%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU544^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:32:23 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU544^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n007.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 13:47:11 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.24 Running first-order model finding
% 0.10/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.30 % (3389097)Will run a generic schedule for satisfiability detection.
% 0.22/0.30 % (3389118)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2430435898:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.30 % (3389114)% WARNING: option uhcvi not known.
% 0.22/0.30 % (3389113)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2865921748_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.30 % (3389114)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=724356739:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.30 % (3389116)dis+10_1_sil=32000:sp=arity:random_seed=4253377996:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.30 % (3389117)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1705702531:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.30 % (3389119)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3224365625:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.30 % (3389115)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3073022263:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.30 % (3389114)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.30 % (3389117)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.30 % (3389118) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3389097-3389118"...
% 0.22/0.30 % (3389118)...printing done.
% 0.22/0.30 % Exception at run slice level
% 0.22/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.30 % (3389114)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.30 % (3389118)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% 0.22/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.30 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.22/0.30 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 0.22/0.30 thf(func_def_3, type, setextAx: $o).
% 0.22/0.30 thf(func_def_5, type, emptysetAx: $o).
% 0.22/0.30 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 0.22/0.30 thf(func_def_7, type, setadjoinAx: $o).
% 0.22/0.30 thf(func_def_8, type, powerset: ($i > $i)).
% 0.22/0.30 thf(func_def_9, type, powersetAx: $o).
% 0.22/0.30 thf(func_def_10, type, setunion: ($i > $i)).
% 0.22/0.30 thf(func_def_11, type, setunionAx: $o).
% 0.22/0.30 thf(func_def_13, type, omega0Ax: $o).
% 0.22/0.30 thf(func_def_14, type, omegaSAx: $o).
% 0.22/0.30 thf(func_def_15, type, omegaIndAx: $o).
% 0.22/0.30 thf(func_def_16, type, replAx: $o).
% 0.22/0.30 thf(func_def_17, type, foundationAx: $o).
% 0.22/0.30 thf(func_def_18, type, wellorderingAx: $o).
% 0.22/0.30 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 0.22/0.30 thf(func_def_20, type, descrp: $o).
% 0.22/0.30 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.22/0.30 thf(func_def_22, type, dsetconstrI: $o).
% 0.22/0.30 thf(func_def_23, type, dsetconstrEL: $o).
% 0.22/0.30 thf(func_def_24, type, dsetconstrER: $o).
% 0.22/0.30 thf(func_def_25, type, exuE1: $o).
% 0.22/0.30 thf(func_def_26, type, prop2set: ($o > $i)).
% 0.22/0.30 thf(func_def_27, type, prop2setE: $o).
% 0.22/0.30 thf(func_def_28, type, emptysetE: $o).
% 0.22/0.30 thf(func_def_29, type, emptysetimpfalse: $o).
% 0.22/0.30 thf(func_def_30, type, notinemptyset: $o).
% 0.22/0.30 thf(func_def_31, type, exuE3e: $o).
% 0.22/0.30 thf(func_def_32, type, setext: $o).
% 0.22/0.30 thf(func_def_33, type, emptyI: $o).
% 0.22/0.30 thf(func_def_34, type, noeltsimpempty: $o).
% 0.22/0.30 thf(func_def_35, type, setbeta: $o).
% 0.22/0.30 thf(func_def_36, type, nonempty: ($i > $o)).
% 0.22/0.30 thf(func_def_37, type, nonemptyE1: $o).
% 0.22/0.30 thf(func_def_38, type, nonemptyI: $o).
% 0.22/0.30 thf(func_def_39, type, nonemptyI1: $o).
% 0.22/0.30 thf(func_def_40, type, setadjoinIL: $o).
% 0.22/0.30 thf(func_def_41, type, emptyinunitempty: $o).
% 0.22/0.30 thf(func_def_42, type, setadjoinIR: $o).
% 0.22/0.30 thf(func_def_43, type, setadjoinE: $o).
% 0.22/0.30 thf(func_def_44, type, setadjoinOr: $o).
% 0.22/0.30 thf(func_def_45, type, setoftrueEq: $o).
% 0.22/0.30 thf(func_def_46, type, powersetI: $o).
% 0.22/0.30 thf(func_def_47, type, emptyinPowerset: $o).
% 0.22/0.30 thf(func_def_48, type, emptyInPowerset: $o).
% 0.22/0.30 thf(func_def_49, type, powersetE: $o).
% 0.22/0.30 thf(func_def_50, type, setunionI: $o).
% 0.22/0.30 thf(func_def_51, type, setunionE: $o).
% 0.22/0.30 thf(func_def_52, type, subPowSU: $o).
% 0.22/0.30 thf(func_def_53, type, exuE2: $o).
% 0.22/0.30 thf(func_def_54, type, nonemptyImpWitness: $o).
% 0.22/0.30 thf(func_def_55, type, uniqinunit: $o).
% 0.22/0.30 thf(func_def_56, type, notinsingleton: $o).
% 0.22/0.30 thf(func_def_57, type, eqinunit: $o).
% 0.22/0.30 thf(func_def_58, type, singletonsswitch: $o).
% 0.22/0.30 thf(func_def_59, type, upairsetE: $o).
% 0.22/0.30 thf(func_def_60, type, upairsetIL: $o).
% 0.22/0.30 thf(func_def_61, type, upairsetIR: $o).
% 0.22/0.30 thf(func_def_62, type, emptyE1: $o).
% 0.22/0.30 thf(func_def_63, type, vacuousDall: $o).
% 0.22/0.30 thf(func_def_64, type, quantDeMorgan1: $o).
% 0.22/0.30 thf(func_def_65, type, quantDeMorgan2: $o).
% 0.22/0.30 thf(func_def_66, type, quantDeMorgan3: $o).
% 0.22/0.30 thf(func_def_67, type, quantDeMorgan4: $o).
% 0.22/0.30 thf(func_def_68, type, prop2setI: $o).
% 0.22/0.30 thf(func_def_69, type, set2prop: ($i > $o)).
% 0.22/0.30 thf(func_def_70, type, prop2set2propI: $o).
% 0.22/0.30 thf(func_def_71, type, notdexE: $o).
% 0.22/0.30 thf(func_def_72, type, notdallE: $o).
% 0.22/0.30 thf(func_def_73, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.30 thf(func_def_74, type, vAND: ($o > $o > $o)).
% 0.22/0.30 thf(func_def_75, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.30 thf(func_def_76, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.30 thf(func_def_77, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.30 thf(func_def_78, type, vIMP: ($o > $o > $o)).
% 0.22/0.30 thf(func_def_79, type, db2: !>[X0: $tType]:(X0)).
% 0.22/0.30 thf(func_def_80, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.30 thf(func_def_81, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.30 thf(func_def_82, type, vIFF: ($o > $o > $o)).
% 0.22/0.30 thf(func_def_83, type, vNOT: ($o > $o)).
% 0.22/0.30 thf(func_def_84, type, vOR: ($o > $o > $o)).
% 0.22/0.30 thf(func_def_85, type, db4: !>[X0: $tType]:(X0)).
% 0.22/0.30 thf(func_def_86, type, db3: !>[X0: $tType]:(X0)).
% 0.22/0.30 thf(func_def_89, type, sK0: ($i > $o)).
% 0.22/0.30 thf(func_def_91, type, sK2: ($i > $i)).
% 0.22/0.30 thf(func_def_92, type, sK3: (($i > $o) > $i > $i)).
% 0.22/0.30 thf(func_def_93, type, sK4: (($i > $o) > $i > $i)).
% 0.22/0.30 thf(func_def_94, type, sK5: (($i > $o) > $i > $i)).
% 0.22/0.30 thf(func_def_95, type, sK6: (($i > $o) > $i > $i)).
% 0.22/0.30 thf(func_def_96, type, sK7: (($i > $o) > $i > $i)).
% 0.22/0.30 thf(func_def_97, type, sK8: (($i > $o) > $i > $i)).
% 0.22/0.30 thf(func_def_98, type, sK9: ($i > $i)).
% 0.22/0.30 thf(func_def_99, type, sK10: (($i > $o) > $i)).
% 0.22/0.30 thf(func_def_100, type, sK11: (($i > $o) > $i > $i)).
% 0.22/0.30 thf(func_def_101, type, sK12: ($o > $i > $i > $i)).
% 0.22/0.30 thf(func_def_102, type, sK13: ($i > $i > $i)).
% 0.22/0.30 thf(func_def_103, type, sK14: ($i > $i)).
% 0.22/0.30 thf(func_def_104, type, sK15: ($i > $i)).
% 0.22/0.30 thf(func_def_105, type, sK16: ($i > $i)).
% 0.22/0.30 thf(func_def_106, type, sK17: ($i > $i > $i)).
% 0.22/0.30 thf(func_def_107, type, sK18: ($i > $i > $i)).
% 0.22/0.30 thf(func_def_108, type, sK19: (($i > $o) > $i)).
% 0.22/0.30 thf(func_def_109, type, sK20: (($i > $o) > $i > $i)).
% 0.22/0.30 thf(func_def_110, type, sK21: (($i > $o) > $i)).
% 0.22/0.30 thf(func_def_111, type, sK22: (($i > $o) > $i > $i)).
% 0.22/0.30 thf(func_def_112, type, sK23: (($i > $o) > $i > $i)).
% 0.22/0.30 thf(func_def_113, type, sK24: ($i > $i)).
% 0.22/0.30 thf(func_def_114, type, sK25: ($i > $i > $i > $i)).
% 0.22/0.30 thf(func_def_115, type, sK26: ($i > $i > $i)).
% 0.22/0.30 thf(func_def_116, type, sK27: ($i > $i > $i)).
% 0.22/0.30 thf(func_def_117, type, sK28: ($i > $i > $i)).
% 0.22/0.30 thf(func_def_118, type, sK29: ($i > $i)).
% 0.22/0.30 thf(func_def_119, type, sK30: ($i > ($i > $i > $o) > $i)).
% 0.22/0.30 thf(func_def_120, type, sK31: ($i > ($i > $i > $o) > $i)).
% 0.22/0.30 thf(func_def_121, type, sK32: ($i > $i > ($i > $i > $o) > $i)).
% 0.22/0.30 thf(func_def_122, type, sK33: ($i > $i > ($i > $i > $o) > $i)).
% 0.22/0.30 thf(func_def_123, type, sK34: ($i > $i > ($i > $i > $o) > $i)).
% 0.22/0.30 thf(func_def_124, type, sK35: ($i > $i > ($i > $i > $o) > $i)).
% 0.22/0.30 thf(func_def_125, type, sK36: ($i > $i)).
% 0.22/0.30 thf(func_def_126, type, sK37: ($i > $i > $i)).
% 0.22/0.30 thf(func_def_127, type, sK38: ($i > $i > $i)).
% 0.22/0.30 thf(func_def_128, type, sK39: ($i > $i > $i)).
% 0.22/0.30 thf(f1,axiom,(
% 0.22/0.30 (exu = (^[X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 0.22/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu)).
% 0.22/0.30 thf(f63,conjecture,(
% 0.22/0.30 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => ! [X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)) => (exu @ (^[X1 : $i] : ((X0 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.22/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI1)).
% 0.22/0.30 thf(f64,negated_conjecture,(
% 0.22/0.30 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => ! [X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)) => (exu @ (^[X1 : $i] : ((X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.22/0.30 inference(negated_conjecture,[status(cth)],[f63])).
% 0.22/0.30 thf(f65,plain,(
% 0.22/0.30 (exu = (^[X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 0.22/0.30 inference(rectify,[],[f1])).
% 0.22/0.30 thf(f66,plain,(
% 0.22/0.30 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 0.22/0.30 inference(fool_elimination,[],[f65])).
% 0.22/0.30 thf(f184,plain,(
% 0.22/0.30 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => ! [X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)) => (exu @ (^[X3 : $i] : ((X0 @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.22/0.30 inference(rectify,[],[f64])).
% 0.22/0.30 thf(f185,plain,(
% 0.22/0.30 ~((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) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ! [X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((((X0 @ X2)) = $true) => (X1 = X2)) & (((X0 @ X1)) = $true)) => ($true = ((exu @ (^[Y0 : $i]: (X0 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.22/0.30 inference(fool_elimination,[],[f184])).
% 0.22/0.30 thf(f186,plain,(
% 0.22/0.30 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : ($i > $o)] : (($true != ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) & ? [X1 : $i] : (! [X2 : $i] : ((X1 = X2) | (((X0 @ X2)) != $true)) & (((X0 @ X1)) = $true))) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (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 = $true)),
% 0.22/0.30 inference(ennf_transformation,[],[f185])).
% 0.22/0.30 thf(f187,plain,(
% 0.22/0.30 ? [X0 : ($i > $o)] : (($true != ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) & ? [X1 : $i] : (! [X2 : $i] : ((X1 = X2) | (((X0 @ X2)) != $true)) & (((X0 @ X1)) = $true))) & (notdallE = $true) & (notdexE = $true) & (prop2set2propI = $true) & (prop2setI = $true) & (quantDeMorgan4 = $true) & (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 = $true)),
% 0.22/0.30 inference(flattening,[],[f186])).
% 0.22/0.30 thf(f188,plain,(
% 0.22/0.30 (($true != ((exu @ (^[Y0 : $i]: (sK0 @ Y0))))) & (! [X2 : $i] : ((sK1 = X2) | ($true != ((sK0 @ X2)))) & ($true = ((sK0 @ sK1))))) & (notdallE = $true) & (notdexE = $true) & (prop2set2propI = $true) & (prop2setI = $true) & (quantDeMorgan4 = $true) & (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)),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f187])).
% 0.22/0.30 thf(f189,plain,(
% 0.22/0.30 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 0.22/0.30 inference(cnf_transformation,[],[f66])).
% 0.22/0.30 thf(f311,plain,(
% 0.22/0.30 ($true = ((sK0 @ sK1)))),
% 0.22/0.30 inference(cnf_transformation,[],[f188])).
% 0.22/0.30 thf(f312,plain,(
% 0.22/0.30 ( ! [X2 : $i] : (($true != ((sK0 @ X2))) | (sK1 = X2)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f188])).
% 0.22/0.30 thf(f313,plain,(
% 0.22/0.30 ($true != ((exu @ (^[Y0 : $i]: (sK0 @ Y0)))))),
% 0.22/0.30 inference(cnf_transformation,[],[f188])).
% 0.22/0.30 thf(f315,definition,(
% 0.22/0.30 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.22/0.30 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.22/0.30 thf(f376,plain,(
% 0.22/0.30 ($true != (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))) @ (^[Y0 : $i]: (sK0 @ Y0)))))),
% 0.22/0.30 inference(definition_unfolding,[],[f313,f189])).
% 0.22/0.30 thf(f377,plain,(
% 0.22/0.30 ($true != ((?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))))))),
% 0.22/0.30 inference(beta-eta_normalization,[],[f376])).
% 0.22/0.30 thf(f378,plain,(
% 0.22/0.30 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))) @ X1)))) )),
% 0.22/0.30 inference(pi_proxy_clausification,[],[f377])).
% 0.22/0.30 thf(f379,plain,(
% 0.22/0.30 ( ! [X1 : $i] : (($false = (((sK0 @ X1) & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X1 = Y0)))))))) )),
% 0.22/0.30 inference(beta-eta_normalization,[],[f378])).
% 0.22/0.30 thf(f380,plain,(
% 0.22/0.30 ( ! [X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X1 = Y0)))))) | ($false = ((sK0 @ X1)))) )),
% 0.22/0.30 inference(and_proxy_clausification,[],[f379])).
% 0.22/0.30 thf(f381,plain,(
% 0.22/0.30 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((sK0 @ Y0) => (X1 = Y0))) @ (sK2 @ X1)))) | ($false = ((sK0 @ X1)))) )),
% 0.22/0.30 inference(sigma_proxy_clausification,[],[f380])).
% 0.22/0.30 thf(f382,plain,(
% 0.22/0.30 ( ! [X1 : $i] : (($false = (((sK0 @ (sK2 @ X1)) => (X1 = (sK2 @ X1))))) | ($false = ((sK0 @ X1)))) )),
% 0.22/0.30 inference(beta-eta_normalization,[],[f381])).
% 0.22/0.30 thf(f383,plain,(
% 0.22/0.30 ( ! [X1 : $i] : (($false = ((X1 = (sK2 @ X1)))) | ($false = ((sK0 @ X1)))) )),
% 0.22/0.30 inference(imp_proxy_clausification,[],[f382])).
% 0.22/0.30 thf(f384,plain,(
% 0.22/0.30 ( ! [X1 : $i] : (($true = ((sK0 @ (sK2 @ X1)))) | ($false = ((sK0 @ X1)))) )),
% 0.22/0.30 inference(imp_proxy_clausification,[],[f382])).
% 0.22/0.30 thf(f385,plain,(
% 0.22/0.30 ( ! [X1 : $i] : ((((sK2 @ X1)) != X1) | ($false = ((sK0 @ X1)))) )),
% 0.22/0.30 inference(equality_proxy_clausification,[],[f383])).
% 0.22/0.30 thf(f1033,definition,(
% 0.22/0.30 spl40_1 <=> ! [X3 : $o] : (($false = X3) | ($true = X3))),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl40_1])],[avatar_definition])).
% 0.22/0.30 thf(f1034,plain,(
% 0.22/0.30 ( ! [X3 : $o] : (($true = X3) | ($false = X3)) ) | ~spl40_1),
% 0.22/0.30 inference(avatar_component_clause,[],[f1033])).
% 0.22/0.30 thf(f1051,plain,(
% 0.22/0.30 spl40_1),
% 0.22/0.30 inference(avatar_split_clause,[],[f315,f1033])).
% 0.22/0.30 thf(f1058,plain,(
% 0.22/0.30 ( ! [X0 : $i] : (($true != $true) | (sK1 = X0) | ($false = ((sK0 @ X0)))) ) | ~spl40_1),
% 0.22/0.30 inference(constrained_superposition,[],[f312,f1034])).
% 0.22/0.30 thf(f1059,plain,(
% 0.22/0.30 ( ! [X0 : $i] : ((sK1 = X0) | ($false = ((sK0 @ X0)))) ) | ~spl40_1),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f1058])).
% 0.22/0.30 thf(f1091,plain,(
% 0.22/0.30 ( ! [X0 : $i] : (($true != $true) | (sK1 = ((sK2 @ X0))) | ($false = ((sK0 @ X0)))) )),
% 0.22/0.30 inference(constrained_superposition,[],[f312,f384])).
% 0.22/0.30 thf(f1092,plain,(
% 0.22/0.30 ( ! [X0 : $i] : ((sK1 = ((sK2 @ X0))) | ($false = ((sK0 @ X0)))) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f1091])).
% 0.22/0.30 thf(f1152,plain,(
% 0.22/0.30 ( ! [X0 : $i] : ((sK1 != X0) | ($false = ((sK0 @ X0))) | ($false = ((sK0 @ X0)))) )),
% 0.22/0.30 inference(constrained_superposition,[],[f385,f1092])).
% 0.22/0.30 thf(f1158,plain,(
% 0.22/0.30 ( ! [X0 : $i] : ((sK1 != X0) | ($false = ((sK0 @ X0)))) )),
% 0.22/0.30 inference(duplicate_literal_removal,[],[f1152])).
% 0.22/0.30 thf(f1163,plain,(
% 0.22/0.30 ( ! [X0 : $i] : (($false = ((sK0 @ X0)))) ) | ~spl40_1),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f1158,f1059])).
% 0.22/0.30 thf(f1166,plain,(
% 0.22/0.30 ($false = $true) | ~spl40_1),
% 0.22/0.30 inference(constrained_superposition,[],[f1163,f311])).
% 0.22/0.30 thf(f1177,plain,(
% 0.22/0.30 $false | ~spl40_1),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f1166])).
% 0.22/0.30 thf(f1178,plain,(
% 0.22/0.30 ~spl40_1),
% 0.22/0.30 inference(avatar_contradiction_clause,[],[f1177])).
% 0.22/0.30 cnf(s5, plain, spl40_1, inference(sat_conversion,[],[f1051])).
% 0.22/0.30 cnf(s7, plain, ~spl40_1, inference(sat_conversion,[],[f1178])).
% 0.22/0.30 cnf(s8, plain, $false, inference(rat,[],[s5,s7])).
% 0.22/0.30 thf(f1181,plain,(
% 0.22/0.30 $false),
% 0.22/0.30 inference(avatar_sat_refutation,[],[s8])).
% 0.22/0.30 % SZS output end Proof for theBenchmark
% 0.22/0.30 % (3389118)------------------------------
% 0.22/0.30 % (3389118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (3389118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (3389118)CaDiCaL version: 2.1.3
% 0.22/0.30 % (3389118)Termination reason: Refutation
% 0.22/0.30 % (3389118)Time elapsed: 0.017 s
% 0.22/0.30 % (3389118)Peak memory usage: 13 MB
% 0.22/0.30 % (3389118)Instructions burned: 64 (million)
% 0.22/0.30 % (3389097)Success in time 0.052 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------