%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU534^1 : 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 : n018.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 08:29:57 AM UTC 2026
% Result : Theorem 0.22s 0.36s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU534^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n018.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:50:57 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.26 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
% 0.22/0.35 % (98903)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.35 % (98911)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=1810058866: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)
% 0.22/0.35 % (98914)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.35 % (98914)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
% 0.22/0.35 % (98909)lrs+10_16_si=on:nwc=1.5:random_seed=1363381642:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.35 % (98908)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3985724631:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.35 % (98910)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=410816766:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.35 % (98912)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3168613037:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.35 % (98913)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4247555265:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.35 % (98914)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=2482348122:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.35 % (98910)Instruction limit reached!
% 0.22/0.35 % (98910)------------------------------
% 0.22/0.35 % (98910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (98910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (98910)CaDiCaL version: 2.1.3
% 0.22/0.35 % (98910)Termination reason: Instruction limit
% 0.22/0.35 % (98910)Termination phase: shuffling
% 0.22/0.35 % (98910)Time elapsed: 0.002 s
% 0.22/0.35 % (98910)Peak memory usage: 9 MB
% 0.22/0.35 % (98910)Instructions burned: 4 (million)
% 0.22/0.35 % (98909)Instruction limit reached!
% 0.22/0.35 % (98909)------------------------------
% 0.22/0.35 % (98909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (98909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (98909)CaDiCaL version: 2.1.3
% 0.22/0.35 % (98909)Termination reason: Instruction limit
% 0.22/0.35 % (98909)Termination phase: Property scanning
% 0.22/0.35 % (98909)Time elapsed: 0.008 s
% 0.22/0.35 % (98909)Peak memory usage: 10 MB
% 0.22/0.35 % (98909)Instructions burned: 19 (million)
% 0.22/0.35 % (98912)Instruction limit reached!
% 0.22/0.35 % (98912)------------------------------
% 0.22/0.35 % (98912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (98912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (98912)CaDiCaL version: 2.1.3
% 0.22/0.35 % (98912)Termination reason: Instruction limit
% 0.22/0.35 % (98912)Termination phase: Property scanning
% 0.22/0.35 % (98912)Time elapsed: 0.012 s
% 0.22/0.35 % (98912)Peak memory usage: 11 MB
% 0.22/0.35 % (98912)Instructions burned: 25 (million)
% 0.22/0.35 % (98927)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2475164136:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.35 % (98927)Instruction limit reached!
% 0.22/0.35 % (98927)------------------------------
% 0.22/0.35 % (98927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (98927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (98927)CaDiCaL version: 2.1.3
% 0.22/0.35 % (98927)Termination reason: Instruction limit
% 0.22/0.35 % (98927)Termination phase: shuffling
% 0.22/0.35 % (98927)Time elapsed: 0.002 s
% 0.22/0.35 % (98927)Peak memory usage: 9 MB
% 0.22/0.35 % (98927)Instructions burned: 4 (million)
% 0.22/0.35 % (98928)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2270163475:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.35 % (98929)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.36 % (98928)Instruction limit reached!
% 0.22/0.36 % (98928)------------------------------
% 0.22/0.36 % (98928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (98928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (98928)CaDiCaL version: 2.1.3
% 0.22/0.36 % (98928)Termination reason: Instruction limit
% 0.22/0.36 % (98928)Termination phase: Property scanning
% 0.22/0.36 % (98928)Time elapsed: 0.003 s
% 0.22/0.36 % (98928)Peak memory usage: 10 MB
% 0.22/0.36 % (98928)Instructions burned: 6 (million)
% 0.22/0.36 % (98929)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1243598814:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.36 % (98929)Instruction limit reached!
% 0.22/0.36 % (98929)------------------------------
% 0.22/0.36 % (98929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (98929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (98929)CaDiCaL version: 2.1.3
% 0.22/0.36 % (98929)Termination reason: Instruction limit
% 0.22/0.36 % (98929)Termination phase: Property scanning
% 0.22/0.36 % (98929)Time elapsed: 0.004 s
% 0.22/0.36 % (98929)Peak memory usage: 9 MB
% 0.22/0.36 % (98929)Instructions burned: 9 (million)
% 0.22/0.36 % (98913)Instruction limit reached!
% 0.22/0.36 % (98913)------------------------------
% 0.22/0.36 % (98913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (98913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (98913)CaDiCaL version: 2.1.3
% 0.22/0.36 % (98913)Termination reason: Instruction limit
% 0.22/0.36 % (98913)Termination phase: Saturation
% 0.22/0.36 % (98913)Time elapsed: 0.039 s
% 0.22/0.36 % (98913)Peak memory usage: 13 MB
% 0.22/0.36 % (98913)Instructions burned: 76 (million)
% 0.22/0.36 % (98933)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1316647539:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.22/0.36 % (98908)Instruction limit reached!
% 0.22/0.36 % (98908)------------------------------
% 0.22/0.36 % (98908)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (98908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (98908)CaDiCaL version: 2.1.3
% 0.22/0.36 % (98908)Termination reason: Instruction limit
% 0.22/0.36 % (98908)Termination phase: Saturation
% 0.22/0.36 % (98908)Time elapsed: 0.045 s
% 0.22/0.36 % (98908)Peak memory usage: 13 MB
% 0.22/0.36 % (98908)Instructions burned: 88 (million)
% 0.22/0.36 % (98937)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
% 0.22/0.36 % (98937)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.36 % (98933)Instruction limit reached!
% 0.22/0.36 % (98933)------------------------------
% 0.22/0.36 % (98933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (98933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (98933)CaDiCaL version: 2.1.3
% 0.22/0.36 % (98933)Termination reason: Instruction limit
% 0.22/0.36 % (98933)Termination phase: SInE selection
% 0.22/0.36 % (98933)Time elapsed: 0.005 s
% 0.22/0.36 % (98933)Peak memory usage: 10 MB
% 0.22/0.36 % (98933)Instructions burned: 12 (million)
% 0.22/0.36 % (98937)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4005086118:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.22/0.36 % (98940)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=357635545:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.22/0.36 % (98911) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-98903-98911"...
% 0.22/0.36 % (98945)lrs+10_1_si=on:cs=on:random_seed=767918524:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.22/0.36 % (98949)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.22/0.36 % (98911)...printing done.
% 0.22/0.36 % (98911)Refutation found. Thanks to Tanya!
% 0.22/0.36 % SZS status Theorem for theBenchmark
% 0.22/0.36 % SZS output start Proof for theBenchmark
% 0.22/0.36 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.36 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.22/0.36 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 0.22/0.36 thf(func_def_3, type, setextAx: $o).
% 0.22/0.36 thf(func_def_5, type, emptysetAx: $o).
% 0.22/0.36 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 0.22/0.36 thf(func_def_7, type, setadjoinAx: $o).
% 0.22/0.36 thf(func_def_8, type, powerset: ($i > $i)).
% 0.22/0.36 thf(func_def_9, type, powersetAx: $o).
% 0.22/0.36 thf(func_def_10, type, setunion: ($i > $i)).
% 0.22/0.36 thf(func_def_11, type, setunionAx: $o).
% 0.22/0.36 thf(func_def_13, type, omega0Ax: $o).
% 0.22/0.36 thf(func_def_14, type, omegaSAx: $o).
% 0.22/0.36 thf(func_def_15, type, omegaIndAx: $o).
% 0.22/0.36 thf(func_def_16, type, replAx: $o).
% 0.22/0.36 thf(func_def_17, type, foundationAx: $o).
% 0.22/0.36 thf(func_def_18, type, wellorderingAx: $o).
% 0.22/0.36 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 0.22/0.36 thf(func_def_20, type, descrp: $o).
% 0.22/0.36 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.22/0.36 thf(func_def_22, type, dsetconstrI: $o).
% 0.22/0.36 thf(func_def_23, type, dsetconstrEL: $o).
% 0.22/0.36 thf(func_def_24, type, dsetconstrER: $o).
% 0.22/0.36 thf(func_def_25, type, exuE1: $o).
% 0.22/0.36 thf(func_def_26, type, prop2set: ($o > $i)).
% 0.22/0.36 thf(func_def_27, type, prop2setE: $o).
% 0.22/0.36 thf(func_def_28, type, emptysetE: $o).
% 0.22/0.36 thf(func_def_29, type, emptysetimpfalse: $o).
% 0.22/0.36 thf(func_def_30, type, notinemptyset: $o).
% 0.22/0.36 thf(func_def_31, type, exuE3e: $o).
% 0.22/0.36 thf(func_def_32, type, setext: $o).
% 0.22/0.36 thf(func_def_33, type, emptyI: $o).
% 0.22/0.36 thf(func_def_34, type, noeltsimpempty: $o).
% 0.22/0.36 thf(func_def_35, type, setbeta: $o).
% 0.22/0.36 thf(func_def_36, type, nonempty: ($i > $o)).
% 0.22/0.36 thf(func_def_37, type, nonemptyE1: $o).
% 0.22/0.36 thf(func_def_38, type, nonemptyI: $o).
% 0.22/0.36 thf(func_def_39, type, nonemptyI1: $o).
% 0.22/0.36 thf(func_def_40, type, setadjoinIL: $o).
% 0.22/0.36 thf(func_def_41, type, emptyinunitempty: $o).
% 0.22/0.36 thf(func_def_42, type, setadjoinIR: $o).
% 0.22/0.36 thf(func_def_43, type, setadjoinE: $o).
% 0.22/0.36 thf(func_def_44, type, setadjoinOr: $o).
% 0.22/0.36 thf(func_def_45, type, setoftrueEq: $o).
% 0.22/0.36 thf(func_def_46, type, powersetI: $o).
% 0.22/0.36 thf(func_def_47, type, emptyinPowerset: $o).
% 0.22/0.36 thf(func_def_48, type, emptyInPowerset: $o).
% 0.22/0.36 thf(func_def_49, type, powersetE: $o).
% 0.22/0.36 thf(func_def_50, type, setunionI: $o).
% 0.22/0.36 thf(func_def_51, type, setunionE: $o).
% 0.22/0.36 thf(func_def_52, type, subPowSU: $o).
% 0.22/0.36 thf(func_def_53, type, exuE2: $o).
% 0.22/0.36 thf(func_def_54, type, nonemptyImpWitness: $o).
% 0.22/0.36 thf(func_def_55, type, uniqinunit: $o).
% 0.22/0.36 thf(func_def_56, type, notinsingleton: $o).
% 0.22/0.36 thf(func_def_57, type, eqinunit: $o).
% 0.22/0.36 thf(func_def_58, type, singletonsswitch: $o).
% 0.22/0.36 thf(func_def_59, type, upairsetE: $o).
% 0.22/0.36 thf(func_def_60, type, upairsetIL: $o).
% 0.22/0.36 thf(func_def_61, type, upairsetIR: $o).
% 0.22/0.36 thf(func_def_64, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.36 thf(func_def_65, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.36 thf(func_def_66, type, vAND: ($o > $o > $o)).
% 0.22/0.36 thf(func_def_67, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.36 thf(func_def_68, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.36 thf(func_def_69, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.36 thf(func_def_70, type, vIMP: ($o > $o > $o)).
% 0.22/0.36 thf(func_def_71, type, db2: !>[X0: $tType]:(X0)).
% 0.22/0.36 thf(func_def_72, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.36 thf(func_def_73, type, vNOT: ($o > $o)).
% 0.22/0.36 thf(func_def_74, type, sP0: ($i > $i > $o)).
% 0.22/0.36 thf(func_def_75, type, sP1: ($i > $o)).
% 0.22/0.36 thf(func_def_76, type, sP2: $o).
% 0.22/0.36 thf(func_def_83, type, sK9: ($i > $o)).
% 0.22/0.36 thf(func_def_87, type, sK13: ($i > $o)).
% 0.22/0.36 thf(func_def_102, type, sK28: (($i > $o) > $i)).
% 0.22/0.36 thf(func_def_103, type, sK29: ($i > $o)).
% 0.22/0.36 thf(func_def_104, type, sK30: ($i > $i)).
% 0.22/0.36 thf(func_def_105, type, sK31: $o).
% 0.22/0.36 thf(func_def_110, type, sK36: ($i > $i)).
% 0.22/0.36 thf(func_def_112, type, sK38: ($i > $o)).
% 0.22/0.36 thf(func_def_116, type, sK42: ($i > $i)).
% 0.22/0.36 thf(func_def_117, type, sK43: ($i > $i)).
% 0.22/0.36 thf(func_def_118, type, sK44: ($i > $i)).
% 0.22/0.36 thf(func_def_119, type, sK45: ($i > $i)).
% 0.22/0.36 thf(func_def_120, type, sK46: ($i > $i)).
% 0.22/0.36 thf(func_def_121, type, sK47: ($i > $i > $i > $i)).
% 0.22/0.36 thf(func_def_122, type, sK48: ($i > $i)).
% 0.22/0.36 thf(func_def_123, type, sK49: ($i > $i)).
% 0.22/0.36 thf(func_def_124, type, sK50: ($i > $i)).
% 0.22/0.36 thf(func_def_125, type, sK51: ($i > $i)).
% 0.22/0.36 thf(func_def_126, type, sK52: ($i > $i > $i)).
% 0.22/0.36 thf(func_def_127, type, sK53: ($i > $i > $i > $i)).
% 0.22/0.36 thf(func_def_128, type, sK54: ($i > $i > $i > $i)).
% 0.22/0.36 thf(func_def_129, type, sK55: ($i > $i > $i > $i)).
% 0.22/0.36 thf(func_def_130, type, sK56: ($i > $i > $i)).
% 0.22/0.36 thf(func_def_131, type, sK57: ($i > $i > $i)).
% 0.22/0.36 thf(func_def_132, type, sK58: ($i > $i > $i)).
% 0.22/0.36 thf(func_def_133, type, sK59: ($i > $i > $i)).
% 0.22/0.36 thf(func_def_136, type, sK62: ($i > $o)).
% 0.22/0.36 thf(func_def_140, type, sK66: ($i > $o)).
% 0.22/0.36 thf(func_def_143, type, sK69: ($i > $i > $i)).
% 0.22/0.36 thf(func_def_152, type, sK78: ($i > $i > $i)).
% 0.22/0.36 thf(func_def_155, type, sK81: $o).
% 0.22/0.36 thf(func_def_156, type, sK82: ($o > $i > $i > $i)).
% 0.22/0.36 thf(func_def_160, type, sK86: ($i > $i > $i)).
% 0.22/0.36 thf(func_def_166, type, sK92: $o).
% 0.22/0.36 thf(func_def_172, type, sK98: ($i > ($i > $i > $o) > $i)).
% 0.22/0.36 thf(func_def_173, type, sK99: ($i > $i > ($i > $i > $o) > $i)).
% 0.22/0.36 thf(func_def_174, type, sK100: ($i > ($i > $i > $o) > $i)).
% 0.22/0.36 thf(func_def_175, type, sK101: ($i > $i > $o)).
% 0.22/0.36 thf(func_def_177, type, sK103: ($i > $i)).
% 0.22/0.36 thf(func_def_178, type, sK104: ($i > $i)).
% 0.22/0.36 thf(func_def_181, type, sK107: (($i > $o) > $i)).
% 0.22/0.36 thf(func_def_182, type, sK108: ($i > $o)).
% 0.22/0.36 thf(func_def_183, type, sK109: ($i > $i)).
% 0.22/0.36 thf(func_def_184, type, sK110: ($i > $i > $i)).
% 0.22/0.36 thf(func_def_185, type, sK111: ($i > $i > $i)).
% 0.22/0.36 thf(func_def_189, type, sK115: ($i > $o)).
% 0.22/0.36 thf(func_def_193, type, sK119: ($i > $i > $i)).
% 0.22/0.36 thf(func_def_194, type, sK120: ($i > $i)).
% 0.22/0.36 thf(func_def_197, type, sK123: ($i > $o)).
% 0.22/0.36 thf(func_def_200, type, sK126: ($i > $i)).
% 0.22/0.36 thf(func_def_201, type, sK127: ($i > $o)).
% 0.22/0.36 thf(func_def_202, type, sK128: (($i > $o) > $i)).
% 0.22/0.36 thf(func_def_204, type, sK130: ($i > $i)).
% 0.22/0.36 thf(func_def_205, type, sK131: ($i > $i)).
% 0.22/0.36 thf(func_def_207, type, sK133: ($i > $i)).
% 0.22/0.36 thf(func_def_211, type, sK137: ($i > $i)).
% 0.22/0.36 thf(func_def_217, type, sK143: $o).
% 0.22/0.36 thf(f22,axiom,(
% 0.22/0.36 (! [X0 : $i] : ~(in @ X0 @ emptyset) = notinemptyset)),
% 0.22/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset)).
% 0.22/0.36 thf(f29,axiom,(
% 0.22/0.36 (! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : (in @ X1 @ X0)) = nonemptyE1)),
% 0.22/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1)).
% 0.22/0.36 thf(f30,axiom,(
% 0.22/0.36 (! [X0 : $i,X2 : $i,X1 : ($i > $o)] : ((in @ X2 @ X0) => ((X1 @ X2) => (nonempty @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))))) = nonemptyI)),
% 0.22/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI)).
% 0.22/0.36 thf(f54,conjecture,(
% 0.22/0.36 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 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => ! [X0 : $i,X1 : ($i > $o)] : (? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2)) => ((emptyset = ((dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2)))))) => $false)))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.22/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyE1)).
% 0.22/0.36 thf(f55,negated_conjecture,(
% 0.22/0.36 ~(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 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => ! [X0 : $i,X1 : ($i > $o)] : (? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2)) => ((emptyset = ((dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2)))))) => $false))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.22/0.36 inference(negated_conjecture,[status(cth)],[f54])).
% 0.22/0.36 thf(f64,plain,(
% 0.22/0.36 (! [X0 : $i] : ~(in @ X0 @ emptyset) = notinemptyset)),
% 0.22/0.36 inference(rectify,[],[f22])).
% 0.22/0.36 thf(f65,plain,(
% 0.22/0.36 ! [X0 : $i] : ~ (((in @ X0 @ emptyset)) = $true) <=> (notinemptyset = $true)),
% 0.22/0.36 inference(fool_elimination,[],[f64])).
% 0.22/0.36 thf(f82,plain,(
% 0.22/0.36 (! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : (in @ X1 @ X0)) = nonemptyE1)),
% 0.22/0.36 inference(rectify,[],[f29])).
% 0.22/0.36 thf(f83,plain,(
% 0.22/0.36 ! [X0 : $i] : ((((nonempty @ X0)) = $true) => ? [X1 : $i] : (((in @ X1 @ X0)) = $true)) <=> (nonemptyE1 = $true)),
% 0.22/0.36 inference(fool_elimination,[],[f82])).
% 0.22/0.36 thf(f149,plain,(
% 0.22/0.36 ~(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 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => ! [X0 : $i,X1 : ($i > $o)] : (? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2)) => ((emptyset = ((dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3)))))) => $false))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.22/0.36 inference(rectify,[],[f55])).
% 0.22/0.36 thf(f150,plain,(
% 0.22/0.36 ~((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) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ! [X0 : $i,X1 : ($i > $o)] : (? [X2 : $i] : ((((X1 @ X2)) = $true) & (((in @ X2 @ X0)) = $true)) => ((emptyset = ((dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))))) => $false))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.22/0.36 inference(fool_elimination,[],[f149])).
% 0.22/0.36 thf(f153,plain,(
% 0.22/0.36 (! [X0 : $i,X1 : $i,X2 : ($i > $o)] : ((in @ X1 @ X0) => ((X2 @ X1) => (nonempty @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X2 @ X3))))))) = nonemptyI)),
% 0.22/0.36 inference(rectify,[],[f30])).
% 0.22/0.36 thf(f154,plain,(
% 0.22/0.36 (nonemptyI = $true) <=> ! [X2 : ($i > $o),X0 : $i,X1 : $i] : ((((in @ X1 @ X0)) = $true) => ((((X2 @ X1)) = $true) => (((nonempty @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) = $true)))),
% 0.22/0.36 inference(fool_elimination,[],[f153])).
% 0.22/0.36 thf(f159,plain,(
% 0.22/0.36 ! [X0 : $i] : (((in @ X0 @ emptyset)) != $true) <=> (notinemptyset = $true)),
% 0.22/0.36 inference(flattening,[],[f65])).
% 0.22/0.36 thf(f171,plain,(
% 0.22/0.36 ~((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) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ! [X0 : $i,X1 : ($i > $o)] : (? [X2 : $i] : ((((X1 @ X2)) = $true) & (((in @ X2 @ X0)) = $true)) => ~ (emptyset = ((dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.22/0.36 inference(true_and_false_elimination,[],[f150])).
% 0.22/0.36 thf(f172,plain,(
% 0.22/0.36 ~((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) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ! [X0 : $i,X1 : ($i > $o)] : (? [X2 : $i] : ((((X1 @ X2)) = $true) & (((in @ X2 @ X0)) = $true)) => (emptyset != ((dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.22/0.36 inference(flattening,[],[f171])).
% 0.22/0.36 thf(f176,plain,(
% 0.22/0.36 (nonemptyI = $true) <=> ! [X2 : ($i > $o),X0 : $i,X1 : $i] : (((((nonempty @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) = $true) | (((X2 @ X1)) != $true)) | (((in @ X1 @ X0)) != $true))),
% 0.22/0.36 inference(ennf_transformation,[],[f154])).
% 0.22/0.36 thf(f177,plain,(
% 0.22/0.36 ! [X1 : $i,X0 : $i,X2 : ($i > $o)] : ((((X2 @ X1)) != $true) | (((in @ X1 @ X0)) != $true) | (((nonempty @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) = $true)) <=> (nonemptyI = $true)),
% 0.22/0.36 inference(flattening,[],[f176])).
% 0.22/0.36 thf(f195,plain,(
% 0.22/0.36 ! [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0)) = $true) | (((nonempty @ X0)) != $true)) <=> (nonemptyE1 = $true)),
% 0.22/0.36 inference(ennf_transformation,[],[f83])).
% 0.22/0.36 thf(f197,plain,(
% 0.22/0.36 (((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : ($i > $o)] : (? [X2 : $i] : ((((X1 @ X2)) = $true) & (((in @ X2 @ X0)) = $true)) & (emptyset = ((dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $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)),
% 0.22/0.36 inference(ennf_transformation,[],[f172])).
% 0.22/0.36 thf(f198,plain,(
% 0.22/0.36 (upairsetE = $true) & (setadjoinIR = $true) & (wellorderingAx = $true) & (prop2setE = $true) & (eqinunit = $true) & (emptysetAx = $true) & (foundationAx = $true) & (setadjoinAx = $true) & (notinemptyset = $true) & (dsetconstrER = $true) & (replAx = $true) & (setextAx = $true) & (dsetconstrEL = $true) & (subPowSU = $true) & (singletonsswitch = $true) & (emptyinunitempty = $true) & (upairsetIR = $true) & (emptysetE = $true) & (powersetAx = $true) & (setunionE = $true) & (upairsetIL = $true) & (setext = $true) & (descrp = $true) & (exuE2 = $true) & (notinsingleton = $true) & (powersetE = $true) & (omegaIndAx = $true) & ? [X0 : $i,X1 : ($i > $o)] : (? [X2 : $i] : ((((X1 @ X2)) = $true) & (((in @ X2 @ X0)) = $true)) & (emptyset = ((dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))) & (nonemptyI = $true) & (dsetconstrI = $true) & (nonemptyI1 = $true) & (uniqinunit = $true) & (setunionAx = $true) & (powersetI = $true) & (emptysetimpfalse = $true) & (setadjoinE = $true) & (setoftrueEq = $true) & (nonemptyE1 = $true) & (noeltsimpempty = $true) & (setbeta = $true) & (emptyInPowerset = $true) & (setunionI = $true) & (exuE3e = $true) & (omegaSAx = $true) & (setadjoinIL = $true) & (nonemptyImpWitness = $true) & (omega0Ax = $true) & (emptyinPowerset = $true) & (emptyI = $true) & (exuE1 = $true) & (setadjoinOr = $true)),
% 0.22/0.36 inference(flattening,[],[f197])).
% 0.22/0.36 thf(f233,plain,(
% 0.22/0.36 (! [X1 : $i,X0 : $i,X2 : ($i > $o)] : ((((X2 @ X1)) != $true) | (((in @ X1 @ X0)) != $true) | (((nonempty @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) = $true)) | (nonemptyI != $true)) & ((nonemptyI = $true) | ? [X1 : $i,X0 : $i,X2 : ($i > $o)] : ((((X2 @ X1)) = $true) & (((in @ X1 @ X0)) = $true) & (((nonempty @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) != $true)))),
% 0.22/0.36 inference(nnf_transformation,[],[f177])).
% 0.22/0.36 thf(f234,plain,(
% 0.22/0.36 (! [X0 : $i,X1 : $i,X2 : ($i > $o)] : ((((X2 @ X0)) != $true) | (((in @ X0 @ X1)) != $true) | (((nonempty @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0))))) = $true)) | (nonemptyI != $true)) & ((nonemptyI = $true) | ? [X3 : $i,X4 : $i,X5 : ($i > $o)] : (($true = ((X5 @ X3))) & (((in @ X3 @ X4)) = $true) & ($true != ((nonempty @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0))))))))),
% 0.22/0.36 inference(rectify,[],[f233])).
% 0.22/0.36 thf(f235,plain,(
% 0.22/0.36 (! [X0 : $i,X1 : $i,X2 : ($i > $o)] : ((((X2 @ X0)) != $true) | (((in @ X0 @ X1)) != $true) | (((nonempty @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0))))) = $true)) | (nonemptyI != $true)) & ((nonemptyI = $true) | ((((sK9 @ sK7)) = $true) & (((in @ sK7 @ sK8)) = $true) & (((nonempty @ (dsetconstr @ sK8 @ (^[Y0 : $i]: (sK9 @ Y0))))) != $true)))),
% 0.22/0.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X3,sK7),skolemize(X4,sK8),skolemize(X5,sK9)],[f234])).
% 0.22/0.36 thf(f288,plain,(
% 0.22/0.36 (upairsetE = $true) & (setadjoinIR = $true) & (wellorderingAx = $true) & (prop2setE = $true) & (eqinunit = $true) & (emptysetAx = $true) & (foundationAx = $true) & (setadjoinAx = $true) & (notinemptyset = $true) & (dsetconstrER = $true) & (replAx = $true) & (setextAx = $true) & (dsetconstrEL = $true) & (subPowSU = $true) & (singletonsswitch = $true) & (emptyinunitempty = $true) & (upairsetIR = $true) & (emptysetE = $true) & (powersetAx = $true) & (setunionE = $true) & (upairsetIL = $true) & (setext = $true) & (descrp = $true) & (exuE2 = $true) & (notinsingleton = $true) & (powersetE = $true) & (omegaIndAx = $true) & (((((sK62 @ sK63)) = $true) & ($true = ((in @ sK63 @ sK61)))) & (emptyset = ((dsetconstr @ sK61 @ (^[Y0 : $i]: (sK62 @ Y0)))))) & (nonemptyI = $true) & (dsetconstrI = $true) & (nonemptyI1 = $true) & (uniqinunit = $true) & (setunionAx = $true) & (powersetI = $true) & (emptysetimpfalse = $true) & (setadjoinE = $true) & (setoftrueEq = $true) & (nonemptyE1 = $true) & (noeltsimpempty = $true) & (setbeta = $true) & (emptyInPowerset = $true) & (setunionI = $true) & (exuE3e = $true) & (omegaSAx = $true) & (setadjoinIL = $true) & (nonemptyImpWitness = $true) & (omega0Ax = $true) & (emptyinPowerset = $true) & (emptyI = $true) & (exuE1 = $true) & (setadjoinOr = $true)),
% 0.22/0.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK61,sK62,sK63]),skolemize(X0,sK61),skolemize(X1,sK62),skolemize(X2,sK63)],[f198])).
% 0.22/0.36 thf(f344,plain,(
% 0.22/0.36 (! [X0 : $i] : (((in @ X0 @ emptyset)) != $true) | (notinemptyset != $true)) & ((notinemptyset = $true) | ? [X0 : $i] : (((in @ X0 @ emptyset)) = $true))),
% 0.22/0.36 inference(nnf_transformation,[],[f159])).
% 0.22/0.36 thf(f345,plain,(
% 0.22/0.36 (! [X0 : $i] : (((in @ X0 @ emptyset)) != $true) | (notinemptyset != $true)) & ((notinemptyset = $true) | ? [X1 : $i] : (((in @ X1 @ emptyset)) = $true))),
% 0.22/0.36 inference(rectify,[],[f344])).
% 0.22/0.36 thf(f346,plain,(
% 0.22/0.36 (! [X0 : $i] : (((in @ X0 @ emptyset)) != $true) | (notinemptyset != $true)) & ((notinemptyset = $true) | (((in @ sK114 @ emptyset)) = $true))),
% 0.22/0.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(X1,sK114)],[f345])).
% 0.22/0.36 thf(f353,plain,(
% 0.22/0.36 (! [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0)) = $true) | (((nonempty @ X0)) != $true)) | (nonemptyE1 != $true)) & ((nonemptyE1 = $true) | ? [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0)) != $true) & (((nonempty @ X0)) = $true)))),
% 0.22/0.36 inference(nnf_transformation,[],[f195])).
% 0.22/0.36 thf(f354,plain,(
% 0.22/0.36 (! [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0)) = $true) | (((nonempty @ X0)) != $true)) | (nonemptyE1 != $true)) & ((nonemptyE1 = $true) | ? [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X2)) != $true) & (((nonempty @ X2)) = $true)))),
% 0.22/0.36 inference(rectify,[],[f353])).
% 0.22/0.36 thf(f355,plain,(
% 0.22/0.36 (! [X0 : $i] : ((((in @ (sK120 @ X0) @ X0)) = $true) | (((nonempty @ X0)) != $true)) | (nonemptyE1 != $true)) & ((nonemptyE1 = $true) | (! [X3 : $i] : ($true != ((in @ X3 @ sK121))) & (((nonempty @ sK121)) = $true)))),
% 0.22/0.36 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK121]),skolemize(X5,sK30 @ X4),skolemize(X2,sK121)],[f354])).
% 0.22/0.36 thf(f389,plain,(
% 0.22/0.36 ( ! [X2 : ($i > $o),X0 : $i,X1 : $i] : ((nonemptyI != $true) | (((X2 @ X0)) != $true) | (((in @ X0 @ X1)) != $true) | (((nonempty @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0))))) = $true)) )),
% 0.22/0.36 inference(cnf_transformation,[],[f235])).
% 0.22/0.36 thf(f493,plain,(
% 0.22/0.36 (nonemptyE1 = $true)),
% 0.22/0.36 inference(cnf_transformation,[],[f288])).
% 0.22/0.36 thf(f502,plain,(
% 0.22/0.36 (nonemptyI = $true)),
% 0.22/0.36 inference(cnf_transformation,[],[f288])).
% 0.22/0.36 thf(f503,plain,(
% 0.22/0.36 (emptyset = ((dsetconstr @ sK61 @ (^[Y0 : $i]: (sK62 @ Y0)))))),
% 0.22/0.36 inference(cnf_transformation,[],[f288])).
% 0.22/0.36 thf(f504,plain,(
% 0.22/0.36 ($true = ((in @ sK63 @ sK61)))),
% 0.22/0.36 inference(cnf_transformation,[],[f288])).
% 0.22/0.36 thf(f505,plain,(
% 0.22/0.36 (((sK62 @ sK63)) = $true)),
% 0.22/0.36 inference(cnf_transformation,[],[f288])).
% 0.22/0.36 thf(f524,plain,(
% 0.22/0.36 (notinemptyset = $true)),
% 0.22/0.36 inference(cnf_transformation,[],[f288])).
% 0.22/0.36 thf(f610,plain,(
% 0.22/0.36 ( ! [X0 : $i] : ((((in @ X0 @ emptyset)) != $true) | (notinemptyset != $true)) )),
% 0.22/0.36 inference(cnf_transformation,[],[f346])).
% 0.22/0.36 thf(f623,plain,(
% 0.22/0.36 ( ! [X0 : $i] : ((nonemptyE1 != $true) | (((nonempty @ X0)) != $true) | (((in @ (sK120 @ X0) @ X0)) = $true)) )),
% 0.22/0.36 inference(cnf_transformation,[],[f355])).
% 0.22/0.36 thf(f669,plain,(
% 0.22/0.36 (emptyset = ((dsetconstr @ sK61 @ sK62)))),
% 0.22/0.36 inference(beta-eta_normalization,[],[f503])).
% 0.22/0.36 thf(f708,plain,(
% 0.22/0.36 ( ! [X2 : ($i > $o),X0 : $i,X1 : $i] : ((((X2 @ X0)) != $true) | (((nonempty @ (dsetconstr @ X1 @ X2))) = $true) | (nonemptyI != $true) | (((in @ X0 @ X1)) != $true)) )),
% 0.22/0.36 inference(beta-eta_normalization,[],[f389])).
% 0.22/0.36 thf(f772,definition,(
% 0.22/0.36 spl144_14 <=> (nonemptyE1 = $true)),
% 0.22/0.36 introduced(definition,[new_symbols(definition,[spl144_14])],[avatar_definition])).
% 0.22/0.36 thf(f827,definition,(
% 0.22/0.36 spl144_27 <=> (((sK62 @ sK63)) = $true)),
% 0.22/0.36 introduced(definition,[new_symbols(definition,[spl144_27])],[avatar_definition])).
% 0.22/0.36 thf(f829,plain,(
% 0.22/0.36 (((sK62 @ sK63)) = $true) | ~spl144_27),
% 0.22/0.36 inference(avatar_component_clause,[],[f827])).
% 0.22/0.36 thf(f830,plain,(
% 0.22/0.36 spl144_27),
% 0.22/0.36 inference(avatar_split_clause,[],[f505,f827])).
% 0.22/0.36 thf(f845,definition,(
% 0.22/0.36 spl144_31 <=> (emptyset = ((dsetconstr @ sK61 @ sK62)))),
% 0.22/0.36 introduced(definition,[new_symbols(definition,[spl144_31])],[avatar_definition])).
% 0.22/0.36 thf(f847,plain,(
% 0.22/0.36 (emptyset = ((dsetconstr @ sK61 @ sK62))) | ~spl144_31),
% 0.22/0.36 inference(avatar_component_clause,[],[f845])).
% 0.22/0.36 thf(f848,plain,(
% 0.22/0.36 spl144_31),
% 0.22/0.36 inference(avatar_split_clause,[],[f669,f845])).
% 0.22/0.36 thf(f850,definition,(
% 0.22/0.36 spl144_32 <=> (nonemptyI = $true)),
% 0.22/0.36 introduced(definition,[new_symbols(definition,[spl144_32])],[avatar_definition])).
% 0.22/0.36 thf(f1232,definition,(
% 0.22/0.36 spl144_117 <=> ! [X0 : $i] : (((in @ X0 @ emptyset)) != $true)),
% 0.22/0.36 introduced(definition,[new_symbols(definition,[spl144_117])],[avatar_definition])).
% 0.22/0.36 thf(f1233,plain,(
% 0.22/0.36 ( ! [X0 : $i] : ((((in @ X0 @ emptyset)) != $true)) ) | ~spl144_117),
% 0.22/0.36 inference(avatar_component_clause,[],[f1232])).
% 0.22/0.36 thf(f1364,plain,(
% 0.22/0.36 spl144_14),
% 0.22/0.36 inference(avatar_split_clause,[],[f493,f772])).
% 0.22/0.36 thf(f1613,plain,(
% 0.22/0.36 spl144_32),
% 0.22/0.36 inference(avatar_split_clause,[],[f502,f850])).
% 0.22/0.36 thf(f1620,definition,(
% 0.22/0.36 spl144_200 <=> ($true = ((in @ sK63 @ sK61)))),
% 0.22/0.36 introduced(definition,[new_symbols(definition,[spl144_200])],[avatar_definition])).
% 0.22/0.36 thf(f1622,plain,(
% 0.22/0.36 ($true = ((in @ sK63 @ sK61))) | ~spl144_200),
% 0.22/0.36 inference(avatar_component_clause,[],[f1620])).
% 0.22/0.36 thf(f1623,plain,(
% 0.22/0.36 spl144_200),
% 0.22/0.36 inference(avatar_split_clause,[],[f504,f1620])).
% 0.22/0.36 thf(f1673,definition,(
% 0.22/0.36 spl144_211 <=> ! [X2 : ($i > $o),X0 : $i,X1 : $i] : ((((X2 @ X0)) != $true) | (((in @ X0 @ X1)) != $true) | (((nonempty @ (dsetconstr @ X1 @ X2))) = $true))),
% 0.22/0.36 introduced(definition,[new_symbols(definition,[spl144_211])],[avatar_definition])).
% 0.22/0.36 thf(f1674,plain,(
% 0.22/0.36 ( ! [X2 : ($i > $o),X0 : $i,X1 : $i] : ((((nonempty @ (dsetconstr @ X1 @ X2))) = $true) | (((in @ X0 @ X1)) != $true) | (((X2 @ X0)) != $true)) ) | ~spl144_211),
% 0.22/0.36 inference(avatar_component_clause,[],[f1673])).
% 0.22/0.36 thf(f1675,plain,(
% 0.22/0.36 ~spl144_32 | spl144_211),
% 0.22/0.36 inference(avatar_split_clause,[],[f708,f1673,f850])).
% 0.22/0.36 thf(f1708,definition,(
% 0.22/0.36 spl144_218 <=> (notinemptyset = $true)),
% 0.22/0.36 introduced(definition,[new_symbols(definition,[spl144_218])],[avatar_definition])).
% 0.22/0.36 thf(f1711,plain,(
% 0.22/0.36 ~spl144_218 | spl144_117),
% 0.22/0.36 inference(avatar_split_clause,[],[f610,f1232,f1708])).
% 0.22/0.36 thf(f1847,definition,(
% 0.22/0.36 spl144_247 <=> ! [X0 : $i] : ((((nonempty @ X0)) != $true) | (((in @ (sK120 @ X0) @ X0)) = $true))),
% 0.22/0.36 introduced(definition,[new_symbols(definition,[spl144_247])],[avatar_definition])).
% 0.22/0.36 thf(f1848,plain,(
% 0.22/0.36 ( ! [X0 : $i] : ((((in @ (sK120 @ X0) @ X0)) = $true) | (((nonempty @ X0)) != $true)) ) | ~spl144_247),
% 0.22/0.36 inference(avatar_component_clause,[],[f1847])).
% 0.22/0.36 thf(f1849,plain,(
% 0.22/0.36 ~spl144_14 | spl144_247),
% 0.22/0.36 inference(avatar_split_clause,[],[f623,f1847,f772])).
% 0.22/0.36 thf(f1883,plain,(
% 0.22/0.36 spl144_218),
% 0.22/0.36 inference(avatar_split_clause,[],[f524,f1708])).
% 0.22/0.36 thf(f1974,definition,(
% 0.22/0.36 spl144_257 <=> (((nonempty @ emptyset)) = $true)),
% 0.22/0.36 introduced(definition,[new_symbols(definition,[spl144_257])],[avatar_definition])).
% 0.22/0.36 thf(f1976,plain,(
% 0.22/0.36 (((nonempty @ emptyset)) != $true) | spl144_257),
% 0.22/0.36 inference(avatar_component_clause,[],[f1974])).
% 0.22/0.36 thf(f1978,plain,(
% 0.22/0.36 (((nonempty @ emptyset)) != $true) | ($true != $true) | (~spl144_117 | ~spl144_247)),
% 0.22/0.36 inference(superposition,[],[f1233,f1848])).
% 0.22/0.36 thf(f1982,plain,(
% 0.22/0.36 (((nonempty @ emptyset)) != $true) | (~spl144_117 | ~spl144_247)),
% 0.22/0.36 inference(trivial_inequality_removal,[],[f1978])).
% 0.22/0.36 thf(f1985,plain,(
% 0.22/0.36 ~spl144_257 | ~spl144_117 | ~spl144_247),
% 0.22/0.36 inference(avatar_split_clause,[],[f1982,f1847,f1232,f1974])).
% 0.22/0.36 thf(f3691,plain,(
% 0.22/0.36 ( ! [X0 : $i] : ((((in @ X0 @ sK61)) != $true) | (((nonempty @ emptyset)) = $true) | (((sK62 @ X0)) != $true)) ) | (~spl144_31 | ~spl144_211)),
% 0.22/0.36 inference(superposition,[],[f1674,f847])).
% 0.22/0.36 thf(f3699,plain,(
% 0.22/0.36 ( ! [X0 : $i] : ((((in @ X0 @ sK61)) != $true) | (((sK62 @ X0)) != $true)) ) | (~spl144_31 | ~spl144_211 | spl144_257)),
% 0.22/0.36 inference(forward_subsumption_resolution,[],[f3691,f1976])).
% 0.22/0.36 thf(f3752,plain,(
% 0.22/0.36 ($true != $true) | (((sK62 @ sK63)) != $true) | (~spl144_31 | ~spl144_200 | ~spl144_211 | spl144_257)),
% 0.22/0.36 inference(superposition,[],[f3699,f1622])).
% 0.22/0.36 thf(f3791,plain,(
% 0.22/0.36 (((sK62 @ sK63)) != $true) | (~spl144_31 | ~spl144_200 | ~spl144_211 | spl144_257)),
% 0.22/0.36 inference(trivial_inequality_removal,[],[f3752])).
% 0.22/0.36 thf(f3826,plain,(
% 0.22/0.36 $false | (~spl144_27 | ~spl144_31 | ~spl144_200 | ~spl144_211 | spl144_257)),
% 0.22/0.36 inference(forward_subsumption_resolution,[],[f3791,f829])).
% 0.22/0.36 thf(f3827,plain,(
% 0.22/0.36 ~spl144_27 | ~spl144_31 | ~spl144_200 | ~spl144_211 | spl144_257),
% 0.22/0.36 inference(avatar_contradiction_clause,[],[f3826])).
% 0.22/0.36 cnf(s17, plain, spl144_27, inference(sat_conversion,[],[f830])).
% 0.22/0.36 cnf(s20, plain, spl144_31, inference(sat_conversion,[],[f848])).
% 0.22/0.36 cnf(s126, plain, spl144_14, inference(sat_conversion,[],[f1364])).
% 0.22/0.36 cnf(s187, plain, spl144_32, inference(sat_conversion,[],[f1613])).
% 0.22/0.36 cnf(s189, plain, spl144_200, inference(sat_conversion,[],[f1623])).
% 0.22/0.36 cnf(s205, plain, ~spl144_32 | spl144_211, inference(sat_conversion,[],[f1675])).
% 0.22/0.36 cnf(s216, plain, spl144_117 | ~spl144_218, inference(sat_conversion,[],[f1711])).
% 0.22/0.36 cnf(s249, plain, ~spl144_14 | spl144_247, inference(sat_conversion,[],[f1849])).
% 0.22/0.36 cnf(s258, plain, spl144_218, inference(sat_conversion,[],[f1883])).
% 0.22/0.36 cnf(s263, plain, ~spl144_117 | ~spl144_247 | ~spl144_257, inference(sat_conversion,[],[f1985])).
% 0.22/0.36 cnf(s316, plain, ~spl144_27 | ~spl144_31 | ~spl144_200 | ~spl144_211 | spl144_257, inference(sat_conversion,[],[f3827])).
% 0.22/0.36 cnf(s322, plain, spl144_117, inference(rat,[],[s216,s258])).
% 0.22/0.36 cnf(s326, plain, spl144_211, inference(rat,[],[s205,s187])).
% 0.22/0.36 cnf(s336, plain, spl144_247, inference(rat,[],[s249,s126])).
% 0.22/0.36 cnf(s337, plain, ~spl144_257, inference(rat,[],[s263,s322,s336])).
% 0.22/0.36 cnf(s394, plain, ~spl144_27, inference(rat,[],[s316,s337,s326,s189,s20])).
% 0.22/0.36 cnf(s395, plain, $false, inference(rat,[],[s17,s394])).
% 0.22/0.36 thf(f3854,plain,(
% 0.22/0.36 $false),
% 0.22/0.36 inference(avatar_sat_refutation,[],[s395])).
% 0.22/0.36 % SZS output end Proof for theBenchmark
% 0.22/0.36 % (98911)------------------------------
% 0.22/0.36 % (98911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (98911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (98911)CaDiCaL version: 2.1.3
% 0.22/0.36 % (98911)Termination reason: Refutation
% 0.22/0.36 % (98911)Time elapsed: 0.069 s
% 0.22/0.36 % (98911)Peak memory usage: 15 MB
% 0.22/0.36 % (98911)Instructions burned: 221 (million)
% 0.22/0.36 % (98903)Success in time 0.088 s
% 0.22/0.36 % Vampire exiting
%------------------------------------------------------------------------------