%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU499^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 08:32:12 AM UTC 2026
% Result : Theorem 0.33s 0.41s
% Output : Refutation 0.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU499^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.29 % Computer : n004.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8046.5625MB
% 0.10/0.29 % OS : Linux 6.8.0-71-generic
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Sep 29 13:45:52 UTC 2026
% 0.28/0.29 % CPUTime :
% 0.28/0.29 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.28/0.34 Running first-order model finding
% 0.28/0.34 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.33/0.41 % (1306358)Will run a generic schedule for satisfiability detection.
% 0.33/0.41 % (1306369)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2752345536:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.33/0.41 % (1306364)% WARNING: option uhcvi not known.
% 0.33/0.41 % (1306366)dis+10_1_sil=32000:sp=arity:random_seed=1348702822:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.33/0.41 % (1306363)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1029351500_2999 on theBenchmark for (2999ds/0Mi)
% 0.33/0.41 % (1306364)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2726488029:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.33/0.41 % (1306365)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1082949922:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.33/0.41 % (1306367)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3133165062:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.33/0.41 % (1306369) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1306358-1306369"...
% 0.33/0.41 % (1306368)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1812151455:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.33/0.41 % (1306369)...printing done.
% 0.33/0.41 % (1306369)Refutation found. Thanks to Tanya!
% 0.33/0.41 % SZS status Theorem for theBenchmark
% 0.33/0.41 % SZS output start Proof for theBenchmark
% 0.33/0.41 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.33/0.41 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.33/0.41 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 0.33/0.41 thf(func_def_3, type, setextAx: $o).
% 0.33/0.41 thf(func_def_5, type, emptysetAx: $o).
% 0.33/0.41 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 0.33/0.41 thf(func_def_7, type, setadjoinAx: $o).
% 0.33/0.41 thf(func_def_8, type, powerset: ($i > $i)).
% 0.33/0.41 thf(func_def_9, type, powersetAx: $o).
% 0.33/0.41 thf(func_def_10, type, setunion: ($i > $i)).
% 0.33/0.41 thf(func_def_11, type, setunionAx: $o).
% 0.33/0.41 thf(func_def_13, type, omega0Ax: $o).
% 0.33/0.41 thf(func_def_14, type, omegaSAx: $o).
% 0.33/0.41 thf(func_def_15, type, omegaIndAx: $o).
% 0.33/0.41 thf(func_def_16, type, replAx: $o).
% 0.33/0.41 thf(func_def_17, type, foundationAx: $o).
% 0.33/0.41 thf(func_def_18, type, wellorderingAx: $o).
% 0.33/0.41 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 0.33/0.41 thf(func_def_20, type, descrp: $o).
% 0.33/0.41 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.33/0.41 thf(func_def_22, type, dsetconstrI: $o).
% 0.33/0.41 thf(func_def_23, type, dsetconstrEL: $o).
% 0.33/0.41 thf(func_def_24, type, dsetconstrER: $o).
% 0.33/0.41 thf(func_def_25, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.33/0.41 thf(func_def_26, type, vAND: ($o > $o > $o)).
% 0.33/0.41 thf(func_def_27, type, db1: !>[X0: $tType]:(X0)).
% 0.33/0.41 thf(func_def_28, type, db0: !>[X0: $tType]:(X0)).
% 0.33/0.41 thf(func_def_29, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.33/0.41 thf(func_def_30, type, vIMP: ($o > $o > $o)).
% 0.33/0.41 thf(func_def_31, type, db2: !>[X0: $tType]:(X0)).
% 0.33/0.41 thf(func_def_32, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.33/0.41 thf(func_def_33, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.33/0.41 thf(func_def_34, type, vIFF: ($o > $o > $o)).
% 0.33/0.41 thf(func_def_35, type, vNOT: ($o > $o)).
% 0.33/0.41 thf(func_def_36, type, vOR: ($o > $o > $o)).
% 0.33/0.41 thf(func_def_37, type, db4: !>[X0: $tType]:(X0)).
% 0.33/0.41 thf(func_def_38, type, db3: !>[X0: $tType]:(X0)).
% 0.33/0.41 thf(func_def_41, type, sK0: ($i > $o)).
% 0.33/0.41 thf(func_def_42, type, sK1: ($i > $i)).
% 0.33/0.41 thf(func_def_44, type, sK3: (($i > $o) > $i > $i)).
% 0.33/0.41 thf(func_def_45, type, sK4: ($i > $i)).
% 0.33/0.41 thf(func_def_46, type, sK5: ($i > $i > $i > $i)).
% 0.33/0.41 thf(func_def_47, type, sK6: ($i > $i > $i)).
% 0.33/0.41 thf(func_def_48, type, sK7: ($i > $i > $i)).
% 0.33/0.41 thf(func_def_49, type, sK8: ($i > $i > $i)).
% 0.33/0.41 thf(func_def_50, type, sK9: ($i > $i)).
% 0.33/0.41 thf(func_def_51, type, sK10: ($i > ($i > $i > $o) > $i)).
% 0.33/0.41 thf(func_def_52, type, sK11: ($i > ($i > $i > $o) > $i)).
% 0.33/0.41 thf(func_def_53, type, sK12: ($i > $i > ($i > $i > $o) > $i)).
% 0.33/0.41 thf(func_def_54, type, sK13: ($i > $i > ($i > $i > $o) > $i)).
% 0.33/0.41 thf(func_def_55, type, sK14: ($i > $i > ($i > $i > $o) > $i)).
% 0.33/0.41 thf(func_def_56, type, sK15: ($i > $i > ($i > $i > $o) > $i)).
% 0.33/0.41 thf(func_def_57, type, sK16: ($i > $i)).
% 0.33/0.41 thf(func_def_58, type, sK17: ($i > $i > $i)).
% 0.33/0.41 thf(func_def_59, type, sK18: ($i > $i > $i)).
% 0.33/0.41 thf(func_def_60, type, sK19: ($i > $i > $i)).
% 0.33/0.41 thf(f1,axiom,(
% 0.33/0.41 (exu = (^[X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 0.33/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu)).
% 0.33/0.41 thf(f17,conjecture,(
% 0.33/0.41 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))))))))))))))),
% 0.33/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1)).
% 0.33/0.41 thf(f18,negated_conjecture,(
% 0.33/0.41 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1))))))))))))))))))),
% 0.33/0.41 inference(negated_conjecture,[status(cth)],[f17])).
% 0.33/0.41 thf(f19,plain,(
% 0.33/0.41 (exu = (^[X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 0.33/0.41 inference(rectify,[],[f1])).
% 0.33/0.41 thf(f20,plain,(
% 0.33/0.41 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 0.33/0.41 inference(fool_elimination,[],[f19])).
% 0.33/0.41 thf(f49,plain,(
% 0.33/0.41 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X2 : $i] : (! [X3 : $i] : ((X0 @ X3) => (X2 = X3)) & (X0 @ X2))))))))))))))))))),
% 0.33/0.41 inference(rectify,[],[f18])).
% 0.33/0.41 thf(f50,plain,(
% 0.33/0.41 ~((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 = $true) => ! [X0 : ($i > $o)] : (($true = ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) => ? [X2 : $i] : (! [X3 : $i] : ((((X0 @ X3)) = $true) => (X2 = X3)) & (((X0 @ X2)) = $true))))))))))))))))))),
% 0.33/0.41 inference(fool_elimination,[],[f49])).
% 0.33/0.41 thf(f51,plain,(
% 0.33/0.41 ~((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 = $true) => ! [X0 : ($i > $o)] : (($true = ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) => ? [X1 : $i] : (! [X2 : $i] : ((((X0 @ X2)) = $true) => (X1 = X2)) & (((X0 @ X1)) = $true))))))))))))))))))),
% 0.33/0.41 inference(rectify,[],[f50])).
% 0.33/0.41 thf(f52,plain,(
% 0.33/0.41 ((((((((((((((? [X0 : ($i > $o)] : (! [X1 : $i] : (? [X2 : $i] : ((X1 != X2) & (((X0 @ X2)) = $true)) | (((X0 @ X1)) != $true)) & ($true = ((exu @ (^[Y0 : $i]: (X0 @ Y0)))))) & (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 = $true)),
% 0.33/0.41 inference(ennf_transformation,[],[f51])).
% 0.33/0.41 thf(f53,plain,(
% 0.33/0.41 ? [X0 : ($i > $o)] : (! [X1 : $i] : (? [X2 : $i] : ((X1 != X2) & (((X0 @ X2)) = $true)) | (((X0 @ X1)) != $true)) & ($true = ((exu @ (^[Y0 : $i]: (X0 @ Y0)))))) & (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)),
% 0.33/0.41 inference(flattening,[],[f52])).
% 0.33/0.41 thf(f54,plain,(
% 0.33/0.41 (! [X1 : $i] : (((((sK1 @ X1)) != X1) & ($true = ((sK0 @ (sK1 @ X1))))) | ($true != ((sK0 @ X1)))) & ($true = ((exu @ (^[Y0 : $i]: (sK0 @ Y0)))))) & (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)),
% 0.33/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP]),skolemize(X0,sK0),skolemize(X2,sK1 @ X1)],[f53])).
% 0.33/0.41 thf(f55,plain,(
% 0.33/0.41 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 0.33/0.41 inference(cnf_transformation,[],[f20])).
% 0.33/0.41 thf(f86,plain,(
% 0.33/0.41 ($true = ((exu @ (^[Y0 : $i]: (sK0 @ Y0)))))),
% 0.33/0.41 inference(cnf_transformation,[],[f54])).
% 0.33/0.41 thf(f87,plain,(
% 0.33/0.41 ( ! [X1 : $i] : (($true != ((sK0 @ X1))) | ($true = ((sK0 @ (sK1 @ X1))))) )),
% 0.33/0.41 inference(cnf_transformation,[],[f54])).
% 0.33/0.41 thf(f88,plain,(
% 0.33/0.41 ( ! [X1 : $i] : (($true != ((sK0 @ X1))) | (((sK1 @ X1)) != X1)) )),
% 0.33/0.41 inference(cnf_transformation,[],[f54])).
% 0.33/0.41 thf(f106,plain,(
% 0.33/0.41 ($true = (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))) @ (^[Y0 : $i]: (sK0 @ Y0)))))),
% 0.33/0.41 inference(definition_unfolding,[],[f86,f55])).
% 0.33/0.41 thf(f107,plain,(
% 0.33/0.41 ($true = ((?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))))))),
% 0.33/0.41 inference(beta-eta_normalization,[],[f106])).
% 0.33/0.41 thf(f108,plain,(
% 0.33/0.41 ($true = (((^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))) @ sK2)))),
% 0.33/0.41 inference(sigma_proxy_clausification,[],[f107])).
% 0.33/0.41 thf(f109,plain,(
% 0.33/0.41 ($true = (((sK0 @ sK2) & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK2 = Y0)))))))),
% 0.33/0.41 inference(beta-eta_normalization,[],[f108])).
% 0.33/0.41 thf(f110,plain,(
% 0.33/0.41 ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK2 = Y0))))))),
% 0.33/0.41 inference(and_proxy_clausification,[],[f109])).
% 0.33/0.41 thf(f111,plain,(
% 0.33/0.41 ($true = ((sK0 @ sK2)))),
% 0.33/0.41 inference(and_proxy_clausification,[],[f109])).
% 0.33/0.41 thf(f112,plain,(
% 0.33/0.41 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((sK0 @ Y0) => (sK2 = Y0))) @ X1)))) )),
% 0.33/0.41 inference(pi_proxy_clausification,[],[f110])).
% 0.33/0.41 thf(f113,plain,(
% 0.33/0.41 ( ! [X1 : $i] : (($true = (((sK0 @ X1) => (sK2 = X1))))) )),
% 0.33/0.41 inference(beta-eta_normalization,[],[f112])).
% 0.33/0.41 thf(f114,plain,(
% 0.33/0.41 ( ! [X1 : $i] : ((((sK0 @ X1)) = $false) | ($true = ((sK2 = X1)))) )),
% 0.33/0.41 inference(imp_proxy_clausification,[],[f113])).
% 0.33/0.41 thf(f115,plain,(
% 0.33/0.41 ( ! [X1 : $i] : ((((sK0 @ X1)) = $false) | (sK2 = X1)) )),
% 0.33/0.41 inference(equality_proxy_clausification,[],[f114])).
% 0.33/0.41 thf(f377,plain,(
% 0.33/0.41 ($true != $true) | (sK2 != ((sK1 @ sK2)))),
% 0.33/0.41 inference(constrained_superposition,[],[f88,f111])).
% 0.33/0.41 thf(f379,plain,(
% 0.33/0.41 (sK2 != ((sK1 @ sK2)))),
% 0.33/0.41 inference(trivial_inequality_removal,[],[f377])).
% 0.33/0.41 thf(f393,plain,(
% 0.33/0.41 ($true != $true) | ($true = ((sK0 @ (sK1 @ sK2))))),
% 0.33/0.41 inference(constrained_superposition,[],[f87,f111])).
% 0.33/0.41 thf(f397,plain,(
% 0.33/0.41 ($true = ((sK0 @ (sK1 @ sK2))))),
% 0.33/0.41 inference(trivial_inequality_removal,[],[f393])).
% 0.33/0.41 thf(f406,plain,(
% 0.33/0.41 ($true = $false) | (sK2 = ((sK1 @ sK2)))),
% 0.33/0.41 inference(constrained_superposition,[],[f115,f397])).
% 0.33/0.41 thf(f407,plain,(
% 0.33/0.41 (sK2 = ((sK1 @ sK2)))),
% 0.33/0.41 inference(trivial_inequality_removal,[],[f406])).
% 0.33/0.41 thf(f417,plain,(
% 0.33/0.41 (sK2 != sK2)),
% 0.33/0.41 inference(constrained_superposition,[],[f379,f407])).
% 0.33/0.41 thf(f420,plain,(
% 0.33/0.41 $false),
% 0.33/0.41 inference(trivial_inequality_removal,[],[f417])).
% 0.33/0.41 % SZS output end Proof for theBenchmark
% 0.33/0.41 % (1306369)------------------------------
% 0.33/0.41 % (1306369)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.41 % (1306369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.41 % (1306369)CaDiCaL version: 2.1.3
% 0.33/0.41 % (1306369)Termination reason: Refutation
% 0.33/0.41 % (1306369)Time elapsed: 0.014 s
% 0.33/0.41 % (1306369)Peak memory usage: 12 MB
% 0.33/0.41 % (1306369)Instructions burned: 28 (million)
% 0.33/0.41 % (1306358)Success in time 0.05 s
% 0.33/0.41 % Vampire exiting
%------------------------------------------------------------------------------