%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU734^2 : 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 : n005.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 08:31:02 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU734^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n005.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:18:31 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.21/0.29 % (1732718)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (1732726)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=1751410260: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)
% 0.21/0.29 % (1732727)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=471953527:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (1732723)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1610711626:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (1732724)lrs+10_16_si=on:nwc=1.5:random_seed=1014775115:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (1732725)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3154465010:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (1732725)Refutation not found, incomplete strategy
% 0.21/0.29 % (1732725)------------------------------
% 0.21/0.29 % (1732725)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (1732725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (1732725)CaDiCaL version: 2.1.3
% 0.21/0.29 % (1732725)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.29 % (1732725)Time elapsed: 0.003 s
% 0.21/0.29 % (1732725)Peak memory usage: 12 MB
% 0.21/0.29 % (1732725)Instructions burned: 4 (million)
% 0.21/0.29 % (1732725)------------------------------
% 0.21/0.29 % (1732725)------------------------------
% 0.21/0.29 % (1732726) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1732718-1732726"...
% 0.21/0.29 % (1732728)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3368326854:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (1732726)...printing done.
% 0.21/0.29 % (1732726)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% 0.21/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.29 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.21/0.29 thf(func_def_1, type, powerset: ($i > $i)).
% 0.21/0.29 thf(func_def_2, type, subset: ($i > $i > $o)).
% 0.21/0.29 thf(func_def_3, type, binintersect: ($i > $i > $i)).
% 0.21/0.29 thf(func_def_4, type, setminus: ($i > $i > $i)).
% 0.21/0.29 thf(func_def_5, type, binintersectT_lem: $o).
% 0.21/0.29 thf(func_def_7, type, complementT_lem: $o).
% 0.21/0.29 thf(func_def_8, type, subsetTI: $o).
% 0.21/0.29 thf(func_def_9, type, complementImpComplementIntersect: $o).
% 0.21/0.29 thf(func_def_16, type, sK4: ($i > $i > $i > $i)).
% 0.21/0.29 thf(f1,axiom,(
% 0.21/0.29 (binintersectT_lem = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ X0)))))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectT_lem)).
% 0.21/0.29 thf(f2,axiom,(
% 0.21/0.29 (complementT_lem = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementT_lem)).
% 0.21/0.29 thf(f3,axiom,(
% 0.21/0.29 (! [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))) => (subset @ X1 @ X2)))) = subsetTI)),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTI)).
% 0.21/0.29 thf(f4,axiom,(
% 0.21/0.29 (complementImpComplementIntersect = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ X1)) => (in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))))))))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementImpComplementIntersect)).
% 0.21/0.29 thf(f5,conjecture,(
% 0.21/0.29 binintersectT_lem => (complementT_lem => (subsetTI => (complementImpComplementIntersect => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))))))))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementSubsetComplementIntersect)).
% 0.21/0.29 thf(f6,negated_conjecture,(
% 0.21/0.29 ~(binintersectT_lem => (complementT_lem => (subsetTI => (complementImpComplementIntersect => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))))))))),
% 0.21/0.29 inference(negated_conjecture,[status(cth)],[f5])).
% 0.21/0.29 thf(f7,plain,(
% 0.21/0.29 (complementImpComplementIntersect = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ X1)) => (in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))))))))),
% 0.21/0.29 inference(rectify,[],[f4])).
% 0.21/0.29 thf(f8,plain,(
% 0.21/0.29 (complementImpComplementIntersect = $true) <=> ! [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 @ X1))) = $true) => (((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true)))))),
% 0.21/0.29 inference(fool_elimination,[],[f7])).
% 0.21/0.29 thf(f9,plain,(
% 0.21/0.29 (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (in @ (setminus @ X1 @ X0) @ (powerset @ X1))))),
% 0.21/0.29 inference(rectify,[],[f2])).
% 0.21/0.29 thf(f10,plain,(
% 0.21/0.29 ! [X1 : $i,X0 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) => ($true = ((in @ (setminus @ X1 @ X0) @ (powerset @ X1))))) <=> (complementT_lem = $true)),
% 0.21/0.29 inference(fool_elimination,[],[f9])).
% 0.21/0.29 thf(f11,plain,(
% 0.21/0.29 ~(binintersectT_lem => (complementT_lem => (subsetTI => (complementImpComplementIntersect => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (subset @ (setminus @ X1 @ X0) @ (setminus @ X1 @ (binintersect @ X0 @ X2)))))))))),
% 0.21/0.29 inference(rectify,[],[f6])).
% 0.21/0.29 thf(f12,plain,(
% 0.21/0.29 ~((binintersectT_lem = $true) => ((complementT_lem = $true) => ((subsetTI = $true) => ((complementImpComplementIntersect = $true) => ! [X1 : $i,X0 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) => ! [X2 : $i] : (($true = ((in @ X2 @ (powerset @ X1)))) => ($true = ((subset @ (setminus @ X1 @ X0) @ (setminus @ X1 @ (binintersect @ X0 @ X2)))))))))))),
% 0.21/0.29 inference(fool_elimination,[],[f11])).
% 0.21/0.29 thf(f13,plain,(
% 0.21/0.29 (! [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))) => (subset @ X0 @ X2)))) = subsetTI)),
% 0.21/0.29 inference(rectify,[],[f3])).
% 0.21/0.29 thf(f14,plain,(
% 0.21/0.29 ! [X1 : $i,X0 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) => ! [X2 : $i] : (($true = ((in @ X2 @ (powerset @ X1)))) => (! [X3 : $i] : ((((in @ X3 @ X1)) = $true) => ((((in @ X3 @ X0)) = $true) => (((in @ X3 @ X2)) = $true))) => ($true = ((subset @ X0 @ X2)))))) <=> (subsetTI = $true)),
% 0.21/0.29 inference(fool_elimination,[],[f13])).
% 0.21/0.29 thf(f15,plain,(
% 0.21/0.29 (binintersectT_lem = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (in @ (binintersect @ X0 @ X2) @ (powerset @ X1)))))),
% 0.21/0.29 inference(rectify,[],[f1])).
% 0.21/0.29 thf(f16,plain,(
% 0.21/0.29 ! [X1 : $i,X0 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) => ! [X2 : $i] : (($true = ((in @ X2 @ (powerset @ X1)))) => ($true = ((in @ (binintersect @ X0 @ X2) @ (powerset @ X1)))))) <=> (binintersectT_lem = $true)),
% 0.21/0.29 inference(fool_elimination,[],[f15])).
% 0.21/0.29 thf(f17,plain,(
% 0.21/0.29 (complementImpComplementIntersect = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : (((((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ X3 @ (setminus @ X0 @ X1))) != $true)) | (((in @ X3 @ X0)) != $true)) | (((in @ X2 @ (powerset @ X0))) != $true)) | (((in @ X1 @ (powerset @ X0))) != $true))),
% 0.21/0.29 inference(ennf_transformation,[],[f8])).
% 0.21/0.29 thf(f18,plain,(
% 0.21/0.29 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) != $true) | ! [X3 : $i] : ((((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ X3 @ X0)) != $true) | (((in @ X3 @ (setminus @ X0 @ X1))) != $true))) | (((in @ X1 @ (powerset @ X0))) != $true)) <=> (complementImpComplementIntersect = $true)),
% 0.21/0.29 inference(flattening,[],[f17])).
% 0.21/0.29 thf(f19,plain,(
% 0.21/0.29 ! [X1 : $i,X0 : $i] : (($true = ((in @ (setminus @ X1 @ X0) @ (powerset @ X1)))) | ($true != ((in @ X0 @ (powerset @ X1))))) <=> (complementT_lem = $true)),
% 0.21/0.29 inference(ennf_transformation,[],[f10])).
% 0.21/0.29 thf(f20,plain,(
% 0.21/0.29 (binintersectT_lem = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (($true = ((in @ (binintersect @ X0 @ X2) @ (powerset @ X1)))) | ($true != ((in @ X2 @ (powerset @ X1))))) | ($true != ((in @ X0 @ (powerset @ X1)))))),
% 0.21/0.29 inference(ennf_transformation,[],[f16])).
% 0.21/0.29 thf(f21,plain,(
% 0.21/0.29 (((? [X1 : $i,X0 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) & ? [X2 : $i] : (($true != ((subset @ (setminus @ X1 @ X0) @ (setminus @ X1 @ (binintersect @ X0 @ X2))))) & ($true = ((in @ X2 @ (powerset @ X1)))))) & (complementImpComplementIntersect = $true)) & (subsetTI = $true)) & (complementT_lem = $true)) & (binintersectT_lem = $true)),
% 0.21/0.29 inference(ennf_transformation,[],[f12])).
% 0.21/0.29 thf(f22,plain,(
% 0.21/0.29 (complementT_lem = $true) & (complementImpComplementIntersect = $true) & (subsetTI = $true) & (binintersectT_lem = $true) & ? [X1 : $i,X0 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) & ? [X2 : $i] : (($true != ((subset @ (setminus @ X1 @ X0) @ (setminus @ X1 @ (binintersect @ X0 @ X2))))) & ($true = ((in @ X2 @ (powerset @ X1))))))),
% 0.21/0.29 inference(flattening,[],[f21])).
% 0.21/0.29 thf(f23,plain,(
% 0.21/0.29 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((($true = ((subset @ X0 @ X2))) | ? [X3 : $i] : (((((in @ X3 @ X2)) != $true) & (((in @ X3 @ X0)) = $true)) & (((in @ X3 @ X1)) = $true))) | ($true != ((in @ X2 @ (powerset @ X1))))) | ($true != ((in @ X0 @ (powerset @ X1))))) <=> (subsetTI = $true)),
% 0.21/0.29 inference(ennf_transformation,[],[f14])).
% 0.21/0.29 thf(f24,plain,(
% 0.21/0.29 ! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) | ! [X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ X2)) != $true) & (((in @ X3 @ X1)) = $true) & (((in @ X3 @ X0)) = $true)) | ($true != ((in @ X2 @ (powerset @ X1)))) | ($true = ((subset @ X0 @ X2))))) <=> (subsetTI = $true)),
% 0.21/0.29 inference(flattening,[],[f23])).
% 0.21/0.29 thf(f25,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) != $true) | ! [X3 : $i] : ((((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ X3 @ X0)) != $true) | (((in @ X3 @ (setminus @ X0 @ X1))) != $true))) | (((in @ X1 @ (powerset @ X0))) != $true)) | (complementImpComplementIntersect != $true)) & ((complementImpComplementIntersect = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) & ? [X3 : $i] : ((((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) != $true) & (((in @ X3 @ X0)) = $true) & (((in @ X3 @ (setminus @ X0 @ X1))) = $true))) & (((in @ X1 @ (powerset @ X0))) = $true)))),
% 0.21/0.29 inference(nnf_transformation,[],[f18])).
% 0.21/0.29 thf(f26,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) != $true) | ! [X3 : $i] : ((((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ X3 @ X0)) != $true) | (((in @ X3 @ (setminus @ X0 @ X1))) != $true))) | (((in @ X1 @ (powerset @ X0))) != $true)) | (complementImpComplementIntersect != $true)) & ((complementImpComplementIntersect = $true) | ? [X4 : $i,X5 : $i] : (? [X6 : $i] : (($true = ((in @ X6 @ (powerset @ X4)))) & ? [X7 : $i] : (($true != ((in @ X7 @ (setminus @ X4 @ (binintersect @ X5 @ X6))))) & ($true = ((in @ X7 @ X4))) & ($true = ((in @ X7 @ (setminus @ X4 @ X5)))))) & ($true = ((in @ X5 @ (powerset @ X4))))))),
% 0.21/0.29 inference(rectify,[],[f25])).
% 0.21/0.29 thf(f27,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) != $true) | ! [X3 : $i] : ((((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ X3 @ X0)) != $true) | (((in @ X3 @ (setminus @ X0 @ X1))) != $true))) | (((in @ X1 @ (powerset @ X0))) != $true)) | (complementImpComplementIntersect != $true)) & ((complementImpComplementIntersect = $true) | ((($true = ((in @ sK2 @ (powerset @ sK0)))) & ((((in @ sK3 @ (setminus @ sK0 @ (binintersect @ sK1 @ sK2)))) != $true) & ($true = ((in @ sK3 @ sK0))) & ($true = ((in @ sK3 @ (setminus @ sK0 @ sK1)))))) & ($true = ((in @ sK1 @ (powerset @ sK0))))))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X4,sK0),skolemize(X5,sK1),skolemize(X6,sK2),skolemize(X7,sK3)],[f26])).
% 0.21/0.29 thf(f28,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) | ! [X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ X2)) != $true) & (((in @ X3 @ X1)) = $true) & (((in @ X3 @ X0)) = $true)) | ($true != ((in @ X2 @ (powerset @ X1)))) | ($true = ((subset @ X0 @ X2))))) | (subsetTI != $true)) & ((subsetTI = $true) | ? [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) & ? [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X2)) = $true) | (((in @ X3 @ X1)) != $true) | (((in @ X3 @ X0)) != $true)) & ($true = ((in @ X2 @ (powerset @ X1)))) & ($true != ((subset @ X0 @ X2))))))),
% 0.21/0.29 inference(nnf_transformation,[],[f24])).
% 0.21/0.29 thf(f29,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) | ! [X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ X2)) != $true) & (((in @ X3 @ X1)) = $true) & (((in @ X3 @ X0)) = $true)) | ($true != ((in @ X2 @ (powerset @ X1)))) | ($true = ((subset @ X0 @ X2))))) | (subsetTI != $true)) & ((subsetTI = $true) | ? [X4 : $i,X5 : $i] : (($true = ((in @ X4 @ (powerset @ X5)))) & ? [X6 : $i] : (! [X7 : $i] : (($true = ((in @ X7 @ X6))) | ($true != ((in @ X7 @ X5))) | ($true != ((in @ X7 @ X4)))) & ($true = ((in @ X6 @ (powerset @ X5)))) & ($true != ((subset @ X4 @ X6))))))),
% 0.21/0.29 inference(rectify,[],[f28])).
% 0.21/0.29 thf(f30,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) | ! [X2 : $i] : ((($true != ((in @ (sK4 @ X2 @ X1 @ X0) @ X2))) & ($true = ((in @ (sK4 @ X2 @ X1 @ X0) @ X1))) & ($true = ((in @ (sK4 @ X2 @ X1 @ X0) @ X0)))) | ($true != ((in @ X2 @ (powerset @ X1)))) | ($true = ((subset @ X0 @ X2))))) | (subsetTI != $true)) & ((subsetTI = $true) | (($true = ((in @ sK5 @ (powerset @ sK6)))) & (! [X7 : $i] : (($true = ((in @ X7 @ sK7))) | ($true != ((in @ X7 @ sK6))) | ($true != ((in @ X7 @ sK5)))) & ($true = ((in @ sK7 @ (powerset @ sK6)))) & ($true != ((subset @ sK5 @ sK7))))))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK5,sK6,sK7]),skolemize(X3,sK4 @ X2 @ X1 @ X0),skolemize(X4,sK5),skolemize(X5,sK6),skolemize(X6,sK7)],[f29])).
% 0.21/0.29 thf(f31,plain,(
% 0.21/0.29 ((binintersectT_lem = $true) | ? [X1 : $i,X0 : $i] : (? [X2 : $i] : (($true != ((in @ (binintersect @ X0 @ X2) @ (powerset @ X1)))) & ($true = ((in @ X2 @ (powerset @ X1))))) & ($true = ((in @ X0 @ (powerset @ X1)))))) & (! [X1 : $i,X0 : $i] : (! [X2 : $i] : (($true = ((in @ (binintersect @ X0 @ X2) @ (powerset @ X1)))) | ($true != ((in @ X2 @ (powerset @ X1))))) | ($true != ((in @ X0 @ (powerset @ X1))))) | (binintersectT_lem != $true))),
% 0.21/0.29 inference(nnf_transformation,[],[f20])).
% 0.21/0.29 thf(f32,plain,(
% 0.21/0.29 ((binintersectT_lem = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ (binintersect @ X1 @ X2) @ (powerset @ X0))) != $true) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true))) & (! [X3 : $i,X4 : $i] : (! [X5 : $i] : (($true = ((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)))) | ($true != ((in @ X5 @ (powerset @ X3))))) | ($true != ((in @ X4 @ (powerset @ X3))))) | (binintersectT_lem != $true))),
% 0.21/0.29 inference(rectify,[],[f31])).
% 0.21/0.29 thf(f33,plain,(
% 0.21/0.29 ((binintersectT_lem = $true) | ((($true != ((in @ (binintersect @ sK9 @ sK10) @ (powerset @ sK8)))) & ($true = ((in @ sK10 @ (powerset @ sK8))))) & ($true = ((in @ sK9 @ (powerset @ sK8)))))) & (! [X3 : $i,X4 : $i] : (! [X5 : $i] : (($true = ((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)))) | ($true != ((in @ X5 @ (powerset @ X3))))) | ($true != ((in @ X4 @ (powerset @ X3))))) | (binintersectT_lem != $true))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10)],[f32])).
% 0.21/0.29 thf(f34,plain,(
% 0.21/0.29 (complementT_lem = $true) & (complementImpComplementIntersect = $true) & (subsetTI = $true) & (binintersectT_lem = $true) & ? [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) & ? [X2 : $i] : ((((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) != $true) & (((in @ X2 @ (powerset @ X0))) = $true)))),
% 0.21/0.29 inference(rectify,[],[f22])).
% 0.21/0.29 thf(f35,plain,(
% 0.21/0.29 (complementT_lem = $true) & (complementImpComplementIntersect = $true) & (subsetTI = $true) & (binintersectT_lem = $true) & (($true = ((in @ sK12 @ (powerset @ sK11)))) & (($true != ((subset @ (setminus @ sK11 @ sK12) @ (setminus @ sK11 @ (binintersect @ sK12 @ sK13))))) & ($true = ((in @ sK13 @ (powerset @ sK11))))))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13)],[f34])).
% 0.21/0.29 thf(f36,plain,(
% 0.21/0.29 (! [X1 : $i,X0 : $i] : (($true = ((in @ (setminus @ X1 @ X0) @ (powerset @ X1)))) | ($true != ((in @ X0 @ (powerset @ X1))))) | (complementT_lem != $true)) & ((complementT_lem = $true) | ? [X1 : $i,X0 : $i] : (($true != ((in @ (setminus @ X1 @ X0) @ (powerset @ X1)))) & ($true = ((in @ X0 @ (powerset @ X1))))))),
% 0.21/0.29 inference(nnf_transformation,[],[f19])).
% 0.21/0.29 thf(f37,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : ((((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $true) | (((in @ X1 @ (powerset @ X0))) != $true)) | (complementT_lem != $true)) & ((complementT_lem = $true) | ? [X2 : $i,X3 : $i] : (($true != ((in @ (setminus @ X2 @ X3) @ (powerset @ X2)))) & ($true = ((in @ X3 @ (powerset @ X2))))))),
% 0.21/0.29 inference(rectify,[],[f36])).
% 0.21/0.29 thf(f38,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : ((((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $true) | (((in @ X1 @ (powerset @ X0))) != $true)) | (complementT_lem != $true)) & ((complementT_lem = $true) | (($true != ((in @ (setminus @ sK14 @ sK15) @ (powerset @ sK14)))) & (((in @ sK15 @ (powerset @ sK14))) = $true)))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X2,sK14),skolemize(X3,sK15)],[f37])).
% 0.21/0.29 thf(f44,plain,(
% 0.21/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((complementImpComplementIntersect != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ X3 @ (setminus @ X0 @ X1))) != $true) | (((in @ X3 @ X0)) != $true) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f27])).
% 0.21/0.29 thf(f49,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((subset @ X0 @ X2))) | (subsetTI != $true) | ($true = ((in @ (sK4 @ X2 @ X1 @ X0) @ X0))) | ($true != ((in @ X2 @ (powerset @ X1)))) | ($true != ((in @ X0 @ (powerset @ X1))))) )),
% 0.21/0.29 inference(cnf_transformation,[],[f30])).
% 0.21/0.29 thf(f50,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((subsetTI != $true) | ($true != ((in @ X2 @ (powerset @ X1)))) | ($true = ((in @ (sK4 @ X2 @ X1 @ X0) @ X1))) | ($true = ((subset @ X0 @ X2))) | ($true != ((in @ X0 @ (powerset @ X1))))) )),
% 0.21/0.29 inference(cnf_transformation,[],[f30])).
% 0.21/0.29 thf(f51,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK4 @ X2 @ X1 @ X0) @ X2))) | ($true != ((in @ X2 @ (powerset @ X1)))) | ($true != ((in @ X0 @ (powerset @ X1)))) | ($true = ((subset @ X0 @ X2))) | (subsetTI != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f30])).
% 0.21/0.29 thf(f52,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((binintersectT_lem != $true) | ($true != ((in @ X4 @ (powerset @ X3)))) | ($true != ((in @ X5 @ (powerset @ X3)))) | ($true = ((in @ (binintersect @ X4 @ X5) @ (powerset @ X3))))) )),
% 0.21/0.29 inference(cnf_transformation,[],[f33])).
% 0.21/0.29 thf(f56,plain,(
% 0.21/0.29 ($true = ((in @ sK13 @ (powerset @ sK11))))),
% 0.21/0.29 inference(cnf_transformation,[],[f35])).
% 0.21/0.29 thf(f57,plain,(
% 0.21/0.29 ($true != ((subset @ (setminus @ sK11 @ sK12) @ (setminus @ sK11 @ (binintersect @ sK12 @ sK13)))))),
% 0.21/0.29 inference(cnf_transformation,[],[f35])).
% 0.21/0.29 thf(f58,plain,(
% 0.21/0.29 ($true = ((in @ sK12 @ (powerset @ sK11))))),
% 0.21/0.29 inference(cnf_transformation,[],[f35])).
% 0.21/0.29 thf(f59,plain,(
% 0.21/0.29 (binintersectT_lem = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f35])).
% 0.21/0.29 thf(f60,plain,(
% 0.21/0.29 (subsetTI = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f35])).
% 0.21/0.29 thf(f61,plain,(
% 0.21/0.29 (complementImpComplementIntersect = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f35])).
% 0.21/0.29 thf(f62,plain,(
% 0.21/0.29 (complementT_lem = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f35])).
% 0.21/0.29 thf(f65,plain,(
% 0.21/0.29 ( ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) | (complementT_lem != $true) | (((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f38])).
% 0.21/0.29 thf(f68,definition,(
% 0.21/0.29 spl16_1 <=> (complementImpComplementIntersect = $true)),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition])).
% 0.21/0.29 thf(f71,plain,(
% 0.21/0.29 spl16_1),
% 0.21/0.29 inference(avatar_split_clause,[],[f61,f68])).
% 0.21/0.29 thf(f78,definition,(
% 0.21/0.29 spl16_3 <=> ($true = ((in @ sK13 @ (powerset @ sK11))))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition])).
% 0.21/0.29 thf(f80,plain,(
% 0.21/0.29 ($true = ((in @ sK13 @ (powerset @ sK11)))) | ~spl16_3),
% 0.21/0.29 inference(avatar_component_clause,[],[f78])).
% 0.21/0.29 thf(f81,plain,(
% 0.21/0.29 spl16_3),
% 0.21/0.29 inference(avatar_split_clause,[],[f56,f78])).
% 0.21/0.29 thf(f83,definition,(
% 0.21/0.29 spl16_4 <=> ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $true))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl16_4])],[avatar_definition])).
% 0.21/0.29 thf(f84,plain,(
% 0.21/0.29 ( ! [X0 : $i,X1 : $i] : ((((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $true) | (((in @ X1 @ (powerset @ X0))) != $true)) ) | ~spl16_4),
% 0.21/0.29 inference(avatar_component_clause,[],[f83])).
% 0.21/0.29 thf(f86,definition,(
% 0.21/0.29 spl16_5 <=> (complementT_lem = $true)),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl16_5])],[avatar_definition])).
% 0.21/0.29 thf(f89,plain,(
% 0.21/0.29 spl16_4 | ~spl16_5),
% 0.21/0.29 inference(avatar_split_clause,[],[f65,f86,f83])).
% 0.21/0.29 thf(f95,definition,(
% 0.21/0.29 spl16_7 <=> (subsetTI = $true)),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl16_7])],[avatar_definition])).
% 0.21/0.29 thf(f109,definition,(
% 0.21/0.29 spl16_10 <=> (binintersectT_lem = $true)),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl16_10])],[avatar_definition])).
% 0.21/0.29 thf(f114,definition,(
% 0.21/0.29 spl16_11 <=> ! [X0 : $i,X3 : $i,X2 : $i,X1 : $i] : ((((in @ X2 @ (powerset @ X0))) != $true) | (((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ X3 @ X0)) != $true) | (((in @ X3 @ (setminus @ X0 @ X1))) != $true))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl16_11])],[avatar_definition])).
% 0.21/0.29 thf(f115,plain,(
% 0.21/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ X3 @ (setminus @ X0 @ X1))) != $true) | (((in @ X3 @ X0)) != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ X1 @ (powerset @ X0))) != $true)) ) | ~spl16_11),
% 0.21/0.29 inference(avatar_component_clause,[],[f114])).
% 0.21/0.29 thf(f116,plain,(
% 0.21/0.29 spl16_11 | ~spl16_1),
% 0.21/0.29 inference(avatar_split_clause,[],[f44,f68,f114])).
% 0.21/0.29 thf(f117,plain,(
% 0.21/0.29 spl16_10),
% 0.21/0.29 inference(avatar_split_clause,[],[f59,f109])).
% 0.21/0.29 thf(f123,plain,(
% 0.21/0.29 spl16_7),
% 0.21/0.29 inference(avatar_split_clause,[],[f60,f95])).
% 0.21/0.29 thf(f125,definition,(
% 0.21/0.29 spl16_13 <=> ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X2 @ (powerset @ X1)))) | ($true != ((in @ X0 @ (powerset @ X1)))) | ($true = ((subset @ X0 @ X2))) | ($true = ((in @ (sK4 @ X2 @ X1 @ X0) @ X1))))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl16_13])],[avatar_definition])).
% 0.21/0.29 thf(f126,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK4 @ X2 @ X1 @ X0) @ X1))) | ($true != ((in @ X0 @ (powerset @ X1)))) | ($true = ((subset @ X0 @ X2))) | ($true != ((in @ X2 @ (powerset @ X1))))) ) | ~spl16_13),
% 0.21/0.29 inference(avatar_component_clause,[],[f125])).
% 0.21/0.29 thf(f127,plain,(
% 0.21/0.29 ~spl16_7 | spl16_13),
% 0.21/0.29 inference(avatar_split_clause,[],[f50,f125,f95])).
% 0.21/0.29 thf(f128,plain,(
% 0.21/0.29 spl16_5),
% 0.21/0.29 inference(avatar_split_clause,[],[f62,f86])).
% 0.21/0.29 thf(f140,definition,(
% 0.21/0.29 spl16_16 <=> ($true = ((subset @ (setminus @ sK11 @ sK12) @ (setminus @ sK11 @ (binintersect @ sK12 @ sK13)))))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl16_16])],[avatar_definition])).
% 0.21/0.29 thf(f142,plain,(
% 0.21/0.29 ($true != ((subset @ (setminus @ sK11 @ sK12) @ (setminus @ sK11 @ (binintersect @ sK12 @ sK13))))) | spl16_16),
% 0.21/0.29 inference(avatar_component_clause,[],[f140])).
% 0.21/0.29 thf(f143,plain,(
% 0.21/0.29 ~spl16_16),
% 0.21/0.29 inference(avatar_split_clause,[],[f57,f140])).
% 0.21/0.29 thf(f164,definition,(
% 0.21/0.29 spl16_21 <=> ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK4 @ X2 @ X1 @ X0) @ X2))) | ($true = ((subset @ X0 @ X2))) | ($true != ((in @ X0 @ (powerset @ X1)))) | ($true != ((in @ X2 @ (powerset @ X1)))))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl16_21])],[avatar_definition])).
% 0.21/0.29 thf(f165,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK4 @ X2 @ X1 @ X0) @ X2))) | ($true != ((in @ X2 @ (powerset @ X1)))) | ($true != ((in @ X0 @ (powerset @ X1)))) | ($true = ((subset @ X0 @ X2)))) ) | ~spl16_21),
% 0.21/0.29 inference(avatar_component_clause,[],[f164])).
% 0.21/0.29 thf(f166,plain,(
% 0.21/0.29 spl16_21 | ~spl16_7),
% 0.21/0.29 inference(avatar_split_clause,[],[f51,f95,f164])).
% 0.21/0.29 thf(f168,definition,(
% 0.21/0.29 spl16_22 <=> ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((subset @ X0 @ X2))) | ($true != ((in @ X0 @ (powerset @ X1)))) | ($true != ((in @ X2 @ (powerset @ X1)))) | ($true = ((in @ (sK4 @ X2 @ X1 @ X0) @ X0))))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl16_22])],[avatar_definition])).
% 0.21/0.29 thf(f169,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK4 @ X2 @ X1 @ X0) @ X0))) | ($true = ((subset @ X0 @ X2))) | ($true != ((in @ X2 @ (powerset @ X1)))) | ($true != ((in @ X0 @ (powerset @ X1))))) ) | ~spl16_22),
% 0.21/0.29 inference(avatar_component_clause,[],[f168])).
% 0.21/0.29 thf(f170,plain,(
% 0.21/0.29 spl16_22 | ~spl16_7),
% 0.21/0.29 inference(avatar_split_clause,[],[f49,f95,f168])).
% 0.21/0.29 thf(f172,definition,(
% 0.21/0.29 spl16_23 <=> ($true = ((in @ sK12 @ (powerset @ sK11))))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl16_23])],[avatar_definition])).
% 0.21/0.29 thf(f174,plain,(
% 0.21/0.29 ($true = ((in @ sK12 @ (powerset @ sK11)))) | ~spl16_23),
% 0.21/0.29 inference(avatar_component_clause,[],[f172])).
% 0.21/0.29 thf(f175,plain,(
% 0.21/0.29 spl16_23),
% 0.21/0.29 inference(avatar_split_clause,[],[f58,f172])).
% 0.21/0.29 thf(f182,definition,(
% 0.21/0.29 spl16_25 <=> ! [X4 : $i,X5 : $i,X3 : $i] : (($true != ((in @ X4 @ (powerset @ X3)))) | ($true = ((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)))) | ($true != ((in @ X5 @ (powerset @ X3)))))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl16_25])],[avatar_definition])).
% 0.21/0.29 thf(f183,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = ((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)))) | ($true != ((in @ X5 @ (powerset @ X3)))) | ($true != ((in @ X4 @ (powerset @ X3))))) ) | ~spl16_25),
% 0.21/0.29 inference(avatar_component_clause,[],[f182])).
% 0.21/0.29 thf(f184,plain,(
% 0.21/0.29 spl16_25 | ~spl16_10),
% 0.21/0.29 inference(avatar_split_clause,[],[f52,f109,f182])).
% 0.21/0.29 thf(f205,plain,(
% 0.21/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)))) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true != $true) | ($true != ((in @ (sK4 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ X1)))) | (((subset @ X4 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ X4 @ (powerset @ X3)))) | ($true != ((in @ (sK4 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ X4) @ X0)))) ) | (~spl16_11 | ~spl16_21)),
% 0.21/0.29 inference(superposition,[],[f165,f115])).
% 0.21/0.29 thf(f206,plain,(
% 0.21/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != ((in @ (sK4 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ X1)))) | (((subset @ X4 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ X4 @ (powerset @ X3)))) | ($true != ((in @ (sK4 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ X4) @ X0))) | ($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)))) | (((in @ X1 @ (powerset @ X0))) != $true)) ) | (~spl16_11 | ~spl16_21)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f205])).
% 0.21/0.29 thf(f233,plain,(
% 0.21/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK4 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ (setminus @ X0 @ X1)) @ X0))) | ($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)))) | (((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | ($true != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ X1) @ (powerset @ X3))) != $true) | (((in @ (setminus @ X0 @ X1) @ (powerset @ X3))) != $true) | (((in @ X1 @ (powerset @ X0))) != $true) | (((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | ($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3))))) ) | (~spl16_11 | ~spl16_21 | ~spl16_22)),
% 0.21/0.29 inference(superposition,[],[f206,f169])).
% 0.21/0.29 thf(f236,plain,(
% 0.21/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ X1) @ (powerset @ X3))) != $true) | ($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)))) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ (sK4 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ (setminus @ X0 @ X1)) @ X0))) | ($true != $true)) ) | (~spl16_11 | ~spl16_21 | ~spl16_22)),
% 0.21/0.29 inference(duplicate_literal_removal,[],[f233])).
% 0.21/0.29 thf(f237,plain,(
% 0.21/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK4 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ (setminus @ X0 @ X1)) @ X0))) | (((in @ X2 @ (powerset @ X0))) != $true) | (((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ X1) @ (powerset @ X3))) != $true) | ($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3))))) ) | (~spl16_11 | ~spl16_21 | ~spl16_22)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f236])).
% 0.21/0.29 thf(f255,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | ($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0)))) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) != $true) | (((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | ($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))))) ) | (~spl16_11 | ~spl16_13 | ~spl16_21 | ~spl16_22)),
% 0.21/0.29 inference(superposition,[],[f237,f126])).
% 0.21/0.29 thf(f256,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) | (((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | ($true != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) != $true) | ($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))))) ) | (~spl16_11 | ~spl16_13 | ~spl16_21 | ~spl16_22)),
% 0.21/0.29 inference(duplicate_literal_removal,[],[f255])).
% 0.21/0.29 thf(f257,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) != $true) | ($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0)))) | (((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ X2 @ (powerset @ X0))) != $true)) ) | (~spl16_11 | ~spl16_13 | ~spl16_21 | ~spl16_22)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f256])).
% 0.21/0.29 thf(f259,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | ($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0)))) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ X2 @ (powerset @ X0))) != $true)) ) | (~spl16_4 | ~spl16_11 | ~spl16_13 | ~spl16_21 | ~spl16_22)),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f257,f84])).
% 0.21/0.29 thf(f270,plain,(
% 0.21/0.29 ($true != ((in @ sK13 @ (powerset @ sK11)))) | ($true != $true) | ($true != ((in @ (setminus @ sK11 @ (binintersect @ sK12 @ sK13)) @ (powerset @ sK11)))) | ($true != ((in @ sK12 @ (powerset @ sK11)))) | (~spl16_4 | ~spl16_11 | ~spl16_13 | spl16_16 | ~spl16_21 | ~spl16_22)),
% 0.21/0.29 inference(superposition,[],[f142,f259])).
% 0.21/0.29 thf(f271,plain,(
% 0.21/0.29 ($true != ((in @ sK13 @ (powerset @ sK11)))) | ($true != ((in @ (setminus @ sK11 @ (binintersect @ sK12 @ sK13)) @ (powerset @ sK11)))) | ($true != ((in @ sK12 @ (powerset @ sK11)))) | (~spl16_4 | ~spl16_11 | ~spl16_13 | spl16_16 | ~spl16_21 | ~spl16_22)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f270])).
% 0.21/0.29 thf(f272,plain,(
% 0.21/0.29 ($true != ((in @ (setminus @ sK11 @ (binintersect @ sK12 @ sK13)) @ (powerset @ sK11)))) | ($true != ((in @ sK12 @ (powerset @ sK11)))) | (~spl16_3 | ~spl16_4 | ~spl16_11 | ~spl16_13 | spl16_16 | ~spl16_21 | ~spl16_22)),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f271,f80])).
% 0.21/0.29 thf(f273,plain,(
% 0.21/0.29 ($true != ((in @ (setminus @ sK11 @ (binintersect @ sK12 @ sK13)) @ (powerset @ sK11)))) | (~spl16_3 | ~spl16_4 | ~spl16_11 | ~spl16_13 | spl16_16 | ~spl16_21 | ~spl16_22 | ~spl16_23)),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f272,f174])).
% 0.21/0.29 thf(f275,definition,(
% 0.21/0.29 spl16_30 <=> ($true = ((in @ (setminus @ sK11 @ (binintersect @ sK12 @ sK13)) @ (powerset @ sK11))))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl16_30])],[avatar_definition])).
% 0.21/0.29 thf(f277,plain,(
% 0.21/0.29 ($true != ((in @ (setminus @ sK11 @ (binintersect @ sK12 @ sK13)) @ (powerset @ sK11)))) | spl16_30),
% 0.21/0.29 inference(avatar_component_clause,[],[f275])).
% 0.21/0.29 thf(f278,plain,(
% 0.21/0.29 ~spl16_30 | ~spl16_3 | ~spl16_4 | ~spl16_11 | ~spl16_13 | spl16_16 | ~spl16_21 | ~spl16_22 | ~spl16_23),
% 0.21/0.29 inference(avatar_split_clause,[],[f273,f172,f168,f164,f140,f125,f114,f83,f78,f275])).
% 0.21/0.29 thf(f279,plain,(
% 0.21/0.29 ($true != $true) | ($true != ((in @ (binintersect @ sK12 @ sK13) @ (powerset @ sK11)))) | (~spl16_4 | spl16_30)),
% 0.21/0.29 inference(superposition,[],[f277,f84])).
% 0.21/0.29 thf(f280,plain,(
% 0.21/0.29 ($true != ((in @ (binintersect @ sK12 @ sK13) @ (powerset @ sK11)))) | (~spl16_4 | spl16_30)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f279])).
% 0.21/0.29 thf(f282,definition,(
% 0.21/0.29 spl16_31 <=> ($true = ((in @ (binintersect @ sK12 @ sK13) @ (powerset @ sK11))))),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl16_31])],[avatar_definition])).
% 0.21/0.29 thf(f284,plain,(
% 0.21/0.29 ($true != ((in @ (binintersect @ sK12 @ sK13) @ (powerset @ sK11)))) | spl16_31),
% 0.21/0.29 inference(avatar_component_clause,[],[f282])).
% 0.21/0.29 thf(f285,plain,(
% 0.21/0.29 ~spl16_31 | ~spl16_4 | spl16_30),
% 0.21/0.29 inference(avatar_split_clause,[],[f280,f275,f83,f282])).
% 0.21/0.29 thf(f332,plain,(
% 0.21/0.29 ($true != ((in @ sK13 @ (powerset @ sK11)))) | ($true != $true) | ($true != ((in @ sK12 @ (powerset @ sK11)))) | (~spl16_25 | spl16_31)),
% 0.21/0.29 inference(superposition,[],[f284,f183])).
% 0.21/0.29 thf(f333,plain,(
% 0.21/0.29 ($true != ((in @ sK12 @ (powerset @ sK11)))) | ($true != ((in @ sK13 @ (powerset @ sK11)))) | (~spl16_25 | spl16_31)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f332])).
% 0.21/0.29 thf(f334,plain,(
% 0.21/0.29 ($true != ((in @ sK13 @ (powerset @ sK11)))) | (~spl16_23 | ~spl16_25 | spl16_31)),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f333,f174])).
% 0.21/0.29 thf(f335,plain,(
% 0.21/0.29 $false | (~spl16_3 | ~spl16_23 | ~spl16_25 | spl16_31)),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f334,f80])).
% 0.21/0.29 thf(f336,plain,(
% 0.21/0.29 ~spl16_3 | ~spl16_23 | ~spl16_25 | spl16_31),
% 0.21/0.29 inference(avatar_contradiction_clause,[],[f335])).
% 0.21/0.29 cnf(s1, plain, spl16_1, inference(sat_conversion,[],[f71])).
% 0.21/0.29 cnf(s3, plain, spl16_3, inference(sat_conversion,[],[f81])).
% 0.21/0.29 cnf(s4, plain, spl16_4 | ~spl16_5, inference(sat_conversion,[],[f89])).
% 0.21/0.29 cnf(s8, plain, ~spl16_1 | spl16_11, inference(sat_conversion,[],[f116])).
% 0.21/0.29 cnf(s9, plain, spl16_10, inference(sat_conversion,[],[f117])).
% 0.21/0.29 cnf(s11, plain, spl16_7, inference(sat_conversion,[],[f123])).
% 0.21/0.29 cnf(s12, plain, ~spl16_7 | spl16_13, inference(sat_conversion,[],[f127])).
% 0.21/0.29 cnf(s13, plain, spl16_5, inference(sat_conversion,[],[f128])).
% 0.21/0.29 cnf(s16, plain, ~spl16_16, inference(sat_conversion,[],[f143])).
% 0.21/0.29 cnf(s21, plain, ~spl16_7 | spl16_21, inference(sat_conversion,[],[f166])).
% 0.21/0.29 cnf(s22, plain, ~spl16_7 | spl16_22, inference(sat_conversion,[],[f170])).
% 0.21/0.29 cnf(s23, plain, spl16_23, inference(sat_conversion,[],[f175])).
% 0.21/0.29 cnf(s25, plain, ~spl16_10 | spl16_25, inference(sat_conversion,[],[f184])).
% 0.21/0.29 cnf(s30, plain, ~spl16_3 | ~spl16_4 | ~spl16_11 | ~spl16_13 | spl16_16 | ~spl16_21 | ~spl16_22 | ~spl16_23 | ~spl16_30, inference(sat_conversion,[],[f278])).
% 0.21/0.29 cnf(s31, plain, ~spl16_4 | spl16_30 | ~spl16_31, inference(sat_conversion,[],[f285])).
% 0.21/0.29 cnf(s32, plain, ~spl16_3 | ~spl16_23 | ~spl16_25 | spl16_31, inference(sat_conversion,[],[f336])).
% 0.21/0.29 cnf(s33, plain, spl16_22, inference(rat,[],[s22,s11])).
% 0.21/0.29 cnf(s34, plain, spl16_21, inference(rat,[],[s21,s11])).
% 0.21/0.29 cnf(s35, plain, spl16_13, inference(rat,[],[s12,s11])).
% 0.21/0.29 cnf(s37, plain, spl16_25, inference(rat,[],[s25,s9])).
% 0.21/0.29 cnf(s38, plain, spl16_4, inference(rat,[],[s4,s13])).
% 0.21/0.29 cnf(s39, plain, spl16_31, inference(rat,[],[s32,s37,s23,s3])).
% 0.21/0.29 cnf(s41, plain, spl16_30, inference(rat,[],[s31,s38,s39])).
% 0.21/0.29 cnf(s42, plain, ~spl16_11, inference(rat,[],[s30,s3,s23,s33,s34,s16,s35,s38,s41])).
% 0.21/0.29 cnf(s43, plain, ~spl16_1, inference(rat,[],[s8,s42])).
% 0.21/0.29 cnf(s49, plain, $false, inference(rat,[],[s1,s43])).
% 0.21/0.29 thf(f337,plain,(
% 0.21/0.29 $false),
% 0.21/0.29 inference(avatar_sat_refutation,[],[s49])).
% 0.21/0.29 % SZS output end Proof for theBenchmark
% 0.21/0.29 % (1732726)------------------------------
% 0.21/0.29 % (1732726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (1732726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (1732726)CaDiCaL version: 2.1.3
% 0.21/0.29 % (1732726)Termination reason: Refutation
% 0.21/0.29 % (1732726)Time elapsed: 0.016 s
% 0.21/0.29 % (1732726)Peak memory usage: 13 MB
% 0.21/0.29 % (1732726)Instructions burned: 52 (million)
% 0.21/0.29 % (1732718)Success in time 0.046 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------