%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU518^1 : 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 : n026.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 0.33s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU518^1 : 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 : n026.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 13:50:42 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
% 0.22/0.33 % (619463)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.33 % (619482)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2792262199:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.33 % (619483)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.33 % (619483)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
% 0.22/0.33 % (619476)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=789229110:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.33 % (619477)lrs+10_16_si=on:nwc=1.5:random_seed=625330946:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.33 % (619478)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3441660841:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.33 % (619479)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=2291873540: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)
% 0.22/0.33 % (619480)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3920232839:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.33 % (619483)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=150549224:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.33 % (619478)Instruction limit reached!
% 0.22/0.33 % (619478)------------------------------
% 0.22/0.33 % (619478)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (619478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (619478)CaDiCaL version: 2.1.3
% 0.22/0.33 % (619478)Termination reason: Instruction limit
% 0.22/0.33 % (619478)Termination phase: shuffling
% 0.22/0.33 % (619478)Time elapsed: 0.002 s
% 0.22/0.33 % (619478)Peak memory usage: 9 MB
% 0.22/0.33 % (619478)Instructions burned: 4 (million)
% 0.22/0.33 % (619477)Instruction limit reached!
% 0.22/0.33 % (619477)------------------------------
% 0.22/0.33 % (619477)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (619477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (619477)CaDiCaL version: 2.1.3
% 0.22/0.33 % (619477)Termination reason: Instruction limit
% 0.22/0.33 % (619477)Termination phase: Saturation
% 0.22/0.33 % (619477)Time elapsed: 0.008 s
% 0.22/0.33 % (619477)Peak memory usage: 11 MB
% 0.22/0.33 % (619477)Instructions burned: 18 (million)
% 0.22/0.33 % (619480)Instruction limit reached!
% 0.22/0.33 % (619480)------------------------------
% 0.22/0.33 % (619480)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (619480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (619480)CaDiCaL version: 2.1.3
% 0.22/0.33 % (619480)Termination reason: Instruction limit
% 0.22/0.33 % (619480)Termination phase: Saturation
% 0.22/0.33 % (619480)Time elapsed: 0.011 s
% 0.22/0.33 % (619480)Peak memory usage: 11 MB
% 0.22/0.33 % (619480)Instructions burned: 25 (million)
% 0.22/0.33 % (619482)Instruction limit reached!
% 0.22/0.33 % (619482)------------------------------
% 0.22/0.33 % (619482)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (619482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (619482)CaDiCaL version: 2.1.3
% 0.22/0.33 % (619482)Termination reason: Instruction limit
% 0.22/0.33 % (619482)Termination phase: Saturation
% 0.22/0.33 % (619482)Time elapsed: 0.022 s
% 0.22/0.33 % (619482)Peak memory usage: 13 MB
% 0.22/0.33 % (619482)Instructions burned: 78 (million)
% 0.22/0.33 % (619501)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=360984748:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.33 % (619501)Instruction limit reached!
% 0.22/0.33 % (619501)------------------------------
% 0.22/0.33 % (619501)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (619501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (619501)CaDiCaL version: 2.1.3
% 0.22/0.33 % (619501)Termination reason: Instruction limit
% 0.22/0.33 % (619501)Termination phase: shuffling
% 0.22/0.33 % (619501)Time elapsed: 0.002 s
% 0.22/0.33 % (619501)Peak memory usage: 9 MB
% 0.22/0.33 % (619501)Instructions burned: 4 (million)
% 0.22/0.33 % (619508)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3984967611:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.22/0.33 % (619505)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=415351215:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.33 % (619507)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.33 % (619508)Instruction limit reached!
% 0.22/0.33 % (619508)------------------------------
% 0.22/0.33 % (619508)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (619508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (619508)CaDiCaL version: 2.1.3
% 0.22/0.33 % (619508)Termination reason: Instruction limit
% 0.22/0.33 % (619508)Termination phase: Property scanning
% 0.22/0.33 % (619508)Time elapsed: 0.003 s
% 0.22/0.33 % (619508)Peak memory usage: 10 MB
% 0.22/0.33 % (619508)Instructions burned: 13 (million)
% 0.22/0.33 % (619505)Instruction limit reached!
% 0.22/0.33 % (619505)------------------------------
% 0.22/0.33 % (619505)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (619505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (619505)CaDiCaL version: 2.1.3
% 0.22/0.33 % (619505)Termination reason: Instruction limit
% 0.22/0.33 % (619505)Termination phase: Property scanning
% 0.22/0.33 % (619505)Time elapsed: 0.003 s
% 0.22/0.33 % (619505)Peak memory usage: 10 MB
% 0.22/0.33 % (619505)Instructions burned: 7 (million)
% 0.22/0.33 % (619507)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=54317183:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.33 % (619507)Instruction limit reached!
% 0.22/0.33 % (619507)------------------------------
% 0.22/0.33 % (619507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (619507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (619507)CaDiCaL version: 2.1.3
% 0.22/0.33 % (619507)Termination reason: Instruction limit
% 0.22/0.33 % (619507)Termination phase: Property scanning
% 0.22/0.33 % (619507)Time elapsed: 0.003 s
% 0.22/0.33 % (619507)Peak memory usage: 9 MB
% 0.22/0.33 % (619507)Instructions burned: 7 (million)
% 0.22/0.33 % (619512)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
% 0.22/0.33 % (619512)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.33 % (619518)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3530187979:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.22/0.33 % (619479) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-619463-619479"...
% 0.22/0.33 % (619512)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=177414058:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.22/0.33 % (619479)...printing done.
% 0.22/0.33 % (619479)Refutation found. Thanks to Tanya!
% 0.22/0.33 % SZS status Theorem for theBenchmark
% 0.22/0.33 % SZS output start Proof for theBenchmark
% 0.22/0.33 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.33 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.22/0.33 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 0.22/0.33 thf(func_def_3, type, setextAx: $o).
% 0.22/0.33 thf(func_def_5, type, emptysetAx: $o).
% 0.22/0.33 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 0.22/0.33 thf(func_def_7, type, setadjoinAx: $o).
% 0.22/0.33 thf(func_def_8, type, powerset: ($i > $i)).
% 0.22/0.33 thf(func_def_9, type, powersetAx: $o).
% 0.22/0.33 thf(func_def_10, type, setunion: ($i > $i)).
% 0.22/0.33 thf(func_def_11, type, setunionAx: $o).
% 0.22/0.33 thf(func_def_13, type, omega0Ax: $o).
% 0.22/0.33 thf(func_def_14, type, omegaSAx: $o).
% 0.22/0.33 thf(func_def_15, type, omegaIndAx: $o).
% 0.22/0.33 thf(func_def_16, type, replAx: $o).
% 0.22/0.33 thf(func_def_17, type, foundationAx: $o).
% 0.22/0.33 thf(func_def_18, type, wellorderingAx: $o).
% 0.22/0.33 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 0.22/0.33 thf(func_def_20, type, descrp: $o).
% 0.22/0.33 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.22/0.33 thf(func_def_22, type, dsetconstrI: $o).
% 0.22/0.33 thf(func_def_23, type, dsetconstrEL: $o).
% 0.22/0.33 thf(func_def_24, type, dsetconstrER: $o).
% 0.22/0.33 thf(func_def_25, type, exuE1: $o).
% 0.22/0.33 thf(func_def_26, type, prop2set: ($o > $i)).
% 0.22/0.33 thf(func_def_27, type, prop2setE: $o).
% 0.22/0.33 thf(func_def_28, type, emptysetE: $o).
% 0.22/0.33 thf(func_def_29, type, emptysetimpfalse: $o).
% 0.22/0.33 thf(func_def_30, type, notinemptyset: $o).
% 0.22/0.33 thf(func_def_31, type, exuE3e: $o).
% 0.22/0.33 thf(func_def_32, type, setext: $o).
% 0.22/0.33 thf(func_def_33, type, emptyI: $o).
% 0.22/0.33 thf(func_def_34, type, noeltsimpempty: $o).
% 0.22/0.33 thf(func_def_35, type, setbeta: $o).
% 0.22/0.33 thf(func_def_36, type, nonempty: ($i > $o)).
% 0.22/0.33 thf(func_def_37, type, nonemptyE1: $o).
% 0.22/0.33 thf(func_def_38, type, nonemptyI: $o).
% 0.22/0.33 thf(func_def_39, type, nonemptyI1: $o).
% 0.22/0.33 thf(func_def_40, type, setadjoinIL: $o).
% 0.22/0.33 thf(func_def_41, type, emptyinunitempty: $o).
% 0.22/0.33 thf(func_def_42, type, setadjoinIR: $o).
% 0.22/0.33 thf(func_def_43, type, setadjoinE: $o).
% 0.22/0.33 thf(func_def_44, type, setadjoinOr: $o).
% 0.22/0.33 thf(func_def_45, type, setoftrueEq: $o).
% 0.22/0.33 thf(func_def_48, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.33 thf(func_def_49, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.33 thf(func_def_50, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.33 thf(func_def_51, type, vNOT: ($o > $o)).
% 0.22/0.33 thf(func_def_52, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.33 thf(func_def_53, type, vAND: ($o > $o > $o)).
% 0.22/0.33 thf(func_def_54, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.33 thf(func_def_55, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.33 thf(func_def_56, type, vIMP: ($o > $o > $o)).
% 0.22/0.33 thf(func_def_57, type, db2: !>[X0: $tType]:(X0)).
% 0.22/0.33 thf(func_def_58, type, sP0: ($i > $i > $o)).
% 0.22/0.33 thf(func_def_59, type, sP1: ($i > $o)).
% 0.22/0.33 thf(func_def_60, type, sP2: $o).
% 0.22/0.33 thf(func_def_61, type, sK3: ($i > $i)).
% 0.22/0.33 thf(func_def_65, type, sK7: ($i > $i > $i)).
% 0.22/0.33 thf(func_def_66, type, sK8: ($i > $o)).
% 0.22/0.33 thf(func_def_71, type, sK13: ($i > $i)).
% 0.22/0.33 thf(func_def_75, type, sK17: ($i > $o)).
% 0.22/0.33 thf(func_def_78, type, sK20: ($i > $o)).
% 0.22/0.33 thf(func_def_80, type, sK22: ($i > $o)).
% 0.22/0.33 thf(func_def_82, type, sK24: (($i > $i > $o) > $i > $i)).
% 0.22/0.33 thf(func_def_83, type, sK25: ($i > ($i > $i > $o) > $i > $i)).
% 0.22/0.33 thf(func_def_84, type, sK26: (($i > $i > $o) > $i > $i)).
% 0.22/0.33 thf(func_def_86, type, sK28: ($i > $i > $o)).
% 0.22/0.33 thf(func_def_87, type, sK29: ($i > $i)).
% 0.22/0.33 thf(func_def_88, type, sK30: ($i > $i)).
% 0.22/0.33 thf(func_def_89, type, sK31: (($i > $o) > $i)).
% 0.22/0.33 thf(func_def_90, type, sK32: ($i > $o)).
% 0.22/0.33 thf(func_def_94, type, sK36: ($i > $i > $i)).
% 0.22/0.33 thf(func_def_95, type, sK37: ($i > $i)).
% 0.22/0.33 thf(func_def_98, type, sK40: ($i > $i)).
% 0.22/0.33 thf(func_def_105, type, sK47: $o).
% 0.22/0.33 thf(func_def_107, type, sK49: ($i > $o)).
% 0.22/0.33 thf(func_def_115, type, sK57: ($i > $o)).
% 0.22/0.33 thf(func_def_116, type, sK58: ($i > $i > $i)).
% 0.22/0.33 thf(func_def_128, type, sK70: (($i > $o) > $i)).
% 0.22/0.33 thf(func_def_129, type, sK71: ($i > $o)).
% 0.22/0.33 thf(func_def_130, type, sK72: ($i > $i)).
% 0.22/0.33 thf(func_def_132, type, sK74: ($i > $i)).
% 0.22/0.33 thf(func_def_133, type, sK75: ($i > $i)).
% 0.22/0.33 thf(func_def_134, type, sK76: ($i > $i)).
% 0.22/0.33 thf(func_def_135, type, sK77: ($i > $i)).
% 0.22/0.33 thf(func_def_136, type, sK78: ($i > $i)).
% 0.22/0.33 thf(func_def_137, type, sK79: ($i > $i > $i > $i)).
% 0.22/0.33 thf(func_def_138, type, sK80: ($i > $i)).
% 0.22/0.33 thf(func_def_139, type, sK81: ($i > $i)).
% 0.22/0.33 thf(func_def_140, type, sK82: ($i > $i)).
% 0.22/0.33 thf(func_def_141, type, sK83: ($i > $i)).
% 0.22/0.33 thf(func_def_142, type, sK84: ($i > $i > $i)).
% 0.22/0.33 thf(func_def_143, type, sK85: ($i > $i > $i > $i)).
% 0.22/0.33 thf(func_def_144, type, sK86: ($i > $i > $i > $i)).
% 0.22/0.33 thf(func_def_145, type, sK87: ($i > $i > $i > $i)).
% 0.22/0.33 thf(func_def_146, type, sK88: ($i > $i > $i)).
% 0.22/0.33 thf(func_def_147, type, sK89: ($i > $i > $i)).
% 0.22/0.33 thf(func_def_148, type, sK90: ($i > $i > $i)).
% 0.22/0.33 thf(func_def_149, type, sK91: ($i > $i > $i)).
% 0.22/0.33 thf(func_def_151, type, sK93: $o).
% 0.22/0.33 thf(func_def_152, type, sK94: $o).
% 0.22/0.33 thf(func_def_155, type, sK97: ($i > $i)).
% 0.22/0.33 thf(func_def_158, type, sK100: ($i > $i)).
% 0.22/0.33 thf(func_def_162, type, sK104: ($i > $i > $i)).
% 0.22/0.33 thf(func_def_163, type, sK105: ($i > $i > $i)).
% 0.22/0.33 thf(f5,axiom,(
% 0.22/0.33 (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) <=> ! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0))) = powersetAx)),
% 0.22/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx)).
% 0.22/0.33 thf(f38,conjecture,(
% 0.22/0.33 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 => ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))))))))))))))))))))))))))))))))))),
% 0.22/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI)).
% 0.22/0.33 thf(f39,negated_conjecture,(
% 0.22/0.33 ~(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 => ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0)))))))))))))))))))))))))))))))))))))),
% 0.22/0.33 inference(negated_conjecture,[status(cth)],[f38])).
% 0.22/0.33 thf(f73,plain,(
% 0.22/0.33 ~(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 => ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0)))))))))))))))))))))))))))))))))))))),
% 0.22/0.33 inference(rectify,[],[f39])).
% 0.22/0.33 thf(f74,plain,(
% 0.22/0.33 ~((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) => ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => (((in @ X1 @ (powerset @ X0))) = $true))))))))))))))))))))))))))))))))))))),
% 0.22/0.33 inference(fool_elimination,[],[f73])).
% 0.22/0.33 thf(f103,plain,(
% 0.22/0.33 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) <=> ! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1))) = powersetAx)),
% 0.22/0.33 inference(rectify,[],[f5])).
% 0.22/0.33 thf(f104,plain,(
% 0.22/0.33 (powersetAx = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) <=> ($true = ((in @ X0 @ (powerset @ X1)))))),
% 0.22/0.33 inference(fool_elimination,[],[f103])).
% 0.22/0.33 thf(f124,plain,(
% 0.22/0.33 (((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $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)),
% 0.22/0.33 inference(ennf_transformation,[],[f74])).
% 0.22/0.33 thf(f125,plain,(
% 0.22/0.33 (exuE3e = $true) & (wellorderingAx = $true) & (setbeta = $true) & (nonemptyE1 = $true) & (dsetconstrI = $true) & (setunionAx = $true) & (descrp = $true) & (foundationAx = $true) & (exuE1 = $true) & (nonemptyI1 = $true) & (powersetAx = $true) & (prop2setE = $true) & (setoftrueEq = $true) & (setadjoinOr = $true) & (nonemptyI = $true) & (omegaSAx = $true) & ? [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true))) & (omega0Ax = $true) & (setadjoinAx = $true) & (noeltsimpempty = $true) & (setext = $true) & (setadjoinIR = $true) & (replAx = $true) & (emptysetE = $true) & (setadjoinIL = $true) & (dsetconstrEL = $true) & (setadjoinE = $true) & (emptyI = $true) & (omegaIndAx = $true) & (dsetconstrER = $true) & (emptysetimpfalse = $true) & (setextAx = $true) & (emptyinunitempty = $true) & (notinemptyset = $true) & (emptysetAx = $true)),
% 0.22/0.33 inference(flattening,[],[f124])).
% 0.22/0.33 thf(f139,plain,(
% 0.22/0.33 (powersetAx = $true) <=> ! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) <=> ! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)))),
% 0.22/0.33 inference(ennf_transformation,[],[f104])).
% 0.22/0.33 thf(f191,plain,(
% 0.22/0.33 ((powersetAx = $true) | ? [X0 : $i,X1 : $i] : ((? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | ($true != ((in @ X0 @ (powerset @ X1))))) & (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)) | ($true = ((in @ X0 @ (powerset @ X1))))))) & (! [X0 : $i,X1 : $i] : ((($true = ((in @ X0 @ (powerset @ X1)))) | ? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true))) & (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)) | ($true != ((in @ X0 @ (powerset @ X1)))))) | (powersetAx != $true))),
% 0.22/0.33 inference(nnf_transformation,[],[f139])).
% 0.22/0.33 thf(f192,plain,(
% 0.22/0.33 ((powersetAx = $true) | ? [X0 : $i,X1 : $i] : ((? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | ($true != ((in @ X0 @ (powerset @ X1))))) & (! [X3 : $i] : ((((in @ X3 @ X1)) = $true) | (((in @ X3 @ X0)) != $true)) | ($true = ((in @ X0 @ (powerset @ X1))))))) & (! [X4 : $i,X5 : $i] : ((($true = ((in @ X4 @ (powerset @ X5)))) | ? [X6 : $i] : (($true != ((in @ X6 @ X5))) & ($true = ((in @ X6 @ X4))))) & (! [X7 : $i] : (($true = ((in @ X7 @ X5))) | (((in @ X7 @ X4)) != $true)) | ($true != ((in @ X4 @ (powerset @ X5)))))) | (powersetAx != $true))),
% 0.22/0.33 inference(rectify,[],[f191])).
% 0.22/0.33 thf(f193,plain,(
% 0.22/0.33 ((powersetAx = $true) | (((($true != ((in @ sK35 @ sK34))) & (((in @ sK35 @ sK33)) = $true)) | ($true != ((in @ sK33 @ (powerset @ sK34))))) & (! [X3 : $i] : (($true = ((in @ X3 @ sK34))) | ($true != ((in @ X3 @ sK33)))) | ($true = ((in @ sK33 @ (powerset @ sK34))))))) & (! [X4 : $i,X5 : $i] : ((($true = ((in @ X4 @ (powerset @ X5)))) | (($true != ((in @ (sK36 @ X5 @ X4) @ X5))) & (((in @ (sK36 @ X5 @ X4) @ X4)) = $true))) & (! [X7 : $i] : (($true = ((in @ X7 @ X5))) | (((in @ X7 @ X4)) != $true)) | ($true != ((in @ X4 @ (powerset @ X5)))))) | (powersetAx != $true))),
% 0.22/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[sK33,sK34,sK35,vAPP]),skolemize(X0,sK33),skolemize(X1,sK34),skolemize(X2,sK35),skolemize(X1,sK3 @ X0)],[f192])).
% 0.22/0.33 thf(f197,plain,(
% 0.22/0.33 (exuE3e = $true) & (wellorderingAx = $true) & (setbeta = $true) & (nonemptyE1 = $true) & (dsetconstrI = $true) & (setunionAx = $true) & (descrp = $true) & (foundationAx = $true) & (exuE1 = $true) & (nonemptyI1 = $true) & (powersetAx = $true) & (prop2setE = $true) & (setoftrueEq = $true) & (setadjoinOr = $true) & (nonemptyI = $true) & (omegaSAx = $true) & ((((in @ sK42 @ (powerset @ sK41))) != $true) & ! [X2 : $i] : (($true != ((in @ X2 @ sK42))) | ($true = ((in @ X2 @ sK41))))) & (omega0Ax = $true) & (setadjoinAx = $true) & (noeltsimpempty = $true) & (setext = $true) & (setadjoinIR = $true) & (replAx = $true) & (emptysetE = $true) & (setadjoinIL = $true) & (dsetconstrEL = $true) & (setadjoinE = $true) & (emptyI = $true) & (omegaIndAx = $true) & (dsetconstrER = $true) & (emptysetimpfalse = $true) & (setextAx = $true) & (emptyinunitempty = $true) & (notinemptyset = $true) & (emptysetAx = $true)),
% 0.22/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[sK41,sK42]),skolemize(X0,sK41),skolemize(X1,sK42)],[f125])).
% 0.22/0.33 thf(f308,plain,(
% 0.22/0.33 ( ! [X4 : $i,X5 : $i] : ((((in @ (sK36 @ X5 @ X4) @ X4)) = $true) | (powersetAx != $true) | ($true = ((in @ X4 @ (powerset @ X5))))) )),
% 0.22/0.33 inference(cnf_transformation,[],[f193])).
% 0.22/0.33 thf(f309,plain,(
% 0.22/0.33 ( ! [X4 : $i,X5 : $i] : ((powersetAx != $true) | ($true != ((in @ (sK36 @ X5 @ X4) @ X5))) | ($true = ((in @ X4 @ (powerset @ X5))))) )),
% 0.22/0.33 inference(cnf_transformation,[],[f193])).
% 0.22/0.33 thf(f336,plain,(
% 0.22/0.33 ( ! [X2 : $i] : (($true = ((in @ X2 @ sK41))) | ($true != ((in @ X2 @ sK42)))) )),
% 0.22/0.33 inference(cnf_transformation,[],[f197])).
% 0.22/0.33 thf(f337,plain,(
% 0.22/0.33 (((in @ sK42 @ (powerset @ sK41))) != $true)),
% 0.22/0.33 inference(cnf_transformation,[],[f197])).
% 0.22/0.33 thf(f343,plain,(
% 0.22/0.33 (powersetAx = $true)),
% 0.22/0.33 inference(cnf_transformation,[],[f197])).
% 0.22/0.33 thf(f842,definition,(
% 0.22/0.33 spl106_74 <=> ! [X4 : $i,X5 : $i] : ((((in @ (sK36 @ X5 @ X4) @ X4)) = $true) | ($true = ((in @ X4 @ (powerset @ X5)))))),
% 0.22/0.33 introduced(definition,[new_symbols(definition,[spl106_74])],[avatar_definition])).
% 0.22/0.33 thf(f843,plain,(
% 0.22/0.33 ( ! [X4 : $i,X5 : $i] : ((((in @ (sK36 @ X5 @ X4) @ X4)) = $true) | ($true = ((in @ X4 @ (powerset @ X5))))) ) | ~spl106_74),
% 0.22/0.33 inference(avatar_component_clause,[],[f842])).
% 0.22/0.33 thf(f845,definition,(
% 0.22/0.33 spl106_75 <=> (powersetAx = $true)),
% 0.22/0.33 introduced(definition,[new_symbols(definition,[spl106_75])],[avatar_definition])).
% 0.22/0.33 thf(f848,plain,(
% 0.22/0.33 spl106_74 | ~spl106_75),
% 0.22/0.33 inference(avatar_split_clause,[],[f308,f845,f842])).
% 0.22/0.33 thf(f964,plain,(
% 0.22/0.33 spl106_75),
% 0.22/0.33 inference(avatar_split_clause,[],[f343,f845])).
% 0.22/0.33 thf(f1264,definition,(
% 0.22/0.33 spl106_165 <=> (((in @ sK42 @ (powerset @ sK41))) = $true)),
% 0.22/0.33 introduced(definition,[new_symbols(definition,[spl106_165])],[avatar_definition])).
% 0.22/0.33 thf(f1266,plain,(
% 0.22/0.33 (((in @ sK42 @ (powerset @ sK41))) != $true) | spl106_165),
% 0.22/0.33 inference(avatar_component_clause,[],[f1264])).
% 0.22/0.33 thf(f1267,plain,(
% 0.22/0.33 ~spl106_165),
% 0.22/0.33 inference(avatar_split_clause,[],[f337,f1264])).
% 0.22/0.33 thf(f1378,definition,(
% 0.22/0.33 spl106_189 <=> ! [X4 : $i,X5 : $i] : (($true != ((in @ (sK36 @ X5 @ X4) @ X5))) | ($true = ((in @ X4 @ (powerset @ X5)))))),
% 0.22/0.33 introduced(definition,[new_symbols(definition,[spl106_189])],[avatar_definition])).
% 0.22/0.33 thf(f1379,plain,(
% 0.22/0.33 ( ! [X4 : $i,X5 : $i] : (($true != ((in @ (sK36 @ X5 @ X4) @ X5))) | ($true = ((in @ X4 @ (powerset @ X5))))) ) | ~spl106_189),
% 0.22/0.33 inference(avatar_component_clause,[],[f1378])).
% 0.22/0.33 thf(f1380,plain,(
% 0.22/0.33 ~spl106_75 | spl106_189),
% 0.22/0.33 inference(avatar_split_clause,[],[f309,f1378,f845])).
% 0.22/0.33 thf(f1528,plain,(
% 0.22/0.33 ( ! [X0 : $i] : (($true != $true) | ($true != ((in @ (sK36 @ sK41 @ X0) @ sK42))) | (((in @ X0 @ (powerset @ sK41))) = $true)) ) | ~spl106_189),
% 0.22/0.33 inference(superposition,[],[f1379,f336])).
% 0.22/0.33 thf(f1533,plain,(
% 0.22/0.33 ( ! [X0 : $i] : (($true != ((in @ (sK36 @ sK41 @ X0) @ sK42))) | (((in @ X0 @ (powerset @ sK41))) = $true)) ) | ~spl106_189),
% 0.22/0.33 inference(trivial_inequality_removal,[],[f1528])).
% 0.22/0.33 thf(f1716,plain,(
% 0.22/0.33 (((in @ sK42 @ (powerset @ sK41))) = $true) | (((in @ sK42 @ (powerset @ sK41))) = $true) | ($true != $true) | (~spl106_74 | ~spl106_189)),
% 0.22/0.33 inference(superposition,[],[f1533,f843])).
% 0.22/0.33 thf(f1717,plain,(
% 0.22/0.33 (((in @ sK42 @ (powerset @ sK41))) = $true) | ($true != $true) | (~spl106_74 | ~spl106_189)),
% 0.22/0.33 inference(duplicate_literal_removal,[],[f1716])).
% 0.22/0.33 thf(f1718,plain,(
% 0.22/0.33 (((in @ sK42 @ (powerset @ sK41))) = $true) | (~spl106_74 | ~spl106_189)),
% 0.22/0.33 inference(trivial_inequality_removal,[],[f1717])).
% 0.22/0.33 thf(f1719,plain,(
% 0.22/0.33 $false | (~spl106_74 | spl106_165 | ~spl106_189)),
% 0.22/0.33 inference(forward_subsumption_resolution,[],[f1718,f1266])).
% 0.22/0.33 thf(f1720,plain,(
% 0.22/0.33 ~spl106_74 | spl106_165 | ~spl106_189),
% 0.22/0.33 inference(avatar_contradiction_clause,[],[f1719])).
% 0.22/0.33 cnf(s51, plain, spl106_74 | ~spl106_75, inference(sat_conversion,[],[f848])).
% 0.22/0.33 cnf(s78, plain, spl106_75, inference(sat_conversion,[],[f964])).
% 0.22/0.33 cnf(s157, plain, ~spl106_165, inference(sat_conversion,[],[f1267])).
% 0.22/0.33 cnf(s189, plain, ~spl106_75 | spl106_189, inference(sat_conversion,[],[f1380])).
% 0.22/0.33 cnf(s200, plain, ~spl106_74 | spl106_165 | ~spl106_189, inference(sat_conversion,[],[f1720])).
% 0.22/0.33 cnf(s221, plain, spl106_189, inference(rat,[],[s189,s78])).
% 0.22/0.33 cnf(s222, plain, ~spl106_74, inference(rat,[],[s200,s157,s221])).
% 0.22/0.33 cnf(s237, plain, $false, inference(rat,[],[s51,s78,s222])).
% 0.22/0.33 thf(f1721,plain,(
% 0.22/0.33 $false),
% 0.22/0.33 inference(avatar_sat_refutation,[],[s237])).
% 0.22/0.33 % SZS output end Proof for theBenchmark
% 0.22/0.33 % (619479)------------------------------
% 0.22/0.33 % (619479)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (619479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (619479)CaDiCaL version: 2.1.3
% 0.22/0.33 % (619479)Termination reason: Refutation
% 0.22/0.33 % (619479)Time elapsed: 0.043 s
% 0.22/0.33 % (619479)Peak memory usage: 14 MB
% 0.22/0.33 % (619479)Instructions burned: 78 (million)
% 0.22/0.33 % (619463)Success in time 0.078 s
% 0.22/0.33 % Vampire exiting
%------------------------------------------------------------------------------