%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU525^1 : 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 : n005.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 08:29:55 AM UTC 2026
% Result : Theorem 0.23s 0.31s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU525^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n005.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:48:31 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 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
% 0.23/0.31 % (1694983)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.31 % (1694994)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1288931216:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.31 % (1695000)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.31 % (1695000)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
% 0.23/0.31 % (1694995)lrs+10_16_si=on:nwc=1.5:random_seed=787288858:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.31 % (1694999)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2838940546:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.31 % (1694997)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=1149181416: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)
% 0.23/0.31 % (1694998)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=977697157:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.31 % (1694996)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=185444112:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.31 % (1695000)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=3995867660:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.31 % (1694996)Instruction limit reached!
% 0.23/0.31 % (1694996)------------------------------
% 0.23/0.31 % (1694996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (1694996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (1694996)CaDiCaL version: 2.1.3
% 0.23/0.31 % (1694996)Termination reason: Instruction limit
% 0.23/0.31 % (1694996)Termination phase: shuffling
% 0.23/0.31 % (1694996)Time elapsed: 0.002 s
% 0.23/0.31 % (1694996)Peak memory usage: 9 MB
% 0.23/0.31 % (1694996)Instructions burned: 4 (million)
% 0.23/0.31 % (1694995)Instruction limit reached!
% 0.23/0.31 % (1694995)------------------------------
% 0.23/0.31 % (1694995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (1694995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (1694995)CaDiCaL version: 2.1.3
% 0.23/0.31 % (1694995)Termination reason: Instruction limit
% 0.23/0.31 % (1694995)Termination phase: Saturation
% 0.23/0.31 % (1694995)Time elapsed: 0.008 s
% 0.23/0.31 % (1694995)Peak memory usage: 11 MB
% 0.23/0.31 % (1694995)Instructions burned: 19 (million)
% 0.23/0.31 % (1694998)Instruction limit reached!
% 0.23/0.31 % (1694998)------------------------------
% 0.23/0.31 % (1694998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (1694998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (1694998)CaDiCaL version: 2.1.3
% 0.23/0.31 % (1694998)Termination reason: Instruction limit
% 0.23/0.31 % (1694998)Termination phase: Property scanning
% 0.23/0.31 % (1694998)Time elapsed: 0.012 s
% 0.23/0.31 % (1694998)Peak memory usage: 11 MB
% 0.23/0.31 % (1694998)Instructions burned: 25 (million)
% 0.23/0.31 % (1694994) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1694983-1694994"...
% 0.23/0.31 % (1694994)...printing done.
% 0.23/0.31 % (1694994)Refutation found. Thanks to Tanya!
% 0.23/0.31 % SZS status Theorem for theBenchmark
% 0.23/0.31 % SZS output start Proof for theBenchmark
% 0.23/0.31 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.31 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.23/0.31 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 0.23/0.31 thf(func_def_3, type, setextAx: $o).
% 0.23/0.31 thf(func_def_5, type, emptysetAx: $o).
% 0.23/0.31 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_7, type, setadjoinAx: $o).
% 0.23/0.31 thf(func_def_8, type, powerset: ($i > $i)).
% 0.23/0.31 thf(func_def_9, type, powersetAx: $o).
% 0.23/0.31 thf(func_def_10, type, setunion: ($i > $i)).
% 0.23/0.31 thf(func_def_11, type, setunionAx: $o).
% 0.23/0.31 thf(func_def_13, type, omega0Ax: $o).
% 0.23/0.31 thf(func_def_14, type, omegaSAx: $o).
% 0.23/0.31 thf(func_def_15, type, omegaIndAx: $o).
% 0.23/0.31 thf(func_def_16, type, replAx: $o).
% 0.23/0.31 thf(func_def_17, type, foundationAx: $o).
% 0.23/0.31 thf(func_def_18, type, wellorderingAx: $o).
% 0.23/0.31 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 0.23/0.31 thf(func_def_20, type, descrp: $o).
% 0.23/0.31 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.23/0.31 thf(func_def_22, type, dsetconstrI: $o).
% 0.23/0.31 thf(func_def_23, type, dsetconstrEL: $o).
% 0.23/0.31 thf(func_def_24, type, dsetconstrER: $o).
% 0.23/0.31 thf(func_def_25, type, exuE1: $o).
% 0.23/0.31 thf(func_def_26, type, prop2set: ($o > $i)).
% 0.23/0.31 thf(func_def_27, type, prop2setE: $o).
% 0.23/0.31 thf(func_def_28, type, emptysetE: $o).
% 0.23/0.31 thf(func_def_29, type, emptysetimpfalse: $o).
% 0.23/0.31 thf(func_def_30, type, notinemptyset: $o).
% 0.23/0.31 thf(func_def_31, type, exuE3e: $o).
% 0.23/0.31 thf(func_def_32, type, setext: $o).
% 0.23/0.31 thf(func_def_33, type, emptyI: $o).
% 0.23/0.31 thf(func_def_34, type, noeltsimpempty: $o).
% 0.23/0.31 thf(func_def_35, type, setbeta: $o).
% 0.23/0.31 thf(func_def_36, type, nonempty: ($i > $o)).
% 0.23/0.31 thf(func_def_37, type, nonemptyE1: $o).
% 0.23/0.31 thf(func_def_38, type, nonemptyI: $o).
% 0.23/0.31 thf(func_def_39, type, nonemptyI1: $o).
% 0.23/0.31 thf(func_def_40, type, setadjoinIL: $o).
% 0.23/0.31 thf(func_def_41, type, emptyinunitempty: $o).
% 0.23/0.31 thf(func_def_42, type, setadjoinIR: $o).
% 0.23/0.31 thf(func_def_43, type, setadjoinE: $o).
% 0.23/0.31 thf(func_def_44, type, setadjoinOr: $o).
% 0.23/0.31 thf(func_def_45, type, setoftrueEq: $o).
% 0.23/0.31 thf(func_def_46, type, powersetI: $o).
% 0.23/0.31 thf(func_def_47, type, emptyinPowerset: $o).
% 0.23/0.31 thf(func_def_48, type, emptyInPowerset: $o).
% 0.23/0.31 thf(func_def_49, type, powersetE: $o).
% 0.23/0.31 thf(func_def_50, type, setunionI: $o).
% 0.23/0.31 thf(func_def_51, type, setunionE: $o).
% 0.23/0.31 thf(func_def_52, type, subPowSU: $o).
% 0.23/0.31 thf(func_def_53, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.23/0.31 thf(func_def_54, type, vAND: ($o > $o > $o)).
% 0.23/0.31 thf(func_def_55, type, db1: !>[X0: $tType]:(X0)).
% 0.23/0.31 thf(func_def_56, type, db0: !>[X0: $tType]:(X0)).
% 0.23/0.31 thf(func_def_57, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.23/0.31 thf(func_def_58, type, vIMP: ($o > $o > $o)).
% 0.23/0.31 thf(func_def_59, type, db2: !>[X0: $tType]:(X0)).
% 0.23/0.31 thf(func_def_60, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.23/0.31 thf(func_def_61, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.23/0.31 thf(func_def_64, type, vNOT: ($o > $o)).
% 0.23/0.31 thf(func_def_65, type, sP0: $o).
% 0.23/0.31 thf(func_def_66, type, sP1: ($i > $i > $o)).
% 0.23/0.31 thf(func_def_67, type, sP2: ($i > $o)).
% 0.23/0.31 thf(func_def_68, type, sP3: ($i > $i > $o)).
% 0.23/0.31 thf(func_def_69, type, sP4: ($i > $i > $o)).
% 0.23/0.31 thf(func_def_71, type, sK6: ($i > $o)).
% 0.23/0.31 thf(func_def_80, type, sK15: ($i > $i)).
% 0.23/0.31 thf(func_def_81, type, sK16: ($i > $i)).
% 0.23/0.31 thf(func_def_83, type, sK18: ($o > $i > $i > $i)).
% 0.23/0.31 thf(func_def_86, type, sK21: $o).
% 0.23/0.31 thf(func_def_89, type, sK24: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_90, type, sK25: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_92, type, sK27: ($i > $i)).
% 0.23/0.31 thf(func_def_94, type, sK29: ($i > $o)).
% 0.23/0.31 thf(func_def_99, type, sK34: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_101, type, sK36: ($i > $i > $o)).
% 0.23/0.31 thf(func_def_102, type, sK37: ($i > $i)).
% 0.23/0.31 thf(func_def_103, type, sK38: ($i > $i)).
% 0.23/0.31 thf(func_def_104, type, sK39: (($i > $i > $o) > $i > $i)).
% 0.23/0.31 thf(func_def_105, type, sK40: (($i > $i > $o) > $i > $i)).
% 0.23/0.31 thf(func_def_106, type, sK41: ($i > ($i > $i > $o) > $i > $i)).
% 0.23/0.31 thf(func_def_107, type, sK42: ($i > $o)).
% 0.23/0.31 thf(func_def_108, type, sK43: ($i > $i)).
% 0.23/0.31 thf(func_def_110, type, sK45: ($i > $o)).
% 0.23/0.31 thf(func_def_113, type, sK48: (($i > $o) > $i)).
% 0.23/0.31 thf(func_def_114, type, sK49: ($i > $o)).
% 0.23/0.31 thf(func_def_115, type, sK50: ($i > $i)).
% 0.23/0.31 thf(func_def_120, type, sK55: ($i > $i)).
% 0.23/0.31 thf(func_def_125, type, sK60: ($i > $o)).
% 0.23/0.31 thf(func_def_129, type, sK64: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_140, type, sK75: ($i > $o)).
% 0.23/0.31 thf(func_def_141, type, sK76: (($i > $o) > $i)).
% 0.23/0.31 thf(func_def_142, type, sK77: ($i > $o)).
% 0.23/0.31 thf(func_def_143, type, sK78: $o).
% 0.23/0.31 thf(func_def_146, type, sK81: $o).
% 0.23/0.31 thf(func_def_149, type, sK84: ($i > $i)).
% 0.23/0.31 thf(func_def_160, type, sK95: $o).
% 0.23/0.31 thf(func_def_161, type, sK96: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_167, type, sK102: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_169, type, sK104: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_170, type, sK105: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_171, type, sK106: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_172, type, sK107: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_173, type, sK108: ($i > $i > $i > $i)).
% 0.23/0.31 thf(func_def_174, type, sK109: ($i > $i)).
% 0.23/0.31 thf(func_def_175, type, sK110: ($i > $i)).
% 0.23/0.31 thf(func_def_176, type, sK111: ($i > $i)).
% 0.23/0.31 thf(func_def_177, type, sK112: ($i > $i)).
% 0.23/0.31 thf(func_def_178, type, sK113: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_179, type, sK114: ($i > $i > $i > $i)).
% 0.23/0.31 thf(func_def_180, type, sK115: ($i > $i > $i > $i)).
% 0.23/0.31 thf(func_def_181, type, sK116: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_182, type, sK117: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_183, type, sK118: ($i > $i)).
% 0.23/0.31 thf(func_def_184, type, sK119: ($i > $i > $i)).
% 0.23/0.31 thf(func_def_186, type, sK121: ($i > $i)).
% 0.23/0.31 thf(func_def_187, type, sK122: ($i > $i)).
% 0.23/0.31 thf(func_def_188, type, sK123: ($i > $o)).
% 0.23/0.31 thf(func_def_189, type, sK124: ($i > $i)).
% 0.23/0.31 thf(func_def_190, type, sK125: ($i > ($i > $i > $o) > $i > $i)).
% 0.23/0.31 thf(func_def_191, type, sK126: ($i > ($i > $o) > $i)).
% 0.23/0.31 thf(func_def_193, type, sK128: ($i > $i)).
% 0.23/0.31 thf(func_def_194, type, sK129: ($i > ($i > $o) > $i)).
% 0.23/0.31 thf(func_def_195, type, sK130: ($i > ($i > $i > $o) > $i > $i)).
% 0.23/0.31 thf(func_def_196, type, sK131: ($i > ($i > $o) > $i)).
% 0.23/0.31 thf(func_def_197, type, sK132: (($i > $o) > $i > $i)).
% 0.23/0.31 thf(func_def_198, type, sK133: ($i > ($i > $i > $o) > $i > $i)).
% 0.23/0.31 thf(f1,axiom,(
% 0.23/0.31 (exu = (^[X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 0.23/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu)).
% 0.23/0.31 thf(f45,conjecture,(
% 0.23/0.31 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X1 : $i] : ! [X2 : $i] : ((X2 = X1) <=> (X0 @ X2)))))))))))))))))))))))))))))))))))))))))))),
% 0.23/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE2)).
% 0.23/0.31 thf(f46,negated_conjecture,(
% 0.23/0.31 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X1 : $i] : ! [X2 : $i] : ((X2 = X1) <=> (X0 @ X2))))))))))))))))))))))))))))))))))))))))))))),
% 0.23/0.31 inference(negated_conjecture,[status(cth)],[f45])).
% 0.23/0.31 thf(f47,plain,(
% 0.23/0.31 (exu = (^[X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 0.23/0.31 inference(rectify,[],[f1])).
% 0.23/0.31 thf(f48,plain,(
% 0.23/0.31 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 0.23/0.31 inference(fool_elimination,[],[f47])).
% 0.23/0.31 thf(f93,plain,(
% 0.23/0.31 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X2 : $i] : ! [X3 : $i] : ((X2 = X3) <=> (X0 @ X3))))))))))))))))))))))))))))))))))))))))))))),
% 0.23/0.32 inference(rectify,[],[f46])).
% 0.23/0.32 thf(f94,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) => ((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 = $true) => ! [X0 : ($i > $o)] : (($true = ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) => ? [X2 : $i] : ! [X3 : $i] : ((X2 = X3) <=> ($true = ((X0 @ X3))))))))))))))))))))))))))))))))))))))))))))))),
% 0.23/0.32 inference(fool_elimination,[],[f93])).
% 0.23/0.32 thf(f136,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) => ((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 = $true) => ! [X0 : ($i > $o)] : (($true = ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) => ? [X1 : $i] : ! [X2 : $i] : ((((X0 @ X2)) = $true) <=> (X1 = X2))))))))))))))))))))))))))))))))))))))))))))),
% 0.23/0.32 inference(rectify,[],[f94])).
% 0.23/0.32 thf(f149,plain,(
% 0.23/0.32 ((((((((((((((((((((((((((((((((((((((((? [X0 : ($i > $o)] : (($true = ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) & ! [X1 : $i] : ? [X2 : $i] : ((((X0 @ X2)) = $true) <~> (X1 = X2))) & (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)),
% 0.23/0.32 inference(ennf_transformation,[],[f136])).
% 0.23/0.32 thf(f150,plain,(
% 0.23/0.32 (powersetAx = $true) & (setunionE = $true) & (emptyInPowerset = $true) & (setunionAx = $true) & (dsetconstrEL = $true) & (replAx = $true) & (setadjoinAx = $true) & (emptyinunitempty = $true) & (powersetI = $true) & (foundationAx = $true) & ? [X0 : ($i > $o)] : (($true = ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) & ! [X1 : $i] : ? [X2 : $i] : ((((X0 @ X2)) = $true) <~> (X1 = X2))) & (setextAx = $true) & (exuE1 = $true) & (subPowSU = $true) & (setext = $true) & (nonemptyE1 = $true) & (setoftrueEq = $true) & (setadjoinOr = $true) & (dsetconstrI = $true) & (powersetE = $true) & (nonemptyI = $true) & (setadjoinIR = $true) & (emptysetAx = $true) & (setadjoinE = $true) & (notinemptyset = $true) & (wellorderingAx = $true) & (omegaSAx = $true) & (emptyinPowerset = $true) & (omegaIndAx = $true) & (emptysetE = $true) & (nonemptyI1 = $true) & (noeltsimpempty = $true) & (setunionI = $true) & (setadjoinIL = $true) & (emptyI = $true) & (prop2setE = $true) & (dsetconstrER = $true) & (descrp = $true) & (omega0Ax = $true) & (setbeta = $true) & (exuE3e = $true) & (emptysetimpfalse = $true)),
% 0.23/0.32 inference(flattening,[],[f149])).
% 0.23/0.32 thf(f322,plain,(
% 0.23/0.32 (powersetAx = $true) & (setunionE = $true) & (emptyInPowerset = $true) & (setunionAx = $true) & (dsetconstrEL = $true) & (replAx = $true) & (setadjoinAx = $true) & (emptyinunitempty = $true) & (powersetI = $true) & (foundationAx = $true) & ? [X0 : ($i > $o)] : (($true = ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) & ! [X1 : $i] : ? [X2 : $i] : (((X1 != X2) | (((X0 @ X2)) != $true)) & ((X1 = X2) | (((X0 @ X2)) = $true)))) & (setextAx = $true) & (exuE1 = $true) & (subPowSU = $true) & (setext = $true) & (nonemptyE1 = $true) & (setoftrueEq = $true) & (setadjoinOr = $true) & (dsetconstrI = $true) & (powersetE = $true) & (nonemptyI = $true) & (setadjoinIR = $true) & (emptysetAx = $true) & (setadjoinE = $true) & (notinemptyset = $true) & (wellorderingAx = $true) & (omegaSAx = $true) & (emptyinPowerset = $true) & (omegaIndAx = $true) & (emptysetE = $true) & (nonemptyI1 = $true) & (noeltsimpempty = $true) & (setunionI = $true) & (setadjoinIL = $true) & (emptyI = $true) & (prop2setE = $true) & (dsetconstrER = $true) & (descrp = $true) & (omega0Ax = $true) & (setbeta = $true) & (exuE3e = $true) & (emptysetimpfalse = $true)),
% 0.23/0.32 inference(nnf_transformation,[],[f150])).
% 0.23/0.32 thf(f323,plain,(
% 0.23/0.32 (powersetAx = $true) & (setunionE = $true) & (emptyInPowerset = $true) & (setunionAx = $true) & (dsetconstrEL = $true) & (replAx = $true) & (setadjoinAx = $true) & (emptyinunitempty = $true) & (powersetI = $true) & (foundationAx = $true) & (($true = ((exu @ (^[Y0 : $i]: (sK123 @ Y0))))) & ! [X1 : $i] : (((((sK124 @ X1)) != X1) | ($true != ((sK123 @ (sK124 @ X1))))) & ((((sK124 @ X1)) = X1) | ($true = ((sK123 @ (sK124 @ X1))))))) & (setextAx = $true) & (exuE1 = $true) & (subPowSU = $true) & (setext = $true) & (nonemptyE1 = $true) & (setoftrueEq = $true) & (setadjoinOr = $true) & (dsetconstrI = $true) & (powersetE = $true) & (nonemptyI = $true) & (setadjoinIR = $true) & (emptysetAx = $true) & (setadjoinE = $true) & (notinemptyset = $true) & (wellorderingAx = $true) & (omegaSAx = $true) & (emptyinPowerset = $true) & (omegaIndAx = $true) & (emptysetE = $true) & (nonemptyI1 = $true) & (noeltsimpempty = $true) & (setunionI = $true) & (setadjoinIL = $true) & (emptyI = $true) & (prop2setE = $true) & (dsetconstrER = $true) & (descrp = $true) & (omega0Ax = $true) & (setbeta = $true) & (exuE3e = $true) & (emptysetimpfalse = $true)),
% 0.23/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK123,vAPP]),skolemize(X0,sK123),skolemize(X6,sK16 @ X4)],[f322])).
% 0.23/0.32 thf(f446,plain,(
% 0.23/0.32 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 0.23/0.32 inference(cnf_transformation,[],[f48])).
% 0.23/0.32 thf(f548,plain,(
% 0.23/0.32 ( ! [X1 : $i] : (($true = ((sK123 @ (sK124 @ X1)))) | (((sK124 @ X1)) = X1)) )),
% 0.23/0.32 inference(cnf_transformation,[],[f323])).
% 0.23/0.32 thf(f549,plain,(
% 0.23/0.32 ( ! [X1 : $i] : (($true != ((sK123 @ (sK124 @ X1)))) | (((sK124 @ X1)) != X1)) )),
% 0.23/0.32 inference(cnf_transformation,[],[f323])).
% 0.23/0.32 thf(f550,plain,(
% 0.23/0.32 ($true = ((exu @ (^[Y0 : $i]: (sK123 @ Y0)))))),
% 0.23/0.32 inference(cnf_transformation,[],[f323])).
% 0.23/0.32 thf(f718,plain,(
% 0.23/0.32 ($true = (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))) @ (^[Y0 : $i]: (sK123 @ Y0)))))),
% 0.23/0.32 inference(definition_unfolding,[],[f550,f446])).
% 0.23/0.32 thf(f768,plain,(
% 0.23/0.32 ($true = ((?? @ $i @ (^[Y0 : $i]: ((sK123 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK123 @ Y1) => (Y0 = Y1)))))))))),
% 0.23/0.32 inference(beta-eta_normalization,[],[f718])).
% 0.23/0.32 thf(f769,plain,(
% 0.23/0.32 ($true = (((^[Y0 : $i]: ((sK123 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK123 @ Y1) => (Y0 = Y1)))))) @ sK127)))),
% 0.23/0.32 inference(sigma_proxy_clausification,[],[f768])).
% 0.23/0.32 thf(f770,plain,(
% 0.23/0.32 ($true = (((sK123 @ sK127) & (!! @ $i @ (^[Y0 : $i]: ((sK123 @ Y0) => (sK127 = Y0)))))))),
% 0.23/0.32 inference(beta-eta_normalization,[],[f769])).
% 0.23/0.32 thf(f771,plain,(
% 0.23/0.32 ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK123 @ Y0) => (sK127 = Y0))))))),
% 0.23/0.32 inference(and_proxy_clausification,[],[f770])).
% 0.23/0.32 thf(f772,plain,(
% 0.23/0.32 ($true = ((sK123 @ sK127)))),
% 0.23/0.32 inference(and_proxy_clausification,[],[f770])).
% 0.23/0.32 thf(f773,plain,(
% 0.23/0.32 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((sK123 @ Y0) => (sK127 = Y0))) @ X1)))) )),
% 0.23/0.32 inference(pi_proxy_clausification,[],[f771])).
% 0.23/0.32 thf(f774,plain,(
% 0.23/0.32 ( ! [X1 : $i] : (($true = (((sK123 @ X1) => (sK127 = X1))))) )),
% 0.23/0.32 inference(beta-eta_normalization,[],[f773])).
% 0.23/0.32 thf(f775,plain,(
% 0.23/0.32 ( ! [X1 : $i] : (($false = ((sK123 @ X1))) | ($true = ((sK127 = X1)))) )),
% 0.23/0.32 inference(imp_proxy_clausification,[],[f774])).
% 0.23/0.32 thf(f776,plain,(
% 0.23/0.32 ( ! [X1 : $i] : (($false = ((sK123 @ X1))) | (sK127 = X1)) )),
% 0.23/0.32 inference(equality_proxy_clausification,[],[f775])).
% 0.23/0.32 thf(f966,plain,(
% 0.23/0.32 ( ! [X0 : $i] : (($true = $false) | (((sK124 @ X0)) = X0) | (((sK124 @ X0)) = sK127)) )),
% 0.23/0.32 inference(constrained_superposition,[],[f548,f776])).
% 0.23/0.32 thf(f968,plain,(
% 0.23/0.32 ( ! [X0 : $i] : ((((sK124 @ X0)) = sK127) | (((sK124 @ X0)) = X0)) )),
% 0.23/0.32 inference(trivial_inequality_removal,[],[f966])).
% 0.23/0.32 thf(f971,plain,(
% 0.23/0.32 ( ! [X0 : $i] : ((sK127 != X0) | (((sK124 @ X0)) = X0)) )),
% 0.23/0.32 inference(equality_factoring,[],[f968])).
% 0.23/0.32 thf(f973,plain,(
% 0.23/0.32 (sK127 = ((sK124 @ sK127))) | (sK127 != sK127)),
% 0.23/0.32 inference(imitation,[],[f971])).
% 0.23/0.32 thf(f975,plain,(
% 0.23/0.32 (sK127 = ((sK124 @ sK127)))),
% 0.23/0.32 inference(trivial_inequality_removal,[],[f973])).
% 0.23/0.32 thf(f981,plain,(
% 0.23/0.32 ($true != ((sK123 @ sK127))) | (sK127 != sK127)),
% 0.23/0.32 inference(constrained_superposition,[],[f549,f975])).
% 0.23/0.32 thf(f985,plain,(
% 0.23/0.32 ($true != ((sK123 @ sK127)))),
% 0.23/0.32 inference(trivial_inequality_removal,[],[f981])).
% 0.23/0.32 thf(f986,plain,(
% 0.23/0.32 $false),
% 0.23/0.32 inference(forward_subsumption_resolution,[],[f985,f772])).
% 0.23/0.32 % SZS output end Proof for theBenchmark
% 0.23/0.32 % (1694994)------------------------------
% 0.23/0.32 % (1694994)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (1694994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (1694994)CaDiCaL version: 2.1.3
% 0.23/0.32 % (1694994)Termination reason: Refutation
% 0.23/0.32 % (1694994)Time elapsed: 0.021 s
% 0.23/0.32 % (1694994)Peak memory usage: 13 MB
% 0.23/0.32 % (1694994)Instructions burned: 52 (million)
% 0.23/0.32 % (1694983)Success in time 0.061 s
% 0.23/0.32 % Vampire exiting
%------------------------------------------------------------------------------