%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU737^2 : 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 : n012.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 08:31:03 AM UTC 2026
% Result : Theorem 0.09s 0.23s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU737^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.13 % Computer : n012.cluster.edu
% 0.09/0.13 % Model : x86_64 x86_64
% 0.09/0.13 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.13 % Memory : 8046.5625MB
% 0.09/0.13 % OS : Linux 6.8.0-71-generic
% 0.09/0.13 % CPULimit : 300
% 0.09/0.13 % WCLimit : 300
% 0.09/0.13 % DateTime : Tue Sep 29 14:18:34 UTC 2026
% 0.09/0.13 % CPUTime :
% 0.09/0.13 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 Running higher-order theorem proving
% 0.09/0.17 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
% 0.09/0.23 % (173117)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.23 % (173123)lrs+10_16_si=on:nwc=1.5:random_seed=194779765:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.09/0.23 % (173124)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4077622146:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.09/0.23 % (173124)Instruction limit reached!
% 0.09/0.23 % (173124)------------------------------
% 0.09/0.23 % (173124)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.23 % (173124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.23 % (173124)CaDiCaL version: 2.1.3
% 0.09/0.23 % (173124)Termination reason: Instruction limit
% 0.09/0.23 % (173124)Termination phase: Saturation
% 0.09/0.23 % (173124)Time elapsed: 0.002 s
% 0.09/0.23 % (173124)Peak memory usage: 12 MB
% 0.09/0.23 % (173124)Instructions burned: 4 (million)
% 0.09/0.23 % (173123)Instruction limit reached!
% 0.09/0.23 % (173123)------------------------------
% 0.09/0.23 % (173123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.23 % (173123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.23 % (173123)CaDiCaL version: 2.1.3
% 0.09/0.23 % (173123)Termination reason: Instruction limit
% 0.09/0.23 % (173123)Termination phase: Saturation
% 0.09/0.23 % (173123)Time elapsed: 0.009 s
% 0.09/0.23 % (173123)Peak memory usage: 12 MB
% 0.09/0.23 % (173123)Instructions burned: 19 (million)
% 0.09/0.23 % (173128)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.09/0.23 % (173128)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
% 0.09/0.23 % (173125)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=1752200910: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)
% 0.09/0.23 % (173122)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2498072065:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.09/0.23 % (173127)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3176123991:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.09/0.23 % (173126)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1947187101:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.09/0.23 % (173128)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=2622855976:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.09/0.23 % (173131)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=798582139:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.09/0.23 % (173126) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-173117-173126"...
% 0.09/0.23 % (173131)Instruction limit reached!
% 0.09/0.23 % (173131)------------------------------
% 0.09/0.23 % (173131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.23 % (173131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.23 % (173131)CaDiCaL version: 2.1.3
% 0.09/0.23 % (173131)Termination reason: Instruction limit
% 0.09/0.23 % (173131)Termination phase: Saturation
% 0.09/0.23 % (173131)Time elapsed: 0.001 s
% 0.09/0.23 % (173131)Peak memory usage: 11 MB
% 0.09/0.23 % (173131)Instructions burned: 4 (million)
% 0.09/0.23 % (173125) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-173117-173125"...
% 0.09/0.23 % (173126)...printing done.
% 0.09/0.23 % (173126)Refutation found. Thanks to Tanya!
% 0.09/0.23 % SZS status Theorem for theBenchmark
% 0.09/0.23 % SZS output start Proof for theBenchmark
% 0.09/0.23 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.23 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.09/0.23 thf(func_def_1, type, powerset: ($i > $i)).
% 0.09/0.23 thf(func_def_2, type, subset: ($i > $i > $o)).
% 0.09/0.23 thf(func_def_3, type, setminus: ($i > $i > $i)).
% 0.09/0.23 thf(func_def_4, type, complementT_lem: $o).
% 0.09/0.23 thf(func_def_6, type, subsetTI: $o).
% 0.09/0.23 thf(func_def_7, type, contraSubsetComplement: $o).
% 0.09/0.23 thf(func_def_13, type, sK3: ($i > $i > $i > $i)).
% 0.09/0.23 thf(f1,axiom,(
% 0.09/0.23 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = complementT_lem)),
% 0.09/0.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementT_lem)).
% 0.09/0.23 thf(f2,axiom,(
% 0.09/0.23 (subsetTI = ! [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)))))),
% 0.09/0.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTI)).
% 0.09/0.23 thf(f3,axiom,(
% 0.09/0.23 (contraSubsetComplement = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ (setminus @ X0 @ X2)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X2) => (in @ X3 @ (setminus @ X0 @ X1))))))))),
% 0.09/0.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contraSubsetComplement)).
% 0.09/0.23 thf(f4,conjecture,(
% 0.09/0.23 complementT_lem => (subsetTI => (contraSubsetComplement => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ (setminus @ X0 @ X2)) => (subset @ X2 @ (setminus @ X0 @ X1)))))))),
% 0.09/0.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTcontraSubset)).
% 0.09/0.23 thf(f5,negated_conjecture,(
% 0.09/0.23 ~(complementT_lem => (subsetTI => (contraSubsetComplement => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ X1 @ (setminus @ X0 @ X2)) => (subset @ X2 @ (setminus @ X0 @ X1))))))))),
% 0.09/0.23 inference(negated_conjecture,[status(cth)],[f4])).
% 0.09/0.23 thf(f6,plain,(
% 0.09/0.23 (contraSubsetComplement = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ((subset @ X0 @ (setminus @ X1 @ X2)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ X2) => (in @ X3 @ (setminus @ X1 @ X0))))))))),
% 0.09/0.23 inference(rectify,[],[f3])).
% 0.09/0.23 thf(f7,plain,(
% 0.09/0.23 ! [X1 : $i,X0 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) => ((((subset @ X0 @ (setminus @ X1 @ X2))) = $true) => ! [X3 : $i] : ((((in @ X3 @ X1)) = $true) => ((((in @ X3 @ X2)) = $true) => ($true = ((in @ X3 @ (setminus @ X1 @ X0))))))))) <=> (contraSubsetComplement = $true)),
% 0.09/0.23 inference(fool_elimination,[],[f6])).
% 0.09/0.23 thf(f8,plain,(
% 0.09/0.23 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = complementT_lem)),
% 0.09/0.23 inference(rectify,[],[f1])).
% 0.09/0.23 thf(f9,plain,(
% 0.09/0.23 ! [X1 : $i,X0 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => (((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $true)) <=> (complementT_lem = $true)),
% 0.09/0.23 inference(fool_elimination,[],[f8])).
% 0.09/0.23 thf(f10,plain,(
% 0.09/0.23 ~(complementT_lem => (subsetTI => (contraSubsetComplement => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ((subset @ X0 @ (setminus @ X1 @ X2)) => (subset @ X2 @ (setminus @ X1 @ X0))))))))),
% 0.09/0.23 inference(rectify,[],[f5])).
% 0.09/0.23 thf(f11,plain,(
% 0.09/0.23 ~((complementT_lem = $true) => ((subsetTI = $true) => ((contraSubsetComplement = $true) => ! [X1 : $i,X0 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) => ((((subset @ X0 @ (setminus @ X1 @ X2))) = $true) => ($true = ((subset @ X2 @ (setminus @ X1 @ X0))))))))))),
% 0.09/0.23 inference(fool_elimination,[],[f10])).
% 0.09/0.23 thf(f12,plain,(
% 0.09/0.23 (subsetTI = ! [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)))))),
% 0.09/0.23 inference(rectify,[],[f2])).
% 0.09/0.23 thf(f13,plain,(
% 0.09/0.23 ! [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)) = $true))) => ($true = ((subset @ X0 @ X2)))))) <=> (subsetTI = $true)),
% 0.09/0.23 inference(fool_elimination,[],[f12])).
% 0.09/0.23 thf(f14,plain,(
% 0.09/0.23 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((! [X3 : $i] : ((($true = ((in @ X3 @ (setminus @ X1 @ X0)))) | (((in @ X3 @ X2)) != $true)) | (((in @ X3 @ X1)) != $true)) | (((subset @ X0 @ (setminus @ X1 @ X2))) != $true)) | (((in @ X2 @ (powerset @ X1))) != $true)) | (((in @ X0 @ (powerset @ X1))) != $true)) <=> (contraSubsetComplement = $true)),
% 0.09/0.23 inference(ennf_transformation,[],[f7])).
% 0.09/0.23 thf(f15,plain,(
% 0.09/0.23 ! [X1 : $i,X0 : $i] : ((((in @ X0 @ (powerset @ X1))) != $true) | ! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) != $true) | (((subset @ X0 @ (setminus @ X1 @ X2))) != $true) | ! [X3 : $i] : (($true = ((in @ X3 @ (setminus @ X1 @ X0)))) | (((in @ X3 @ X2)) != $true) | (((in @ X3 @ X1)) != $true)))) <=> (contraSubsetComplement = $true)),
% 0.09/0.23 inference(flattening,[],[f14])).
% 0.09/0.23 thf(f16,plain,(
% 0.09/0.23 ((? [X1 : $i,X0 : $i] : (? [X2 : $i] : ((($true != ((subset @ X2 @ (setminus @ X1 @ X0)))) & (((subset @ X0 @ (setminus @ X1 @ X2))) = $true)) & (((in @ X2 @ (powerset @ X1))) = $true)) & (((in @ X0 @ (powerset @ X1))) = $true)) & (contraSubsetComplement = $true)) & (subsetTI = $true)) & (complementT_lem = $true)),
% 0.09/0.24 inference(ennf_transformation,[],[f11])).
% 0.09/0.24 thf(f17,plain,(
% 0.09/0.24 ? [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((subset @ X0 @ (setminus @ X1 @ X2))) = $true) & ($true != ((subset @ X2 @ (setminus @ X1 @ X0)))) & (((in @ X2 @ (powerset @ X1))) = $true)) & (((in @ X0 @ (powerset @ X1))) = $true)) & (contraSubsetComplement = $true) & (subsetTI = $true) & (complementT_lem = $true)),
% 0.09/0.24 inference(flattening,[],[f16])).
% 0.09/0.24 thf(f18,plain,(
% 0.09/0.24 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((($true = ((subset @ X0 @ X2))) | ? [X3 : $i] : (((((in @ X3 @ X2)) != $true) & (((in @ X3 @ X0)) = $true)) & (((in @ X3 @ X1)) = $true))) | (((in @ X2 @ (powerset @ X1))) != $true)) | (((in @ X0 @ (powerset @ X1))) != $true)) <=> (subsetTI = $true)),
% 0.09/0.24 inference(ennf_transformation,[],[f13])).
% 0.09/0.24 thf(f19,plain,(
% 0.09/0.24 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ X1)) = $true) & (((in @ X3 @ X2)) != $true) & (((in @ X3 @ X0)) = $true)) | ($true = ((subset @ X0 @ X2))) | (((in @ X2 @ (powerset @ X1))) != $true)) | (((in @ X0 @ (powerset @ X1))) != $true)) <=> (subsetTI = $true)),
% 0.09/0.24 inference(flattening,[],[f18])).
% 0.09/0.24 thf(f20,plain,(
% 0.09/0.24 (complementT_lem = $true) <=> ! [X0 : $i,X1 : $i] : ((((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $true) | (((in @ X1 @ (powerset @ X0))) != $true))),
% 0.09/0.24 inference(ennf_transformation,[],[f9])).
% 0.09/0.24 thf(f21,plain,(
% 0.09/0.24 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((subset @ X1 @ (setminus @ X0 @ X2))) = $true) & (((subset @ X2 @ (setminus @ X0 @ X1))) != $true) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (contraSubsetComplement = $true) & (subsetTI = $true) & (complementT_lem = $true)),
% 0.09/0.24 inference(rectify,[],[f17])).
% 0.09/0.24 thf(f22,plain,(
% 0.09/0.24 ((($true = ((subset @ sK1 @ (setminus @ sK0 @ sK2)))) & ($true != ((subset @ sK2 @ (setminus @ sK0 @ sK1)))) & (((in @ sK2 @ (powerset @ sK0))) = $true)) & ($true = ((in @ sK1 @ (powerset @ sK0))))) & (contraSubsetComplement = $true) & (subsetTI = $true) & (complementT_lem = $true)),
% 0.09/0.24 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f21])).
% 0.09/0.24 thf(f23,plain,(
% 0.09/0.24 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ X1)) = $true) & (((in @ X3 @ X2)) != $true) & (((in @ X3 @ X0)) = $true)) | ($true = ((subset @ X0 @ X2))) | (((in @ X2 @ (powerset @ X1))) != $true)) | (((in @ X0 @ (powerset @ X1))) != $true)) | (subsetTI != $true)) & ((subsetTI = $true) | ? [X1 : $i,X0 : $i] : (? [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X1)) != $true) | (((in @ X3 @ X2)) = $true) | (((in @ X3 @ X0)) != $true)) & ($true != ((subset @ X0 @ X2))) & (((in @ X2 @ (powerset @ X1))) = $true)) & (((in @ X0 @ (powerset @ X1))) = $true)))),
% 0.09/0.24 inference(nnf_transformation,[],[f19])).
% 0.09/0.24 thf(f24,plain,(
% 0.09/0.24 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & (((in @ X3 @ X2)) != $true) & (((in @ X3 @ X1)) = $true)) | (((subset @ X1 @ X2)) = $true) | (((in @ X2 @ (powerset @ X0))) != $true)) | (((in @ X1 @ (powerset @ X0))) != $true)) | (subsetTI != $true)) & ((subsetTI = $true) | ? [X4 : $i,X5 : $i] : (? [X6 : $i] : (! [X7 : $i] : (($true != ((in @ X7 @ X4))) | ($true = ((in @ X7 @ X6))) | (((in @ X7 @ X5)) != $true)) & ($true != ((subset @ X5 @ X6))) & ($true = ((in @ X6 @ (powerset @ X4))))) & ($true = ((in @ X5 @ (powerset @ X4))))))),
% 0.09/0.24 inference(rectify,[],[f23])).
% 0.09/0.24 thf(f25,plain,(
% 0.09/0.24 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((($true = ((in @ (sK3 @ X2 @ X1 @ X0) @ X0))) & (((in @ (sK3 @ X2 @ X1 @ X0) @ X2)) != $true) & ($true = ((in @ (sK3 @ X2 @ X1 @ X0) @ X1)))) | (((subset @ X1 @ X2)) = $true) | (((in @ X2 @ (powerset @ X0))) != $true)) | (((in @ X1 @ (powerset @ X0))) != $true)) | (subsetTI != $true)) & ((subsetTI = $true) | ((! [X7 : $i] : (($true != ((in @ X7 @ sK4))) | ($true = ((in @ X7 @ sK6))) | (((in @ X7 @ sK5)) != $true)) & (((subset @ sK5 @ sK6)) != $true) & ($true = ((in @ sK6 @ (powerset @ sK4))))) & (((in @ sK5 @ (powerset @ sK4))) = $true)))),
% 0.09/0.24 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK4,sK5,sK6]),skolemize(X3,sK3 @ X2 @ X1 @ X0),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6)],[f24])).
% 0.09/0.24 thf(f26,plain,(
% 0.09/0.24 ((complementT_lem = $true) | ? [X0 : $i,X1 : $i] : ((((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) != $true) & (((in @ X1 @ (powerset @ X0))) = $true))) & (! [X0 : $i,X1 : $i] : ((((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $true) | (((in @ X1 @ (powerset @ X0))) != $true)) | (complementT_lem != $true))),
% 0.09/0.24 inference(nnf_transformation,[],[f20])).
% 0.09/0.24 thf(f27,plain,(
% 0.09/0.24 ((complementT_lem = $true) | ? [X0 : $i,X1 : $i] : ((((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) != $true) & (((in @ X1 @ (powerset @ X0))) = $true))) & (! [X2 : $i,X3 : $i] : (($true = ((in @ (setminus @ X2 @ X3) @ (powerset @ X2)))) | ($true != ((in @ X3 @ (powerset @ X2))))) | (complementT_lem != $true))),
% 0.09/0.24 inference(rectify,[],[f26])).
% 0.09/0.24 thf(f28,plain,(
% 0.09/0.24 ((complementT_lem = $true) | (($true != ((in @ (setminus @ sK7 @ sK8) @ (powerset @ sK7)))) & (((in @ sK8 @ (powerset @ sK7))) = $true))) & (! [X2 : $i,X3 : $i] : (($true = ((in @ (setminus @ X2 @ X3) @ (powerset @ X2)))) | ($true != ((in @ X3 @ (powerset @ X2))))) | (complementT_lem != $true))),
% 0.09/0.24 inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f27])).
% 0.09/0.24 thf(f29,plain,(
% 0.09/0.24 (! [X1 : $i,X0 : $i] : ((((in @ X0 @ (powerset @ X1))) != $true) | ! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) != $true) | (((subset @ X0 @ (setminus @ X1 @ X2))) != $true) | ! [X3 : $i] : (($true = ((in @ X3 @ (setminus @ X1 @ X0)))) | (((in @ X3 @ X2)) != $true) | (((in @ X3 @ X1)) != $true)))) | (contraSubsetComplement != $true)) & ((contraSubsetComplement = $true) | ? [X1 : $i,X0 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) & ? [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) & (((subset @ X0 @ (setminus @ X1 @ X2))) = $true) & ? [X3 : $i] : (($true != ((in @ X3 @ (setminus @ X1 @ X0)))) & (((in @ X3 @ X2)) = $true) & (((in @ X3 @ X1)) = $true)))))),
% 0.09/0.24 inference(nnf_transformation,[],[f15])).
% 0.09/0.24 thf(f30,plain,(
% 0.09/0.24 (! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) | ! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) != $true) | (((subset @ X1 @ (setminus @ X0 @ X2))) != $true) | ! [X3 : $i] : ((((in @ X3 @ (setminus @ X0 @ X1))) = $true) | (((in @ X3 @ X2)) != $true) | (((in @ X3 @ X0)) != $true)))) | (contraSubsetComplement != $true)) & ((contraSubsetComplement = $true) | ? [X4 : $i,X5 : $i] : (($true = ((in @ X5 @ (powerset @ X4)))) & ? [X6 : $i] : (($true = ((in @ X6 @ (powerset @ X4)))) & (((subset @ X5 @ (setminus @ X4 @ X6))) = $true) & ? [X7 : $i] : (($true != ((in @ X7 @ (setminus @ X4 @ X5)))) & ($true = ((in @ X7 @ X6))) & ($true = ((in @ X7 @ X4)))))))),
% 0.09/0.24 inference(rectify,[],[f29])).
% 0.09/0.24 thf(f31,plain,(
% 0.09/0.24 (! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) | ! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) != $true) | (((subset @ X1 @ (setminus @ X0 @ X2))) != $true) | ! [X3 : $i] : ((((in @ X3 @ (setminus @ X0 @ X1))) = $true) | (((in @ X3 @ X2)) != $true) | (((in @ X3 @ X0)) != $true)))) | (contraSubsetComplement != $true)) & ((contraSubsetComplement = $true) | (($true = ((in @ sK10 @ (powerset @ sK9)))) & (($true = ((in @ sK11 @ (powerset @ sK9)))) & ($true = ((subset @ sK10 @ (setminus @ sK9 @ sK11)))) & (($true != ((in @ sK12 @ (setminus @ sK9 @ sK10)))) & ($true = ((in @ sK12 @ sK11))) & ($true = ((in @ sK12 @ sK9)))))))),
% 0.09/0.24 inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12]),skolemize(X4,sK9),skolemize(X5,sK10),skolemize(X6,sK11),skolemize(X7,sK12)],[f30])).
% 0.09/0.24 thf(f32,plain,(
% 0.09/0.24 (complementT_lem = $true)),
% 0.09/0.24 inference(cnf_transformation,[],[f22])).
% 0.09/0.24 thf(f33,plain,(
% 0.09/0.24 (subsetTI = $true)),
% 0.09/0.24 inference(cnf_transformation,[],[f22])).
% 0.09/0.24 thf(f34,plain,(
% 0.09/0.24 (contraSubsetComplement = $true)),
% 0.09/0.24 inference(cnf_transformation,[],[f22])).
% 0.09/0.24 thf(f35,plain,(
% 0.09/0.24 ($true = ((in @ sK1 @ (powerset @ sK0))))),
% 0.09/0.24 inference(cnf_transformation,[],[f22])).
% 0.09/0.24 thf(f36,plain,(
% 0.09/0.24 (((in @ sK2 @ (powerset @ sK0))) = $true)),
% 0.09/0.24 inference(cnf_transformation,[],[f22])).
% 0.09/0.24 thf(f37,plain,(
% 0.09/0.24 ($true != ((subset @ sK2 @ (setminus @ sK0 @ sK1))))),
% 0.09/0.24 inference(cnf_transformation,[],[f22])).
% 0.09/0.24 thf(f38,plain,(
% 0.09/0.24 ($true = ((subset @ sK1 @ (setminus @ sK0 @ sK2))))),
% 0.09/0.24 inference(cnf_transformation,[],[f22])).
% 0.09/0.24 thf(f43,plain,(
% 0.09/0.24 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) | ($true = ((in @ (sK3 @ X2 @ X1 @ X0) @ X1))) | (((in @ X2 @ (powerset @ X0))) != $true) | (subsetTI != $true) | (((subset @ X1 @ X2)) = $true)) )),
% 0.09/0.24 inference(cnf_transformation,[],[f25])).
% 0.09/0.24 thf(f44,plain,(
% 0.09/0.24 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((subsetTI != $true) | (((subset @ X1 @ X2)) = $true) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ (sK3 @ X2 @ X1 @ X0) @ X2)) != $true)) )),
% 0.09/0.24 inference(cnf_transformation,[],[f25])).
% 0.09/0.24 thf(f45,plain,(
% 0.09/0.24 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (powerset @ X0))) != $true) | ($true = ((in @ (sK3 @ X2 @ X1 @ X0) @ X0))) | (subsetTI != $true) | (((in @ X1 @ (powerset @ X0))) != $true) | (((subset @ X1 @ X2)) = $true)) )),
% 0.09/0.24 inference(cnf_transformation,[],[f25])).
% 0.09/0.24 thf(f46,plain,(
% 0.09/0.24 ( ! [X2 : $i,X3 : $i] : (($true != ((in @ X3 @ (powerset @ X2)))) | (complementT_lem != $true) | ($true = ((in @ (setminus @ X2 @ X3) @ (powerset @ X2))))) )),
% 0.09/0.24 inference(cnf_transformation,[],[f28])).
% 0.09/0.24 thf(f55,plain,(
% 0.09/0.24 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((contraSubsetComplement != $true) | (((in @ X3 @ X0)) != $true) | (((in @ X1 @ (powerset @ X0))) != $true) | (((subset @ X1 @ (setminus @ X0 @ X2))) != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ X3 @ (setminus @ X0 @ X1))) = $true) | (((in @ X3 @ X2)) != $true)) )),
% 0.09/0.24 inference(cnf_transformation,[],[f31])).
% 0.09/0.24 thf(f60,plain,(
% 0.09/0.24 ( ! [X2 : $i,X3 : $i] : (($true = ((in @ (setminus @ X2 @ X3) @ (powerset @ X2)))) | ($true != ((in @ X3 @ (powerset @ X2))))) )),
% 0.09/0.24 inference(forward_subsumption_resolution,[],[f46,f32])).
% 0.09/0.24 thf(f61,plain,(
% 0.09/0.24 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK3 @ X2 @ X1 @ X0) @ X1))) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((subset @ X1 @ X2)) = $true)) )),
% 0.09/0.24 inference(forward_subsumption_resolution,[],[f43,f33])).
% 0.09/0.24 thf(f62,plain,(
% 0.09/0.24 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK3 @ X2 @ X1 @ X0) @ X2)) != $true) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((subset @ X1 @ X2)) = $true)) )),
% 0.09/0.24 inference(forward_subsumption_resolution,[],[f44,f33])).
% 0.09/0.24 thf(f66,plain,(
% 0.09/0.24 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK3 @ X2 @ X1 @ X0) @ X0))) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ X1 @ (powerset @ X0))) != $true) | (((subset @ X1 @ X2)) = $true)) )),
% 0.09/0.24 inference(forward_subsumption_resolution,[],[f45,f33])).
% 0.09/0.24 thf(f80,plain,(
% 0.09/0.24 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((subset @ X1 @ (setminus @ X0 @ X2))) != $true) | (((in @ X3 @ (setminus @ X0 @ X1))) = $true) | (((in @ X3 @ X0)) != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ X3 @ X2)) != $true) | (((in @ X1 @ (powerset @ X0))) != $true)) )),
% 0.09/0.24 inference(forward_subsumption_resolution,[],[f55,f34])).
% 0.09/0.24 thf(f81,plain,(
% 0.09/0.24 ( ! [X0 : $i] : (($true = ((in @ X0 @ (setminus @ sK0 @ sK1)))) | ($true != ((in @ X0 @ sK0))) | ($true != ((in @ sK1 @ (powerset @ sK0)))) | (((in @ sK2 @ (powerset @ sK0))) != $true) | (((in @ X0 @ sK2)) != $true) | ($true != $true)) )),
% 0.09/0.24 inference(superposition,[],[f80,f38])).
% 0.09/0.24 thf(f83,plain,(
% 0.09/0.24 ( ! [X0 : $i] : (($true != ((in @ sK1 @ (powerset @ sK0)))) | ($true != ((in @ X0 @ sK0))) | ($true = ((in @ X0 @ (setminus @ sK0 @ sK1)))) | (((in @ sK2 @ (powerset @ sK0))) != $true) | (((in @ X0 @ sK2)) != $true)) )),
% 0.09/0.24 inference(trivial_inequality_removal,[],[f81])).
% 0.09/0.24 thf(f86,plain,(
% 0.09/0.24 ( ! [X0 : $i] : ((((in @ sK2 @ (powerset @ sK0))) != $true) | ($true = ((in @ X0 @ (setminus @ sK0 @ sK1)))) | (((in @ X0 @ sK2)) != $true) | ($true != ((in @ X0 @ sK0)))) )),
% 0.09/0.24 inference(forward_subsumption_resolution,[],[f83,f35])).
% 0.09/0.24 thf(f88,plain,(
% 0.09/0.24 ( ! [X0 : $i] : (($true = ((in @ X0 @ (setminus @ sK0 @ sK1)))) | ($true != ((in @ X0 @ sK0))) | (((in @ X0 @ sK2)) != $true)) )),
% 0.09/0.24 inference(forward_subsumption_resolution,[],[f86,f36])).
% 0.09/0.24 thf(f89,plain,(
% 0.09/0.24 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK3 @ (setminus @ sK0 @ sK1) @ X0 @ X1) @ sK0)) != $true) | ($true != ((in @ (sK3 @ (setminus @ sK0 @ sK1) @ X0 @ X1) @ sK2))) | ($true != ((in @ (setminus @ sK0 @ sK1) @ (powerset @ X1)))) | ($true != $true) | ($true = ((subset @ X0 @ (setminus @ sK0 @ sK1)))) | (((in @ X0 @ (powerset @ X1))) != $true)) )),
% 0.09/0.24 inference(superposition,[],[f62,f88])).
% 0.09/0.24 thf(f90,plain,(
% 0.09/0.24 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK3 @ (setminus @ sK0 @ sK1) @ X0 @ X1) @ sK2))) | ($true != ((in @ (setminus @ sK0 @ sK1) @ (powerset @ X1)))) | (((in @ X0 @ (powerset @ X1))) != $true) | ($true = ((subset @ X0 @ (setminus @ sK0 @ sK1)))) | (((in @ (sK3 @ (setminus @ sK0 @ sK1) @ X0 @ X1) @ sK0)) != $true)) )),
% 0.09/0.24 inference(trivial_inequality_removal,[],[f89])).
% 0.09/0.24 thf(f93,plain,(
% 0.09/0.24 ( ! [X0 : $i] : (($true != ((in @ (setminus @ sK0 @ sK1) @ (powerset @ X0)))) | (((in @ (sK3 @ (setminus @ sK0 @ sK1) @ sK2 @ X0) @ sK0)) != $true) | ($true = ((subset @ sK2 @ (setminus @ sK0 @ sK1)))) | ($true != ((in @ (setminus @ sK0 @ sK1) @ (powerset @ X0)))) | ($true != $true) | ($true != ((in @ sK2 @ (powerset @ X0)))) | ($true != ((in @ sK2 @ (powerset @ X0)))) | ($true = ((subset @ sK2 @ (setminus @ sK0 @ sK1))))) )),
% 0.09/0.24 inference(superposition,[],[f90,f61])).
% 0.09/0.24 thf(f95,plain,(
% 0.09/0.24 ( ! [X0 : $i] : (($true != ((in @ (setminus @ sK0 @ sK1) @ (powerset @ X0)))) | ($true != ((in @ sK2 @ (powerset @ X0)))) | ($true = ((subset @ sK2 @ (setminus @ sK0 @ sK1)))) | ($true != $true) | (((in @ (sK3 @ (setminus @ sK0 @ sK1) @ sK2 @ X0) @ sK0)) != $true)) )),
% 0.09/0.24 inference(duplicate_literal_removal,[],[f93])).
% 0.09/0.24 thf(f96,plain,(
% 0.09/0.24 ( ! [X0 : $i] : (($true != ((in @ sK2 @ (powerset @ X0)))) | ($true != ((in @ (setminus @ sK0 @ sK1) @ (powerset @ X0)))) | (((in @ (sK3 @ (setminus @ sK0 @ sK1) @ sK2 @ X0) @ sK0)) != $true) | ($true = ((subset @ sK2 @ (setminus @ sK0 @ sK1))))) )),
% 0.09/0.24 inference(trivial_inequality_removal,[],[f95])).
% 0.09/0.24 thf(f99,plain,(
% 0.09/0.24 ( ! [X0 : $i] : ((((in @ (sK3 @ (setminus @ sK0 @ sK1) @ sK2 @ X0) @ sK0)) != $true) | ($true != ((in @ sK2 @ (powerset @ X0)))) | ($true != ((in @ (setminus @ sK0 @ sK1) @ (powerset @ X0))))) )),
% 0.09/0.24 inference(forward_subsumption_resolution,[],[f96,f37])).
% 0.09/0.24 thf(f100,plain,(
% 0.09/0.24 ($true != $true) | (((in @ sK2 @ (powerset @ sK0))) != $true) | ($true != ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))) | ($true = ((subset @ sK2 @ (setminus @ sK0 @ sK1)))) | ($true != ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))) | (((in @ sK2 @ (powerset @ sK0))) != $true)),
% 0.09/0.24 inference(superposition,[],[f99,f66])).
% 0.09/0.24 thf(f101,plain,(
% 0.09/0.24 ($true != $true) | ($true != ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))) | ($true = ((subset @ sK2 @ (setminus @ sK0 @ sK1)))) | (((in @ sK2 @ (powerset @ sK0))) != $true)),
% 0.09/0.24 inference(duplicate_literal_removal,[],[f100])).
% 0.09/0.24 thf(f102,plain,(
% 0.09/0.24 (((in @ sK2 @ (powerset @ sK0))) != $true) | ($true = ((subset @ sK2 @ (setminus @ sK0 @ sK1)))) | ($true != ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0))))),
% 0.09/0.24 inference(trivial_inequality_removal,[],[f101])).
% 0.09/0.24 thf(f103,plain,(
% 0.09/0.24 ($true != ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))) | ($true = ((subset @ sK2 @ (setminus @ sK0 @ sK1))))),
% 0.09/0.24 inference(forward_subsumption_resolution,[],[f102,f36])).
% 0.09/0.24 thf(f104,plain,(
% 0.09/0.24 ($true != ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0))))),
% 0.09/0.24 inference(forward_subsumption_resolution,[],[f103,f37])).
% 0.09/0.24 thf(f108,plain,(
% 0.09/0.24 ($true != $true) | ($true != ((in @ sK1 @ (powerset @ sK0))))),
% 0.09/0.24 inference(superposition,[],[f104,f60])).
% 0.09/0.24 thf(f109,plain,(
% 0.09/0.24 ($true != ((in @ sK1 @ (powerset @ sK0))))),
% 0.09/0.24 inference(trivial_inequality_removal,[],[f108])).
% 0.09/0.24 thf(f110,plain,(
% 0.09/0.24 $false),
% 0.09/0.24 inference(forward_subsumption_resolution,[],[f109,f35])).
% 0.09/0.24 % SZS output end Proof for theBenchmark
% 0.09/0.24 % (173126)------------------------------
% 0.09/0.24 % (173126)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.24 % (173126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.24 % (173126)CaDiCaL version: 2.1.3
% 0.09/0.24 % (173126)Termination reason: Refutation
% 0.09/0.24 % (173126)Time elapsed: 0.010 s
% 0.09/0.24 % (173126)Peak memory usage: 12 MB
% 0.09/0.24 % (173126)Instructions burned: 19 (million)
% 0.09/0.24 % (173117)Success in time 0.063 s
% 0.09/0.24 % Vampire exiting
%------------------------------------------------------------------------------