%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU526^1 : 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 : n003.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 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU526^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n003.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:49:59 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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
% 0.21/0.30 % (2528565)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (2528576)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.30 % (2528576)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
% 0.21/0.30 % (2528576)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=4102287174:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.30 % (2528572)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1022889893:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.30 % (2528574)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4100397114:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.30 % (2528570)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3246227382:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.30 % (2528571)lrs+10_16_si=on:nwc=1.5:random_seed=2499159375:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.30 % (2528575)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3373380126:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.30 % (2528573)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=289718642: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)
% 0.21/0.30 % (2528572)Instruction limit reached!
% 0.21/0.30 % (2528572)------------------------------
% 0.21/0.30 % (2528572)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (2528572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (2528572)CaDiCaL version: 2.1.3
% 0.21/0.30 % (2528572)Termination reason: Instruction limit
% 0.21/0.30 % (2528572)Termination phase: shuffling
% 0.21/0.30 % (2528572)Time elapsed: 0.002 s
% 0.21/0.30 % (2528572)Peak memory usage: 9 MB
% 0.21/0.30 % (2528572)Instructions burned: 4 (million)
% 0.21/0.30 % (2528571)Instruction limit reached!
% 0.21/0.30 % (2528571)------------------------------
% 0.21/0.30 % (2528571)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (2528571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (2528571)CaDiCaL version: 2.1.3
% 0.21/0.30 % (2528571)Termination reason: Instruction limit
% 0.21/0.30 % (2528571)Termination phase: Saturation
% 0.21/0.30 % (2528571)Time elapsed: 0.008 s
% 0.21/0.30 % (2528571)Peak memory usage: 11 MB
% 0.21/0.30 % (2528571)Instructions burned: 19 (million)
% 0.21/0.30 % (2528574)Instruction limit reached!
% 0.21/0.30 % (2528574)------------------------------
% 0.21/0.30 % (2528574)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (2528574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (2528574)CaDiCaL version: 2.1.3
% 0.21/0.30 % (2528574)Termination reason: Instruction limit
% 0.21/0.30 % (2528574)Termination phase: Property scanning
% 0.21/0.30 % (2528574)Time elapsed: 0.012 s
% 0.21/0.30 % (2528574)Peak memory usage: 11 MB
% 0.21/0.30 % (2528574)Instructions burned: 26 (million)
% 0.21/0.30 % (2528584)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3347347151:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.30 % (2528584)Instruction limit reached!
% 0.21/0.30 % (2528584)------------------------------
% 0.21/0.30 % (2528584)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (2528584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (2528584)CaDiCaL version: 2.1.3
% 0.21/0.30 % (2528584)Termination reason: Instruction limit
% 0.21/0.30 % (2528584)Termination phase: shuffling
% 0.21/0.30 % (2528584)Time elapsed: 0.002 s
% 0.21/0.30 % (2528584)Peak memory usage: 9 MB
% 0.21/0.30 % (2528584)Instructions burned: 4 (million)
% 0.21/0.30 % (2528570) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2528565-2528570"...
% 0.21/0.30 % (2528586)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.30 % (2528570)...printing done.
% 0.21/0.30 % (2528585)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2228132752:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.30 % (2528570)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% 0.21/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.30 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.21/0.30 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 0.21/0.30 thf(func_def_3, type, setextAx: $o).
% 0.21/0.30 thf(func_def_5, type, emptysetAx: $o).
% 0.21/0.30 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 0.21/0.30 thf(func_def_7, type, setadjoinAx: $o).
% 0.21/0.30 thf(func_def_8, type, powerset: ($i > $i)).
% 0.21/0.30 thf(func_def_9, type, powersetAx: $o).
% 0.21/0.30 thf(func_def_10, type, setunion: ($i > $i)).
% 0.21/0.30 thf(func_def_11, type, setunionAx: $o).
% 0.21/0.30 thf(func_def_13, type, omega0Ax: $o).
% 0.21/0.30 thf(func_def_14, type, omegaSAx: $o).
% 0.21/0.30 thf(func_def_15, type, omegaIndAx: $o).
% 0.21/0.30 thf(func_def_16, type, replAx: $o).
% 0.21/0.30 thf(func_def_17, type, foundationAx: $o).
% 0.21/0.30 thf(func_def_18, type, wellorderingAx: $o).
% 0.21/0.30 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 0.21/0.30 thf(func_def_20, type, descrp: $o).
% 0.21/0.30 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.21/0.30 thf(func_def_22, type, dsetconstrI: $o).
% 0.21/0.30 thf(func_def_23, type, dsetconstrEL: $o).
% 0.21/0.30 thf(func_def_24, type, dsetconstrER: $o).
% 0.21/0.30 thf(func_def_25, type, exuE1: $o).
% 0.21/0.30 thf(func_def_26, type, prop2set: ($o > $i)).
% 0.21/0.30 thf(func_def_27, type, prop2setE: $o).
% 0.21/0.30 thf(func_def_28, type, emptysetE: $o).
% 0.21/0.30 thf(func_def_29, type, emptysetimpfalse: $o).
% 0.21/0.30 thf(func_def_30, type, notinemptyset: $o).
% 0.21/0.30 thf(func_def_31, type, exuE3e: $o).
% 0.21/0.30 thf(func_def_32, type, setext: $o).
% 0.21/0.30 thf(func_def_33, type, emptyI: $o).
% 0.21/0.30 thf(func_def_34, type, noeltsimpempty: $o).
% 0.21/0.30 thf(func_def_35, type, setbeta: $o).
% 0.21/0.30 thf(func_def_36, type, nonempty: ($i > $o)).
% 0.21/0.30 thf(func_def_37, type, nonemptyE1: $o).
% 0.21/0.30 thf(func_def_38, type, nonemptyI: $o).
% 0.21/0.30 thf(func_def_39, type, nonemptyI1: $o).
% 0.21/0.30 thf(func_def_40, type, setadjoinIL: $o).
% 0.21/0.30 thf(func_def_41, type, emptyinunitempty: $o).
% 0.21/0.30 thf(func_def_42, type, setadjoinIR: $o).
% 0.21/0.30 thf(func_def_43, type, setadjoinE: $o).
% 0.21/0.30 thf(func_def_44, type, setadjoinOr: $o).
% 0.21/0.30 thf(func_def_45, type, setoftrueEq: $o).
% 0.21/0.30 thf(func_def_46, type, powersetI: $o).
% 0.21/0.30 thf(func_def_47, type, emptyinPowerset: $o).
% 0.21/0.30 thf(func_def_48, type, emptyInPowerset: $o).
% 0.21/0.30 thf(func_def_49, type, powersetE: $o).
% 0.21/0.30 thf(func_def_50, type, setunionI: $o).
% 0.21/0.30 thf(func_def_51, type, setunionE: $o).
% 0.21/0.30 thf(func_def_52, type, subPowSU: $o).
% 0.21/0.30 thf(func_def_53, type, exuE2: $o).
% 0.21/0.30 thf(func_def_56, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.30 thf(func_def_57, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.30 thf(func_def_58, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.30 thf(func_def_59, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.30 thf(func_def_60, type, vAND: ($o > $o > $o)).
% 0.21/0.30 thf(func_def_61, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.30 thf(func_def_62, type, vIMP: ($o > $o > $o)).
% 0.21/0.30 thf(func_def_63, type, db2: !>[X0: $tType]:(X0)).
% 0.21/0.30 thf(func_def_64, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.30 thf(func_def_65, type, vNOT: ($o > $o)).
% 0.21/0.30 thf(func_def_66, type, sP0: $o).
% 0.21/0.30 thf(func_def_67, type, sP1: ($i > $i > $o)).
% 0.21/0.30 thf(func_def_68, type, sP2: ($i > $o)).
% 0.21/0.30 thf(func_def_69, type, sP3: ($i > $i > $o)).
% 0.21/0.30 thf(func_def_70, type, sP4: ($i > $i > $o)).
% 0.21/0.30 thf(func_def_72, type, sK6: ($i > $o)).
% 0.21/0.30 thf(func_def_74, type, sK8: ($i > $i > $o)).
% 0.21/0.30 thf(func_def_76, type, sK10: ($i > $i)).
% 0.21/0.30 thf(func_def_77, type, sK11: ($i > $i)).
% 0.21/0.30 thf(func_def_78, type, sK12: ($i > ($i > $i > $o) > $i)).
% 0.21/0.30 thf(func_def_79, type, sK13: ($i > $i > ($i > $i > $o) > $i)).
% 0.21/0.30 thf(func_def_80, type, sK14: ($i > ($i > $i > $o) > $i)).
% 0.21/0.30 thf(func_def_81, type, sK15: ($i > $i > $i)).
% 0.21/0.30 thf(func_def_82, type, sK16: ($i > $i > $i)).
% 0.21/0.30 thf(func_def_83, type, sK17: ($i > $i > $i)).
% 0.21/0.30 thf(func_def_84, type, sK18: ($i > $i > $i)).
% 0.21/0.30 thf(func_def_85, type, sK19: ($i > $i > $i > $i)).
% 0.21/0.30 thf(func_def_86, type, sK20: ($i > $i)).
% 0.21/0.30 thf(func_def_87, type, sK21: ($i > $i)).
% 0.21/0.30 thf(func_def_88, type, sK22: ($i > $i)).
% 0.21/0.30 thf(func_def_89, type, sK23: ($i > $i)).
% 0.21/0.30 thf(func_def_90, type, sK24: ($i > $i > $i)).
% 0.21/0.30 thf(func_def_91, type, sK25: ($i > $i > $i > $i)).
% 0.21/0.30 thf(func_def_92, type, sK26: ($i > $i > $i > $i)).
% 0.21/0.30 thf(func_def_93, type, sK27: ($i > $i > $i)).
% 0.21/0.30 thf(func_def_94, type, sK28: ($i > $i > $i)).
% 0.21/0.30 thf(func_def_95, type, sK29: ($i > $i)).
% 0.21/0.30 thf(func_def_96, type, sK30: ($i > $i > $i)).
% 0.21/0.30 thf(func_def_98, type, sK32: ($i > $i)).
% 0.21/0.30 thf(func_def_99, type, sK33: ($i > $i)).
% 0.21/0.30 thf(func_def_103, type, sK37: ($i > $i)).
% 0.21/0.30 thf(func_def_107, type, sK41: ($i > $i)).
% 0.21/0.30 thf(func_def_113, type, sK47: ($i > $o)).
% 0.21/0.30 thf(func_def_114, type, sK48: ($i > $o)).
% 0.21/0.30 thf(func_def_115, type, sK49: (($i > $o) > $i)).
% 0.21/0.30 thf(func_def_116, type, sK50: (($i > $o) > $i)).
% 0.21/0.30 thf(func_def_117, type, sK51: ($i > $o)).
% 0.21/0.30 thf(func_def_118, type, sK52: ($i > $i)).
% 0.21/0.30 thf(func_def_119, type, sK53: ($i > $i > $i)).
% 0.21/0.30 thf(func_def_123, type, sK57: (($i > $o) > $i)).
% 0.21/0.30 thf(func_def_124, type, sK58: ($i > $o)).
% 0.21/0.30 thf(func_def_125, type, sK59: ($i > $i)).
% 0.21/0.30 thf(func_def_129, type, sK63: ($i > $o)).
% 0.21/0.30 thf(func_def_130, type, sK64: ($o > $i > $i > $i)).
% 0.21/0.30 thf(func_def_133, type, sK67: $o).
% 0.21/0.30 thf(func_def_134, type, sK68: ($i > $i > $i)).
% 0.21/0.30 thf(func_def_135, type, sK69: ($i > $i > $i)).
% 0.21/0.30 thf(func_def_147, type, sK81: $o).
% 0.21/0.30 thf(func_def_151, type, sK85: $o).
% 0.21/0.30 thf(func_def_156, type, sK90: ($i > $i)).
% 0.21/0.30 thf(func_def_158, type, sK92: ($i > $i > $i)).
% 0.21/0.30 thf(func_def_162, type, sK96: ($i > $o)).
% 0.21/0.30 thf(func_def_164, type, sK98: ($i > $i)).
% 0.21/0.30 thf(func_def_167, type, sK101: ($i > $i)).
% 0.21/0.30 thf(func_def_168, type, sK102: ($i > $i)).
% 0.21/0.30 thf(func_def_174, type, sK108: ($i > $i > $i)).
% 0.21/0.30 thf(func_def_177, type, sK111: ($i > $o)).
% 0.21/0.30 thf(func_def_180, type, sK114: $o).
% 0.21/0.30 thf(func_def_183, type, sK117: ($i > $o)).
% 0.21/0.30 thf(func_def_192, type, sK126: ($i > $i > $i)).
% 0.21/0.30 thf(func_def_193, type, sK127: ($i > ($i > $i > $o) > $i > $i)).
% 0.21/0.30 thf(func_def_194, type, sK128: ($i > $i)).
% 0.21/0.30 thf(func_def_195, type, sK129: ($i > ($i > $o) > $i)).
% 0.21/0.30 thf(func_def_196, type, sK130: ($i > ($i > $o) > $i)).
% 0.21/0.30 thf(func_def_197, type, sK131: ($i > ($i > $o) > $i)).
% 0.21/0.30 thf(func_def_198, type, sK132: ($i > ($i > $i > $o) > $i > $i)).
% 0.21/0.30 thf(func_def_199, type, sK133: ($i > ($i > $i > $o) > $i > $i)).
% 0.21/0.30 thf(func_def_200, type, sK134: ($i > ($i > $o) > $i)).
% 0.21/0.30 thf(func_def_201, type, sK135: ($i > ($i > $o) > $i)).
% 0.21/0.30 thf(func_def_202, type, sK136: ($i > ($i > $o) > $i)).
% 0.21/0.30 thf(f25,axiom,(
% 0.21/0.30 (! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)) = emptyI)),
% 0.21/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI)).
% 0.21/0.30 thf(f28,axiom,(
% 0.21/0.30 (nonempty = (^[X0 : $i] : ((X0 != emptyset))))),
% 0.21/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty)).
% 0.21/0.30 thf(f46,conjecture,(
% 0.21/0.30 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 => (exuE2 => ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ($true & (in @ X1 @ X0))))))))))))))))))))))))))))))))))))))))))))),
% 0.21/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness)).
% 0.21/0.30 thf(f47,negated_conjecture,(
% 0.21/0.30 ~(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 => (exuE2 => ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ($true & (in @ X1 @ X0)))))))))))))))))))))))))))))))))))))))))))))),
% 0.21/0.30 inference(negated_conjecture,[status(cth)],[f46])).
% 0.21/0.30 thf(f56,plain,(
% 0.21/0.30 ~(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 => (exuE2 => ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ($true & (in @ X1 @ X0)))))))))))))))))))))))))))))))))))))))))))))),
% 0.21/0.30 inference(rectify,[],[f47])).
% 0.21/0.30 thf(f57,plain,(
% 0.21/0.30 ~((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) => ((exuE2 = $true) => ! [X0 : $i] : ((((nonempty @ X0)) = $true) => ? [X1 : $i] : ($true & (((in @ X1 @ X0)) = $true)))))))))))))))))))))))))))))))))))))))))))))),
% 0.21/0.30 inference(fool_elimination,[],[f56])).
% 0.21/0.30 thf(f108,plain,(
% 0.21/0.30 (! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)) = emptyI)),
% 0.21/0.30 inference(rectify,[],[f25])).
% 0.21/0.30 thf(f109,plain,(
% 0.21/0.30 ! [X0 : $i] : (! [X1 : $i] : ~ (((in @ X1 @ X0)) = $true) => (emptyset = X0)) <=> (emptyI = $true)),
% 0.21/0.30 inference(fool_elimination,[],[f108])).
% 0.21/0.30 thf(f128,plain,(
% 0.21/0.30 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 0.21/0.30 inference(fool_elimination,[],[f28])).
% 0.21/0.30 thf(f136,plain,(
% 0.21/0.30 ~((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) => ((exuE2 = $true) => ! [X0 : $i] : ((((nonempty @ X0)) = $true) => ? [X1 : $i] : (((in @ X1 @ X0)) = $true))))))))))))))))))))))))))))))))))))))))))))),
% 0.21/0.30 inference(true_and_false_elimination,[],[f57])).
% 0.21/0.30 thf(f145,plain,(
% 0.21/0.30 ! [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0)) != $true) => (emptyset = X0)) <=> (emptyI = $true)),
% 0.21/0.30 inference(flattening,[],[f109])).
% 0.21/0.30 thf(f164,plain,(
% 0.21/0.30 ! [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0)) = $true) | (emptyset = X0)) <=> (emptyI = $true)),
% 0.21/0.30 inference(ennf_transformation,[],[f145])).
% 0.21/0.30 thf(f166,plain,(
% 0.21/0.30 (((((((((((((((((((((((((((((((((((((((((? [X0 : $i] : ((((nonempty @ X0)) = $true) & ! [X1 : $i] : (((in @ X1 @ X0)) != $true)) & (exuE2 = $true)) & (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)),
% 0.21/0.30 inference(ennf_transformation,[],[f136])).
% 0.21/0.30 thf(f167,plain,(
% 0.21/0.30 (nonemptyE1 = $true) & (exuE2 = $true) & (descrp = $true) & (noeltsimpempty = $true) & (setextAx = $true) & (powersetE = $true) & (omegaSAx = $true) & (notinemptyset = $true) & (wellorderingAx = $true) & (emptysetAx = $true) & (setadjoinOr = $true) & (dsetconstrEL = $true) & (emptyinPowerset = $true) & (setunionAx = $true) & (nonemptyI1 = $true) & (setadjoinAx = $true) & (subPowSU = $true) & (omegaIndAx = $true) & (setunionI = $true) & (foundationAx = $true) & (setoftrueEq = $true) & (emptyinunitempty = $true) & (emptyI = $true) & (replAx = $true) & (powersetAx = $true) & (powersetI = $true) & (emptysetE = $true) & (setext = $true) & (nonemptyI = $true) & (emptysetimpfalse = $true) & (setbeta = $true) & ? [X0 : $i] : ((((nonempty @ X0)) = $true) & ! [X1 : $i] : (((in @ X1 @ X0)) != $true)) & (exuE1 = $true) & (prop2setE = $true) & (setadjoinIL = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (exuE3e = $true) & (setunionE = $true) & (dsetconstrI = $true) & (dsetconstrER = $true) & (omega0Ax = $true) & (emptyInPowerset = $true)),
% 0.21/0.30 inference(flattening,[],[f166])).
% 0.21/0.30 thf(f282,plain,(
% 0.21/0.30 (nonemptyE1 = $true) & (exuE2 = $true) & (descrp = $true) & (noeltsimpempty = $true) & (setextAx = $true) & (powersetE = $true) & (omegaSAx = $true) & (notinemptyset = $true) & (wellorderingAx = $true) & (emptysetAx = $true) & (setadjoinOr = $true) & (dsetconstrEL = $true) & (emptyinPowerset = $true) & (setunionAx = $true) & (nonemptyI1 = $true) & (setadjoinAx = $true) & (subPowSU = $true) & (omegaIndAx = $true) & (setunionI = $true) & (foundationAx = $true) & (setoftrueEq = $true) & (emptyinunitempty = $true) & (emptyI = $true) & (replAx = $true) & (powersetAx = $true) & (powersetI = $true) & (emptysetE = $true) & (setext = $true) & (nonemptyI = $true) & (emptysetimpfalse = $true) & (setbeta = $true) & (($true = ((nonempty @ sK89))) & ! [X1 : $i] : ($true != ((in @ X1 @ sK89)))) & (exuE1 = $true) & (prop2setE = $true) & (setadjoinIL = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (exuE3e = $true) & (setunionE = $true) & (dsetconstrI = $true) & (dsetconstrER = $true) & (omega0Ax = $true) & (emptyInPowerset = $true)),
% 0.21/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(X0,sK89)],[f167])).
% 0.21/0.30 thf(f295,plain,(
% 0.21/0.30 (! [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0)) = $true) | (emptyset = X0)) | (emptyI != $true)) & ((emptyI = $true) | ? [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0)) != $true) & (emptyset != X0)))),
% 0.21/0.30 inference(nnf_transformation,[],[f164])).
% 0.21/0.30 thf(f296,plain,(
% 0.21/0.30 (! [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0)) = $true) | (emptyset = X0)) | (emptyI != $true)) & ((emptyI = $true) | ? [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X2)) != $true) & (emptyset != X2)))),
% 0.21/0.30 inference(rectify,[],[f295])).
% 0.21/0.30 thf(f297,plain,(
% 0.21/0.30 (! [X0 : $i] : (($true = ((in @ (sK102 @ X0) @ X0))) | (emptyset = X0)) | (emptyI != $true)) & ((emptyI = $true) | (! [X3 : $i] : ($true != ((in @ X3 @ sK103))) & (emptyset != sK103)))),
% 0.21/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK103]),skolemize(X13,sK14 @ X8 @ X7),skolemize(X2,sK103)],[f296])).
% 0.21/0.30 thf(f335,plain,(
% 0.21/0.30 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 0.21/0.30 inference(cnf_transformation,[],[f128])).
% 0.21/0.30 thf(f486,plain,(
% 0.21/0.30 ( ! [X1 : $i] : (($true != ((in @ X1 @ sK89)))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f282])).
% 0.21/0.30 thf(f487,plain,(
% 0.21/0.30 ($true = ((nonempty @ sK89)))),
% 0.21/0.30 inference(cnf_transformation,[],[f282])).
% 0.21/0.30 thf(f496,plain,(
% 0.21/0.30 (emptyI = $true)),
% 0.21/0.30 inference(cnf_transformation,[],[f282])).
% 0.21/0.30 thf(f537,plain,(
% 0.21/0.30 ( ! [X0 : $i] : (($true = ((in @ (sK102 @ X0) @ X0))) | (emptyset = X0) | (emptyI != $true)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f297])).
% 0.21/0.30 thf(f681,plain,(
% 0.21/0.30 ((((^[Y0 : $i]: (~ (emptyset = Y0))) @ sK89)) = $true)),
% 0.21/0.30 inference(definition_unfolding,[],[f487,f335])).
% 0.21/0.30 thf(f698,plain,(
% 0.21/0.30 ( ! [X0 : $i] : (($true != $true) | (emptyset = X0) | ($true = ((in @ (sK102 @ X0) @ X0)))) )),
% 0.21/0.30 inference(definition_unfolding,[],[f537,f496])).
% 0.21/0.30 thf(f764,plain,(
% 0.21/0.30 ( ! [X0 : $i] : (($true = ((in @ (sK102 @ X0) @ X0))) | (emptyset = X0)) )),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f698])).
% 0.21/0.30 thf(f765,plain,(
% 0.21/0.30 ($true = ((~ (emptyset = sK89))))),
% 0.21/0.30 inference(beta-eta_normalization,[],[f681])).
% 0.21/0.30 thf(f766,plain,(
% 0.21/0.30 ($false = ((emptyset = sK89)))),
% 0.21/0.30 inference(not_proxy_clausification,[],[f765])).
% 0.21/0.30 thf(f767,plain,(
% 0.21/0.30 (emptyset != sK89)),
% 0.21/0.30 inference(equality_proxy_clausification,[],[f766])).
% 0.21/0.30 thf(f999,plain,(
% 0.21/0.30 ($true != $true) | (emptyset = sK89)),
% 0.21/0.30 inference(constrained_superposition,[],[f486,f764])).
% 0.21/0.30 thf(f1000,plain,(
% 0.21/0.30 (emptyset = sK89)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f999])).
% 0.21/0.30 thf(f1001,plain,(
% 0.21/0.30 $false),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f1000,f767])).
% 0.21/0.30 % SZS output end Proof for theBenchmark
% 0.21/0.30 % (2528570)------------------------------
% 0.21/0.30 % (2528570)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (2528570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (2528570)CaDiCaL version: 2.1.3
% 0.21/0.31 % (2528570)Termination reason: Refutation
% 0.21/0.31 % (2528570)Time elapsed: 0.026 s
% 0.21/0.31 % (2528570)Peak memory usage: 13 MB
% 0.21/0.31 % (2528570)Instructions burned: 52 (million)
% 0.21/0.31 % (2528565)Success in time 0.061 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------