TSTP Solution File: SEU539^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU539^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %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 May 21 04:05:50 EDT 2024
% Result : Theorem 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU539^1 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 16:39:07 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % (2320)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (2327)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.13/0.37 % (2325)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.38 % (2322)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.38 % (2321)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.38 % (2323)WARNING: value z3 for option sas not known
% 0.13/0.38 % (2323)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.38 % (2326)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.13/0.38 % (2324)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.40 % (2327)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.41 % Exception at run slice level
% 0.20/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.41 % Exception at run slice level
% 0.20/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.42 % Exception at run slice level
% 0.20/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.42 % (2329)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.20/0.43 % (2328)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.44 % (2323)First to succeed.
% 0.20/0.44 % (2323)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2320"
% 0.20/0.44 % (2330)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.20/0.44 % (2323)Refutation found. Thanks to Tanya!
% 0.20/0.44 % SZS status Theorem for theBenchmark
% 0.20/0.44 % SZS output start Proof for theBenchmark
% 0.20/0.44 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.44 thf(func_def_0, type, in: $i > $i > $o).
% 0.20/0.44 thf(func_def_1, type, exu: ($i > $o) > $o).
% 0.20/0.44 thf(func_def_3, type, setextAx: $o).
% 0.20/0.44 thf(func_def_5, type, emptysetAx: $o).
% 0.20/0.44 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 0.20/0.44 thf(func_def_7, type, setadjoinAx: $o).
% 0.20/0.44 thf(func_def_8, type, powerset: $i > $i).
% 0.20/0.44 thf(func_def_9, type, powersetAx: $o).
% 0.20/0.44 thf(func_def_10, type, setunion: $i > $i).
% 0.20/0.44 thf(func_def_11, type, setunionAx: $o).
% 0.20/0.44 thf(func_def_13, type, omega0Ax: $o).
% 0.20/0.44 thf(func_def_14, type, omegaSAx: $o).
% 0.20/0.44 thf(func_def_15, type, omegaIndAx: $o).
% 0.20/0.44 thf(func_def_16, type, replAx: $o).
% 0.20/0.44 thf(func_def_17, type, foundationAx: $o).
% 0.20/0.44 thf(func_def_18, type, wellorderingAx: $o).
% 0.20/0.44 thf(func_def_19, type, descr: ($i > $o) > $i).
% 0.20/0.44 thf(func_def_20, type, descrp: $o).
% 0.20/0.44 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 0.20/0.44 thf(func_def_22, type, dsetconstrI: $o).
% 0.20/0.44 thf(func_def_23, type, dsetconstrEL: $o).
% 0.20/0.44 thf(func_def_24, type, dsetconstrER: $o).
% 0.20/0.44 thf(func_def_25, type, exuE1: $o).
% 0.20/0.44 thf(func_def_26, type, prop2set: $o > $i).
% 0.20/0.44 thf(func_def_27, type, prop2setE: $o).
% 0.20/0.44 thf(func_def_28, type, emptysetE: $o).
% 0.20/0.44 thf(func_def_29, type, emptysetimpfalse: $o).
% 0.20/0.44 thf(func_def_30, type, notinemptyset: $o).
% 0.20/0.44 thf(func_def_31, type, exuE3e: $o).
% 0.20/0.44 thf(func_def_32, type, setext: $o).
% 0.20/0.44 thf(func_def_33, type, emptyI: $o).
% 0.20/0.44 thf(func_def_34, type, noeltsimpempty: $o).
% 0.20/0.44 thf(func_def_35, type, setbeta: $o).
% 0.20/0.44 thf(func_def_36, type, nonempty: $i > $o).
% 0.20/0.44 thf(func_def_37, type, nonemptyE1: $o).
% 0.20/0.44 thf(func_def_38, type, nonemptyI: $o).
% 0.20/0.44 thf(func_def_39, type, nonemptyI1: $o).
% 0.20/0.44 thf(func_def_40, type, setadjoinIL: $o).
% 0.20/0.44 thf(func_def_41, type, emptyinunitempty: $o).
% 0.20/0.44 thf(func_def_42, type, setadjoinIR: $o).
% 0.20/0.44 thf(func_def_43, type, setadjoinE: $o).
% 0.20/0.44 thf(func_def_44, type, setadjoinOr: $o).
% 0.20/0.44 thf(func_def_45, type, setoftrueEq: $o).
% 0.20/0.44 thf(func_def_46, type, powersetI: $o).
% 0.20/0.44 thf(func_def_47, type, emptyinPowerset: $o).
% 0.20/0.44 thf(func_def_48, type, emptyInPowerset: $o).
% 0.20/0.44 thf(func_def_49, type, powersetE: $o).
% 0.20/0.44 thf(func_def_50, type, setunionI: $o).
% 0.20/0.44 thf(func_def_51, type, setunionE: $o).
% 0.20/0.44 thf(func_def_52, type, subPowSU: $o).
% 0.20/0.44 thf(func_def_53, type, exuE2: $o).
% 0.20/0.44 thf(func_def_54, type, nonemptyImpWitness: $o).
% 0.20/0.44 thf(func_def_55, type, uniqinunit: $o).
% 0.20/0.44 thf(func_def_56, type, notinsingleton: $o).
% 0.20/0.44 thf(func_def_57, type, eqinunit: $o).
% 0.20/0.44 thf(func_def_58, type, singletonsswitch: $o).
% 0.20/0.44 thf(func_def_59, type, upairsetE: $o).
% 0.20/0.44 thf(func_def_60, type, upairsetIL: $o).
% 0.20/0.44 thf(func_def_61, type, upairsetIR: $o).
% 0.20/0.44 thf(func_def_62, type, emptyE1: $o).
% 0.20/0.44 thf(func_def_63, type, vacuousDall: $o).
% 0.20/0.44 thf(func_def_64, type, quantDeMorgan1: $o).
% 0.20/0.44 thf(func_def_65, type, quantDeMorgan2: $o).
% 0.20/0.44 thf(func_def_66, type, quantDeMorgan3: $o).
% 0.20/0.44 thf(func_def_69, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
% 0.20/0.44 thf(func_def_70, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)).
% 0.20/0.44 thf(func_def_71, type, vPI: !>[X0: $tType]:((X0 > $o) > $o)).
% 0.20/0.44 thf(func_def_72, type, cCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > X1 > X0 > X2)).
% 0.20/0.44 thf(func_def_73, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)).
% 0.20/0.44 thf(func_def_74, type, iCOMB: !>[X0: $tType]:(X0 > X0)).
% 0.20/0.44 thf(func_def_75, type, sCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > (X0 > X1) > X0 > X2)).
% 0.20/0.44 thf(func_def_76, type, vIMP: $o > $o > $o).
% 0.20/0.44 thf(func_def_77, type, vAND: $o > $o > $o).
% 0.20/0.44 thf(func_def_78, type, vNOT: $o > $o).
% 0.20/0.44 thf(func_def_79, type, vSIGMA: !>[X0: $tType]:((X0 > $o) > $o)).
% 0.20/0.44 thf(func_def_80, type, vIFF: $o > $o > $o).
% 0.20/0.44 thf(func_def_81, type, vOR: $o > $o > $o).
% 0.20/0.44 thf(func_def_83, type, sK1: $i > $o).
% 0.20/0.44 thf(func_def_109, type, sK27: $i > $o).
% 0.20/0.44 thf(func_def_114, type, sK32: $i > $o).
% 0.20/0.44 thf(func_def_115, type, sK33: $i > $o).
% 0.20/0.44 thf(func_def_116, type, sK34: $i > $o).
% 0.20/0.44 thf(func_def_124, type, sK42: $i > $o).
% 0.20/0.44 thf(func_def_125, type, sK43: $i > $o).
% 0.20/0.44 thf(func_def_126, type, sK44: $i > $o).
% 0.20/0.44 thf(func_def_127, type, sK45: $i > $o).
% 0.20/0.44 thf(f604,plain,(
% 0.20/0.44 $false),
% 0.20/0.44 inference(subsumption_resolution,[],[f603,f239])).
% 0.20/0.44 thf(f239,plain,(
% 0.20/0.44 ($true != vAPP($i,$o,sK1,sK2))),
% 0.20/0.44 inference(cnf_transformation,[],[f182])).
% 0.20/0.44 thf(f182,plain,(
% 0.20/0.44 (! [X2] : (($true = vAPP($i,$o,sK1,X2)) | ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X2),sK0))) & (($true != vAPP($i,$o,sK1,sK2)) & ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),in,sK2),sK0)))) & (quantDeMorgan3 = $true) & (quantDeMorgan2 = $true) & (quantDeMorgan1 = $true) & (vacuousDall = $true) & (emptyE1 = $true) & (upairsetIR = $true) & (upairsetIL = $true) & (upairsetE = $true) & (singletonsswitch = $true) & (eqinunit = $true) & (notinsingleton = $true) & (uniqinunit = $true) & (nonemptyImpWitness = $true) & (exuE2 = $true) & (subPowSU = $true) & (setunionE = $true) & (setunionI = $true) & (powersetE = $true) & (emptyInPowerset = $true) & (emptyinPowerset = $true) & (powersetI = $true) & (setoftrueEq = $true) & (setadjoinOr = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (emptyinunitempty = $true) & (setadjoinIL = $true) & (nonemptyI1 = $true) & (nonemptyI = $true) & (nonemptyE1 = $true) & (setbeta = $true) & (noeltsimpempty = $true) & (emptyI = $true) & (setext = $true) & (exuE3e = $true) & (notinemptyset = $true) & (emptysetimpfalse = $true) & (emptysetE = $true) & (prop2setE = $true) & (exuE1 = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (dsetconstrI = $true) & (descrp = $true) & (wellorderingAx = $true) & (foundationAx = $true) & (replAx = $true) & (omegaIndAx = $true) & (omegaSAx = $true) & (omega0Ax = $true) & (setunionAx = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (emptysetAx = $true) & (setextAx = $true)),
% 0.20/0.44 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f179,f181,f180])).
% 0.20/0.44 thf(f180,plain,(
% 0.20/0.44 ? [X0,X1 : $i > $o] : (! [X2] : (($true = vAPP($i,$o,X1,X2)) | ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X2),X0))) & ? [X3] : (($true != vAPP($i,$o,X1,X3)) & ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X3),X0)))) => (! [X2] : (($true = vAPP($i,$o,sK1,X2)) | ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X2),sK0))) & ? [X3] : (($true != vAPP($i,$o,sK1,X3)) & ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X3),sK0))))),
% 0.20/0.44 introduced(choice_axiom,[])).
% 0.20/0.44 thf(f181,plain,(
% 0.20/0.44 ? [X3] : (($true != vAPP($i,$o,sK1,X3)) & ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X3),sK0))) => (($true != vAPP($i,$o,sK1,sK2)) & ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),in,sK2),sK0)))),
% 0.20/0.44 introduced(choice_axiom,[])).
% 0.20/0.44 thf(f179,plain,(
% 0.20/0.44 ? [X0,X1 : $i > $o] : (! [X2] : (($true = vAPP($i,$o,X1,X2)) | ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X2),X0))) & ? [X3] : (($true != vAPP($i,$o,X1,X3)) & ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X3),X0)))) & (quantDeMorgan3 = $true) & (quantDeMorgan2 = $true) & (quantDeMorgan1 = $true) & (vacuousDall = $true) & (emptyE1 = $true) & (upairsetIR = $true) & (upairsetIL = $true) & (upairsetE = $true) & (singletonsswitch = $true) & (eqinunit = $true) & (notinsingleton = $true) & (uniqinunit = $true) & (nonemptyImpWitness = $true) & (exuE2 = $true) & (subPowSU = $true) & (setunionE = $true) & (setunionI = $true) & (powersetE = $true) & (emptyInPowerset = $true) & (emptyinPowerset = $true) & (powersetI = $true) & (setoftrueEq = $true) & (setadjoinOr = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (emptyinunitempty = $true) & (setadjoinIL = $true) & (nonemptyI1 = $true) & (nonemptyI = $true) & (nonemptyE1 = $true) & (setbeta = $true) & (noeltsimpempty = $true) & (emptyI = $true) & (setext = $true) & (exuE3e = $true) & (notinemptyset = $true) & (emptysetimpfalse = $true) & (emptysetE = $true) & (prop2setE = $true) & (exuE1 = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (dsetconstrI = $true) & (descrp = $true) & (wellorderingAx = $true) & (foundationAx = $true) & (replAx = $true) & (omegaIndAx = $true) & (omegaSAx = $true) & (omega0Ax = $true) & (setunionAx = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (emptysetAx = $true) & (setextAx = $true)),
% 0.20/0.44 inference(rectify,[],[f178])).
% 0.20/0.44 thf(f178,plain,(
% 0.20/0.44 ? [X0,X1 : $i > $o] : (! [X3] : (($true = vAPP($i,$o,X1,X3)) | ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X3),X0))) & ? [X2] : (($true != vAPP($i,$o,X1,X2)) & ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X2),X0)))) & (quantDeMorgan3 = $true) & (quantDeMorgan2 = $true) & (quantDeMorgan1 = $true) & (vacuousDall = $true) & (emptyE1 = $true) & (upairsetIR = $true) & (upairsetIL = $true) & (upairsetE = $true) & (singletonsswitch = $true) & (eqinunit = $true) & (notinsingleton = $true) & (uniqinunit = $true) & (nonemptyImpWitness = $true) & (exuE2 = $true) & (subPowSU = $true) & (setunionE = $true) & (setunionI = $true) & (powersetE = $true) & (emptyInPowerset = $true) & (emptyinPowerset = $true) & (powersetI = $true) & (setoftrueEq = $true) & (setadjoinOr = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (emptyinunitempty = $true) & (setadjoinIL = $true) & (nonemptyI1 = $true) & (nonemptyI = $true) & (nonemptyE1 = $true) & (setbeta = $true) & (noeltsimpempty = $true) & (emptyI = $true) & (setext = $true) & (exuE3e = $true) & (notinemptyset = $true) & (emptysetimpfalse = $true) & (emptysetE = $true) & (prop2setE = $true) & (exuE1 = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (dsetconstrI = $true) & (descrp = $true) & (wellorderingAx = $true) & (foundationAx = $true) & (replAx = $true) & (omegaIndAx = $true) & (omegaSAx = $true) & (omega0Ax = $true) & (setunionAx = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (emptysetAx = $true) & (setextAx = $true)),
% 0.20/0.44 inference(flattening,[],[f177])).
% 0.20/0.44 thf(f177,plain,(
% 0.20/0.44 ((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0,X1 : $i > $o] : (! [X3] : (($true = vAPP($i,$o,X1,X3)) | ($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X3),X0))) & ? [X2] : (($true != vAPP($i,$o,X1,X2)) & ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X2),X0)))) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 0.20/0.44 inference(ennf_transformation,[],[f176])).
% 0.20/0.44 thf(f176,plain,(
% 0.20/0.44 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ! [X0,X1 : $i > $o] : (? [X2] : (($true != vAPP($i,$o,X1,X2)) & ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X2),X0))) => ~! [X3] : (($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X3),X0)) => ($true = vAPP($i,$o,X1,X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.20/0.44 inference(flattening,[],[f64])).
% 0.20/0.44 thf(f64,plain,(
% 0.20/0.44 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ! [X0,X1 : $i > $o] : (? [X2] : (~($true = vAPP($i,$o,X1,X2)) & ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X2),X0))) => ~! [X3] : (($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X3),X0)) => ($true = vAPP($i,$o,X1,X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.20/0.44 inference(fool_elimination,[],[f63])).
% 0.20/0.44 thf(f63,plain,(
% 0.20/0.44 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => ! [X0,X1 : $i > $o] : (? [X2] : (~vAPP($i,$o,X1,X2) & vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X2),X0)) => ~! [X3] : (vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X3),X0) => vAPP($i,$o,X1,X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.20/0.44 inference(rectify,[],[f60])).
% 0.20/0.44 thf(f60,negated_conjecture,(
% 0.20/0.44 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => ! [X3,X0 : $i > $o] : (? [X1] : (~vAPP($i,$o,X0,X1) & vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X1),X3)) => ~! [X1] : (vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X1),X3) => vAPP($i,$o,X0,X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.20/0.44 inference(negated_conjecture,[],[f59])).
% 0.20/0.44 thf(f59,conjecture,(
% 0.20/0.44 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => ! [X3,X0 : $i > $o] : (? [X1] : (~vAPP($i,$o,X0,X1) & vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X1),X3)) => ~! [X1] : (vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X1),X3) => vAPP($i,$o,X0,X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.20/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4)).
% 0.20/0.44 thf(f603,plain,(
% 0.20/0.44 ($true = vAPP($i,$o,sK1,sK2))),
% 0.20/0.44 inference(trivial_inequality_removal,[],[f600])).
% 0.20/0.44 thf(f600,plain,(
% 0.20/0.44 ($true != $true) | ($true = vAPP($i,$o,sK1,sK2))),
% 0.20/0.44 inference(superposition,[],[f240,f238])).
% 0.20/0.44 thf(f238,plain,(
% 0.20/0.44 ($true = vAPP($i,$o,vAPP($i,sTfun($i,$o),in,sK2),sK0))),
% 0.20/0.44 inference(cnf_transformation,[],[f182])).
% 0.20/0.44 thf(f240,plain,(
% 0.20/0.44 ( ! [X2 : $i] : (($true != vAPP($i,$o,vAPP($i,sTfun($i,$o),in,X2),sK0)) | ($true = vAPP($i,$o,sK1,X2))) )),
% 0.20/0.44 inference(cnf_transformation,[],[f182])).
% 0.20/0.44 % SZS output end Proof for theBenchmark
% 0.20/0.44 % (2323)------------------------------
% 0.20/0.44 % (2323)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.44 % (2323)Termination reason: Refutation
% 0.20/0.44
% 0.20/0.44 % (2323)Memory used [KB]: 1470
% 0.20/0.44 % (2323)Time elapsed: 0.059 s
% 0.20/0.44 % (2323)Instructions burned: 135 (million)
% 0.20/0.44 % (2320)Success in time 0.089 s
%------------------------------------------------------------------------------