%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n015.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 08:08:32 AM UTC 2026
% Result : Theorem 0.21s 0.32s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP144^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n015.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 20:03:19 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.21/0.26 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.32 % (4043880)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.32 % (4043885)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4266367924:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.32 % (4043891)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.32 % (4043891)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.32 % (4043886)lrs+10_16_si=on:nwc=1.5:random_seed=1733584601:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.32 % (4043887)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=886716625:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.32 % (4043888)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=1472524119:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.32 % (4043889)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4060127653:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.32 % (4043890)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3468170960:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.32 % (4043891)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=4224221443:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.32 % (4043887)Instruction limit reached!
% 0.21/0.32 % (4043887)------------------------------
% 0.21/0.32 % (4043887)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (4043887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (4043887)CaDiCaL version: 2.1.3
% 0.21/0.32 % (4043887)Termination reason: Instruction limit
% 0.21/0.32 % (4043887)Termination phase: shuffling
% 0.21/0.32 % (4043887)Time elapsed: 0.002 s
% 0.21/0.32 % (4043887)Peak memory usage: 10 MB
% 0.21/0.32 % (4043887)Instructions burned: 4 (million)
% 0.21/0.32 % (4043886)Instruction limit reached!
% 0.21/0.32 % (4043886)------------------------------
% 0.21/0.32 % (4043886)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (4043886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (4043886)CaDiCaL version: 2.1.3
% 0.21/0.32 % (4043886)Termination reason: Instruction limit
% 0.21/0.32 % (4043886)Termination phase: Property scanning
% 0.21/0.32 % (4043886)Time elapsed: 0.009 s
% 0.21/0.32 % (4043886)Peak memory usage: 10 MB
% 0.21/0.32 % (4043886)Instructions burned: 19 (million)
% 0.21/0.32 % (4043885) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4043880-4043885"...
% 0.21/0.32 % (4043885)...printing done.
% 0.21/0.32 % (4043885)Refutation found. Thanks to Tanya!
% 0.21/0.32 % SZS status Theorem for theBenchmark
% 0.21/0.32 % SZS output start Proof for theBenchmark
% 0.21/0.32 thf(type_def_5, type, set_set_b: $tType).
% 0.21/0.32 thf(type_def_6, type, set_b: $tType).
% 0.21/0.32 thf(type_def_7, type, b: $tType).
% 0.21/0.32 thf(type_def_8, type, a: $tType).
% 0.21/0.32 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.32 thf(func_def_0, type, bij_betw_b_b: ((b > b) > set_b > set_b > $o)).
% 0.21/0.32 thf(func_def_1, type, inj_on_b_set_b: ((b > set_b) > set_b > $o)).
% 0.21/0.32 thf(func_def_2, type, inj_on_b_b: ((b > b) > set_b > $o)).
% 0.21/0.32 thf(func_def_3, type, minus_minus_set_b: (set_b > set_b > set_b)).
% 0.21/0.32 thf(func_def_4, type, hilbert_Eps_b: ((b > $o) > b)).
% 0.21/0.32 thf(func_def_5, type, hilbert_inv_into_b_b: (set_b > (b > b) > b > b)).
% 0.21/0.32 thf(func_def_6, type, bot_bot_b_o: (b > $o)).
% 0.21/0.32 thf(func_def_7, type, bot_bot_set_b: set_b).
% 0.21/0.32 thf(func_def_8, type, top_top_b_o: (b > $o)).
% 0.21/0.32 thf(func_def_9, type, top_top_set_b: set_b).
% 0.21/0.32 thf(func_def_10, type, collect_b: ((b > $o) > set_b)).
% 0.21/0.32 thf(func_def_11, type, image_set_b_set_b: ((set_b > set_b) > set_set_b > set_set_b)).
% 0.21/0.32 thf(func_def_12, type, image_b_b: ((b > b) > set_b > set_b)).
% 0.21/0.32 thf(func_def_13, type, insert_b: (b > set_b > set_b)).
% 0.21/0.32 thf(func_def_14, type, is_empty_b: (set_b > $o)).
% 0.21/0.32 thf(func_def_15, type, is_singleton_b: (set_b > $o)).
% 0.21/0.32 thf(func_def_16, type, remove_b: (b > set_b > set_b)).
% 0.21/0.32 thf(func_def_17, type, the_elem_b: (set_b > b)).
% 0.21/0.32 thf(func_def_18, type, member_set_b: (set_b > set_set_b > $o)).
% 0.21/0.32 thf(func_def_19, type, member_b: (b > set_b > $o)).
% 0.21/0.32 thf(func_def_20, type, p: (a > $o)).
% 0.21/0.32 thf(func_def_21, type, q: (a > b > $o)).
% 0.21/0.32 thf(func_def_25, type, vNOT: ($o > $o)).
% 0.21/0.32 thf(func_def_26, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.32 thf(func_def_27, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.32 thf(func_def_28, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.32 thf(func_def_29, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.32 thf(func_def_30, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.32 thf(func_def_31, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.32 thf(func_def_32, type, vAND: ($o > $o > $o)).
% 0.21/0.32 thf(func_def_33, type, db2: !>[X0: $tType]:(X0)).
% 0.21/0.32 thf(func_def_34, type, vOR: ($o > $o > $o)).
% 0.21/0.32 thf(func_def_35, type, sP0: (set_b > set_b > b > b > $o)).
% 0.21/0.32 thf(func_def_36, type, sP1: (b > set_b > b > set_b > $o)).
% 0.21/0.32 thf(func_def_37, type, sK2: (set_b > b)).
% 0.21/0.32 thf(func_def_38, type, sK3: ((b > $o) > b)).
% 0.21/0.32 thf(func_def_39, type, sK4: (a > b)).
% 0.21/0.32 thf(func_def_40, type, sK5: (set_b > b)).
% 0.21/0.32 thf(func_def_41, type, sK6: ((b > $o) > (b > $o) > b)).
% 0.21/0.32 thf(func_def_42, type, sK7: ((b > $o) > (b > $o) > b)).
% 0.21/0.32 thf(func_def_43, type, sK8: (b > (b > $o) > b)).
% 0.21/0.32 thf(func_def_44, type, sK9: ((b > $o) > b)).
% 0.21/0.32 thf(func_def_45, type, sK10: ((b > b) > set_b > b > b)).
% 0.21/0.32 thf(func_def_46, type, sK11: b).
% 0.21/0.32 thf(func_def_47, type, sK12: (set_b > b)).
% 0.21/0.32 thf(func_def_48, type, sK13: (b > set_b > set_b)).
% 0.21/0.32 thf(func_def_49, type, sK14: ((b > $o) > b > b)).
% 0.21/0.32 thf(func_def_50, type, sK15: ((b > $o) > b)).
% 0.21/0.32 thf(func_def_51, type, sK16: (set_b > b)).
% 0.21/0.32 thf(func_def_52, type, sK17: (set_b > b)).
% 0.21/0.32 thf(func_def_53, type, sK18: (set_b > b)).
% 0.21/0.32 thf(func_def_54, type, sK19: a).
% 0.21/0.32 thf(func_def_55, type, sK20: ((b > $o) > (b > $o) > b)).
% 0.21/0.32 thf(func_def_56, type, sK21: ((b > $o) > (b > $o) > b)).
% 0.21/0.32 thf(func_def_57, type, sK22: ((b > $o) > b)).
% 0.21/0.32 thf(func_def_58, type, sK23: ((b > $o) > b)).
% 0.21/0.32 thf(func_def_59, type, sK24: ((b > $o) > (b > $o) > b)).
% 0.21/0.32 thf(func_def_60, type, sK25: ((b > b) > b > set_b > set_b > b)).
% 0.21/0.32 thf(func_def_61, type, sK26: ((b > b) > b > set_b > set_b > set_b)).
% 0.21/0.32 thf(func_def_62, type, sK27: ((b > $o) > b)).
% 0.21/0.32 thf(func_def_63, type, sK28: (set_b > b > set_b)).
% 0.21/0.32 thf(func_def_64, type, sK29: ((b > $o) > b)).
% 0.21/0.32 thf(func_def_65, type, sK30: (set_b > set_b > b > b > set_b)).
% 0.21/0.32 thf(func_def_66, type, sK31: ((b > $o) > b)).
% 0.21/0.32 thf(func_def_67, type, sK32: (set_set_b > b > set_b)).
% 0.21/0.32 thf(func_def_68, type, sK33: (set_b > b)).
% 0.21/0.32 thf(func_def_69, type, sK34: ((b > $o) > b)).
% 0.21/0.32 thf(func_def_70, type, sK35: (set_b > (b > $o) > (b > $o) > b)).
% 0.21/0.32 thf(func_def_71, type, sK36: (set_b > b)).
% 0.21/0.32 thf(func_def_72, type, sK37: (b > b)).
% 0.21/0.32 thf(func_def_73, type, sK38: (set_b > b)).
% 0.21/0.32 thf(func_def_74, type, sK39: (set_b > b)).
% 0.21/0.32 thf(f21,axiom,(
% 0.21/0.32 ! [X1 : (b > $o),X0 : b] : ((X0 = ((hilbert_Eps_b @ X1))) => (((X1 @ X0)) = ? [X2 : b] : (X1 @ X2)))),
% 0.21/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_verit__sko__ex__indirect)).
% 0.21/0.32 thf(f25,axiom,(
% 0.21/0.32 ! [X0 : (b > $o)] : ((bot_bot_set_b = ((collect_b @ X0))) = ! [X1 : b] : ~(X0 @ X1))),
% 0.21/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_empty__Collect__eq)).
% 0.21/0.32 thf(f26,axiom,(
% 0.21/0.32 ! [X0 : (b > $o)] : ((((collect_b @ X0)) = bot_bot_set_b) = ! [X1 : b] : ~(X0 @ X1))),
% 0.21/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_Collect__empty__eq)).
% 0.21/0.32 thf(f111,axiom,(
% 0.21/0.32 ! [X0 : a] : ((p @ X0) => ? [X1 : b] : (q @ X0 @ X1))),
% 0.21/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.21/0.32 thf(f112,conjecture,(
% 0.21/0.32 ! [X0 : a] : (~(p @ X0) | (q @ X0 @ (hilbert_Eps_b @ (q @ X0))))),
% 0.21/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)).
% 0.21/0.32 thf(f113,negated_conjecture,(
% 0.21/0.32 ~ ! [X0 : a] : (~(p @ X0) | (q @ X0 @ (hilbert_Eps_b @ (q @ X0))))),
% 0.21/0.32 inference(negated_conjecture,[status(cth)],[f112])).
% 0.21/0.32 thf(f140,plain,(
% 0.21/0.32 ! [X0 : (b > $o),X1 : b] : ((((hilbert_Eps_b @ X0)) = X1) => (((X0 @ X1)) = ? [X2 : b] : (X0 @ X2)))),
% 0.21/0.32 inference(rectify,[],[f21])).
% 0.21/0.32 thf(f141,plain,(
% 0.21/0.32 ! [X1 : b,X0 : (b > $o)] : ((((hilbert_Eps_b @ X0)) = X1) => (? [X2 : b] : (((X0 @ X2)) = $true) <=> (((X0 @ X1)) = $true)))),
% 0.21/0.32 inference(fool_elimination,[],[f140])).
% 0.21/0.32 thf(f203,plain,(
% 0.21/0.32 ! [X0 : a] : ((p @ X0) => ? [X1 : b] : (q @ X0 @ X1))),
% 0.21/0.32 inference(rectify,[],[f111])).
% 0.21/0.32 thf(f204,plain,(
% 0.21/0.32 ! [X0 : a] : ((((p @ X0)) = $true) => ? [X1 : b] : (((q @ X0 @ X1)) = $true))),
% 0.21/0.32 inference(fool_elimination,[],[f203])).
% 0.21/0.32 thf(f268,plain,(
% 0.21/0.32 ! [X0 : (b > $o)] : ((((collect_b @ X0)) = bot_bot_set_b) = ! [X1 : b] : ~(X0 @ X1))),
% 0.21/0.32 inference(rectify,[],[f26])).
% 0.21/0.32 thf(f269,plain,(
% 0.21/0.32 ! [X0 : (b > $o)] : ((bot_bot_set_b = ((collect_b @ X0))) <=> ! [X1 : b] : ~ (((X0 @ X1)) = $true))),
% 0.21/0.32 inference(fool_elimination,[],[f268])).
% 0.21/0.32 thf(f272,plain,(
% 0.21/0.32 ~ ! [X0 : a] : (~(p @ X0) | (q @ X0 @ (hilbert_Eps_b @ (q @ X0))))),
% 0.21/0.32 inference(rectify,[],[f113])).
% 0.21/0.32 thf(f273,plain,(
% 0.21/0.32 ~ ! [X0 : a] : (~ (((p @ X0)) = $true) | (((q @ X0 @ (hilbert_Eps_b @ (q @ X0)))) = $true))),
% 0.21/0.32 inference(fool_elimination,[],[f272])).
% 0.21/0.32 thf(f293,plain,(
% 0.21/0.32 ! [X0 : (b > $o)] : ((bot_bot_set_b = ((collect_b @ X0))) = ! [X1 : b] : ~(X0 @ X1))),
% 0.21/0.32 inference(rectify,[],[f25])).
% 0.21/0.32 thf(f294,plain,(
% 0.21/0.32 ! [X0 : (b > $o)] : ((bot_bot_set_b = ((collect_b @ X0))) <=> ! [X1 : b] : ~ (((X0 @ X1)) = $true))),
% 0.21/0.32 inference(fool_elimination,[],[f293])).
% 0.21/0.32 thf(f323,plain,(
% 0.21/0.32 ! [X0 : (b > $o)] : ((bot_bot_set_b = ((collect_b @ X0))) <=> ! [X1 : b] : (((X0 @ X1)) != $true))),
% 0.21/0.32 inference(flattening,[],[f269])).
% 0.21/0.32 thf(f324,plain,(
% 0.21/0.32 ~ ! [X0 : a] : ((((q @ X0 @ (hilbert_Eps_b @ (q @ X0)))) = $true) | (((p @ X0)) != $true))),
% 0.21/0.32 inference(flattening,[],[f273])).
% 0.21/0.32 thf(f329,plain,(
% 0.21/0.32 ! [X0 : (b > $o)] : (! [X1 : b] : (((X0 @ X1)) != $true) <=> (bot_bot_set_b = ((collect_b @ X0))))),
% 0.21/0.32 inference(flattening,[],[f294])).
% 0.21/0.32 thf(f370,plain,(
% 0.21/0.32 ! [X0 : (b > $o),X1 : b] : ((((hilbert_Eps_b @ X0)) != X1) | (? [X2 : b] : (((X0 @ X2)) = $true) <=> (((X0 @ X1)) = $true)))),
% 0.21/0.32 inference(ennf_transformation,[],[f141])).
% 0.21/0.32 thf(f374,plain,(
% 0.21/0.32 ! [X0 : a] : ((((p @ X0)) != $true) | ? [X1 : b] : (((q @ X0 @ X1)) = $true))),
% 0.21/0.32 inference(ennf_transformation,[],[f204])).
% 0.21/0.32 thf(f375,plain,(
% 0.21/0.32 ? [X0 : a] : ((((q @ X0 @ (hilbert_Eps_b @ (q @ X0)))) != $true) & (((p @ X0)) = $true))),
% 0.21/0.32 inference(ennf_transformation,[],[f324])).
% 0.21/0.32 thf(f422,plain,(
% 0.21/0.32 ! [X0 : a] : ((((p @ X0)) != $true) | ($true = ((q @ X0 @ (sK4 @ X0)))))),
% 0.21/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK2 @ X0)],[f374])).
% 0.21/0.32 thf(f459,plain,(
% 0.21/0.32 ! [X0 : (b > $o)] : ((! [X1 : b] : (((X0 @ X1)) != $true) | (bot_bot_set_b != ((collect_b @ X0)))) & ((bot_bot_set_b = ((collect_b @ X0))) | ? [X1 : b] : (((X0 @ X1)) = $true)))),
% 0.21/0.32 inference(nnf_transformation,[],[f329])).
% 0.21/0.32 thf(f460,plain,(
% 0.21/0.32 ! [X0 : (b > $o)] : ((! [X1 : b] : (((X0 @ X1)) != $true) | (bot_bot_set_b != ((collect_b @ X0)))) & ((bot_bot_set_b = ((collect_b @ X0))) | ? [X2 : b] : (((X0 @ X2)) = $true)))),
% 0.21/0.32 inference(rectify,[],[f459])).
% 0.21/0.32 thf(f461,plain,(
% 0.21/0.32 ! [X0 : (b > $o)] : ((! [X1 : b] : (((X0 @ X1)) != $true) | (bot_bot_set_b != ((collect_b @ X0)))) & ((bot_bot_set_b = ((collect_b @ X0))) | (((X0 @ (sK15 @ X0))) = $true)))),
% 0.21/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK2 @ X0)],[f460])).
% 0.21/0.32 thf(f473,plain,(
% 0.21/0.32 ($true != ((q @ sK19 @ (hilbert_Eps_b @ (q @ sK19))))) & ($true = ((p @ sK19)))),
% 0.21/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X0,sK19)],[f375])).
% 0.21/0.32 thf(f496,plain,(
% 0.21/0.32 ! [X0 : (b > $o)] : (((bot_bot_set_b = ((collect_b @ X0))) | ? [X1 : b] : (((X0 @ X1)) = $true)) & (! [X1 : b] : (((X0 @ X1)) != $true) | (bot_bot_set_b != ((collect_b @ X0)))))),
% 0.21/0.32 inference(nnf_transformation,[],[f323])).
% 0.21/0.32 thf(f497,plain,(
% 0.21/0.32 ! [X0 : (b > $o)] : (((bot_bot_set_b = ((collect_b @ X0))) | ? [X1 : b] : (((X0 @ X1)) = $true)) & (! [X2 : b] : (((X0 @ X2)) != $true) | (bot_bot_set_b != ((collect_b @ X0)))))),
% 0.21/0.32 inference(rectify,[],[f496])).
% 0.21/0.32 thf(f498,plain,(
% 0.21/0.32 ! [X0 : (b > $o)] : (((bot_bot_set_b = ((collect_b @ X0))) | (((X0 @ (sK29 @ X0))) = $true)) & (! [X2 : b] : (((X0 @ X2)) != $true) | (bot_bot_set_b != ((collect_b @ X0)))))),
% 0.21/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK2 @ X0)],[f497])).
% 0.21/0.32 thf(f507,plain,(
% 0.21/0.32 ! [X0 : (b > $o),X1 : b] : ((((hilbert_Eps_b @ X0)) != X1) | ((? [X2 : b] : (((X0 @ X2)) = $true) | (((X0 @ X1)) != $true)) & ((((X0 @ X1)) = $true) | ! [X2 : b] : (((X0 @ X2)) != $true))))),
% 0.21/0.32 inference(nnf_transformation,[],[f370])).
% 0.21/0.32 thf(f508,plain,(
% 0.21/0.32 ! [X0 : (b > $o),X1 : b] : ((((hilbert_Eps_b @ X0)) != X1) | ((? [X2 : b] : (((X0 @ X2)) = $true) | (((X0 @ X1)) != $true)) & ((((X0 @ X1)) = $true) | ! [X3 : b] : (((X0 @ X3)) != $true))))),
% 0.21/0.32 inference(rectify,[],[f507])).
% 0.21/0.32 thf(f509,plain,(
% 0.21/0.32 ! [X0 : (b > $o),X1 : b] : ((((hilbert_Eps_b @ X0)) != X1) | (((((X0 @ (sK31 @ X0))) = $true) | (((X0 @ X1)) != $true)) & ((((X0 @ X1)) = $true) | ! [X3 : b] : (((X0 @ X3)) != $true))))),
% 0.21/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK2 @ X0)],[f508])).
% 0.21/0.32 thf(f541,plain,(
% 0.21/0.32 ( ! [X0 : a] : ((((p @ X0)) != $true) | ($true = ((q @ X0 @ (sK4 @ X0))))) )),
% 0.21/0.32 inference(cnf_transformation,[],[f422])).
% 0.21/0.32 thf(f601,plain,(
% 0.21/0.32 ( ! [X0 : (b > $o)] : ((((X0 @ (sK15 @ X0))) = $true) | (bot_bot_set_b = ((collect_b @ X0)))) )),
% 0.21/0.32 inference(cnf_transformation,[],[f461])).
% 0.21/0.32 thf(f623,plain,(
% 0.21/0.32 ($true = ((p @ sK19)))),
% 0.21/0.32 inference(cnf_transformation,[],[f473])).
% 0.21/0.32 thf(f624,plain,(
% 0.21/0.32 ($true != ((q @ sK19 @ (hilbert_Eps_b @ (q @ sK19)))))),
% 0.21/0.32 inference(cnf_transformation,[],[f473])).
% 0.21/0.32 thf(f657,plain,(
% 0.21/0.32 ( ! [X2 : b,X0 : (b > $o)] : ((bot_bot_set_b != ((collect_b @ X0))) | (((X0 @ X2)) != $true)) )),
% 0.21/0.32 inference(cnf_transformation,[],[f498])).
% 0.21/0.32 thf(f677,plain,(
% 0.21/0.32 ( ! [X3 : b,X0 : (b > $o),X1 : b] : ((((hilbert_Eps_b @ X0)) != X1) | (((X0 @ X1)) = $true) | (((X0 @ X3)) != $true)) )),
% 0.21/0.32 inference(cnf_transformation,[],[f509])).
% 0.21/0.32 thf(f834,plain,(
% 0.21/0.32 ( ! [X3 : b,X0 : (b > $o)] : ((((X0 @ X3)) != $true) | (((X0 @ (hilbert_Eps_b @ X0))) = $true)) )),
% 0.21/0.32 inference(equality_resolution,[],[f677])).
% 0.21/0.32 thf(f984,plain,(
% 0.21/0.32 ( ! [X0 : (b > $o)] : ((((X0 @ (hilbert_Eps_b @ X0))) = $true) | ($true != $true) | (bot_bot_set_b = ((collect_b @ X0)))) )),
% 0.21/0.32 inference(constrained_superposition,[],[f834,f601])).
% 0.21/0.32 thf(f990,plain,(
% 0.21/0.32 ( ! [X0 : (b > $o)] : ((((X0 @ (hilbert_Eps_b @ X0))) = $true) | (bot_bot_set_b = ((collect_b @ X0)))) )),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f984])).
% 0.21/0.32 thf(f1005,plain,(
% 0.21/0.32 ($true != $true) | (bot_bot_set_b = ((collect_b @ (q @ sK19))))),
% 0.21/0.32 inference(constrained_superposition,[],[f624,f990])).
% 0.21/0.32 thf(f1010,plain,(
% 0.21/0.32 (bot_bot_set_b = ((collect_b @ (q @ sK19))))),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f1005])).
% 0.21/0.32 thf(f1013,plain,(
% 0.21/0.32 ( ! [X0 : b] : ((bot_bot_set_b != bot_bot_set_b) | (((q @ sK19 @ X0)) != $true)) )),
% 0.21/0.32 inference(constrained_superposition,[],[f657,f1010])).
% 0.21/0.32 thf(f1014,plain,(
% 0.21/0.32 ( ! [X0 : b] : ((((q @ sK19 @ X0)) != $true)) )),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f1013])).
% 0.21/0.32 thf(f1028,plain,(
% 0.21/0.32 ($true = ((q @ sK19 @ (sK4 @ sK19)))) | ($true != $true)),
% 0.21/0.32 inference(constrained_superposition,[],[f541,f623])).
% 0.21/0.32 thf(f1029,plain,(
% 0.21/0.32 ($true = ((q @ sK19 @ (sK4 @ sK19))))),
% 0.21/0.32 inference(trivial_inequality_removal,[],[f1028])).
% 0.21/0.32 thf(f1030,plain,(
% 0.21/0.32 $false),
% 0.21/0.32 inference(forward_subsumption_resolution,[],[f1029,f1014])).
% 0.21/0.32 % SZS output end Proof for theBenchmark
% 0.21/0.32 % (4043885)------------------------------
% 0.21/0.32 % (4043885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (4043885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (4043885)CaDiCaL version: 2.1.3
% 0.21/0.32 % (4043885)Termination reason: Refutation
% 0.21/0.32 % (4043885)Time elapsed: 0.018 s
% 0.21/0.32 % (4043885)Peak memory usage: 13 MB
% 0.21/0.32 % (4043885)Instructions burned: 69 (million)
% 0.21/0.32 % (4043880)Success in time 0.045 s
% 0.21/0.32 % Vampire exiting
%------------------------------------------------------------------------------