%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU715^2 : 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 : n026.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 08:30:55 AM UTC 2026
% Result : Theorem 0.20s 0.31s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU715^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n026.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 14:16:42 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.20/0.31 % (665208)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.31 % (665229)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=3790264696: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)
% 0.20/0.31 % (665232)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.31 % (665232)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
% 0.20/0.31 % (665227)lrs+10_16_si=on:nwc=1.5:random_seed=2714720464:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.31 % (665226)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=250052648:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.31 % (665230)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2456104523:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.31 % (665231)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1053337724:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.31 % (665228)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2978582609:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.31 % (665232)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=1725820649:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.31 % (665228)Instruction limit reached!
% 0.20/0.31 % (665228)------------------------------
% 0.20/0.31 % (665228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (665228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (665228)CaDiCaL version: 2.1.3
% 0.20/0.31 % (665228)Termination reason: Instruction limit
% 0.20/0.31 % (665228)Time elapsed: 0.002 s
% 0.20/0.31 % (665228)Peak memory usage: 12 MB
% 0.20/0.31 % (665228)Instructions burned: 3 (million)
% 0.20/0.31 % (665226) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-665208-665226"...
% 0.20/0.31 % (665230) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-665208-665230"...
% 0.20/0.31 % (665231) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-665208-665231"...
% 0.20/0.31 % (665226)...printing done.
% 0.20/0.31 % (665226)Refutation found. Thanks to Tanya!
% 0.20/0.31 % SZS status Theorem for theBenchmark
% 0.20/0.31 % SZS output start Proof for theBenchmark
% 0.20/0.31 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.31 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.20/0.31 thf(func_def_1, type, powerset: ($i > $i)).
% 0.20/0.31 thf(func_def_2, type, setext: $o).
% 0.20/0.31 thf(func_def_4, type, powersetE: $o).
% 0.20/0.31 thf(func_def_10, type, sK3: ($i > $i > $i)).
% 0.20/0.31 thf(func_def_11, type, sK4: ($i > $i > $i)).
% 0.20/0.31 thf(func_def_17, type, vNOT: ($o > $o)).
% 0.20/0.31 thf(f1,axiom,(
% 0.20/0.31 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (X0 = X1))) = setext)),
% 0.20/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext)).
% 0.20/0.31 thf(f2,axiom,(
% 0.20/0.31 (powersetE = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))))),
% 0.20/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE)).
% 0.20/0.31 thf(f3,conjecture,(
% 0.20/0.31 setext => (powersetE => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X2) => (in @ X3 @ X1))) => (X1 = X2))))))),
% 0.20/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextT)).
% 0.20/0.31 thf(f4,negated_conjecture,(
% 0.20/0.31 ~(setext => (powersetE => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X2) => (in @ X3 @ X1))) => (X1 = X2)))))))),
% 0.20/0.31 inference(negated_conjecture,[status(cth)],[f3])).
% 0.20/0.31 thf(f5,plain,(
% 0.20/0.31 (powersetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (powerset @ X2)) => ((in @ X1 @ X0) => (in @ X1 @ X2))))),
% 0.20/0.31 inference(rectify,[],[f2])).
% 0.20/0.31 thf(f6,plain,(
% 0.20/0.31 (powersetE = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X2)))) => ((((in @ X1 @ X0)) = $true) => ($true = ((in @ X1 @ X2)))))),
% 0.20/0.31 inference(fool_elimination,[],[f5])).
% 0.20/0.31 thf(f7,plain,(
% 0.20/0.31 ~(setext => (powersetE => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ X0) => (in @ X3 @ X2))) => (! [X4 : $i] : ((in @ X4 @ X1) => ((in @ X4 @ X2) => (in @ X4 @ X0))) => (X0 = X2)))))))),
% 0.20/0.31 inference(rectify,[],[f4])).
% 0.20/0.31 thf(f8,plain,(
% 0.20/0.31 ~((setext = $true) => ((powersetE = $true) => ! [X1 : $i,X0 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) => ! [X2 : $i] : (($true = ((in @ X2 @ (powerset @ X1)))) => (! [X3 : $i] : ((((in @ X3 @ X1)) = $true) => ((((in @ X3 @ X0)) = $true) => (((in @ X3 @ X2)) = $true))) => (! [X4 : $i] : (($true = ((in @ X4 @ X1))) => (($true = ((in @ X4 @ X2))) => (((in @ X4 @ X0)) = $true))) => (X0 = X2)))))))),
% 0.20/0.31 inference(fool_elimination,[],[f7])).
% 0.20/0.31 thf(f9,plain,(
% 0.20/0.31 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => (in @ X3 @ X1)) => (X0 = X1))) = setext)),
% 0.20/0.31 inference(rectify,[],[f1])).
% 0.20/0.31 thf(f10,plain,(
% 0.20/0.31 (setext = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => (! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => (((in @ X3 @ X1)) = $true)) => (X0 = X1)))),
% 0.20/0.31 inference(fool_elimination,[],[f9])).
% 0.20/0.31 thf(f11,plain,(
% 0.20/0.31 (powersetE = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((($true = ((in @ X1 @ X2))) | (((in @ X1 @ X0)) != $true)) | ($true != ((in @ X0 @ (powerset @ X2)))))),
% 0.20/0.31 inference(ennf_transformation,[],[f6])).
% 0.20/0.31 thf(f12,plain,(
% 0.20/0.31 (powersetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) != $true) | ($true = ((in @ X1 @ X2))) | ($true != ((in @ X0 @ (powerset @ X2)))))),
% 0.20/0.31 inference(flattening,[],[f11])).
% 0.20/0.31 thf(f13,plain,(
% 0.20/0.31 (? [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((X0 != X2) & ! [X4 : $i] : (((((in @ X4 @ X0)) = $true) | ($true != ((in @ X4 @ X2)))) | ($true != ((in @ X4 @ X1))))) & ! [X3 : $i] : (((((in @ X3 @ X2)) = $true) | (((in @ X3 @ X0)) != $true)) | (((in @ X3 @ X1)) != $true))) & ($true = ((in @ X2 @ (powerset @ X1))))) & (((in @ X0 @ (powerset @ X1))) = $true)) & (powersetE = $true)) & (setext = $true)),
% 0.20/0.31 inference(ennf_transformation,[],[f8])).
% 0.20/0.31 thf(f14,plain,(
% 0.20/0.31 ? [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) & ? [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X2)) = $true) | (((in @ X3 @ X0)) != $true) | (((in @ X3 @ X1)) != $true)) & (X0 != X2) & ($true = ((in @ X2 @ (powerset @ X1)))) & ! [X4 : $i] : (($true != ((in @ X4 @ X1))) | ($true != ((in @ X4 @ X2))) | (((in @ X4 @ X0)) = $true)))) & (powersetE = $true) & (setext = $true)),
% 0.20/0.31 inference(flattening,[],[f13])).
% 0.20/0.31 thf(f15,plain,(
% 0.20/0.31 (setext = $true) <=> ! [X0 : $i,X1 : $i] : (((X0 = X1) | ? [X3 : $i] : ((((in @ X3 @ X1)) != $true) & (((in @ X3 @ X0)) = $true))) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)))),
% 0.20/0.31 inference(ennf_transformation,[],[f10])).
% 0.20/0.31 thf(f16,plain,(
% 0.20/0.31 ! [X1 : $i,X0 : $i] : ((X0 = X1) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | ? [X3 : $i] : ((((in @ X3 @ X1)) != $true) & (((in @ X3 @ X0)) = $true))) <=> (setext = $true)),
% 0.20/0.31 inference(flattening,[],[f15])).
% 0.20/0.31 thf(f17,plain,(
% 0.20/0.31 (($true = ((in @ sK0 @ (powerset @ sK1)))) & (! [X3 : $i] : ((((in @ X3 @ sK2)) = $true) | ($true != ((in @ X3 @ sK0))) | ($true != ((in @ X3 @ sK1)))) & (sK2 != sK0) & (((in @ sK2 @ (powerset @ sK1))) = $true) & ! [X4 : $i] : (($true != ((in @ X4 @ sK1))) | ($true != ((in @ X4 @ sK2))) | ($true = ((in @ X4 @ sK0)))))) & (powersetE = $true) & (setext = $true)),
% 0.20/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f14])).
% 0.20/0.31 thf(f18,plain,(
% 0.20/0.31 (! [X1 : $i,X0 : $i] : ((X0 = X1) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | ? [X3 : $i] : ((((in @ X3 @ X1)) != $true) & (((in @ X3 @ X0)) = $true))) | (setext != $true)) & ((setext = $true) | ? [X1 : $i,X0 : $i] : ((X0 != X1) & ! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) & ! [X3 : $i] : ((((in @ X3 @ X1)) = $true) | (((in @ X3 @ X0)) != $true))))),
% 0.20/0.31 inference(nnf_transformation,[],[f16])).
% 0.20/0.31 thf(f19,plain,(
% 0.20/0.31 (! [X0 : $i,X1 : $i] : ((X0 = X1) | ? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | ? [X3 : $i] : ((((in @ X3 @ X0)) != $true) & (((in @ X3 @ X1)) = $true))) | (setext != $true)) & ((setext = $true) | ? [X4 : $i,X5 : $i] : ((X4 != X5) & ! [X6 : $i] : (($true = ((in @ X6 @ X5))) | ($true != ((in @ X6 @ X4)))) & ! [X7 : $i] : (($true = ((in @ X7 @ X4))) | ($true != ((in @ X7 @ X5))))))),
% 0.20/0.31 inference(rectify,[],[f18])).
% 0.20/0.31 thf(f20,plain,(
% 0.20/0.31 (! [X0 : $i,X1 : $i] : ((X0 = X1) | (($true != ((in @ (sK3 @ X1 @ X0) @ X1))) & ($true = ((in @ (sK3 @ X1 @ X0) @ X0)))) | (($true != ((in @ (sK4 @ X1 @ X0) @ X0))) & (((in @ (sK4 @ X1 @ X0) @ X1)) = $true))) | (setext != $true)) & ((setext = $true) | ((sK5 != sK6) & ! [X6 : $i] : ((((in @ X6 @ sK6)) = $true) | ($true != ((in @ X6 @ sK5)))) & ! [X7 : $i] : ((((in @ X7 @ sK5)) = $true) | (((in @ X7 @ sK6)) != $true))))),
% 0.20/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,sK5,sK6]),skolemize(X3,sK4 @ X1 @ X0),skolemize(X3,sK4 @ X1 @ X0),skolemize(X4,sK5),skolemize(X5,sK6)],[f19])).
% 0.20/0.31 thf(f21,plain,(
% 0.20/0.31 ((powersetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) = $true) & ($true != ((in @ X1 @ X2))) & ($true = ((in @ X0 @ (powerset @ X2)))))) & (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) != $true) | ($true = ((in @ X1 @ X2))) | ($true != ((in @ X0 @ (powerset @ X2))))) | (powersetE != $true))),
% 0.20/0.31 inference(nnf_transformation,[],[f12])).
% 0.20/0.31 thf(f22,plain,(
% 0.20/0.31 ((powersetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) = $true) & ($true != ((in @ X1 @ X2))) & ($true = ((in @ X0 @ (powerset @ X2)))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X4 @ X3))) | ($true = ((in @ X4 @ X5))) | (((in @ X3 @ (powerset @ X5))) != $true)) | (powersetE != $true))),
% 0.20/0.31 inference(rectify,[],[f21])).
% 0.20/0.31 thf(f23,plain,(
% 0.20/0.31 ((powersetE = $true) | (($true = ((in @ sK8 @ sK7))) & ($true != ((in @ sK8 @ sK9))) & (((in @ sK7 @ (powerset @ sK9))) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X4 @ X3))) | ($true = ((in @ X4 @ X5))) | (((in @ X3 @ (powerset @ X5))) != $true)) | (powersetE != $true))),
% 0.20/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9)],[f22])).
% 0.20/0.31 thf(f24,plain,(
% 0.20/0.31 (setext = $true)),
% 0.20/0.31 inference(cnf_transformation,[],[f17])).
% 0.20/0.31 thf(f25,plain,(
% 0.20/0.31 (powersetE = $true)),
% 0.20/0.31 inference(cnf_transformation,[],[f17])).
% 0.20/0.31 thf(f26,plain,(
% 0.20/0.31 ( ! [X4 : $i] : (($true != ((in @ X4 @ sK2))) | ($true = ((in @ X4 @ sK0))) | ($true != ((in @ X4 @ sK1)))) )),
% 0.20/0.31 inference(cnf_transformation,[],[f17])).
% 0.20/0.31 thf(f27,plain,(
% 0.20/0.31 (((in @ sK2 @ (powerset @ sK1))) = $true)),
% 0.20/0.31 inference(cnf_transformation,[],[f17])).
% 0.20/0.31 thf(f28,plain,(
% 0.20/0.31 (sK2 != sK0)),
% 0.20/0.31 inference(cnf_transformation,[],[f17])).
% 0.20/0.31 thf(f29,plain,(
% 0.20/0.31 ( ! [X3 : $i] : (($true != ((in @ X3 @ sK1))) | (((in @ X3 @ sK2)) = $true) | ($true != ((in @ X3 @ sK0)))) )),
% 0.20/0.31 inference(cnf_transformation,[],[f17])).
% 0.20/0.31 thf(f30,plain,(
% 0.20/0.31 ($true = ((in @ sK0 @ (powerset @ sK1))))),
% 0.20/0.31 inference(cnf_transformation,[],[f17])).
% 0.20/0.31 thf(f34,plain,(
% 0.20/0.31 ( ! [X0 : $i,X1 : $i] : ((X0 = X1) | ($true = ((in @ (sK3 @ X1 @ X0) @ X0))) | (((in @ (sK4 @ X1 @ X0) @ X1)) = $true) | (setext != $true)) )),
% 0.20/0.31 inference(cnf_transformation,[],[f20])).
% 0.20/0.31 thf(f35,plain,(
% 0.20/0.31 ( ! [X0 : $i,X1 : $i] : ((X0 = X1) | ($true = ((in @ (sK3 @ X1 @ X0) @ X0))) | ($true != ((in @ (sK4 @ X1 @ X0) @ X0))) | (setext != $true)) )),
% 0.20/0.31 inference(cnf_transformation,[],[f20])).
% 0.20/0.31 thf(f36,plain,(
% 0.20/0.31 ( ! [X0 : $i,X1 : $i] : ((X0 = X1) | ($true != ((in @ (sK3 @ X1 @ X0) @ X1))) | (((in @ (sK4 @ X1 @ X0) @ X1)) = $true) | (setext != $true)) )),
% 0.20/0.31 inference(cnf_transformation,[],[f20])).
% 0.20/0.31 thf(f37,plain,(
% 0.20/0.31 ( ! [X0 : $i,X1 : $i] : ((X0 = X1) | ($true != ((in @ (sK3 @ X1 @ X0) @ X1))) | ($true != ((in @ (sK4 @ X1 @ X0) @ X0))) | (setext != $true)) )),
% 0.20/0.31 inference(cnf_transformation,[],[f20])).
% 0.20/0.31 thf(f38,plain,(
% 0.20/0.31 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X4 @ X3))) | ($true = ((in @ X4 @ X5))) | (((in @ X3 @ (powerset @ X5))) != $true) | (powersetE != $true)) )),
% 0.20/0.31 inference(cnf_transformation,[],[f23])).
% 0.20/0.31 thf(f44,plain,(
% 0.20/0.31 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK3 @ X1 @ X0) @ X1))) | ($true != ((in @ (sK4 @ X1 @ X0) @ X0))) | (X0 = X1) | ($true != $true)) )),
% 0.20/0.31 inference(definition_unfolding,[],[f37,f24])).
% 0.20/0.31 thf(f45,plain,(
% 0.20/0.31 ( ! [X0 : $i,X1 : $i] : ((X0 = X1) | (((in @ (sK4 @ X1 @ X0) @ X1)) = $true) | ($true != ((in @ (sK3 @ X1 @ X0) @ X1))) | ($true != $true)) )),
% 0.20/0.31 inference(definition_unfolding,[],[f36,f24])).
% 0.20/0.31 thf(f46,plain,(
% 0.20/0.31 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK4 @ X1 @ X0) @ X0))) | (X0 = X1) | ($true != $true) | ($true = ((in @ (sK3 @ X1 @ X0) @ X0)))) )),
% 0.20/0.31 inference(definition_unfolding,[],[f35,f24])).
% 0.20/0.31 thf(f47,plain,(
% 0.20/0.31 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK3 @ X1 @ X0) @ X0))) | (((in @ (sK4 @ X1 @ X0) @ X1)) = $true) | (X0 = X1) | ($true != $true)) )),
% 0.20/0.31 inference(definition_unfolding,[],[f34,f24])).
% 0.20/0.31 thf(f54,plain,(
% 0.20/0.31 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ($true = ((in @ X4 @ X5))) | ($true != ((in @ X4 @ X3))) | (((in @ X3 @ (powerset @ X5))) != $true)) )),
% 0.20/0.31 inference(definition_unfolding,[],[f38,f25])).
% 0.20/0.31 thf(f55,plain,(
% 0.20/0.31 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK4 @ X1 @ X0) @ X0))) | ($true = ((in @ (sK3 @ X1 @ X0) @ X0))) | (X0 = X1)) )),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f46])).
% 0.20/0.31 thf(f56,plain,(
% 0.20/0.31 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK3 @ X1 @ X0) @ X0))) | (((in @ (sK4 @ X1 @ X0) @ X1)) = $true) | (X0 = X1)) )),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f47])).
% 0.20/0.31 thf(f57,plain,(
% 0.20/0.31 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK3 @ X1 @ X0) @ X1))) | (((in @ (sK4 @ X1 @ X0) @ X1)) = $true) | (X0 = X1)) )),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f45])).
% 0.20/0.31 thf(f58,plain,(
% 0.20/0.31 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X3 @ (powerset @ X5))) != $true) | ($true = ((in @ X4 @ X5))) | ($true != ((in @ X4 @ X3)))) )),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f54])).
% 0.20/0.31 thf(f59,plain,(
% 0.20/0.31 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK4 @ X1 @ X0) @ X0))) | (X0 = X1) | ($true != ((in @ (sK3 @ X1 @ X0) @ X1)))) )),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f44])).
% 0.20/0.31 thf(f60,plain,(
% 0.20/0.31 ( ! [X0 : $i] : (($true != $true) | ($true != ((in @ X0 @ sK2))) | (((in @ X0 @ sK1)) = $true)) )),
% 0.20/0.31 inference(constrained_superposition,[],[f58,f27])).
% 0.20/0.31 thf(f61,plain,(
% 0.20/0.31 ( ! [X0 : $i] : ((((in @ X0 @ sK1)) = $true) | ($true != $true) | ($true != ((in @ X0 @ sK0)))) )),
% 0.20/0.31 inference(constrained_superposition,[],[f58,f30])).
% 0.20/0.31 thf(f62,plain,(
% 0.20/0.31 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK2))) | (((in @ X0 @ sK1)) = $true)) )),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f60])).
% 0.20/0.31 thf(f63,plain,(
% 0.20/0.31 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK0))) | (((in @ X0 @ sK1)) = $true)) )),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f61])).
% 0.20/0.31 thf(f68,plain,(
% 0.20/0.31 ( ! [X0 : $i] : (($true != $true) | (((in @ (sK4 @ sK2 @ X0) @ sK1)) = $true) | ($true = ((in @ (sK3 @ sK2 @ X0) @ X0))) | (sK2 = X0)) )),
% 0.20/0.31 inference(constrained_superposition,[],[f62,f56])).
% 0.20/0.31 thf(f69,plain,(
% 0.20/0.31 ( ! [X0 : $i] : (($true != $true) | ($true = ((in @ (sK3 @ sK2 @ X0) @ X0))) | (((in @ (sK4 @ sK2 @ X0) @ sK1)) != $true) | (((in @ (sK4 @ sK2 @ X0) @ sK0)) = $true) | (sK2 = X0)) )),
% 0.20/0.31 inference(constrained_superposition,[],[f26,f56])).
% 0.20/0.31 thf(f72,plain,(
% 0.20/0.31 ( ! [X0 : $i] : ((sK2 = X0) | (((in @ (sK4 @ sK2 @ X0) @ sK1)) = $true) | ($true = ((in @ (sK3 @ sK2 @ X0) @ X0)))) )),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f68])).
% 0.20/0.31 thf(f73,plain,(
% 0.20/0.31 ( ! [X0 : $i] : (($true = ((in @ (sK3 @ sK2 @ X0) @ X0))) | (((in @ (sK4 @ sK2 @ X0) @ sK0)) = $true) | (((in @ (sK4 @ sK2 @ X0) @ sK1)) != $true) | (sK2 = X0)) )),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f69])).
% 0.20/0.31 thf(f76,plain,(
% 0.20/0.31 ( ! [X0 : $i] : (($true = ((in @ (sK3 @ sK2 @ X0) @ X0))) | (((in @ (sK4 @ sK2 @ X0) @ sK0)) = $true) | (sK2 = X0)) )),
% 0.20/0.31 inference(forward_subsumption_resolution,[],[f73,f72])).
% 0.20/0.31 thf(f79,plain,(
% 0.20/0.31 (sK2 = sK0) | ($true = ((in @ (sK3 @ sK2 @ sK0) @ sK0))) | (sK2 = sK0) | ($true = ((in @ (sK3 @ sK2 @ sK0) @ sK0))) | ($true != $true)),
% 0.20/0.31 inference(constrained_superposition,[],[f55,f76])).
% 0.20/0.31 thf(f84,plain,(
% 0.20/0.31 (sK2 = sK0) | ($true = ((in @ (sK3 @ sK2 @ sK0) @ sK0))) | ($true != $true)),
% 0.20/0.31 inference(duplicate_literal_removal,[],[f79])).
% 0.20/0.31 thf(f85,plain,(
% 0.20/0.31 (sK2 = sK0) | ($true = ((in @ (sK3 @ sK2 @ sK0) @ sK0)))),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f84])).
% 0.20/0.31 thf(f88,plain,(
% 0.20/0.31 ($true = ((in @ (sK3 @ sK2 @ sK0) @ sK0)))),
% 0.20/0.31 inference(forward_subsumption_resolution,[],[f85,f28])).
% 0.20/0.31 thf(f90,definition,(
% 0.20/0.31 spl10_1 <=> (((in @ (sK3 @ sK2 @ sK0) @ sK2)) = $true)),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition])).
% 0.20/0.31 thf(f91,plain,(
% 0.20/0.31 (((in @ (sK3 @ sK2 @ sK0) @ sK2)) = $true) | ~spl10_1),
% 0.20/0.31 inference(avatar_component_clause,[],[f90])).
% 0.20/0.31 thf(f94,definition,(
% 0.20/0.31 spl10_2 <=> ($true = ((in @ (sK3 @ sK2 @ sK0) @ sK0)))),
% 0.20/0.31 introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition])).
% 0.20/0.31 thf(f96,plain,(
% 0.20/0.31 ($true = ((in @ (sK3 @ sK2 @ sK0) @ sK0))) | ~spl10_2),
% 0.20/0.31 inference(avatar_component_clause,[],[f94])).
% 0.20/0.31 thf(f98,plain,(
% 0.20/0.31 spl10_2),
% 0.20/0.31 inference(avatar_split_clause,[],[f88,f94])).
% 0.20/0.31 thf(f99,plain,(
% 0.20/0.31 (((in @ (sK3 @ sK2 @ sK0) @ sK1)) = $true) | ($true != $true) | ~spl10_2),
% 0.20/0.31 inference(constrained_superposition,[],[f63,f96])).
% 0.20/0.31 thf(f100,plain,(
% 0.20/0.31 (((in @ (sK3 @ sK2 @ sK0) @ sK1)) = $true) | ~spl10_2),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f99])).
% 0.20/0.31 thf(f101,plain,(
% 0.20/0.31 (((in @ (sK3 @ sK2 @ sK0) @ sK2)) = $true) | ($true != ((in @ (sK3 @ sK2 @ sK0) @ sK0))) | ($true != $true) | ~spl10_2),
% 0.20/0.31 inference(constrained_superposition,[],[f29,f100])).
% 0.20/0.31 thf(f102,plain,(
% 0.20/0.31 ($true != ((in @ (sK3 @ sK2 @ sK0) @ sK0))) | (((in @ (sK3 @ sK2 @ sK0) @ sK2)) = $true) | ~spl10_2),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f101])).
% 0.20/0.31 thf(f103,plain,(
% 0.20/0.31 (((in @ (sK3 @ sK2 @ sK0) @ sK2)) = $true) | ~spl10_2),
% 0.20/0.31 inference(forward_subsumption_resolution,[],[f102,f96])).
% 0.20/0.31 thf(f104,plain,(
% 0.20/0.31 spl10_1 | ~spl10_2),
% 0.20/0.31 inference(avatar_split_clause,[],[f103,f94,f90])).
% 0.20/0.31 thf(f105,plain,(
% 0.20/0.31 ($true != $true) | (((in @ (sK4 @ sK2 @ sK0) @ sK2)) = $true) | (sK2 = sK0) | ~spl10_1),
% 0.20/0.31 inference(constrained_superposition,[],[f57,f91])).
% 0.20/0.31 thf(f110,plain,(
% 0.20/0.31 (((in @ (sK4 @ sK2 @ sK0) @ sK2)) = $true) | (sK2 = sK0) | ~spl10_1),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f105])).
% 0.20/0.31 thf(f111,plain,(
% 0.20/0.31 (((in @ (sK4 @ sK2 @ sK0) @ sK2)) = $true) | ~spl10_1),
% 0.20/0.31 inference(forward_subsumption_resolution,[],[f110,f28])).
% 0.20/0.31 thf(f112,plain,(
% 0.20/0.31 (((in @ (sK4 @ sK2 @ sK0) @ sK1)) = $true) | ($true != $true) | ~spl10_1),
% 0.20/0.31 inference(constrained_superposition,[],[f62,f111])).
% 0.20/0.31 thf(f113,plain,(
% 0.20/0.31 (((in @ (sK4 @ sK2 @ sK0) @ sK1)) != $true) | (((in @ (sK4 @ sK2 @ sK0) @ sK0)) = $true) | ($true != $true) | ~spl10_1),
% 0.20/0.31 inference(constrained_superposition,[],[f26,f111])).
% 0.20/0.31 thf(f114,plain,(
% 0.20/0.31 (((in @ (sK4 @ sK2 @ sK0) @ sK1)) = $true) | ~spl10_1),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f112])).
% 0.20/0.31 thf(f115,plain,(
% 0.20/0.31 (((in @ (sK4 @ sK2 @ sK0) @ sK1)) != $true) | (((in @ (sK4 @ sK2 @ sK0) @ sK0)) = $true) | ~spl10_1),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f113])).
% 0.20/0.31 thf(f116,plain,(
% 0.20/0.31 (((in @ (sK4 @ sK2 @ sK0) @ sK0)) = $true) | ~spl10_1),
% 0.20/0.31 inference(forward_subsumption_resolution,[],[f115,f114])).
% 0.20/0.31 thf(f119,plain,(
% 0.20/0.31 (sK2 = sK0) | (((in @ (sK3 @ sK2 @ sK0) @ sK2)) != $true) | ($true != $true) | ~spl10_1),
% 0.20/0.31 inference(constrained_superposition,[],[f59,f116])).
% 0.20/0.31 thf(f122,plain,(
% 0.20/0.31 (((in @ (sK3 @ sK2 @ sK0) @ sK2)) != $true) | (sK2 = sK0) | ~spl10_1),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f119])).
% 0.20/0.31 thf(f125,plain,(
% 0.20/0.31 (sK2 = sK0) | ~spl10_1),
% 0.20/0.31 inference(forward_subsumption_resolution,[],[f122,f91])).
% 0.20/0.31 thf(f126,plain,(
% 0.20/0.31 $false | ~spl10_1),
% 0.20/0.31 inference(forward_subsumption_resolution,[],[f125,f28])).
% 0.20/0.31 thf(f127,plain,(
% 0.20/0.31 ~spl10_1),
% 0.20/0.31 inference(avatar_contradiction_clause,[],[f126])).
% 0.20/0.31 cnf(s2, plain, spl10_2, inference(sat_conversion,[],[f98])).
% 0.20/0.31 cnf(s3, plain, spl10_1 | ~spl10_2, inference(sat_conversion,[],[f104])).
% 0.20/0.31 cnf(s4, plain, ~spl10_1, inference(sat_conversion,[],[f127])).
% 0.20/0.31 cnf(s5, plain, ~spl10_2, inference(rat,[],[s3,s4])).
% 0.20/0.31 cnf(s6, plain, $false, inference(rat,[],[s2,s5])).
% 0.20/0.31 thf(f128,plain,(
% 0.20/0.31 $false),
% 0.20/0.31 inference(avatar_sat_refutation,[],[s6])).
% 0.20/0.31 % SZS output end Proof for theBenchmark
% 0.20/0.31 % (665226)------------------------------
% 0.20/0.31 % (665226)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (665226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (665226)CaDiCaL version: 2.1.3
% 0.20/0.31 % (665226)Termination reason: Refutation
% 0.20/0.31 % (665226)Time elapsed: 0.009 s
% 0.20/0.31 % (665226)Peak memory usage: 13 MB
% 0.20/0.31 % (665226)Instructions burned: 14 (million)
% 0.20/0.31 % (665208)Success in time 0.054 s
% 0.20/0.31 % Vampire exiting
%------------------------------------------------------------------------------