzAzT0)) => (sdtlseqdt0(W055_55, W156_56) <=> sdtlseqdt0(szszuzczcdt0(W055_55), szszuzczcdt0(W156_56))))), ! [W057_57] : ((aElementOf0(W057_57, szNzAzT0) => sdtlseqdt0(W057_57, szszuzczcdt0(W057_57)))), ! [W058_58] : ((aElementOf0(W058_58, szNzAzT0) => sdtlseqdt0(W058_58, W058_58))), ! [W059_59, W160_60] : (((aElementOf0(W059_59, szNzAzT0) & aElementOf0(W160_60, szNzAzT0)) => ((sdtlseqdt0(W059_59, W160_60) & sdtlseqdt0(W160_60, W059_59)) => =(W059_59, W160_60)))), ! [W061_61, W162_62, W263_63] : ((((aElementOf0(W061_61, szNzAzT0) & aElementOf0(W162_62, szNzAzT0)) & aElementOf0(W263_63, szNzAzT0)) => ((sdtlseqdt0(W061_61, W162_62) & sdtlseqdt0(W162_62, W263_63)) => sdtlseqdt0(W061_61, W263_63)))), ! [W064_64, W165_65] : (((aElementOf0(W064_64, szNzAzT0) & aElementOf0(W165_65, szNzAzT0)) => (sdtlseqdt0(W064_64, W165_65) | sdtlseqdt0(szszuzczcdt0(W165_65), W064_64)))), ! [W066_66, W167_67] : (((aElementOf0(W066_66, szNzAzT0) & aElementOf0(W167_67, szNzAzT0)) => (iLess0(W066_66, W167_67) => $true))), ! [W068_68] : ((aElementOf0(W068_68, szNzAzT0) => iLess0(W068_68, szszuzczcdt0(W068_68)))), ! [W069_69] : ((aSet0(W069_69) => aElement0(sbrdtbr0(W069_69)))), ! [W070_70] : ((aSet0(W070_70) => (aElementOf0(sbrdtbr0(W070_70), szNzAzT0) <=> isFinite0(W070_70)))), ! [W071_71] : ((aSet0(W071_71) => (=(sbrdtbr0(W071_71), sz00) <=> =(W071_71, slcrc0)))), ! [W072_72] : (((aSet0(W072_72) & isFinite0(W072_72)) => ! [W173_73] : ((aElement0(W173_73) => (~aElementOf0(W173_73, W072_72) => =(sbrdtbr0(sdtpldt0(W072_72, W173_73)), szszuzczcdt0(sbrdtbr0(W072_72)))))))), ! [W074_74] : ((aSet0(W074_74) => ! [W175_75] : (((isFinite0(W074_74) & aElementOf0(W175_75, W074_74)) => =(szszuzczcdt0(sbrdtbr0(sdtmndt0(W074_74, W175_75))), sbrdtbr0(W074_74)))))), ! [W076_76] : ((aSet0(W076_76) => ! [W177_77] : (((isFinite0(W076_76) & aSubsetOf0(W177_77, W076_76)) => sdtlseqdt0(sbrdtbr0(W177_77), sbrdtbr0(W076_76)))))), ! [W078_78, W179_79] : (((aSet0(W078_78) & aElementOf0(W179_79, szNzAzT0)) => ((isFinite0(W078_78) & sdtlseqdt0(W179_79, sbrdtbr0(W078_78))) => ? [W280_80] : ((aSubsetOf0(W280_80, W078_78) & =(sbrdtbr0(W280_80), W179_79)))))), ! [W081_81] : (((aSubsetOf0(W081_81, szNzAzT0) & ~=(W081_81, slcrc0)) => ! [W182_82] : ((=(W182_82, szmzizndt0(W081_81)) <=> (aElementOf0(W182_82, W081_81) & ! [W283_83] : ((aElementOf0(W283_83, W081_81) => sdtlseqdt0(W182_82, W283_83)))))))), ! [W084_84] : ((((aSubsetOf0(W084_84, szNzAzT0) & isFinite0(W084_84)) & ~=(W084_84, slcrc0)) => ! [W185_85] : ((=(W185_85, szmzazxdt0(W084_84)) <=> (aElementOf0(W185_85, W084_84) & ! [W286_86] : ((aElementOf0(W286_86, W084_84) => sdtlseqdt0(W286_86, W185_85)))))))), ! [W087_87, W188_88] : (((((aSubsetOf0(W087_87, szNzAzT0) & aSubsetOf0(W188_88, szNzAzT0)) & ~=(W087_87, slcrc0)) & ~=(W188_88, slcrc0)) => ((aElementOf0(szmzizndt0(W087_87), W188_88) & aElementOf0(szmzizndt0(W188_88), W087_87)) => =(szmzizndt0(W087_87), szmzizndt0(W188_88))))), ! [W089_89] : ((aElementOf0(W089_89, szNzAzT0) => ! [W190_90] : ((=(W190_90, slbdtrb0(W089_89)) <=> (aSet0(W190_90) & ! [W291_91] : ((aElementOf0(W291_91, W190_90) <=> (aElementOf0(W291_91, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W291_91), W089_89))))))))), ! [W092_92] : ((aElementOf0(W092_92, szNzAzT0) => isFinite0(slbdtrb0(W092_92)))), =(slbdtrb0(sz00), slcrc0), ! [W093_93, W194_94] : (((aElementOf0(W093_93, szNzAzT0) & aElementOf0(W194_94, szNzAzT0)) => (aElementOf0(W093_93, slbdtrb0(szszuzczcdt0(W194_94))) <=> (aElementOf0(W093_93, slbdtrb0(W194_94)) | =(W093_93, W194_94))))), ! [W095_95, W196_96] : (((aElementOf0(W095_95, szNzAzT0) & aElementOf0(W196_96, szNzAzT0)) => (sdtlseqdt0(W095_95, W196_96) <=> aSubsetOf0(slbdtrb0(W095_95), slbdtrb0(W196_96))))), ! [W097_97] : (((aSubsetOf0(W097_97, szNzAzT0) & isFinite0(W097_97)) => ? [W198_98] : ((aElementOf0(W198_98, szNzAzT0) & aSubsetOf0(W097_97, slbdtrb0(W198_98)))))), ! [W099_99] : ((aElementOf0(W099_99, szNzAzT0) => =(sbrdtbr0(slbdtrb0(W099_99)), W099_99))), ! [W0100_100, W1101_101] : (((aSet0(W0100_100) & aElementOf0(W1101_101, szNzAzT0)) => ! [W2102_102] : ((=(W2102_102, slbdtsldtrb0(W0100_100, W1101_101)) <=> (aSet0(W2102_102) & ! [W3103_103] : ((aElementOf0(W3103_103, W2102_102) <=> (aSubsetOf0(W3103_103, W0100_100) & =(sbrdtbr0(W3103_103), W1101_101))))))))), ! [W0104_104] : (((aSet0(W0104_104) & isFinite0(W0104_104)) => ! [W1105_105] : ((aElementOf0(W1105_105, szNzAzT0) => isFinite0(slbdtsldtrb0(W0104_104, W1105_105)))))), ! [W0106_106] : (((aSet0(W0106_106) & ~isFinite0(W0106_106)) => ! [W1107_107] : ((aElementOf0(W1107_107, szNzAzT0) => ~=(slbdtsldtrb0(W0106_106, W1107_107), slcrc0))))), ! [W0108_108] : (((aSet0(W0108_108) & isCountable0(W0108_108)) => ! [W1109_109] : (((aElementOf0(W1109_109, szNzAzT0) & ~=(W1109_109, sz00)) => isCountable0(slbdtsldtrb0(W0108_108, W1109_109)))))), aElementOf0(xk, szNzAzT0), ((aSet0(xS) & aSet0(xT)) & ~=(xk, sz00)), ((((((aSet0(slbdtsldtrb0(xS, xk)) & ! [W0110_110] : (((aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)) => (((aSet0(W0110_110) & ! [W1111_111] : ((aElementOf0(W1111_111, W0110_110) => aElementOf0(W1111_111, xS)))) & aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk))) & ((((aSet0(W0110_110) & ! [W1112_112] : ((aElementOf0(W1112_112, W0110_110) => aElementOf0(W1112_112, xS)))) | aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk)) => aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)))))) & aSet0(slbdtsldtrb0(xT, xk))) & ! [W0113_113] : (((aElementOf0(W0113_113, slbdtsldtrb0(xT, xk)) => (((aSet0(W0113_113) & ! [W1114_114] : ((aElementOf0(W1114_114, W0113_113) => aElementOf0(W1114_114, xT)))) & aSubsetOf0(W0113_113, xT)) & =(sbrdtbr0(W0113_113), xk))) & ((((aSet0(W0113_113) & ! [W1115_115] : ((aElementOf0(W1115_115, W0113_113) => aElementOf0(W1115_115, xT)))) | aSubsetOf0(W0113_113, xT)) & =(sbrdtbr0(W0113_113), xk)) => aElementOf0(W0113_113, slbdtsldtrb0(xT, xk)))))) & ! [W0116_116] : ((aElementOf0(W0116_116, slbdtsldtrb0(xS, xk)) => aElementOf0(W0116_116, slbdtsldtrb0(xT, xk))))) & aSubsetOf0(slbdtsldtrb0(xS, xk), slbdtsldtrb0(xT, xk))) & ~(! [W0117_117] : (((aElementOf0(W0117_117, slbdtsldtrb0(xS, xk)) => (((aSet0(W0117_117) & ! [W1118_118] : ((aElementOf0(W1118_118, W0117_117) => aElementOf0(W1118_118, xS)))) & aSubsetOf0(W0117_117, xS)) & =(sbrdtbr0(W0117_117), xk))) & ((((aSet0(W0117_117) & ! [W1119_119] : ((aElementOf0(W1119_119, W0117_117) => aElementOf0(W1119_119, xS)))) | aSubsetOf0(W0117_117, xS)) & =(sbrdtbr0(W0117_117), xk)) => aElementOf0(W0117_117, slbdtsldtrb0(xS, xk))))) => (~? [W0120_120] : (aElementOf0(W0120_120, slbdtsldtrb0(xS, xk))) | =(slbdtsldtrb0(xS, xk), slcrc0)))), aElementOf0(xx, xS), ((((aSet0(xQ) & ! [W0121_121] : ((aElementOf0(W0121_121, xQ) => aElementOf0(W0121_121, xS)))) & aSubsetOf0(xQ, xS)) & =(sbrdtbr0(xQ), xk)) & aElementOf0(xQ, slbdtsldtrb0(xS, xk))), ((aSet0(xQ) & isFinite0(xQ)) & =(sbrdtbr0(xQ), xk)), (aElement0(xy) & aElementOf0(xy, xQ)), ~aElementOf0(xx, xQ), ((((aSet0(sdtmndt0(xQ, xy)) & ! [W0122_122] : ((aElementOf0(W0122_122, sdtmndt0(xQ, xy)) <=> ((aElement0(W0122_122) & aElementOf0(W0122_122, xQ)) & ~=(W0122_122, xy))))) & aSet0(xP)) & ! [W0123_123] : ((aElementOf0(W0123_123, xP) <=> (aElement0(W0123_123) & (aElementOf0(W0123_123, sdtmndt0(xQ, xy)) | =(W0123_123, xx)))))) & =(xP, sdtpldt0(sdtmndt0(xQ, xy), xx))), ((~aElementOf0(xx, sdtmndt0(xQ, xy)) & aSet0(sdtmndt0(xQ, xy))) & ! [W0124_124] : ((aElementOf0(W0124_124, sdtmndt0(xQ, xy)) <=> ((aElement0(W0124_124) & aElementOf0(W0124_124, xQ)) & ~=(W0124_124, xy))))), ((! [W0125_125] : ((aElementOf0(W0125_125, xP) => aElementOf0(W0125_125, xS))) & aSubsetOf0(xP, xS)) & =(sbrdtbr0(xP), xk)), ~(((! [W0126_126] : ((aElementOf0(W0126_126, xP) => aElementOf0(W0126_126, xS))) | aSubsetOf0(xP, xS)) & =(sbrdtbr0(xP), xk)) | aElementOf0(xP, slbdtsldtrb0(xS, xk)))
% 11.08/8.89
% 11.08/8.89 [1] ALPHA_AND : (aSet0(szNzAzT0) & isCountable0(szNzAzT0))
% 11.08/8.89 -> [2] aSet0(szNzAzT0), isCountable0(szNzAzT0)
% 11.08/8.89
% 11.08/8.89 [2] ALPHA_AND : ((aSet0(xS) & aSet0(xT)) & ~=(xk, sz00))
% 11.08/8.89 -> [3] (aSet0(xS) & aSet0(xT)), ~=(xk, sz00)
% 11.08/8.89
% 11.08/8.89 [3] ALPHA_AND : ((((((aSet0(slbdtsldtrb0(xS, xk)) & ! [W0110_110] : (((aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)) => (((aSet0(W0110_110) & ! [W1111_111] : ((aElementOf0(W1111_111, W0110_110) => aElementOf0(W1111_111, xS)))) & aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk))) & ((((aSet0(W0110_110) & ! [W1112_112] : ((aElementOf0(W1112_112, W0110_110) => aElementOf0(W1112_112, xS)))) | aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk)) => aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)))))) & aSet0(slbdtsldtrb0(xT, xk))) & ! [W0113_113] : (((aElementOf0(W0113_113, slbdtsldtrb0(xT, xk)) => (((aSet0(W0113_113) & ! [W1114_114] : ((aElementOf0(W1114_114, W0113_113) => aElementOf0(W1114_114, xT)))) & aSubsetOf0(W0113_113, xT)) & =(sbrdtbr0(W0113_113), xk))) & ((((aSet0(W0113_113) & ! [W1115_115] : ((aElementOf0(W1115_115, W0113_113) => aElementOf0(W1115_115, xT)))) | aSubsetOf0(W0113_113, xT)) & =(sbrdtbr0(W0113_113), xk)) => aElementOf0(W0113_113, slbdtsldtrb0(xT, xk)))))) & ! [W0116_116] : ((aElementOf0(W0116_116, slbdtsldtrb0(xS, xk)) => aElementOf0(W0116_116, slbdtsldtrb0(xT, xk))))) & aSubsetOf0(slbdtsldtrb0(xS, xk), slbdtsldtrb0(xT, xk))) & ~(! [W0117_117] : (((aElementOf0(W0117_117, slbdtsldtrb0(xS, xk)) => (((aSet0(W0117_117) & ! [W1118_118] : ((aElementOf0(W1118_118, W0117_117) => aElementOf0(W1118_118, xS)))) & aSubsetOf0(W0117_117, xS)) & =(sbrdtbr0(W0117_117), xk))) & ((((aSet0(W0117_117) & ! [W1119_119] : ((aElementOf0(W1119_119, W0117_117) => aElementOf0(W1119_119, xS)))) | aSubsetOf0(W0117_117, xS)) & =(sbrdtbr0(W0117_117), xk)) => aElementOf0(W0117_117, slbdtsldtrb0(xS, xk))))) => (~? [W0120_120] : (aElementOf0(W0120_120, slbdtsldtrb0(xS, xk))) | =(slbdtsldtrb0(xS, xk), slcrc0))))
% 11.08/8.89 -> [4] (((((aSet0(slbdtsldtrb0(xS, xk)) & ! [W0110_110] : (((aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)) => (((aSet0(W0110_110) & ! [W1111_111] : ((aElementOf0(W1111_111, W0110_110) => aElementOf0(W1111_111, xS)))) & aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk))) & ((((aSet0(W0110_110) & ! [W1112_112] : ((aElementOf0(W1112_112, W0110_110) => aElementOf0(W1112_112, xS)))) | aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk)) => aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)))))) & aSet0(slbdtsldtrb0(xT, xk))) & ! [W0113_113] : (((aElementOf0(W0113_113, slbdtsldtrb0(xT, xk)) => (((aSet0(W0113_113) & ! [W1114_114] : ((aElementOf0(W1114_114, W0113_113) => aElementOf0(W1114_114, xT)))) & aSubsetOf0(W0113_113, xT)) & =(sbrdtbr0(W0113_113), xk))) & ((((aSet0(W0113_113) & ! [W1115_115] : ((aElementOf0(W1115_115, W0113_113) => aElementOf0(W1115_115, xT)))) | aSubsetOf0(W0113_113, xT)) & =(sbrdtbr0(W0113_113), xk)) => aElementOf0(W0113_113, slbdtsldtrb0(xT, xk)))))) & ! [W0116_116] : ((aElementOf0(W0116_116, slbdtsldtrb0(xS, xk)) => aElementOf0(W0116_116, slbdtsldtrb0(xT, xk))))) & aSubsetOf0(slbdtsldtrb0(xS, xk), slbdtsldtrb0(xT, xk))), ~(! [W0117_117] : (((aElementOf0(W0117_117, slbdtsldtrb0(xS, xk)) => (((aSet0(W0117_117) & ! [W1118_118] : ((aElementOf0(W1118_118, W0117_117) => aElementOf0(W1118_118, xS)))) & aSubsetOf0(W0117_117, xS)) & =(sbrdtbr0(W0117_117), xk))) & ((((aSet0(W0117_117) & ! [W1119_119] : ((aElementOf0(W1119_119, W0117_117) => aElementOf0(W1119_119, xS)))) | aSubsetOf0(W0117_117, xS)) & =(sbrdtbr0(W0117_117), xk)) => aElementOf0(W0117_117, slbdtsldtrb0(xS, xk))))) => (~? [W0120_120] : (aElementOf0(W0120_120, slbdtsldtrb0(xS, xk))) | =(slbdtsldtrb0(xS, xk), slcrc0)))
% 11.08/8.89
% 11.08/8.89 [4] ALPHA_AND : ((((aSet0(xQ) & ! [W0121_121] : ((aElementOf0(W0121_121, xQ) => aElementOf0(W0121_121, xS)))) & aSubsetOf0(xQ, xS)) & =(sbrdtbr0(xQ), xk)) & aElementOf0(xQ, slbdtsldtrb0(xS, xk)))
% 11.08/8.89 -> [5] (((aSet0(xQ) & ! [W0121_121] : ((aElementOf0(W0121_121, xQ) => aElementOf0(W0121_121, xS)))) & aSubsetOf0(xQ, xS)) & =(sbrdtbr0(xQ), xk)), aElementOf0(xQ, slbdtsldtrb0(xS, xk))
% 11.08/8.89
% 11.08/8.89 [5] ALPHA_AND : ((aSet0(xQ) & isFinite0(xQ)) & =(sbrdtbr0(xQ), xk))
% 11.08/8.89 -> [6] (aSet0(xQ) & isFinite0(xQ)), =(sbrdtbr0(xQ), xk)
% 11.08/8.89
% 11.08/8.89 [6] ALPHA_AND : (aElement0(xy) & aElementOf0(xy, xQ))
% 11.08/8.89 -> [7] aElement0(xy), aElementOf0(xy, xQ)
% 11.08/8.89
% 11.08/8.89 [7] ALPHA_AND : ((((aSet0(sdtmndt0(xQ, xy)) & ! [W0122_122] : ((aElementOf0(W0122_122, sdtmndt0(xQ, xy)) <=> ((aElement0(W0122_122) & aElementOf0(W0122_122, xQ)) & ~=(W0122_122, xy))))) & aSet0(xP)) & ! [W0123_123] : ((aElementOf0(W0123_123, xP) <=> (aElement0(W0123_123) & (aElementOf0(W0123_123, sdtmndt0(xQ, xy)) | =(W0123_123, xx)))))) & =(xP, sdtpldt0(sdtmndt0(xQ, xy), xx)))
% 11.08/8.89 -> [8] (((aSet0(sdtmndt0(xQ, xy)) & ! [W0122_122] : ((aElementOf0(W0122_122, sdtmndt0(xQ, xy)) <=> ((aElement0(W0122_122) & aElementOf0(W0122_122, xQ)) & ~=(W0122_122, xy))))) & aSet0(xP)) & ! [W0123_123] : ((aElementOf0(W0123_123, xP) <=> (aElement0(W0123_123) & (aElementOf0(W0123_123, sdtmndt0(xQ, xy)) | =(W0123_123, xx)))))), =(xP, sdtpldt0(sdtmndt0(xQ, xy), xx))
% 11.08/8.89
% 11.08/8.89 [8] ALPHA_AND : ((~aElementOf0(xx, sdtmndt0(xQ, xy)) & aSet0(sdtmndt0(xQ, xy))) & ! [W0124_124] : ((aElementOf0(W0124_124, sdtmndt0(xQ, xy)) <=> ((aElement0(W0124_124) & aElementOf0(W0124_124, xQ)) & ~=(W0124_124, xy)))))
% 11.08/8.89 -> [9] (~aElementOf0(xx, sdtmndt0(xQ, xy)) & aSet0(sdtmndt0(xQ, xy))), ! [W0124_124] : ((aElementOf0(W0124_124, sdtmndt0(xQ, xy)) <=> ((aElement0(W0124_124) & aElementOf0(W0124_124, xQ)) & ~=(W0124_124, xy))))
% 11.08/8.89
% 11.08/8.89 [9] ALPHA_AND : ((! [W0125_125] : ((aElementOf0(W0125_125, xP) => aElementOf0(W0125_125, xS))) & aSubsetOf0(xP, xS)) & =(sbrdtbr0(xP), xk))
% 11.08/8.89 -> [10] (! [W0125_125] : ((aElementOf0(W0125_125, xP) => aElementOf0(W0125_125, xS))) & aSubsetOf0(xP, xS)), =(sbrdtbr0(xP), xk)
% 11.08/8.89
% 11.08/8.89 [10] ALPHA_NOT_OR : ~(((! [W0126_126] : ((aElementOf0(W0126_126, xP) => aElementOf0(W0126_126, xS))) | aSubsetOf0(xP, xS)) & =(sbrdtbr0(xP), xk)) | aElementOf0(xP, slbdtsldtrb0(xS, xk)))
% 11.08/8.89 -> [11] ~((! [W0126_126] : ((aElementOf0(W0126_126, xP) => aElementOf0(W0126_126, xS))) | aSubsetOf0(xP, xS)) & =(sbrdtbr0(xP), xk)), ~aElementOf0(xP, slbdtsldtrb0(xS, xk))
% 11.08/8.89
% 11.08/8.89 [11] ALPHA_AND : (aSet0(xS) & aSet0(xT))
% 11.08/8.89 -> [12] aSet0(xS), aSet0(xT)
% 11.08/8.89
% 11.08/8.89 [12] ALPHA_AND : (((((aSet0(slbdtsldtrb0(xS, xk)) & ! [W0110_110] : (((aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)) => (((aSet0(W0110_110) & ! [W1111_111] : ((aElementOf0(W1111_111, W0110_110) => aElementOf0(W1111_111, xS)))) & aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk))) & ((((aSet0(W0110_110) & ! [W1112_112] : ((aElementOf0(W1112_112, W0110_110) => aElementOf0(W1112_112, xS)))) | aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk)) => aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)))))) & aSet0(slbdtsldtrb0(xT, xk))) & ! [W0113_113] : (((aElementOf0(W0113_113, slbdtsldtrb0(xT, xk)) => (((aSet0(W0113_113) & ! [W1114_114] : ((aElementOf0(W1114_114, W0113_113) => aElementOf0(W1114_114, xT)))) & aSubsetOf0(W0113_113, xT)) & =(sbrdtbr0(W0113_113), xk))) & ((((aSet0(W0113_113) & ! [W1115_115] : ((aElementOf0(W1115_115, W0113_113) => aElementOf0(W1115_115, xT)))) | aSubsetOf0(W0113_113, xT)) & =(sbrdtbr0(W0113_113), xk)) => aElementOf0(W0113_113, slbdtsldtrb0(xT, xk)))))) & ! [W0116_116] : ((aElementOf0(W0116_116, slbdtsldtrb0(xS, xk)) => aElementOf0(W0116_116, slbdtsldtrb0(xT, xk))))) & aSubsetOf0(slbdtsldtrb0(xS, xk), slbdtsldtrb0(xT, xk)))
% 11.08/8.89 -> [13] ((((aSet0(slbdtsldtrb0(xS, xk)) & ! [W0110_110] : (((aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)) => (((aSet0(W0110_110) & ! [W1111_111] : ((aElementOf0(W1111_111, W0110_110) => aElementOf0(W1111_111, xS)))) & aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk))) & ((((aSet0(W0110_110) & ! [W1112_112] : ((aElementOf0(W1112_112, W0110_110) => aElementOf0(W1112_112, xS)))) | aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk)) => aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)))))) & aSet0(slbdtsldtrb0(xT, xk))) & ! [W0113_113] : (((aElementOf0(W0113_113, slbdtsldtrb0(xT, xk)) => (((aSet0(W0113_113) & ! [W1114_114] : ((aElementOf0(W1114_114, W0113_113) => aElementOf0(W1114_114, xT)))) & aSubsetOf0(W0113_113, xT)) & =(sbrdtbr0(W0113_113), xk))) & ((((aSet0(W0113_113) & ! [W1115_115] : ((aElementOf0(W1115_115, W0113_113) => aElementOf0(W1115_115, xT)))) | aSubsetOf0(W0113_113, xT)) & =(sbrdtbr0(W0113_113), xk)) => aElementOf0(W0113_113, slbdtsldtrb0(xT, xk)))))) & ! [W0116_116] : ((aElementOf0(W0116_116, slbdtsldtrb0(xS, xk)) => aElementOf0(W0116_116, slbdtsldtrb0(xT, xk))))), aSubsetOf0(slbdtsldtrb0(xS, xk), slbdtsldtrb0(xT, xk))
% 11.08/8.89
% 11.08/8.89 [13] ALPHA_NOT_IMPLY : ~(! [W0117_117] : (((aElementOf0(W0117_117, slbdtsldtrb0(xS, xk)) => (((aSet0(W0117_117) & ! [W1118_118] : ((aElementOf0(W1118_118, W0117_117) => aElementOf0(W1118_118, xS)))) & aSubsetOf0(W0117_117, xS)) & =(sbrdtbr0(W0117_117), xk))) & ((((aSet0(W0117_117) & ! [W1119_119] : ((aElementOf0(W1119_119, W0117_117) => aElementOf0(W1119_119, xS)))) | aSubsetOf0(W0117_117, xS)) & =(sbrdtbr0(W0117_117), xk)) => aElementOf0(W0117_117, slbdtsldtrb0(xS, xk))))) => (~? [W0120_120] : (aElementOf0(W0120_120, slbdtsldtrb0(xS, xk))) | =(slbdtsldtrb0(xS, xk), slcrc0)))
% 11.08/8.89 -> [14] ! [W0117_117] : (((aElementOf0(W0117_117, slbdtsldtrb0(xS, xk)) => (((aSet0(W0117_117) & ! [W1118_118] : ((aElementOf0(W1118_118, W0117_117) => aElementOf0(W1118_118, xS)))) & aSubsetOf0(W0117_117, xS)) & =(sbrdtbr0(W0117_117), xk))) & ((((aSet0(W0117_117) & ! [W1119_119] : ((aElementOf0(W1119_119, W0117_117) => aElementOf0(W1119_119, xS)))) | aSubsetOf0(W0117_117, xS)) & =(sbrdtbr0(W0117_117), xk)) => aElementOf0(W0117_117, slbdtsldtrb0(xS, xk))))), ~(~? [W0120_120] : (aElementOf0(W0120_120, slbdtsldtrb0(xS, xk))) | =(slbdtsldtrb0(xS, xk), slcrc0))
% 11.08/8.89
% 11.08/8.89 [14] ALPHA_AND : (((aSet0(xQ) & ! [W0121_121] : ((aElementOf0(W0121_121, xQ) => aElementOf0(W0121_121, xS)))) & aSubsetOf0(xQ, xS)) & =(sbrdtbr0(xQ), xk))
% 11.08/8.89 -> [15] ((aSet0(xQ) & ! [W0121_121] : ((aElementOf0(W0121_121, xQ) => aElementOf0(W0121_121, xS)))) & aSubsetOf0(xQ, xS)), =(sbrdtbr0(xQ), xk)
% 11.08/8.89
% 11.08/8.89 [15] ALPHA_AND : (aSet0(xQ) & isFinite0(xQ))
% 11.08/8.89 -> [16] aSet0(xQ), isFinite0(xQ)
% 11.08/8.89
% 11.08/8.89 [16] ALPHA_AND : (((aSet0(sdtmndt0(xQ, xy)) & ! [W0122_122] : ((aElementOf0(W0122_122, sdtmndt0(xQ, xy)) <=> ((aElement0(W0122_122) & aElementOf0(W0122_122, xQ)) & ~=(W0122_122, xy))))) & aSet0(xP)) & ! [W0123_123] : ((aElementOf0(W0123_123, xP) <=> (aElement0(W0123_123) & (aElementOf0(W0123_123, sdtmndt0(xQ, xy)) | =(W0123_123, xx))))))
% 11.08/8.89 -> [17] ((aSet0(sdtmndt0(xQ, xy)) & ! [W0122_122] : ((aElementOf0(W0122_122, sdtmndt0(xQ, xy)) <=> ((aElement0(W0122_122) & aElementOf0(W0122_122, xQ)) & ~=(W0122_122, xy))))) & aSet0(xP)), ! [W0123_123] : ((aElementOf0(W0123_123, xP) <=> (aElement0(W0123_123) & (aElementOf0(W0123_123, sdtmndt0(xQ, xy)) | =(W0123_123, xx)))))
% 11.08/8.89
% 11.08/8.89 [17] ALPHA_AND : (~aElementOf0(xx, sdtmndt0(xQ, xy)) & aSet0(sdtmndt0(xQ, xy)))
% 11.08/8.89 -> [18] ~aElementOf0(xx, sdtmndt0(xQ, xy)), aSet0(sdtmndt0(xQ, xy))
% 11.08/8.89
% 11.08/8.89 [18] ALPHA_AND : (! [W0125_125] : ((aElementOf0(W0125_125, xP) => aElementOf0(W0125_125, xS))) & aSubsetOf0(xP, xS))
% 11.08/8.89 -> [19] ! [W0125_125] : ((aElementOf0(W0125_125, xP) => aElementOf0(W0125_125, xS))), aSubsetOf0(xP, xS)
% 11.08/8.89
% 11.08/8.89 [19] ALPHA_AND : ((((aSet0(slbdtsldtrb0(xS, xk)) & ! [W0110_110] : (((aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)) => (((aSet0(W0110_110) & ! [W1111_111] : ((aElementOf0(W1111_111, W0110_110) => aElementOf0(W1111_111, xS)))) & aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk))) & ((((aSet0(W0110_110) & ! [W1112_112] : ((aElementOf0(W1112_112, W0110_110) => aElementOf0(W1112_112, xS)))) | aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk)) => aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)))))) & aSet0(slbdtsldtrb0(xT, xk))) & ! [W0113_113] : (((aElementOf0(W0113_113, slbdtsldtrb0(xT, xk)) => (((aSet0(W0113_113) & ! [W1114_114] : ((aElementOf0(W1114_114, W0113_113) => aElementOf0(W1114_114, xT)))) & aSubsetOf0(W0113_113, xT)) & =(sbrdtbr0(W0113_113), xk))) & ((((aSet0(W0113_113) & ! [W1115_115] : ((aElementOf0(W1115_115, W0113_113) => aElementOf0(W1115_115, xT)))) | aSubsetOf0(W0113_113, xT)) & =(sbrdtbr0(W0113_113), xk)) => aElementOf0(W0113_113, slbdtsldtrb0(xT, xk)))))) & ! [W0116_116] : ((aElementOf0(W0116_116, slbdtsldtrb0(xS, xk)) => aElementOf0(W0116_116, slbdtsldtrb0(xT, xk)))))
% 11.08/8.89 -> [20] (((aSet0(slbdtsldtrb0(xS, xk)) & ! [W0110_110] : (((aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)) => (((aSet0(W0110_110) & ! [W1111_111] : ((aElementOf0(W1111_111, W0110_110) => aElementOf0(W1111_111, xS)))) & aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk))) & ((((aSet0(W0110_110) & ! [W1112_112] : ((aElementOf0(W1112_112, W0110_110) => aElementOf0(W1112_112, xS)))) | aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk)) => aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)))))) & aSet0(slbdtsldtrb0(xT, xk))) & ! [W0113_113] : (((aElementOf0(W0113_113, slbdtsldtrb0(xT, xk)) => (((aSet0(W0113_113) & ! [W1114_114] : ((aElementOf0(W1114_114, W0113_113) => aElementOf0(W1114_114, xT)))) & aSubsetOf0(W0113_113, xT)) & =(sbrdtbr0(W0113_113), xk))) & ((((aSet0(W0113_113) & ! [W1115_115] : ((aElementOf0(W1115_115, W0113_113) => aElementOf0(W1115_115, xT)))) | aSubsetOf0(W0113_113, xT)) & =(sbrdtbr0(W0113_113), xk)) => aElementOf0(W0113_113, slbdtsldtrb0(xT, xk)))))), ! [W0116_116] : ((aElementOf0(W0116_116, slbdtsldtrb0(xS, xk)) => aElementOf0(W0116_116, slbdtsldtrb0(xT, xk))))
% 11.08/8.89
% 11.08/8.89 [20] ALPHA_NOT_OR : ~(~? [W0120_120] : (aElementOf0(W0120_120, slbdtsldtrb0(xS, xk))) | =(slbdtsldtrb0(xS, xk), slcrc0))
% 11.08/8.89 -> [21] ~~? [W0120_120] : (aElementOf0(W0120_120, slbdtsldtrb0(xS, xk))), ~=(slbdtsldtrb0(xS, xk), slcrc0)
% 11.08/8.89
% 11.08/8.89 [21] ALPHA_AND : ((aSet0(xQ) & ! [W0121_121] : ((aElementOf0(W0121_121, xQ) => aElementOf0(W0121_121, xS)))) & aSubsetOf0(xQ, xS))
% 11.08/8.89 -> [22] (aSet0(xQ) & ! [W0121_121] : ((aElementOf0(W0121_121, xQ) => aElementOf0(W0121_121, xS)))), aSubsetOf0(xQ, xS)
% 11.08/8.89
% 11.08/8.89 [22] ALPHA_AND : ((aSet0(sdtmndt0(xQ, xy)) & ! [W0122_122] : ((aElementOf0(W0122_122, sdtmndt0(xQ, xy)) <=> ((aElement0(W0122_122) & aElementOf0(W0122_122, xQ)) & ~=(W0122_122, xy))))) & aSet0(xP))
% 11.08/8.89 -> [23] (aSet0(sdtmndt0(xQ, xy)) & ! [W0122_122] : ((aElementOf0(W0122_122, sdtmndt0(xQ, xy)) <=> ((aElement0(W0122_122) & aElementOf0(W0122_122, xQ)) & ~=(W0122_122, xy))))), aSet0(xP)
% 11.08/8.89
% 11.08/8.89 [23] ALPHA_AND : (((aSet0(slbdtsldtrb0(xS, xk)) & ! [W0110_110] : (((aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)) => (((aSet0(W0110_110) & ! [W1111_111] : ((aElementOf0(W1111_111, W0110_110) => aElementOf0(W1111_111, xS)))) & aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk))) & ((((aSet0(W0110_110) & ! [W1112_112] : ((aElementOf0(W1112_112, W0110_110) => aElementOf0(W1112_112, xS)))) | aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk)) => aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)))))) & aSet0(slbdtsldtrb0(xT, xk))) & ! [W0113_113] : (((aElementOf0(W0113_113, slbdtsldtrb0(xT, xk)) => (((aSet0(W0113_113) & ! [W1114_114] : ((aElementOf0(W1114_114, W0113_113) => aElementOf0(W1114_114, xT)))) & aSubsetOf0(W0113_113, xT)) & =(sbrdtbr0(W0113_113), xk))) & ((((aSet0(W0113_113) & ! [W1115_115] : ((aElementOf0(W1115_115, W0113_113) => aElementOf0(W1115_115, xT)))) | aSubsetOf0(W0113_113, xT)) & =(sbrdtbr0(W0113_113), xk)) => aElementOf0(W0113_113, slbdtsldtrb0(xT, xk))))))
% 11.08/8.89 -> [24] ((aSet0(slbdtsldtrb0(xS, xk)) & ! [W0110_110] : (((aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)) => (((aSet0(W0110_110) & ! [W1111_111] : ((aElementOf0(W1111_111, W0110_110) => aElementOf0(W1111_111, xS)))) & aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk))) & ((((aSet0(W0110_110) & ! [W1112_112] : ((aElementOf0(W1112_112, W0110_110) => aElementOf0(W1112_112, xS)))) | aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk)) => aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)))))) & aSet0(slbdtsldtrb0(xT, xk))), ! [W0113_113] : (((aElementOf0(W0113_113, slbdtsldtrb0(xT, xk)) => (((aSet0(W0113_113) & ! [W1114_114] : ((aElementOf0(W1114_114, W0113_113) => aElementOf0(W1114_114, xT)))) & aSubsetOf0(W0113_113, xT)) & =(sbrdtbr0(W0113_113), xk))) & ((((aSet0(W0113_113) & ! [W1115_115] : ((aElementOf0(W1115_115, W0113_113) => aElementOf0(W1115_115, xT)))) | aSubsetOf0(W0113_113, xT)) & =(sbrdtbr0(W0113_113), xk)) => aElementOf0(W0113_113, slbdtsldtrb0(xT, xk)))))
% 11.08/8.89
% 11.08/8.89 [24] ALPHA_NOT_NOT : ~~? [W0120_120] : (aElementOf0(W0120_120, slbdtsldtrb0(xS, xk)))
% 11.08/8.89 -> [25] ? [W0120_120] : (aElementOf0(W0120_120, slbdtsldtrb0(xS, xk)))
% 11.08/8.89
% 11.08/8.89 [25] ALPHA_AND : (aSet0(xQ) & ! [W0121_121] : ((aElementOf0(W0121_121, xQ) => aElementOf0(W0121_121, xS))))
% 11.08/8.89 -> [26] aSet0(xQ), ! [W0121_121] : ((aElementOf0(W0121_121, xQ) => aElementOf0(W0121_121, xS)))
% 11.08/8.89
% 11.08/8.89 [26] ALPHA_AND : (aSet0(sdtmndt0(xQ, xy)) & ! [W0122_122] : ((aElementOf0(W0122_122, sdtmndt0(xQ, xy)) <=> ((aElement0(W0122_122) & aElementOf0(W0122_122, xQ)) & ~=(W0122_122, xy)))))
% 11.08/8.89 -> [27] aSet0(sdtmndt0(xQ, xy)), ! [W0122_122] : ((aElementOf0(W0122_122, sdtmndt0(xQ, xy)) <=> ((aElement0(W0122_122) & aElementOf0(W0122_122, xQ)) & ~=(W0122_122, xy))))
% 11.08/8.89
% 11.08/8.89 [27] ALPHA_AND : ((aSet0(slbdtsldtrb0(xS, xk)) & ! [W0110_110] : (((aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)) => (((aSet0(W0110_110) & ! [W1111_111] : ((aElementOf0(W1111_111, W0110_110) => aElementOf0(W1111_111, xS)))) & aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk))) & ((((aSet0(W0110_110) & ! [W1112_112] : ((aElementOf0(W1112_112, W0110_110) => aElementOf0(W1112_112, xS)))) | aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk)) => aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)))))) & aSet0(slbdtsldtrb0(xT, xk)))
% 11.08/8.89 -> [28] (aSet0(slbdtsldtrb0(xS, xk)) & ! [W0110_110] : (((aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)) => (((aSet0(W0110_110) & ! [W1111_111] : ((aElementOf0(W1111_111, W0110_110) => aElementOf0(W1111_111, xS)))) & aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk))) & ((((aSet0(W0110_110) & ! [W1112_112] : ((aElementOf0(W1112_112, W0110_110) => aElementOf0(W1112_112, xS)))) | aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk)) => aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)))))), aSet0(slbdtsldtrb0(xT, xk))
% 11.08/8.89
% 11.08/8.89 [28] ALPHA_AND : (aSet0(slbdtsldtrb0(xS, xk)) & ! [W0110_110] : (((aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)) => (((aSet0(W0110_110) & ! [W1111_111] : ((aElementOf0(W1111_111, W0110_110) => aElementOf0(W1111_111, xS)))) & aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk))) & ((((aSet0(W0110_110) & ! [W1112_112] : ((aElementOf0(W1112_112, W0110_110) => aElementOf0(W1112_112, xS)))) | aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk)) => aElementOf0(W0110_110, slbdtsldtrb0(xS, xk))))))
% 11.08/8.89 -> [29] aSet0(slbdtsldtrb0(xS, xk)), ! [W0110_110] : (((aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)) => (((aSet0(W0110_110) & ! [W1111_111] : ((aElementOf0(W1111_111, W0110_110) => aElementOf0(W1111_111, xS)))) & aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk))) & ((((aSet0(W0110_110) & ! [W1112_112] : ((aElementOf0(W1112_112, W0110_110) => aElementOf0(W1112_112, xS)))) | aSubsetOf0(W0110_110, xS)) & =(sbrdtbr0(W0110_110), xk)) => aElementOf0(W0110_110, slbdtsldtrb0(xS, xk)))))
% 11.08/8.89
% 11.08/8.89 [29] DELTA_EXISTS : ? [W0120_120] : (aElementOf0(W0120_120, slbdtsldtrb0(xS, xk)))
% 11.08/8.89 -> [30] aElementOf0(skolem_W0120120, slbdtsldtrb0(xS, xk))
% 11.08/8.89
% 11.08/8.89 [30] BETA_NOT_AND : ~((! [W0126_126] : ((aElementOf0(W0126_126, xP) => aElementOf0(W0126_126, xS))) | aSubsetOf0(xP, xS)) & =(sbrdtbr0(xP), xk))
% 11.08/8.89 -> [31] ~(! [W0126_126] : ((aElementOf0(W0126_126, xP) => aElementOf0(W0126_126, xS))) | aSubsetOf0(xP, xS))
% 11.08/8.89 -> [32] ~=(sbrdtbr0(xP), xk)
% 11.08/8.89
% 11.08/8.89 [32] CLOSURE : ~=(sbrdtbr0(xP), xk)
% 11.08/8.89
% 11.08/8.89 [31] ALPHA_NOT_OR : ~(! [W0126_126] : ((aElementOf0(W0126_126, xP) => aElementOf0(W0126_126, xS))) | aSubsetOf0(xP, xS))
% 11.08/8.89 -> [33] ~! [W0126_126] : ((aElementOf0(W0126_126, xP) => aElementOf0(W0126_126, xS))), ~aSubsetOf0(xP, xS)
% 11.08/8.89
% 11.08/8.89 [33] CLOSURE : ~aSubsetOf0(xP, xS)
% 11.08/8.89
% 11.08/8.89 % SZS output end Proof for theBenchmark.p
% 11.08/8.89 [8.529435s][1][Res] 53969 goroutines created
% 11.08/8.89 ==== Result ====
% 11.08/8.89 [8.529477s][1][Res] VALID
% 11.08/8.89 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------