%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU534^2 : 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 : n017.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 08:29:58 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU534^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:44:07 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.21/0.30 % (360907)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (360914)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3722992448:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.30 % (360914)Refutation not found, incomplete strategy
% 0.21/0.30 % (360914)------------------------------
% 0.21/0.30 % (360914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (360914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (360914)CaDiCaL version: 2.1.3
% 0.21/0.30 % (360914)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.30 % (360914)Time elapsed: 0.002 s
% 0.21/0.30 % (360914)Peak memory usage: 12 MB
% 0.21/0.30 % (360914)Instructions burned: 3 (million)
% 0.21/0.30 % (360914)------------------------------
% 0.21/0.30 % (360914)------------------------------
% 0.21/0.30 % (360921)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.30 % (360921)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
% 0.21/0.30 % (360916)lrs+10_16_si=on:nwc=1.5:random_seed=3688022170:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.30 % (360920)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3626862054:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.30 % (360919)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3020394393:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.30 % (360917)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4195490518:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.30 % (360921)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=3466743053:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.30 % (360918)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=2824833338: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)
% 0.21/0.30 % (360917)Refutation not found, incomplete strategy
% 0.21/0.30 % (360917)------------------------------
% 0.21/0.30 % (360917)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (360917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (360917)CaDiCaL version: 2.1.3
% 0.21/0.30 % (360917)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.30 % (360917)Time elapsed: 0.002 s
% 0.21/0.30 % (360917)Peak memory usage: 12 MB
% 0.21/0.30 % (360917)Instructions burned: 2 (million)
% 0.21/0.30 % (360916)Refutation not found, incomplete strategy
% 0.21/0.30 % (360916)------------------------------
% 0.21/0.30 % (360916)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (360916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (360916)CaDiCaL version: 2.1.3
% 0.21/0.30 % (360916)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.30 % (360916)Time elapsed: 0.002 s
% 0.21/0.30 % (360916)Peak memory usage: 12 MB
% 0.21/0.30 % (360916)Instructions burned: 2 (million)
% 0.21/0.30 % (360919) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-360907-360919"...
% 0.21/0.30 % (360917)------------------------------
% 0.21/0.30 % (360917)------------------------------
% 0.21/0.30 % (360916)------------------------------
% 0.21/0.30 % (360916)------------------------------
% 0.21/0.30 % (360918)Refutation not found, incomplete strategy
% 0.21/0.30 % (360918)------------------------------
% 0.21/0.30 % (360918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (360918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (360918)CaDiCaL version: 2.1.3
% 0.21/0.30 % (360918)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.30 % (360918)Time elapsed: 0.003 s
% 0.21/0.30 % (360918)Peak memory usage: 12 MB
% 0.21/0.30 % (360918)Instructions burned: 3 (million)
% 0.21/0.30 % (360920) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-360907-360920"...
% 0.21/0.30 % (360918)------------------------------
% 0.21/0.30 % (360918)------------------------------
% 0.21/0.30 % (360919)...printing done.
% 0.21/0.30 % (360921) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-360907-360921"...
% 0.21/0.30 % (360919)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% 0.21/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.30 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.21/0.30 thf(func_def_2, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.21/0.30 thf(func_def_3, type, dsetconstrI: $o).
% 0.21/0.30 thf(func_def_5, type, emptysetE: $o).
% 0.21/0.30 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.30 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.30 thf(func_def_10, type, sK0: ($i > $o)).
% 0.21/0.30 thf(func_def_14, type, sK4: ($i > $o)).
% 0.21/0.30 thf(func_def_17, type, sK7: $o).
% 0.21/0.30 thf(func_def_18, type, vNOT: ($o > $o)).
% 0.21/0.30 thf(f1,axiom,(
% 0.21/0.30 (dsetconstrI = ! [X2 : $i,X1 : ($i > $o),X0 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))))))),
% 0.21/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI)).
% 0.21/0.30 thf(f2,axiom,(
% 0.21/0.30 (! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1) = emptysetE)),
% 0.21/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE)).
% 0.21/0.30 thf(f3,conjecture,(
% 0.21/0.30 dsetconstrI => (emptysetE => ! [X1 : ($i > $o),X0 : $i] : (? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2)) => ((emptyset = ((dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2)))))) => $false)))),
% 0.21/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1)).
% 0.21/0.30 thf(f4,negated_conjecture,(
% 0.21/0.30 ~(dsetconstrI => (emptysetE => ! [X1 : ($i > $o),X0 : $i] : (? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2)) => ((emptyset = ((dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2)))))) => $false))))),
% 0.21/0.30 inference(negated_conjecture,[status(cth)],[f3])).
% 0.21/0.30 thf(f5,plain,(
% 0.21/0.30 (! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1) = emptysetE)),
% 0.21/0.30 inference(rectify,[],[f2])).
% 0.21/0.30 thf(f6,plain,(
% 0.21/0.30 ! [X0 : $i] : ((((in @ X0 @ emptyset)) = $true) => ! [X1 : $o] : ($true = X1)) <=> (emptysetE = $true)),
% 0.21/0.30 inference(fool_elimination,[],[f5])).
% 0.21/0.30 thf(f7,plain,(
% 0.21/0.30 (dsetconstrI = ! [X0 : $i,X1 : ($i > $o),X2 : $i] : ((in @ X0 @ X2) => ((X1 @ X0) => (in @ X0 @ (dsetconstr @ X2 @ (^[X3 : $i] : ((X1 @ X3))))))))),
% 0.21/0.30 inference(rectify,[],[f1])).
% 0.21/0.30 thf(f8,plain,(
% 0.21/0.30 (dsetconstrI = $true) <=> ! [X0 : $i,X2 : $i,X1 : ($i > $o)] : ((((in @ X0 @ X2)) = $true) => ((((X1 @ X0)) = $true) => (((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0))))) = $true)))),
% 0.21/0.30 inference(fool_elimination,[],[f7])).
% 0.21/0.30 thf(f9,plain,(
% 0.21/0.30 ~(dsetconstrI => (emptysetE => ! [X0 : ($i > $o),X1 : $i] : (? [X2 : $i] : ((in @ X2 @ X1) & (X0 @ X2)) => ((emptyset = ((dsetconstr @ X1 @ (^[X3 : $i] : ((X0 @ X3)))))) => $false))))),
% 0.21/0.30 inference(rectify,[],[f4])).
% 0.21/0.30 thf(f10,plain,(
% 0.21/0.30 ~((dsetconstrI = $true) => ((emptysetE = $true) => ! [X0 : ($i > $o),X1 : $i] : (? [X2 : $i] : (($true = ((in @ X2 @ X1))) & ($true = ((X0 @ X2)))) => ((emptyset = ((dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) => $false))))),
% 0.21/0.30 inference(fool_elimination,[],[f9])).
% 0.21/0.30 thf(f11,plain,(
% 0.21/0.30 ~((dsetconstrI = $true) => ((emptysetE = $true) => ! [X0 : ($i > $o),X1 : $i] : (? [X2 : $i] : (($true = ((in @ X2 @ X1))) & ($true = ((X0 @ X2)))) => ~ (emptyset = ((dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))))))),
% 0.21/0.30 inference(true_and_false_elimination,[],[f10])).
% 0.21/0.30 thf(f12,plain,(
% 0.21/0.30 ~((dsetconstrI = $true) => ((emptysetE = $true) => ! [X1 : $i,X0 : ($i > $o)] : (? [X2 : $i] : (($true = ((in @ X2 @ X1))) & ($true = ((X0 @ X2)))) => (emptyset != ((dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))))))),
% 0.21/0.30 inference(flattening,[],[f11])).
% 0.21/0.30 thf(f13,plain,(
% 0.21/0.30 (dsetconstrI = $true) <=> ! [X0 : $i,X2 : $i,X1 : ($i > $o)] : (((((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0))))) = $true) | (((X1 @ X0)) != $true)) | (((in @ X0 @ X2)) != $true))),
% 0.21/0.30 inference(ennf_transformation,[],[f8])).
% 0.21/0.30 thf(f14,plain,(
% 0.21/0.30 ! [X1 : ($i > $o),X0 : $i,X2 : $i] : ((((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0))))) = $true) | (((in @ X0 @ X2)) != $true) | (((X1 @ X0)) != $true)) <=> (dsetconstrI = $true)),
% 0.21/0.30 inference(flattening,[],[f13])).
% 0.21/0.30 thf(f15,plain,(
% 0.21/0.30 ! [X0 : $i] : ((((in @ X0 @ emptyset)) != $true) | ! [X1 : $o] : ($true = X1)) <=> (emptysetE = $true)),
% 0.21/0.30 inference(ennf_transformation,[],[f6])).
% 0.21/0.30 thf(f16,plain,(
% 0.21/0.30 (? [X1 : $i,X0 : ($i > $o)] : (? [X2 : $i] : (($true = ((in @ X2 @ X1))) & ($true = ((X0 @ X2)))) & (emptyset = ((dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))))) & (emptysetE = $true)) & (dsetconstrI = $true)),
% 0.21/0.30 inference(ennf_transformation,[],[f12])).
% 0.21/0.30 thf(f17,plain,(
% 0.21/0.30 (emptysetE = $true) & (dsetconstrI = $true) & ? [X1 : $i,X0 : ($i > $o)] : (? [X2 : $i] : (($true = ((in @ X2 @ X1))) & ($true = ((X0 @ X2)))) & (emptyset = ((dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))))),
% 0.21/0.30 inference(flattening,[],[f16])).
% 0.21/0.30 thf(f18,plain,(
% 0.21/0.30 (! [X1 : ($i > $o),X0 : $i,X2 : $i] : ((((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0))))) = $true) | (((in @ X0 @ X2)) != $true) | (((X1 @ X0)) != $true)) | (dsetconstrI != $true)) & ((dsetconstrI = $true) | ? [X1 : ($i > $o),X0 : $i,X2 : $i] : ((((in @ X0 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X1 @ Y0))))) != $true) & (((in @ X0 @ X2)) = $true) & (((X1 @ X0)) = $true)))),
% 0.21/0.30 inference(nnf_transformation,[],[f14])).
% 0.21/0.30 thf(f19,plain,(
% 0.21/0.30 (! [X0 : ($i > $o),X1 : $i,X2 : $i] : ((((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true) | (((in @ X1 @ X2)) != $true) | (((X0 @ X1)) != $true)) | (dsetconstrI != $true)) & ((dsetconstrI = $true) | ? [X3 : ($i > $o),X4 : $i,X5 : $i] : ((((in @ X4 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X3 @ Y0))))) != $true) & ($true = ((in @ X4 @ X5))) & ($true = ((X3 @ X4)))))),
% 0.21/0.30 inference(rectify,[],[f18])).
% 0.21/0.30 thf(f20,plain,(
% 0.21/0.30 (! [X0 : ($i > $o),X1 : $i,X2 : $i] : ((((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true) | (((in @ X1 @ X2)) != $true) | (((X0 @ X1)) != $true)) | (dsetconstrI != $true)) & ((dsetconstrI = $true) | (($true != ((in @ sK1 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (sK0 @ Y0)))))) & (((in @ sK1 @ sK2)) = $true) & (((sK0 @ sK1)) = $true)))),
% 0.21/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0),skolemize(X4,sK1),skolemize(X5,sK2)],[f19])).
% 0.21/0.30 thf(f21,plain,(
% 0.21/0.30 (emptysetE = $true) & (dsetconstrI = $true) & ? [X0 : $i,X1 : ($i > $o)] : (? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((X1 @ X2)) = $true)) & (emptyset = ((dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))))))),
% 0.21/0.30 inference(rectify,[],[f17])).
% 0.21/0.30 thf(f22,plain,(
% 0.21/0.30 (emptysetE = $true) & (dsetconstrI = $true) & (((((in @ sK5 @ sK3)) = $true) & ($true = ((sK4 @ sK5)))) & (emptyset = ((dsetconstr @ sK3 @ (^[Y0 : $i]: (sK4 @ Y0))))))),
% 0.21/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f21])).
% 0.21/0.30 thf(f23,plain,(
% 0.21/0.30 (! [X0 : $i] : ((((in @ X0 @ emptyset)) != $true) | ! [X1 : $o] : ($true = X1)) | (emptysetE != $true)) & ((emptysetE = $true) | ? [X0 : $i] : ((((in @ X0 @ emptyset)) = $true) & ? [X1 : $o] : ($true != X1)))),
% 0.21/0.30 inference(nnf_transformation,[],[f15])).
% 0.21/0.30 thf(f24,plain,(
% 0.21/0.30 (! [X0 : $i] : ((((in @ X0 @ emptyset)) != $true) | ! [X1 : $o] : ($true = X1)) | (emptysetE != $true)) & ((emptysetE = $true) | ? [X2 : $i] : ((((in @ X2 @ emptyset)) = $true) & ? [X3 : $o] : ($true != X3)))),
% 0.21/0.30 inference(rectify,[],[f23])).
% 0.21/0.30 thf(f25,plain,(
% 0.21/0.30 (! [X0 : $i] : ((((in @ X0 @ emptyset)) != $true) | ! [X1 : $o] : ($true = X1)) | (emptysetE != $true)) & ((emptysetE = $true) | ((((in @ sK6 @ emptyset)) = $true) & (sK7 != $true)))),
% 0.21/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X2,sK6),skolemize(X3,sK7)],[f24])).
% 0.21/0.30 thf(f29,plain,(
% 0.21/0.30 ( ! [X2 : $i,X0 : ($i > $o),X1 : $i] : ((((X0 @ X1)) != $true) | (dsetconstrI != $true) | (((in @ X1 @ X2)) != $true) | (((in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f20])).
% 0.21/0.30 thf(f30,plain,(
% 0.21/0.30 (emptyset = ((dsetconstr @ sK3 @ (^[Y0 : $i]: (sK4 @ Y0)))))),
% 0.21/0.30 inference(cnf_transformation,[],[f22])).
% 0.21/0.30 thf(f31,plain,(
% 0.21/0.30 ($true = ((sK4 @ sK5)))),
% 0.21/0.30 inference(cnf_transformation,[],[f22])).
% 0.21/0.30 thf(f32,plain,(
% 0.21/0.30 (((in @ sK5 @ sK3)) = $true)),
% 0.21/0.30 inference(cnf_transformation,[],[f22])).
% 0.21/0.30 thf(f33,plain,(
% 0.21/0.30 (dsetconstrI = $true)),
% 0.21/0.30 inference(cnf_transformation,[],[f22])).
% 0.21/0.30 thf(f34,plain,(
% 0.21/0.30 (emptysetE = $true)),
% 0.21/0.30 inference(cnf_transformation,[],[f22])).
% 0.21/0.30 thf(f37,plain,(
% 0.21/0.30 ( ! [X0 : $i,X1 : $o] : (($true = X1) | (((in @ X0 @ emptyset)) != $true) | (emptysetE != $true)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f25])).
% 0.21/0.30 thf(f38,definition,(
% 0.21/0.30 ($false != $true)),
% 0.21/0.30 introduced(theory,[fool_distinctness_axiom])).
% 0.21/0.30 thf(f40,plain,(
% 0.21/0.30 ( ! [X2 : $i,X0 : ($i > $o),X1 : $i] : ((dsetconstrI != $true) | (((in @ X1 @ X2)) != $true) | (((X0 @ X1)) != $true) | ($true = ((in @ X1 @ (dsetconstr @ X2 @ X0))))) )),
% 0.21/0.30 inference(beta-eta_normalization,[],[f29])).
% 0.21/0.30 thf(f41,plain,(
% 0.21/0.30 (emptyset = ((dsetconstr @ sK3 @ sK4)))),
% 0.21/0.30 inference(beta-eta_normalization,[],[f30])).
% 0.21/0.30 thf(f44,plain,(
% 0.21/0.30 ( ! [X0 : $i,X1 : $o] : ((((in @ X0 @ emptyset)) != $true) | ($true = X1)) )),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f37,f34])).
% 0.21/0.30 thf(f45,plain,(
% 0.21/0.30 ( ! [X2 : $i,X0 : ($i > $o),X1 : $i] : (($true = ((in @ X1 @ (dsetconstr @ X2 @ X0)))) | (((in @ X1 @ X2)) != $true) | (((X0 @ X1)) != $true)) )),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f40,f33])).
% 0.21/0.30 thf(f46,plain,(
% 0.21/0.30 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK3))) | (((in @ X0 @ emptyset)) = $true) | ($true != ((sK4 @ X0)))) )),
% 0.21/0.30 inference(superposition,[],[f45,f41])).
% 0.21/0.30 thf(f47,plain,(
% 0.21/0.30 (((in @ sK5 @ emptyset)) = $true) | ($true != ((sK4 @ sK5))) | ($true != $true)),
% 0.21/0.30 inference(superposition,[],[f46,f32])).
% 0.21/0.30 thf(f48,plain,(
% 0.21/0.30 (((in @ sK5 @ emptyset)) = $true) | ($true != ((sK4 @ sK5)))),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f47])).
% 0.21/0.30 thf(f49,plain,(
% 0.21/0.30 (((in @ sK5 @ emptyset)) = $true)),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f48,f31])).
% 0.21/0.30 thf(f50,plain,(
% 0.21/0.30 ( ! [X0 : $o] : (($true = X0) | ($true != $true)) )),
% 0.21/0.30 inference(superposition,[],[f44,f49])).
% 0.21/0.30 thf(f51,plain,(
% 0.21/0.30 ( ! [X0 : $o] : (($true = X0)) )),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f50])).
% 0.21/0.30 thf(f53,plain,(
% 0.21/0.30 ( ! [X0 : $o] : (($false != X0)) )),
% 0.21/0.30 inference(superposition,[],[f38,f51])).
% 0.21/0.30 thf(f61,plain,(
% 0.21/0.30 $false),
% 0.21/0.30 inference(equality_resolution,[],[f53])).
% 0.21/0.30 % SZS output end Proof for theBenchmark
% 0.21/0.30 % (360919)------------------------------
% 0.21/0.30 % (360919)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (360919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (360919)CaDiCaL version: 2.1.3
% 0.21/0.30 % (360919)Termination reason: Refutation
% 0.21/0.30 % (360919)Time elapsed: 0.004 s
% 0.21/0.30 % (360919)Peak memory usage: 12 MB
% 0.21/0.30 % (360919)Instructions burned: 5 (million)
% 0.21/0.30 % (360907)Success in time 0.047 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------