%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU530^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:29:56 AM UTC 2026
% Result : Theorem 0.12s 0.28s
% Output : Refutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU530^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.17 % Computer : n003.cluster.edu
% 0.12/0.17 % Model : x86_64 x86_64
% 0.12/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.17 % Memory : 8046.5625MB
% 0.12/0.17 % OS : Linux 6.8.0-71-generic
% 0.12/0.17 % CPULimit : 300
% 0.12/0.17 % WCLimit : 300
% 0.12/0.17 % DateTime : Tue Sep 29 13:50:14 UTC 2026
% 0.12/0.17 % CPUTime :
% 0.12/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.21 Running higher-order theorem proving
% 0.12/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.28 % (2529135)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.12/0.28 % (2529150)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=4272504239:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.12/0.28 % (2529154)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.12/0.28 % (2529154)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.12/0.28 % (2529147)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2018916735:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.12/0.28 % (2529149)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=750606098:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.12/0.28 % (2529152)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2033732620:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.12/0.28 % (2529151)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1870716040:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.12/0.28 % (2529154)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=894013276:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.12/0.28 % (2529149)Instruction limit reached!
% 0.12/0.28 % (2529149)------------------------------
% 0.12/0.28 % (2529149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.28 % (2529149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.28 % (2529149)CaDiCaL version: 2.1.3
% 0.12/0.28 % (2529149)Termination reason: Instruction limit
% 0.12/0.28 % (2529149)Termination phase: shuffling
% 0.12/0.28 % (2529149)Time elapsed: 0.002 s
% 0.12/0.28 % (2529149)Peak memory usage: 9 MB
% 0.12/0.28 % (2529149)Instructions burned: 3 (million)
% 0.12/0.28 % (2529148)lrs+10_16_si=on:nwc=1.5:random_seed=1738244948:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.12/0.28 % (2529150) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2529135-2529150"...
% 0.12/0.28 % (2529150)...printing done.
% 0.12/0.28 % (2529151)Instruction limit reached!
% 0.12/0.28 % (2529151)------------------------------
% 0.12/0.28 % (2529151)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.28 % (2529151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.28 % (2529150)Refutation found. Thanks to Tanya!
% 0.12/0.28 % SZS status Theorem for theBenchmark
% 0.12/0.28 % SZS output start Proof for theBenchmark
% 0.12/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.12/0.28 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.12/0.28 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 0.12/0.28 thf(func_def_3, type, setextAx: $o).
% 0.12/0.28 thf(func_def_5, type, emptysetAx: $o).
% 0.12/0.28 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 0.12/0.28 thf(func_def_7, type, setadjoinAx: $o).
% 0.12/0.28 thf(func_def_8, type, powerset: ($i > $i)).
% 0.12/0.28 thf(func_def_9, type, powersetAx: $o).
% 0.12/0.28 thf(func_def_10, type, setunion: ($i > $i)).
% 0.12/0.28 thf(func_def_11, type, setunionAx: $o).
% 0.12/0.28 thf(func_def_13, type, omega0Ax: $o).
% 0.12/0.28 thf(func_def_14, type, omegaSAx: $o).
% 0.12/0.28 thf(func_def_15, type, omegaIndAx: $o).
% 0.12/0.28 thf(func_def_16, type, replAx: $o).
% 0.12/0.28 thf(func_def_17, type, foundationAx: $o).
% 0.12/0.28 thf(func_def_18, type, wellorderingAx: $o).
% 0.12/0.28 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 0.12/0.28 thf(func_def_20, type, descrp: $o).
% 0.12/0.28 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.12/0.28 thf(func_def_22, type, dsetconstrI: $o).
% 0.12/0.28 thf(func_def_23, type, dsetconstrEL: $o).
% 0.12/0.28 thf(func_def_24, type, dsetconstrER: $o).
% 0.12/0.28 thf(func_def_25, type, exuE1: $o).
% 0.12/0.28 thf(func_def_26, type, prop2set: ($o > $i)).
% 0.12/0.28 thf(func_def_27, type, prop2setE: $o).
% 0.12/0.28 thf(func_def_28, type, emptysetE: $o).
% 0.12/0.28 thf(func_def_29, type, emptysetimpfalse: $o).
% 0.12/0.28 thf(func_def_30, type, notinemptyset: $o).
% 0.12/0.28 thf(func_def_31, type, exuE3e: $o).
% 0.12/0.28 thf(func_def_32, type, setext: $o).
% 0.12/0.28 thf(func_def_33, type, emptyI: $o).
% 0.12/0.28 thf(func_def_34, type, noeltsimpempty: $o).
% 0.12/0.28 thf(func_def_35, type, setbeta: $o).
% 0.12/0.28 thf(func_def_36, type, nonempty: ($i > $o)).
% 0.12/0.28 thf(func_def_37, type, nonemptyE1: $o).
% 0.12/0.28 thf(func_def_38, type, nonemptyI: $o).
% 0.12/0.28 thf(func_def_39, type, nonemptyI1: $o).
% 0.12/0.28 thf(func_def_40, type, setadjoinIL: $o).
% 0.12/0.28 thf(func_def_41, type, emptyinunitempty: $o).
% 0.12/0.28 thf(func_def_42, type, setadjoinIR: $o).
% 0.12/0.28 thf(func_def_43, type, setadjoinE: $o).
% 0.12/0.28 thf(func_def_44, type, setadjoinOr: $o).
% 0.12/0.28 thf(func_def_45, type, setoftrueEq: $o).
% 0.12/0.28 thf(func_def_46, type, powersetI: $o).
% 0.12/0.28 thf(func_def_47, type, emptyinPowerset: $o).
% 0.12/0.28 thf(func_def_48, type, emptyInPowerset: $o).
% 0.12/0.28 thf(func_def_49, type, powersetE: $o).
% 0.12/0.28 thf(func_def_50, type, setunionI: $o).
% 0.12/0.28 thf(func_def_51, type, setunionE: $o).
% 0.12/0.28 thf(func_def_52, type, subPowSU: $o).
% 0.12/0.28 thf(func_def_53, type, exuE2: $o).
% 0.12/0.28 thf(func_def_54, type, nonemptyImpWitness: $o).
% 0.12/0.28 thf(func_def_55, type, uniqinunit: $o).
% 0.12/0.28 thf(func_def_56, type, notinsingleton: $o).
% 0.12/0.28 thf(func_def_57, type, eqinunit: $o).
% 0.12/0.28 thf(func_def_60, type, db0: !>[X0: $tType]:(X0)).
% 0.12/0.28 thf(func_def_61, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.12/0.28 thf(func_def_62, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.12/0.28 thf(func_def_63, type, vAND: ($o > $o > $o)).
% 0.12/0.28 thf(func_def_64, type, db1: !>[X0: $tType]:(X0)).
% 0.12/0.28 thf(func_def_65, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.12/0.28 thf(func_def_66, type, vIMP: ($o > $o > $o)).
% 0.12/0.28 thf(func_def_67, type, db2: !>[X0: $tType]:(X0)).
% 0.12/0.28 thf(func_def_68, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.12/0.28 thf(func_def_69, type, vNOT: ($o > $o)).
% 0.12/0.28 thf(func_def_70, type, sP0: ($i > $i > $o)).
% 0.12/0.28 thf(func_def_71, type, sP1: ($i > $o)).
% 0.12/0.28 thf(func_def_72, type, sP2: $o).
% 0.12/0.28 thf(func_def_73, type, sK3: ($i > $i)).
% 0.12/0.28 thf(func_def_76, type, sK6: ($i > $i)).
% 0.12/0.28 thf(func_def_77, type, sK7: ($i > $o)).
% 0.12/0.28 thf(func_def_85, type, sK15: ($i > $i > $i)).
% 0.12/0.28 thf(func_def_88, type, sK18: (($i > $o) > $i)).
% 0.12/0.28 thf(func_def_89, type, sK19: ($i > $o)).
% 0.12/0.28 thf(func_def_91, type, sK21: ($i > $i)).
% 0.12/0.28 thf(func_def_93, type, sK23: ($i > $i)).
% 0.12/0.28 thf(func_def_94, type, sK24: ($o > $i > $i > $i)).
% 0.12/0.28 thf(func_def_97, type, sK27: $o).
% 0.12/0.28 thf(func_def_99, type, sK29: (($i > $o) > $i)).
% 0.12/0.28 thf(func_def_100, type, sK30: ($i > $o)).
% 0.12/0.28 thf(func_def_101, type, sK31: ($i > $i)).
% 0.12/0.28 thf(func_def_105, type, sK35: ($i > $o)).
% 0.12/0.28 thf(func_def_106, type, sK36: ($i > $i > $i)).
% 0.12/0.28 thf(func_def_107, type, sK37: ($i > $i > $i)).
% 0.12/0.28 thf(func_def_117, type, sK47: ($i > $o)).
% 0.12/0.28 thf(func_def_121, type, sK51: $o).
% 0.12/0.28 thf(func_def_124, type, sK54: ($i > $i)).
% 0.12/0.28 thf(func_def_127, type, sK57: ($i > $i > $i)).
% 0.12/0.28 thf(func_def_128, type, sK58: ($i > $o)).
% 0.12/0.28 thf(func_def_132, type, sK62: $o).
% 0.12/0.28 thf(func_def_133, type, sK63: ($i > $i)).
% 0.12/0.28 thf(func_def_140, type, sK70: ($i > $i > $i)).
% 0.12/0.28 thf(func_def_141, type, sK71: ($i > $i > $i)).
% 0.12/0.28 thf(func_def_149, type, sK79: ($i > $o)).
% 0.12/0.28 thf(func_def_158, type, sK88: $o).
% 0.12/0.28 thf(func_def_169, type, sK99: ($i > $i)).
% 0.12/0.28 thf(func_def_170, type, sK100: ($i > $i)).
% 0.12/0.28 thf(func_def_171, type, sK101: ($i > $i)).
% 0.12/0.28 thf(func_def_172, type, sK102: ($i > $i)).
% 0.12/0.28 thf(func_def_173, type, sK103: ($i > $i)).
% 0.12/0.28 thf(func_def_174, type, sK104: ($i > $i > $i > $i)).
% 0.12/0.28 thf(func_def_175, type, sK105: ($i > $i)).
% 0.12/0.28 thf(func_def_176, type, sK106: ($i > $i)).
% 0.12/0.28 thf(func_def_177, type, sK107: ($i > $i)).
% 0.12/0.28 thf(func_def_178, type, sK108: ($i > $i)).
% 0.12/0.28 thf(func_def_179, type, sK109: ($i > $i > $i)).
% 0.12/0.28 thf(func_def_180, type, sK110: ($i > $i > $i > $i)).
% 0.12/0.28 thf(func_def_181, type, sK111: ($i > $i > $i > $i)).
% 0.12/0.28 thf(func_def_182, type, sK112: ($i > $i > $i > $i)).
% 0.12/0.28 thf(func_def_183, type, sK113: ($i > $i > $i)).
% 0.12/0.28 thf(func_def_184, type, sK114: ($i > $i > $i)).
% 0.12/0.28 thf(func_def_185, type, sK115: ($i > $i > $i)).
% 0.12/0.28 thf(func_def_186, type, sK116: ($i > $i > $i)).
% 0.12/0.28 thf(func_def_187, type, sK117: (($i > $i > $o) > $i > $i)).
% 0.12/0.28 thf(func_def_188, type, sK118: (($i > $i > $o) > $i > $i)).
% 0.12/0.28 thf(func_def_189, type, sK119: ($i > ($i > $i > $o) > $i > $i)).
% 0.12/0.28 thf(func_def_191, type, sK121: ($i > $i > $o)).
% 0.12/0.28 thf(func_def_192, type, sK122: ($i > $i)).
% 0.12/0.28 thf(func_def_193, type, sK123: ($i > $i)).
% 0.12/0.28 thf(func_def_195, type, sK125: (($i > $o) > $i)).
% 0.12/0.28 thf(func_def_196, type, sK126: ($i > $o)).
% 0.12/0.28 thf(func_def_197, type, sK127: ($i > $i)).
% 0.12/0.28 thf(func_def_198, type, sK128: ($i > $i)).
% 0.12/0.28 thf(func_def_203, type, sK133: ($i > $o)).
% 0.12/0.28 thf(f47,axiom,(
% 0.12/0.28 (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 0.12/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit)).
% 0.12/0.28 thf(f50,conjecture,(
% 0.12/0.28 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 => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (in @ X1 @ (setadjoin @ X0 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.12/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsswitch)).
% 0.12/0.28 thf(f51,negated_conjecture,(
% 0.12/0.28 ~(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 => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (in @ X1 @ (setadjoin @ X0 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.12/0.28 inference(negated_conjecture,[status(cth)],[f50])).
% 0.12/0.28 thf(f122,plain,(
% 0.12/0.28 ~(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 => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (in @ X1 @ (setadjoin @ X0 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.12/0.28 inference(rectify,[],[f51])).
% 0.12/0.28 thf(f123,plain,(
% 0.12/0.28 ~((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) => ! [X1 : $i,X0 : $i] : ((((in @ X0 @ (setadjoin @ X1 @ emptyset))) = $true) => (((in @ X1 @ (setadjoin @ X0 @ emptyset))) = $true))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.12/0.28 inference(fool_elimination,[],[f122])).
% 0.12/0.28 thf(f141,plain,(
% 0.12/0.28 (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 0.12/0.28 inference(rectify,[],[f47])).
% 0.12/0.28 thf(f142,plain,(
% 0.12/0.28 ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (setadjoin @ X1 @ emptyset))) = $true) => (X0 = X1)) <=> (uniqinunit = $true)),
% 0.12/0.28 inference(fool_elimination,[],[f141])).
% 0.12/0.28 thf(f182,plain,(
% 0.12/0.28 (((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : ((((in @ X1 @ (setadjoin @ X0 @ emptyset))) != $true) & (((in @ X0 @ (setadjoin @ X1 @ emptyset))) = $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)),
% 0.12/0.28 inference(ennf_transformation,[],[f123])).
% 0.12/0.28 thf(f183,plain,(
% 0.12/0.28 (exuE3e = $true) & (omega0Ax = $true) & (powersetE = $true) & (setadjoinOr = $true) & (emptyInPowerset = $true) & (replAx = $true) & (omegaIndAx = $true) & (exuE1 = $true) & (descrp = $true) & (dsetconstrEL = $true) & (setadjoinAx = $true) & (noeltsimpempty = $true) & (setadjoinIL = $true) & (dsetconstrI = $true) & (setbeta = $true) & (setunionE = $true) & (foundationAx = $true) & (nonemptyI1 = $true) & (nonemptyImpWitness = $true) & (emptysetE = $true) & (powersetAx = $true) & (emptyinPowerset = $true) & (omegaSAx = $true) & (setadjoinE = $true) & (exuE2 = $true) & (subPowSU = $true) & (emptyI = $true) & (uniqinunit = $true) & (nonemptyE1 = $true) & (setoftrueEq = $true) & (notinsingleton = $true) & (dsetconstrER = $true) & (setunionAx = $true) & (nonemptyI = $true) & (setadjoinIR = $true) & (wellorderingAx = $true) & (powersetI = $true) & (setunionI = $true) & (setext = $true) & (notinemptyset = $true) & ? [X0 : $i,X1 : $i] : ((((in @ X1 @ (setadjoin @ X0 @ emptyset))) != $true) & (((in @ X0 @ (setadjoin @ X1 @ emptyset))) = $true)) & (setextAx = $true) & (emptysetimpfalse = $true) & (emptyinunitempty = $true) & (eqinunit = $true) & (emptysetAx = $true) & (prop2setE = $true)),
% 0.12/0.29 inference(flattening,[],[f182])).
% 0.12/0.29 thf(f191,plain,(
% 0.12/0.29 (uniqinunit = $true) <=> ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (setadjoin @ X1 @ emptyset))) != $true) | (X0 = X1))),
% 0.12/0.29 inference(ennf_transformation,[],[f142])).
% 0.12/0.29 thf(f283,plain,(
% 0.12/0.29 ((uniqinunit = $true) | ? [X0 : $i,X1 : $i] : ((((in @ X0 @ (setadjoin @ X1 @ emptyset))) = $true) & (X0 != X1))) & (! [X0 : $i,X1 : $i] : ((((in @ X0 @ (setadjoin @ X1 @ emptyset))) != $true) | (X0 = X1)) | (uniqinunit != $true))),
% 0.12/0.29 inference(nnf_transformation,[],[f191])).
% 0.12/0.29 thf(f284,plain,(
% 0.12/0.29 ((uniqinunit = $true) | ? [X0 : $i,X1 : $i] : ((((in @ X0 @ (setadjoin @ X1 @ emptyset))) = $true) & (X0 != X1))) & (! [X2 : $i,X3 : $i] : (($true != ((in @ X2 @ (setadjoin @ X3 @ emptyset)))) | (X2 = X3)) | (uniqinunit != $true))),
% 0.12/0.29 inference(rectify,[],[f283])).
% 0.12/0.29 thf(f285,plain,(
% 0.12/0.29 ((uniqinunit = $true) | ((((in @ sK65 @ (setadjoin @ sK66 @ emptyset))) = $true) & (sK66 != sK65))) & (! [X2 : $i,X3 : $i] : (($true != ((in @ X2 @ (setadjoin @ X3 @ emptyset)))) | (X2 = X3)) | (uniqinunit != $true))),
% 0.12/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK65,sK66]),skolemize(X0,sK65),skolemize(X1,sK66)],[f284])).
% 0.12/0.29 thf(f298,plain,(
% 0.12/0.29 (exuE3e = $true) & (omega0Ax = $true) & (powersetE = $true) & (setadjoinOr = $true) & (emptyInPowerset = $true) & (replAx = $true) & (omegaIndAx = $true) & (exuE1 = $true) & (descrp = $true) & (dsetconstrEL = $true) & (setadjoinAx = $true) & (noeltsimpempty = $true) & (setadjoinIL = $true) & (dsetconstrI = $true) & (setbeta = $true) & (setunionE = $true) & (foundationAx = $true) & (nonemptyI1 = $true) & (nonemptyImpWitness = $true) & (emptysetE = $true) & (powersetAx = $true) & (emptyinPowerset = $true) & (omegaSAx = $true) & (setadjoinE = $true) & (exuE2 = $true) & (subPowSU = $true) & (emptyI = $true) & (uniqinunit = $true) & (nonemptyE1 = $true) & (setoftrueEq = $true) & (notinsingleton = $true) & (dsetconstrER = $true) & (setunionAx = $true) & (nonemptyI = $true) & (setadjoinIR = $true) & (wellorderingAx = $true) & (powersetI = $true) & (setunionI = $true) & (setext = $true) & (notinemptyset = $true) & (($true != ((in @ sK81 @ (setadjoin @ sK80 @ emptyset)))) & ($true = ((in @ sK80 @ (setadjoin @ sK81 @ emptyset))))) & (setextAx = $true) & (emptysetimpfalse = $true) & (emptyinunitempty = $true) & (eqinunit = $true) & (emptysetAx = $true) & (prop2setE = $true)),
% 0.12/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK80,sK81]),skolemize(X0,sK80),skolemize(X1,sK81)],[f183])).
% 0.12/0.29 thf(f449,plain,(
% 0.12/0.29 ( ! [X2 : $i,X3 : $i] : ((uniqinunit != $true) | (X2 = X3) | ($true != ((in @ X2 @ (setadjoin @ X3 @ emptyset))))) )),
% 0.12/0.29 inference(cnf_transformation,[],[f285])).
% 0.12/0.29 thf(f476,plain,(
% 0.12/0.29 ($true = ((in @ sK80 @ (setadjoin @ sK81 @ emptyset))))),
% 0.12/0.29 inference(cnf_transformation,[],[f298])).
% 0.12/0.29 thf(f477,plain,(
% 0.12/0.29 ($true != ((in @ sK81 @ (setadjoin @ sK80 @ emptyset))))),
% 0.12/0.29 inference(cnf_transformation,[],[f298])).
% 0.12/0.29 thf(f490,plain,(
% 0.12/0.29 (uniqinunit = $true)),
% 0.12/0.29 inference(cnf_transformation,[],[f298])).
% 0.12/0.29 thf(f932,definition,(
% 0.12/0.29 spl134_61 <=> (uniqinunit = $true)),
% 0.12/0.29 introduced(definition,[new_symbols(definition,[spl134_61])],[avatar_definition])).
% 0.12/0.29 thf(f1064,definition,(
% 0.12/0.29 spl134_91 <=> ! [X2 : $i,X3 : $i] : ((X2 = X3) | ($true != ((in @ X3 @ (setadjoin @ X2 @ emptyset)))))),
% 0.12/0.29 introduced(definition,[new_symbols(definition,[spl134_91])],[avatar_definition])).
% 0.12/0.29 thf(f1065,plain,(
% 0.12/0.29 ( ! [X2 : $i,X3 : $i] : (($true != ((in @ X3 @ (setadjoin @ X2 @ emptyset)))) | (X2 = X3)) ) | ~spl134_91),
% 0.12/0.29 inference(avatar_component_clause,[],[f1064])).
% 0.12/0.29 thf(f1090,definition,(
% 0.12/0.29 spl134_97 <=> ($true = ((in @ sK81 @ (setadjoin @ sK80 @ emptyset))))),
% 0.12/0.29 introduced(definition,[new_symbols(definition,[spl134_97])],[avatar_definition])).
% 0.12/0.29 thf(f1093,plain,(
% 0.12/0.29 ~spl134_97),
% 0.12/0.29 inference(avatar_split_clause,[],[f477,f1090])).
% 0.12/0.29 thf(f1475,plain,(
% 0.12/0.29 ~spl134_61 | spl134_91),
% 0.12/0.29 inference(avatar_split_clause,[],[f449,f1064,f932])).
% 0.12/0.29 thf(f1563,definition,(
% 0.12/0.29 spl134_197 <=> ($true = ((in @ sK80 @ (setadjoin @ sK81 @ emptyset))))),
% 0.12/0.29 introduced(definition,[new_symbols(definition,[spl134_197])],[avatar_definition])).
% 0.12/0.29 thf(f1565,plain,(
% 0.12/0.29 ($true = ((in @ sK80 @ (setadjoin @ sK81 @ emptyset)))) | ~spl134_197),
% 0.12/0.29 inference(avatar_component_clause,[],[f1563])).
% 0.12/0.29 thf(f1566,plain,(
% 0.12/0.29 spl134_197),
% 0.12/0.29 inference(avatar_split_clause,[],[f476,f1563])).
% 0.12/0.29 thf(f1743,plain,(
% 0.12/0.29 spl134_61),
% 0.12/0.29 inference(avatar_split_clause,[],[f490,f932])).
% 0.12/0.29 thf(f1864,plain,(
% 0.12/0.29 ($true != $true) | (sK80 = sK81) | (~spl134_91 | ~spl134_197)),
% 0.12/0.29 inference(superposition,[],[f1065,f1565])).
% 0.12/0.29 thf(f1870,plain,(
% 0.12/0.29 (sK80 = sK81) | (~spl134_91 | ~spl134_197)),
% 0.12/0.29 inference(trivial_inequality_removal,[],[f1864])).
% 0.12/0.29 thf(f1875,definition,(
% 0.12/0.29 spl134_242 <=> (sK80 = sK81)),
% 0.12/0.29 introduced(definition,[new_symbols(definition,[spl134_242])],[avatar_definition])).
% 0.12/0.29 thf(f1878,plain,(
% 0.12/0.29 spl134_242 | ~spl134_91 | ~spl134_197),
% 0.12/0.29 inference(avatar_split_clause,[],[f1870,f1563,f1064,f1875])).
% 0.12/0.29 thf(f1879,definition,(
% 0.12/0.29 (sK80 != sK81) | ($true != ((in @ sK80 @ (setadjoin @ sK81 @ emptyset)))) | ($true = ((in @ sK81 @ (setadjoin @ sK80 @ emptyset))))),
% 0.12/0.29 introduced(theory,[theory_tautology_sat_conflict])).
% 0.12/0.29 cnf(s69, plain, ~spl134_97, inference(sat_conversion,[],[f1093])).
% 0.12/0.29 cnf(s165, plain, ~spl134_61 | spl134_91, inference(sat_conversion,[],[f1475])).
% 0.12/0.29 cnf(s189, plain, spl134_197, inference(sat_conversion,[],[f1566])).
% 0.12/0.29 cnf(s237, plain, spl134_61, inference(sat_conversion,[],[f1743])).
% 0.12/0.29 cnf(s250, plain, ~spl134_91 | ~spl134_197 | spl134_242, inference(sat_conversion,[],[f1878])).
% 0.12/0.29 cnf(s251, plain, spl134_97 | ~spl134_197 | ~spl134_242, inference(sat_conversion,[],[f1879])).
% 0.12/0.29 cnf(s257, plain, spl134_91, inference(rat,[],[s165,s237])).
% 0.12/0.29 cnf(s258, plain, spl134_242, inference(rat,[],[s250,s189,s257])).
% 0.12/0.29 cnf(s259, plain, spl134_97, inference(rat,[],[s251,s189,s258])).
% 0.12/0.29 cnf(s286, plain, $false, inference(rat,[],[s69,s259])).
% 0.12/0.29 thf(f1880,plain,(
% 0.12/0.29 $false),
% 0.12/0.29 inference(avatar_sat_refutation,[],[s286])).
% 0.12/0.29 % SZS output end Proof for theBenchmark
% 0.12/0.29 % (2529150)------------------------------
% 0.12/0.29 % (2529150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.29 % (2529150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.29 % (2529150)CaDiCaL version: 2.1.3
% 0.12/0.29 % (2529150)Termination reason: Refutation
% 0.12/0.29 % (2529150)Time elapsed: 0.018 s
% 0.12/0.29 % (2529150)Peak memory usage: 14 MB
% 0.12/0.29 % (2529150)Instructions burned: 63 (million)
% 0.12/0.29 % (2529135)Success in time 0.049 s
% 0.12/0.29 % Vampire exiting
%------------------------------------------------------------------------------