%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU509^1 : 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 : n001.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 0.23s 0.32s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU509^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n001.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 13:52:50 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.25 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
% 0.23/0.32 % (1269217)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.32 % (1269228)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.32 % (1269228)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
% 0.23/0.32 % (1269227)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=717880155:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.32 % (1269224)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3893908722:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.32 % (1269223)lrs+10_16_si=on:nwc=1.5:random_seed=2891009169:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.32 % (1269226)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=125919422:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.32 % (1269222)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2249046667:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.32 % (1269225)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=2625029917: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)
% 0.23/0.32 % (1269228)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=579413871:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.32 % (1269224)Instruction limit reached!
% 0.23/0.32 % (1269224)------------------------------
% 0.23/0.32 % (1269224)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (1269224)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (1269224)CaDiCaL version: 2.1.3
% 0.23/0.32 % (1269224)Termination reason: Instruction limit
% 0.23/0.32 % (1269224)Termination phase: Property scanning
% 0.23/0.32 % (1269224)Time elapsed: 0.002 s
% 0.23/0.32 % (1269224)Peak memory usage: 9 MB
% 0.23/0.32 % (1269224)Instructions burned: 4 (million)
% 0.23/0.32 % (1269223)Instruction limit reached!
% 0.23/0.32 % (1269223)------------------------------
% 0.23/0.32 % (1269223)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (1269223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (1269223)CaDiCaL version: 2.1.3
% 0.23/0.32 % (1269223)Termination reason: Instruction limit
% 0.23/0.32 % (1269223)Termination phase: Saturation
% 0.23/0.32 % (1269223)Time elapsed: 0.008 s
% 0.23/0.32 % (1269223)Peak memory usage: 11 MB
% 0.23/0.32 % (1269223)Instructions burned: 18 (million)
% 0.23/0.32 % (1269226)Instruction limit reached!
% 0.23/0.32 % (1269226)------------------------------
% 0.23/0.32 % (1269226)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (1269226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (1269226)CaDiCaL version: 2.1.3
% 0.23/0.32 % (1269226)Termination reason: Instruction limit
% 0.23/0.32 % (1269226)Termination phase: Saturation
% 0.23/0.32 % (1269226)Time elapsed: 0.011 s
% 0.23/0.32 % (1269226)Peak memory usage: 11 MB
% 0.23/0.32 % (1269226)Instructions burned: 24 (million)
% 0.23/0.32 % (1269222) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1269217-1269222"...
% 0.23/0.32 % (1269236)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2674969157:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.32 % (1269222)...printing done.
% 0.23/0.32 % (1269227) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1269217-1269227"...
% 0.23/0.32 % (1269222)Refutation found. Thanks to Tanya!
% 0.23/0.32 % SZS status Theorem for theBenchmark
% 0.23/0.32 % SZS output start Proof for theBenchmark
% 0.23/0.32 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.32 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.23/0.32 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 0.23/0.32 thf(func_def_3, type, setextAx: $o).
% 0.23/0.32 thf(func_def_5, type, emptysetAx: $o).
% 0.23/0.32 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 0.23/0.32 thf(func_def_7, type, setadjoinAx: $o).
% 0.23/0.32 thf(func_def_8, type, powerset: ($i > $i)).
% 0.23/0.32 thf(func_def_9, type, powersetAx: $o).
% 0.23/0.32 thf(func_def_10, type, setunion: ($i > $i)).
% 0.23/0.32 thf(func_def_11, type, setunionAx: $o).
% 0.23/0.32 thf(func_def_13, type, omega0Ax: $o).
% 0.23/0.32 thf(func_def_14, type, omegaSAx: $o).
% 0.23/0.32 thf(func_def_15, type, omegaIndAx: $o).
% 0.23/0.32 thf(func_def_16, type, replAx: $o).
% 0.23/0.32 thf(func_def_17, type, foundationAx: $o).
% 0.23/0.32 thf(func_def_18, type, wellorderingAx: $o).
% 0.23/0.32 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 0.23/0.32 thf(func_def_20, type, descrp: $o).
% 0.23/0.32 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.23/0.32 thf(func_def_22, type, dsetconstrI: $o).
% 0.23/0.32 thf(func_def_23, type, dsetconstrEL: $o).
% 0.23/0.32 thf(func_def_24, type, dsetconstrER: $o).
% 0.23/0.32 thf(func_def_25, type, exuE1: $o).
% 0.23/0.32 thf(func_def_26, type, prop2set: ($o > $i)).
% 0.23/0.32 thf(func_def_27, type, prop2setE: $o).
% 0.23/0.32 thf(func_def_28, type, emptysetE: $o).
% 0.23/0.32 thf(func_def_29, type, emptysetimpfalse: $o).
% 0.23/0.32 thf(func_def_30, type, notinemptyset: $o).
% 0.23/0.32 thf(func_def_31, type, exuE3e: $o).
% 0.23/0.32 thf(func_def_32, type, setext: $o).
% 0.23/0.32 thf(func_def_33, type, emptyI: $o).
% 0.23/0.32 thf(func_def_34, type, noeltsimpempty: $o).
% 0.23/0.32 thf(func_def_35, type, setbeta: $o).
% 0.23/0.32 thf(func_def_36, type, nonempty: ($i > $o)).
% 0.23/0.32 thf(func_def_37, type, db0: !>[X0: $tType]:(X0)).
% 0.23/0.32 thf(func_def_38, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.23/0.32 thf(func_def_39, type, vNOT: ($o > $o)).
% 0.23/0.32 thf(func_def_40, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.23/0.32 thf(func_def_43, type, db1: !>[X0: $tType]:(X0)).
% 0.23/0.32 thf(func_def_44, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.23/0.32 thf(func_def_45, type, vAND: ($o > $o > $o)).
% 0.23/0.32 thf(func_def_46, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.23/0.32 thf(func_def_47, type, vIMP: ($o > $o > $o)).
% 0.23/0.32 thf(func_def_48, type, db2: !>[X0: $tType]:(X0)).
% 0.23/0.32 thf(func_def_49, type, sP0: $o).
% 0.23/0.32 thf(func_def_50, type, sP1: ($i > $i > $o)).
% 0.23/0.32 thf(func_def_51, type, sP2: ($i > $o)).
% 0.23/0.32 thf(func_def_52, type, sP3: ($i > $i > $o)).
% 0.23/0.32 thf(func_def_53, type, sP4: ($i > $i > $o)).
% 0.23/0.32 thf(func_def_54, type, sK5: ($i > $i > $o)).
% 0.23/0.32 thf(func_def_56, type, sK7: ($i > $i)).
% 0.23/0.32 thf(func_def_57, type, sK8: ($i > $i)).
% 0.23/0.32 thf(func_def_58, type, sK9: ($i > ($i > $i > $o) > $i)).
% 0.23/0.32 thf(func_def_59, type, sK10: ($i > $i > ($i > $i > $o) > $i)).
% 0.23/0.32 thf(func_def_60, type, sK11: ($i > ($i > $i > $o) > $i)).
% 0.23/0.32 thf(func_def_63, type, sK14: ($i > $i)).
% 0.23/0.32 thf(func_def_64, type, sK15: ($i > $i > $i)).
% 0.23/0.32 thf(func_def_65, type, sK16: ($i > $i > $i)).
% 0.23/0.32 thf(func_def_68, type, sK19: ($i > $o)).
% 0.23/0.32 thf(func_def_71, type, sK22: ($i > $i > $i)).
% 0.23/0.32 thf(func_def_77, type, sK28: ($i > $i)).
% 0.23/0.32 thf(func_def_78, type, sK29: ($i > $o)).
% 0.23/0.32 thf(func_def_79, type, sK30: (($i > $o) > $i)).
% 0.23/0.32 thf(func_def_81, type, sK32: $o).
% 0.23/0.32 thf(func_def_83, type, sK34: ($i > $i)).
% 0.23/0.32 thf(func_def_85, type, sK36: ($i > $i)).
% 0.23/0.32 thf(func_def_88, type, sK39: ($i > $i)).
% 0.23/0.32 thf(func_def_89, type, sK40: ($i > $o)).
% 0.23/0.32 thf(func_def_90, type, sK41: ($i > $i)).
% 0.23/0.32 thf(func_def_91, type, sK42: (($i > $o) > $i)).
% 0.23/0.32 thf(func_def_93, type, sK44: ($i > $o)).
% 0.23/0.32 thf(func_def_96, type, sK47: ($i > $i > $i)).
% 0.23/0.32 thf(func_def_97, type, sK48: ($i > $i > $i)).
% 0.23/0.32 thf(func_def_98, type, sK49: ($i > $i > $i)).
% 0.23/0.32 thf(func_def_99, type, sK50: ($i > $i > $i)).
% 0.23/0.32 thf(func_def_100, type, sK51: ($i > $i > $i > $i)).
% 0.23/0.32 thf(func_def_101, type, sK52: ($i > $i)).
% 0.23/0.32 thf(func_def_102, type, sK53: ($i > $i)).
% 0.23/0.32 thf(func_def_103, type, sK54: ($i > $i)).
% 0.23/0.32 thf(func_def_104, type, sK55: ($i > $i)).
% 0.23/0.32 thf(func_def_105, type, sK56: ($i > $i > $i > $i)).
% 0.23/0.32 thf(func_def_106, type, sK57: ($i > $i > $i > $i)).
% 0.23/0.32 thf(func_def_107, type, sK58: ($i > $i > $i)).
% 0.23/0.32 thf(func_def_108, type, sK59: ($i > $i > $i)).
% 0.23/0.32 thf(func_def_109, type, sK60: ($i > $i > $i)).
% 0.23/0.32 thf(func_def_111, type, sK62: ($i > $i)).
% 0.23/0.32 thf(func_def_112, type, sK63: ($i > $i)).
% 0.23/0.32 thf(func_def_113, type, sK64: ($i > $i)).
% 0.23/0.32 thf(func_def_114, type, sK65: ($i > $i > $i)).
% 0.23/0.32 thf(func_def_116, type, sK67: ($i > $o)).
% 0.23/0.32 thf(func_def_120, type, sK71: ($i > $i > $i)).
% 0.23/0.32 thf(func_def_122, type, sK73: $o).
% 0.23/0.32 thf(func_def_123, type, sK74: ($i > $o)).
% 0.23/0.32 thf(func_def_126, type, sK77: ($i > $o)).
% 0.23/0.32 thf(func_def_131, type, sK82: ($i > $i > $i)).
% 0.23/0.32 thf(func_def_136, type, sK87: ($i > ($i > $o) > $i)).
% 0.23/0.32 thf(func_def_137, type, sK88: ($i > ($i > $i > $o) > $i > $i)).
% 0.23/0.32 thf(func_def_138, type, sK89: ($i > $i)).
% 0.23/0.32 thf(func_def_139, type, sK90: (($i > $o) > $i > $i)).
% 0.23/0.32 thf(func_def_140, type, sK91: ($i > ($i > $o) > $i)).
% 0.23/0.32 thf(func_def_141, type, sK92: ($i > ($i > $i > $o) > $i > $i)).
% 0.23/0.32 thf(func_def_142, type, sK93: ($i > ($i > $i > $o) > $i > $i)).
% 0.23/0.32 thf(func_def_143, type, sK94: (($i > $o) > $i > $i)).
% 0.23/0.32 thf(f26,axiom,(
% 0.23/0.32 (noeltsimpempty = ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)))),
% 0.23/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty)).
% 0.23/0.32 thf(f28,axiom,(
% 0.23/0.32 ((^[X0 : $i] : ((X0 != emptyset))) = nonempty)),
% 0.23/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty)).
% 0.23/0.32 thf(f29,conjecture,(
% 0.23/0.32 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 => ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : (in @ X1 @ X0))))))))))))))))))))))))))),
% 0.23/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1)).
% 0.23/0.32 thf(f30,negated_conjecture,(
% 0.23/0.32 ~(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 => ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : (in @ X1 @ X0)))))))))))))))))))))))))))),
% 0.23/0.32 inference(negated_conjecture,[status(cth)],[f29])).
% 0.23/0.32 thf(f31,plain,(
% 0.23/0.32 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 0.23/0.32 inference(fool_elimination,[],[f28])).
% 0.23/0.32 thf(f60,plain,(
% 0.23/0.32 ~(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 => ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : (in @ X1 @ X0)))))))))))))))))))))))))))),
% 0.23/0.32 inference(rectify,[],[f30])).
% 0.23/0.32 thf(f61,plain,(
% 0.23/0.32 ~((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) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ! [X0 : $i] : ((((nonempty @ X0)) = $true) => ? [X1 : $i] : (((in @ X1 @ X0)) = $true)))))))))))))))))))))))))))),
% 0.23/0.32 inference(fool_elimination,[],[f60])).
% 0.23/0.32 thf(f74,plain,(
% 0.23/0.32 (noeltsimpempty = ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)))),
% 0.23/0.32 inference(rectify,[],[f26])).
% 0.23/0.32 thf(f75,plain,(
% 0.23/0.32 (noeltsimpempty = $true) <=> ! [X0 : $i] : (! [X1 : $i] : ~ (((in @ X1 @ X0)) = $true) => (emptyset = X0))),
% 0.23/0.32 inference(fool_elimination,[],[f74])).
% 0.23/0.32 thf(f91,plain,(
% 0.23/0.32 (noeltsimpempty = $true) <=> ! [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0)) != $true) => (emptyset = X0))),
% 0.23/0.32 inference(flattening,[],[f75])).
% 0.23/0.32 thf(f99,plain,(
% 0.23/0.32 (noeltsimpempty = $true) <=> ! [X0 : $i] : ((emptyset = X0) | ? [X1 : $i] : (((in @ X1 @ X0)) = $true))),
% 0.23/0.32 inference(ennf_transformation,[],[f91])).
% 0.23/0.32 thf(f105,plain,(
% 0.23/0.32 ((((((((((((((((((((((((? [X0 : $i] : ((((nonempty @ X0)) = $true) & ! [X1 : $i] : (((in @ X1 @ X0)) != $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)),
% 0.23/0.32 inference(ennf_transformation,[],[f61])).
% 0.23/0.32 thf(f106,plain,(
% 0.23/0.32 (emptyI = $true) & ? [X0 : $i] : ((((nonempty @ X0)) = $true) & ! [X1 : $i] : (((in @ X1 @ X0)) != $true)) & (omegaIndAx = $true) & (foundationAx = $true) & (emptysetimpfalse = $true) & (powersetAx = $true) & (descrp = $true) & (setextAx = $true) & (omega0Ax = $true) & (setbeta = $true) & (exuE1 = $true) & (setunionAx = $true) & (omegaSAx = $true) & (emptysetAx = $true) & (dsetconstrI = $true) & (setext = $true) & (noeltsimpempty = $true) & (exuE3e = $true) & (setadjoinAx = $true) & (notinemptyset = $true) & (replAx = $true) & (dsetconstrEL = $true) & (emptysetE = $true) & (wellorderingAx = $true) & (prop2setE = $true) & (dsetconstrER = $true)),
% 0.23/0.32 inference(flattening,[],[f105])).
% 0.23/0.32 thf(f146,plain,(
% 0.23/0.32 ((noeltsimpempty = $true) | ? [X0 : $i] : ((emptyset != X0) & ! [X1 : $i] : (((in @ X1 @ X0)) != $true))) & (! [X0 : $i] : ((emptyset = X0) | ? [X1 : $i] : (((in @ X1 @ X0)) = $true)) | (noeltsimpempty != $true))),
% 0.23/0.32 inference(nnf_transformation,[],[f99])).
% 0.23/0.32 thf(f147,plain,(
% 0.23/0.32 ((noeltsimpempty = $true) | ? [X0 : $i] : ((emptyset != X0) & ! [X1 : $i] : (((in @ X1 @ X0)) != $true))) & (! [X2 : $i] : ((emptyset = X2) | ? [X3 : $i] : (((in @ X3 @ X2)) = $true)) | (noeltsimpempty != $true))),
% 0.23/0.32 inference(rectify,[],[f146])).
% 0.23/0.32 thf(f148,plain,(
% 0.23/0.32 ((noeltsimpempty = $true) | ((emptyset != sK27) & ! [X1 : $i] : (((in @ X1 @ sK27)) != $true))) & (! [X2 : $i] : ((emptyset = X2) | ($true = ((in @ (sK28 @ X2) @ X2)))) | (noeltsimpempty != $true))),
% 0.23/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK27,vAPP]),skolemize(X0,sK27),skolemize(X13,sK11 @ X8 @ X7)],[f147])).
% 0.23/0.32 thf(f170,plain,(
% 0.23/0.32 (emptyI = $true) & (($true = ((nonempty @ sK46))) & ! [X1 : $i] : ($true != ((in @ X1 @ sK46)))) & (omegaIndAx = $true) & (foundationAx = $true) & (emptysetimpfalse = $true) & (powersetAx = $true) & (descrp = $true) & (setextAx = $true) & (omega0Ax = $true) & (setbeta = $true) & (exuE1 = $true) & (setunionAx = $true) & (omegaSAx = $true) & (emptysetAx = $true) & (dsetconstrI = $true) & (setext = $true) & (noeltsimpempty = $true) & (exuE3e = $true) & (setadjoinAx = $true) & (notinemptyset = $true) & (replAx = $true) & (dsetconstrEL = $true) & (emptysetE = $true) & (wellorderingAx = $true) & (prop2setE = $true) & (dsetconstrER = $true)),
% 0.23/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(X0,sK46)],[f106])).
% 0.23/0.32 thf(f255,plain,(
% 0.23/0.32 ( ! [X2 : $i] : ((emptyset = X2) | ($true = ((in @ (sK28 @ X2) @ X2))) | (noeltsimpempty != $true)) )),
% 0.23/0.32 inference(cnf_transformation,[],[f148])).
% 0.23/0.32 thf(f291,plain,(
% 0.23/0.32 (noeltsimpempty = $true)),
% 0.23/0.32 inference(cnf_transformation,[],[f170])).
% 0.23/0.32 thf(f306,plain,(
% 0.23/0.32 ( ! [X1 : $i] : (($true != ((in @ X1 @ sK46)))) )),
% 0.23/0.32 inference(cnf_transformation,[],[f170])).
% 0.23/0.32 thf(f307,plain,(
% 0.23/0.32 ($true = ((nonempty @ sK46)))),
% 0.23/0.32 inference(cnf_transformation,[],[f170])).
% 0.23/0.32 thf(f370,plain,(
% 0.23/0.32 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 0.23/0.32 inference(cnf_transformation,[],[f31])).
% 0.23/0.32 thf(f416,plain,(
% 0.23/0.32 ( ! [X2 : $i] : ((emptyset = X2) | ($true = ((in @ (sK28 @ X2) @ X2))) | ($true != $true)) )),
% 0.23/0.32 inference(definition_unfolding,[],[f255,f291])).
% 0.23/0.32 thf(f441,plain,(
% 0.23/0.32 ((((^[Y0 : $i]: (~ (emptyset = Y0))) @ sK46)) = $true)),
% 0.23/0.32 inference(definition_unfolding,[],[f307,f370])).
% 0.23/0.32 thf(f564,plain,(
% 0.23/0.32 ( ! [X2 : $i] : (($true = ((in @ (sK28 @ X2) @ X2))) | (emptyset = X2)) )),
% 0.23/0.32 inference(trivial_inequality_removal,[],[f416])).
% 0.23/0.32 thf(f578,plain,(
% 0.23/0.32 ($true = ((~ (emptyset = sK46))))),
% 0.23/0.32 inference(beta-eta_normalization,[],[f441])).
% 0.23/0.32 thf(f579,plain,(
% 0.23/0.32 ($false = ((emptyset = sK46)))),
% 0.23/0.32 inference(not_proxy_clausification,[],[f578])).
% 0.23/0.32 thf(f580,plain,(
% 0.23/0.32 (emptyset != sK46)),
% 0.23/0.32 inference(equality_proxy_clausification,[],[f579])).
% 0.23/0.32 thf(f628,plain,(
% 0.23/0.32 (emptyset = sK46) | ($true != $true)),
% 0.23/0.32 inference(constrained_superposition,[],[f306,f564])).
% 0.23/0.32 thf(f629,plain,(
% 0.23/0.32 (emptyset = sK46)),
% 0.23/0.32 inference(trivial_inequality_removal,[],[f628])).
% 0.23/0.32 thf(f630,plain,(
% 0.23/0.32 $false),
% 0.23/0.32 inference(forward_subsumption_resolution,[],[f629,f580])).
% 0.23/0.32 % SZS output end Proof for theBenchmark
% 0.23/0.32 % (1269222)------------------------------
% 0.23/0.32 % (1269222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (1269222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (1269222)CaDiCaL version: 2.1.3
% 0.23/0.32 % (1269222)Termination reason: Refutation
% 0.23/0.32 % (1269222)Time elapsed: 0.021 s
% 0.23/0.32 % (1269222)Peak memory usage: 12 MB
% 0.23/0.32 % (1269222)Instructions burned: 40 (million)
% 0.23/0.32 % (1269217)Success in time 0.062 s
% 0.23/0.32 % Vampire exiting
%------------------------------------------------------------------------------