%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU519^1 : 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 : n013.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 0.20s 0.32s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU519^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n013.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 13:47:06 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.32 % (2139610)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.32 % (2139619)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3354801672:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.32 % (2139621)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.32 % (2139621)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
% 0.20/0.32 % (2139619)Instruction limit reached!
% 0.20/0.32 % (2139619)------------------------------
% 0.20/0.32 % (2139619)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (2139619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (2139619)CaDiCaL version: 2.1.3
% 0.20/0.32 % (2139619)Termination reason: Instruction limit
% 0.20/0.32 % (2139619)Termination phase: Saturation
% 0.20/0.32 % (2139619)Time elapsed: 0.006 s
% 0.20/0.32 % (2139619)Peak memory usage: 11 MB
% 0.20/0.32 % (2139619)Instructions burned: 25 (million)
% 0.20/0.32 % (2139616)lrs+10_16_si=on:nwc=1.5:random_seed=1311610421:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.32 % (2139615)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2787959650:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.32 % (2139617)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2186728305:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.32 % (2139620)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=41448769:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.32 % (2139621)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=662547495:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.32 % (2139617)Instruction limit reached!
% 0.20/0.32 % (2139617)------------------------------
% 0.20/0.32 % (2139617)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (2139617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (2139617)CaDiCaL version: 2.1.3
% 0.20/0.32 % (2139617)Termination reason: Instruction limit
% 0.20/0.32 % (2139617)Termination phase: shuffling
% 0.20/0.32 % (2139617)Time elapsed: 0.002 s
% 0.20/0.32 % (2139617)Peak memory usage: 9 MB
% 0.20/0.32 % (2139617)Instructions burned: 4 (million)
% 0.20/0.32 % (2139618)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=2782878262: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)
% 0.20/0.32 % (2139616)Instruction limit reached!
% 0.20/0.32 % (2139616)------------------------------
% 0.20/0.32 % (2139616)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (2139616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (2139616)CaDiCaL version: 2.1.3
% 0.20/0.32 % (2139616)Termination reason: Instruction limit
% 0.20/0.32 % (2139616)Termination phase: Saturation
% 0.20/0.32 % (2139616)Time elapsed: 0.008 s
% 0.20/0.32 % (2139616)Peak memory usage: 11 MB
% 0.20/0.32 % (2139616)Instructions burned: 19 (million)
% 0.20/0.32 % (2139625)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2253942737:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.32 % (2139625)Instruction limit reached!
% 0.20/0.32 % (2139625)------------------------------
% 0.20/0.32 % (2139625)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (2139625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (2139625)CaDiCaL version: 2.1.3
% 0.20/0.32 % (2139625)Termination reason: Instruction limit
% 0.20/0.32 % (2139625)Termination phase: shuffling
% 0.20/0.32 % (2139625)Time elapsed: 0.0000 s
% 0.20/0.32 % (2139625)Peak memory usage: 9 MB
% 0.20/0.32 % (2139625)Instructions burned: 2 (million)
% 0.20/0.32 % (2139629)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1711866898:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.32 % (2139631)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.32 % (2139629)Instruction limit reached!
% 0.20/0.32 % (2139629)------------------------------
% 0.20/0.32 % (2139629)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (2139629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (2139629)CaDiCaL version: 2.1.3
% 0.20/0.32 % (2139629)Termination reason: Instruction limit
% 0.20/0.32 % (2139629)Termination phase: Property scanning
% 0.20/0.32 % (2139629)Time elapsed: 0.003 s
% 0.20/0.32 % (2139629)Peak memory usage: 10 MB
% 0.20/0.32 % (2139629)Instructions burned: 7 (million)
% 0.20/0.32 % (2139633)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=188578662:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.32 % (2139631)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1067606135:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.32 % (2139633)Instruction limit reached!
% 0.20/0.32 % (2139633)------------------------------
% 0.20/0.32 % (2139633)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (2139633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (2139633)CaDiCaL version: 2.1.3
% 0.20/0.32 % (2139633)Termination reason: Instruction limit
% 0.20/0.32 % (2139633)Termination phase: Property scanning
% 0.20/0.32 % (2139633)Time elapsed: 0.005 s
% 0.20/0.32 % (2139633)Peak memory usage: 10 MB
% 0.20/0.32 % (2139633)Instructions burned: 13 (million)
% 0.20/0.32 % (2139631)Instruction limit reached!
% 0.20/0.32 % (2139631)------------------------------
% 0.20/0.32 % (2139631)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (2139631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (2139631)CaDiCaL version: 2.1.3
% 0.20/0.32 % (2139631)Termination reason: Instruction limit
% 0.20/0.32 % (2139631)Termination phase: Property scanning
% 0.20/0.32 % (2139631)Time elapsed: 0.004 s
% 0.20/0.32 % (2139631)Peak memory usage: 10 MB
% 0.20/0.32 % (2139631)Instructions burned: 9 (million)
% 0.20/0.32 % (2139615) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2139610-2139615"...
% 0.20/0.32 % (2139620) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2139610-2139620"...
% 0.20/0.32 % (2139615)...printing done.
% 0.20/0.32 % (2139615)Refutation found. Thanks to Tanya!
% 0.20/0.32 % SZS status Theorem for theBenchmark
% 0.20/0.32 % SZS output start Proof for theBenchmark
% 0.20/0.32 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.32 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.20/0.32 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 0.20/0.32 thf(func_def_3, type, setextAx: $o).
% 0.20/0.32 thf(func_def_5, type, emptysetAx: $o).
% 0.20/0.32 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 0.20/0.32 thf(func_def_7, type, setadjoinAx: $o).
% 0.20/0.32 thf(func_def_8, type, powerset: ($i > $i)).
% 0.20/0.32 thf(func_def_9, type, powersetAx: $o).
% 0.20/0.32 thf(func_def_10, type, setunion: ($i > $i)).
% 0.20/0.32 thf(func_def_11, type, setunionAx: $o).
% 0.20/0.32 thf(func_def_13, type, omega0Ax: $o).
% 0.20/0.32 thf(func_def_14, type, omegaSAx: $o).
% 0.20/0.32 thf(func_def_15, type, omegaIndAx: $o).
% 0.20/0.32 thf(func_def_16, type, replAx: $o).
% 0.20/0.32 thf(func_def_17, type, foundationAx: $o).
% 0.20/0.32 thf(func_def_18, type, wellorderingAx: $o).
% 0.20/0.32 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 0.20/0.32 thf(func_def_20, type, descrp: $o).
% 0.20/0.32 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.20/0.32 thf(func_def_22, type, dsetconstrI: $o).
% 0.20/0.32 thf(func_def_23, type, dsetconstrEL: $o).
% 0.20/0.32 thf(func_def_24, type, dsetconstrER: $o).
% 0.20/0.32 thf(func_def_25, type, exuE1: $o).
% 0.20/0.32 thf(func_def_26, type, prop2set: ($o > $i)).
% 0.20/0.32 thf(func_def_27, type, prop2setE: $o).
% 0.20/0.32 thf(func_def_28, type, emptysetE: $o).
% 0.20/0.32 thf(func_def_29, type, emptysetimpfalse: $o).
% 0.20/0.32 thf(func_def_30, type, notinemptyset: $o).
% 0.20/0.32 thf(func_def_31, type, exuE3e: $o).
% 0.20/0.32 thf(func_def_32, type, setext: $o).
% 0.20/0.32 thf(func_def_33, type, emptyI: $o).
% 0.20/0.32 thf(func_def_34, type, noeltsimpempty: $o).
% 0.20/0.32 thf(func_def_35, type, setbeta: $o).
% 0.20/0.32 thf(func_def_36, type, nonempty: ($i > $o)).
% 0.20/0.32 thf(func_def_37, type, nonemptyE1: $o).
% 0.20/0.32 thf(func_def_38, type, nonemptyI: $o).
% 0.20/0.32 thf(func_def_39, type, nonemptyI1: $o).
% 0.20/0.32 thf(func_def_40, type, setadjoinIL: $o).
% 0.20/0.33 thf(func_def_41, type, emptyinunitempty: $o).
% 0.20/0.33 thf(func_def_42, type, setadjoinIR: $o).
% 0.20/0.33 thf(func_def_43, type, setadjoinE: $o).
% 0.20/0.33 thf(func_def_44, type, setadjoinOr: $o).
% 0.20/0.33 thf(func_def_45, type, setoftrueEq: $o).
% 0.20/0.33 thf(func_def_46, type, powersetI: $o).
% 0.20/0.33 thf(func_def_47, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.33 thf(func_def_48, type, vAND: ($o > $o > $o)).
% 0.20/0.33 thf(func_def_49, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.33 thf(func_def_50, type, vIMP: ($o > $o > $o)).
% 0.20/0.33 thf(func_def_51, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.33 thf(func_def_52, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.33 thf(func_def_53, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.33 thf(func_def_54, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.33 thf(func_def_55, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.33 thf(func_def_58, type, vNOT: ($o > $o)).
% 0.20/0.33 thf(func_def_59, type, sP0: ($i > $i > $o)).
% 0.20/0.33 thf(func_def_60, type, sP1: ($i > $o)).
% 0.20/0.33 thf(func_def_61, type, sP2: ($i > $i > $o)).
% 0.20/0.33 thf(func_def_62, type, sP3: ($i > $i > $o)).
% 0.20/0.33 thf(func_def_63, type, sP4: $o).
% 0.20/0.33 thf(func_def_67, type, sK8: ($i > $i > $i)).
% 0.20/0.33 thf(func_def_68, type, sK9: ($i > $i > $i)).
% 0.20/0.33 thf(func_def_69, type, sK10: ($i > $i > $i)).
% 0.20/0.33 thf(func_def_70, type, sK11: ($i > $i > $i)).
% 0.20/0.33 thf(func_def_71, type, sK12: ($i > $i > $i)).
% 0.20/0.33 thf(func_def_72, type, sK13: ($i > $i > $i)).
% 0.20/0.33 thf(func_def_73, type, sK14: ($i > $i > $i)).
% 0.20/0.33 thf(func_def_74, type, sK15: ($i > $i > $i > $i)).
% 0.20/0.33 thf(func_def_75, type, sK16: ($i > $i)).
% 0.20/0.33 thf(func_def_76, type, sK17: ($i > $i)).
% 0.20/0.33 thf(func_def_77, type, sK18: ($i > $i)).
% 0.20/0.33 thf(func_def_78, type, sK19: ($i > $i)).
% 0.20/0.33 thf(func_def_79, type, sK20: ($i > $i > $i)).
% 0.20/0.33 thf(func_def_80, type, sK21: ($i > $i > $i > $i)).
% 0.20/0.33 thf(func_def_81, type, sK22: ($i > $i > $i > $i)).
% 0.20/0.33 thf(func_def_82, type, sK23: ($i > $i > $i)).
% 0.20/0.33 thf(func_def_83, type, sK24: ($i > $i > $i)).
% 0.20/0.33 thf(func_def_84, type, sK25: ($i > $i)).
% 0.20/0.33 thf(func_def_86, type, sK27: ($i > $i)).
% 0.20/0.33 thf(func_def_87, type, sK28: ($i > $i)).
% 0.20/0.33 thf(func_def_90, type, sK31: ($i > $i > $i)).
% 0.20/0.33 thf(func_def_93, type, sK34: ($i > $i)).
% 0.20/0.33 thf(func_def_94, type, sK35: ($i > $i)).
% 0.20/0.33 thf(func_def_96, type, sK37: $o).
% 0.20/0.33 thf(func_def_98, type, sK39: ($i > $i)).
% 0.20/0.33 thf(func_def_100, type, sK41: ($i > $i)).
% 0.20/0.33 thf(func_def_104, type, sK45: $o).
% 0.20/0.33 thf(func_def_110, type, sK51: ($i > $o)).
% 0.20/0.33 thf(func_def_111, type, sK52: ($i > $i > $i)).
% 0.20/0.33 thf(func_def_118, type, sK59: ($i > $o)).
% 0.20/0.33 thf(func_def_121, type, sK62: $o).
% 0.20/0.33 thf(func_def_125, type, sK66: ($i > $o)).
% 0.20/0.33 thf(func_def_129, type, sK70: (($i > $o) > $i)).
% 0.20/0.33 thf(func_def_130, type, sK71: ($i > $o)).
% 0.20/0.33 thf(func_def_132, type, sK73: ($i > $i > $o)).
% 0.20/0.33 thf(func_def_133, type, sK74: ($i > $i)).
% 0.20/0.33 thf(func_def_134, type, sK75: ($i > $i)).
% 0.20/0.33 thf(func_def_135, type, sK76: (($i > $i > $o) > $i > $i)).
% 0.20/0.33 thf(func_def_136, type, sK77: ($i > ($i > $i > $o) > $i > $i)).
% 0.20/0.33 thf(func_def_137, type, sK78: (($i > $i > $o) > $i > $i)).
% 0.20/0.33 thf(func_def_140, type, sK81: ($i > $o)).
% 0.20/0.33 thf(func_def_146, type, sK87: ($i > $i > $i)).
% 0.20/0.33 thf(func_def_152, type, sK93: ($i > $i > $i)).
% 0.20/0.33 thf(func_def_155, type, sK96: ($i > $o)).
% 0.20/0.33 thf(func_def_157, type, sK98: ($i > $o)).
% 0.20/0.33 thf(func_def_160, type, sK101: ($i > $i)).
% 0.20/0.33 thf(func_def_165, type, sK106: ($i > $i)).
% 0.20/0.33 thf(func_def_166, type, sK107: (($i > $o) > $i)).
% 0.20/0.33 thf(func_def_167, type, sK108: ($i > $o)).
% 0.20/0.33 thf(func_def_168, type, sK109: ($i > $i)).
% 0.20/0.33 thf(func_def_169, type, sK110: ($i > $i)).
% 0.20/0.33 thf(func_def_170, type, sK111: ($i > ($i > $o) > $i)).
% 0.20/0.33 thf(func_def_171, type, sK112: ($i > ($i > $o) > $i)).
% 0.20/0.33 thf(func_def_172, type, sK113: ($i > ($i > $i > $o) > $i > $i)).
% 0.20/0.33 thf(func_def_173, type, sK114: ($i > ($i > $o) > $i)).
% 0.20/0.33 thf(func_def_174, type, sK115: ($i > ($i > $i > $o) > $i > $i)).
% 0.20/0.33 thf(func_def_175, type, sK116: ($i > ($i > $i > $o) > $i > $i)).
% 0.20/0.33 thf(func_def_176, type, sK117: ($i > ($i > $o) > $i)).
% 0.20/0.33 thf(f3,axiom,(
% 0.20/0.33 (! [X0 : $i] : ~(in @ X0 @ emptyset) = emptysetAx)),
% 0.20/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx)).
% 0.20/0.33 thf(f5,axiom,(
% 0.20/0.33 (powersetAx = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) <=> (in @ X1 @ (powerset @ X0))))),
% 0.20/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx)).
% 0.20/0.33 thf(f39,conjecture,(
% 0.20/0.33 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 => (powersetI => ! [X0 : $i] : (in @ emptyset @ (powerset @ X0))))))))))))))))))))))))))))))))))))),
% 0.20/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset)).
% 0.20/0.33 thf(f40,negated_conjecture,(
% 0.20/0.33 ~(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 => (powersetI => ! [X0 : $i] : (in @ emptyset @ (powerset @ X0)))))))))))))))))))))))))))))))))))))),
% 0.20/0.33 inference(negated_conjecture,[status(cth)],[f39])).
% 0.20/0.33 thf(f91,plain,(
% 0.20/0.33 (powersetAx = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) <=> (in @ X1 @ (powerset @ X0))))),
% 0.20/0.33 inference(rectify,[],[f5])).
% 0.20/0.33 thf(f92,plain,(
% 0.20/0.33 (powersetAx = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) <=> (((in @ X1 @ (powerset @ X0))) = $true))),
% 0.20/0.33 inference(fool_elimination,[],[f91])).
% 0.20/0.33 thf(f104,plain,(
% 0.20/0.33 ~(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 => (powersetI => ! [X0 : $i] : (in @ emptyset @ (powerset @ X0)))))))))))))))))))))))))))))))))))))),
% 0.20/0.33 inference(rectify,[],[f40])).
% 0.20/0.33 thf(f105,plain,(
% 0.20/0.33 ~((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) => ((powersetI = $true) => ! [X0 : $i] : (((in @ emptyset @ (powerset @ X0))) = $true))))))))))))))))))))))))))))))))))))),
% 0.20/0.33 inference(fool_elimination,[],[f104])).
% 0.20/0.33 thf(f108,plain,(
% 0.20/0.33 (! [X0 : $i] : ~(in @ X0 @ emptyset) = emptysetAx)),
% 0.20/0.33 inference(rectify,[],[f3])).
% 0.20/0.33 thf(f109,plain,(
% 0.20/0.33 ! [X0 : $i] : ~ (((in @ X0 @ emptyset)) = $true) <=> (emptysetAx = $true)),
% 0.20/0.33 inference(fool_elimination,[],[f108])).
% 0.20/0.33 thf(f122,plain,(
% 0.20/0.33 (emptysetAx = $true) <=> ! [X0 : $i] : (((in @ X0 @ emptyset)) != $true)),
% 0.20/0.33 inference(flattening,[],[f109])).
% 0.20/0.33 thf(f130,plain,(
% 0.20/0.33 ! [X1 : $i,X0 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) <=> ! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true))) <=> (powersetAx = $true)),
% 0.20/0.33 inference(ennf_transformation,[],[f92])).
% 0.20/0.33 thf(f141,plain,(
% 0.20/0.33 ((((((((((((((((((((((((((((((((((? [X0 : $i] : (((in @ emptyset @ (powerset @ X0))) != $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)),
% 0.20/0.33 inference(ennf_transformation,[],[f105])).
% 0.20/0.33 thf(f142,plain,(
% 0.20/0.33 (dsetconstrEL = $true) & (dsetconstrI = $true) & (setadjoinOr = $true) & ? [X0 : $i] : (((in @ emptyset @ (powerset @ X0))) != $true) & (setadjoinAx = $true) & (nonemptyI = $true) & (notinemptyset = $true) & (emptyinunitempty = $true) & (nonemptyE1 = $true) & (descrp = $true) & (powersetAx = $true) & (exuE3e = $true) & (omega0Ax = $true) & (emptyI = $true) & (noeltsimpempty = $true) & (powersetI = $true) & (dsetconstrER = $true) & (replAx = $true) & (setadjoinIL = $true) & (omegaSAx = $true) & (prop2setE = $true) & (wellorderingAx = $true) & (setadjoinE = $true) & (emptysetAx = $true) & (exuE1 = $true) & (omegaIndAx = $true) & (emptysetE = $true) & (setunionAx = $true) & (setext = $true) & (nonemptyI1 = $true) & (setbeta = $true) & (setextAx = $true) & (setadjoinIR = $true) & (foundationAx = $true) & (setoftrueEq = $true) & (emptysetimpfalse = $true)),
% 0.20/0.33 inference(flattening,[],[f141])).
% 0.20/0.33 thf(f211,plain,(
% 0.20/0.33 (! [X1 : $i,X0 : $i] : (((((in @ X1 @ (powerset @ X0))) = $true) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true))) & (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) | (((in @ X1 @ (powerset @ X0))) != $true))) | (powersetAx != $true)) & ((powersetAx = $true) | ? [X1 : $i,X0 : $i] : ((? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | (((in @ X1 @ (powerset @ X0))) != $true)) & (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) | (((in @ X1 @ (powerset @ X0))) = $true))))),
% 0.20/0.33 inference(nnf_transformation,[],[f130])).
% 0.20/0.33 thf(f212,plain,(
% 0.20/0.33 (! [X0 : $i,X1 : $i] : (((((in @ X0 @ (powerset @ X1))) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true))) & (! [X3 : $i] : ((((in @ X3 @ X1)) = $true) | (((in @ X3 @ X0)) != $true)) | (((in @ X0 @ (powerset @ X1))) != $true))) | (powersetAx != $true)) & ((powersetAx = $true) | ? [X4 : $i,X5 : $i] : ((? [X6 : $i] : ((((in @ X6 @ X5)) != $true) & (((in @ X6 @ X4)) = $true)) | (((in @ X4 @ (powerset @ X5))) != $true)) & (! [X7 : $i] : ((((in @ X7 @ X5)) = $true) | ($true != ((in @ X7 @ X4)))) | (((in @ X4 @ (powerset @ X5))) = $true))))),
% 0.20/0.33 inference(rectify,[],[f211])).
% 0.20/0.33 thf(f213,plain,(
% 0.20/0.33 (! [X0 : $i,X1 : $i] : (((((in @ X0 @ (powerset @ X1))) = $true) | ((((in @ (sK52 @ X1 @ X0) @ X1)) != $true) & ($true = ((in @ (sK52 @ X1 @ X0) @ X0))))) & (! [X3 : $i] : ((((in @ X3 @ X1)) = $true) | (((in @ X3 @ X0)) != $true)) | (((in @ X0 @ (powerset @ X1))) != $true))) | (powersetAx != $true)) & ((powersetAx = $true) | ((((((in @ sK55 @ sK54)) != $true) & (((in @ sK55 @ sK53)) = $true)) | (((in @ sK53 @ (powerset @ sK54))) != $true)) & (! [X7 : $i] : ((((in @ X7 @ sK54)) = $true) | (((in @ X7 @ sK53)) != $true)) | (((in @ sK53 @ (powerset @ sK54))) = $true))))),
% 0.20/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK53,sK54,sK55]),skolemize(X7,sK9 @ X5 @ X4),skolemize(X4,sK53),skolemize(X5,sK54),skolemize(X6,sK55)],[f212])).
% 0.20/0.33 thf(f263,plain,(
% 0.20/0.33 ((emptysetAx = $true) | ? [X0 : $i] : (((in @ X0 @ emptyset)) = $true)) & (! [X0 : $i] : (((in @ X0 @ emptyset)) != $true) | (emptysetAx != $true))),
% 0.20/0.33 inference(nnf_transformation,[],[f122])).
% 0.20/0.33 thf(f264,plain,(
% 0.20/0.33 ((emptysetAx = $true) | ? [X0 : $i] : (((in @ X0 @ emptyset)) = $true)) & (! [X1 : $i] : ($true != ((in @ X1 @ emptyset))) | (emptysetAx != $true))),
% 0.20/0.33 inference(rectify,[],[f263])).
% 0.20/0.33 thf(f265,plain,(
% 0.20/0.33 ((emptysetAx = $true) | (((in @ sK99 @ emptyset)) = $true)) & (! [X1 : $i] : ($true != ((in @ X1 @ emptyset))) | (emptysetAx != $true))),
% 0.20/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(X0,sK99)],[f264])).
% 0.20/0.33 thf(f269,plain,(
% 0.20/0.33 (dsetconstrEL = $true) & (dsetconstrI = $true) & (setadjoinOr = $true) & (((in @ emptyset @ (powerset @ sK102))) != $true) & (setadjoinAx = $true) & (nonemptyI = $true) & (notinemptyset = $true) & (emptyinunitempty = $true) & (nonemptyE1 = $true) & (descrp = $true) & (powersetAx = $true) & (exuE3e = $true) & (omega0Ax = $true) & (emptyI = $true) & (noeltsimpempty = $true) & (powersetI = $true) & (dsetconstrER = $true) & (replAx = $true) & (setadjoinIL = $true) & (omegaSAx = $true) & (prop2setE = $true) & (wellorderingAx = $true) & (setadjoinE = $true) & (emptysetAx = $true) & (exuE1 = $true) & (omegaIndAx = $true) & (emptysetE = $true) & (setunionAx = $true) & (setext = $true) & (nonemptyI1 = $true) & (setbeta = $true) & (setextAx = $true) & (setadjoinIR = $true) & (foundationAx = $true) & (setoftrueEq = $true) & (emptysetimpfalse = $true)),
% 0.20/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(X0,sK102)],[f142])).
% 0.20/0.33 thf(f367,plain,(
% 0.20/0.33 ( ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) | ($true = ((in @ (sK52 @ X1 @ X0) @ X0))) | (powersetAx != $true)) )),
% 0.20/0.33 inference(cnf_transformation,[],[f213])).
% 0.20/0.33 thf(f431,plain,(
% 0.20/0.33 ( ! [X1 : $i] : (($true != ((in @ X1 @ emptyset))) | (emptysetAx != $true)) )),
% 0.20/0.33 inference(cnf_transformation,[],[f265])).
% 0.20/0.33 thf(f448,plain,(
% 0.20/0.33 (emptysetAx = $true)),
% 0.20/0.33 inference(cnf_transformation,[],[f269])).
% 0.20/0.33 thf(f461,plain,(
% 0.20/0.33 (powersetAx = $true)),
% 0.20/0.33 inference(cnf_transformation,[],[f269])).
% 0.20/0.33 thf(f468,plain,(
% 0.20/0.33 (((in @ emptyset @ (powerset @ sK102))) != $true)),
% 0.20/0.33 inference(cnf_transformation,[],[f269])).
% 0.20/0.33 thf(f542,plain,(
% 0.20/0.33 ( ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) | ($true = ((in @ (sK52 @ X1 @ X0) @ X0))) | ($true != $true)) )),
% 0.20/0.33 inference(definition_unfolding,[],[f367,f461])).
% 0.20/0.33 thf(f604,plain,(
% 0.20/0.33 ( ! [X1 : $i] : (($true != ((in @ X1 @ emptyset))) | ($true != $true)) )),
% 0.20/0.33 inference(definition_unfolding,[],[f431,f448])).
% 0.20/0.33 thf(f628,plain,(
% 0.20/0.33 ( ! [X1 : $i] : (($true != ((in @ X1 @ emptyset)))) )),
% 0.20/0.33 inference(trivial_inequality_removal,[],[f604])).
% 0.20/0.33 thf(f662,plain,(
% 0.20/0.33 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK52 @ X1 @ X0) @ X0))) | (((in @ X0 @ (powerset @ X1))) = $true)) )),
% 0.20/0.33 inference(trivial_inequality_removal,[],[f542])).
% 0.20/0.33 thf(f1086,plain,(
% 0.20/0.33 ( ! [X0 : $i] : ((((in @ emptyset @ (powerset @ X0))) = $true) | ($true != $true)) )),
% 0.20/0.33 inference(constrained_superposition,[],[f628,f662])).
% 0.20/0.33 thf(f1091,plain,(
% 0.20/0.33 ( ! [X0 : $i] : ((((in @ emptyset @ (powerset @ X0))) = $true)) )),
% 0.20/0.33 inference(trivial_inequality_removal,[],[f1086])).
% 0.20/0.33 thf(f1099,plain,(
% 0.20/0.33 ($true != $true)),
% 0.20/0.33 inference(constrained_superposition,[],[f468,f1091])).
% 0.20/0.33 thf(f1102,plain,(
% 0.20/0.33 $false),
% 0.20/0.33 inference(trivial_inequality_removal,[],[f1099])).
% 0.20/0.33 % SZS output end Proof for theBenchmark
% 0.20/0.33 % (2139615)------------------------------
% 0.20/0.33 % (2139615)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (2139615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (2139615)CaDiCaL version: 2.1.3
% 0.20/0.33 % (2139615)Termination reason: Refutation
% 0.20/0.33 % (2139615)Time elapsed: 0.035 s
% 0.20/0.33 % (2139615)Peak memory usage: 13 MB
% 0.20/0.33 % (2139615)Instructions burned: 66 (million)
% 0.20/0.33 % (2139610)Success in time 0.075 s
% 0.20/0.33 % Vampire exiting
%------------------------------------------------------------------------------