%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU506^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:29:51 AM UTC 2026
% Result : Theorem 0.22s 0.32s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU506^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n008.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:47:39 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.32 % (3176868)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.32 % (3176878)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3960136927:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.32 % (3176879)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.32 % (3176879)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
% 0.22/0.32 % (3176874)lrs+10_16_si=on:nwc=1.5:random_seed=4043325292:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.32 % (3176876)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=2666345198: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)
% 0.22/0.32 % (3176875)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3269240484:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.32 % (3176873)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=552558950:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.32 % (3176877)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1036964761:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.32 % (3176879)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=3951241677:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.32 % (3176875)Instruction limit reached!
% 0.22/0.32 % (3176875)------------------------------
% 0.22/0.32 % (3176875)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (3176875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (3176875)CaDiCaL version: 2.1.3
% 0.22/0.32 % (3176875)Termination reason: Instruction limit
% 0.22/0.32 % (3176875)Termination phase: shuffling
% 0.22/0.32 % (3176875)Time elapsed: 0.001 s
% 0.22/0.32 % (3176875)Peak memory usage: 9 MB
% 0.22/0.32 % (3176875)Instructions burned: 3 (million)
% 0.22/0.32 % (3176874)Instruction limit reached!
% 0.22/0.32 % (3176874)------------------------------
% 0.22/0.32 % (3176874)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (3176874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (3176874)CaDiCaL version: 2.1.3
% 0.22/0.32 % (3176874)Termination reason: Instruction limit
% 0.22/0.32 % (3176874)Termination phase: Saturation
% 0.22/0.32 % (3176874)Time elapsed: 0.009 s
% 0.22/0.32 % (3176874)Peak memory usage: 11 MB
% 0.22/0.32 % (3176874)Instructions burned: 20 (million)
% 0.22/0.32 % (3176877)Instruction limit reached!
% 0.22/0.32 % (3176877)------------------------------
% 0.22/0.32 % (3176877)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (3176877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (3176877)CaDiCaL version: 2.1.3
% 0.22/0.32 % (3176877)Termination reason: Instruction limit
% 0.22/0.32 % (3176877)Termination phase: Saturation
% 0.22/0.32 % (3176877)Time elapsed: 0.012 s
% 0.22/0.32 % (3176877)Peak memory usage: 11 MB
% 0.22/0.32 % (3176877)Instructions burned: 25 (million)
% 0.22/0.32 % (3176878) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3176868-3176878"...
% 0.22/0.32 % (3176878)...printing done.
% 0.22/0.32 % (3176878)Refutation found. Thanks to Tanya!
% 0.22/0.32 % SZS status Theorem for theBenchmark
% 0.22/0.32 % SZS output start Proof for theBenchmark
% 0.22/0.32 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.32 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.22/0.32 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 0.22/0.32 thf(func_def_3, type, setextAx: $o).
% 0.22/0.32 thf(func_def_5, type, emptysetAx: $o).
% 0.22/0.32 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 0.22/0.32 thf(func_def_7, type, setadjoinAx: $o).
% 0.22/0.32 thf(func_def_8, type, powerset: ($i > $i)).
% 0.22/0.32 thf(func_def_9, type, powersetAx: $o).
% 0.22/0.32 thf(func_def_10, type, setunion: ($i > $i)).
% 0.22/0.32 thf(func_def_11, type, setunionAx: $o).
% 0.22/0.32 thf(func_def_13, type, omega0Ax: $o).
% 0.22/0.32 thf(func_def_14, type, omegaSAx: $o).
% 0.22/0.32 thf(func_def_15, type, omegaIndAx: $o).
% 0.22/0.32 thf(func_def_16, type, replAx: $o).
% 0.22/0.32 thf(func_def_17, type, foundationAx: $o).
% 0.22/0.32 thf(func_def_18, type, wellorderingAx: $o).
% 0.22/0.32 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 0.22/0.32 thf(func_def_20, type, descrp: $o).
% 0.22/0.32 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.22/0.32 thf(func_def_22, type, dsetconstrI: $o).
% 0.22/0.32 thf(func_def_23, type, dsetconstrEL: $o).
% 0.22/0.32 thf(func_def_24, type, dsetconstrER: $o).
% 0.22/0.32 thf(func_def_25, type, exuE1: $o).
% 0.22/0.32 thf(func_def_26, type, prop2set: ($o > $i)).
% 0.22/0.32 thf(func_def_27, type, prop2setE: $o).
% 0.22/0.32 thf(func_def_28, type, emptysetE: $o).
% 0.22/0.32 thf(func_def_29, type, emptysetimpfalse: $o).
% 0.22/0.32 thf(func_def_30, type, notinemptyset: $o).
% 0.22/0.32 thf(func_def_31, type, exuE3e: $o).
% 0.22/0.32 thf(func_def_32, type, setext: $o).
% 0.22/0.32 thf(func_def_35, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.32 thf(func_def_36, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.32 thf(func_def_37, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.32 thf(func_def_38, type, vAND: ($o > $o > $o)).
% 0.22/0.32 thf(func_def_39, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.32 thf(func_def_40, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.32 thf(func_def_41, type, vIMP: ($o > $o > $o)).
% 0.22/0.32 thf(func_def_42, type, db2: !>[X0: $tType]:(X0)).
% 0.22/0.32 thf(func_def_43, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.32 thf(func_def_44, type, sP0: $o).
% 0.22/0.32 thf(func_def_45, type, sP1: ($i > $i > $o)).
% 0.22/0.32 thf(func_def_46, type, sP2: ($i > $o)).
% 0.22/0.32 thf(func_def_47, type, sP3: ($i > $i > $o)).
% 0.22/0.32 thf(func_def_48, type, sP4: ($i > $i > $o)).
% 0.22/0.32 thf(func_def_52, type, sK8: ($i > $i > $i)).
% 0.22/0.32 thf(func_def_53, type, sK9: ($i > $i > $i)).
% 0.22/0.32 thf(func_def_58, type, sK14: ($i > $o)).
% 0.22/0.32 thf(func_def_59, type, sK15: (($i > $o) > $i)).
% 0.22/0.32 thf(func_def_60, type, sK16: ($i > $o)).
% 0.22/0.32 thf(func_def_61, type, sK17: ($i > $i)).
% 0.22/0.32 thf(func_def_65, type, sK21: $o).
% 0.22/0.32 thf(func_def_67, type, sK23: ($i > $o)).
% 0.22/0.32 thf(func_def_68, type, sK24: (($i > $o) > $i)).
% 0.22/0.32 thf(func_def_69, type, sK25: ($i > $i)).
% 0.22/0.32 thf(func_def_72, type, sK28: ($i > $i > $i)).
% 0.22/0.32 thf(func_def_76, type, sK32: ($i > $o)).
% 0.22/0.32 thf(func_def_79, type, sK35: ($i > $i)).
% 0.22/0.32 thf(func_def_81, type, sK37: ($i > $i)).
% 0.22/0.32 thf(func_def_84, type, sK40: ($i > $i > $o)).
% 0.22/0.32 thf(func_def_85, type, sK41: ($i > $i)).
% 0.22/0.32 thf(func_def_86, type, sK42: ($i > $i)).
% 0.22/0.32 thf(func_def_87, type, sK43: (($i > $i > $o) > $i > $i)).
% 0.22/0.32 thf(func_def_88, type, sK44: (($i > $i > $o) > $i > $i)).
% 0.22/0.32 thf(func_def_89, type, sK45: ($i > ($i > $i > $o) > $i > $i)).
% 0.22/0.32 thf(func_def_92, type, sK48: $o).
% 0.22/0.32 thf(func_def_96, type, sK52: ($i > $o)).
% 0.22/0.32 thf(func_def_100, type, sK56: ($i > $i > $i)).
% 0.22/0.32 thf(func_def_101, type, sK57: ($i > $i > $i)).
% 0.22/0.32 thf(func_def_102, type, sK58: ($i > $i > $i)).
% 0.22/0.32 thf(func_def_103, type, sK59: ($i > $i > $i)).
% 0.22/0.32 thf(func_def_104, type, sK60: ($i > $i > $i)).
% 0.22/0.32 thf(func_def_105, type, sK61: ($i > $i > $i > $i)).
% 0.22/0.32 thf(func_def_106, type, sK62: ($i > $i)).
% 0.22/0.32 thf(func_def_107, type, sK63: ($i > $i)).
% 0.22/0.32 thf(func_def_108, type, sK64: ($i > $i)).
% 0.22/0.32 thf(func_def_109, type, sK65: ($i > $i)).
% 0.22/0.32 thf(func_def_110, type, sK66: ($i > $i > $i > $i)).
% 0.22/0.32 thf(func_def_111, type, sK67: ($i > $i > $i > $i)).
% 0.22/0.32 thf(func_def_112, type, sK68: ($i > $i > $i)).
% 0.22/0.32 thf(func_def_113, type, sK69: ($i > $i > $i)).
% 0.22/0.32 thf(func_def_114, type, sK70: ($i > $i > $i)).
% 0.22/0.32 thf(func_def_116, type, sK72: ($i > $i)).
% 0.22/0.32 thf(func_def_117, type, sK73: ($i > $i)).
% 0.22/0.32 thf(func_def_118, type, sK74: ($i > $i)).
% 0.22/0.32 thf(func_def_119, type, sK75: ($i > $o)).
% 0.22/0.32 thf(func_def_122, type, sK78: ($i > $i > $i)).
% 0.22/0.32 thf(func_def_123, type, sK79: ($i > $i > $i)).
% 0.22/0.32 thf(func_def_124, type, vNOT: ($o > $o)).
% 0.22/0.32 thf(func_def_125, type, sK80: ($i > ($i > $i > $o) > $i > $i)).
% 0.22/0.32 thf(func_def_126, type, sK81: ($i > $i)).
% 0.22/0.32 thf(func_def_127, type, sK82: ($i > ($i > $i > $o) > $i > $i)).
% 0.22/0.32 thf(func_def_128, type, sK83: (($i > $o) > $i > $i)).
% 0.22/0.32 thf(func_def_129, type, sK84: ($i > ($i > $i > $o) > $i > $i)).
% 0.22/0.32 thf(func_def_130, type, sK85: ($i > ($i > $o) > $i)).
% 0.22/0.32 thf(func_def_131, type, sK86: ($i > ($i > $o) > $i)).
% 0.22/0.32 thf(func_def_132, type, sK87: ($i > ($i > $o) > $i)).
% 0.22/0.32 thf(f3,axiom,(
% 0.22/0.32 (! [X0 : $i] : ~(in @ X0 @ emptyset) = emptysetAx)),
% 0.22/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx)).
% 0.22/0.32 thf(f24,axiom,(
% 0.22/0.32 (setext = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (X0 = X1))))),
% 0.22/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext)).
% 0.22/0.32 thf(f25,conjecture,(
% 0.22/0.32 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)))))))))))))))))))))))),
% 0.22/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI)).
% 0.22/0.32 thf(f26,negated_conjecture,(
% 0.22/0.32 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset))))))))))))))))))))))))),
% 0.22/0.32 inference(negated_conjecture,[status(cth)],[f25])).
% 0.22/0.32 thf(f33,plain,(
% 0.22/0.32 (setext = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => (in @ X3 @ X1)) => (X0 = X1))))),
% 0.22/0.32 inference(rectify,[],[f24])).
% 0.22/0.32 thf(f34,plain,(
% 0.22/0.32 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => (! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => (((in @ X3 @ X1)) = $true)) => (X0 = X1))) <=> (setext = $true)),
% 0.22/0.32 inference(fool_elimination,[],[f33])).
% 0.22/0.32 thf(f47,plain,(
% 0.22/0.32 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset))))))))))))))))))))))))),
% 0.22/0.32 inference(rectify,[],[f26])).
% 0.22/0.32 thf(f48,plain,(
% 0.22/0.32 ~((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) => ! [X0 : $i] : (! [X1 : $i] : ~ (((in @ X1 @ X0)) = $true) => (emptyset = X0))))))))))))))))))))))))),
% 0.22/0.32 inference(fool_elimination,[],[f47])).
% 0.22/0.32 thf(f69,plain,(
% 0.22/0.32 (! [X0 : $i] : ~(in @ X0 @ emptyset) = emptysetAx)),
% 0.22/0.32 inference(rectify,[],[f3])).
% 0.22/0.32 thf(f70,plain,(
% 0.22/0.32 ! [X0 : $i] : ~ (((in @ X0 @ emptyset)) = $true) <=> (emptysetAx = $true)),
% 0.22/0.32 inference(fool_elimination,[],[f69])).
% 0.22/0.32 thf(f80,plain,(
% 0.22/0.32 ~((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) => ! [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0)) != $true) => (emptyset = X0))))))))))))))))))))))))),
% 0.22/0.32 inference(flattening,[],[f48])).
% 0.22/0.32 thf(f82,plain,(
% 0.22/0.32 ! [X0 : $i] : (((in @ X0 @ emptyset)) != $true) <=> (emptysetAx = $true)),
% 0.22/0.32 inference(flattening,[],[f70])).
% 0.22/0.32 thf(f85,plain,(
% 0.22/0.32 (((((((((((((((((((((? [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0)) != $true) & (emptyset != X0)) & (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)),
% 0.22/0.32 inference(ennf_transformation,[],[f80])).
% 0.22/0.32 thf(f86,plain,(
% 0.22/0.32 (exuE3e = $true) & (dsetconstrEL = $true) & (omegaIndAx = $true) & ? [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0)) != $true) & (emptyset != X0)) & (setadjoinAx = $true) & (dsetconstrER = $true) & (replAx = $true) & (prop2setE = $true) & (omegaSAx = $true) & (emptysetimpfalse = $true) & (descrp = $true) & (setunionAx = $true) & (emptysetE = $true) & (notinemptyset = $true) & (setext = $true) & (omega0Ax = $true) & (emptysetAx = $true) & (setextAx = $true) & (foundationAx = $true) & (exuE1 = $true) & (dsetconstrI = $true) & (wellorderingAx = $true) & (powersetAx = $true)),
% 0.22/0.32 inference(flattening,[],[f85])).
% 0.22/0.32 thf(f103,plain,(
% 0.22/0.32 ! [X1 : $i,X0 : $i] : (((X0 = X1) | ? [X3 : $i] : ((((in @ X3 @ X1)) != $true) & (((in @ X3 @ X0)) = $true))) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true))) <=> (setext = $true)),
% 0.22/0.32 inference(ennf_transformation,[],[f34])).
% 0.22/0.32 thf(f104,plain,(
% 0.22/0.32 (setext = $true) <=> ! [X0 : $i,X1 : $i] : (? [X3 : $i] : ((((in @ X3 @ X1)) != $true) & (((in @ X3 @ X0)) = $true)) | (X0 = X1) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true)))),
% 0.22/0.32 inference(flattening,[],[f103])).
% 0.22/0.32 thf(f150,plain,(
% 0.22/0.32 (exuE3e = $true) & (dsetconstrEL = $true) & (omegaIndAx = $true) & (! [X1 : $i] : (((in @ X1 @ sK46)) != $true) & (emptyset != sK46)) & (setadjoinAx = $true) & (dsetconstrER = $true) & (replAx = $true) & (prop2setE = $true) & (omegaSAx = $true) & (emptysetimpfalse = $true) & (descrp = $true) & (setunionAx = $true) & (emptysetE = $true) & (notinemptyset = $true) & (setext = $true) & (omega0Ax = $true) & (emptysetAx = $true) & (setextAx = $true) & (foundationAx = $true) & (exuE1 = $true) & (dsetconstrI = $true) & (wellorderingAx = $true) & (powersetAx = $true)),
% 0.22/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(X0,sK46)],[f86])).
% 0.22/0.32 thf(f157,plain,(
% 0.22/0.32 (! [X0 : $i] : (((in @ X0 @ emptyset)) != $true) | (emptysetAx != $true)) & ((emptysetAx = $true) | ? [X0 : $i] : (((in @ X0 @ emptyset)) = $true))),
% 0.22/0.32 inference(nnf_transformation,[],[f82])).
% 0.22/0.32 thf(f158,plain,(
% 0.22/0.32 (! [X0 : $i] : (((in @ X0 @ emptyset)) != $true) | (emptysetAx != $true)) & ((emptysetAx = $true) | ? [X1 : $i] : (((in @ X1 @ emptyset)) = $true))),
% 0.22/0.32 inference(rectify,[],[f157])).
% 0.22/0.32 thf(f159,plain,(
% 0.22/0.32 (! [X0 : $i] : (((in @ X0 @ emptyset)) != $true) | (emptysetAx != $true)) & ((emptysetAx = $true) | (((in @ sK50 @ emptyset)) = $true))),
% 0.22/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(X1,sK50)],[f158])).
% 0.22/0.32 thf(f187,plain,(
% 0.22/0.32 ((setext = $true) | ? [X0 : $i,X1 : $i] : (! [X3 : $i] : ((((in @ X3 @ X1)) = $true) | (((in @ X3 @ X0)) != $true)) & (X0 != X1) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)))) & (! [X0 : $i,X1 : $i] : (? [X3 : $i] : ((((in @ X3 @ X1)) != $true) & (((in @ X3 @ X0)) = $true)) | (X0 = X1) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true))) | (setext != $true))),
% 0.22/0.32 inference(nnf_transformation,[],[f104])).
% 0.22/0.32 thf(f188,plain,(
% 0.22/0.32 ((setext = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)) & (X0 != X1) & ! [X3 : $i] : ((((in @ X3 @ X1)) != $true) | (((in @ X3 @ X0)) = $true)))) & (! [X4 : $i,X5 : $i] : (? [X6 : $i] : ((((in @ X6 @ X5)) != $true) & (((in @ X6 @ X4)) = $true)) | (X4 = X5) | ? [X7 : $i] : (($true = ((in @ X7 @ X5))) & ($true != ((in @ X7 @ X4))))) | (setext != $true))),
% 0.22/0.32 inference(rectify,[],[f187])).
% 0.22/0.32 thf(f189,plain,(
% 0.22/0.32 ((setext = $true) | (! [X2 : $i] : (($true = ((in @ X2 @ sK77))) | (((in @ X2 @ sK76)) != $true)) & (sK76 != sK77) & ! [X3 : $i] : ((((in @ X3 @ sK77)) != $true) | (((in @ X3 @ sK76)) = $true)))) & (! [X4 : $i,X5 : $i] : (((((in @ (sK78 @ X5 @ X4) @ X5)) != $true) & (((in @ (sK78 @ X5 @ X4) @ X4)) = $true)) | (X4 = X5) | ((((in @ (sK79 @ X5 @ X4) @ X5)) = $true) & ($true != ((in @ (sK79 @ X5 @ X4) @ X4))))) | (setext != $true))),
% 0.22/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK76,sK77,vAPP,vAPP]),skolemize(X0,sK76),skolemize(X1,sK77),skolemize(X7,sK8 @ X5 @ X4),skolemize(X7,sK8 @ X5 @ X4)],[f188])).
% 0.22/0.32 thf(f261,plain,(
% 0.22/0.32 (emptysetAx = $true)),
% 0.22/0.32 inference(cnf_transformation,[],[f150])).
% 0.22/0.32 thf(f263,plain,(
% 0.22/0.32 (setext = $true)),
% 0.22/0.32 inference(cnf_transformation,[],[f150])).
% 0.22/0.32 thf(f274,plain,(
% 0.22/0.32 (emptyset != sK46)),
% 0.22/0.32 inference(cnf_transformation,[],[f150])).
% 0.22/0.32 thf(f275,plain,(
% 0.22/0.32 ( ! [X1 : $i] : ((((in @ X1 @ sK46)) != $true)) )),
% 0.22/0.32 inference(cnf_transformation,[],[f150])).
% 0.22/0.32 thf(f286,plain,(
% 0.22/0.32 ( ! [X0 : $i] : ((((in @ X0 @ emptyset)) != $true) | (emptysetAx != $true)) )),
% 0.22/0.32 inference(cnf_transformation,[],[f159])).
% 0.22/0.32 thf(f336,plain,(
% 0.22/0.32 ( ! [X4 : $i,X5 : $i] : ((((in @ (sK78 @ X5 @ X4) @ X4)) = $true) | (X4 = X5) | (((in @ (sK79 @ X5 @ X4) @ X5)) = $true) | (setext != $true)) )),
% 0.22/0.32 inference(cnf_transformation,[],[f189])).
% 0.22/0.32 thf(f407,plain,(
% 0.22/0.32 ( ! [X0 : $i] : ((((in @ X0 @ emptyset)) != $true) | ($true != $true)) )),
% 0.22/0.32 inference(definition_unfolding,[],[f286,f261])).
% 0.22/0.32 thf(f432,plain,(
% 0.22/0.32 ( ! [X4 : $i,X5 : $i] : ((X4 = X5) | ($true != $true) | (((in @ (sK79 @ X5 @ X4) @ X5)) = $true) | (((in @ (sK78 @ X5 @ X4) @ X4)) = $true)) )),
% 0.22/0.32 inference(definition_unfolding,[],[f336,f263])).
% 0.22/0.32 thf(f446,plain,(
% 0.22/0.32 ( ! [X0 : $i] : ((((in @ X0 @ emptyset)) != $true)) )),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f407])).
% 0.22/0.32 thf(f464,plain,(
% 0.22/0.32 ( ! [X4 : $i,X5 : $i] : ((((in @ (sK78 @ X5 @ X4) @ X4)) = $true) | (X4 = X5) | (((in @ (sK79 @ X5 @ X4) @ X5)) = $true)) )),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f432])).
% 0.22/0.32 thf(f829,plain,(
% 0.22/0.32 ( ! [X0 : $i] : ((emptyset = X0) | ($true != $true) | (((in @ (sK79 @ X0 @ emptyset) @ X0)) = $true)) )),
% 0.22/0.32 inference(constrained_superposition,[],[f446,f464])).
% 0.22/0.32 thf(f840,plain,(
% 0.22/0.32 ( ! [X0 : $i] : ((((in @ (sK79 @ X0 @ emptyset) @ X0)) = $true) | (emptyset = X0)) )),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f829])).
% 0.22/0.32 thf(f862,plain,(
% 0.22/0.32 (emptyset = sK46) | ($true != $true)),
% 0.22/0.32 inference(constrained_superposition,[],[f275,f840])).
% 0.22/0.32 thf(f864,plain,(
% 0.22/0.32 (emptyset = sK46)),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f862])).
% 0.22/0.32 thf(f878,plain,(
% 0.22/0.32 $false),
% 0.22/0.32 inference(forward_subsumption_resolution,[],[f864,f274])).
% 0.22/0.32 % SZS output end Proof for theBenchmark
% 0.22/0.32 % (3176878)------------------------------
% 0.22/0.32 % (3176878)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (3176878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (3176878)CaDiCaL version: 2.1.3
% 0.22/0.32 % (3176878)Termination reason: Refutation
% 0.22/0.32 % (3176878)Time elapsed: 0.024 s
% 0.22/0.32 % (3176878)Peak memory usage: 13 MB
% 0.22/0.32 % (3176878)Instructions burned: 80 (million)
% 0.22/0.32 % (3176868)Success in time 0.065 s
% 0.22/0.32 % Vampire exiting
%------------------------------------------------------------------------------