%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU712^2 : 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 08:30:54 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU712^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n013.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 14:13:06 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.23 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
% 0.20/0.29 % (2181087)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (2181093)lrs+10_16_si=on:nwc=1.5:random_seed=949766382:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (2181093)Instruction limit reached!
% 0.20/0.29 % (2181093)------------------------------
% 0.20/0.29 % (2181093)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2181093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2181093)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2181093)Termination reason: Instruction limit
% 0.20/0.29 % (2181093)Termination phase: Saturation
% 0.20/0.29 % (2181093)Time elapsed: 0.006 s
% 0.20/0.29 % (2181093)Peak memory usage: 12 MB
% 0.20/0.29 % (2181093)Instructions burned: 19 (million)
% 0.20/0.29 % (2181098)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (2181098)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
% 0.20/0.29 % (2181092)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2874491450:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (2181094)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=660519159:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (2181095)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=2721793018: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)
% 0.20/0.29 % (2181094)Refutation not found, incomplete strategy
% 0.20/0.29 % (2181094)------------------------------
% 0.20/0.29 % (2181094)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2181094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2181094)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2181094)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.29 % (2181094)Time elapsed: 0.002 s
% 0.20/0.29 % (2181094)Peak memory usage: 12 MB
% 0.20/0.29 % (2181094)Instructions burned: 2 (million)
% 0.20/0.29 % (2181094)------------------------------
% 0.20/0.29 % (2181094)------------------------------
% 0.20/0.29 % (2181098)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=3956461235:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.29 % (2181092) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2181087-2181092"...
% 0.20/0.29 % (2181095) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2181087-2181095"...
% 0.20/0.29 % (2181092)...printing done.
% 0.20/0.29 % (2181092)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% 0.20/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.29 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.20/0.29 thf(func_def_1, type, powerset: ($i > $i)).
% 0.20/0.29 thf(func_def_2, type, powersetI: $o).
% 0.20/0.29 thf(func_def_4, type, powersetE: $o).
% 0.20/0.29 thf(func_def_7, type, sK0: ($i > $i > $i)).
% 0.20/0.29 thf(func_def_15, type, vNOT: ($o > $o)).
% 0.20/0.29 thf(f1,axiom,(
% 0.20/0.29 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))) = powersetI)),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI)).
% 0.20/0.29 thf(f2,axiom,(
% 0.20/0.29 (! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))) = powersetE)),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE)).
% 0.20/0.29 thf(f3,conjecture,(
% 0.20/0.29 powersetI => (powersetE => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (powerset @ X1) @ (powerset @ (powerset @ X0)))))),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetT_lem)).
% 0.20/0.29 thf(f4,negated_conjecture,(
% 0.20/0.29 ~(powersetI => (powersetE => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (powerset @ X1) @ (powerset @ (powerset @ X0))))))),
% 0.20/0.29 inference(negated_conjecture,[status(cth)],[f3])).
% 0.20/0.29 thf(f5,plain,(
% 0.20/0.29 ~(powersetI => (powersetE => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (powerset @ X1) @ (powerset @ (powerset @ X0))))))),
% 0.20/0.29 inference(rectify,[],[f4])).
% 0.20/0.29 thf(f6,plain,(
% 0.20/0.29 ~((powersetI = $true) => ((powersetE = $true) => ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => (((in @ (powerset @ X1) @ (powerset @ (powerset @ X0)))) = $true))))),
% 0.20/0.29 inference(fool_elimination,[],[f5])).
% 0.20/0.29 thf(f7,plain,(
% 0.20/0.29 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((in @ X1 @ X2) => (in @ X1 @ X0))) = powersetE)),
% 0.20/0.29 inference(rectify,[],[f2])).
% 0.20/0.29 thf(f8,plain,(
% 0.20/0.29 ! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) => (($true = ((in @ X1 @ X2))) => ($true = ((in @ X1 @ X0))))) <=> (powersetE = $true)),
% 0.20/0.29 inference(fool_elimination,[],[f7])).
% 0.20/0.29 thf(f9,plain,(
% 0.20/0.29 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (in @ X0 @ (powerset @ X1))) = powersetI)),
% 0.20/0.29 inference(rectify,[],[f1])).
% 0.20/0.29 thf(f10,plain,(
% 0.20/0.29 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => ($true = ((in @ X0 @ (powerset @ X1))))) <=> (powersetI = $true)),
% 0.20/0.29 inference(fool_elimination,[],[f9])).
% 0.20/0.29 thf(f11,plain,(
% 0.20/0.29 (? [X0 : $i,X1 : $i] : ((((in @ (powerset @ X1) @ (powerset @ (powerset @ X0)))) != $true) & (((in @ X1 @ (powerset @ X0))) = $true)) & (powersetE = $true)) & (powersetI = $true)),
% 0.20/0.29 inference(ennf_transformation,[],[f6])).
% 0.20/0.29 thf(f12,plain,(
% 0.20/0.29 (powersetI = $true) & ? [X0 : $i,X1 : $i] : ((((in @ (powerset @ X1) @ (powerset @ (powerset @ X0)))) != $true) & (((in @ X1 @ (powerset @ X0))) = $true)) & (powersetE = $true)),
% 0.20/0.29 inference(flattening,[],[f11])).
% 0.20/0.29 thf(f13,plain,(
% 0.20/0.29 ! [X1 : $i,X0 : $i,X2 : $i] : ((($true = ((in @ X1 @ X0))) | ($true != ((in @ X1 @ X2)))) | (((in @ X2 @ (powerset @ X0))) != $true)) <=> (powersetE = $true)),
% 0.20/0.29 inference(ennf_transformation,[],[f8])).
% 0.20/0.29 thf(f14,plain,(
% 0.20/0.29 (powersetE = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (($true != ((in @ X1 @ X2))) | ($true = ((in @ X1 @ X0))) | (((in @ X2 @ (powerset @ X0))) != $true))),
% 0.20/0.29 inference(flattening,[],[f13])).
% 0.20/0.29 thf(f15,plain,(
% 0.20/0.29 ! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) | ? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true))) <=> (powersetI = $true)),
% 0.20/0.29 inference(ennf_transformation,[],[f10])).
% 0.20/0.29 thf(f16,plain,(
% 0.20/0.29 (! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) | ? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true))) | (powersetI != $true)) & ((powersetI = $true) | ? [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) & ! [X2 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ X1)) = $true))))),
% 0.20/0.29 inference(nnf_transformation,[],[f15])).
% 0.20/0.29 thf(f17,plain,(
% 0.20/0.29 (! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) | ? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true))) | (powersetI != $true)) & ((powersetI = $true) | ? [X3 : $i,X4 : $i] : (($true != ((in @ X3 @ (powerset @ X4)))) & ! [X5 : $i] : (($true != ((in @ X5 @ X3))) | (((in @ X5 @ X4)) = $true))))),
% 0.20/0.29 inference(rectify,[],[f16])).
% 0.20/0.29 thf(f18,plain,(
% 0.20/0.29 (! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) | ((((in @ (sK0 @ X1 @ X0) @ X0)) = $true) & ($true != ((in @ (sK0 @ X1 @ X0) @ X1))))) | (powersetI != $true)) & ((powersetI = $true) | (($true != ((in @ sK1 @ (powerset @ sK2)))) & ! [X5 : $i] : (($true != ((in @ X5 @ sK1))) | ($true = ((in @ X5 @ sK2))))))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1,sK2]),skolemize(X2,sK0 @ X1 @ X0),skolemize(X3,sK1),skolemize(X4,sK2)],[f17])).
% 0.20/0.29 thf(f19,plain,(
% 0.20/0.29 (powersetI = $true) & (($true != ((in @ (powerset @ sK4) @ (powerset @ (powerset @ sK3))))) & ($true = ((in @ sK4 @ (powerset @ sK3))))) & (powersetE = $true)),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f12])).
% 0.20/0.29 thf(f20,plain,(
% 0.20/0.29 ((powersetE = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : (($true = ((in @ X1 @ X2))) & ($true != ((in @ X1 @ X0))) & (((in @ X2 @ (powerset @ X0))) = $true))) & (! [X0 : $i,X2 : $i,X1 : $i] : (($true != ((in @ X1 @ X2))) | ($true = ((in @ X1 @ X0))) | (((in @ X2 @ (powerset @ X0))) != $true)) | (powersetE != $true))),
% 0.20/0.29 inference(nnf_transformation,[],[f14])).
% 0.20/0.29 thf(f21,plain,(
% 0.20/0.29 ((powersetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true) & (((in @ X1 @ (powerset @ X0))) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ X4)) != $true) | ($true = ((in @ X5 @ X3))) | ($true != ((in @ X4 @ (powerset @ X3))))) | (powersetE != $true))),
% 0.20/0.29 inference(rectify,[],[f20])).
% 0.20/0.29 thf(f22,plain,(
% 0.20/0.29 ((powersetE = $true) | (($true = ((in @ sK7 @ sK6))) & (((in @ sK7 @ sK5)) != $true) & (((in @ sK6 @ (powerset @ sK5))) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ X4)) != $true) | ($true = ((in @ X5 @ X3))) | ($true != ((in @ X4 @ (powerset @ X3))))) | (powersetE != $true))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f21])).
% 0.20/0.29 thf(f25,plain,(
% 0.20/0.29 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) | ($true != ((in @ (sK0 @ X1 @ X0) @ X1))) | (powersetI != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f18])).
% 0.20/0.29 thf(f26,plain,(
% 0.20/0.29 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) | (((in @ (sK0 @ X1 @ X0) @ X0)) = $true) | (powersetI != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f18])).
% 0.20/0.29 thf(f27,plain,(
% 0.20/0.29 (powersetE = $true)),
% 0.20/0.29 inference(cnf_transformation,[],[f19])).
% 0.20/0.29 thf(f28,plain,(
% 0.20/0.29 ($true = ((in @ sK4 @ (powerset @ sK3))))),
% 0.20/0.29 inference(cnf_transformation,[],[f19])).
% 0.20/0.29 thf(f29,plain,(
% 0.20/0.29 ($true != ((in @ (powerset @ sK4) @ (powerset @ (powerset @ sK3)))))),
% 0.20/0.29 inference(cnf_transformation,[],[f19])).
% 0.20/0.29 thf(f30,plain,(
% 0.20/0.29 (powersetI = $true)),
% 0.20/0.29 inference(cnf_transformation,[],[f19])).
% 0.20/0.29 thf(f31,plain,(
% 0.20/0.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ X4)) != $true) | ($true = ((in @ X5 @ X3))) | ($true != ((in @ X4 @ (powerset @ X3)))) | (powersetE != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f22])).
% 0.20/0.29 thf(f37,plain,(
% 0.20/0.29 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK0 @ X1 @ X0) @ X0)) = $true) | ($true != $true) | ($true = ((in @ X0 @ (powerset @ X1))))) )),
% 0.20/0.29 inference(definition_unfolding,[],[f26,f30])).
% 0.20/0.29 thf(f38,plain,(
% 0.20/0.29 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) | ($true != ((in @ (sK0 @ X1 @ X0) @ X1))) | ($true != $true)) )),
% 0.20/0.29 inference(definition_unfolding,[],[f25,f30])).
% 0.20/0.29 thf(f44,plain,(
% 0.20/0.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X5 @ X3))) | ($true != ((in @ X4 @ (powerset @ X3)))) | (((in @ X5 @ X4)) != $true) | ($true != $true)) )),
% 0.20/0.29 inference(definition_unfolding,[],[f31,f27])).
% 0.20/0.29 thf(f45,plain,(
% 0.20/0.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X4 @ (powerset @ X3)))) | ($true = ((in @ X5 @ X3))) | (((in @ X5 @ X4)) != $true)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f44])).
% 0.20/0.29 thf(f46,plain,(
% 0.20/0.29 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK0 @ X1 @ X0) @ X0)) = $true) | ($true = ((in @ X0 @ (powerset @ X1))))) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f37])).
% 0.20/0.29 thf(f47,plain,(
% 0.20/0.29 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK0 @ X1 @ X0) @ X1))) | ($true = ((in @ X0 @ (powerset @ X1))))) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f38])).
% 0.20/0.29 thf(f51,plain,(
% 0.20/0.29 ( ! [X0 : $i] : (($true != $true) | ($true != ((in @ X0 @ sK4))) | ($true = ((in @ X0 @ sK3)))) )),
% 0.20/0.29 inference(constrained_superposition,[],[f45,f28])).
% 0.20/0.29 thf(f52,plain,(
% 0.20/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != ((in @ X2 @ (sK0 @ X0 @ (powerset @ X1))))) | ($true = ((in @ (powerset @ X1) @ (powerset @ X0)))) | (((in @ X2 @ X1)) = $true)) )),
% 0.20/0.29 inference(constrained_superposition,[],[f45,f46])).
% 0.20/0.29 thf(f54,plain,(
% 0.20/0.29 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK4))) | ($true = ((in @ X0 @ sK3)))) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f51])).
% 0.20/0.29 thf(f55,plain,(
% 0.20/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X2 @ (sK0 @ X0 @ (powerset @ X1))))) | (((in @ X2 @ X1)) = $true) | ($true = ((in @ (powerset @ X1) @ (powerset @ X0))))) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f52])).
% 0.20/0.29 thf(f61,plain,(
% 0.20/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (powerset @ X2) @ (powerset @ X1))) = $true) | ($true != $true) | (((in @ (sK0 @ X1 @ (powerset @ X2)) @ (powerset @ X0))) = $true) | (((in @ (sK0 @ X0 @ (sK0 @ X1 @ (powerset @ X2))) @ X2)) = $true)) )),
% 0.20/0.29 inference(constrained_superposition,[],[f55,f46])).
% 0.20/0.29 thf(f62,plain,(
% 0.20/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK0 @ X0 @ (sK0 @ X1 @ (powerset @ X2))) @ X2)) = $true) | (((in @ (powerset @ X2) @ (powerset @ X1))) = $true) | (((in @ (sK0 @ X1 @ (powerset @ X2)) @ (powerset @ X0))) = $true)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f61])).
% 0.20/0.29 thf(f66,plain,(
% 0.20/0.29 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK0 @ X0 @ (sK0 @ X1 @ (powerset @ sK4))) @ sK3))) | ($true = ((in @ (sK0 @ X1 @ (powerset @ sK4)) @ (powerset @ X0)))) | ($true != $true) | (((in @ (powerset @ sK4) @ (powerset @ X1))) = $true)) )),
% 0.20/0.29 inference(constrained_superposition,[],[f54,f62])).
% 0.20/0.29 thf(f67,plain,(
% 0.20/0.29 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK0 @ X0 @ (sK0 @ X1 @ (powerset @ sK4))) @ sK3))) | (((in @ (powerset @ sK4) @ (powerset @ X1))) = $true) | ($true = ((in @ (sK0 @ X1 @ (powerset @ sK4)) @ (powerset @ X0))))) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f66])).
% 0.20/0.29 thf(f72,plain,(
% 0.20/0.29 ( ! [X0 : $i] : (($true != $true) | ($true = ((in @ (sK0 @ X0 @ (powerset @ sK4)) @ (powerset @ sK3)))) | ($true = ((in @ (sK0 @ X0 @ (powerset @ sK4)) @ (powerset @ sK3)))) | (((in @ (powerset @ sK4) @ (powerset @ X0))) = $true)) )),
% 0.20/0.29 inference(constrained_superposition,[],[f47,f67])).
% 0.20/0.29 thf(f73,plain,(
% 0.20/0.29 ( ! [X0 : $i] : ((((in @ (powerset @ sK4) @ (powerset @ X0))) = $true) | ($true = ((in @ (sK0 @ X0 @ (powerset @ sK4)) @ (powerset @ sK3)))) | ($true != $true)) )),
% 0.20/0.29 inference(duplicate_literal_removal,[],[f72])).
% 0.20/0.29 thf(f74,plain,(
% 0.20/0.29 ( ! [X0 : $i] : (($true = ((in @ (sK0 @ X0 @ (powerset @ sK4)) @ (powerset @ sK3)))) | (((in @ (powerset @ sK4) @ (powerset @ X0))) = $true)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f73])).
% 0.20/0.29 thf(f75,plain,(
% 0.20/0.29 ($true = ((in @ (powerset @ sK4) @ (powerset @ (powerset @ sK3))))) | ($true != $true) | ($true = ((in @ (powerset @ sK4) @ (powerset @ (powerset @ sK3)))))),
% 0.20/0.29 inference(constrained_superposition,[],[f47,f74])).
% 0.20/0.29 thf(f77,plain,(
% 0.20/0.29 ($true = ((in @ (powerset @ sK4) @ (powerset @ (powerset @ sK3))))) | ($true != $true)),
% 0.20/0.29 inference(duplicate_literal_removal,[],[f75])).
% 0.20/0.29 thf(f78,plain,(
% 0.20/0.29 ($true = ((in @ (powerset @ sK4) @ (powerset @ (powerset @ sK3)))))),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f77])).
% 0.20/0.29 thf(f80,plain,(
% 0.20/0.29 $false),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f78,f29])).
% 0.20/0.29 % SZS output end Proof for theBenchmark
% 0.20/0.29 % (2181092)------------------------------
% 0.20/0.29 % (2181092)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2181092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2181092)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2181092)Termination reason: Refutation
% 0.20/0.29 % (2181092)Time elapsed: 0.006 s
% 0.20/0.29 % (2181092)Peak memory usage: 12 MB
% 0.20/0.29 % (2181092)Instructions burned: 9 (million)
% 0.20/0.29 % (2181087)Success in time 0.05 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------