%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU523^1 : 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 : n012.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 0.08s 0.19s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU523^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 13:47:34 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.13 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
% 0.08/0.19 % (127825)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.19 % (127837)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.19 % (127837)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
% 0.08/0.19 % (127833)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=470464153:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.08/0.19 % (127834)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=2098559200: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)
% 0.08/0.19 % (127831)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3340522551:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.19 % (127835)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1620105893:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.08/0.19 % (127832)lrs+10_16_si=on:nwc=1.5:random_seed=1542619227:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.19 % (127837)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=1115233223:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.08/0.19 % (127836)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1974815985:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.19 % (127833)Instruction limit reached!
% 0.08/0.19 % (127833)------------------------------
% 0.08/0.19 % (127833)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.19 % (127833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.19 % (127833)CaDiCaL version: 2.1.3
% 0.08/0.19 % (127833)Termination reason: Instruction limit
% 0.08/0.19 % (127833)Termination phase: shuffling
% 0.08/0.19 % (127833)Time elapsed: 0.001 s
% 0.08/0.19 % (127833)Peak memory usage: 9 MB
% 0.08/0.19 % (127833)Instructions burned: 4 (million)
% 0.08/0.19 % (127832)Instruction limit reached!
% 0.08/0.19 % (127832)------------------------------
% 0.08/0.19 % (127832)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.19 % (127832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.19 % (127832)CaDiCaL version: 2.1.3
% 0.08/0.19 % (127832)Termination reason: Instruction limit
% 0.08/0.19 % (127832)Termination phase: Property scanning
% 0.08/0.19 % (127832)Time elapsed: 0.004 s
% 0.08/0.19 % (127832)Peak memory usage: 10 MB
% 0.08/0.19 % (127832)Instructions burned: 18 (million)
% 0.08/0.19 % (127835)Instruction limit reached!
% 0.08/0.19 % (127835)------------------------------
% 0.08/0.19 % (127835)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.19 % (127835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.19 % (127835)CaDiCaL version: 2.1.3
% 0.08/0.19 % (127835)Termination reason: Instruction limit
% 0.08/0.19 % (127835)Termination phase: Property scanning
% 0.08/0.19 % (127835)Time elapsed: 0.006 s
% 0.08/0.19 % (127835)Peak memory usage: 11 MB
% 0.08/0.19 % (127835)Instructions burned: 26 (million)
% 0.08/0.19 % (127845)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3593663912:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.08/0.19 % (127845)Instruction limit reached!
% 0.08/0.19 % (127845)------------------------------
% 0.08/0.19 % (127845)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.19 % (127845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.19 % (127845)CaDiCaL version: 2.1.3
% 0.08/0.19 % (127845)Termination reason: Instruction limit
% 0.08/0.19 % (127845)Termination phase: shuffling
% 0.08/0.19 % (127845)Time elapsed: 0.001 s
% 0.08/0.19 % (127845)Peak memory usage: 9 MB
% 0.08/0.19 % (127845)Instructions burned: 4 (million)
% 0.08/0.19 % (127847)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.08/0.19 % (127846)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1986603771:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.08/0.19 % (127847)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2791261609:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.08/0.19 % (127846)Instruction limit reached!
% 0.08/0.19 % (127846)------------------------------
% 0.08/0.19 % (127846)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.19 % (127846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.19 % (127846)CaDiCaL version: 2.1.3
% 0.08/0.19 % (127846)Termination reason: Instruction limit
% 0.08/0.19 % (127846)Termination phase: Property scanning
% 0.08/0.19 % (127846)Time elapsed: 0.002 s
% 0.08/0.19 % (127846)Peak memory usage: 10 MB
% 0.08/0.19 % (127846)Instructions burned: 8 (million)
% 0.08/0.19 % (127847)Instruction limit reached!
% 0.08/0.19 % (127847)------------------------------
% 0.08/0.19 % (127847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.19 % (127847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.19 % (127847)CaDiCaL version: 2.1.3
% 0.08/0.19 % (127847)Termination reason: Instruction limit
% 0.08/0.19 % (127847)Termination phase: Property scanning
% 0.08/0.19 % (127847)Time elapsed: 0.002 s
% 0.08/0.19 % (127847)Peak memory usage: 9 MB
% 0.08/0.19 % (127847)Instructions burned: 9 (million)
% 0.08/0.19 % (127836) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-127825-127836"...
% 0.08/0.19 % (127836)...printing done.
% 0.08/0.19 % (127836)Refutation found. Thanks to Tanya!
% 0.08/0.19 % SZS status Theorem for theBenchmark
% 0.08/0.19 % SZS output start Proof for theBenchmark
% 0.08/0.19 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.19 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.08/0.19 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 0.08/0.19 thf(func_def_3, type, setextAx: $o).
% 0.08/0.19 thf(func_def_5, type, emptysetAx: $o).
% 0.08/0.19 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 0.08/0.19 thf(func_def_7, type, setadjoinAx: $o).
% 0.08/0.19 thf(func_def_8, type, powerset: ($i > $i)).
% 0.08/0.19 thf(func_def_9, type, powersetAx: $o).
% 0.08/0.19 thf(func_def_10, type, setunion: ($i > $i)).
% 0.08/0.19 thf(func_def_11, type, setunionAx: $o).
% 0.08/0.19 thf(func_def_13, type, omega0Ax: $o).
% 0.08/0.19 thf(func_def_14, type, omegaSAx: $o).
% 0.08/0.19 thf(func_def_15, type, omegaIndAx: $o).
% 0.08/0.19 thf(func_def_16, type, replAx: $o).
% 0.08/0.19 thf(func_def_17, type, foundationAx: $o).
% 0.08/0.19 thf(func_def_18, type, wellorderingAx: $o).
% 0.08/0.19 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 0.08/0.19 thf(func_def_20, type, descrp: $o).
% 0.08/0.19 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.08/0.19 thf(func_def_22, type, dsetconstrI: $o).
% 0.08/0.19 thf(func_def_23, type, dsetconstrEL: $o).
% 0.08/0.19 thf(func_def_24, type, dsetconstrER: $o).
% 0.08/0.19 thf(func_def_25, type, exuE1: $o).
% 0.08/0.19 thf(func_def_26, type, prop2set: ($o > $i)).
% 0.08/0.19 thf(func_def_27, type, prop2setE: $o).
% 0.08/0.19 thf(func_def_28, type, emptysetE: $o).
% 0.08/0.19 thf(func_def_29, type, emptysetimpfalse: $o).
% 0.08/0.19 thf(func_def_30, type, notinemptyset: $o).
% 0.08/0.19 thf(func_def_31, type, exuE3e: $o).
% 0.08/0.19 thf(func_def_32, type, setext: $o).
% 0.08/0.19 thf(func_def_33, type, emptyI: $o).
% 0.08/0.19 thf(func_def_34, type, noeltsimpempty: $o).
% 0.08/0.19 thf(func_def_35, type, setbeta: $o).
% 0.08/0.19 thf(func_def_36, type, nonempty: ($i > $o)).
% 0.08/0.19 thf(func_def_37, type, nonemptyE1: $o).
% 0.08/0.19 thf(func_def_38, type, nonemptyI: $o).
% 0.08/0.19 thf(func_def_39, type, nonemptyI1: $o).
% 0.08/0.19 thf(func_def_40, type, setadjoinIL: $o).
% 0.08/0.19 thf(func_def_41, type, emptyinunitempty: $o).
% 0.08/0.19 thf(func_def_42, type, setadjoinIR: $o).
% 0.08/0.19 thf(func_def_43, type, setadjoinE: $o).
% 0.08/0.19 thf(func_def_44, type, setadjoinOr: $o).
% 0.08/0.19 thf(func_def_45, type, setoftrueEq: $o).
% 0.08/0.19 thf(func_def_46, type, powersetI: $o).
% 0.08/0.19 thf(func_def_47, type, emptyinPowerset: $o).
% 0.08/0.19 thf(func_def_48, type, emptyInPowerset: $o).
% 0.08/0.19 thf(func_def_49, type, powersetE: $o).
% 0.08/0.19 thf(func_def_50, type, setunionI: $o).
% 0.08/0.19 thf(func_def_53, type, db0: !>[X0: $tType]:(X0)).
% 0.08/0.19 thf(func_def_54, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.08/0.19 thf(func_def_55, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.08/0.19 thf(func_def_56, type, vNOT: ($o > $o)).
% 0.08/0.19 thf(func_def_57, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.08/0.19 thf(func_def_58, type, vAND: ($o > $o > $o)).
% 0.08/0.19 thf(func_def_59, type, db1: !>[X0: $tType]:(X0)).
% 0.08/0.19 thf(func_def_60, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.08/0.19 thf(func_def_61, type, vIMP: ($o > $o > $o)).
% 0.08/0.19 thf(func_def_62, type, db2: !>[X0: $tType]:(X0)).
% 0.08/0.19 thf(func_def_63, type, sP0: ($i > $i > $o)).
% 0.08/0.19 thf(func_def_64, type, sP1: ($i > $o)).
% 0.08/0.19 thf(func_def_65, type, sP2: ($i > $i > $o)).
% 0.08/0.19 thf(func_def_66, type, sP3: ($i > $i > $o)).
% 0.08/0.19 thf(func_def_67, type, sP4: $o).
% 0.08/0.19 thf(func_def_71, type, sK8: ($i > $i > $i)).
% 0.08/0.19 thf(func_def_72, type, sK9: ($i > $o)).
% 0.08/0.19 thf(func_def_79, type, sK16: ($i > $i > $i)).
% 0.08/0.19 thf(func_def_80, type, sK17: ($i > $i > $i)).
% 0.08/0.19 thf(func_def_83, type, sK20: ($i > $i > $i)).
% 0.08/0.19 thf(func_def_84, type, sK21: ($i > $i > $i)).
% 0.08/0.19 thf(func_def_85, type, sK22: ($i > $i > $i)).
% 0.08/0.19 thf(func_def_86, type, sK23: ($i > $i > $i)).
% 0.08/0.19 thf(func_def_87, type, sK24: ($i > $i > $i > $i)).
% 0.08/0.19 thf(func_def_88, type, sK25: ($i > $i)).
% 0.08/0.19 thf(func_def_89, type, sK26: ($i > $i)).
% 0.08/0.19 thf(func_def_90, type, sK27: ($i > $i)).
% 0.08/0.19 thf(func_def_91, type, sK28: ($i > $i)).
% 0.08/0.19 thf(func_def_92, type, sK29: ($i > $i > $i)).
% 0.08/0.19 thf(func_def_93, type, sK30: ($i > $i > $i > $i)).
% 0.08/0.19 thf(func_def_94, type, sK31: ($i > $i > $i > $i)).
% 0.08/0.19 thf(func_def_95, type, sK32: ($i > $i > $i)).
% 0.08/0.19 thf(func_def_96, type, sK33: ($i > $i > $i)).
% 0.08/0.19 thf(func_def_97, type, sK34: ($i > $i)).
% 0.08/0.19 thf(func_def_98, type, sK35: ($i > $i > $i)).
% 0.08/0.19 thf(func_def_100, type, sK37: ($i > $i)).
% 0.08/0.19 thf(func_def_101, type, sK38: ($i > $i)).
% 0.08/0.19 thf(func_def_108, type, sK45: ($i > $i > $o)).
% 0.08/0.19 thf(func_def_110, type, sK47: ($i > $i)).
% 0.08/0.19 thf(func_def_111, type, sK48: ($i > $i)).
% 0.08/0.19 thf(func_def_112, type, sK49: ($i > ($i > $i > $o) > $i)).
% 0.08/0.19 thf(func_def_113, type, sK50: ($i > $i > ($i > $i > $o) > $i)).
% 0.08/0.19 thf(func_def_114, type, sK51: ($i > ($i > $i > $o) > $i)).
% 0.08/0.19 thf(func_def_117, type, sK54: ($i > $i)).
% 0.08/0.19 thf(func_def_118, type, sK55: ($i > $o)).
% 0.08/0.19 thf(func_def_119, type, sK56: (($i > $o) > $i)).
% 0.08/0.19 thf(func_def_121, type, sK58: ($i > $i)).
% 0.08/0.19 thf(func_def_123, type, sK60: $o).
% 0.08/0.19 thf(func_def_126, type, sK63: ($i > $i > $i)).
% 0.08/0.19 thf(func_def_127, type, sK64: ($i > $o)).
% 0.08/0.19 thf(func_def_131, type, sK68: ($i > $i)).
% 0.08/0.19 thf(func_def_133, type, sK70: ($i > $i)).
% 0.08/0.19 thf(func_def_136, type, sK73: ($i > $i)).
% 0.08/0.19 thf(func_def_139, type, sK76: ($i > $o)).
% 0.08/0.19 thf(func_def_146, type, sK83: $o).
% 0.08/0.19 thf(func_def_157, type, sK94: ($i > $o)).
% 0.08/0.19 thf(func_def_159, type, sK96: ($i > $o)).
% 0.08/0.19 thf(func_def_165, type, sK102: $o).
% 0.08/0.19 thf(func_def_166, type, sK103: ($i > $i)).
% 0.08/0.19 thf(func_def_169, type, sK106: $o).
% 0.08/0.19 thf(func_def_172, type, sK109: ($i > $i > $i)).
% 0.08/0.19 thf(func_def_173, type, sK110: (($i > $o) > $i)).
% 0.08/0.19 thf(func_def_174, type, sK111: ($i > $o)).
% 0.08/0.19 thf(func_def_175, type, sK112: ($i > $i)).
% 0.08/0.19 thf(func_def_178, type, sK115: ($i > $o)).
% 0.08/0.19 thf(func_def_182, type, sK119: ($i > $i > $i)).
% 0.08/0.19 thf(func_def_183, type, sK120: (($i > $o) > $i > $i)).
% 0.08/0.19 thf(func_def_184, type, sK121: ($i > ($i > $o) > $i)).
% 0.08/0.19 thf(func_def_185, type, sK122: ($i > ($i > $i > $o) > $i > $i)).
% 0.08/0.19 thf(func_def_186, type, sK123: ($i > ($i > $o) > $i)).
% 0.08/0.19 thf(func_def_187, type, sK124: ($i > ($i > $i > $o) > $i > $i)).
% 0.08/0.19 thf(func_def_188, type, sK125: ($i > $i)).
% 0.08/0.19 thf(func_def_189, type, sK126: ($i > ($i > $i > $o) > $i > $i)).
% 0.08/0.19 thf(func_def_190, type, sK127: ($i > ($i > $o) > $i)).
% 0.08/0.19 thf(f6,axiom,(
% 0.08/0.19 (setunionAx = ! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((in @ X1 @ X2) & (in @ X2 @ X0)) <=> (in @ X1 @ (setunion @ X0))))),
% 0.08/0.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionAx)).
% 0.08/0.19 thf(f43,conjecture,(
% 0.08/0.19 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 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2))))))))))))))))))))))))))))))))))))))))),
% 0.08/0.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE)).
% 0.08/0.19 thf(f44,negated_conjecture,(
% 0.08/0.19 ~(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 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2)))))))))))))))))))))))))))))))))))))))))),
% 0.08/0.19 inference(negated_conjecture,[status(cth)],[f43])).
% 0.08/0.19 thf(f90,plain,(
% 0.08/0.19 (setunionAx = ! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((in @ X0 @ X2) & (in @ X2 @ X1)) <=> (in @ X0 @ (setunion @ X1))))),
% 0.08/0.19 inference(rectify,[],[f6])).
% 0.08/0.19 thf(f91,plain,(
% 0.08/0.19 (setunionAx = $true) <=> ! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X0 @ X2)) = $true) & (((in @ X2 @ X1)) = $true)) <=> (((in @ X0 @ (setunion @ X1))) = $true))),
% 0.08/0.19 inference(fool_elimination,[],[f90])).
% 0.08/0.19 thf(f92,plain,(
% 0.08/0.19 ~(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 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2)))))))))))))))))))))))))))))))))))))))))),
% 0.08/0.19 inference(rectify,[],[f44])).
% 0.08/0.19 thf(f93,plain,(
% 0.08/0.19 ~((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) => ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (setunion @ X0))) = $true) => ! [X2 : $o] : (! [X3 : $i] : ((((in @ X1 @ X3)) = $true) => ((((in @ X3 @ X0)) = $true) => ($true = X2))) => ($true = X2))))))))))))))))))))))))))))))))))))))))))),
% 0.08/0.19 inference(fool_elimination,[],[f92])).
% 0.08/0.19 thf(f139,plain,(
% 0.08/0.19 ((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (? [X2 : $o] : (($true != X2) & ! [X3 : $i] : ((($true = X2) | (((in @ X3 @ X0)) != $true)) | (((in @ X1 @ X3)) != $true))) & (((in @ X1 @ (setunion @ X0))) = $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)),
% 0.08/0.19 inference(ennf_transformation,[],[f93])).
% 0.08/0.19 thf(f140,plain,(
% 0.08/0.19 (omega0Ax = $true) & (descrp = $true) & (dsetconstrI = $true) & (setextAx = $true) & (exuE1 = $true) & (emptysetAx = $true) & (foundationAx = $true) & (emptyinunitempty = $true) & (prop2setE = $true) & (powersetAx = $true) & (dsetconstrEL = $true) & ? [X0 : $i,X1 : $i] : ((((in @ X1 @ (setunion @ X0))) = $true) & ? [X2 : $o] : (! [X3 : $i] : ((((in @ X1 @ X3)) != $true) | ($true = X2) | (((in @ X3 @ X0)) != $true)) & ($true != X2))) & (omegaIndAx = $true) & (nonemptyI = $true) & (setext = $true) & (setunionAx = $true) & (setoftrueEq = $true) & (exuE3e = $true) & (replAx = $true) & (emptyinPowerset = $true) & (omegaSAx = $true) & (powersetE = $true) & (dsetconstrER = $true) & (setadjoinIL = $true) & (setunionI = $true) & (emptyInPowerset = $true) & (noeltsimpempty = $true) & (emptyI = $true) & (setadjoinOr = $true) & (nonemptyI1 = $true) & (wellorderingAx = $true) & (emptysetimpfalse = $true) & (setadjoinIR = $true) & (powersetI = $true) & (notinemptyset = $true) & (emptysetE = $true) & (setbeta = $true) & (setadjoinAx = $true) & (nonemptyE1 = $true) & (setadjoinE = $true)),
% 0.08/0.19 inference(flattening,[],[f139])).
% 0.08/0.19 thf(f260,plain,(
% 0.08/0.19 (omega0Ax = $true) & (descrp = $true) & (dsetconstrI = $true) & (setextAx = $true) & (exuE1 = $true) & (emptysetAx = $true) & (foundationAx = $true) & (emptyinunitempty = $true) & (prop2setE = $true) & (powersetAx = $true) & (dsetconstrEL = $true) & ((((in @ sK82 @ (setunion @ sK81))) = $true) & (! [X3 : $i] : ((((in @ sK82 @ X3)) != $true) | ($true = sK83) | ($true != ((in @ X3 @ sK81)))) & ($true != sK83))) & (omegaIndAx = $true) & (nonemptyI = $true) & (setext = $true) & (setunionAx = $true) & (setoftrueEq = $true) & (exuE3e = $true) & (replAx = $true) & (emptyinPowerset = $true) & (omegaSAx = $true) & (powersetE = $true) & (dsetconstrER = $true) & (setadjoinIL = $true) & (setunionI = $true) & (emptyInPowerset = $true) & (noeltsimpempty = $true) & (emptyI = $true) & (setadjoinOr = $true) & (nonemptyI1 = $true) & (wellorderingAx = $true) & (emptysetimpfalse = $true) & (setadjoinIR = $true) & (powersetI = $true) & (notinemptyset = $true) & (emptysetE = $true) & (setbeta = $true) & (setadjoinAx = $true) & (nonemptyE1 = $true) & (setadjoinE = $true)),
% 0.08/0.19 inference(skolemize,[status(esa),new_symbols(skolem,[sK81,sK82,sK83]),skolemize(X0,sK81),skolemize(X1,sK82),skolemize(X2,sK83)],[f140])).
% 0.08/0.19 thf(f304,plain,(
% 0.08/0.19 ((setunionAx = $true) | ? [X1 : $i,X0 : $i] : (((((in @ X0 @ (setunion @ X1))) != $true) | ! [X2 : $i] : ((((in @ X0 @ X2)) != $true) | (((in @ X2 @ X1)) != $true))) & ((((in @ X0 @ (setunion @ X1))) = $true) | ? [X2 : $i] : ((((in @ X0 @ X2)) = $true) & (((in @ X2 @ X1)) = $true))))) & (! [X1 : $i,X0 : $i] : ((? [X2 : $i] : ((((in @ X0 @ X2)) = $true) & (((in @ X2 @ X1)) = $true)) | (((in @ X0 @ (setunion @ X1))) != $true)) & ((((in @ X0 @ (setunion @ X1))) = $true) | ! [X2 : $i] : ((((in @ X0 @ X2)) != $true) | (((in @ X2 @ X1)) != $true)))) | (setunionAx != $true))),
% 0.08/0.19 inference(nnf_transformation,[],[f91])).
% 0.08/0.19 thf(f305,plain,(
% 0.08/0.19 ((setunionAx = $true) | ? [X0 : $i,X1 : $i] : (((((in @ X1 @ (setunion @ X0))) != $true) | ! [X2 : $i] : ((((in @ X1 @ X2)) != $true) | (((in @ X2 @ X0)) != $true))) & ((((in @ X1 @ (setunion @ X0))) = $true) | ? [X3 : $i] : ((((in @ X1 @ X3)) = $true) & (((in @ X3 @ X0)) = $true))))) & (! [X4 : $i,X5 : $i] : ((? [X6 : $i] : (($true = ((in @ X5 @ X6))) & (((in @ X6 @ X4)) = $true)) | ($true != ((in @ X5 @ (setunion @ X4))))) & (($true = ((in @ X5 @ (setunion @ X4)))) | ! [X7 : $i] : (($true != ((in @ X5 @ X7))) | (((in @ X7 @ X4)) != $true)))) | (setunionAx != $true))),
% 0.08/0.19 inference(rectify,[],[f304])).
% 0.08/0.19 thf(f306,plain,(
% 0.08/0.19 ((setunionAx = $true) | (((((in @ sK117 @ (setunion @ sK116))) != $true) | ! [X2 : $i] : (($true != ((in @ sK117 @ X2))) | (((in @ X2 @ sK116)) != $true))) & ((((in @ sK117 @ (setunion @ sK116))) = $true) | ((((in @ sK117 @ sK118)) = $true) & ($true = ((in @ sK118 @ sK116))))))) & (! [X4 : $i,X5 : $i] : (((($true = ((in @ X5 @ (sK119 @ X5 @ X4)))) & ($true = ((in @ (sK119 @ X5 @ X4) @ X4)))) | ($true != ((in @ X5 @ (setunion @ X4))))) & (($true = ((in @ X5 @ (setunion @ X4)))) | ! [X7 : $i] : (($true != ((in @ X5 @ X7))) | (((in @ X7 @ X4)) != $true)))) | (setunionAx != $true))),
% 0.08/0.19 inference(skolemize,[status(esa),new_symbols(skolem,[sK116,sK117,sK118,vAPP]),skolemize(X0,sK116),skolemize(X1,sK117),skolemize(X3,sK118),skolemize(X6,sK8 @ X5 @ X4)],[f305])).
% 0.08/0.19 thf(f458,plain,(
% 0.08/0.19 (setunionAx = $true)),
% 0.08/0.19 inference(cnf_transformation,[],[f260])).
% 0.08/0.19 thf(f462,plain,(
% 0.08/0.19 ($true != sK83)),
% 0.08/0.19 inference(cnf_transformation,[],[f260])).
% 0.08/0.19 thf(f463,plain,(
% 0.08/0.19 ( ! [X3 : $i] : ((((in @ sK82 @ X3)) != $true) | ($true = sK83) | ($true != ((in @ X3 @ sK81)))) )),
% 0.08/0.19 inference(cnf_transformation,[],[f260])).
% 0.08/0.19 thf(f464,plain,(
% 0.08/0.19 (((in @ sK82 @ (setunion @ sK81))) = $true)),
% 0.08/0.19 inference(cnf_transformation,[],[f260])).
% 0.08/0.19 thf(f528,plain,(
% 0.08/0.19 ( ! [X4 : $i,X5 : $i] : (($true = ((in @ (sK119 @ X5 @ X4) @ X4))) | ($true != ((in @ X5 @ (setunion @ X4)))) | (setunionAx != $true)) )),
% 0.08/0.19 inference(cnf_transformation,[],[f306])).
% 0.08/0.19 thf(f529,plain,(
% 0.08/0.19 ( ! [X4 : $i,X5 : $i] : (($true = ((in @ X5 @ (sK119 @ X5 @ X4)))) | ($true != ((in @ X5 @ (setunion @ X4)))) | (setunionAx != $true)) )),
% 0.08/0.19 inference(cnf_transformation,[],[f306])).
% 0.08/0.19 thf(f678,plain,(
% 0.08/0.19 ( ! [X4 : $i,X5 : $i] : (($true != ((in @ X5 @ (setunion @ X4)))) | ($true = ((in @ X5 @ (sK119 @ X5 @ X4)))) | ($true != $true)) )),
% 0.08/0.19 inference(definition_unfolding,[],[f529,f458])).
% 0.08/0.19 thf(f679,plain,(
% 0.08/0.19 ( ! [X4 : $i,X5 : $i] : (($true = ((in @ (sK119 @ X5 @ X4) @ X4))) | ($true != $true) | ($true != ((in @ X5 @ (setunion @ X4))))) )),
% 0.08/0.19 inference(definition_unfolding,[],[f528,f458])).
% 0.08/0.19 thf(f702,plain,(
% 0.08/0.19 ( ! [X4 : $i,X5 : $i] : (($true != ((in @ X5 @ (setunion @ X4)))) | ($true = ((in @ X5 @ (sK119 @ X5 @ X4))))) )),
% 0.08/0.19 inference(trivial_inequality_removal,[],[f678])).
% 0.08/0.19 thf(f721,plain,(
% 0.08/0.19 ( ! [X4 : $i,X5 : $i] : (($true != ((in @ X5 @ (setunion @ X4)))) | ($true = ((in @ (sK119 @ X5 @ X4) @ X4)))) )),
% 0.08/0.19 inference(trivial_inequality_removal,[],[f679])).
% 0.08/0.19 thf(f843,definition,(
% 0.08/0.19 spl128_1 <=> ($true = sK83)),
% 0.08/0.19 introduced(definition,[new_symbols(definition,[spl128_1])],[avatar_definition])).
% 0.08/0.19 thf(f844,plain,(
% 0.08/0.19 ($true = sK83) | ~spl128_1),
% 0.08/0.19 inference(avatar_component_clause,[],[f843])).
% 0.08/0.19 thf(f846,definition,(
% 0.08/0.19 spl128_2 <=> ! [X3 : $i] : ((((in @ sK82 @ X3)) != $true) | ($true != ((in @ X3 @ sK81))))),
% 0.08/0.19 introduced(definition,[new_symbols(definition,[spl128_2])],[avatar_definition])).
% 0.08/0.19 thf(f847,plain,(
% 0.08/0.19 ( ! [X3 : $i] : (($true != ((in @ X3 @ sK81))) | (((in @ sK82 @ X3)) != $true)) ) | ~spl128_2),
% 0.08/0.19 inference(avatar_component_clause,[],[f846])).
% 0.08/0.19 thf(f848,plain,(
% 0.08/0.19 spl128_1 | spl128_2),
% 0.08/0.19 inference(avatar_split_clause,[],[f463,f846,f843])).
% 0.08/0.19 thf(f1055,plain,(
% 0.08/0.19 ($true != $true) | ($true = ((in @ sK82 @ (sK119 @ sK82 @ sK81))))),
% 0.08/0.19 inference(constrained_superposition,[],[f702,f464])).
% 0.08/0.19 thf(f1061,plain,(
% 0.08/0.19 ($true = ((in @ sK82 @ (sK119 @ sK82 @ sK81))))),
% 0.08/0.19 inference(trivial_inequality_removal,[],[f1055])).
% 0.08/0.19 thf(f1071,plain,(
% 0.08/0.19 ($true = ((in @ (sK119 @ sK82 @ sK81) @ sK81))) | ($true != $true)),
% 0.08/0.19 inference(constrained_superposition,[],[f721,f464])).
% 0.08/0.19 thf(f1079,plain,(
% 0.08/0.19 ($true = ((in @ (sK119 @ sK82 @ sK81) @ sK81)))),
% 0.08/0.19 inference(trivial_inequality_removal,[],[f1071])).
% 0.08/0.19 thf(f1084,plain,(
% 0.08/0.19 ($true != $true) | ($true != ((in @ sK82 @ (sK119 @ sK82 @ sK81)))) | ~spl128_2),
% 0.08/0.19 inference(constrained_superposition,[],[f847,f1079])).
% 0.08/0.19 thf(f1086,plain,(
% 0.08/0.19 ($true != ((in @ sK82 @ (sK119 @ sK82 @ sK81)))) | ~spl128_2),
% 0.08/0.19 inference(trivial_inequality_removal,[],[f1084])).
% 0.08/0.19 thf(f1089,plain,(
% 0.08/0.19 $false | ~spl128_2),
% 0.08/0.19 inference(forward_subsumption_resolution,[],[f1086,f1061])).
% 0.08/0.19 thf(f1090,plain,(
% 0.08/0.19 ~spl128_2),
% 0.08/0.19 inference(avatar_contradiction_clause,[],[f1089])).
% 0.08/0.19 thf(f1091,plain,(
% 0.08/0.19 $false | ~spl128_1),
% 0.08/0.19 inference(forward_subsumption_resolution,[],[f844,f462])).
% 0.08/0.19 thf(f1092,plain,(
% 0.08/0.19 ~spl128_1),
% 0.08/0.19 inference(avatar_contradiction_clause,[],[f1091])).
% 0.08/0.19 cnf(s1, plain, spl128_1 | spl128_2, inference(sat_conversion,[],[f848])).
% 0.08/0.19 cnf(s24, plain, ~spl128_2, inference(sat_conversion,[],[f1090])).
% 0.08/0.19 cnf(s25, plain, ~spl128_1, inference(sat_conversion,[],[f1092])).
% 0.08/0.19 cnf(s35, plain, $false, inference(rat,[],[s1,s24,s25])).
% 0.08/0.19 thf(f1093,plain,(
% 0.08/0.19 $false),
% 0.08/0.19 inference(avatar_sat_refutation,[],[s35])).
% 0.08/0.19 % SZS output end Proof for theBenchmark
% 0.08/0.19 % (127836)------------------------------
% 0.08/0.19 % (127836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.19 % (127836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.19 % (127836)CaDiCaL version: 2.1.3
% 0.08/0.19 % (127836)Termination reason: Refutation
% 0.08/0.19 % (127836)Time elapsed: 0.021 s
% 0.08/0.19 % (127836)Peak memory usage: 14 MB
% 0.08/0.19 % (127836)Instructions burned: 72 (million)
% 0.08/0.19 % (127825)Success in time 0.051 s
% 0.08/0.19 % Vampire exiting
%------------------------------------------------------------------------------