%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU521^1 : 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 : n019.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 08:29:54 AM UTC 2026
% Result : Theorem 0.22s 0.34s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU521^1 : 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 : n019.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 13:48:03 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.22/0.34 % (790982)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.34 % (790993)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.34 % (790993)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
% 0.22/0.34 % (790993)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=2442432304:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.34 % (790990)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=3833758803: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)
% 0.22/0.34 % (790988)lrs+10_16_si=on:nwc=1.5:random_seed=4129444641:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.34 % (790987)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1106802773:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.34 % (790992)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=907252437:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.34 % (790989)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1555134917:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.34 % (790989)Instruction limit reached!
% 0.22/0.34 % (790989)------------------------------
% 0.22/0.34 % (790989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (790989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (790989)CaDiCaL version: 2.1.3
% 0.22/0.34 % (790989)Termination reason: Instruction limit
% 0.22/0.34 % (790989)Termination phase: Property scanning
% 0.22/0.34 % (790989)Time elapsed: 0.003 s
% 0.22/0.34 % (790989)Peak memory usage: 10 MB
% 0.22/0.34 % (790989)Instructions burned: 5 (million)
% 0.22/0.34 % (790988)Instruction limit reached!
% 0.22/0.34 % (790988)------------------------------
% 0.22/0.34 % (790988)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (790988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (790988)CaDiCaL version: 2.1.3
% 0.22/0.34 % (790988)Termination reason: Instruction limit
% 0.22/0.34 % (790988)Termination phase: Saturation
% 0.22/0.34 % (790988)Time elapsed: 0.009 s
% 0.22/0.34 % (790988)Peak memory usage: 11 MB
% 0.22/0.34 % (790988)Instructions burned: 20 (million)
% 0.22/0.34 % (790991)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1847018151:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.34 % (791000)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3300007367:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.34 % (791000)Instruction limit reached!
% 0.22/0.34 % (791000)------------------------------
% 0.22/0.34 % (791000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (791000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (791000)CaDiCaL version: 2.1.3
% 0.22/0.34 % (791000)Termination reason: Instruction limit
% 0.22/0.34 % (791000)Termination phase: shuffling
% 0.22/0.34 % (791000)Time elapsed: 0.002 s
% 0.22/0.34 % (791000)Peak memory usage: 9 MB
% 0.22/0.34 % (791000)Instructions burned: 4 (million)
% 0.22/0.34 % (791001)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=994756339:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.34 % (791001)Instruction limit reached!
% 0.22/0.34 % (791001)------------------------------
% 0.22/0.34 % (791001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (791001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (791001)CaDiCaL version: 2.1.3
% 0.22/0.34 % (791001)Termination reason: Instruction limit
% 0.22/0.34 % (791001)Termination phase: Property scanning
% 0.22/0.34 % (791001)Time elapsed: 0.003 s
% 0.22/0.34 % (791001)Peak memory usage: 10 MB
% 0.22/0.34 % (791001)Instructions burned: 7 (million)
% 0.22/0.34 % (790991)Instruction limit reached!
% 0.22/0.34 % (790991)------------------------------
% 0.22/0.34 % (790991)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (790991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (790991)CaDiCaL version: 2.1.3
% 0.22/0.34 % (790991)Termination reason: Instruction limit
% 0.22/0.34 % (790991)Termination phase: Saturation
% 0.22/0.34 % (790991)Time elapsed: 0.021 s
% 0.22/0.34 % (790991)Peak memory usage: 11 MB
% 0.22/0.34 % (790991)Instructions burned: 25 (million)
% 0.22/0.34 % (790990) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-790982-790990"...
% 0.22/0.34 % (790990)...printing done.
% 0.22/0.34 % (790992)Instruction limit reached!
% 0.22/0.34 % (790992)------------------------------
% 0.22/0.34 % (790992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (790992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (790992)CaDiCaL version: 2.1.3
% 0.22/0.34 % (790992)Termination reason: Instruction limit
% 0.22/0.34 % (790992)Termination phase: Saturation
% 0.22/0.34 % (790992)Time elapsed: 0.040 s
% 0.22/0.34 % (790992)Peak memory usage: 13 MB
% 0.22/0.34 % (790992)Instructions burned: 77 (million)
% 0.22/0.34 % (790993)Instruction limit reached!
% 0.22/0.34 % (790993)------------------------------
% 0.22/0.34 % (790993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (790993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (790993)CaDiCaL version: 2.1.3
% 0.22/0.34 % (790993)Termination reason: Instruction limit
% 0.22/0.34 % (790993)Termination phase: Saturation
% 0.22/0.34 % (790993)Time elapsed: 0.046 s
% 0.22/0.34 % (790993)Peak memory usage: 14 MB
% 0.22/0.34 % (790993)Instructions burned: 173 (million)
% 0.22/0.34 % (791004)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.34 % (790990)Refutation found. Thanks to Tanya!
% 0.22/0.34 % SZS status Theorem for theBenchmark
% 0.22/0.34 % SZS output start Proof for theBenchmark
% 0.22/0.34 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.34 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.22/0.34 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 0.22/0.34 thf(func_def_3, type, setextAx: $o).
% 0.22/0.34 thf(func_def_5, type, emptysetAx: $o).
% 0.22/0.34 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 0.22/0.34 thf(func_def_7, type, setadjoinAx: $o).
% 0.22/0.34 thf(func_def_8, type, powerset: ($i > $i)).
% 0.22/0.34 thf(func_def_9, type, powersetAx: $o).
% 0.22/0.34 thf(func_def_10, type, setunion: ($i > $i)).
% 0.22/0.34 thf(func_def_11, type, setunionAx: $o).
% 0.22/0.34 thf(func_def_13, type, omega0Ax: $o).
% 0.22/0.34 thf(func_def_14, type, omegaSAx: $o).
% 0.22/0.34 thf(func_def_15, type, omegaIndAx: $o).
% 0.22/0.34 thf(func_def_16, type, replAx: $o).
% 0.22/0.34 thf(func_def_17, type, foundationAx: $o).
% 0.22/0.34 thf(func_def_18, type, wellorderingAx: $o).
% 0.22/0.34 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 0.22/0.34 thf(func_def_20, type, descrp: $o).
% 0.22/0.34 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.22/0.34 thf(func_def_22, type, dsetconstrI: $o).
% 0.22/0.34 thf(func_def_23, type, dsetconstrEL: $o).
% 0.22/0.34 thf(func_def_24, type, dsetconstrER: $o).
% 0.22/0.34 thf(func_def_25, type, exuE1: $o).
% 0.22/0.34 thf(func_def_26, type, prop2set: ($o > $i)).
% 0.22/0.34 thf(func_def_27, type, prop2setE: $o).
% 0.22/0.34 thf(func_def_28, type, emptysetE: $o).
% 0.22/0.34 thf(func_def_29, type, emptysetimpfalse: $o).
% 0.22/0.34 thf(func_def_30, type, notinemptyset: $o).
% 0.22/0.34 thf(func_def_31, type, exuE3e: $o).
% 0.22/0.34 thf(func_def_32, type, setext: $o).
% 0.22/0.34 thf(func_def_33, type, emptyI: $o).
% 0.22/0.34 thf(func_def_34, type, noeltsimpempty: $o).
% 0.22/0.34 thf(func_def_35, type, setbeta: $o).
% 0.22/0.34 thf(func_def_36, type, nonempty: ($i > $o)).
% 0.22/0.34 thf(func_def_37, type, nonemptyE1: $o).
% 0.22/0.34 thf(func_def_38, type, nonemptyI: $o).
% 0.22/0.34 thf(func_def_39, type, nonemptyI1: $o).
% 0.22/0.34 thf(func_def_40, type, setadjoinIL: $o).
% 0.22/0.34 thf(func_def_41, type, emptyinunitempty: $o).
% 0.22/0.34 thf(func_def_42, type, setadjoinIR: $o).
% 0.22/0.34 thf(func_def_43, type, setadjoinE: $o).
% 0.22/0.34 thf(func_def_44, type, setadjoinOr: $o).
% 0.22/0.34 thf(func_def_45, type, setoftrueEq: $o).
% 0.22/0.34 thf(func_def_46, type, powersetI: $o).
% 0.22/0.34 thf(func_def_47, type, emptyinPowerset: $o).
% 0.22/0.34 thf(func_def_48, type, emptyInPowerset: $o).
% 0.22/0.34 thf(func_def_49, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.34 thf(func_def_50, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.34 thf(func_def_53, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.34 thf(func_def_54, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.34 thf(func_def_55, type, vNOT: ($o > $o)).
% 0.22/0.34 thf(func_def_56, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.34 thf(func_def_57, type, vAND: ($o > $o > $o)).
% 0.22/0.34 thf(func_def_58, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.34 thf(func_def_59, type, vIMP: ($o > $o > $o)).
% 0.22/0.34 thf(func_def_60, type, db2: !>[X0: $tType]:(X0)).
% 0.22/0.34 thf(func_def_61, type, sP0: ($i > $i > $o)).
% 0.22/0.34 thf(func_def_62, type, sP1: ($i > $o)).
% 0.22/0.34 thf(func_def_63, type, sP2: $o).
% 0.22/0.34 thf(func_def_64, type, sK3: ($i > $i > $i)).
% 0.22/0.34 thf(func_def_72, type, sK11: ($i > $o)).
% 0.22/0.34 thf(func_def_76, type, sK15: ($i > $o)).
% 0.22/0.34 thf(func_def_79, type, sK18: ($i > $o)).
% 0.22/0.34 thf(func_def_82, type, sK21: ($i > $i)).
% 0.22/0.34 thf(func_def_85, type, sK24: ($i > $i > $i)).
% 0.22/0.34 thf(func_def_86, type, sK25: ($i > $o)).
% 0.22/0.34 thf(func_def_92, type, sK31: $o).
% 0.22/0.34 thf(func_def_94, type, sK33: $o).
% 0.22/0.34 thf(func_def_95, type, sK34: ($i > $o)).
% 0.22/0.34 thf(func_def_96, type, sK35: ($i > $i)).
% 0.22/0.34 thf(func_def_97, type, sK36: (($i > $o) > $i)).
% 0.22/0.34 thf(func_def_99, type, sK38: ($i > $i)).
% 0.22/0.34 thf(func_def_100, type, sK39: ($i > $i)).
% 0.22/0.34 thf(func_def_101, type, sK40: ($i > $i)).
% 0.22/0.34 thf(func_def_102, type, sK41: ($i > $i)).
% 0.22/0.34 thf(func_def_103, type, sK42: ($i > $i)).
% 0.22/0.34 thf(func_def_104, type, sK43: ($i > $i > $i > $i)).
% 0.22/0.34 thf(func_def_105, type, sK44: ($i > $i)).
% 0.22/0.34 thf(func_def_106, type, sK45: ($i > $i)).
% 0.22/0.34 thf(func_def_107, type, sK46: ($i > $i)).
% 0.22/0.34 thf(func_def_108, type, sK47: ($i > $i)).
% 0.22/0.34 thf(func_def_109, type, sK48: ($i > $i > $i)).
% 0.22/0.34 thf(func_def_110, type, sK49: ($i > $i > $i)).
% 0.22/0.34 thf(func_def_111, type, sK50: ($i > $i > $i > $i)).
% 0.22/0.34 thf(func_def_112, type, sK51: ($i > $i > $i > $i)).
% 0.22/0.34 thf(func_def_113, type, sK52: ($i > $i > $i > $i)).
% 0.22/0.34 thf(func_def_114, type, sK53: ($i > $i > $i)).
% 0.22/0.34 thf(func_def_115, type, sK54: ($i > $i > $i)).
% 0.22/0.34 thf(func_def_116, type, sK55: ($i > $i > $i)).
% 0.22/0.34 thf(func_def_117, type, sK56: ($i > $i)).
% 0.22/0.34 thf(func_def_120, type, sK59: ($i > $i)).
% 0.22/0.34 thf(func_def_121, type, sK60: ($i > ($i > $i > $o) > $i)).
% 0.22/0.34 thf(func_def_122, type, sK61: ($i > $i > ($i > $i > $o) > $i)).
% 0.22/0.34 thf(func_def_123, type, sK62: ($i > ($i > $i > $o) > $i)).
% 0.22/0.34 thf(func_def_124, type, sK63: ($i > $i > $o)).
% 0.22/0.34 thf(func_def_126, type, sK65: ($i > $i)).
% 0.22/0.34 thf(func_def_127, type, sK66: ($i > $i)).
% 0.22/0.34 thf(func_def_128, type, sK67: ($i > $i)).
% 0.22/0.34 thf(func_def_136, type, sK75: $o).
% 0.22/0.34 thf(func_def_142, type, sK81: ($i > $o)).
% 0.22/0.34 thf(func_def_151, type, sK90: ($i > $o)).
% 0.22/0.34 thf(func_def_152, type, sK91: (($i > $o) > $i)).
% 0.22/0.34 thf(func_def_155, type, sK94: ($i > $i > $i)).
% 0.22/0.34 thf(func_def_158, type, sK97: ($i > $i)).
% 0.22/0.34 thf(func_def_160, type, sK99: ($i > $i)).
% 0.22/0.34 thf(func_def_161, type, sK100: ($i > $o)).
% 0.22/0.34 thf(func_def_167, type, sK106: ($i > $i > $i)).
% 0.22/0.34 thf(func_def_169, type, sK108: ($i > $i > $i)).
% 0.22/0.34 thf(func_def_170, type, sK109: ($i > $i > $i)).
% 0.22/0.34 thf(f5,axiom,(
% 0.22/0.34 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) <=> ! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0))) = powersetAx)),
% 0.22/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx)).
% 0.22/0.34 thf(f41,conjecture,(
% 0.22/0.34 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 => ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0)))))))))))))))))))))))))))))))))))))))),
% 0.22/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE)).
% 0.22/0.34 thf(f42,negated_conjecture,(
% 0.22/0.34 ~(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 => ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))))))))))))))))))))))))))))))))))))))))),
% 0.22/0.34 inference(negated_conjecture,[status(cth)],[f41])).
% 0.22/0.34 thf(f82,plain,(
% 0.22/0.34 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (powerset @ X1)) => ((in @ X2 @ X0) => (in @ X2 @ X1))))))))))))))))))))))))))))))))))))))))),
% 0.22/0.34 inference(rectify,[],[f42])).
% 0.22/0.34 thf(f83,plain,(
% 0.22/0.34 ~((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) => ! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) => ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true))))))))))))))))))))))))))))))))))))))))),
% 0.22/0.34 inference(fool_elimination,[],[f82])).
% 0.22/0.34 thf(f112,plain,(
% 0.22/0.34 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) <=> ! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0))) = powersetAx)),
% 0.22/0.34 inference(rectify,[],[f5])).
% 0.22/0.34 thf(f113,plain,(
% 0.22/0.34 (powersetAx = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) <=> (((in @ X1 @ (powerset @ X0))) = $true))),
% 0.22/0.34 inference(fool_elimination,[],[f112])).
% 0.22/0.34 thf(f144,plain,(
% 0.22/0.34 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)) <=> (((in @ X1 @ (powerset @ X0))) = $true)) <=> (powersetAx = $true)),
% 0.22/0.34 inference(ennf_transformation,[],[f113])).
% 0.22/0.34 thf(f151,plain,(
% 0.22/0.34 ((((((((((((((((((((((((((((((((((((? [X2 : $i,X1 : $i,X0 : $i] : (((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) & (((in @ X0 @ (powerset @ X1))) = $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)),
% 0.22/0.34 inference(ennf_transformation,[],[f83])).
% 0.22/0.34 thf(f152,plain,(
% 0.22/0.34 (setadjoinIR = $true) & (setadjoinE = $true) & (setadjoinAx = $true) & (dsetconstrI = $true) & (foundationAx = $true) & (emptysetAx = $true) & (setbeta = $true) & (emptysetE = $true) & (exuE1 = $true) & (setoftrueEq = $true) & (omega0Ax = $true) & (setext = $true) & (nonemptyI = $true) & (notinemptyset = $true) & (wellorderingAx = $true) & (emptyInPowerset = $true) & (emptyI = $true) & (noeltsimpempty = $true) & (emptysetimpfalse = $true) & ? [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X0 @ (powerset @ X1))) = $true) & (((in @ X2 @ X0)) = $true)) & (dsetconstrEL = $true) & (powersetAx = $true) & (prop2setE = $true) & (descrp = $true) & (setextAx = $true) & (emptyinunitempty = $true) & (nonemptyE1 = $true) & (replAx = $true) & (emptyinPowerset = $true) & (nonemptyI1 = $true) & (setunionAx = $true) & (omegaSAx = $true) & (dsetconstrER = $true) & (setadjoinOr = $true) & (setadjoinIL = $true) & (powersetI = $true) & (exuE3e = $true) & (omegaIndAx = $true)),
% 0.22/0.34 inference(flattening,[],[f151])).
% 0.22/0.34 thf(f168,plain,(
% 0.22/0.34 (! [X0 : $i,X1 : $i] : ((! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)) | (((in @ X1 @ (powerset @ X0))) != $true)) & ((((in @ X1 @ (powerset @ X0))) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true)))) | (powersetAx != $true)) & ((powersetAx = $true) | ? [X0 : $i,X1 : $i] : (((((in @ X1 @ (powerset @ X0))) != $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true))) & ((((in @ X1 @ (powerset @ X0))) = $true) | ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)))))),
% 0.22/0.34 inference(nnf_transformation,[],[f144])).
% 0.22/0.34 thf(f169,plain,(
% 0.22/0.34 (! [X0 : $i,X1 : $i] : ((! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)) | (((in @ X1 @ (powerset @ X0))) != $true)) & ((((in @ X1 @ (powerset @ X0))) = $true) | ? [X3 : $i] : ((((in @ X3 @ X1)) = $true) & (((in @ X3 @ X0)) != $true)))) | (powersetAx != $true)) & ((powersetAx = $true) | ? [X4 : $i,X5 : $i] : (((((in @ X5 @ (powerset @ X4))) != $true) | ? [X6 : $i] : ((((in @ X6 @ X5)) = $true) & (((in @ X6 @ X4)) != $true))) & ((((in @ X5 @ (powerset @ X4))) = $true) | ! [X7 : $i] : ((((in @ X7 @ X5)) != $true) | (((in @ X7 @ X4)) = $true)))))),
% 0.22/0.34 inference(rectify,[],[f168])).
% 0.22/0.34 thf(f170,plain,(
% 0.22/0.34 (! [X0 : $i,X1 : $i] : ((! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)) | (((in @ X1 @ (powerset @ X0))) != $true)) & ((((in @ X1 @ (powerset @ X0))) = $true) | ((((in @ (sK3 @ X1 @ X0) @ X1)) = $true) & ($true != ((in @ (sK3 @ X1 @ X0) @ X0)))))) | (powersetAx != $true)) & ((powersetAx = $true) | (((((in @ sK5 @ (powerset @ sK4))) != $true) | ((((in @ sK6 @ sK5)) = $true) & (((in @ sK6 @ sK4)) != $true))) & ((((in @ sK5 @ (powerset @ sK4))) = $true) | ! [X7 : $i] : ((((in @ X7 @ sK5)) != $true) | (((in @ X7 @ sK4)) = $true)))))),
% 0.22/0.34 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK4,sK5,sK6]),skolemize(X3,sK3 @ X1 @ X0),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6)],[f169])).
% 0.22/0.34 thf(f171,plain,(
% 0.22/0.34 (setadjoinIR = $true) & (setadjoinE = $true) & (setadjoinAx = $true) & (dsetconstrI = $true) & (foundationAx = $true) & (emptysetAx = $true) & (setbeta = $true) & (emptysetE = $true) & (exuE1 = $true) & (setoftrueEq = $true) & (omega0Ax = $true) & (setext = $true) & (nonemptyI = $true) & (notinemptyset = $true) & (wellorderingAx = $true) & (emptyInPowerset = $true) & (emptyI = $true) & (noeltsimpempty = $true) & (emptysetimpfalse = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X2)) != $true) & (((in @ X0 @ (powerset @ X2))) = $true) & (((in @ X1 @ X0)) = $true)) & (dsetconstrEL = $true) & (powersetAx = $true) & (prop2setE = $true) & (descrp = $true) & (setextAx = $true) & (emptyinunitempty = $true) & (nonemptyE1 = $true) & (replAx = $true) & (emptyinPowerset = $true) & (nonemptyI1 = $true) & (setunionAx = $true) & (omegaSAx = $true) & (dsetconstrER = $true) & (setadjoinOr = $true) & (setadjoinIL = $true) & (powersetI = $true) & (exuE3e = $true) & (omegaIndAx = $true)),
% 0.22/0.34 inference(rectify,[],[f152])).
% 0.22/0.34 thf(f172,plain,(
% 0.22/0.34 (setadjoinIR = $true) & (setadjoinE = $true) & (setadjoinAx = $true) & (dsetconstrI = $true) & (foundationAx = $true) & (emptysetAx = $true) & (setbeta = $true) & (emptysetE = $true) & (exuE1 = $true) & (setoftrueEq = $true) & (omega0Ax = $true) & (setext = $true) & (nonemptyI = $true) & (notinemptyset = $true) & (wellorderingAx = $true) & (emptyInPowerset = $true) & (emptyI = $true) & (noeltsimpempty = $true) & (emptysetimpfalse = $true) & ((((in @ sK8 @ sK9)) != $true) & (((in @ sK7 @ (powerset @ sK9))) = $true) & (((in @ sK8 @ sK7)) = $true)) & (dsetconstrEL = $true) & (powersetAx = $true) & (prop2setE = $true) & (descrp = $true) & (setextAx = $true) & (emptyinunitempty = $true) & (nonemptyE1 = $true) & (replAx = $true) & (emptyinPowerset = $true) & (nonemptyI1 = $true) & (setunionAx = $true) & (omegaSAx = $true) & (dsetconstrER = $true) & (setadjoinOr = $true) & (setadjoinIL = $true) & (powersetI = $true) & (exuE3e = $true) & (omegaIndAx = $true)),
% 0.22/0.34 inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9)],[f171])).
% 0.22/0.34 thf(f288,plain,(
% 0.22/0.34 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((powersetAx != $true) | (((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true) | (((in @ X1 @ (powerset @ X0))) != $true)) )),
% 0.22/0.34 inference(cnf_transformation,[],[f170])).
% 0.22/0.34 thf(f305,plain,(
% 0.22/0.34 (powersetAx = $true)),
% 0.22/0.34 inference(cnf_transformation,[],[f172])).
% 0.22/0.34 thf(f307,plain,(
% 0.22/0.34 (((in @ sK8 @ sK7)) = $true)),
% 0.22/0.34 inference(cnf_transformation,[],[f172])).
% 0.22/0.34 thf(f308,plain,(
% 0.22/0.34 (((in @ sK7 @ (powerset @ sK9))) = $true)),
% 0.22/0.34 inference(cnf_transformation,[],[f172])).
% 0.22/0.34 thf(f309,plain,(
% 0.22/0.34 (((in @ sK8 @ sK9)) != $true)),
% 0.22/0.34 inference(cnf_transformation,[],[f172])).
% 0.22/0.34 thf(f699,definition,(
% 0.22/0.34 spl112_34 <=> (powersetAx = $true)),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl112_34])],[avatar_definition])).
% 0.22/0.34 thf(f702,plain,(
% 0.22/0.34 spl112_34),
% 0.22/0.34 inference(avatar_split_clause,[],[f305,f699])).
% 0.22/0.34 thf(f1002,definition,(
% 0.22/0.34 spl112_102 <=> (((in @ sK8 @ sK7)) = $true)),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl112_102])],[avatar_definition])).
% 0.22/0.34 thf(f1004,plain,(
% 0.22/0.34 (((in @ sK8 @ sK7)) = $true) | ~spl112_102),
% 0.22/0.34 inference(avatar_component_clause,[],[f1002])).
% 0.22/0.34 thf(f1005,plain,(
% 0.22/0.34 spl112_102),
% 0.22/0.34 inference(avatar_split_clause,[],[f307,f1002])).
% 0.22/0.34 thf(f1085,definition,(
% 0.22/0.34 spl112_119 <=> (((in @ sK8 @ sK9)) = $true)),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl112_119])],[avatar_definition])).
% 0.22/0.34 thf(f1087,plain,(
% 0.22/0.34 (((in @ sK8 @ sK9)) != $true) | spl112_119),
% 0.22/0.34 inference(avatar_component_clause,[],[f1085])).
% 0.22/0.34 thf(f1088,plain,(
% 0.22/0.34 ~spl112_119),
% 0.22/0.34 inference(avatar_split_clause,[],[f309,f1085])).
% 0.22/0.34 thf(f1264,definition,(
% 0.22/0.34 spl112_157 <=> (((in @ sK7 @ (powerset @ sK9))) = $true)),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl112_157])],[avatar_definition])).
% 0.22/0.34 thf(f1266,plain,(
% 0.22/0.34 (((in @ sK7 @ (powerset @ sK9))) = $true) | ~spl112_157),
% 0.22/0.34 inference(avatar_component_clause,[],[f1264])).
% 0.22/0.34 thf(f1267,plain,(
% 0.22/0.34 spl112_157),
% 0.22/0.34 inference(avatar_split_clause,[],[f308,f1264])).
% 0.22/0.34 thf(f1399,definition,(
% 0.22/0.34 spl112_186 <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ X2 @ X1)) != $true))),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl112_186])],[avatar_definition])).
% 0.22/0.34 thf(f1400,plain,(
% 0.22/0.34 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) | (((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)) ) | ~spl112_186),
% 0.22/0.34 inference(avatar_component_clause,[],[f1399])).
% 0.22/0.34 thf(f1401,plain,(
% 0.22/0.34 spl112_186 | ~spl112_34),
% 0.22/0.34 inference(avatar_split_clause,[],[f288,f699,f1399])).
% 0.22/0.34 thf(f1703,plain,(
% 0.22/0.34 ( ! [X0 : $i] : ((((in @ X0 @ sK9)) = $true) | (((in @ X0 @ sK7)) != $true) | ($true != $true)) ) | (~spl112_157 | ~spl112_186)),
% 0.22/0.34 inference(superposition,[],[f1400,f1266])).
% 0.22/0.34 thf(f1710,plain,(
% 0.22/0.34 ( ! [X0 : $i] : ((((in @ X0 @ sK9)) = $true) | (((in @ X0 @ sK7)) != $true)) ) | (~spl112_157 | ~spl112_186)),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f1703])).
% 0.22/0.34 thf(f1720,plain,(
% 0.22/0.34 ($true != $true) | (((in @ sK8 @ sK7)) != $true) | (spl112_119 | ~spl112_157 | ~spl112_186)),
% 0.22/0.34 inference(superposition,[],[f1087,f1710])).
% 0.22/0.34 thf(f1721,plain,(
% 0.22/0.34 (((in @ sK8 @ sK7)) != $true) | (spl112_119 | ~spl112_157 | ~spl112_186)),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f1720])).
% 0.22/0.34 thf(f1729,plain,(
% 0.22/0.34 $false | (~spl112_102 | spl112_119 | ~spl112_157 | ~spl112_186)),
% 0.22/0.34 inference(forward_subsumption_resolution,[],[f1721,f1004])).
% 0.22/0.34 thf(f1730,plain,(
% 0.22/0.34 ~spl112_102 | spl112_119 | ~spl112_157 | ~spl112_186),
% 0.22/0.34 inference(avatar_contradiction_clause,[],[f1729])).
% 0.22/0.34 cnf(s22, plain, spl112_34, inference(sat_conversion,[],[f702])).
% 0.22/0.34 cnf(s84, plain, spl112_102, inference(sat_conversion,[],[f1005])).
% 0.22/0.34 cnf(s106, plain, ~spl112_119, inference(sat_conversion,[],[f1088])).
% 0.22/0.34 cnf(s153, plain, spl112_157, inference(sat_conversion,[],[f1267])).
% 0.22/0.34 cnf(s186, plain, ~spl112_34 | spl112_186, inference(sat_conversion,[],[f1401])).
% 0.22/0.34 cnf(s213, plain, ~spl112_102 | spl112_119 | ~spl112_157 | ~spl112_186, inference(sat_conversion,[],[f1730])).
% 0.22/0.34 cnf(s227, plain, ~spl112_186, inference(rat,[],[s213,s106,s153,s84])).
% 0.22/0.34 cnf(s228, plain, ~spl112_34, inference(rat,[],[s186,s227])).
% 0.22/0.34 cnf(s260, plain, $false, inference(rat,[],[s22,s228])).
% 0.22/0.34 thf(f1759,plain,(
% 0.22/0.34 $false),
% 0.22/0.34 inference(avatar_sat_refutation,[],[s260])).
% 0.22/0.34 % SZS output end Proof for theBenchmark
% 0.22/0.34 % (790990)------------------------------
% 0.22/0.34 % (790990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (790990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (790990)CaDiCaL version: 2.1.3
% 0.22/0.34 % (790990)Termination reason: Refutation
% 0.22/0.34 % (790990)Time elapsed: 0.039 s
% 0.22/0.34 % (790990)Peak memory usage: 14 MB
% 0.22/0.34 % (790990)Instructions burned: 72 (million)
% 0.22/0.34 % (790982)Success in time 0.083 s
% 0.22/0.34 % Vampire exiting
%------------------------------------------------------------------------------