%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU517^2 : 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 : n019.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 08:29:53 AM UTC 2026
% Result : Theorem 0.22s 0.31s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU517^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.20 % Computer : n019.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Sep 29 13:47:48 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 Running higher-order theorem proving
% 0.11/0.25 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
% 0.22/0.31 % (790135)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.31 % (790143)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=3213208387: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)
% 0.22/0.31 % (790146)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.31 % (790146)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
% 0.22/0.31 % (790142)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1829994091:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.31 % (790141)lrs+10_16_si=on:nwc=1.5:random_seed=4071892680:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.31 % (790140)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=168743574:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.31 % (790145)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3448832138:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.31 % (790144)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3044187205:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.31 % (790146)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=1051486946:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.31 % (790142)Refutation not found, incomplete strategy
% 0.22/0.31 % (790142)------------------------------
% 0.22/0.31 % (790142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (790142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (790142)CaDiCaL version: 2.1.3
% 0.22/0.31 % (790142)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.31 % (790142)Time elapsed: 0.002 s
% 0.22/0.31 % (790142)Peak memory usage: 12 MB
% 0.22/0.31 % (790142)Instructions burned: 2 (million)
% 0.22/0.31 % (790142)------------------------------
% 0.22/0.31 % (790142)------------------------------
% 0.22/0.31 % (790141)Instruction limit reached!
% 0.22/0.31 % (790141)------------------------------
% 0.22/0.31 % (790141)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (790141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (790141)CaDiCaL version: 2.1.3
% 0.22/0.31 % (790141)Termination reason: Instruction limit
% 0.22/0.31 % (790141)Termination phase: Saturation
% 0.22/0.31 % (790141)Time elapsed: 0.011 s
% 0.22/0.31 % (790141)Peak memory usage: 12 MB
% 0.22/0.31 % (790141)Instructions burned: 19 (million)
% 0.22/0.31 % (790144) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-790135-790144"...
% 0.22/0.31 % (790146) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-790135-790146"...
% 0.22/0.31 % (790144)...printing done.
% 0.22/0.31 % (790144)Refutation found. Thanks to Tanya!
% 0.22/0.31 % SZS status Theorem for theBenchmark
% 0.22/0.31 % SZS output start Proof for theBenchmark
% 0.22/0.31 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.31 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.22/0.31 thf(func_def_1, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.22/0.31 thf(func_def_2, type, dsetconstrI: $o).
% 0.22/0.31 thf(func_def_4, type, dsetconstrEL: $o).
% 0.22/0.31 thf(func_def_5, type, setext: $o).
% 0.22/0.31 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.31 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.31 thf(func_def_12, type, sK2: ($i > $i > $i)).
% 0.22/0.31 thf(func_def_13, type, sK3: ($i > $i > $i)).
% 0.22/0.31 thf(func_def_16, type, sK6: ($i > $o)).
% 0.22/0.31 thf(func_def_20, type, sK10: ($i > $o)).
% 0.22/0.31 thf(func_def_21, type, vNOT: ($o > $o)).
% 0.22/0.31 thf(f1,axiom,(
% 0.22/0.31 (! [X1 : ($i > $o),X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))))) = dsetconstrI)),
% 0.22/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI)).
% 0.22/0.31 thf(f2,axiom,(
% 0.22/0.31 (! [X0 : $i,X2 : $i,X1 : ($i > $o)] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))) => (in @ X2 @ X0)) = dsetconstrEL)),
% 0.22/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL)).
% 0.22/0.31 thf(f3,axiom,(
% 0.22/0.31 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (X0 = X1))) = setext)),
% 0.22/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext)).
% 0.22/0.31 thf(f4,conjecture,(
% 0.22/0.31 dsetconstrI => (dsetconstrEL => (setext => ! [X0 : $i] : (X0 = ((dsetconstr @ X0 @ (^[X1 : $i] : ($true)))))))),
% 0.22/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq)).
% 0.22/0.31 thf(f5,negated_conjecture,(
% 0.22/0.31 ~(dsetconstrI => (dsetconstrEL => (setext => ! [X0 : $i] : (X0 = ((dsetconstr @ X0 @ (^[X1 : $i] : ($true))))))))),
% 0.22/0.31 inference(negated_conjecture,[status(cth)],[f4])).
% 0.22/0.31 thf(f6,plain,(
% 0.22/0.31 (! [X0 : ($i > $o),X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ((X0 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : ((X0 @ X3))))))) = dsetconstrI)),
% 0.22/0.31 inference(rectify,[],[f1])).
% 0.22/0.31 thf(f7,plain,(
% 0.22/0.31 (dsetconstrI = $true) <=> ! [X2 : $i,X0 : ($i > $o),X1 : $i] : ((((in @ X1 @ X2)) = $true) => (($true = ((X0 @ X1))) => ($true = ((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))))))),
% 0.22/0.31 inference(fool_elimination,[],[f6])).
% 0.22/0.31 thf(f8,plain,(
% 0.22/0.31 ~(dsetconstrI => (dsetconstrEL => (setext => ! [X0 : $i] : (X0 = ((dsetconstr @ X0 @ (^[X1 : $i] : ($true))))))))),
% 0.22/0.31 inference(rectify,[],[f5])).
% 0.22/0.31 thf(f9,plain,(
% 0.22/0.31 ~((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((setext = $true) => ! [X0 : $i] : (((dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) = X0))))),
% 0.22/0.31 inference(fool_elimination,[],[f8])).
% 0.22/0.31 thf(f10,plain,(
% 0.22/0.31 (! [X0 : $i,X1 : $i,X2 : ($i > $o)] : ((in @ X1 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X2 @ X3))))) => (in @ X1 @ X0)) = dsetconstrEL)),
% 0.22/0.31 inference(rectify,[],[f2])).
% 0.22/0.31 thf(f11,plain,(
% 0.22/0.31 ! [X2 : ($i > $o),X0 : $i,X1 : $i] : (($true = ((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))))) => (((in @ X1 @ X0)) = $true)) <=> (dsetconstrEL = $true)),
% 0.22/0.31 inference(fool_elimination,[],[f10])).
% 0.22/0.31 thf(f12,plain,(
% 0.22/0.31 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => (in @ X3 @ X0)) => (X0 = X1))) = setext)),
% 0.22/0.31 inference(rectify,[],[f3])).
% 0.22/0.31 thf(f13,plain,(
% 0.22/0.31 (setext = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => (! [X3 : $i] : (($true = ((in @ X3 @ X1))) => ($true = ((in @ X3 @ X0)))) => (X0 = X1)))),
% 0.22/0.31 inference(fool_elimination,[],[f12])).
% 0.22/0.31 thf(f14,plain,(
% 0.22/0.31 (dsetconstrI = $true) <=> ! [X2 : $i,X0 : ($i > $o),X1 : $i] : ((($true = ((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))))) | ($true != ((X0 @ X1)))) | (((in @ X1 @ X2)) != $true))),
% 0.22/0.31 inference(ennf_transformation,[],[f7])).
% 0.22/0.31 thf(f15,plain,(
% 0.22/0.31 (dsetconstrI = $true) <=> ! [X1 : $i,X2 : $i,X0 : ($i > $o)] : (($true = ((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))))) | (((in @ X1 @ X2)) != $true) | ($true != ((X0 @ X1))))),
% 0.22/0.31 inference(flattening,[],[f14])).
% 0.22/0.31 thf(f16,plain,(
% 0.22/0.31 (dsetconstrEL = $true) <=> ! [X1 : $i,X0 : $i,X2 : ($i > $o)] : ((((in @ X1 @ X0)) = $true) | ($true != ((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))))))),
% 0.22/0.31 inference(ennf_transformation,[],[f11])).
% 0.22/0.31 thf(f17,plain,(
% 0.22/0.31 (setext = $true) <=> ! [X0 : $i,X1 : $i] : (((X0 = X1) | ? [X3 : $i] : (($true != ((in @ X3 @ X0))) & ($true = ((in @ X3 @ X1))))) | ? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true)))),
% 0.22/0.31 inference(ennf_transformation,[],[f13])).
% 0.22/0.31 thf(f18,plain,(
% 0.22/0.31 (setext = $true) <=> ! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true)) | (X0 = X1) | ? [X3 : $i] : (($true != ((in @ X3 @ X0))) & ($true = ((in @ X3 @ X1)))))),
% 0.22/0.31 inference(flattening,[],[f17])).
% 0.22/0.31 thf(f19,plain,(
% 0.22/0.31 ((? [X0 : $i] : (((dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) != X0) & (setext = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)),
% 0.22/0.31 inference(ennf_transformation,[],[f9])).
% 0.22/0.31 thf(f20,plain,(
% 0.22/0.31 (dsetconstrI = $true) & (dsetconstrEL = $true) & ? [X0 : $i] : (((dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) != X0) & (setext = $true)),
% 0.22/0.31 inference(flattening,[],[f19])).
% 0.22/0.31 thf(f21,plain,(
% 0.22/0.31 ((setext = $true) | ? [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ X1)) = $true)) & (X0 != X1) & ! [X3 : $i] : (($true = ((in @ X3 @ X0))) | ($true != ((in @ X3 @ X1)))))) & (! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true)) | (X0 = X1) | ? [X3 : $i] : (($true != ((in @ X3 @ X0))) & ($true = ((in @ X3 @ X1))))) | (setext != $true))),
% 0.22/0.31 inference(nnf_transformation,[],[f18])).
% 0.22/0.31 thf(f22,plain,(
% 0.22/0.31 ((setext = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)) & (X0 != X1) & ! [X3 : $i] : (($true = ((in @ X3 @ X1))) | ($true != ((in @ X3 @ X0)))))) & (! [X4 : $i,X5 : $i] : (? [X6 : $i] : (($true = ((in @ X6 @ X5))) & (((in @ X6 @ X4)) != $true)) | (X4 = X5) | ? [X7 : $i] : (($true != ((in @ X7 @ X5))) & (((in @ X7 @ X4)) = $true))) | (setext != $true))),
% 0.22/0.31 inference(rectify,[],[f21])).
% 0.22/0.31 thf(f23,plain,(
% 0.22/0.31 ((setext = $true) | (! [X2 : $i] : ((((in @ X2 @ sK1)) != $true) | ($true = ((in @ X2 @ sK0)))) & (sK0 != sK1) & ! [X3 : $i] : ((((in @ X3 @ sK1)) = $true) | (((in @ X3 @ sK0)) != $true)))) & (! [X4 : $i,X5 : $i] : ((($true = ((in @ (sK2 @ X5 @ X4) @ X5))) & (((in @ (sK2 @ X5 @ X4) @ X4)) != $true)) | (X4 = X5) | ((((in @ (sK3 @ X5 @ X4) @ X5)) != $true) & (((in @ (sK3 @ X5 @ X4) @ X4)) = $true))) | (setext != $true))),
% 0.22/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X7,sK3 @ X5 @ X4),skolemize(X7,sK3 @ X5 @ X4)],[f22])).
% 0.22/0.31 thf(f24,plain,(
% 0.22/0.31 ((dsetconstrEL = $true) | ? [X1 : $i,X0 : $i,X2 : ($i > $o)] : ((((in @ X1 @ X0)) != $true) & ($true = ((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))))))) & (! [X1 : $i,X0 : $i,X2 : ($i > $o)] : ((((in @ X1 @ X0)) = $true) | ($true != ((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))))) | (dsetconstrEL != $true))),
% 0.22/0.31 inference(nnf_transformation,[],[f16])).
% 0.22/0.31 thf(f25,plain,(
% 0.22/0.31 ((dsetconstrEL = $true) | ? [X0 : $i,X1 : $i,X2 : ($i > $o)] : ((((in @ X0 @ X1)) != $true) & ($true = ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))))))) & (! [X3 : $i,X4 : $i,X5 : ($i > $o)] : ((((in @ X3 @ X4)) = $true) | (((in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0))))) != $true)) | (dsetconstrEL != $true))),
% 0.22/0.31 inference(rectify,[],[f24])).
% 0.22/0.31 thf(f26,plain,(
% 0.22/0.31 ((dsetconstrEL = $true) | (($true != ((in @ sK4 @ sK5))) & (((in @ sK4 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (sK6 @ Y0))))) = $true))) & (! [X3 : $i,X4 : $i,X5 : ($i > $o)] : ((((in @ X3 @ X4)) = $true) | (((in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0))))) != $true)) | (dsetconstrEL != $true))),
% 0.22/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f25])).
% 0.22/0.31 thf(f27,plain,(
% 0.22/0.31 (dsetconstrI = $true) & (dsetconstrEL = $true) & (sK7 != ((dsetconstr @ sK7 @ (^[Y0 : $i]: ($true))))) & (setext = $true)),
% 0.22/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X0,sK7)],[f20])).
% 0.22/0.31 thf(f28,plain,(
% 0.22/0.31 ((dsetconstrI = $true) | ? [X1 : $i,X2 : $i,X0 : ($i > $o)] : (($true != ((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))))) & (((in @ X1 @ X2)) = $true) & ($true = ((X0 @ X1))))) & (! [X1 : $i,X2 : $i,X0 : ($i > $o)] : (($true = ((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))))) | (((in @ X1 @ X2)) != $true) | ($true != ((X0 @ X1)))) | (dsetconstrI != $true))),
% 0.22/0.31 inference(nnf_transformation,[],[f15])).
% 0.22/0.31 thf(f29,plain,(
% 0.22/0.31 ((dsetconstrI = $true) | ? [X0 : $i,X1 : $i,X2 : ($i > $o)] : (($true != ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))))) & (((in @ X0 @ X1)) = $true) & (((X2 @ X0)) = $true))) & (! [X3 : $i,X4 : $i,X5 : ($i > $o)] : ((((in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0))))) = $true) | (((in @ X3 @ X4)) != $true) | (((X5 @ X3)) != $true)) | (dsetconstrI != $true))),
% 0.22/0.31 inference(rectify,[],[f28])).
% 0.22/0.31 thf(f30,plain,(
% 0.22/0.31 ((dsetconstrI = $true) | ((((in @ sK8 @ (dsetconstr @ sK9 @ (^[Y0 : $i]: (sK10 @ Y0))))) != $true) & ($true = ((in @ sK8 @ sK9))) & (((sK10 @ sK8)) = $true))) & (! [X3 : $i,X4 : $i,X5 : ($i > $o)] : ((((in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0))))) = $true) | (((in @ X3 @ X4)) != $true) | (((X5 @ X3)) != $true)) | (dsetconstrI != $true))),
% 0.22/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10)],[f29])).
% 0.22/0.31 thf(f31,plain,(
% 0.22/0.31 ( ! [X4 : $i,X5 : $i] : ((X4 = X5) | (setext != $true) | (((in @ (sK2 @ X5 @ X4) @ X4)) != $true) | (((in @ (sK3 @ X5 @ X4) @ X4)) = $true)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f23])).
% 0.22/0.31 thf(f32,plain,(
% 0.22/0.31 ( ! [X4 : $i,X5 : $i] : ((setext != $true) | (((in @ (sK2 @ X5 @ X4) @ X4)) != $true) | (((in @ (sK3 @ X5 @ X4) @ X5)) != $true) | (X4 = X5)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f23])).
% 0.22/0.31 thf(f33,plain,(
% 0.22/0.31 ( ! [X4 : $i,X5 : $i] : ((X4 = X5) | ($true = ((in @ (sK2 @ X5 @ X4) @ X5))) | (((in @ (sK3 @ X5 @ X4) @ X4)) = $true) | (setext != $true)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f23])).
% 0.22/0.31 thf(f34,plain,(
% 0.22/0.31 ( ! [X4 : $i,X5 : $i] : (($true = ((in @ (sK2 @ X5 @ X4) @ X5))) | (setext != $true) | (((in @ (sK3 @ X5 @ X4) @ X5)) != $true) | (X4 = X5)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f23])).
% 0.22/0.31 thf(f38,plain,(
% 0.22/0.31 ( ! [X3 : $i,X4 : $i,X5 : ($i > $o)] : ((dsetconstrEL != $true) | (((in @ X3 @ X4)) = $true) | (((in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0))))) != $true)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f26])).
% 0.22/0.31 thf(f41,plain,(
% 0.22/0.31 (setext = $true)),
% 0.22/0.31 inference(cnf_transformation,[],[f27])).
% 0.22/0.31 thf(f42,plain,(
% 0.22/0.31 (sK7 != ((dsetconstr @ sK7 @ (^[Y0 : $i]: ($true)))))),
% 0.22/0.31 inference(cnf_transformation,[],[f27])).
% 0.22/0.31 thf(f43,plain,(
% 0.22/0.31 (dsetconstrEL = $true)),
% 0.22/0.31 inference(cnf_transformation,[],[f27])).
% 0.22/0.31 thf(f44,plain,(
% 0.22/0.31 (dsetconstrI = $true)),
% 0.22/0.31 inference(cnf_transformation,[],[f27])).
% 0.22/0.31 thf(f45,plain,(
% 0.22/0.31 ( ! [X3 : $i,X4 : $i,X5 : ($i > $o)] : ((((X5 @ X3)) != $true) | (dsetconstrI != $true) | (((in @ X3 @ X4)) != $true) | (((in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0))))) = $true)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f30])).
% 0.22/0.31 thf(f51,plain,(
% 0.22/0.31 ( ! [X3 : $i,X4 : $i,X5 : ($i > $o)] : ((((in @ X3 @ X4)) = $true) | (dsetconstrEL != $true) | (((in @ X3 @ (dsetconstr @ X4 @ X5))) != $true)) )),
% 0.22/0.31 inference(beta-eta_normalization,[],[f38])).
% 0.22/0.31 thf(f52,plain,(
% 0.22/0.31 ( ! [X3 : $i,X4 : $i,X5 : ($i > $o)] : ((((X5 @ X3)) != $true) | (((in @ X3 @ (dsetconstr @ X4 @ X5))) = $true) | (((in @ X3 @ X4)) != $true) | (dsetconstrI != $true)) )),
% 0.22/0.31 inference(beta-eta_normalization,[],[f45])).
% 0.22/0.31 thf(f57,plain,(
% 0.22/0.31 ( ! [X3 : $i,X4 : $i,X5 : ($i > $o)] : ((((in @ X3 @ (dsetconstr @ X4 @ X5))) != $true) | (((in @ X3 @ X4)) = $true)) )),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f51,f43])).
% 0.22/0.31 thf(f58,plain,(
% 0.22/0.31 ( ! [X3 : $i,X4 : $i,X5 : ($i > $o)] : ((((in @ X3 @ (dsetconstr @ X4 @ X5))) = $true) | (((X5 @ X3)) != $true) | (((in @ X3 @ X4)) != $true)) )),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f52,f44])).
% 0.22/0.31 thf(f60,plain,(
% 0.22/0.31 ( ! [X4 : $i,X5 : $i] : ((((in @ (sK2 @ X5 @ X4) @ X4)) != $true) | (X4 = X5) | (((in @ (sK3 @ X5 @ X4) @ X4)) = $true)) )),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f31,f41])).
% 0.22/0.31 thf(f61,plain,(
% 0.22/0.31 ( ! [X2 : ($i > $o),X0 : $i,X1 : $i] : (($true != ((X2 @ (sK2 @ X0 @ (dsetconstr @ X1 @ X2))))) | (((dsetconstr @ X1 @ X2)) = X0) | (((in @ (sK2 @ X0 @ (dsetconstr @ X1 @ X2)) @ X1)) != $true) | (((in @ (sK3 @ X0 @ (dsetconstr @ X1 @ X2)) @ (dsetconstr @ X1 @ X2))) = $true) | ($true != $true)) )),
% 0.22/0.31 inference(superposition,[],[f60,f58])).
% 0.22/0.31 thf(f62,plain,(
% 0.22/0.31 ( ! [X2 : ($i > $o),X0 : $i,X1 : $i] : ((((in @ (sK3 @ X0 @ (dsetconstr @ X1 @ X2)) @ (dsetconstr @ X1 @ X2))) = $true) | ($true != ((X2 @ (sK2 @ X0 @ (dsetconstr @ X1 @ X2))))) | (((dsetconstr @ X1 @ X2)) = X0) | (((in @ (sK2 @ X0 @ (dsetconstr @ X1 @ X2)) @ X1)) != $true)) )),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f61])).
% 0.22/0.31 thf(f63,plain,(
% 0.22/0.31 ( ! [X2 : ($i > $o),X0 : $i,X1 : $i] : (($true = ((in @ (sK3 @ X0 @ (dsetconstr @ X1 @ X2)) @ X1))) | (((in @ (sK2 @ X0 @ (dsetconstr @ X1 @ X2)) @ X1)) != $true) | (((dsetconstr @ X1 @ X2)) = X0) | ($true != $true) | ($true != ((X2 @ (sK2 @ X0 @ (dsetconstr @ X1 @ X2)))))) )),
% 0.22/0.31 inference(superposition,[],[f57,f62])).
% 0.22/0.31 thf(f64,plain,(
% 0.22/0.31 ( ! [X2 : ($i > $o),X0 : $i,X1 : $i] : ((((in @ (sK2 @ X0 @ (dsetconstr @ X1 @ X2)) @ X1)) != $true) | (((dsetconstr @ X1 @ X2)) = X0) | ($true = ((in @ (sK3 @ X0 @ (dsetconstr @ X1 @ X2)) @ X1))) | ($true != ((X2 @ (sK2 @ X0 @ (dsetconstr @ X1 @ X2)))))) )),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f63])).
% 0.22/0.31 thf(f67,plain,(
% 0.22/0.31 ( ! [X4 : $i,X5 : $i] : ((((in @ (sK2 @ X5 @ X4) @ X4)) != $true) | (((in @ (sK3 @ X5 @ X4) @ X5)) != $true) | (X4 = X5)) )),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f32,f41])).
% 0.22/0.31 thf(f68,plain,(
% 0.22/0.31 ( ! [X2 : ($i > $o),X0 : $i,X1 : $i] : ((((in @ (sK3 @ X0 @ (dsetconstr @ X1 @ X2)) @ X0)) != $true) | (((dsetconstr @ X1 @ X2)) = X0) | ($true != $true) | ($true != ((X2 @ (sK2 @ X0 @ (dsetconstr @ X1 @ X2))))) | (((in @ (sK2 @ X0 @ (dsetconstr @ X1 @ X2)) @ X1)) != $true)) )),
% 0.22/0.31 inference(superposition,[],[f67,f58])).
% 0.22/0.31 thf(f69,plain,(
% 0.22/0.31 ( ! [X2 : ($i > $o),X0 : $i,X1 : $i] : ((((in @ (sK3 @ X0 @ (dsetconstr @ X1 @ X2)) @ X0)) != $true) | (((dsetconstr @ X1 @ X2)) = X0) | (((in @ (sK2 @ X0 @ (dsetconstr @ X1 @ X2)) @ X1)) != $true) | ($true != ((X2 @ (sK2 @ X0 @ (dsetconstr @ X1 @ X2)))))) )),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f68])).
% 0.22/0.31 thf(f76,plain,(
% 0.22/0.31 ( ! [X4 : $i,X5 : $i] : ((((in @ (sK3 @ X5 @ X4) @ X4)) = $true) | ($true = ((in @ (sK2 @ X5 @ X4) @ X5))) | (X4 = X5)) )),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f33,f41])).
% 0.22/0.31 thf(f77,plain,(
% 0.22/0.31 ( ! [X2 : ($i > $o),X0 : $i,X1 : $i] : (($true != $true) | (((dsetconstr @ X1 @ X2)) = X0) | ($true = ((in @ (sK3 @ X0 @ (dsetconstr @ X1 @ X2)) @ X1))) | (((in @ (sK2 @ X0 @ (dsetconstr @ X1 @ X2)) @ X0)) = $true)) )),
% 0.22/0.31 inference(superposition,[],[f57,f76])).
% 0.22/0.31 thf(f80,plain,(
% 0.22/0.31 ( ! [X2 : ($i > $o),X0 : $i,X1 : $i] : ((((in @ (sK2 @ X0 @ (dsetconstr @ X1 @ X2)) @ X0)) = $true) | ($true = ((in @ (sK3 @ X0 @ (dsetconstr @ X1 @ X2)) @ X1))) | (((dsetconstr @ X1 @ X2)) = X0)) )),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f77])).
% 0.22/0.31 thf(f93,plain,(
% 0.22/0.31 ( ! [X0 : $i,X1 : ($i > $o)] : ((((dsetconstr @ X0 @ X1)) = X0) | (((in @ (sK3 @ X0 @ (dsetconstr @ X0 @ X1)) @ X0)) = $true) | ($true != ((X1 @ (sK2 @ X0 @ (dsetconstr @ X0 @ X1))))) | (((dsetconstr @ X0 @ X1)) = X0) | ($true != $true) | (((in @ (sK3 @ X0 @ (dsetconstr @ X0 @ X1)) @ X0)) = $true)) )),
% 0.22/0.31 inference(superposition,[],[f64,f80])).
% 0.22/0.31 thf(f101,plain,(
% 0.22/0.31 ( ! [X0 : $i,X1 : ($i > $o)] : ((((dsetconstr @ X0 @ X1)) = X0) | ($true != $true) | (((in @ (sK3 @ X0 @ (dsetconstr @ X0 @ X1)) @ X0)) = $true) | ($true != ((X1 @ (sK2 @ X0 @ (dsetconstr @ X0 @ X1)))))) )),
% 0.22/0.31 inference(duplicate_literal_removal,[],[f93])).
% 0.22/0.31 thf(f102,plain,(
% 0.22/0.31 ( ! [X0 : $i,X1 : ($i > $o)] : (($true != ((X1 @ (sK2 @ X0 @ (dsetconstr @ X0 @ X1))))) | (((in @ (sK3 @ X0 @ (dsetconstr @ X0 @ X1)) @ X0)) = $true) | (((dsetconstr @ X0 @ X1)) = X0)) )),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f101])).
% 0.22/0.31 thf(f103,plain,(
% 0.22/0.31 ( ! [X4 : $i,X5 : $i] : (($true = ((in @ (sK2 @ X5 @ X4) @ X5))) | (((in @ (sK3 @ X5 @ X4) @ X5)) != $true) | (X4 = X5)) )),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f34,f41])).
% 0.22/0.31 thf(f118,plain,(
% 0.22/0.31 ( ! [X0 : $i] : (((((^[Y0 : $i]: ($true)) @ (sK2 @ X0 @ (dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))))) != $true) | ($true = ((in @ (sK3 @ X0 @ (dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) @ X0))) | (((dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) = X0)) )),
% 0.22/0.31 inference(imitation,[],[f102])).
% 0.22/0.31 thf(f119,plain,(
% 0.22/0.31 ( ! [X0 : $i] : (($true != $true) | ($true = ((in @ (sK3 @ X0 @ (dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) @ X0))) | (((dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) = X0)) )),
% 0.22/0.31 inference(beta-eta_normalization,[],[f118])).
% 0.22/0.31 thf(f120,plain,(
% 0.22/0.31 ( ! [X0 : $i] : (($true = ((in @ (sK3 @ X0 @ (dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) @ X0))) | (((dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) = X0)) )),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f119])).
% 0.22/0.31 thf(f126,plain,(
% 0.22/0.31 ( ! [X0 : $i] : (($true != $true) | (((in @ (sK2 @ X0 @ (dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) @ X0)) != $true) | (((dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) = X0) | ((((^[Y0 : $i]: ($true)) @ (sK2 @ X0 @ (dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))))) != $true) | (((dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) = X0)) )),
% 0.22/0.31 inference(superposition,[],[f69,f120])).
% 0.22/0.31 thf(f128,plain,(
% 0.22/0.31 ( ! [X0 : $i] : (($true != $true) | (((dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) = X0) | ((((^[Y0 : $i]: ($true)) @ (sK2 @ X0 @ (dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))))) != $true) | (((in @ (sK2 @ X0 @ (dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) @ X0)) != $true)) )),
% 0.22/0.31 inference(duplicate_literal_removal,[],[f126])).
% 0.22/0.31 thf(f129,plain,(
% 0.22/0.31 ( ! [X0 : $i] : ((((in @ (sK2 @ X0 @ (dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) @ X0)) != $true) | ((((^[Y0 : $i]: ($true)) @ (sK2 @ X0 @ (dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))))) != $true) | (((dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) = X0)) )),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f128])).
% 0.22/0.31 thf(f130,plain,(
% 0.22/0.31 ( ! [X0 : $i] : ((((dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) = X0) | ($true != $true) | (((in @ (sK2 @ X0 @ (dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) @ X0)) != $true)) )),
% 0.22/0.31 inference(beta-eta_normalization,[],[f129])).
% 0.22/0.31 thf(f131,plain,(
% 0.22/0.31 ( ! [X0 : $i] : ((((in @ (sK2 @ X0 @ (dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) @ X0)) != $true) | (((dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) = X0)) )),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f130])).
% 0.22/0.31 thf(f139,plain,(
% 0.22/0.31 ( ! [X0 : $i] : ((((dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) = X0) | ($true != ((in @ (sK3 @ X0 @ (dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) @ X0))) | ($true != $true) | (((dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) = X0)) )),
% 0.22/0.31 inference(superposition,[],[f131,f103])).
% 0.22/0.31 thf(f144,plain,(
% 0.22/0.31 ( ! [X0 : $i] : (($true != ((in @ (sK3 @ X0 @ (dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) @ X0))) | ($true != $true) | (((dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) = X0)) )),
% 0.22/0.31 inference(duplicate_literal_removal,[],[f139])).
% 0.22/0.31 thf(f145,plain,(
% 0.22/0.31 ( ! [X0 : $i] : ((((dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) = X0) | ($true != ((in @ (sK3 @ X0 @ (dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) @ X0)))) )),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f144])).
% 0.22/0.31 thf(f146,plain,(
% 0.22/0.31 ( ! [X0 : $i] : ((((dsetconstr @ X0 @ (^[Y0 : $i]: ($true)))) = X0)) )),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f145,f120])).
% 0.22/0.31 thf(f147,plain,(
% 0.22/0.31 (sK7 != sK7)),
% 0.22/0.31 inference(superposition,[],[f42,f146])).
% 0.22/0.31 thf(f162,plain,(
% 0.22/0.31 $false),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f147])).
% 0.22/0.31 % SZS output end Proof for theBenchmark
% 0.22/0.31 % (790144)------------------------------
% 0.22/0.31 % (790144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (790144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (790144)CaDiCaL version: 2.1.3
% 0.22/0.31 % (790144)Termination reason: Refutation
% 0.22/0.31 % (790144)Time elapsed: 0.013 s
% 0.22/0.31 % (790144)Peak memory usage: 12 MB
% 0.22/0.31 % (790144)Instructions burned: 23 (million)
% 0.22/0.31 % (790135)Success in time 0.048 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------