%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU522^1 : 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 : n011.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 0.21s 0.33s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU522^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n011.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 13:48:02 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.21/0.33 % (122493)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.33 % (122503)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2270412959:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.33 % (122504)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.33 % (122504)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
% 0.21/0.33 % (122498)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3895792678:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.33 % (122499)lrs+10_16_si=on:nwc=1.5:random_seed=908816551:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.33 % (122500)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4039885558:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.33 % (122502)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1804837227:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.33 % (122501)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=4131129219: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)
% 0.21/0.33 % (122504)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=2020780716:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.33 % (122500)Instruction limit reached!
% 0.21/0.33 % (122500)------------------------------
% 0.21/0.33 % (122500)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.33 % (122500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.33 % (122500)CaDiCaL version: 2.1.3
% 0.21/0.33 % (122500)Termination reason: Instruction limit
% 0.21/0.33 % (122500)Termination phase: shuffling
% 0.21/0.33 % (122500)Time elapsed: 0.002 s
% 0.21/0.33 % (122500)Peak memory usage: 9 MB
% 0.21/0.33 % (122500)Instructions burned: 4 (million)
% 0.21/0.33 % (122499)Instruction limit reached!
% 0.21/0.33 % (122499)------------------------------
% 0.21/0.33 % (122499)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.33 % (122499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.33 % (122499)CaDiCaL version: 2.1.3
% 0.21/0.33 % (122499)Termination reason: Instruction limit
% 0.21/0.33 % (122499)Termination phase: Saturation
% 0.21/0.33 % (122499)Time elapsed: 0.008 s
% 0.21/0.33 % (122499)Peak memory usage: 11 MB
% 0.21/0.33 % (122499)Instructions burned: 19 (million)
% 0.21/0.33 % (122502)Instruction limit reached!
% 0.21/0.33 % (122502)------------------------------
% 0.21/0.33 % (122502)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.33 % (122502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.33 % (122502)CaDiCaL version: 2.1.3
% 0.21/0.33 % (122502)Termination reason: Instruction limit
% 0.21/0.33 % (122502)Termination phase: Property scanning
% 0.21/0.33 % (122502)Time elapsed: 0.012 s
% 0.21/0.33 % (122502)Peak memory usage: 11 MB
% 0.21/0.33 % (122502)Instructions burned: 25 (million)
% 0.21/0.33 % (122503)Instruction limit reached!
% 0.21/0.33 % (122503)------------------------------
% 0.21/0.33 % (122503)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.33 % (122503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.33 % (122503)CaDiCaL version: 2.1.3
% 0.21/0.33 % (122503)Termination reason: Instruction limit
% 0.21/0.33 % (122503)Termination phase: Saturation
% 0.21/0.33 % (122503)Time elapsed: 0.022 s
% 0.21/0.33 % (122503)Peak memory usage: 13 MB
% 0.21/0.33 % (122503)Instructions burned: 78 (million)
% 0.21/0.33 % (122512)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2016191080:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.33 % (122512)Instruction limit reached!
% 0.21/0.33 % (122512)------------------------------
% 0.21/0.33 % (122512)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.33 % (122512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.33 % (122512)CaDiCaL version: 2.1.3
% 0.21/0.33 % (122512)Termination reason: Instruction limit
% 0.21/0.33 % (122512)Termination phase: shuffling
% 0.21/0.33 % (122512)Time elapsed: 0.002 s
% 0.21/0.33 % (122512)Peak memory usage: 9 MB
% 0.21/0.33 % (122512)Instructions burned: 4 (million)
% 0.21/0.33 % (122515)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3341104024:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.33 % (122514)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.33 % (122513)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2312510304:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.33 % (122515)Instruction limit reached!
% 0.21/0.33 % (122515)------------------------------
% 0.21/0.33 % (122515)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.33 % (122515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.33 % (122515)CaDiCaL version: 2.1.3
% 0.21/0.33 % (122515)Termination reason: Instruction limit
% 0.21/0.33 % (122515)Termination phase: Property scanning
% 0.21/0.33 % (122515)Time elapsed: 0.003 s
% 0.21/0.33 % (122515)Peak memory usage: 10 MB
% 0.21/0.33 % (122515)Instructions burned: 13 (million)
% 0.21/0.33 % (122514)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3323807219:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.33 % (122513)Instruction limit reached!
% 0.21/0.33 % (122513)------------------------------
% 0.21/0.33 % (122513)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.33 % (122513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.33 % (122513)CaDiCaL version: 2.1.3
% 0.21/0.33 % (122513)Termination reason: Instruction limit
% 0.21/0.33 % (122513)Termination phase: Property scanning
% 0.21/0.33 % (122513)Time elapsed: 0.003 s
% 0.21/0.33 % (122513)Peak memory usage: 10 MB
% 0.21/0.33 % (122513)Instructions burned: 6 (million)
% 0.21/0.33 % (122514)Instruction limit reached!
% 0.21/0.33 % (122514)------------------------------
% 0.21/0.33 % (122514)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.33 % (122514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.33 % (122514)CaDiCaL version: 2.1.3
% 0.21/0.33 % (122514)Termination reason: Instruction limit
% 0.21/0.33 % (122514)Termination phase: Property scanning
% 0.21/0.33 % (122514)Time elapsed: 0.003 s
% 0.21/0.33 % (122514)Peak memory usage: 10 MB
% 0.21/0.33 % (122514)Instructions burned: 7 (million)
% 0.21/0.33 % (122520)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=988914222:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.21/0.33 % (122501) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-122493-122501"...
% 0.21/0.33 % (122517)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
% 0.21/0.33 % (122517)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.33 % (122501)...printing done.
% 0.21/0.33 % (122517)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=435972093:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.21/0.33 % (122501)Refutation found. Thanks to Tanya!
% 0.21/0.33 % SZS status Theorem for theBenchmark
% 0.21/0.33 % SZS output start Proof for theBenchmark
% 0.21/0.33 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.33 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.21/0.33 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 0.21/0.33 thf(func_def_3, type, setextAx: $o).
% 0.21/0.33 thf(func_def_5, type, emptysetAx: $o).
% 0.21/0.33 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 0.21/0.33 thf(func_def_7, type, setadjoinAx: $o).
% 0.21/0.33 thf(func_def_8, type, powerset: ($i > $i)).
% 0.21/0.33 thf(func_def_9, type, powersetAx: $o).
% 0.21/0.33 thf(func_def_10, type, setunion: ($i > $i)).
% 0.21/0.33 thf(func_def_11, type, setunionAx: $o).
% 0.21/0.33 thf(func_def_13, type, omega0Ax: $o).
% 0.21/0.33 thf(func_def_14, type, omegaSAx: $o).
% 0.21/0.33 thf(func_def_15, type, omegaIndAx: $o).
% 0.21/0.33 thf(func_def_16, type, replAx: $o).
% 0.21/0.33 thf(func_def_17, type, foundationAx: $o).
% 0.21/0.33 thf(func_def_18, type, wellorderingAx: $o).
% 0.21/0.33 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 0.21/0.33 thf(func_def_20, type, descrp: $o).
% 0.21/0.33 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.21/0.33 thf(func_def_22, type, dsetconstrI: $o).
% 0.21/0.33 thf(func_def_23, type, dsetconstrEL: $o).
% 0.21/0.33 thf(func_def_24, type, dsetconstrER: $o).
% 0.21/0.33 thf(func_def_25, type, exuE1: $o).
% 0.21/0.33 thf(func_def_26, type, prop2set: ($o > $i)).
% 0.21/0.33 thf(func_def_27, type, prop2setE: $o).
% 0.21/0.33 thf(func_def_28, type, emptysetE: $o).
% 0.21/0.33 thf(func_def_29, type, emptysetimpfalse: $o).
% 0.21/0.33 thf(func_def_30, type, notinemptyset: $o).
% 0.21/0.33 thf(func_def_31, type, exuE3e: $o).
% 0.21/0.33 thf(func_def_32, type, setext: $o).
% 0.21/0.33 thf(func_def_33, type, emptyI: $o).
% 0.21/0.33 thf(func_def_34, type, noeltsimpempty: $o).
% 0.21/0.33 thf(func_def_35, type, setbeta: $o).
% 0.21/0.33 thf(func_def_36, type, nonempty: ($i > $o)).
% 0.21/0.33 thf(func_def_37, type, nonemptyE1: $o).
% 0.21/0.33 thf(func_def_38, type, nonemptyI: $o).
% 0.21/0.33 thf(func_def_39, type, nonemptyI1: $o).
% 0.21/0.33 thf(func_def_40, type, setadjoinIL: $o).
% 0.21/0.33 thf(func_def_41, type, emptyinunitempty: $o).
% 0.21/0.33 thf(func_def_42, type, setadjoinIR: $o).
% 0.21/0.33 thf(func_def_43, type, setadjoinE: $o).
% 0.21/0.33 thf(func_def_44, type, setadjoinOr: $o).
% 0.21/0.33 thf(func_def_45, type, setoftrueEq: $o).
% 0.21/0.33 thf(func_def_46, type, powersetI: $o).
% 0.21/0.33 thf(func_def_47, type, emptyinPowerset: $o).
% 0.21/0.33 thf(func_def_48, type, emptyInPowerset: $o).
% 0.21/0.33 thf(func_def_49, type, powersetE: $o).
% 0.21/0.33 thf(func_def_52, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.33 thf(func_def_53, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.33 thf(func_def_54, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.33 thf(func_def_55, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.33 thf(func_def_56, type, vAND: ($o > $o > $o)).
% 0.21/0.33 thf(func_def_57, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.33 thf(func_def_58, type, vIMP: ($o > $o > $o)).
% 0.21/0.33 thf(func_def_59, type, db2: !>[X0: $tType]:(X0)).
% 0.21/0.33 thf(func_def_60, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.33 thf(func_def_61, type, vNOT: ($o > $o)).
% 0.21/0.33 thf(func_def_62, type, sP0: ($i > $i > $o)).
% 0.21/0.33 thf(func_def_63, type, sP1: ($i > $o)).
% 0.21/0.33 thf(func_def_64, type, sP2: $o).
% 0.21/0.33 thf(func_def_68, type, sK6: ($i > $i > $i)).
% 0.21/0.33 thf(func_def_69, type, sK7: ($i > $i > $i)).
% 0.21/0.33 thf(func_def_70, type, sK8: (($i > $o) > $i)).
% 0.21/0.33 thf(func_def_71, type, sK9: ($i > $o)).
% 0.21/0.33 thf(func_def_72, type, sK10: ($i > $i)).
% 0.21/0.33 thf(func_def_73, type, sK11: $o).
% 0.21/0.33 thf(func_def_81, type, sK19: ($i > $i)).
% 0.21/0.33 thf(func_def_84, type, sK22: ($i > $i > $i)).
% 0.21/0.33 thf(func_def_93, type, sK31: ($i > $i > $i)).
% 0.21/0.33 thf(func_def_97, type, sK35: $o).
% 0.21/0.33 thf(func_def_98, type, sK36: ($i > $i > $i)).
% 0.21/0.33 thf(func_def_102, type, sK40: $o).
% 0.21/0.33 thf(func_def_103, type, sK41: ($i > $i)).
% 0.21/0.33 thf(func_def_105, type, sK43: ($i > $o)).
% 0.21/0.33 thf(func_def_112, type, sK50: ($i > $i)).
% 0.21/0.33 thf(func_def_115, type, sK53: ($i > $i)).
% 0.21/0.33 thf(func_def_116, type, sK54: ($i > $i)).
% 0.21/0.33 thf(func_def_117, type, sK55: ($i > $i)).
% 0.21/0.33 thf(func_def_118, type, sK56: ($i > $i)).
% 0.21/0.33 thf(func_def_119, type, sK57: ($i > $i)).
% 0.21/0.33 thf(func_def_120, type, sK58: ($i > $i > $i > $i)).
% 0.21/0.33 thf(func_def_121, type, sK59: ($i > $i)).
% 0.21/0.33 thf(func_def_122, type, sK60: ($i > $i)).
% 0.21/0.33 thf(func_def_123, type, sK61: ($i > $i)).
% 0.21/0.33 thf(func_def_124, type, sK62: ($i > $i)).
% 0.21/0.33 thf(func_def_125, type, sK63: ($i > $i > $i)).
% 0.21/0.33 thf(func_def_126, type, sK64: ($i > $i > $i)).
% 0.21/0.33 thf(func_def_127, type, sK65: ($i > $i > $i > $i)).
% 0.21/0.33 thf(func_def_128, type, sK66: ($i > $i > $i > $i)).
% 0.21/0.33 thf(func_def_129, type, sK67: ($i > $i > $i > $i)).
% 0.21/0.33 thf(func_def_130, type, sK68: ($i > $i > $i)).
% 0.21/0.33 thf(func_def_131, type, sK69: ($i > $i > $i)).
% 0.21/0.33 thf(func_def_132, type, sK70: ($i > $i > $i)).
% 0.21/0.33 thf(func_def_133, type, sK71: ($i > ($i > $i > $o) > $i)).
% 0.21/0.33 thf(func_def_134, type, sK72: ($i > $i > ($i > $i > $o) > $i)).
% 0.21/0.33 thf(func_def_135, type, sK73: ($i > ($i > $i > $o) > $i)).
% 0.21/0.33 thf(func_def_136, type, sK74: ($i > $i > $o)).
% 0.21/0.33 thf(func_def_138, type, sK76: ($i > $i)).
% 0.21/0.33 thf(func_def_139, type, sK77: ($i > $i)).
% 0.21/0.33 thf(func_def_145, type, sK83: ($i > $o)).
% 0.21/0.33 thf(func_def_148, type, sK86: ($i > $o)).
% 0.21/0.33 thf(func_def_153, type, sK91: ($i > $o)).
% 0.21/0.33 thf(func_def_156, type, sK94: ($i > $i)).
% 0.21/0.33 thf(func_def_159, type, sK97: ($i > $i)).
% 0.21/0.33 thf(func_def_163, type, sK101: ($i > $i > $i)).
% 0.21/0.33 thf(func_def_167, type, sK105: ($i > $o)).
% 0.21/0.33 thf(func_def_168, type, sK106: (($i > $o) > $i)).
% 0.21/0.33 thf(func_def_169, type, sK107: ($i > $o)).
% 0.21/0.33 thf(func_def_172, type, sK110: ($i > $o)).
% 0.21/0.33 thf(func_def_176, type, sK114: ($i > $i)).
% 0.21/0.33 thf(f6,axiom,(
% 0.21/0.33 (setunionAx = ! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((in @ X2 @ X0) & (in @ X1 @ X2)) <=> (in @ X1 @ (setunion @ X0))))),
% 0.21/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx)).
% 0.21/0.33 thf(f42,conjecture,(
% 0.21/0.33 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 => (emptyinPowerset => (emptyInPowerset => (powersetE => ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X1 @ X2) => ((in @ X2 @ X0) => (in @ X1 @ (setunion @ X0)))))))))))))))))))))))))))))))))))))))))),
% 0.21/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI)).
% 0.21/0.33 thf(f43,negated_conjecture,(
% 0.21/0.33 ~(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 => (emptyinPowerset => (emptyInPowerset => (powersetE => ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X1 @ X2) => ((in @ X2 @ X0) => (in @ X1 @ (setunion @ X0))))))))))))))))))))))))))))))))))))))))))),
% 0.21/0.33 inference(negated_conjecture,[status(cth)],[f42])).
% 0.21/0.33 thf(f50,plain,(
% 0.21/0.33 ~(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 => (emptyinPowerset => (emptyInPowerset => (powersetE => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ((in @ X1 @ X0) => (in @ X2 @ (setunion @ X0))))))))))))))))))))))))))))))))))))))))))),
% 0.21/0.33 inference(rectify,[],[f43])).
% 0.21/0.33 thf(f51,plain,(
% 0.21/0.33 ~((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) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ! [X1 : $i,X2 : $i,X0 : $i] : ((((in @ X2 @ X1)) = $true) => ((((in @ X1 @ X0)) = $true) => ($true = ((in @ X2 @ (setunion @ X0))))))))))))))))))))))))))))))))))))))))))))),
% 0.21/0.33 inference(fool_elimination,[],[f50])).
% 0.21/0.33 thf(f52,plain,(
% 0.21/0.33 (setunionAx = ! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((in @ X2 @ X0) & (in @ X1 @ X2)) <=> (in @ X1 @ (setunion @ X0))))),
% 0.21/0.33 inference(rectify,[],[f6])).
% 0.21/0.33 thf(f53,plain,(
% 0.21/0.33 (setunionAx = $true) <=> ! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X1 @ X2)) = $true) & (((in @ X2 @ X0)) = $true)) <=> (((in @ X1 @ (setunion @ X0))) = $true))),
% 0.21/0.33 inference(fool_elimination,[],[f52])).
% 0.21/0.33 thf(f144,plain,(
% 0.21/0.33 (((((((((((((((((((((((((((((((((((((? [X1 : $i,X2 : $i,X0 : $i] : ((($true != ((in @ X2 @ (setunion @ X0)))) & (((in @ X1 @ X0)) = $true)) & (((in @ X2 @ X1)) = $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)),
% 0.21/0.33 inference(ennf_transformation,[],[f51])).
% 0.21/0.33 thf(f145,plain,(
% 0.21/0.33 (prop2setE = $true) & (replAx = $true) & (emptysetE = $true) & (nonemptyI1 = $true) & (omega0Ax = $true) & (nonemptyE1 = $true) & (foundationAx = $true) & (dsetconstrER = $true) & (dsetconstrI = $true) & (exuE1 = $true) & (nonemptyI = $true) & (wellorderingAx = $true) & ? [X0 : $i,X2 : $i,X1 : $i] : (($true != ((in @ X2 @ (setunion @ X0)))) & (((in @ X1 @ X0)) = $true) & (((in @ X2 @ X1)) = $true)) & (powersetI = $true) & (emptyinPowerset = $true) & (omegaIndAx = $true) & (emptysetAx = $true) & (powersetAx = $true) & (setbeta = $true) & (omegaSAx = $true) & (exuE3e = $true) & (setext = $true) & (dsetconstrEL = $true) & (setadjoinE = $true) & (noeltsimpempty = $true) & (powersetE = $true) & (setadjoinAx = $true) & (setadjoinOr = $true) & (emptysetimpfalse = $true) & (setunionAx = $true) & (emptyInPowerset = $true) & (setextAx = $true) & (descrp = $true) & (setadjoinIR = $true) & (emptyI = $true) & (notinemptyset = $true) & (setadjoinIL = $true) & (emptyinunitempty = $true) & (setoftrueEq = $true)),
% 0.21/0.33 inference(flattening,[],[f144])).
% 0.21/0.33 thf(f209,plain,(
% 0.21/0.33 ((setunionAx = $true) | ? [X0 : $i,X1 : $i] : (((((in @ X1 @ (setunion @ X0))) != $true) | ! [X2 : $i] : ((((in @ X1 @ X2)) != $true) | (((in @ X2 @ X0)) != $true))) & ((((in @ X1 @ (setunion @ X0))) = $true) | ? [X2 : $i] : ((((in @ X1 @ X2)) = $true) & (((in @ X2 @ X0)) = $true))))) & (! [X0 : $i,X1 : $i] : ((? [X2 : $i] : ((((in @ X1 @ X2)) = $true) & (((in @ X2 @ X0)) = $true)) | (((in @ X1 @ (setunion @ X0))) != $true)) & ((((in @ X1 @ (setunion @ X0))) = $true) | ! [X2 : $i] : ((((in @ X1 @ X2)) != $true) | (((in @ X2 @ X0)) != $true)))) | (setunionAx != $true))),
% 0.21/0.33 inference(nnf_transformation,[],[f53])).
% 0.21/0.33 thf(f210,plain,(
% 0.21/0.33 ((setunionAx = $true) | ? [X0 : $i,X1 : $i] : (((((in @ X1 @ (setunion @ X0))) != $true) | ! [X2 : $i] : ((((in @ X1 @ X2)) != $true) | (((in @ X2 @ X0)) != $true))) & ((((in @ X1 @ (setunion @ X0))) = $true) | ? [X3 : $i] : (($true = ((in @ X1 @ X3))) & (((in @ X3 @ X0)) = $true))))) & (! [X4 : $i,X5 : $i] : ((? [X6 : $i] : (($true = ((in @ X5 @ X6))) & (((in @ X6 @ X4)) = $true)) | (((in @ X5 @ (setunion @ X4))) != $true)) & ((((in @ X5 @ (setunion @ X4))) = $true) | ! [X7 : $i] : (($true != ((in @ X5 @ X7))) | ($true != ((in @ X7 @ X4)))))) | (setunionAx != $true))),
% 0.21/0.33 inference(rectify,[],[f209])).
% 0.21/0.33 thf(f211,plain,(
% 0.21/0.33 ((setunionAx = $true) | ((($true != ((in @ sK29 @ (setunion @ sK28)))) | ! [X2 : $i] : ((((in @ sK29 @ X2)) != $true) | ($true != ((in @ X2 @ sK28))))) & (($true = ((in @ sK29 @ (setunion @ sK28)))) | ((((in @ sK29 @ sK30)) = $true) & ($true = ((in @ sK30 @ sK28))))))) & (! [X4 : $i,X5 : $i] : ((((((in @ X5 @ (sK31 @ X5 @ X4))) = $true) & ($true = ((in @ (sK31 @ X5 @ X4) @ X4)))) | (((in @ X5 @ (setunion @ X4))) != $true)) & ((((in @ X5 @ (setunion @ X4))) = $true) | ! [X7 : $i] : (($true != ((in @ X5 @ X7))) | ($true != ((in @ X7 @ X4)))))) | (setunionAx != $true))),
% 0.21/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[sK28,sK29,sK30,vAPP]),skolemize(X0,sK28),skolemize(X1,sK29),skolemize(X3,sK30),skolemize(X7,sK7 @ X5 @ X4)],[f210])).
% 0.21/0.33 thf(f274,plain,(
% 0.21/0.33 (prop2setE = $true) & (replAx = $true) & (emptysetE = $true) & (nonemptyI1 = $true) & (omega0Ax = $true) & (nonemptyE1 = $true) & (foundationAx = $true) & (dsetconstrER = $true) & (dsetconstrI = $true) & (exuE1 = $true) & (nonemptyI = $true) & (wellorderingAx = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ (setunion @ X0))) != $true) & (((in @ X2 @ X0)) = $true) & (((in @ X1 @ X2)) = $true)) & (powersetI = $true) & (emptyinPowerset = $true) & (omegaIndAx = $true) & (emptysetAx = $true) & (powersetAx = $true) & (setbeta = $true) & (omegaSAx = $true) & (exuE3e = $true) & (setext = $true) & (dsetconstrEL = $true) & (setadjoinE = $true) & (noeltsimpempty = $true) & (powersetE = $true) & (setadjoinAx = $true) & (setadjoinOr = $true) & (emptysetimpfalse = $true) & (setunionAx = $true) & (emptyInPowerset = $true) & (setextAx = $true) & (descrp = $true) & (setadjoinIR = $true) & (emptyI = $true) & (notinemptyset = $true) & (setadjoinIL = $true) & (emptyinunitempty = $true) & (setoftrueEq = $true)),
% 0.21/0.33 inference(rectify,[],[f145])).
% 0.21/0.33 thf(f275,plain,(
% 0.21/0.33 (prop2setE = $true) & (replAx = $true) & (emptysetE = $true) & (nonemptyI1 = $true) & (omega0Ax = $true) & (nonemptyE1 = $true) & (foundationAx = $true) & (dsetconstrER = $true) & (dsetconstrI = $true) & (exuE1 = $true) & (nonemptyI = $true) & (wellorderingAx = $true) & ((((in @ sK99 @ (setunion @ sK98))) != $true) & ($true = ((in @ sK100 @ sK98))) & (((in @ sK99 @ sK100)) = $true)) & (powersetI = $true) & (emptyinPowerset = $true) & (omegaIndAx = $true) & (emptysetAx = $true) & (powersetAx = $true) & (setbeta = $true) & (omegaSAx = $true) & (exuE3e = $true) & (setext = $true) & (dsetconstrEL = $true) & (setadjoinE = $true) & (noeltsimpempty = $true) & (powersetE = $true) & (setadjoinAx = $true) & (setadjoinOr = $true) & (emptysetimpfalse = $true) & (setunionAx = $true) & (emptyInPowerset = $true) & (setextAx = $true) & (descrp = $true) & (setadjoinIR = $true) & (emptyI = $true) & (notinemptyset = $true) & (setadjoinIL = $true) & (emptyinunitempty = $true) & (setoftrueEq = $true)),
% 0.21/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[sK98,sK99,sK100]),skolemize(X0,sK98),skolemize(X1,sK99),skolemize(X2,sK100)],[f274])).
% 0.21/0.33 thf(f335,plain,(
% 0.21/0.33 ( ! [X7 : $i,X4 : $i,X5 : $i] : ((setunionAx != $true) | ($true != ((in @ X7 @ X4))) | ($true != ((in @ X5 @ X7))) | (((in @ X5 @ (setunion @ X4))) = $true)) )),
% 0.21/0.33 inference(cnf_transformation,[],[f211])).
% 0.21/0.33 thf(f464,plain,(
% 0.21/0.33 (setunionAx = $true)),
% 0.21/0.33 inference(cnf_transformation,[],[f275])).
% 0.21/0.33 thf(f481,plain,(
% 0.21/0.33 (((in @ sK99 @ sK100)) = $true)),
% 0.21/0.33 inference(cnf_transformation,[],[f275])).
% 0.21/0.33 thf(f482,plain,(
% 0.21/0.33 ($true = ((in @ sK100 @ sK98)))),
% 0.21/0.33 inference(cnf_transformation,[],[f275])).
% 0.21/0.33 thf(f483,plain,(
% 0.21/0.33 (((in @ sK99 @ (setunion @ sK98))) != $true)),
% 0.21/0.33 inference(cnf_transformation,[],[f275])).
% 0.21/0.33 thf(f641,definition,(
% 0.21/0.33 spl115_19 <=> (setunionAx = $true)),
% 0.21/0.33 introduced(definition,[new_symbols(definition,[spl115_19])],[avatar_definition])).
% 0.21/0.33 thf(f888,definition,(
% 0.21/0.33 spl115_75 <=> ! [X4 : $i,X5 : $i,X7 : $i] : (($true != ((in @ X7 @ X4))) | (((in @ X5 @ (setunion @ X4))) = $true) | ($true != ((in @ X5 @ X7))))),
% 0.21/0.33 introduced(definition,[new_symbols(definition,[spl115_75])],[avatar_definition])).
% 0.21/0.33 thf(f889,plain,(
% 0.21/0.33 ( ! [X7 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ (setunion @ X4))) = $true) | ($true != ((in @ X7 @ X4))) | ($true != ((in @ X5 @ X7)))) ) | ~spl115_75),
% 0.21/0.33 inference(avatar_component_clause,[],[f888])).
% 0.21/0.33 thf(f890,plain,(
% 0.21/0.33 ~spl115_19 | spl115_75),
% 0.21/0.33 inference(avatar_split_clause,[],[f335,f888,f641])).
% 0.21/0.33 thf(f958,definition,(
% 0.21/0.33 spl115_91 <=> (((in @ sK99 @ (setunion @ sK98))) = $true)),
% 0.21/0.33 introduced(definition,[new_symbols(definition,[spl115_91])],[avatar_definition])).
% 0.21/0.33 thf(f960,plain,(
% 0.21/0.33 (((in @ sK99 @ (setunion @ sK98))) != $true) | spl115_91),
% 0.21/0.33 inference(avatar_component_clause,[],[f958])).
% 0.21/0.33 thf(f961,plain,(
% 0.21/0.33 ~spl115_91),
% 0.21/0.33 inference(avatar_split_clause,[],[f483,f958])).
% 0.21/0.33 thf(f1296,definition,(
% 0.21/0.33 spl115_164 <=> ($true = ((in @ sK100 @ sK98)))),
% 0.21/0.33 introduced(definition,[new_symbols(definition,[spl115_164])],[avatar_definition])).
% 0.21/0.33 thf(f1298,plain,(
% 0.21/0.33 ($true = ((in @ sK100 @ sK98))) | ~spl115_164),
% 0.21/0.33 inference(avatar_component_clause,[],[f1296])).
% 0.21/0.33 thf(f1299,plain,(
% 0.21/0.33 spl115_164),
% 0.21/0.33 inference(avatar_split_clause,[],[f482,f1296])).
% 0.21/0.33 thf(f1343,definition,(
% 0.21/0.33 spl115_173 <=> (((in @ sK99 @ sK100)) = $true)),
% 0.21/0.33 introduced(definition,[new_symbols(definition,[spl115_173])],[avatar_definition])).
% 0.21/0.33 thf(f1345,plain,(
% 0.21/0.33 (((in @ sK99 @ sK100)) = $true) | ~spl115_173),
% 0.21/0.33 inference(avatar_component_clause,[],[f1343])).
% 0.21/0.33 thf(f1346,plain,(
% 0.21/0.33 spl115_173),
% 0.21/0.33 inference(avatar_split_clause,[],[f481,f1343])).
% 0.21/0.33 thf(f1361,plain,(
% 0.21/0.33 spl115_19),
% 0.21/0.33 inference(avatar_split_clause,[],[f464,f641])).
% 0.21/0.33 thf(f1743,plain,(
% 0.21/0.33 ( ! [X0 : $i] : (($true != $true) | ($true != ((in @ X0 @ sK98))) | (((in @ sK99 @ X0)) != $true)) ) | (~spl115_75 | spl115_91)),
% 0.21/0.33 inference(superposition,[],[f960,f889])).
% 0.21/0.33 thf(f1746,plain,(
% 0.21/0.33 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK98))) | (((in @ sK99 @ X0)) != $true)) ) | (~spl115_75 | spl115_91)),
% 0.21/0.33 inference(trivial_inequality_removal,[],[f1743])).
% 0.21/0.33 thf(f1760,plain,(
% 0.21/0.33 ($true != $true) | (((in @ sK99 @ sK100)) != $true) | (~spl115_75 | spl115_91 | ~spl115_164)),
% 0.21/0.33 inference(superposition,[],[f1746,f1298])).
% 0.21/0.33 thf(f1764,plain,(
% 0.21/0.33 (((in @ sK99 @ sK100)) != $true) | (~spl115_75 | spl115_91 | ~spl115_164)),
% 0.21/0.33 inference(trivial_inequality_removal,[],[f1760])).
% 0.21/0.33 thf(f1783,plain,(
% 0.21/0.33 $false | (~spl115_75 | spl115_91 | ~spl115_164 | ~spl115_173)),
% 0.21/0.33 inference(forward_subsumption_resolution,[],[f1764,f1345])).
% 0.21/0.33 thf(f1784,plain,(
% 0.21/0.33 ~spl115_75 | spl115_91 | ~spl115_164 | ~spl115_173),
% 0.21/0.33 inference(avatar_contradiction_clause,[],[f1783])).
% 0.21/0.33 cnf(s54, plain, ~spl115_19 | spl115_75, inference(sat_conversion,[],[f890])).
% 0.21/0.33 cnf(s66, plain, ~spl115_91, inference(sat_conversion,[],[f961])).
% 0.21/0.33 cnf(s148, plain, spl115_164, inference(sat_conversion,[],[f1299])).
% 0.21/0.33 cnf(s162, plain, spl115_173, inference(sat_conversion,[],[f1346])).
% 0.21/0.33 cnf(s166, plain, spl115_19, inference(sat_conversion,[],[f1361])).
% 0.21/0.33 cnf(s219, plain, ~spl115_75 | spl115_91 | ~spl115_164 | ~spl115_173, inference(sat_conversion,[],[f1784])).
% 0.21/0.33 cnf(s246, plain, ~spl115_75, inference(rat,[],[s219,s162,s148,s66])).
% 0.21/0.33 cnf(s249, plain, $false, inference(rat,[],[s54,s246,s166])).
% 0.21/0.33 thf(f1799,plain,(
% 0.21/0.33 $false),
% 0.21/0.33 inference(avatar_sat_refutation,[],[s249])).
% 0.21/0.33 % SZS output end Proof for theBenchmark
% 0.21/0.33 % (122501)------------------------------
% 0.21/0.33 % (122501)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.33 % (122501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.33 % (122501)CaDiCaL version: 2.1.3
% 0.21/0.33 % (122501)Termination reason: Refutation
% 0.21/0.33 % (122501)Time elapsed: 0.041 s
% 0.21/0.33 % (122501)Peak memory usage: 14 MB
% 0.21/0.33 % (122501)Instructions burned: 74 (million)
% 0.21/0.33 % (122493)Success in time 0.076 s
% 0.21/0.33 % Vampire exiting
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