%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU680^2 : 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 : n008.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 08:30:43 AM UTC 2026
% Result : Theorem 0.31s 0.40s
% Output : Refutation 0.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU680^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.26 % Computer : n008.cluster.edu
% 0.11/0.26 % Model : x86_64 x86_64
% 0.11/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.26 % Memory : 8046.5625MB
% 0.11/0.26 % OS : Linux 6.8.0-71-generic
% 0.11/0.26 % CPULimit : 300
% 0.11/0.26 % WCLimit : 300
% 0.11/0.26 % DateTime : Tue Sep 29 14:09:04 UTC 2026
% 0.11/0.27 % CPUTime :
% 0.11/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.32 Running higher-order theorem proving
% 0.24/0.34 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
% 0.31/0.40 % (3214184)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.31/0.40 % (3214191)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2003954057:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.31/0.40 % (3214191)Instruction limit reached!
% 0.31/0.40 % (3214191)------------------------------
% 0.31/0.40 % (3214191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.40 % (3214191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.40 % (3214191)CaDiCaL version: 2.1.3
% 0.31/0.40 % (3214191)Termination reason: Instruction limit
% 0.31/0.40 % (3214191)Termination phase: Saturation
% 0.31/0.40 % (3214191)Time elapsed: 0.002 s
% 0.31/0.40 % (3214191)Peak memory usage: 11 MB
% 0.31/0.40 % (3214191)Instructions burned: 4 (million)
% 0.31/0.40 % (3214190)lrs+10_16_si=on:nwc=1.5:random_seed=3663234708:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.31/0.40 % (3214189)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=654724071:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.31/0.40 % (3214195)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.31/0.40 % (3214195)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
% 0.31/0.40 % (3214193)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2623512242:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.31/0.40 % (3214192)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=941023761: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)
% 0.31/0.40 % (3214194)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2693485765:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.31/0.40 % (3214195)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=2913338658:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.31/0.40 % (3214192) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3214184-3214192"...
% 0.31/0.40 % (3214193) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3214184-3214193"...
% 0.31/0.40 % (3214189)Refutation not found, incomplete strategy
% 0.31/0.40 % (3214189)------------------------------
% 0.31/0.40 % (3214189)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.40 % (3214189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.40 % (3214189)CaDiCaL version: 2.1.3
% 0.31/0.40 % (3214189)Termination reason: Refutation not found, incomplete strategy
% 0.31/0.40 % (3214189)Time elapsed: 0.015 s
% 0.31/0.40 % (3214189)Peak memory usage: 12 MB
% 0.31/0.40 % (3214189)Instructions burned: 15 (million)
% 0.31/0.40 % (3214189)------------------------------
% 0.31/0.40 % (3214189)------------------------------
% 0.31/0.40 % (3214190)Instruction limit reached!
% 0.31/0.40 % (3214190)------------------------------
% 0.31/0.40 % (3214190)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.40 % (3214190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.40 % (3214190)CaDiCaL version: 2.1.3
% 0.31/0.40 % (3214190)Termination reason: Instruction limit
% 0.31/0.40 % (3214190)Termination phase: Saturation
% 0.31/0.40 % (3214190)Time elapsed: 0.017 s
% 0.31/0.40 % (3214190)Peak memory usage: 12 MB
% 0.31/0.40 % (3214190)Instructions burned: 18 (million)
% 0.31/0.40 % (3214193)...printing done.
% 0.31/0.40 % (3214192)...printing done.
% 0.31/0.40 % (3214193)Refutation found. Thanks to Tanya!
% 0.31/0.40 % SZS status Theorem for theBenchmark
% 0.31/0.40 % SZS output start Proof for theBenchmark
% 0.31/0.40 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.31/0.40 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.31/0.40 thf(func_def_2, type, setadjoin: ($i > $i > $i)).
% 0.31/0.40 thf(func_def_3, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.31/0.40 thf(func_def_4, type, subset: ($i > $i > $o)).
% 0.31/0.40 thf(func_def_5, type, kpair: ($i > $i > $i)).
% 0.31/0.40 thf(func_def_6, type, cartprod: ($i > $i > $i)).
% 0.31/0.40 thf(func_def_7, type, singleton: ($i > $o)).
% 0.31/0.40 thf(func_def_9, type, ex1: ($i > ($i > $o) > $o)).
% 0.31/0.40 thf(func_def_10, type, breln: ($i > $i > $i > $o)).
% 0.31/0.40 thf(func_def_11, type, dpsetconstr: ($i > $i > ($i > $i > $o) > $i)).
% 0.31/0.40 thf(func_def_12, type, func: ($i > $i > $i > $o)).
% 0.31/0.40 thf(func_def_13, type, funcSet: ($i > $i > $i)).
% 0.31/0.40 thf(func_def_14, type, funcinfuncset: $o).
% 0.31/0.40 thf(func_def_15, type, lam: ($i > $i > ($i > $i) > $i)).
% 0.31/0.40 thf(func_def_16, type, lamp: $o).
% 0.31/0.40 thf(func_def_19, type, vAND: ($o > $o > $o)).
% 0.31/0.40 thf(func_def_20, type, db2: !>[X0: $tType]:(X0)).
% 0.31/0.40 thf(func_def_21, type, db1: !>[X0: $tType]:(X0)).
% 0.31/0.40 thf(func_def_22, type, db0: !>[X0: $tType]:(X0)).
% 0.31/0.40 thf(func_def_23, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.31/0.40 thf(func_def_24, type, vIMP: ($o > $o > $o)).
% 0.31/0.40 thf(func_def_25, type, db3: !>[X0: $tType]:(X0)).
% 0.31/0.40 thf(func_def_26, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.31/0.40 thf(func_def_27, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.31/0.40 thf(func_def_28, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.31/0.40 thf(func_def_33, type, sK4: ($i > $i)).
% 0.31/0.40 thf(func_def_35, type, sK6: (($i > $i) > $i > $i > $i)).
% 0.31/0.40 thf(func_def_38, type, sK9: ($i > $i)).
% 0.31/0.40 thf(func_def_39, type, sK10: ($i > $i)).
% 0.31/0.40 thf(f5,axiom,(
% 0.31/0.40 (funcinfuncset = ! [X0 : $i,X2 : $i,X1 : $i] : ((func @ X0 @ X1 @ X2) => (in @ X2 @ (funcSet @ X0 @ X1))))),
% 0.31/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcinfuncset)).
% 0.31/0.40 thf(f7,axiom,(
% 0.31/0.40 (! [X2 : ($i > $i),X1 : $i,X0 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => (func @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X3 : $i] : ((X2 @ X3)))))) = lamp)),
% 0.31/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamp)).
% 0.31/0.40 thf(f8,conjecture,(
% 0.31/0.40 funcinfuncset => (lamp => ! [X0 : $i,X1 : $i,X2 : ($i > $i)] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => (in @ (lam @ X0 @ X1 @ (^[X3 : $i] : ((X2 @ X3)))) @ (funcSet @ X0 @ X1))))),
% 0.31/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lam2p)).
% 0.31/0.40 thf(f9,negated_conjecture,(
% 0.31/0.40 ~(funcinfuncset => (lamp => ! [X0 : $i,X1 : $i,X2 : ($i > $i)] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => (in @ (lam @ X0 @ X1 @ (^[X3 : $i] : ((X2 @ X3)))) @ (funcSet @ X0 @ X1)))))),
% 0.31/0.40 inference(negated_conjecture,[status(cth)],[f8])).
% 0.31/0.40 thf(f10,plain,(
% 0.31/0.40 (funcinfuncset = ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X0 @ X2 @ X1) => (in @ X1 @ (funcSet @ X0 @ X2))))),
% 0.31/0.40 inference(rectify,[],[f5])).
% 0.31/0.40 thf(f11,plain,(
% 0.31/0.40 (funcinfuncset = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((func @ X0 @ X2 @ X1))) => ($true = ((in @ X1 @ (funcSet @ X0 @ X2)))))),
% 0.31/0.40 inference(fool_elimination,[],[f10])).
% 0.31/0.40 thf(f14,plain,(
% 0.31/0.40 (! [X0 : ($i > $i),X1 : $i,X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X2) => (in @ (X0 @ X3) @ X1)) => (func @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[X4 : $i] : ((X0 @ X4)))))) = lamp)),
% 0.31/0.40 inference(rectify,[],[f7])).
% 0.31/0.40 thf(f15,plain,(
% 0.31/0.40 ! [X0 : ($i > $i),X1 : $i,X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X2)) = $true) => (((in @ (X0 @ X3) @ X1)) = $true)) => (((func @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true)) <=> (lamp = $true)),
% 0.31/0.40 inference(fool_elimination,[],[f14])).
% 0.31/0.40 thf(f21,plain,(
% 0.31/0.40 ~(funcinfuncset => (lamp => ! [X0 : $i,X1 : $i,X2 : ($i > $i)] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => (in @ (lam @ X0 @ X1 @ (^[X4 : $i] : ((X2 @ X4)))) @ (funcSet @ X0 @ X1)))))),
% 0.31/0.40 inference(rectify,[],[f9])).
% 0.31/0.40 thf(f22,plain,(
% 0.31/0.40 ~((funcinfuncset = $true) => ((lamp = $true) => ! [X0 : $i,X2 : ($i > $i),X1 : $i] : (! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => (((in @ (X2 @ X3) @ X1)) = $true)) => (((in @ (lam @ X0 @ X1 @ (^[Y0 : $i]: (X2 @ Y0))) @ (funcSet @ X0 @ X1))) = $true))))),
% 0.31/0.40 inference(fool_elimination,[],[f21])).
% 0.31/0.40 thf(f25,plain,(
% 0.31/0.40 ! [X1 : $i,X2 : $i,X0 : ($i > $i)] : ((((func @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true) | ? [X3 : $i] : ((((in @ X3 @ X2)) = $true) & (((in @ (X0 @ X3) @ X1)) != $true))) <=> (lamp = $true)),
% 0.31/0.40 inference(ennf_transformation,[],[f15])).
% 0.31/0.40 thf(f26,plain,(
% 0.31/0.40 (? [X1 : $i,X2 : ($i > $i),X0 : $i] : (! [X3 : $i] : ((((in @ (X2 @ X3) @ X1)) = $true) | (((in @ X3 @ X0)) != $true)) & (((in @ (lam @ X0 @ X1 @ (^[Y0 : $i]: (X2 @ Y0))) @ (funcSet @ X0 @ X1))) != $true)) & (lamp = $true)) & (funcinfuncset = $true)),
% 0.31/0.41 inference(ennf_transformation,[],[f22])).
% 0.31/0.41 thf(f27,plain,(
% 0.31/0.41 (lamp = $true) & (funcinfuncset = $true) & ? [X1 : $i,X2 : ($i > $i),X0 : $i] : (! [X3 : $i] : ((((in @ (X2 @ X3) @ X1)) = $true) | (((in @ X3 @ X0)) != $true)) & (((in @ (lam @ X0 @ X1 @ (^[Y0 : $i]: (X2 @ Y0))) @ (funcSet @ X0 @ X1))) != $true))),
% 0.31/0.41 inference(flattening,[],[f26])).
% 0.31/0.41 thf(f28,plain,(
% 0.31/0.41 (funcinfuncset = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : (($true != ((func @ X0 @ X2 @ X1))) | ($true = ((in @ X1 @ (funcSet @ X0 @ X2)))))),
% 0.31/0.41 inference(ennf_transformation,[],[f11])).
% 0.31/0.41 thf(f29,plain,(
% 0.31/0.41 ((funcinfuncset = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : (($true = ((func @ X0 @ X2 @ X1))) & ($true != ((in @ X1 @ (funcSet @ X0 @ X2)))))) & (! [X2 : $i,X1 : $i,X0 : $i] : (($true != ((func @ X0 @ X2 @ X1))) | ($true = ((in @ X1 @ (funcSet @ X0 @ X2))))) | (funcinfuncset != $true))),
% 0.31/0.41 inference(nnf_transformation,[],[f28])).
% 0.31/0.41 thf(f30,plain,(
% 0.31/0.41 ((funcinfuncset = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((func @ X2 @ X0 @ X1)) = $true) & (((in @ X1 @ (funcSet @ X2 @ X0))) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((((func @ X5 @ X3 @ X4)) != $true) | (((in @ X4 @ (funcSet @ X5 @ X3))) = $true)) | (funcinfuncset != $true))),
% 0.31/0.41 inference(rectify,[],[f29])).
% 0.31/0.41 thf(f31,plain,(
% 0.31/0.41 ((funcinfuncset = $true) | ((((func @ sK2 @ sK0 @ sK1)) = $true) & (((in @ sK1 @ (funcSet @ sK2 @ sK0))) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((((func @ X5 @ X3 @ X4)) != $true) | (((in @ X4 @ (funcSet @ X5 @ X3))) = $true)) | (funcinfuncset != $true))),
% 0.31/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f30])).
% 0.31/0.41 thf(f32,plain,(
% 0.31/0.41 (lamp = $true) & (funcinfuncset = $true) & ? [X0 : $i,X1 : ($i > $i),X2 : $i] : (! [X3 : $i] : ((((in @ (X1 @ X3) @ X0)) = $true) | (((in @ X3 @ X2)) != $true)) & (((in @ (lam @ X2 @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ (funcSet @ X2 @ X0))) != $true))),
% 0.31/0.41 inference(rectify,[],[f27])).
% 0.31/0.41 thf(f33,plain,(
% 0.31/0.41 (lamp = $true) & (funcinfuncset = $true) & (! [X3 : $i] : ((((in @ (sK4 @ X3) @ sK3)) = $true) | (((in @ X3 @ sK5)) != $true)) & (((in @ (lam @ sK5 @ sK3 @ (^[Y0 : $i]: (sK4 @ Y0))) @ (funcSet @ sK5 @ sK3))) != $true))),
% 0.31/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f32])).
% 0.31/0.41 thf(f34,plain,(
% 0.31/0.41 (! [X1 : $i,X2 : $i,X0 : ($i > $i)] : ((((func @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true) | ? [X3 : $i] : ((((in @ X3 @ X2)) = $true) & (((in @ (X0 @ X3) @ X1)) != $true))) | (lamp != $true)) & ((lamp = $true) | ? [X1 : $i,X2 : $i,X0 : ($i > $i)] : ((((func @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) != $true) & ! [X3 : $i] : ((((in @ X3 @ X2)) != $true) | (((in @ (X0 @ X3) @ X1)) = $true))))),
% 0.31/0.41 inference(nnf_transformation,[],[f25])).
% 0.31/0.41 thf(f35,plain,(
% 0.31/0.41 (! [X0 : $i,X1 : $i,X2 : ($i > $i)] : ((((func @ X1 @ X0 @ (lam @ X1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) = $true) | ? [X3 : $i] : ((((in @ X3 @ X1)) = $true) & (((in @ (X2 @ X3) @ X0)) != $true))) | (lamp != $true)) & ((lamp = $true) | ? [X4 : $i,X5 : $i,X6 : ($i > $i)] : ((((func @ X5 @ X4 @ (lam @ X5 @ X4 @ (^[Y0 : $i]: (X6 @ Y0))))) != $true) & ! [X7 : $i] : ((((in @ X7 @ X5)) != $true) | (((in @ (X6 @ X7) @ X4)) = $true))))),
% 0.31/0.41 inference(rectify,[],[f34])).
% 0.31/0.41 thf(f36,plain,(
% 0.31/0.41 (! [X0 : $i,X1 : $i,X2 : ($i > $i)] : ((((func @ X1 @ X0 @ (lam @ X1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) = $true) | ((((in @ (sK6 @ X2 @ X1 @ X0) @ X1)) = $true) & (((in @ (X2 @ (sK6 @ X2 @ X1 @ X0)) @ X0)) != $true))) | (lamp != $true)) & ((lamp = $true) | ((((func @ sK8 @ sK7 @ (lam @ sK8 @ sK7 @ (^[Y0 : $i]: (sK9 @ Y0))))) != $true) & ! [X7 : $i] : ((((in @ X7 @ sK8)) != $true) | (((in @ (sK9 @ X7) @ sK7)) = $true))))),
% 0.31/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK7,sK8,sK9]),skolemize(X3,sK6 @ X2 @ X1 @ X0),skolemize(X4,sK7),skolemize(X5,sK8),skolemize(X6,sK9)],[f35])).
% 0.31/0.41 thf(f38,plain,(
% 0.31/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((func @ X5 @ X3 @ X4)) != $true) | (((in @ X4 @ (funcSet @ X5 @ X3))) = $true) | (funcinfuncset != $true)) )),
% 0.31/0.41 inference(cnf_transformation,[],[f31])).
% 0.31/0.41 thf(f44,plain,(
% 0.31/0.41 (((in @ (lam @ sK5 @ sK3 @ (^[Y0 : $i]: (sK4 @ Y0))) @ (funcSet @ sK5 @ sK3))) != $true)),
% 0.31/0.41 inference(cnf_transformation,[],[f33])).
% 0.31/0.41 thf(f45,plain,(
% 0.31/0.41 ( ! [X3 : $i] : ((((in @ (sK4 @ X3) @ sK3)) = $true) | (((in @ X3 @ sK5)) != $true)) )),
% 0.31/0.41 inference(cnf_transformation,[],[f33])).
% 0.31/0.41 thf(f46,plain,(
% 0.31/0.41 (funcinfuncset = $true)),
% 0.31/0.41 inference(cnf_transformation,[],[f33])).
% 0.31/0.41 thf(f47,plain,(
% 0.31/0.41 (lamp = $true)),
% 0.31/0.41 inference(cnf_transformation,[],[f33])).
% 0.31/0.41 thf(f50,plain,(
% 0.31/0.41 ( ! [X2 : ($i > $i),X0 : $i,X1 : $i] : ((lamp != $true) | (((func @ X1 @ X0 @ (lam @ X1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) = $true) | (((in @ (X2 @ (sK6 @ X2 @ X1 @ X0)) @ X0)) != $true)) )),
% 0.31/0.41 inference(cnf_transformation,[],[f36])).
% 0.31/0.41 thf(f51,plain,(
% 0.31/0.41 ( ! [X2 : ($i > $i),X0 : $i,X1 : $i] : ((((in @ (sK6 @ X2 @ X1 @ X0) @ X1)) = $true) | (((func @ X1 @ X0 @ (lam @ X1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) = $true) | (lamp != $true)) )),
% 0.31/0.41 inference(cnf_transformation,[],[f36])).
% 0.31/0.41 thf(f54,plain,(
% 0.31/0.41 ( ! [X2 : ($i > $i),X0 : $i,X1 : $i] : ((((func @ X1 @ X0 @ (lam @ X1 @ X0 @ X2))) = $true) | (lamp != $true) | (((in @ (sK6 @ X2 @ X1 @ X0) @ X1)) = $true)) )),
% 0.31/0.41 inference(beta-eta_normalization,[],[f51])).
% 0.31/0.41 thf(f58,plain,(
% 0.31/0.41 ( ! [X2 : ($i > $i),X0 : $i,X1 : $i] : ((((in @ (X2 @ (sK6 @ X2 @ X1 @ X0)) @ X0)) != $true) | (lamp != $true) | (((func @ X1 @ X0 @ (lam @ X1 @ X0 @ X2))) = $true)) )),
% 0.31/0.41 inference(beta-eta_normalization,[],[f50])).
% 0.31/0.41 thf(f59,plain,(
% 0.31/0.41 ($true != ((in @ (lam @ sK5 @ sK3 @ sK4) @ (funcSet @ sK5 @ sK3))))),
% 0.31/0.41 inference(beta-eta_normalization,[],[f44])).
% 0.31/0.41 thf(f78,plain,(
% 0.31/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X4 @ (funcSet @ X5 @ X3))) = $true) | (((func @ X5 @ X3 @ X4)) != $true)) )),
% 0.31/0.41 inference(forward_subsumption_resolution,[],[f38,f46])).
% 0.31/0.41 thf(f79,plain,(
% 0.31/0.41 (((func @ sK5 @ sK3 @ (lam @ sK5 @ sK3 @ sK4))) != $true) | ($true != $true)),
% 0.31/0.41 inference(superposition,[],[f59,f78])).
% 0.31/0.41 thf(f80,plain,(
% 0.31/0.41 (((func @ sK5 @ sK3 @ (lam @ sK5 @ sK3 @ sK4))) != $true)),
% 0.31/0.41 inference(trivial_inequality_removal,[],[f79])).
% 0.31/0.41 thf(f105,plain,(
% 0.31/0.41 ( ! [X2 : ($i > $i),X0 : $i,X1 : $i] : ((((func @ X1 @ X0 @ (lam @ X1 @ X0 @ X2))) = $true) | (((in @ (sK6 @ X2 @ X1 @ X0) @ X1)) = $true)) )),
% 0.31/0.41 inference(forward_subsumption_resolution,[],[f54,f47])).
% 0.31/0.41 thf(f106,plain,(
% 0.31/0.41 (((in @ (sK6 @ sK4 @ sK5 @ sK3) @ sK5)) = $true) | ($true != $true)),
% 0.31/0.41 inference(superposition,[],[f80,f105])).
% 0.31/0.41 thf(f107,plain,(
% 0.31/0.41 (((in @ (sK6 @ sK4 @ sK5 @ sK3) @ sK5)) = $true)),
% 0.31/0.41 inference(trivial_inequality_removal,[],[f106])).
% 0.31/0.41 thf(f129,plain,(
% 0.31/0.41 ( ! [X2 : ($i > $i),X0 : $i,X1 : $i] : ((((in @ (X2 @ (sK6 @ X2 @ X1 @ X0)) @ X0)) != $true) | (((func @ X1 @ X0 @ (lam @ X1 @ X0 @ X2))) = $true)) )),
% 0.31/0.41 inference(forward_subsumption_resolution,[],[f58,f47])).
% 0.31/0.41 thf(f134,plain,(
% 0.31/0.41 ( ! [X0 : $i] : ((((func @ X0 @ sK3 @ (lam @ X0 @ sK3 @ sK4))) = $true) | (((in @ (sK6 @ sK4 @ X0 @ sK3) @ sK5)) != $true) | ($true != $true)) )),
% 0.31/0.41 inference(superposition,[],[f129,f45])).
% 0.31/0.41 thf(f135,plain,(
% 0.31/0.41 ( ! [X0 : $i] : ((((func @ X0 @ sK3 @ (lam @ X0 @ sK3 @ sK4))) = $true) | (((in @ (sK6 @ sK4 @ X0 @ sK3) @ sK5)) != $true)) )),
% 0.31/0.41 inference(trivial_inequality_removal,[],[f134])).
% 0.31/0.41 thf(f139,plain,(
% 0.31/0.41 ($true != $true) | (((in @ (sK6 @ sK4 @ sK5 @ sK3) @ sK5)) != $true)),
% 0.31/0.41 inference(superposition,[],[f80,f135])).
% 0.31/0.41 thf(f141,plain,(
% 0.31/0.41 (((in @ (sK6 @ sK4 @ sK5 @ sK3) @ sK5)) != $true)),
% 0.31/0.41 inference(trivial_inequality_removal,[],[f139])).
% 0.31/0.41 thf(f143,plain,(
% 0.31/0.41 $false),
% 0.31/0.41 inference(forward_subsumption_resolution,[],[f141,f107])).
% 0.31/0.41 % SZS output end Proof for theBenchmark
% 0.31/0.41 % (3214193)------------------------------
% 0.31/0.41 % (3214193)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.41 % (3214193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.41 % (3214193)CaDiCaL version: 2.1.3
% 0.31/0.41 % (3214193)Termination reason: Refutation
% 0.31/0.41 % (3214193)Time elapsed: 0.016 s
% 0.31/0.41 % (3214193)Peak memory usage: 12 MB
% 0.31/0.41 % (3214193)Instructions burned: 15 (million)
% 0.31/0.41 % (3214184)Success in time 0.054 s
% 0.31/0.41 % Vampire exiting
%------------------------------------------------------------------------------