%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU749^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:31:07 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU749^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n020.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:21:29 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.22/0.30 % (1123109)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (1123117)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=3600386952: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)
% 0.22/0.30 % (1123120)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.30 % (1123120)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
% 0.22/0.30 % (1123118)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2815386248:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.30 % (1123115)lrs+10_16_si=on:nwc=1.5:random_seed=918947577:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (1123114)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1388998334:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (1123116)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3060558608:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (1123120)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=3688886398:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.30 % (1123119)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1651568958:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.30 % (1123116)Instruction limit reached!
% 0.22/0.30 % (1123116)------------------------------
% 0.22/0.30 % (1123116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (1123116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (1123116)CaDiCaL version: 2.1.3
% 0.22/0.30 % (1123116)Termination reason: Instruction limit
% 0.22/0.30 % (1123116)Termination phase: Saturation
% 0.22/0.30 % (1123116)Time elapsed: 0.002 s
% 0.22/0.30 % (1123116)Peak memory usage: 11 MB
% 0.22/0.30 % (1123116)Instructions burned: 3 (million)
% 0.22/0.30 % (1123117) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1123109-1123117"...
% 0.22/0.30 % (1123117)...printing done.
% 0.22/0.30 % (1123117)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% 0.22/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.30 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.22/0.30 thf(func_def_1, type, powerset: ($i > $i)).
% 0.22/0.30 thf(func_def_2, type, binunion: ($i > $i > $i)).
% 0.22/0.30 thf(func_def_3, type, setminus: ($i > $i > $i)).
% 0.22/0.30 thf(func_def_4, type, binunionT_lem: $o).
% 0.22/0.30 thf(func_def_6, type, complementT_lem: $o).
% 0.22/0.30 thf(func_def_7, type, powersetTI1: $o).
% 0.22/0.30 thf(func_def_8, type, demorgan2a1: $o).
% 0.22/0.30 thf(func_def_14, type, sK3: ($i > $i > $i > $i)).
% 0.22/0.30 thf(f1,axiom,(
% 0.22/0.30 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binunion @ X1 @ X2) @ (powerset @ X0)))) = binunionT_lem)),
% 0.22/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionT_lem)).
% 0.22/0.30 thf(f2,axiom,(
% 0.22/0.30 (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 0.22/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementT_lem)).
% 0.22/0.30 thf(f3,axiom,(
% 0.22/0.30 (! [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))) => (in @ X1 @ (powerset @ X2))))) = powersetTI1)),
% 0.22/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTI1)).
% 0.22/0.30 thf(f4,axiom,(
% 0.22/0.30 (demorgan2a1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) => (in @ X3 @ (setminus @ X0 @ X1)))))))),
% 0.22/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2a1)).
% 0.22/0.30 thf(f5,conjecture,(
% 0.22/0.30 binunionT_lem => (complementT_lem => (powersetTI1 => (demorgan2a1 => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1))))))))),
% 0.22/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementUnionInPowersetComplement)).
% 0.22/0.30 thf(f6,negated_conjecture,(
% 0.22/0.30 ~(binunionT_lem => (complementT_lem => (powersetTI1 => (demorgan2a1 => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1)))))))))),
% 0.22/0.30 inference(negated_conjecture,[status(cth)],[f5])).
% 0.22/0.30 thf(f7,plain,(
% 0.22/0.30 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binunion @ X1 @ X2) @ (powerset @ X0)))) = binunionT_lem)),
% 0.22/0.30 inference(rectify,[],[f1])).
% 0.22/0.30 thf(f8,plain,(
% 0.22/0.30 (binunionT_lem = $true) <=> ! [X1 : $i,X0 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) => (((in @ (binunion @ X1 @ X2) @ (powerset @ X0))) = $true)))),
% 0.22/0.30 inference(fool_elimination,[],[f7])).
% 0.22/0.30 thf(f9,plain,(
% 0.22/0.30 (! [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))) => (in @ X0 @ (powerset @ X2))))) = powersetTI1)),
% 0.22/0.30 inference(rectify,[],[f3])).
% 0.22/0.30 thf(f10,plain,(
% 0.22/0.30 ! [X1 : $i,X0 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) => (! [X3 : $i] : ((((in @ X3 @ X1)) = $true) => ((((in @ X3 @ X0)) = $true) => (((in @ X3 @ X2)) = $true))) => (((in @ X0 @ (powerset @ X2))) = $true)))) <=> (powersetTI1 = $true)),
% 0.22/0.30 inference(fool_elimination,[],[f9])).
% 0.22/0.30 thf(f11,plain,(
% 0.22/0.30 ~(binunionT_lem => (complementT_lem => (powersetTI1 => (demorgan2a1 => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (in @ (setminus @ X1 @ (binunion @ X0 @ X2)) @ (powerset @ (setminus @ X1 @ X0)))))))))),
% 0.22/0.30 inference(rectify,[],[f6])).
% 0.22/0.30 thf(f12,plain,(
% 0.22/0.30 ~((binunionT_lem = $true) => ((complementT_lem = $true) => ((powersetTI1 = $true) => ((demorgan2a1 = $true) => ! [X1 : $i,X0 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) => ($true = ((in @ (setminus @ X1 @ (binunion @ X0 @ X2)) @ (powerset @ (setminus @ X1 @ X0)))))))))))),
% 0.22/0.30 inference(fool_elimination,[],[f11])).
% 0.22/0.30 thf(f13,plain,(
% 0.22/0.30 (demorgan2a1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) => (in @ X3 @ (setminus @ X0 @ X1)))))))),
% 0.22/0.30 inference(rectify,[],[f4])).
% 0.22/0.30 thf(f14,plain,(
% 0.22/0.30 ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) => ! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => ((((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2)))) = $true) => (((in @ X3 @ (setminus @ X0 @ X1))) = $true))))) <=> (demorgan2a1 = $true)),
% 0.22/0.30 inference(fool_elimination,[],[f13])).
% 0.22/0.30 thf(f15,plain,(
% 0.22/0.30 (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 0.22/0.30 inference(rectify,[],[f2])).
% 0.22/0.30 thf(f16,plain,(
% 0.22/0.30 ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => (((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $true)) <=> (complementT_lem = $true)),
% 0.22/0.30 inference(fool_elimination,[],[f15])).
% 0.22/0.30 thf(f17,plain,(
% 0.22/0.30 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : (((((in @ X3 @ (setminus @ X0 @ X1))) = $true) | (((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2)))) != $true)) | (((in @ X3 @ X0)) != $true)) | (((in @ X2 @ (powerset @ X0))) != $true)) | (((in @ X1 @ (powerset @ X0))) != $true)) <=> (demorgan2a1 = $true)),
% 0.22/0.30 inference(ennf_transformation,[],[f14])).
% 0.22/0.30 thf(f18,plain,(
% 0.22/0.30 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X0)) != $true) | (((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2)))) != $true) | (((in @ X3 @ (setminus @ X0 @ X1))) = $true)) | (((in @ X2 @ (powerset @ X0))) != $true)) | (((in @ X1 @ (powerset @ X0))) != $true)) <=> (demorgan2a1 = $true)),
% 0.22/0.30 inference(flattening,[],[f17])).
% 0.22/0.30 thf(f19,plain,(
% 0.22/0.30 (complementT_lem = $true) <=> ! [X1 : $i,X0 : $i] : ((((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $true) | (((in @ X1 @ (powerset @ X0))) != $true))),
% 0.22/0.30 inference(ennf_transformation,[],[f16])).
% 0.22/0.30 thf(f20,plain,(
% 0.22/0.30 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (((((in @ X0 @ (powerset @ X2))) = $true) | ? [X3 : $i] : (((((in @ X3 @ X2)) != $true) & (((in @ X3 @ X0)) = $true)) & (((in @ X3 @ X1)) = $true))) | (((in @ X2 @ (powerset @ X1))) != $true)) | (((in @ X0 @ (powerset @ X1))) != $true)) <=> (powersetTI1 = $true)),
% 0.22/0.30 inference(ennf_transformation,[],[f10])).
% 0.22/0.30 thf(f21,plain,(
% 0.22/0.30 (powersetTI1 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X0 @ (powerset @ X2))) = $true) | (((in @ X2 @ (powerset @ X1))) != $true) | ? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & (((in @ X3 @ X2)) != $true) & (((in @ X3 @ X1)) = $true))) | (((in @ X0 @ (powerset @ X1))) != $true))),
% 0.22/0.30 inference(flattening,[],[f20])).
% 0.22/0.30 thf(f22,plain,(
% 0.22/0.30 (binunionT_lem = $true) <=> ! [X1 : $i,X0 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) | ! [X2 : $i] : ((((in @ (binunion @ X1 @ X2) @ (powerset @ X0))) = $true) | (((in @ X2 @ (powerset @ X0))) != $true)))),
% 0.22/0.30 inference(ennf_transformation,[],[f8])).
% 0.22/0.30 thf(f23,plain,(
% 0.22/0.30 (((? [X1 : $i,X0 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) & ? [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) & ($true != ((in @ (setminus @ X1 @ (binunion @ X0 @ X2)) @ (powerset @ (setminus @ X1 @ X0))))))) & (demorgan2a1 = $true)) & (powersetTI1 = $true)) & (complementT_lem = $true)) & (binunionT_lem = $true)),
% 0.22/0.30 inference(ennf_transformation,[],[f12])).
% 0.22/0.30 thf(f24,plain,(
% 0.22/0.30 (demorgan2a1 = $true) & ? [X1 : $i,X0 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) & ? [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) & ($true != ((in @ (setminus @ X1 @ (binunion @ X0 @ X2)) @ (powerset @ (setminus @ X1 @ X0))))))) & (powersetTI1 = $true) & (binunionT_lem = $true) & (complementT_lem = $true)),
% 0.22/0.30 inference(flattening,[],[f23])).
% 0.22/0.30 thf(f25,plain,(
% 0.22/0.30 ((powersetTI1 = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X0 @ (powerset @ X2))) != $true) & (((in @ X2 @ (powerset @ X1))) = $true) & ! [X3 : $i] : ((((in @ X3 @ X0)) != $true) | (((in @ X3 @ X2)) = $true) | (((in @ X3 @ X1)) != $true))) & (((in @ X0 @ (powerset @ X1))) = $true))) & (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X0 @ (powerset @ X2))) = $true) | (((in @ X2 @ (powerset @ X1))) != $true) | ? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & (((in @ X3 @ X2)) != $true) & (((in @ X3 @ X1)) = $true))) | (((in @ X0 @ (powerset @ X1))) != $true)) | (powersetTI1 != $true))),
% 0.22/0.30 inference(nnf_transformation,[],[f21])).
% 0.22/0.30 thf(f26,plain,(
% 0.22/0.30 ((powersetTI1 = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X0 @ (powerset @ X2))) != $true) & (((in @ X2 @ (powerset @ X1))) = $true) & ! [X3 : $i] : ((((in @ X3 @ X0)) != $true) | (((in @ X3 @ X2)) = $true) | (((in @ X3 @ X1)) != $true))) & (((in @ X0 @ (powerset @ X1))) = $true))) & (! [X4 : $i,X5 : $i] : (! [X6 : $i] : (($true = ((in @ X4 @ (powerset @ X6)))) | ($true != ((in @ X6 @ (powerset @ X5)))) | ? [X7 : $i] : (($true = ((in @ X7 @ X4))) & ($true != ((in @ X7 @ X6))) & ($true = ((in @ X7 @ X5))))) | ($true != ((in @ X4 @ (powerset @ X5))))) | (powersetTI1 != $true))),
% 0.22/0.30 inference(rectify,[],[f25])).
% 0.22/0.30 thf(f27,plain,(
% 0.22/0.30 ((powersetTI1 = $true) | (((((in @ sK0 @ (powerset @ sK2))) != $true) & (((in @ sK2 @ (powerset @ sK1))) = $true) & ! [X3 : $i] : (($true != ((in @ X3 @ sK0))) | ($true = ((in @ X3 @ sK2))) | ($true != ((in @ X3 @ sK1))))) & ($true = ((in @ sK0 @ (powerset @ sK1)))))) & (! [X4 : $i,X5 : $i] : (! [X6 : $i] : (($true = ((in @ X4 @ (powerset @ X6)))) | ($true != ((in @ X6 @ (powerset @ X5)))) | ((((in @ (sK3 @ X6 @ X5 @ X4) @ X4)) = $true) & ($true != ((in @ (sK3 @ X6 @ X5 @ X4) @ X6))) & ($true = ((in @ (sK3 @ X6 @ X5 @ X4) @ X5))))) | ($true != ((in @ X4 @ (powerset @ X5))))) | (powersetTI1 != $true))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X7,sK3 @ X6 @ X5 @ X4)],[f26])).
% 0.22/0.30 thf(f28,plain,(
% 0.22/0.30 ((binunionT_lem = $true) | ? [X1 : $i,X0 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) & ? [X2 : $i] : ((((in @ (binunion @ X1 @ X2) @ (powerset @ X0))) != $true) & (((in @ X2 @ (powerset @ X0))) = $true)))) & (! [X1 : $i,X0 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) | ! [X2 : $i] : ((((in @ (binunion @ X1 @ X2) @ (powerset @ X0))) = $true) | (((in @ X2 @ (powerset @ X0))) != $true))) | (binunionT_lem != $true))),
% 0.22/0.30 inference(nnf_transformation,[],[f22])).
% 0.22/0.30 thf(f29,plain,(
% 0.22/0.30 ((binunionT_lem = $true) | ? [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) & ? [X2 : $i] : ((((in @ (binunion @ X0 @ X2) @ (powerset @ X1))) != $true) & (((in @ X2 @ (powerset @ X1))) = $true)))) & (! [X3 : $i,X4 : $i] : ((((in @ X3 @ (powerset @ X4))) != $true) | ! [X5 : $i] : (($true = ((in @ (binunion @ X3 @ X5) @ (powerset @ X4)))) | (((in @ X5 @ (powerset @ X4))) != $true))) | (binunionT_lem != $true))),
% 0.22/0.30 inference(rectify,[],[f28])).
% 0.22/0.30 thf(f30,plain,(
% 0.22/0.30 ((binunionT_lem = $true) | ((((in @ sK4 @ (powerset @ sK5))) = $true) & ((((in @ (binunion @ sK4 @ sK6) @ (powerset @ sK5))) != $true) & ($true = ((in @ sK6 @ (powerset @ sK5))))))) & (! [X3 : $i,X4 : $i] : ((((in @ X3 @ (powerset @ X4))) != $true) | ! [X5 : $i] : (($true = ((in @ (binunion @ X3 @ X5) @ (powerset @ X4)))) | (((in @ X5 @ (powerset @ X4))) != $true))) | (binunionT_lem != $true))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f29])).
% 0.22/0.30 thf(f31,plain,(
% 0.22/0.30 ((complementT_lem = $true) | ? [X1 : $i,X0 : $i] : ((((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) != $true) & (((in @ X1 @ (powerset @ X0))) = $true))) & (! [X1 : $i,X0 : $i] : ((((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $true) | (((in @ X1 @ (powerset @ X0))) != $true)) | (complementT_lem != $true))),
% 0.22/0.30 inference(nnf_transformation,[],[f19])).
% 0.22/0.30 thf(f32,plain,(
% 0.22/0.30 ((complementT_lem = $true) | ? [X0 : $i,X1 : $i] : (($true != ((in @ (setminus @ X1 @ X0) @ (powerset @ X1)))) & (((in @ X0 @ (powerset @ X1))) = $true))) & (! [X2 : $i,X3 : $i] : (($true = ((in @ (setminus @ X3 @ X2) @ (powerset @ X3)))) | ($true != ((in @ X2 @ (powerset @ X3))))) | (complementT_lem != $true))),
% 0.22/0.30 inference(rectify,[],[f31])).
% 0.22/0.30 thf(f33,plain,(
% 0.22/0.30 ((complementT_lem = $true) | ((((in @ (setminus @ sK8 @ sK7) @ (powerset @ sK8))) != $true) & ($true = ((in @ sK7 @ (powerset @ sK8)))))) & (! [X2 : $i,X3 : $i] : (($true = ((in @ (setminus @ X3 @ X2) @ (powerset @ X3)))) | ($true != ((in @ X2 @ (powerset @ X3))))) | (complementT_lem != $true))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f32])).
% 0.22/0.30 thf(f34,plain,(
% 0.22/0.30 (demorgan2a1 = $true) & ? [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) & ? [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) & (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1)))) != $true))) & (powersetTI1 = $true) & (binunionT_lem = $true) & (complementT_lem = $true)),
% 0.22/0.30 inference(rectify,[],[f24])).
% 0.22/0.30 thf(f35,plain,(
% 0.22/0.30 (demorgan2a1 = $true) & (($true = ((in @ sK10 @ (powerset @ sK9)))) & (($true = ((in @ sK11 @ (powerset @ sK9)))) & ($true != ((in @ (setminus @ sK9 @ (binunion @ sK10 @ sK11)) @ (powerset @ (setminus @ sK9 @ sK10))))))) & (powersetTI1 = $true) & (binunionT_lem = $true) & (complementT_lem = $true)),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11)],[f34])).
% 0.22/0.30 thf(f36,plain,(
% 0.22/0.30 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X0)) != $true) | (((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2)))) != $true) | (((in @ X3 @ (setminus @ X0 @ X1))) = $true)) | (((in @ X2 @ (powerset @ X0))) != $true)) | (((in @ X1 @ (powerset @ X0))) != $true)) | (demorgan2a1 != $true)) & ((demorgan2a1 = $true) | ? [X1 : $i,X0 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & (((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2)))) = $true) & (((in @ X3 @ (setminus @ X0 @ X1))) != $true)) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)))),
% 0.22/0.30 inference(nnf_transformation,[],[f18])).
% 0.22/0.30 thf(f37,plain,(
% 0.22/0.30 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X1)) != $true) | (((in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))) != $true) | (((in @ X3 @ (setminus @ X1 @ X0))) = $true)) | (((in @ X2 @ (powerset @ X1))) != $true)) | (((in @ X0 @ (powerset @ X1))) != $true)) | (demorgan2a1 != $true)) & ((demorgan2a1 = $true) | ? [X4 : $i,X5 : $i] : (? [X6 : $i] : (? [X7 : $i] : (($true = ((in @ X7 @ X5))) & (((in @ X7 @ (setminus @ X5 @ (binunion @ X4 @ X6)))) = $true) & (((in @ X7 @ (setminus @ X5 @ X4))) != $true)) & ($true = ((in @ X6 @ (powerset @ X5))))) & ($true = ((in @ X4 @ (powerset @ X5))))))),
% 0.22/0.30 inference(rectify,[],[f36])).
% 0.22/0.30 thf(f38,plain,(
% 0.22/0.30 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X1)) != $true) | (((in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))) != $true) | (((in @ X3 @ (setminus @ X1 @ X0))) = $true)) | (((in @ X2 @ (powerset @ X1))) != $true)) | (((in @ X0 @ (powerset @ X1))) != $true)) | (demorgan2a1 != $true)) & ((demorgan2a1 = $true) | ((((((in @ sK15 @ sK13)) = $true) & ($true = ((in @ sK15 @ (setminus @ sK13 @ (binunion @ sK12 @ sK14))))) & ($true != ((in @ sK15 @ (setminus @ sK13 @ sK12))))) & (((in @ sK14 @ (powerset @ sK13))) = $true)) & ($true = ((in @ sK12 @ (powerset @ sK13))))))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15]),skolemize(X4,sK12),skolemize(X5,sK13),skolemize(X6,sK14),skolemize(X7,sK15)],[f37])).
% 0.22/0.30 thf(f39,plain,(
% 0.22/0.30 ( ! [X6 : $i,X4 : $i,X5 : $i] : ((powersetTI1 != $true) | ($true != ((in @ X4 @ (powerset @ X5)))) | ($true = ((in @ (sK3 @ X6 @ X5 @ X4) @ X5))) | ($true != ((in @ X6 @ (powerset @ X5)))) | ($true = ((in @ X4 @ (powerset @ X6))))) )),
% 0.22/0.30 inference(cnf_transformation,[],[f27])).
% 0.22/0.30 thf(f40,plain,(
% 0.22/0.30 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X6 @ (powerset @ X5)))) | ($true = ((in @ X4 @ (powerset @ X6)))) | ($true != ((in @ X4 @ (powerset @ X5)))) | ($true != ((in @ (sK3 @ X6 @ X5 @ X4) @ X6))) | (powersetTI1 != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f27])).
% 0.22/0.30 thf(f41,plain,(
% 0.22/0.30 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X4 @ (powerset @ X6)))) | (((in @ (sK3 @ X6 @ X5 @ X4) @ X4)) = $true) | ($true != ((in @ X6 @ (powerset @ X5)))) | ($true != ((in @ X4 @ (powerset @ X5)))) | (powersetTI1 != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f27])).
% 0.22/0.30 thf(f46,plain,(
% 0.22/0.30 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((binunionT_lem != $true) | ($true = ((in @ (binunion @ X3 @ X5) @ (powerset @ X4)))) | (((in @ X5 @ (powerset @ X4))) != $true) | (((in @ X3 @ (powerset @ X4))) != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f30])).
% 0.22/0.30 thf(f50,plain,(
% 0.22/0.30 ( ! [X2 : $i,X3 : $i] : (($true != ((in @ X2 @ (powerset @ X3)))) | ($true = ((in @ (setminus @ X3 @ X2) @ (powerset @ X3)))) | (complementT_lem != $true)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f33])).
% 0.22/0.31 thf(f53,plain,(
% 0.22/0.31 (complementT_lem = $true)),
% 0.22/0.31 inference(cnf_transformation,[],[f35])).
% 0.22/0.31 thf(f54,plain,(
% 0.22/0.31 (binunionT_lem = $true)),
% 0.22/0.31 inference(cnf_transformation,[],[f35])).
% 0.22/0.31 thf(f55,plain,(
% 0.22/0.31 (powersetTI1 = $true)),
% 0.22/0.31 inference(cnf_transformation,[],[f35])).
% 0.22/0.31 thf(f56,plain,(
% 0.22/0.31 ($true != ((in @ (setminus @ sK9 @ (binunion @ sK10 @ sK11)) @ (powerset @ (setminus @ sK9 @ sK10)))))),
% 0.22/0.31 inference(cnf_transformation,[],[f35])).
% 0.22/0.31 thf(f57,plain,(
% 0.22/0.31 ($true = ((in @ sK11 @ (powerset @ sK9))))),
% 0.22/0.31 inference(cnf_transformation,[],[f35])).
% 0.22/0.31 thf(f58,plain,(
% 0.22/0.31 ($true = ((in @ sK10 @ (powerset @ sK9))))),
% 0.22/0.31 inference(cnf_transformation,[],[f35])).
% 0.22/0.31 thf(f59,plain,(
% 0.22/0.31 (demorgan2a1 = $true)),
% 0.22/0.31 inference(cnf_transformation,[],[f35])).
% 0.22/0.31 thf(f65,plain,(
% 0.22/0.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) != $true) | (((in @ X3 @ (setminus @ X1 @ X0))) = $true) | (((in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))) != $true) | (((in @ X2 @ (powerset @ X1))) != $true) | (demorgan2a1 != $true) | (((in @ X3 @ X1)) != $true)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f38])).
% 0.22/0.31 thf(f72,definition,(
% 0.22/0.31 spl16_2 <=> (powersetTI1 = $true)),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition])).
% 0.22/0.31 thf(f77,definition,(
% 0.22/0.31 spl16_3 <=> (demorgan2a1 = $true)),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition])).
% 0.22/0.31 thf(f86,definition,(
% 0.22/0.31 spl16_5 <=> (complementT_lem = $true)),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl16_5])],[avatar_definition])).
% 0.22/0.31 thf(f100,definition,(
% 0.22/0.31 spl16_8 <=> (binunionT_lem = $true)),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl16_8])],[avatar_definition])).
% 0.22/0.31 thf(f109,definition,(
% 0.22/0.31 spl16_10 <=> ! [X6 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X4 @ (powerset @ X6)))) | ($true != ((in @ X4 @ (powerset @ X5)))) | ($true != ((in @ X6 @ (powerset @ X5)))) | (((in @ (sK3 @ X6 @ X5 @ X4) @ X4)) = $true))),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl16_10])],[avatar_definition])).
% 0.22/0.31 thf(f110,plain,(
% 0.22/0.31 ( ! [X6 : $i,X4 : $i,X5 : $i] : ((((in @ (sK3 @ X6 @ X5 @ X4) @ X4)) = $true) | ($true != ((in @ X4 @ (powerset @ X5)))) | ($true != ((in @ X6 @ (powerset @ X5)))) | ($true = ((in @ X4 @ (powerset @ X6))))) ) | ~spl16_10),
% 0.22/0.31 inference(avatar_component_clause,[],[f109])).
% 0.22/0.31 thf(f111,plain,(
% 0.22/0.31 ~spl16_2 | spl16_10),
% 0.22/0.31 inference(avatar_split_clause,[],[f41,f109,f72])).
% 0.22/0.31 thf(f122,plain,(
% 0.22/0.31 spl16_2),
% 0.22/0.31 inference(avatar_split_clause,[],[f55,f72])).
% 0.22/0.31 thf(f124,definition,(
% 0.22/0.31 spl16_13 <=> ($true = ((in @ sK11 @ (powerset @ sK9))))),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl16_13])],[avatar_definition])).
% 0.22/0.31 thf(f126,plain,(
% 0.22/0.31 ($true = ((in @ sK11 @ (powerset @ sK9)))) | ~spl16_13),
% 0.22/0.31 inference(avatar_component_clause,[],[f124])).
% 0.22/0.31 thf(f127,plain,(
% 0.22/0.31 spl16_13),
% 0.22/0.31 inference(avatar_split_clause,[],[f57,f124])).
% 0.22/0.31 thf(f133,plain,(
% 0.22/0.31 spl16_3),
% 0.22/0.31 inference(avatar_split_clause,[],[f59,f77])).
% 0.22/0.31 thf(f140,definition,(
% 0.22/0.31 spl16_16 <=> ($true = ((in @ (setminus @ sK9 @ (binunion @ sK10 @ sK11)) @ (powerset @ (setminus @ sK9 @ sK10)))))),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl16_16])],[avatar_definition])).
% 0.22/0.31 thf(f142,plain,(
% 0.22/0.31 ($true != ((in @ (setminus @ sK9 @ (binunion @ sK10 @ sK11)) @ (powerset @ (setminus @ sK9 @ sK10))))) | spl16_16),
% 0.22/0.31 inference(avatar_component_clause,[],[f140])).
% 0.22/0.31 thf(f143,plain,(
% 0.22/0.31 ~spl16_16),
% 0.22/0.31 inference(avatar_split_clause,[],[f56,f140])).
% 0.22/0.31 thf(f145,definition,(
% 0.22/0.31 spl16_17 <=> ! [X6 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X4 @ (powerset @ X5)))) | ($true = ((in @ X4 @ (powerset @ X6)))) | ($true != ((in @ X6 @ (powerset @ X5)))) | ($true = ((in @ (sK3 @ X6 @ X5 @ X4) @ X5))))),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl16_17])],[avatar_definition])).
% 0.22/0.31 thf(f146,plain,(
% 0.22/0.31 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true = ((in @ (sK3 @ X6 @ X5 @ X4) @ X5))) | ($true = ((in @ X4 @ (powerset @ X6)))) | ($true != ((in @ X4 @ (powerset @ X5)))) | ($true != ((in @ X6 @ (powerset @ X5))))) ) | ~spl16_17),
% 0.22/0.31 inference(avatar_component_clause,[],[f145])).
% 0.22/0.31 thf(f147,plain,(
% 0.22/0.31 spl16_17 | ~spl16_2),
% 0.22/0.31 inference(avatar_split_clause,[],[f39,f72,f145])).
% 0.22/0.31 thf(f153,plain,(
% 0.22/0.31 spl16_5),
% 0.22/0.31 inference(avatar_split_clause,[],[f53,f86])).
% 0.22/0.31 thf(f155,definition,(
% 0.22/0.31 spl16_19 <=> ($true = ((in @ sK10 @ (powerset @ sK9))))),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl16_19])],[avatar_definition])).
% 0.22/0.31 thf(f157,plain,(
% 0.22/0.31 ($true = ((in @ sK10 @ (powerset @ sK9)))) | ~spl16_19),
% 0.22/0.31 inference(avatar_component_clause,[],[f155])).
% 0.22/0.31 thf(f158,plain,(
% 0.22/0.31 spl16_19),
% 0.22/0.31 inference(avatar_split_clause,[],[f58,f155])).
% 0.22/0.31 thf(f175,definition,(
% 0.22/0.31 spl16_23 <=> ! [X6 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X6 @ (powerset @ X5)))) | ($true != ((in @ (sK3 @ X6 @ X5 @ X4) @ X6))) | ($true != ((in @ X4 @ (powerset @ X5)))) | ($true = ((in @ X4 @ (powerset @ X6)))))),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl16_23])],[avatar_definition])).
% 0.22/0.31 thf(f176,plain,(
% 0.22/0.31 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != ((in @ (sK3 @ X6 @ X5 @ X4) @ X6))) | ($true = ((in @ X4 @ (powerset @ X6)))) | ($true != ((in @ X4 @ (powerset @ X5)))) | ($true != ((in @ X6 @ (powerset @ X5))))) ) | ~spl16_23),
% 0.22/0.31 inference(avatar_component_clause,[],[f175])).
% 0.22/0.31 thf(f177,plain,(
% 0.22/0.31 spl16_23 | ~spl16_2),
% 0.22/0.31 inference(avatar_split_clause,[],[f40,f72,f175])).
% 0.22/0.31 thf(f182,plain,(
% 0.22/0.31 spl16_8),
% 0.22/0.31 inference(avatar_split_clause,[],[f54,f100])).
% 0.22/0.31 thf(f184,definition,(
% 0.22/0.31 spl16_25 <=> ! [X4 : $i,X5 : $i,X3 : $i] : (($true = ((in @ (binunion @ X3 @ X5) @ (powerset @ X4)))) | (((in @ X3 @ (powerset @ X4))) != $true) | (((in @ X5 @ (powerset @ X4))) != $true))),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl16_25])],[avatar_definition])).
% 0.22/0.31 thf(f185,plain,(
% 0.22/0.31 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = ((in @ (binunion @ X3 @ X5) @ (powerset @ X4)))) | (((in @ X3 @ (powerset @ X4))) != $true) | (((in @ X5 @ (powerset @ X4))) != $true)) ) | ~spl16_25),
% 0.22/0.31 inference(avatar_component_clause,[],[f184])).
% 0.22/0.31 thf(f186,plain,(
% 0.22/0.31 ~spl16_8 | spl16_25),
% 0.22/0.31 inference(avatar_split_clause,[],[f46,f184,f100])).
% 0.22/0.31 thf(f188,definition,(
% 0.22/0.31 spl16_26 <=> ! [X2 : $i,X3 : $i] : (($true != ((in @ X2 @ (powerset @ X3)))) | ($true = ((in @ (setminus @ X3 @ X2) @ (powerset @ X3)))))),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl16_26])],[avatar_definition])).
% 0.22/0.31 thf(f189,plain,(
% 0.22/0.31 ( ! [X2 : $i,X3 : $i] : (($true = ((in @ (setminus @ X3 @ X2) @ (powerset @ X3)))) | ($true != ((in @ X2 @ (powerset @ X3))))) ) | ~spl16_26),
% 0.22/0.31 inference(avatar_component_clause,[],[f188])).
% 0.22/0.31 thf(f190,plain,(
% 0.22/0.31 ~spl16_5 | spl16_26),
% 0.22/0.31 inference(avatar_split_clause,[],[f50,f188,f86])).
% 0.22/0.31 thf(f192,definition,(
% 0.22/0.31 spl16_27 <=> ! [X0 : $i,X3 : $i,X2 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) != $true) | (((in @ X3 @ X1)) != $true) | (((in @ X2 @ (powerset @ X1))) != $true) | (((in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))) != $true) | (((in @ X3 @ (setminus @ X1 @ X0))) = $true))),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl16_27])],[avatar_definition])).
% 0.22/0.31 thf(f193,plain,(
% 0.22/0.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))) != $true) | (((in @ X2 @ (powerset @ X1))) != $true) | (((in @ X3 @ X1)) != $true) | (((in @ X3 @ (setminus @ X1 @ X0))) = $true) | (((in @ X0 @ (powerset @ X1))) != $true)) ) | ~spl16_27),
% 0.22/0.31 inference(avatar_component_clause,[],[f192])).
% 0.22/0.31 thf(f194,plain,(
% 0.22/0.31 ~spl16_3 | spl16_27),
% 0.22/0.31 inference(avatar_split_clause,[],[f65,f192,f77])).
% 0.22/0.31 thf(f204,plain,(
% 0.22/0.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != $true) | (((in @ (sK3 @ X0 @ X1 @ (setminus @ X2 @ (binunion @ X3 @ X4))) @ (setminus @ X2 @ X3))) = $true) | ($true != ((in @ X3 @ (powerset @ X2)))) | ($true != ((in @ (sK3 @ X0 @ X1 @ (setminus @ X2 @ (binunion @ X3 @ X4))) @ X2))) | (((in @ X0 @ (powerset @ X1))) != $true) | ($true = ((in @ (setminus @ X2 @ (binunion @ X3 @ X4)) @ (powerset @ X0)))) | ($true != ((in @ (setminus @ X2 @ (binunion @ X3 @ X4)) @ (powerset @ X1)))) | (((in @ X4 @ (powerset @ X2))) != $true)) ) | (~spl16_10 | ~spl16_27)),
% 0.22/0.31 inference(superposition,[],[f193,f110])).
% 0.22/0.31 thf(f206,plain,(
% 0.22/0.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((((in @ (sK3 @ X0 @ X1 @ (setminus @ X2 @ (binunion @ X3 @ X4))) @ (setminus @ X2 @ X3))) = $true) | ($true != ((in @ (sK3 @ X0 @ X1 @ (setminus @ X2 @ (binunion @ X3 @ X4))) @ X2))) | (((in @ X4 @ (powerset @ X2))) != $true) | ($true != ((in @ (setminus @ X2 @ (binunion @ X3 @ X4)) @ (powerset @ X1)))) | ($true != ((in @ X3 @ (powerset @ X2)))) | ($true = ((in @ (setminus @ X2 @ (binunion @ X3 @ X4)) @ (powerset @ X0)))) | (((in @ X0 @ (powerset @ X1))) != $true)) ) | (~spl16_10 | ~spl16_27)),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f204])).
% 0.22/0.31 thf(f209,plain,(
% 0.22/0.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ (setminus @ X0 @ (binunion @ X1 @ X3)) @ (powerset @ (setminus @ X0 @ X1)))) = $true) | (((in @ (setminus @ X0 @ (binunion @ X1 @ X3)) @ (powerset @ X2))) != $true) | ($true != ((in @ (setminus @ X0 @ X1) @ (powerset @ X2)))) | (((in @ X3 @ (powerset @ X0))) != $true) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true != ((in @ (sK3 @ (setminus @ X0 @ X1) @ X2 @ (setminus @ X0 @ (binunion @ X1 @ X3))) @ X0))) | (((in @ (setminus @ X0 @ (binunion @ X1 @ X3)) @ (powerset @ X2))) != $true) | ($true != ((in @ (setminus @ X0 @ X1) @ (powerset @ X2)))) | ($true != $true) | (((in @ (setminus @ X0 @ (binunion @ X1 @ X3)) @ (powerset @ (setminus @ X0 @ X1)))) = $true)) ) | (~spl16_10 | ~spl16_23 | ~spl16_27)),
% 0.22/0.31 inference(superposition,[],[f176,f206])).
% 0.22/0.31 thf(f212,plain,(
% 0.22/0.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ (setminus @ X0 @ (binunion @ X1 @ X3)) @ (powerset @ (setminus @ X0 @ X1)))) = $true) | (((in @ X3 @ (powerset @ X0))) != $true) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true != ((in @ (sK3 @ (setminus @ X0 @ X1) @ X2 @ (setminus @ X0 @ (binunion @ X1 @ X3))) @ X0))) | ($true != $true) | (((in @ (setminus @ X0 @ (binunion @ X1 @ X3)) @ (powerset @ X2))) != $true) | ($true != ((in @ (setminus @ X0 @ X1) @ (powerset @ X2))))) ) | (~spl16_10 | ~spl16_23 | ~spl16_27)),
% 0.22/0.31 inference(duplicate_literal_removal,[],[f209])).
% 0.22/0.31 thf(f213,plain,(
% 0.22/0.31 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK3 @ (setminus @ X0 @ X1) @ X2 @ (setminus @ X0 @ (binunion @ X1 @ X3))) @ X0))) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ (binunion @ X1 @ X3)) @ (powerset @ (setminus @ X0 @ X1)))) = $true) | ($true != ((in @ (setminus @ X0 @ X1) @ (powerset @ X2)))) | (((in @ (setminus @ X0 @ (binunion @ X1 @ X3)) @ (powerset @ X2))) != $true) | (((in @ X3 @ (powerset @ X0))) != $true)) ) | (~spl16_10 | ~spl16_23 | ~spl16_27)),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f212])).
% 0.22/0.31 thf(f215,plain,(
% 0.22/0.31 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X0))) != $true) | ($true != $true) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1)))) = $true) | (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1)))) = $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) != $true)) ) | (~spl16_10 | ~spl16_17 | ~spl16_23 | ~spl16_27)),
% 0.22/0.31 inference(superposition,[],[f213,f146])).
% 0.22/0.31 thf(f216,plain,(
% 0.22/0.31 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (powerset @ X0))) != $true) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1)))) = $true) | (((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) != $true) | ($true != $true)) ) | (~spl16_10 | ~spl16_17 | ~spl16_23 | ~spl16_27)),
% 0.22/0.31 inference(duplicate_literal_removal,[],[f215])).
% 0.22/0.31 thf(f217,plain,(
% 0.22/0.31 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1)))) = $true) | (((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X0))) != $true)) ) | (~spl16_10 | ~spl16_17 | ~spl16_23 | ~spl16_27)),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f216])).
% 0.22/0.31 thf(f218,plain,(
% 0.22/0.31 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1)))) = $true) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X0))) != $true) | (((in @ X2 @ (powerset @ X0))) != $true)) ) | (~spl16_10 | ~spl16_17 | ~spl16_23 | ~spl16_26 | ~spl16_27)),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f217,f189])).
% 0.22/0.31 thf(f255,plain,(
% 0.22/0.31 ($true != ((in @ sK11 @ (powerset @ sK9)))) | ($true != $true) | ($true != ((in @ (setminus @ sK9 @ (binunion @ sK10 @ sK11)) @ (powerset @ sK9)))) | ($true != ((in @ sK10 @ (powerset @ sK9)))) | (~spl16_10 | spl16_16 | ~spl16_17 | ~spl16_23 | ~spl16_26 | ~spl16_27)),
% 0.22/0.31 inference(superposition,[],[f142,f218])).
% 0.22/0.31 thf(f256,plain,(
% 0.22/0.31 ($true != ((in @ sK10 @ (powerset @ sK9)))) | ($true != ((in @ (setminus @ sK9 @ (binunion @ sK10 @ sK11)) @ (powerset @ sK9)))) | ($true != ((in @ sK11 @ (powerset @ sK9)))) | (~spl16_10 | spl16_16 | ~spl16_17 | ~spl16_23 | ~spl16_26 | ~spl16_27)),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f255])).
% 0.22/0.31 thf(f257,plain,(
% 0.22/0.31 ($true != ((in @ (setminus @ sK9 @ (binunion @ sK10 @ sK11)) @ (powerset @ sK9)))) | ($true != ((in @ sK11 @ (powerset @ sK9)))) | (~spl16_10 | spl16_16 | ~spl16_17 | ~spl16_19 | ~spl16_23 | ~spl16_26 | ~spl16_27)),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f256,f157])).
% 0.22/0.31 thf(f258,plain,(
% 0.22/0.31 ($true != ((in @ (setminus @ sK9 @ (binunion @ sK10 @ sK11)) @ (powerset @ sK9)))) | (~spl16_10 | ~spl16_13 | spl16_16 | ~spl16_17 | ~spl16_19 | ~spl16_23 | ~spl16_26 | ~spl16_27)),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f257,f126])).
% 0.22/0.31 thf(f260,definition,(
% 0.22/0.31 spl16_28 <=> ($true = ((in @ (setminus @ sK9 @ (binunion @ sK10 @ sK11)) @ (powerset @ sK9))))),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl16_28])],[avatar_definition])).
% 0.22/0.31 thf(f262,plain,(
% 0.22/0.31 ($true != ((in @ (setminus @ sK9 @ (binunion @ sK10 @ sK11)) @ (powerset @ sK9)))) | spl16_28),
% 0.22/0.31 inference(avatar_component_clause,[],[f260])).
% 0.22/0.31 thf(f263,plain,(
% 0.22/0.31 ~spl16_28 | ~spl16_10 | ~spl16_13 | spl16_16 | ~spl16_17 | ~spl16_19 | ~spl16_23 | ~spl16_26 | ~spl16_27),
% 0.22/0.31 inference(avatar_split_clause,[],[f258,f192,f188,f175,f155,f145,f140,f124,f109,f260])).
% 0.22/0.31 thf(f264,plain,(
% 0.22/0.31 ($true != ((in @ (binunion @ sK10 @ sK11) @ (powerset @ sK9)))) | ($true != $true) | (~spl16_26 | spl16_28)),
% 0.22/0.31 inference(superposition,[],[f262,f189])).
% 0.22/0.31 thf(f265,plain,(
% 0.22/0.31 ($true != ((in @ (binunion @ sK10 @ sK11) @ (powerset @ sK9)))) | (~spl16_26 | spl16_28)),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f264])).
% 0.22/0.31 thf(f267,definition,(
% 0.22/0.31 spl16_29 <=> ($true = ((in @ (binunion @ sK10 @ sK11) @ (powerset @ sK9))))),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl16_29])],[avatar_definition])).
% 0.22/0.31 thf(f269,plain,(
% 0.22/0.31 ($true != ((in @ (binunion @ sK10 @ sK11) @ (powerset @ sK9)))) | spl16_29),
% 0.22/0.31 inference(avatar_component_clause,[],[f267])).
% 0.22/0.31 thf(f270,plain,(
% 0.22/0.31 ~spl16_29 | ~spl16_26 | spl16_28),
% 0.22/0.31 inference(avatar_split_clause,[],[f265,f260,f188,f267])).
% 0.22/0.31 thf(f281,plain,(
% 0.22/0.31 ($true != ((in @ sK10 @ (powerset @ sK9)))) | ($true != $true) | ($true != ((in @ sK11 @ (powerset @ sK9)))) | (~spl16_25 | spl16_29)),
% 0.22/0.31 inference(superposition,[],[f269,f185])).
% 0.22/0.31 thf(f282,plain,(
% 0.22/0.31 ($true != ((in @ sK11 @ (powerset @ sK9)))) | ($true != ((in @ sK10 @ (powerset @ sK9)))) | (~spl16_25 | spl16_29)),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f281])).
% 0.22/0.31 thf(f283,plain,(
% 0.22/0.31 ($true != ((in @ sK10 @ (powerset @ sK9)))) | (~spl16_13 | ~spl16_25 | spl16_29)),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f282,f126])).
% 0.22/0.31 thf(f284,plain,(
% 0.22/0.31 $false | (~spl16_13 | ~spl16_19 | ~spl16_25 | spl16_29)),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f283,f157])).
% 0.22/0.31 thf(f285,plain,(
% 0.22/0.31 ~spl16_13 | ~spl16_19 | ~spl16_25 | spl16_29),
% 0.22/0.31 inference(avatar_contradiction_clause,[],[f284])).
% 0.22/0.31 cnf(s6, plain, ~spl16_2 | spl16_10, inference(sat_conversion,[],[f111])).
% 0.22/0.31 cnf(s9, plain, spl16_2, inference(sat_conversion,[],[f122])).
% 0.22/0.31 cnf(s10, plain, spl16_13, inference(sat_conversion,[],[f127])).
% 0.22/0.31 cnf(s12, plain, spl16_3, inference(sat_conversion,[],[f133])).
% 0.22/0.31 cnf(s14, plain, ~spl16_16, inference(sat_conversion,[],[f143])).
% 0.22/0.31 cnf(s15, plain, ~spl16_2 | spl16_17, inference(sat_conversion,[],[f147])).
% 0.22/0.31 cnf(s17, plain, spl16_5, inference(sat_conversion,[],[f153])).
% 0.22/0.31 cnf(s18, plain, spl16_19, inference(sat_conversion,[],[f158])).
% 0.22/0.31 cnf(s22, plain, ~spl16_2 | spl16_23, inference(sat_conversion,[],[f177])).
% 0.22/0.31 cnf(s24, plain, spl16_8, inference(sat_conversion,[],[f182])).
% 0.22/0.31 cnf(s25, plain, ~spl16_8 | spl16_25, inference(sat_conversion,[],[f186])).
% 0.22/0.31 cnf(s26, plain, ~spl16_5 | spl16_26, inference(sat_conversion,[],[f190])).
% 0.22/0.31 cnf(s27, plain, ~spl16_3 | spl16_27, inference(sat_conversion,[],[f194])).
% 0.22/0.31 cnf(s28, plain, ~spl16_10 | ~spl16_13 | spl16_16 | ~spl16_17 | ~spl16_19 | ~spl16_23 | ~spl16_26 | ~spl16_27 | ~spl16_28, inference(sat_conversion,[],[f263])).
% 0.22/0.31 cnf(s29, plain, ~spl16_26 | spl16_28 | ~spl16_29, inference(sat_conversion,[],[f270])).
% 0.22/0.31 cnf(s30, plain, ~spl16_13 | ~spl16_19 | ~spl16_25 | spl16_29, inference(sat_conversion,[],[f285])).
% 0.22/0.31 cnf(s31, plain, spl16_25, inference(rat,[],[s25,s24])).
% 0.22/0.31 cnf(s32, plain, spl16_26, inference(rat,[],[s26,s17])).
% 0.22/0.31 cnf(s33, plain, spl16_27, inference(rat,[],[s27,s12])).
% 0.22/0.31 cnf(s34, plain, spl16_29, inference(rat,[],[s30,s18,s31,s10])).
% 0.22/0.31 cnf(s35, plain, spl16_28, inference(rat,[],[s29,s32,s34])).
% 0.22/0.31 cnf(s36, plain, spl16_23, inference(rat,[],[s22,s9])).
% 0.22/0.31 cnf(s37, plain, spl16_17, inference(rat,[],[s15,s9])).
% 0.22/0.31 cnf(s38, plain, ~spl16_10, inference(rat,[],[s28,s35,s33,s32,s36,s18,s10,s14,s37])).
% 0.22/0.31 cnf(s39, plain, $false, inference(rat,[],[s6,s38,s9])).
% 0.22/0.31 thf(f286,plain,(
% 0.22/0.31 $false),
% 0.22/0.31 inference(avatar_sat_refutation,[],[s39])).
% 0.22/0.31 % SZS output end Proof for theBenchmark
% 0.22/0.31 % (1123117)------------------------------
% 0.22/0.31 % (1123117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (1123117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (1123117)CaDiCaL version: 2.1.3
% 0.22/0.31 % (1123117)Termination reason: Refutation
% 0.22/0.31 % (1123117)Time elapsed: 0.012 s
% 0.22/0.31 % (1123117)Peak memory usage: 13 MB
% 0.22/0.31 % (1123117)Instructions burned: 38 (million)
% 0.22/0.31 % (1123109)Success in time 0.047 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------