%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP144^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 08:10:52 AM UTC 2026
% Result : Theorem 0.33s 0.43s
% Output : Refutation 0.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP144^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.28 % Computer : n017.cluster.edu
% 0.12/0.28 % Model : x86_64 x86_64
% 0.12/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.28 % Memory : 8046.5625MB
% 0.12/0.28 % OS : Linux 6.8.0-71-generic
% 0.12/0.28 % CPULimit : 300
% 0.12/0.28 % WCLimit : 300
% 0.12/0.28 % DateTime : Tue Sep 29 19:55:44 UTC 2026
% 0.12/0.28 % CPUTime :
% 0.12/0.28 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.28/0.33 Running first-order model finding
% 0.28/0.33 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
% 0.33/0.43 % (820636)Will run a generic schedule for satisfiability detection.
% 0.33/0.43 % (820643)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4030894582:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.33/0.43 % (820642)% WARNING: option uhcvi not known.
% 0.33/0.43 % (820641)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2883401433_2999 on theBenchmark for (2999ds/0Mi)
% 0.33/0.43 % (820642)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2266487751:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.33/0.43 % (820644)dis+10_1_sil=32000:sp=arity:random_seed=912042740:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.33/0.43 % (820645)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3340273100:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.33/0.43 % (820647)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2536728139:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.33/0.43 % (820646)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3771735977:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.33/0.43 % (820642)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.33/0.43 % (820645)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.33/0.43 % Exception at run slice level
% 0.33/0.43 % (820642)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.33/0.43 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.33/0.43 % (820643) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-820636-820643"...
% 0.33/0.43 % (820643)...printing done.
% 0.33/0.43 % (820643)Refutation found. Thanks to Tanya!
% 0.33/0.43 % SZS status Theorem for theBenchmark
% 0.33/0.43 % SZS output start Proof for theBenchmark
% 0.33/0.43 thf(type_def_5, type, set_set_b: $tType).
% 0.33/0.43 thf(type_def_6, type, set_b: $tType).
% 0.33/0.43 thf(type_def_7, type, b: $tType).
% 0.33/0.43 thf(type_def_8, type, a: $tType).
% 0.33/0.43 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.33/0.43 thf(func_def_0, type, bij_betw_b_b: ((b > b) > set_b > set_b > $o)).
% 0.33/0.43 thf(func_def_1, type, inj_on_b_set_b: ((b > set_b) > set_b > $o)).
% 0.33/0.43 thf(func_def_2, type, inj_on_b_b: ((b > b) > set_b > $o)).
% 0.33/0.43 thf(func_def_3, type, minus_minus_set_b: (set_b > set_b > set_b)).
% 0.33/0.43 thf(func_def_4, type, hilbert_Eps_b: ((b > $o) > b)).
% 0.33/0.43 thf(func_def_5, type, hilbert_inv_into_b_b: (set_b > (b > b) > b > b)).
% 0.33/0.43 thf(func_def_6, type, bot_bot_b_o: (b > $o)).
% 0.33/0.43 thf(func_def_7, type, bot_bot_set_b: set_b).
% 0.33/0.43 thf(func_def_8, type, top_top_b_o: (b > $o)).
% 0.33/0.43 thf(func_def_9, type, top_top_set_b: set_b).
% 0.33/0.43 thf(func_def_10, type, collect_b: ((b > $o) > set_b)).
% 0.33/0.43 thf(func_def_11, type, image_set_b_set_b: ((set_b > set_b) > set_set_b > set_set_b)).
% 0.33/0.43 thf(func_def_12, type, image_b_b: ((b > b) > set_b > set_b)).
% 0.33/0.43 thf(func_def_13, type, insert_b: (b > set_b > set_b)).
% 0.33/0.43 thf(func_def_14, type, is_empty_b: (set_b > $o)).
% 0.33/0.43 thf(func_def_15, type, is_singleton_b: (set_b > $o)).
% 0.33/0.43 thf(func_def_16, type, remove_b: (b > set_b > set_b)).
% 0.33/0.43 thf(func_def_17, type, the_elem_b: (set_b > b)).
% 0.33/0.43 thf(func_def_18, type, member_set_b: (set_b > set_set_b > $o)).
% 0.33/0.43 thf(func_def_19, type, member_b: (b > set_b > $o)).
% 0.33/0.43 thf(func_def_20, type, p: (a > $o)).
% 0.33/0.43 thf(func_def_21, type, q: (a > b > $o)).
% 0.33/0.43 thf(func_def_25, type, db0: !>[X0: $tType]:(X0)).
% 0.33/0.43 thf(func_def_26, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.33/0.43 thf(func_def_27, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.33/0.43 thf(func_def_28, type, db1: !>[X0: $tType]:(X0)).
% 0.33/0.43 thf(func_def_29, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.33/0.43 thf(func_def_30, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.33/0.43 thf(func_def_31, type, vNOT: ($o > $o)).
% 0.33/0.43 thf(func_def_32, type, vAND: ($o > $o > $o)).
% 0.33/0.43 thf(func_def_33, type, vOR: ($o > $o > $o)).
% 0.33/0.43 thf(func_def_34, type, vIMP: ($o > $o > $o)).
% 0.33/0.43 thf(func_def_35, type, db2: !>[X0: $tType]:(X0)).
% 0.33/0.43 thf(func_def_36, type, sK0: (b > (b > $o) > b)).
% 0.33/0.43 thf(func_def_37, type, sK1: ((b > $o) > (b > $o) > b)).
% 0.33/0.43 thf(func_def_38, type, sK2: ((b > $o) > (b > $o) > b)).
% 0.33/0.43 thf(func_def_39, type, sK3: ((b > $o) > (b > $o) > set_b > b)).
% 0.33/0.43 thf(func_def_40, type, sK4: ((b > $o) > (b > $o) > b)).
% 0.33/0.43 thf(func_def_41, type, sK5: ((b > $o) > (b > $o) > b)).
% 0.33/0.43 thf(func_def_42, type, sK6: (b > (b > $o) > b)).
% 0.33/0.43 thf(func_def_43, type, sK7: ((b > $o) > (b > $o) > b)).
% 0.33/0.43 thf(func_def_44, type, sK8: (set_b > b)).
% 0.33/0.43 thf(func_def_45, type, sK9: (set_b > b)).
% 0.33/0.43 thf(func_def_46, type, sK10: (set_b > b)).
% 0.33/0.43 thf(func_def_47, type, sK11: (set_b > b)).
% 0.33/0.43 thf(func_def_48, type, sK12: b).
% 0.33/0.43 thf(func_def_49, type, sK13: (set_b > b > set_b)).
% 0.33/0.43 thf(func_def_50, type, sK14: (set_b > b > set_b)).
% 0.33/0.43 thf(func_def_51, type, sK15: (set_b > b)).
% 0.33/0.43 thf(func_def_52, type, sK16: (set_b > (b > b) > b > b)).
% 0.33/0.43 thf(func_def_53, type, sK17: (set_b > b > set_b > (b > b) > b)).
% 0.33/0.43 thf(func_def_54, type, sK18: (set_b > b > set_b > (b > b) > set_b)).
% 0.33/0.43 thf(func_def_55, type, sK19: (b > set_set_b > set_b)).
% 0.33/0.43 thf(func_def_56, type, sK20: (a > b)).
% 0.33/0.43 thf(func_def_57, type, sK21: a).
% 0.33/0.43 thf(func_def_58, type, sK22: (set_b > b > set_b > b > set_b)).
% 0.33/0.43 thf(func_def_59, type, sK23: (b > b)).
% 0.33/0.43 thf(func_def_60, type, sK24: (set_b > b)).
% 0.33/0.43 thf(func_def_61, type, sK25: (set_b > b)).
% 0.33/0.43 thf(func_def_62, type, sK26: (set_b > b)).
% 0.33/0.43 thf(func_def_63, type, sK27: (set_b > b)).
% 0.33/0.43 thf(func_def_64, type, sK28: (set_b > b)).
% 0.33/0.43 thf(func_def_65, type, sK29: ((b > $o) > b)).
% 0.33/0.43 thf(func_def_66, type, sK30: ((b > $o) > b)).
% 0.33/0.43 thf(func_def_67, type, sK31: ((b > $o) > b)).
% 0.33/0.43 thf(func_def_68, type, sK32: ((b > $o) > b)).
% 0.33/0.43 thf(func_def_69, type, sK33: ((b > $o) > b)).
% 0.33/0.43 thf(func_def_70, type, sK34: ((b > $o) > b)).
% 0.33/0.43 thf(func_def_71, type, sK35: ((b > $o) > b)).
% 0.33/0.43 thf(func_def_72, type, sK36: ((b > $o) > b)).
% 0.33/0.43 thf(func_def_73, type, sK37: ((b > $o) > b)).
% 0.33/0.43 thf(func_def_75, type, sK39: ((b > a) > b)).
% 0.33/0.43 thf(func_def_76, type, sK40: (b > (b > $o) > b)).
% 0.33/0.43 thf(func_def_77, type, sK41: (b > (b > $o) > b)).
% 0.33/0.43 thf(f24,axiom,(
% 0.33/0.43 ! [X0 : (b > $o),X1 : b] : (? [X2 : b] : (X0 @ X2) => ((X1 = ((hilbert_Eps_b @ X0))) => (X0 @ X1)))),
% 0.33/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_exE__some)).
% 0.33/0.43 thf(f111,axiom,(
% 0.33/0.43 ! [X0 : a] : ((p @ X0) => ? [X1 : b] : (q @ X0 @ X1))),
% 0.33/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.33/0.43 thf(f112,conjecture,(
% 0.33/0.43 ! [X0 : a] : ((q @ X0 @ (hilbert_Eps_b @ (q @ X0))) | ~(p @ X0))),
% 0.33/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)).
% 0.33/0.43 thf(f113,negated_conjecture,(
% 0.33/0.43 ~ ! [X0 : a] : ((q @ X0 @ (hilbert_Eps_b @ (q @ X0))) | ~(p @ X0))),
% 0.33/0.43 inference(negated_conjecture,[status(cth)],[f112])).
% 0.33/0.43 thf(f157,plain,(
% 0.33/0.43 ! [X0 : (b > $o),X1 : b] : (? [X2 : b] : (X0 @ X2) => ((X1 = ((hilbert_Eps_b @ X0))) => (X0 @ X1)))),
% 0.33/0.43 inference(rectify,[],[f24])).
% 0.33/0.43 thf(f158,plain,(
% 0.33/0.43 ! [X0 : (b > $o),X1 : b] : (? [X2 : b] : (((X0 @ X2)) = $true) => ((((hilbert_Eps_b @ X0)) = X1) => (((X0 @ X1)) = $true)))),
% 0.33/0.43 inference(fool_elimination,[],[f157])).
% 0.33/0.43 thf(f292,plain,(
% 0.33/0.43 ! [X0 : a] : ((p @ X0) => ? [X1 : b] : (q @ X0 @ X1))),
% 0.33/0.43 inference(rectify,[],[f111])).
% 0.33/0.43 thf(f293,plain,(
% 0.33/0.43 ! [X0 : a] : ((((p @ X0)) = $true) => ? [X1 : b] : (((q @ X0 @ X1)) = $true))),
% 0.33/0.43 inference(fool_elimination,[],[f292])).
% 0.33/0.43 thf(f294,plain,(
% 0.33/0.43 ~ ! [X0 : a] : ((q @ X0 @ (hilbert_Eps_b @ (q @ X0))) | ~(p @ X0))),
% 0.33/0.43 inference(rectify,[],[f113])).
% 0.33/0.43 thf(f295,plain,(
% 0.33/0.43 ~ ! [X0 : a] : ((((q @ X0 @ (hilbert_Eps_b @ (q @ X0)))) = $true) | ~ (((p @ X0)) = $true))),
% 0.33/0.43 inference(fool_elimination,[],[f294])).
% 0.33/0.43 thf(f317,plain,(
% 0.33/0.43 ~ ! [X0 : a] : ((((q @ X0 @ (hilbert_Eps_b @ (q @ X0)))) = $true) | (((p @ X0)) != $true))),
% 0.33/0.43 inference(flattening,[],[f295])).
% 0.33/0.43 thf(f345,plain,(
% 0.33/0.43 ! [X0 : (b > $o),X1 : b] : (((((X0 @ X1)) = $true) | (((hilbert_Eps_b @ X0)) != X1)) | ! [X2 : b] : (((X0 @ X2)) != $true))),
% 0.33/0.43 inference(ennf_transformation,[],[f158])).
% 0.33/0.43 thf(f346,plain,(
% 0.33/0.43 ! [X0 : (b > $o),X1 : b] : ((((X0 @ X1)) = $true) | (((hilbert_Eps_b @ X0)) != X1) | ! [X2 : b] : (((X0 @ X2)) != $true))),
% 0.33/0.43 inference(flattening,[],[f345])).
% 0.33/0.43 thf(f394,plain,(
% 0.33/0.43 ! [X0 : a] : (? [X1 : b] : (((q @ X0 @ X1)) = $true) | (((p @ X0)) != $true))),
% 0.33/0.43 inference(ennf_transformation,[],[f293])).
% 0.33/0.43 thf(f395,plain,(
% 0.33/0.43 ? [X0 : a] : ((((q @ X0 @ (hilbert_Eps_b @ (q @ X0)))) != $true) & (((p @ X0)) = $true))),
% 0.33/0.43 inference(ennf_transformation,[],[f317])).
% 0.33/0.43 thf(f416,plain,(
% 0.33/0.43 ! [X0 : a] : (($true = ((q @ X0 @ (sK20 @ X0)))) | (((p @ X0)) != $true))),
% 0.33/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X1 @ X0)],[f394])).
% 0.33/0.43 thf(f417,plain,(
% 0.33/0.43 ($true != ((q @ sK21 @ (hilbert_Eps_b @ (q @ sK21))))) & ($true = ((p @ sK21)))),
% 0.33/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(X0,sK21)],[f395])).
% 0.33/0.43 thf(f447,plain,(
% 0.33/0.43 ( ! [X2 : b,X0 : (b > $o),X1 : b] : ((((X0 @ X1)) = $true) | (((hilbert_Eps_b @ X0)) != X1) | (((X0 @ X2)) != $true)) )),
% 0.33/0.43 inference(cnf_transformation,[],[f346])).
% 0.33/0.43 thf(f550,plain,(
% 0.33/0.43 ( ! [X0 : a] : ((((p @ X0)) != $true) | ($true = ((q @ X0 @ (sK20 @ X0))))) )),
% 0.33/0.43 inference(cnf_transformation,[],[f416])).
% 0.33/0.43 thf(f551,plain,(
% 0.33/0.43 ($true = ((p @ sK21)))),
% 0.33/0.43 inference(cnf_transformation,[],[f417])).
% 0.33/0.43 thf(f552,plain,(
% 0.33/0.43 ($true != ((q @ sK21 @ (hilbert_Eps_b @ (q @ sK21)))))),
% 0.33/0.43 inference(cnf_transformation,[],[f417])).
% 0.33/0.43 thf(f554,definition,(
% 0.33/0.43 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.33/0.43 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.33/0.43 thf(f625,plain,(
% 0.33/0.43 ( ! [X2 : b,X0 : (b > $o)] : ((((X0 @ (hilbert_Eps_b @ X0))) = $true) | (((X0 @ X2)) != $true)) )),
% 0.33/0.43 inference(equality_resolution,[],[f447])).
% 0.33/0.43 thf(f978,plain,(
% 0.33/0.43 ( ! [X0 : (b > $o),X1 : b] : ((((X0 @ X1)) != $true) | (((X0 @ (hilbert_Eps_b @ X0))) = $true)) )),
% 0.33/0.43 inference(global_subsumption,[],[f625])).
% 0.33/0.43 thf(f1049,plain,(
% 0.33/0.43 ( ! [X0 : (b > $o),X1 : b] : (($true != $true) | (((X0 @ (hilbert_Eps_b @ X0))) = $true) | (((X0 @ X1)) = $false)) )),
% 0.33/0.43 inference(constrained_superposition,[],[f978,f554])).
% 0.33/0.43 thf(f1052,plain,(
% 0.33/0.43 ( ! [X0 : (b > $o),X1 : b] : ((((X0 @ (hilbert_Eps_b @ X0))) = $true) | (((X0 @ X1)) = $false)) )),
% 0.33/0.43 inference(trivial_inequality_removal,[],[f1049])).
% 0.33/0.43 thf(f1165,plain,(
% 0.33/0.43 ( ! [X0 : (b > a),X1 : b] : (($true != $true) | ($false = (((^[Y0 : b]: (q @ (X0 @ Y0) @ ((^[Y1 : b]: (Y1)) @ Y0))) @ X1))) | ((^[Y0 : b]: (sK21)) != X0) | (sK21 != ((X0 @ (hilbert_Eps_b @ (^[Y0 : b]: (q @ (X0 @ Y0) @ Y0))))))) )),
% 0.33/0.43 inference(constrained_superposition,[],[f552,f1052])).
% 0.33/0.43 thf(f1215,plain,(
% 0.33/0.43 ( ! [X0 : (b > a),X1 : b] : (($false = (((^[Y0 : b]: (q @ (X0 @ Y0) @ ((^[Y1 : b]: (Y1)) @ Y0))) @ X1))) | ((^[Y0 : b]: (sK21)) != X0) | (sK21 != ((X0 @ (hilbert_Eps_b @ (^[Y0 : b]: (q @ (X0 @ Y0) @ Y0))))))) )),
% 0.33/0.43 inference(trivial_inequality_removal,[],[f1165])).
% 0.33/0.43 thf(f1216,plain,(
% 0.33/0.43 ( ! [X0 : (b > a),X1 : b] : ((sK21 != ((X0 @ (hilbert_Eps_b @ (^[Y0 : b]: (q @ (X0 @ Y0) @ Y0)))))) | ((^[Y0 : b]: (sK21)) != X0) | ($false = ((q @ (X0 @ X1) @ X1)))) )),
% 0.33/0.43 inference(beta-eta_normalization,[],[f1215])).
% 0.33/0.43 thf(f1263,plain,(
% 0.33/0.43 ( ! [X0 : b] : (((^[Y0 : b]: (sK21)) != (^[Y0 : b]: (sK21))) | ($false = ((q @ ((^[Y0 : b]: (sK21)) @ X0) @ X0)))) )),
% 0.33/0.43 inference(equality_resolution,[],[f1216])).
% 0.33/0.43 thf(f1264,plain,(
% 0.33/0.43 ( ! [X0 : b] : (($false = ((q @ ((^[Y0 : b]: (sK21)) @ X0) @ X0)))) )),
% 0.33/0.43 inference(trivial_inequality_removal,[],[f1263])).
% 0.33/0.43 thf(f1265,plain,(
% 0.33/0.43 ( ! [X0 : b] : (($false = ((q @ sK21 @ X0)))) )),
% 0.33/0.43 inference(beta-eta_normalization,[],[f1264])).
% 0.33/0.43 thf(f1594,plain,(
% 0.33/0.43 ($true != $true) | ($true = ((q @ sK21 @ (sK20 @ sK21))))),
% 0.33/0.43 inference(constrained_superposition,[],[f550,f551])).
% 0.33/0.43 thf(f1600,plain,(
% 0.33/0.43 ($true = ((q @ sK21 @ (sK20 @ sK21))))),
% 0.33/0.43 inference(trivial_inequality_removal,[],[f1594])).
% 0.33/0.43 thf(f1602,plain,(
% 0.33/0.43 ($true = $false)),
% 0.33/0.43 inference(forward_demodulation,[],[f1600,f1265])).
% 0.33/0.43 thf(f1603,plain,(
% 0.33/0.43 $false),
% 0.33/0.43 inference(trivial_inequality_removal,[],[f1602])).
% 0.33/0.43 % SZS output end Proof for theBenchmark
% 0.33/0.43 % (820643)------------------------------
% 0.33/0.43 % (820643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.43 % (820643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.43 % (820643)CaDiCaL version: 2.1.3
% 0.33/0.43 % (820643)Termination reason: Refutation
% 0.33/0.43 % (820643)Time elapsed: 0.047 s
% 0.33/0.43 % (820643)Peak memory usage: 13 MB
% 0.33/0.43 % (820643)Instructions burned: 96 (million)
% 0.33/0.43 % (820636)Success in time 0.086 s
% 0.33/0.43 % Vampire exiting
%------------------------------------------------------------------------------