%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU507^1 : 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 : n006.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 0.21s 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU507^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n006.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 13:46:55 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 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
% 0.21/0.31 % (740392)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.31 % (740398)lrs+10_16_si=on:nwc=1.5:random_seed=263954009:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.31 % (740403)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.31 % (740403)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
% 0.21/0.31 % (740398)Instruction limit reached!
% 0.21/0.31 % (740398)------------------------------
% 0.21/0.31 % (740398)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (740398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (740398)CaDiCaL version: 2.1.3
% 0.21/0.31 % (740398)Termination reason: Instruction limit
% 0.21/0.31 % (740398)Termination phase: Saturation
% 0.21/0.31 % (740398)Time elapsed: 0.005 s
% 0.21/0.31 % (740398)Peak memory usage: 12 MB
% 0.21/0.31 % (740398)Instructions burned: 21 (million)
% 0.21/0.31 % (740397)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2171621752:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.31 % (740403)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=1457224830:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.31 % (740400)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=3798941501: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)
% 0.21/0.31 % (740401)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3583877898:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.31 % (740402)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=340724136:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.31 % (740399)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3050217419:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.31 % (740399)Instruction limit reached!
% 0.21/0.31 % (740399)------------------------------
% 0.21/0.31 % (740399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (740399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (740399)CaDiCaL version: 2.1.3
% 0.21/0.31 % (740399)Termination reason: Instruction limit
% 0.21/0.31 % (740399)Termination phase: shuffling
% 0.21/0.31 % (740399)Time elapsed: 0.003 s
% 0.21/0.31 % (740399)Peak memory usage: 10 MB
% 0.21/0.31 % (740399)Instructions burned: 3 (million)
% 0.21/0.31 % (740405)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=823003495:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.31 % (740401)Instruction limit reached!
% 0.21/0.31 % (740401)------------------------------
% 0.21/0.31 % (740401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (740401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (740401)CaDiCaL version: 2.1.3
% 0.21/0.31 % (740401)Termination reason: Instruction limit
% 0.21/0.31 % (740401)Termination phase: Saturation
% 0.21/0.31 % (740401)Time elapsed: 0.012 s
% 0.21/0.31 % (740401)Peak memory usage: 12 MB
% 0.21/0.31 % (740401)Instructions burned: 25 (million)
% 0.21/0.31 % (740405)Instruction limit reached!
% 0.21/0.31 % (740405)------------------------------
% 0.21/0.31 % (740405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (740405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (740405)CaDiCaL version: 2.1.3
% 0.21/0.31 % (740405)Termination reason: Instruction limit
% 0.21/0.31 % (740405)Termination phase: Saturation
% 0.21/0.31 % (740405)Time elapsed: 0.004 s
% 0.21/0.31 % (740405)Peak memory usage: 12 MB
% 0.21/0.31 % (740405)Instructions burned: 16 (million)
% 0.21/0.31 % (740397) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-740392-740397"...
% 0.21/0.31 % (740400) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-740392-740400"...
% 0.21/0.31 % (740397)...printing done.
% 0.21/0.31 % (740397)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% 0.21/0.31 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.31 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.21/0.31 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 0.21/0.31 thf(func_def_3, type, setextAx: $o).
% 0.21/0.31 thf(func_def_5, type, emptysetAx: $o).
% 0.21/0.31 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 0.21/0.31 thf(func_def_7, type, setadjoinAx: $o).
% 0.21/0.31 thf(func_def_8, type, powerset: ($i > $i)).
% 0.21/0.31 thf(func_def_9, type, powersetAx: $o).
% 0.21/0.31 thf(func_def_10, type, setunion: ($i > $i)).
% 0.21/0.31 thf(func_def_11, type, setunionAx: $o).
% 0.21/0.31 thf(func_def_13, type, omega0Ax: $o).
% 0.21/0.31 thf(func_def_14, type, omegaSAx: $o).
% 0.21/0.31 thf(func_def_15, type, omegaIndAx: $o).
% 0.21/0.31 thf(func_def_16, type, replAx: $o).
% 0.21/0.31 thf(func_def_17, type, foundationAx: $o).
% 0.21/0.31 thf(func_def_18, type, wellorderingAx: $o).
% 0.21/0.31 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 0.21/0.31 thf(func_def_20, type, descrp: $o).
% 0.21/0.31 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.21/0.31 thf(func_def_22, type, dsetconstrI: $o).
% 0.21/0.31 thf(func_def_23, type, dsetconstrEL: $o).
% 0.21/0.31 thf(func_def_24, type, dsetconstrER: $o).
% 0.21/0.31 thf(func_def_25, type, exuE1: $o).
% 0.21/0.31 thf(func_def_26, type, prop2set: ($o > $i)).
% 0.21/0.31 thf(func_def_27, type, prop2setE: $o).
% 0.21/0.31 thf(func_def_28, type, emptysetE: $o).
% 0.21/0.31 thf(func_def_29, type, emptysetimpfalse: $o).
% 0.21/0.31 thf(func_def_30, type, notinemptyset: $o).
% 0.21/0.31 thf(func_def_31, type, exuE3e: $o).
% 0.21/0.31 thf(func_def_32, type, setext: $o).
% 0.21/0.31 thf(func_def_33, type, emptyI: $o).
% 0.21/0.31 thf(func_def_36, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.31 thf(func_def_37, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.31 thf(func_def_38, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.31 thf(func_def_39, type, vAND: ($o > $o > $o)).
% 0.21/0.31 thf(func_def_40, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.31 thf(func_def_41, type, vIMP: ($o > $o > $o)).
% 0.21/0.31 thf(func_def_42, type, db2: !>[X0: $tType]:(X0)).
% 0.21/0.31 thf(func_def_43, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.31 thf(func_def_44, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.31 thf(func_def_45, type, sP0: ($i > $i > $o)).
% 0.21/0.31 thf(func_def_46, type, sP1: ($i > $o)).
% 0.21/0.31 thf(func_def_47, type, sP2: ($i > $i > $o)).
% 0.21/0.31 thf(func_def_48, type, sP3: ($i > $i > $o)).
% 0.21/0.31 thf(func_def_49, type, sP4: $o).
% 0.21/0.31 thf(func_def_51, type, sK6: $o).
% 0.21/0.31 thf(func_def_52, type, sK7: ($i > $o)).
% 0.21/0.31 thf(func_def_53, type, sK8: ($i > $i > $i)).
% 0.21/0.31 thf(func_def_58, type, sK13: ($i > $o)).
% 0.21/0.31 thf(func_def_62, type, sK17: ($i > $i > $i)).
% 0.21/0.31 thf(func_def_63, type, sK18: ($i > $i > $i)).
% 0.21/0.31 thf(func_def_64, type, sK19: ($i > $o)).
% 0.21/0.31 thf(func_def_69, type, sK24: ($i > $i > $i)).
% 0.21/0.31 thf(func_def_73, type, sK28: ($i > $i > $i)).
% 0.21/0.31 thf(func_def_74, type, sK29: ($i > $i > $i)).
% 0.21/0.31 thf(func_def_75, type, sK30: ($i > $i > $i)).
% 0.21/0.31 thf(func_def_76, type, sK31: ($i > $i > $i)).
% 0.21/0.31 thf(func_def_77, type, sK32: ($i > $i > $i)).
% 0.21/0.31 thf(func_def_78, type, sK33: ($i > $i > $i > $i)).
% 0.21/0.31 thf(func_def_79, type, sK34: ($i > $i)).
% 0.21/0.31 thf(func_def_80, type, sK35: ($i > $i)).
% 0.21/0.31 thf(func_def_81, type, sK36: ($i > $i)).
% 0.21/0.31 thf(func_def_82, type, sK37: ($i > $i)).
% 0.21/0.31 thf(func_def_83, type, sK38: ($i > $i > $i)).
% 0.21/0.31 thf(func_def_84, type, sK39: ($i > $i > $i > $i)).
% 0.21/0.31 thf(func_def_85, type, sK40: ($i > $i > $i > $i)).
% 0.21/0.31 thf(func_def_86, type, sK41: ($i > $i > $i)).
% 0.21/0.31 thf(func_def_87, type, sK42: ($i > $i > $i)).
% 0.21/0.31 thf(func_def_89, type, sK44: ($i > $i)).
% 0.21/0.31 thf(func_def_90, type, sK45: ($i > $i)).
% 0.21/0.31 thf(func_def_91, type, sK46: ($i > $i)).
% 0.21/0.31 thf(func_def_92, type, sK47: ($i > $o)).
% 0.21/0.31 thf(func_def_93, type, sK48: ($i > $i)).
% 0.21/0.31 thf(func_def_94, type, sK49: (($i > $o) > $i)).
% 0.21/0.31 thf(func_def_95, type, sK50: ($i > $i > $i)).
% 0.21/0.31 thf(func_def_98, type, sK53: ($i > $i > $o)).
% 0.21/0.31 thf(func_def_100, type, sK55: ($i > $i)).
% 0.21/0.31 thf(func_def_101, type, sK56: ($i > $i)).
% 0.21/0.31 thf(func_def_102, type, sK57: ($i > ($i > $i > $o) > $i)).
% 0.21/0.31 thf(func_def_103, type, sK58: ($i > ($i > $i > $o) > $i)).
% 0.21/0.31 thf(func_def_104, type, sK59: ($i > $i > ($i > $i > $o) > $i)).
% 0.21/0.31 thf(func_def_105, type, sK60: ($i > $i)).
% 0.21/0.31 thf(func_def_107, type, sK62: ($i > $i)).
% 0.21/0.31 thf(func_def_110, type, sK65: (($i > $o) > $i)).
% 0.21/0.31 thf(func_def_111, type, sK66: ($i > $o)).
% 0.21/0.31 thf(func_def_117, type, sK72: ($i > $o)).
% 0.21/0.31 thf(func_def_120, type, sK75: ($i > $i)).
% 0.21/0.31 thf(func_def_122, type, sK77: $o).
% 0.21/0.31 thf(func_def_126, type, sK81: ($i > $i)).
% 0.21/0.31 thf(func_def_127, type, vNOT: ($o > $o)).
% 0.21/0.31 thf(func_def_128, type, sK82: ($i > ($i > $i > $o) > $i > $i)).
% 0.21/0.31 thf(func_def_129, type, sK83: (($i > $o) > $i > $i)).
% 0.21/0.31 thf(func_def_130, type, sK84: ($i > ($i > $i > $o) > $i > $i)).
% 0.21/0.31 thf(func_def_131, type, sK85: (($i > $o) > $i > $i)).
% 0.21/0.31 thf(func_def_132, type, sK86: ($i > ($i > $o) > $i)).
% 0.21/0.31 thf(func_def_133, type, sK87: ($i > $i)).
% 0.21/0.31 thf(func_def_134, type, sK88: ($i > ($i > $o) > $i)).
% 0.21/0.31 thf(func_def_135, type, sK89: ($i > ($i > $i > $o) > $i > $i)).
% 0.21/0.31 thf(f25,axiom,(
% 0.21/0.31 (! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)) = emptyI)),
% 0.21/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI)).
% 0.21/0.31 thf(f26,conjecture,(
% 0.21/0.31 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset))))))))))))))))))))))))),
% 0.21/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty)).
% 0.21/0.31 thf(f27,negated_conjecture,(
% 0.21/0.31 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)))))))))))))))))))))))))),
% 0.21/0.31 inference(negated_conjecture,[status(cth)],[f26])).
% 0.21/0.31 thf(f28,plain,(
% 0.21/0.31 (! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)) = emptyI)),
% 0.21/0.31 inference(rectify,[],[f25])).
% 0.21/0.31 thf(f29,plain,(
% 0.21/0.31 ! [X0 : $i] : (! [X1 : $i] : ~ (((in @ X1 @ X0)) = $true) => (emptyset = X0)) <=> (emptyI = $true)),
% 0.21/0.31 inference(fool_elimination,[],[f28])).
% 0.21/0.31 thf(f42,plain,(
% 0.21/0.31 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)))))))))))))))))))))))))),
% 0.21/0.31 inference(rectify,[],[f27])).
% 0.21/0.31 thf(f43,plain,(
% 0.21/0.31 ~((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) => ! [X0 : $i] : (! [X1 : $i] : ~ (((in @ X1 @ X0)) = $true) => (emptyset = X0)))))))))))))))))))))))))),
% 0.21/0.31 inference(fool_elimination,[],[f42])).
% 0.21/0.31 thf(f78,plain,(
% 0.21/0.31 ! [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0)) != $true) => (emptyset = X0)) <=> (emptyI = $true)),
% 0.21/0.31 inference(flattening,[],[f29])).
% 0.21/0.31 thf(f81,plain,(
% 0.21/0.31 ~((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) => ! [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0)) != $true) => (emptyset = X0)))))))))))))))))))))))))),
% 0.21/0.31 inference(flattening,[],[f43])).
% 0.21/0.31 thf(f89,plain,(
% 0.21/0.31 (emptyI = $true) <=> ! [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0)) = $true) | (emptyset = X0))),
% 0.21/0.31 inference(ennf_transformation,[],[f78])).
% 0.21/0.31 thf(f98,plain,(
% 0.21/0.31 ((((((((((((((((((((((? [X0 : $i] : ((emptyset != X0) & ! [X1 : $i] : (((in @ X1 @ X0)) != $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)),
% 0.21/0.31 inference(ennf_transformation,[],[f81])).
% 0.21/0.31 thf(f99,plain,(
% 0.21/0.31 (exuE1 = $true) & ? [X0 : $i] : ((emptyset != X0) & ! [X1 : $i] : (((in @ X1 @ X0)) != $true)) & (powersetAx = $true) & (emptysetimpfalse = $true) & (foundationAx = $true) & (wellorderingAx = $true) & (emptyI = $true) & (dsetconstrER = $true) & (emptysetE = $true) & (dsetconstrEL = $true) & (omegaSAx = $true) & (setadjoinAx = $true) & (setext = $true) & (replAx = $true) & (omega0Ax = $true) & (omegaIndAx = $true) & (notinemptyset = $true) & (setunionAx = $true) & (setextAx = $true) & (exuE3e = $true) & (emptysetAx = $true) & (prop2setE = $true) & (descrp = $true) & (dsetconstrI = $true)),
% 0.21/0.31 inference(flattening,[],[f98])).
% 0.21/0.31 thf(f138,plain,(
% 0.21/0.31 (exuE1 = $true) & ((emptyset != sK23) & ! [X1 : $i] : (((in @ X1 @ sK23)) != $true)) & (powersetAx = $true) & (emptysetimpfalse = $true) & (foundationAx = $true) & (wellorderingAx = $true) & (emptyI = $true) & (dsetconstrER = $true) & (emptysetE = $true) & (dsetconstrEL = $true) & (omegaSAx = $true) & (setadjoinAx = $true) & (setext = $true) & (replAx = $true) & (omega0Ax = $true) & (omegaIndAx = $true) & (notinemptyset = $true) & (setunionAx = $true) & (setextAx = $true) & (exuE3e = $true) & (emptysetAx = $true) & (prop2setE = $true) & (descrp = $true) & (dsetconstrI = $true)),
% 0.21/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(X0,sK23)],[f99])).
% 0.21/0.31 thf(f186,plain,(
% 0.21/0.31 ((emptyI = $true) | ? [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0)) != $true) & (emptyset != X0))) & (! [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0)) = $true) | (emptyset = X0)) | (emptyI != $true))),
% 0.21/0.31 inference(nnf_transformation,[],[f89])).
% 0.21/0.31 thf(f187,plain,(
% 0.21/0.31 ((emptyI = $true) | ? [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0)) != $true) & (emptyset != X0))) & (! [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X2)) = $true) | (emptyset = X2)) | (emptyI != $true))),
% 0.21/0.31 inference(rectify,[],[f186])).
% 0.21/0.31 thf(f188,plain,(
% 0.21/0.31 ((emptyI = $true) | (! [X1 : $i] : ($true != ((in @ X1 @ sK74))) & (emptyset != sK74))) & (! [X2 : $i] : ((((in @ (sK75 @ X2) @ X2)) = $true) | (emptyset = X2)) | (emptyI != $true))),
% 0.21/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK74,vAPP]),skolemize(X0,sK74),skolemize(X2,sK8 @ X1 @ X0)],[f187])).
% 0.21/0.31 thf(f245,plain,(
% 0.21/0.31 (emptyI = $true)),
% 0.21/0.31 inference(cnf_transformation,[],[f138])).
% 0.21/0.31 thf(f250,plain,(
% 0.21/0.31 ( ! [X1 : $i] : ((((in @ X1 @ sK23)) != $true)) )),
% 0.21/0.31 inference(cnf_transformation,[],[f138])).
% 0.21/0.31 thf(f251,plain,(
% 0.21/0.31 (emptyset != sK23)),
% 0.21/0.31 inference(cnf_transformation,[],[f138])).
% 0.21/0.31 thf(f339,plain,(
% 0.21/0.31 ( ! [X2 : $i] : ((((in @ (sK75 @ X2) @ X2)) = $true) | (emptyset = X2) | (emptyI != $true)) )),
% 0.21/0.31 inference(cnf_transformation,[],[f188])).
% 0.21/0.31 thf(f436,plain,(
% 0.21/0.31 ( ! [X2 : $i] : (($true != $true) | (emptyset = X2) | (((in @ (sK75 @ X2) @ X2)) = $true)) )),
% 0.21/0.31 inference(definition_unfolding,[],[f339,f245])).
% 0.21/0.31 thf(f467,plain,(
% 0.21/0.31 ( ! [X2 : $i] : ((((in @ (sK75 @ X2) @ X2)) = $true) | (emptyset = X2)) )),
% 0.21/0.31 inference(trivial_inequality_removal,[],[f436])).
% 0.21/0.31 thf(f634,plain,(
% 0.21/0.31 ($true != $true) | (emptyset = sK23)),
% 0.21/0.31 inference(constrained_superposition,[],[f250,f467])).
% 0.21/0.31 thf(f635,plain,(
% 0.21/0.31 (emptyset = sK23)),
% 0.21/0.31 inference(trivial_inequality_removal,[],[f634])).
% 0.21/0.31 thf(f636,plain,(
% 0.21/0.31 $false),
% 0.21/0.31 inference(forward_subsumption_resolution,[],[f635,f251])).
% 0.21/0.31 % SZS output end Proof for theBenchmark
% 0.21/0.31 % (740397)------------------------------
% 0.21/0.31 % (740397)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (740397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (740397)CaDiCaL version: 2.1.3
% 0.21/0.31 % (740397)Termination reason: Refutation
% 0.21/0.31 % (740397)Time elapsed: 0.020 s
% 0.21/0.31 % (740397)Peak memory usage: 13 MB
% 0.21/0.31 % (740397)Instructions burned: 38 (million)
% 0.21/0.31 % (740392)Success in time 0.061 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------