%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU563^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:30:05 AM UTC 2026
% Result : Theorem 0.21s 0.32s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU563^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n001.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 13:56:21 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.32 % (1280785)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.32 % (1280793)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=3843856245:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.32 % (1280796)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.32 % (1280796)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.32 % (1280790)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3942578259:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.32 % (1280791)lrs+10_16_si=on:nwc=1.5:random_seed=1605082387:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.32 % (1280792)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1479213249:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.32 % (1280795)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=824175616:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.32 % (1280796)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=312770038:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.32 % (1280794)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4171913505:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.32 % (1280792)Instruction limit reached!
% 0.21/0.32 % (1280792)------------------------------
% 0.21/0.32 % (1280792)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (1280792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (1280792)CaDiCaL version: 2.1.3
% 0.21/0.32 % (1280792)Termination reason: Instruction limit
% 0.21/0.32 % (1280792)Termination phase: shuffling
% 0.21/0.32 % (1280792)Time elapsed: 0.003 s
% 0.21/0.32 % (1280792)Peak memory usage: 10 MB
% 0.21/0.32 % (1280792)Instructions burned: 6 (million)
% 0.21/0.32 % (1280791)Instruction limit reached!
% 0.21/0.32 % (1280791)------------------------------
% 0.21/0.32 % (1280791)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (1280791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (1280791)CaDiCaL version: 2.1.3
% 0.21/0.32 % (1280791)Termination reason: Instruction limit
% 0.21/0.32 % (1280791)Termination phase: Property scanning
% 0.21/0.32 % (1280791)Time elapsed: 0.009 s
% 0.21/0.32 % (1280791)Peak memory usage: 10 MB
% 0.21/0.32 % (1280791)Instructions burned: 20 (million)
% 0.21/0.32 % (1280794)Instruction limit reached!
% 0.21/0.32 % (1280794)------------------------------
% 0.21/0.32 % (1280794)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (1280794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (1280794)CaDiCaL version: 2.1.3
% 0.21/0.32 % (1280794)Termination reason: Instruction limit
% 0.21/0.32 % (1280794)Termination phase: Property scanning
% 0.21/0.32 % (1280794)Time elapsed: 0.012 s
% 0.21/0.32 % (1280794)Peak memory usage: 11 MB
% 0.21/0.32 % (1280794)Instructions burned: 25 (million)
% 0.21/0.32 % (1280804)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1915691113:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.32 % (1280804)Instruction limit reached!
% 0.21/0.32 % (1280804)------------------------------
% 0.21/0.32 % (1280804)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (1280804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (1280804)CaDiCaL version: 2.1.3
% 0.21/0.32 % (1280804)Termination reason: Instruction limit
% 0.21/0.32 % (1280804)Termination phase: shuffling
% 0.21/0.32 % (1280804)Time elapsed: 0.002 s
% 0.21/0.32 % (1280804)Peak memory usage: 10 MB
% 0.21/0.32 % (1280804)Instructions burned: 4 (million)
% 0.21/0.32 % (1280805)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1615033622:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.32 % (1280806)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.32 % (1280805)Instruction limit reached!
% 0.21/0.32 % (1280805)------------------------------
% 0.21/0.32 % (1280805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (1280805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (1280805)CaDiCaL version: 2.1.3
% 0.21/0.32 % (1280805)Termination reason: Instruction limit
% 0.21/0.32 % (1280805)Termination phase: shuffling
% 0.21/0.32 % (1280805)Time elapsed: 0.003 s
% 0.21/0.32 % (1280805)Peak memory usage: 10 MB
% 0.21/0.32 % (1280805)Instructions burned: 6 (million)
% 0.21/0.32 % (1280806)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3331258955:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.32 % (1280795)Instruction limit reached!
% 0.21/0.32 % (1280795)------------------------------
% 0.21/0.32 % (1280795)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (1280795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (1280795)CaDiCaL version: 2.1.3
% 0.21/0.32 % (1280795)Termination reason: Instruction limit
% 0.21/0.32 % (1280795)Termination phase: Saturation
% 0.21/0.32 % (1280795)Time elapsed: 0.036 s
% 0.21/0.32 % (1280795)Peak memory usage: 13 MB
% 0.21/0.32 % (1280795)Instructions burned: 76 (million)
% 0.21/0.32 % (1280806)Instruction limit reached!
% 0.21/0.32 % (1280806)------------------------------
% 0.21/0.32 % (1280806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (1280806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (1280806)CaDiCaL version: 2.1.3
% 0.21/0.32 % (1280806)Termination reason: Instruction limit
% 0.21/0.32 % (1280806)Termination phase: shuffling
% 0.21/0.32 % (1280806)Time elapsed: 0.004 s
% 0.21/0.32 % (1280806)Peak memory usage: 10 MB
% 0.21/0.32 % (1280806)Instructions burned: 9 (million)
% 0.21/0.32 % (1280793) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1280785-1280793"...
% 0.21/0.32 % (1280790) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1280785-1280790"...
% 0.21/0.32 % (1280793)...printing done.
% 0.21/0.32 % (1280793)Refutation found. Thanks to Tanya!
% 0.21/0.32 % SZS status Theorem for theBenchmark
% 0.21/0.32 % SZS output start Proof for theBenchmark
% 0.21/0.32 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.32 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.21/0.32 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 0.21/0.32 thf(func_def_3, type, setextAx: $o).
% 0.21/0.32 thf(func_def_5, type, emptysetAx: $o).
% 0.21/0.32 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 0.21/0.32 thf(func_def_7, type, setadjoinAx: $o).
% 0.21/0.32 thf(func_def_8, type, powerset: ($i > $i)).
% 0.21/0.32 thf(func_def_9, type, powersetAx: $o).
% 0.21/0.32 thf(func_def_10, type, setunion: ($i > $i)).
% 0.21/0.32 thf(func_def_11, type, setunionAx: $o).
% 0.21/0.32 thf(func_def_13, type, omega0Ax: $o).
% 0.21/0.32 thf(func_def_14, type, omegaSAx: $o).
% 0.21/0.32 thf(func_def_15, type, omegaIndAx: $o).
% 0.21/0.32 thf(func_def_16, type, replAx: $o).
% 0.21/0.32 thf(func_def_17, type, foundationAx: $o).
% 0.21/0.32 thf(func_def_18, type, wellorderingAx: $o).
% 0.21/0.32 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 0.21/0.32 thf(func_def_20, type, descrp: $o).
% 0.21/0.32 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.21/0.32 thf(func_def_22, type, dsetconstrI: $o).
% 0.21/0.32 thf(func_def_23, type, dsetconstrEL: $o).
% 0.21/0.32 thf(func_def_24, type, dsetconstrER: $o).
% 0.21/0.32 thf(func_def_25, type, exuE1: $o).
% 0.21/0.32 thf(func_def_26, type, prop2set: ($o > $i)).
% 0.21/0.32 thf(func_def_27, type, prop2setE: $o).
% 0.21/0.32 thf(func_def_28, type, emptysetE: $o).
% 0.21/0.32 thf(func_def_29, type, emptysetimpfalse: $o).
% 0.21/0.32 thf(func_def_30, type, notinemptyset: $o).
% 0.21/0.32 thf(func_def_31, type, exuE3e: $o).
% 0.21/0.32 thf(func_def_32, type, setext: $o).
% 0.21/0.32 thf(func_def_33, type, emptyI: $o).
% 0.21/0.32 thf(func_def_34, type, noeltsimpempty: $o).
% 0.21/0.32 thf(func_def_35, type, setbeta: $o).
% 0.21/0.32 thf(func_def_36, type, nonempty: ($i > $o)).
% 0.21/0.32 thf(func_def_37, type, nonemptyE1: $o).
% 0.21/0.32 thf(func_def_38, type, nonemptyI: $o).
% 0.21/0.32 thf(func_def_39, type, nonemptyI1: $o).
% 0.21/0.32 thf(func_def_40, type, setadjoinIL: $o).
% 0.21/0.32 thf(func_def_41, type, emptyinunitempty: $o).
% 0.21/0.32 thf(func_def_42, type, setadjoinIR: $o).
% 0.21/0.32 thf(func_def_43, type, setadjoinE: $o).
% 0.21/0.32 thf(func_def_44, type, setadjoinOr: $o).
% 0.21/0.32 thf(func_def_45, type, setoftrueEq: $o).
% 0.21/0.32 thf(func_def_46, type, powersetI: $o).
% 0.21/0.32 thf(func_def_47, type, emptyinPowerset: $o).
% 0.21/0.32 thf(func_def_48, type, emptyInPowerset: $o).
% 0.21/0.32 thf(func_def_49, type, powersetE: $o).
% 0.21/0.32 thf(func_def_50, type, setunionI: $o).
% 0.21/0.32 thf(func_def_51, type, setunionE: $o).
% 0.21/0.32 thf(func_def_52, type, subPowSU: $o).
% 0.21/0.32 thf(func_def_53, type, exuE2: $o).
% 0.21/0.32 thf(func_def_54, type, nonemptyImpWitness: $o).
% 0.21/0.32 thf(func_def_55, type, uniqinunit: $o).
% 0.21/0.32 thf(func_def_56, type, notinsingleton: $o).
% 0.21/0.32 thf(func_def_57, type, eqinunit: $o).
% 0.21/0.32 thf(func_def_58, type, singletonsswitch: $o).
% 0.21/0.32 thf(func_def_59, type, upairsetE: $o).
% 0.21/0.32 thf(func_def_60, type, upairsetIL: $o).
% 0.21/0.32 thf(func_def_61, type, upairsetIR: $o).
% 0.21/0.32 thf(func_def_62, type, emptyE1: $o).
% 0.21/0.32 thf(func_def_63, type, vacuousDall: $o).
% 0.21/0.32 thf(func_def_64, type, quantDeMorgan1: $o).
% 0.21/0.32 thf(func_def_65, type, quantDeMorgan2: $o).
% 0.21/0.32 thf(func_def_66, type, quantDeMorgan3: $o).
% 0.21/0.32 thf(func_def_67, type, quantDeMorgan4: $o).
% 0.21/0.32 thf(func_def_68, type, prop2setI: $o).
% 0.21/0.32 thf(func_def_69, type, set2prop: ($i > $o)).
% 0.21/0.32 thf(func_def_70, type, prop2set2propI: $o).
% 0.21/0.32 thf(func_def_71, type, notdexE: $o).
% 0.21/0.32 thf(func_def_72, type, notdallE: $o).
% 0.21/0.32 thf(func_def_73, type, exuI1: $o).
% 0.21/0.32 thf(func_def_74, type, exuI3: $o).
% 0.21/0.32 thf(func_def_75, type, exuI2: $o).
% 0.21/0.32 thf(func_def_76, type, inCongP: $o).
% 0.21/0.32 thf(func_def_77, type, in__Cong: $o).
% 0.21/0.32 thf(func_def_78, type, exuE3u: $o).
% 0.21/0.32 thf(func_def_79, type, exu__Cong: $o).
% 0.21/0.32 thf(func_def_80, type, emptyset__Cong: $o).
% 0.21/0.32 thf(func_def_81, type, setadjoin__Cong: $o).
% 0.21/0.32 thf(func_def_82, type, powerset__Cong: $o).
% 0.21/0.32 thf(func_def_83, type, setunion__Cong: $o).
% 0.21/0.32 thf(func_def_84, type, omega__Cong: $o).
% 0.21/0.32 thf(func_def_85, type, exuEu: $o).
% 0.21/0.32 thf(func_def_86, type, descr__Cong: $o).
% 0.21/0.32 thf(func_def_87, type, dsetconstr__Cong: $o).
% 0.21/0.32 thf(func_def_88, type, subset: ($i > $i > $o)).
% 0.21/0.32 thf(func_def_89, type, disjoint: ($i > $i > $o)).
% 0.21/0.32 thf(func_def_90, type, setsmeet: ($i > $i > $o)).
% 0.21/0.32 thf(func_def_91, type, subsetI1: $o).
% 0.21/0.32 thf(func_def_92, type, eqimpsubset2: $o).
% 0.21/0.32 thf(func_def_93, type, eqimpsubset1: $o).
% 0.21/0.32 thf(func_def_94, type, subsetI2: $o).
% 0.21/0.32 thf(func_def_95, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.32 thf(func_def_96, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.32 thf(func_def_99, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.32 thf(func_def_100, type, vIMP: ($o > $o > $o)).
% 0.21/0.32 thf(func_def_101, type, db2: !>[X0: $tType]:(X0)).
% 0.21/0.32 thf(func_def_102, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.32 thf(func_def_103, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.32 thf(func_def_104, type, vNOT: ($o > $o)).
% 0.21/0.32 thf(func_def_105, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.32 thf(func_def_106, type, vAND: ($o > $o > $o)).
% 0.21/0.32 thf(func_def_107, type, sP0: ($i > $i > $o)).
% 0.21/0.32 thf(func_def_108, type, sP1: ($i > $o)).
% 0.21/0.32 thf(func_def_109, type, sP2: $o).
% 0.21/0.32 thf(func_def_112, type, sK5: ($i > $o)).
% 0.21/0.32 thf(func_def_115, type, sK8: ($i > $i)).
% 0.21/0.32 thf(func_def_116, type, sK9: ($i > $i)).
% 0.21/0.32 thf(func_def_120, type, sK13: ($i > $i > $i)).
% 0.21/0.32 thf(func_def_121, type, sK14: ($i > ($i > $i > $o) > $i)).
% 0.21/0.32 thf(func_def_122, type, sK15: ($i > $i > ($i > $i > $o) > $i)).
% 0.21/0.32 thf(func_def_123, type, sK16: ($i > ($i > $i > $o) > $i)).
% 0.21/0.32 thf(func_def_124, type, sK17: ($i > $i > $o)).
% 0.21/0.32 thf(func_def_126, type, sK19: ($i > $i)).
% 0.21/0.32 thf(func_def_127, type, sK20: ($i > $i)).
% 0.21/0.32 thf(func_def_132, type, sK25: ($i > $o)).
% 0.21/0.32 thf(func_def_135, type, sK28: ($i > ($i > $o) > $i)).
% 0.21/0.32 thf(func_def_136, type, sK29: $o).
% 0.21/0.32 thf(func_def_137, type, sK30: ($i > ($i > $o) > $i)).
% 0.21/0.32 thf(func_def_138, type, sK31: ($i > $o)).
% 0.21/0.32 thf(func_def_142, type, sK35: ($i > $i)).
% 0.21/0.32 thf(func_def_143, type, sK36: ($i > $o)).
% 0.21/0.32 thf(func_def_145, type, sK38: (($i > $o) > $i)).
% 0.21/0.32 thf(func_def_146, type, sK39: (($i > $o) > $i)).
% 0.21/0.32 thf(func_def_153, type, sK46: ($o > $i > $i > $i)).
% 0.21/0.32 thf(func_def_156, type, sK49: $o).
% 0.21/0.32 thf(func_def_173, type, sK66: $o).
% 0.21/0.32 thf(func_def_174, type, sK67: (($i > $o) > ($i > $o) > $i)).
% 0.21/0.32 thf(func_def_175, type, sK68: (($i > $o) > ($i > $o) > $i)).
% 0.21/0.32 thf(func_def_176, type, sK69: ($i > $o)).
% 0.21/0.32 thf(func_def_177, type, sK70: ($i > $o)).
% 0.21/0.32 thf(func_def_179, type, sK72: ($i > $i)).
% 0.21/0.32 thf(func_def_180, type, sK73: ($i > ($i > $o) > $i)).
% 0.21/0.32 thf(func_def_181, type, sK74: ($i > $o)).
% 0.21/0.32 thf(func_def_185, type, sK78: ($i > $o)).
% 0.21/0.32 thf(func_def_187, type, sK80: (($i > $o) > $i > $i)).
% 0.21/0.32 thf(func_def_192, type, sK85: ($i > $i > $i)).
% 0.21/0.32 thf(func_def_193, type, sK86: ($i > $o)).
% 0.21/0.32 thf(func_def_197, type, sK90: (($i > $o) > ($i > $o) > $i)).
% 0.21/0.32 thf(func_def_198, type, sK91: (($i > $o) > ($i > $o) > $i)).
% 0.21/0.32 thf(func_def_199, type, sK92: ($i > $o)).
% 0.21/0.32 thf(func_def_200, type, sK93: ($i > $o)).
% 0.21/0.32 thf(func_def_201, type, sK94: ($i > $o)).
% 0.21/0.32 thf(func_def_202, type, sK95: ($i > $i)).
% 0.21/0.32 thf(func_def_203, type, sK96: (($i > $o) > $i)).
% 0.21/0.32 thf(func_def_204, type, sK97: ($i > $o)).
% 0.21/0.32 thf(func_def_211, type, sK104: (($i > $o) > ($i > $o) > $i > $i > $i)).
% 0.21/0.32 thf(func_def_212, type, sK105: (($i > $o) > ($i > $o) > $i > $i > $i)).
% 0.21/0.32 thf(func_def_215, type, sK108: ($i > $o)).
% 0.21/0.32 thf(func_def_216, type, sK109: ($i > $o)).
% 0.21/0.32 thf(func_def_217, type, sK110: (($i > $o) > $i)).
% 0.21/0.32 thf(func_def_218, type, sK111: ($i > $o)).
% 0.21/0.32 thf(func_def_226, type, sK119: ($i > $o)).
% 0.21/0.32 thf(func_def_227, type, sK120: ($i > $o)).
% 0.21/0.32 thf(func_def_229, type, sK122: ($i > $i > $i)).
% 0.21/0.32 thf(func_def_233, type, sK126: $o).
% 0.21/0.32 thf(func_def_234, type, sK127: ($i > $i > $i)).
% 0.21/0.32 thf(func_def_235, type, sK128: ($i > $i > $i)).
% 0.21/0.32 thf(func_def_238, type, sK131: ($i > $i)).
% 0.21/0.32 thf(func_def_244, type, sK137: ($i > $i)).
% 0.21/0.32 thf(func_def_245, type, sK138: ($i > $i)).
% 0.21/0.32 thf(func_def_246, type, sK139: ($i > $i)).
% 0.21/0.32 thf(func_def_247, type, sK140: ($i > $i)).
% 0.21/0.32 thf(func_def_248, type, sK141: ($i > $i)).
% 0.21/0.32 thf(func_def_249, type, sK142: ($i > $i > $i > $i)).
% 0.21/0.32 thf(func_def_250, type, sK143: ($i > $i)).
% 0.21/0.32 thf(func_def_251, type, sK144: ($i > $i)).
% 0.21/0.32 thf(func_def_252, type, sK145: ($i > $i)).
% 0.21/0.32 thf(func_def_253, type, sK146: ($i > $i)).
% 0.21/0.32 thf(func_def_254, type, sK147: ($i > $i > $i)).
% 0.21/0.32 thf(func_def_255, type, sK148: ($i > $i > $i > $i)).
% 0.21/0.32 thf(func_def_256, type, sK149: ($i > $i > $i > $i)).
% 0.21/0.32 thf(func_def_257, type, sK150: ($i > $i > $i > $i)).
% 0.21/0.32 thf(func_def_258, type, sK151: ($i > $i > $i)).
% 0.21/0.32 thf(func_def_259, type, sK152: ($i > $i > $i)).
% 0.21/0.32 thf(func_def_260, type, sK153: ($i > $i > $i)).
% 0.21/0.32 thf(func_def_261, type, sK154: ($i > $i > $i)).
% 0.21/0.32 thf(func_def_263, type, sK156: ($i > $o)).
% 0.21/0.32 thf(func_def_266, type, sK159: ($i > $o)).
% 0.21/0.32 thf(func_def_270, type, sK163: $o).
% 0.21/0.32 thf(func_def_271, type, sK164: ($i > ($i > $o) > $i)).
% 0.21/0.32 thf(func_def_272, type, sK165: ($i > $o)).
% 0.21/0.32 thf(func_def_275, type, sK168: ($i > $o)).
% 0.21/0.32 thf(func_def_277, type, sK170: ($i > $i)).
% 0.21/0.32 thf(func_def_286, type, sK179: ($i > $o)).
% 0.21/0.32 thf(func_def_288, type, sK181: ($i > $i)).
% 0.21/0.32 thf(func_def_289, type, sK182: ($i > $i > $i)).
% 0.21/0.32 thf(func_def_297, type, sK190: (($i > $o) > $i > $i)).
% 0.21/0.32 thf(func_def_299, type, sK192: ($i > $o)).
% 0.21/0.32 thf(func_def_305, type, sK198: ($i > $o)).
% 0.21/0.32 thf(func_def_308, type, sK201: ($i > ($i > $o) > $i)).
% 0.21/0.32 thf(func_def_310, type, sK203: ($i > $o)).
% 0.21/0.32 thf(func_def_314, type, sK207: (($i > $o) > $i)).
% 0.21/0.32 thf(func_def_315, type, sK208: ($i > $o)).
% 0.21/0.32 thf(func_def_316, type, sK209: ($i > $i)).
% 0.21/0.32 thf(func_def_317, type, sK210: ($i > ($i > $o) > $i)).
% 0.21/0.32 thf(func_def_318, type, sK211: ($i > $o)).
% 0.21/0.32 thf(func_def_324, type, sK217: ($i > $i > $i)).
% 0.21/0.32 thf(func_def_331, type, sK224: $o).
% 0.21/0.32 thf(func_def_332, type, sK225: ($i > $i > $i)).
% 0.21/0.32 thf(f3,axiom,(
% 0.21/0.32 (! [X0 : $i] : ~(in @ X0 @ emptyset) = emptysetAx)),
% 0.21/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx)).
% 0.21/0.32 thf(f79,axiom,(
% 0.21/0.32 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 0.21/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1)).
% 0.21/0.32 thf(f83,conjecture,(
% 0.21/0.32 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 => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => ! [X0 : $i] : (subset @ emptyset @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.21/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset)).
% 0.21/0.32 thf(f84,negated_conjecture,(
% 0.21/0.32 ~(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 => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => ! [X0 : $i] : (subset @ emptyset @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.21/0.32 inference(negated_conjecture,[status(cth)],[f83])).
% 0.21/0.32 thf(f106,plain,(
% 0.21/0.32 (! [X0 : $i] : ~(in @ X0 @ emptyset) = emptysetAx)),
% 0.21/0.32 inference(rectify,[],[f3])).
% 0.21/0.32 thf(f107,plain,(
% 0.21/0.32 ! [X0 : $i] : ~ (((in @ X0 @ emptyset)) = $true) <=> (emptysetAx = $true)),
% 0.21/0.32 inference(fool_elimination,[],[f106])).
% 0.21/0.32 thf(f133,plain,(
% 0.21/0.32 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 0.21/0.32 inference(rectify,[],[f79])).
% 0.21/0.32 thf(f134,plain,(
% 0.21/0.32 (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => (((subset @ X0 @ X1)) = $true))),
% 0.21/0.32 inference(fool_elimination,[],[f133])).
% 0.21/0.32 thf(f204,plain,(
% 0.21/0.32 ~(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 => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => ! [X0 : $i] : (subset @ emptyset @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.21/0.32 inference(rectify,[],[f84])).
% 0.21/0.32 thf(f205,plain,(
% 0.21/0.32 ~((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) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ! [X0 : $i] : (((subset @ emptyset @ X0)) = $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 0.21/0.32 inference(fool_elimination,[],[f204])).
% 0.21/0.32 thf(f249,plain,(
% 0.21/0.32 (emptysetAx = $true) <=> ! [X0 : $i] : (((in @ X0 @ emptyset)) != $true)),
% 0.21/0.32 inference(flattening,[],[f107])).
% 0.21/0.32 thf(f271,plain,(
% 0.21/0.32 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i] : (((subset @ emptyset @ X0)) != $true) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (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)),
% 0.21/0.32 inference(ennf_transformation,[],[f205])).
% 0.21/0.32 thf(f272,plain,(
% 0.21/0.32 (notinemptyset = $true) & (noeltsimpempty = $true) & (prop2setI = $true) & (omega0Ax = $true) & (powersetAx = $true) & (in__Cong = $true) & (uniqinunit = $true) & (eqimpsubset1 = $true) & (dsetconstrER = $true) & (eqimpsubset2 = $true) & (emptyInPowerset = $true) & (quantDeMorgan1 = $true) & (setextAx = $true) & (exuEu = $true) & (nonemptyE1 = $true) & (setadjoinIL = $true) & (quantDeMorgan2 = $true) & (prop2set2propI = $true) & (subsetI2 = $true) & (notdexE = $true) & (prop2setE = $true) & (subsetI1 = $true) & (exuE3u = $true) & (emptyinunitempty = $true) & (omegaIndAx = $true) & (dsetconstrEL = $true) & (descrp = $true) & (exuI3 = $true) & (omega__Cong = $true) & (quantDeMorgan3 = $true) & ? [X0 : $i] : (((subset @ emptyset @ X0)) != $true) & (setadjoinE = $true) & (setbeta = $true) & (wellorderingAx = $true) & (emptyinPowerset = $true) & (vacuousDall = $true) & (omegaSAx = $true) & (setadjoinOr = $true) & (exu__Cong = $true) & (exuE1 = $true) & (quantDeMorgan4 = $true) & (emptysetE = $true) & (setadjoinIR = $true) & (eqinunit = $true) & (descr__Cong = $true) & (setoftrueEq = $true) & (inCongP = $true) & (powersetE = $true) & (notinsingleton = $true) & (exuE3e = $true) & (emptyset__Cong = $true) & (subPowSU = $true) & (upairsetE = $true) & (setext = $true) & (foundationAx = $true) & (nonemptyI = $true) & (emptyI = $true) & (nonemptyImpWitness = $true) & (setunionI = $true) & (exuI2 = $true) & (setadjoin__Cong = $true) & (setunionAx = $true) & (replAx = $true) & (emptyE1 = $true) & (dsetconstrI = $true) & (notdallE = $true) & (upairsetIL = $true) & (upairsetIR = $true) & (setunion__Cong = $true) & (singletonsswitch = $true) & (nonemptyI1 = $true) & (exuI1 = $true) & (emptysetimpfalse = $true) & (setunionE = $true) & (exuE2 = $true) & (dsetconstr__Cong = $true) & (powersetI = $true) & (setadjoinAx = $true) & (powerset__Cong = $true) & (emptysetAx = $true)),
% 0.21/0.32 inference(flattening,[],[f271])).
% 0.21/0.32 thf(f345,plain,(
% 0.21/0.32 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((subset @ X0 @ X1)) = $true)) <=> (subsetI1 = $true)),
% 0.21/0.32 inference(ennf_transformation,[],[f134])).
% 0.21/0.32 thf(f486,plain,(
% 0.21/0.32 (notinemptyset = $true) & (noeltsimpempty = $true) & (prop2setI = $true) & (omega0Ax = $true) & (powersetAx = $true) & (in__Cong = $true) & (uniqinunit = $true) & (eqimpsubset1 = $true) & (dsetconstrER = $true) & (eqimpsubset2 = $true) & (emptyInPowerset = $true) & (quantDeMorgan1 = $true) & (setextAx = $true) & (exuEu = $true) & (nonemptyE1 = $true) & (setadjoinIL = $true) & (quantDeMorgan2 = $true) & (prop2set2propI = $true) & (subsetI2 = $true) & (notdexE = $true) & (prop2setE = $true) & (subsetI1 = $true) & (exuE3u = $true) & (emptyinunitempty = $true) & (omegaIndAx = $true) & (dsetconstrEL = $true) & (descrp = $true) & (exuI3 = $true) & (omega__Cong = $true) & (quantDeMorgan3 = $true) & ($true != ((subset @ emptyset @ sK135))) & (setadjoinE = $true) & (setbeta = $true) & (wellorderingAx = $true) & (emptyinPowerset = $true) & (vacuousDall = $true) & (omegaSAx = $true) & (setadjoinOr = $true) & (exu__Cong = $true) & (exuE1 = $true) & (quantDeMorgan4 = $true) & (emptysetE = $true) & (setadjoinIR = $true) & (eqinunit = $true) & (descr__Cong = $true) & (setoftrueEq = $true) & (inCongP = $true) & (powersetE = $true) & (notinsingleton = $true) & (exuE3e = $true) & (emptyset__Cong = $true) & (subPowSU = $true) & (upairsetE = $true) & (setext = $true) & (foundationAx = $true) & (nonemptyI = $true) & (emptyI = $true) & (nonemptyImpWitness = $true) & (setunionI = $true) & (exuI2 = $true) & (setadjoin__Cong = $true) & (setunionAx = $true) & (replAx = $true) & (emptyE1 = $true) & (dsetconstrI = $true) & (notdallE = $true) & (upairsetIL = $true) & (upairsetIR = $true) & (setunion__Cong = $true) & (singletonsswitch = $true) & (nonemptyI1 = $true) & (exuI1 = $true) & (emptysetimpfalse = $true) & (setunionE = $true) & (exuE2 = $true) & (dsetconstr__Cong = $true) & (powersetI = $true) & (setadjoinAx = $true) & (powerset__Cong = $true) & (emptysetAx = $true)),
% 0.21/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(X0,sK135)],[f272])).
% 0.21/0.32 thf(f558,plain,(
% 0.21/0.32 ((emptysetAx = $true) | ? [X0 : $i] : (((in @ X0 @ emptyset)) = $true)) & (! [X0 : $i] : (((in @ X0 @ emptyset)) != $true) | (emptysetAx != $true))),
% 0.21/0.32 inference(nnf_transformation,[],[f249])).
% 0.21/0.32 thf(f559,plain,(
% 0.21/0.32 ((emptysetAx = $true) | ? [X0 : $i] : (((in @ X0 @ emptyset)) = $true)) & (! [X1 : $i] : (((in @ X1 @ emptyset)) != $true) | (emptysetAx != $true))),
% 0.21/0.32 inference(rectify,[],[f558])).
% 0.21/0.32 thf(f560,plain,(
% 0.21/0.32 ((emptysetAx = $true) | (((in @ sK206 @ emptyset)) = $true)) & (! [X1 : $i] : (((in @ X1 @ emptyset)) != $true) | (emptysetAx != $true))),
% 0.21/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK206]),skolemize(X0,sK206)],[f559])).
% 0.21/0.32 thf(f582,plain,(
% 0.21/0.32 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((subset @ X0 @ X1)) = $true)) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)) & (((subset @ X0 @ X1)) != $true)))),
% 0.21/0.32 inference(nnf_transformation,[],[f345])).
% 0.21/0.32 thf(f583,plain,(
% 0.21/0.32 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((subset @ X0 @ X1)) = $true)) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X3 : $i,X4 : $i] : (! [X5 : $i] : ((((in @ X5 @ X4)) = $true) | (((in @ X5 @ X3)) != $true)) & (((subset @ X3 @ X4)) != $true)))),
% 0.21/0.32 inference(rectify,[],[f582])).
% 0.21/0.32 thf(f584,plain,(
% 0.21/0.32 (! [X0 : $i,X1 : $i] : (((((in @ (sK225 @ X1 @ X0) @ X1)) != $true) & ($true = ((in @ (sK225 @ X1 @ X0) @ X0)))) | (((subset @ X0 @ X1)) = $true)) | (subsetI1 != $true)) & ((subsetI1 = $true) | (! [X5 : $i] : ((((in @ X5 @ sK227)) = $true) | (((in @ X5 @ sK226)) != $true)) & (((subset @ sK226 @ sK227)) != $true)))),
% 0.21/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK226,sK227]),skolemize(X6,sK9 @ X4),skolemize(X3,sK226),skolemize(X4,sK227)],[f583])).
% 0.21/0.32 thf(f779,plain,(
% 0.21/0.32 (emptysetAx = $true)),
% 0.21/0.32 inference(cnf_transformation,[],[f486])).
% 0.21/0.32 thf(f828,plain,(
% 0.21/0.32 ($true != ((subset @ emptyset @ sK135)))),
% 0.21/0.32 inference(cnf_transformation,[],[f486])).
% 0.21/0.32 thf(f837,plain,(
% 0.21/0.32 (subsetI1 = $true)),
% 0.21/0.32 inference(cnf_transformation,[],[f486])).
% 0.21/0.32 thf(f979,plain,(
% 0.21/0.32 ( ! [X1 : $i] : ((emptysetAx != $true) | (((in @ X1 @ emptyset)) != $true)) )),
% 0.21/0.32 inference(cnf_transformation,[],[f560])).
% 0.21/0.32 thf(f1013,plain,(
% 0.21/0.32 ( ! [X0 : $i,X1 : $i] : ((subsetI1 != $true) | ($true = ((in @ (sK225 @ X1 @ X0) @ X0))) | (((subset @ X0 @ X1)) = $true)) )),
% 0.21/0.32 inference(cnf_transformation,[],[f584])).
% 0.21/0.32 thf(f1300,definition,(
% 0.21/0.32 spl229_34 <=> (emptysetAx = $true)),
% 0.21/0.32 introduced(definition,[new_symbols(definition,[spl229_34])],[avatar_definition])).
% 0.21/0.32 thf(f1391,definition,(
% 0.21/0.32 spl229_55 <=> (subsetI1 = $true)),
% 0.21/0.32 introduced(definition,[new_symbols(definition,[spl229_55])],[avatar_definition])).
% 0.21/0.32 thf(f1540,definition,(
% 0.21/0.32 spl229_88 <=> ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK225 @ X1 @ X0) @ X0))) | (((subset @ X0 @ X1)) = $true))),
% 0.21/0.32 introduced(definition,[new_symbols(definition,[spl229_88])],[avatar_definition])).
% 0.21/0.32 thf(f1541,plain,(
% 0.21/0.32 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK225 @ X1 @ X0) @ X0))) | (((subset @ X0 @ X1)) = $true)) ) | ~spl229_88),
% 0.21/0.32 inference(avatar_component_clause,[],[f1540])).
% 0.21/0.32 thf(f1542,plain,(
% 0.21/0.32 ~spl229_55 | spl229_88),
% 0.21/0.32 inference(avatar_split_clause,[],[f1013,f1540,f1391])).
% 0.21/0.32 thf(f1757,definition,(
% 0.21/0.32 spl229_137 <=> ! [X2 : $i] : (((in @ X2 @ emptyset)) != $true)),
% 0.21/0.32 introduced(definition,[new_symbols(definition,[spl229_137])],[avatar_definition])).
% 0.21/0.32 thf(f1758,plain,(
% 0.21/0.32 ( ! [X2 : $i] : ((((in @ X2 @ emptyset)) != $true)) ) | ~spl229_137),
% 0.21/0.32 inference(avatar_component_clause,[],[f1757])).
% 0.21/0.32 thf(f2266,definition,(
% 0.21/0.32 spl229_245 <=> ($true = ((subset @ emptyset @ sK135)))),
% 0.21/0.32 introduced(definition,[new_symbols(definition,[spl229_245])],[avatar_definition])).
% 0.21/0.32 thf(f2268,plain,(
% 0.21/0.32 ($true != ((subset @ emptyset @ sK135))) | spl229_245),
% 0.21/0.32 inference(avatar_component_clause,[],[f2266])).
% 0.21/0.32 thf(f2269,plain,(
% 0.21/0.32 ~spl229_245),
% 0.21/0.32 inference(avatar_split_clause,[],[f828,f2266])).
% 0.21/0.32 thf(f2334,plain,(
% 0.21/0.32 spl229_34),
% 0.21/0.32 inference(avatar_split_clause,[],[f779,f1300])).
% 0.21/0.32 thf(f2609,plain,(
% 0.21/0.32 spl229_55),
% 0.21/0.32 inference(avatar_split_clause,[],[f837,f1391])).
% 0.21/0.32 thf(f2964,plain,(
% 0.21/0.32 spl229_137 | ~spl229_34),
% 0.21/0.32 inference(avatar_split_clause,[],[f979,f1300,f1757])).
% 0.21/0.32 thf(f3200,plain,(
% 0.21/0.32 ( ! [X0 : $i] : (($true != $true) | (((subset @ emptyset @ X0)) = $true)) ) | (~spl229_88 | ~spl229_137)),
% 0.21/0.32 inference(superposition,[],[f1758,f1541])).
% 0.21/0.32 thf(f3211,plain,(
% 0.21/0.32 ( ! [X0 : $i] : ((((subset @ emptyset @ X0)) = $true)) ) | (~spl229_88 | ~spl229_137)),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f3200])).
% 0.21/0.32 thf(f3847,plain,(
% 0.21/0.32 ($true != $true) | (~spl229_88 | ~spl229_137 | spl229_245)),
% 0.21/0.32 inference(superposition,[],[f2268,f3211])).
% 0.21/0.32 thf(f3848,plain,(
% 0.21/0.32 $false | (~spl229_88 | ~spl229_137 | spl229_245)),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f3847])).
% 0.21/0.32 thf(f3849,plain,(
% 0.21/0.32 ~spl229_88 | ~spl229_137 | spl229_245),
% 0.21/0.32 inference(avatar_contradiction_clause,[],[f3848])).
% 0.21/0.32 cnf(s58, plain, ~spl229_55 | spl229_88, inference(sat_conversion,[],[f1542])).
% 0.21/0.32 cnf(s206, plain, ~spl229_245, inference(sat_conversion,[],[f2269])).
% 0.21/0.32 cnf(s222, plain, spl229_34, inference(sat_conversion,[],[f2334])).
% 0.21/0.32 cnf(s293, plain, spl229_55, inference(sat_conversion,[],[f2609])).
% 0.21/0.32 cnf(s393, plain, ~spl229_34 | spl229_137, inference(sat_conversion,[],[f2964])).
% 0.21/0.32 cnf(s437, plain, ~spl229_88 | ~spl229_137 | spl229_245, inference(sat_conversion,[],[f3849])).
% 0.21/0.32 cnf(s465, plain, spl229_137, inference(rat,[],[s393,s222])).
% 0.21/0.32 cnf(s474, plain, ~spl229_88, inference(rat,[],[s437,s465,s206])).
% 0.21/0.32 cnf(s523, plain, $false, inference(rat,[],[s58,s474,s293])).
% 0.21/0.32 thf(f3850,plain,(
% 0.21/0.32 $false),
% 0.21/0.32 inference(avatar_sat_refutation,[],[s523])).
% 0.21/0.32 % SZS output end Proof for theBenchmark
% 0.21/0.32 % (1280793)------------------------------
% 0.21/0.32 % (1280793)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (1280793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (1280793)CaDiCaL version: 2.1.3
% 0.21/0.32 % (1280793)Termination reason: Refutation
% 0.21/0.32 % (1280793)Time elapsed: 0.047 s
% 0.21/0.32 % (1280793)Peak memory usage: 15 MB
% 0.21/0.32 % (1280793)Instructions burned: 159 (million)
% 0.21/0.32 % (1280785)Success in time 0.074 s
% 0.21/0.32 % Vampire exiting
%------------------------------------------------------------------------------