%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU699^2 : 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 : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:30:50 AM UTC 2026
% Result : Theorem 0.18s 0.28s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU699^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n005.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:11:46 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 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
% 0.18/0.28 % (1725820)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.18/0.28 % (1725828)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=1673623651: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)
% 0.18/0.28 % (1725829)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3385368888:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.18/0.28 % (1725825)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2890443566:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.18/0.28 % (1725826)lrs+10_16_si=on:nwc=1.5:random_seed=485554979:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.18/0.28 % (1725827)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1733269548:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.18/0.28 % (1725827)Instruction limit reached!
% 0.18/0.28 % (1725827)------------------------------
% 0.18/0.28 % (1725827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.28 % (1725827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.28 % (1725827)CaDiCaL version: 2.1.3
% 0.18/0.28 % (1725827)Termination reason: Instruction limit
% 0.18/0.28 % (1725827)Termination phase: Saturation
% 0.18/0.28 % (1725827)Time elapsed: 0.002 s
% 0.18/0.28 % (1725827)Peak memory usage: 11 MB
% 0.18/0.28 % (1725827)Instructions burned: 3 (million)
% 0.18/0.28 % (1725828) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1725820-1725828"...
% 0.18/0.28 % (1725831)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.18/0.28 % (1725831)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
% 0.18/0.28 % (1725828)...printing done.
% 0.18/0.28 % (1725826)Instruction limit reached!
% 0.18/0.28 % (1725826)------------------------------
% 0.18/0.28 % (1725826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.28 % (1725826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.28 % (1725826)CaDiCaL version: 2.1.3
% 0.18/0.28 % (1725826)Termination reason: Instruction limit
% 0.18/0.28 % (1725826)Termination phase: Saturation
% 0.18/0.28 % (1725826)Time elapsed: 0.011 s
% 0.18/0.28 % (1725826)Peak memory usage: 12 MB
% 0.18/0.28 % (1725826)Instructions burned: 20 (million)
% 0.18/0.28 % (1725828)Refutation found. Thanks to Tanya!
% 0.18/0.28 % SZS status Theorem for theBenchmark
% 0.18/0.28 % SZS output start Proof for theBenchmark
% 0.18/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.18/0.28 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.18/0.28 thf(func_def_1, type, funcSet: ($i > $i > $i)).
% 0.18/0.28 thf(func_def_2, type, ap: ($i > $i > $i > $i > $i)).
% 0.18/0.28 thf(func_def_3, type, ap2p: $o).
% 0.18/0.28 thf(func_def_5, type, lam: ($i > $i > ($i > $i) > $i)).
% 0.18/0.28 thf(func_def_6, type, lam2p: $o).
% 0.18/0.28 thf(func_def_7, type, funcext2: $o).
% 0.18/0.28 thf(func_def_8, type, beta2: $o).
% 0.18/0.28 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.18/0.28 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.18/0.28 thf(func_def_17, type, sK4: ($i > $i > $i > $i > $i)).
% 0.18/0.28 thf(func_def_22, type, sK9: ($i > $i > ($i > $i) > $i)).
% 0.18/0.28 thf(func_def_23, type, sK10: ($i > $i)).
% 0.18/0.28 thf(func_def_30, type, sK17: (($i > $i) > $i > $i > $i)).
% 0.18/0.28 thf(func_def_33, type, sK20: ($i > $i)).
% 0.18/0.28 thf(f1,axiom,(
% 0.18/0.28 (ap2p = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (ap @ X0 @ X1 @ X2 @ X3) @ X1))))),
% 0.18/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p)).
% 0.18/0.28 thf(f2,axiom,(
% 0.18/0.28 (! [X2 : ($i > $i),X1 : $i,X0 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => (in @ (lam @ X0 @ X1 @ (^[X3 : $i] : ((X2 @ X3)))) @ (funcSet @ X0 @ X1))) = lam2p)),
% 0.18/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2p)).
% 0.18/0.28 thf(f3,axiom,(
% 0.18/0.28 (funcext2 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X3 : $i] : ((in @ X3 @ (funcSet @ X0 @ X1)) => (! [X4 : $i] : ((in @ X4 @ X0) => (((ap @ X0 @ X1 @ X2 @ X4)) = ((ap @ X0 @ X1 @ X3 @ X4)))) => (X2 = X3)))))),
% 0.18/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext2)).
% 0.18/0.28 thf(f4,axiom,(
% 0.18/0.28 (! [X0 : $i,X1 : $i,X2 : ($i > $i)] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => (((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X4 : $i] : ((X2 @ X4)))) @ X3)) = ((X2 @ X3))))) = beta2)),
% 0.18/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta2)).
% 0.18/0.28 thf(f5,conjecture,(
% 0.18/0.28 ap2p => (lam2p => (funcext2 => (beta2 => ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => (((lam @ X0 @ X1 @ (^[X3 : $i] : ((ap @ X0 @ X1 @ X2 @ X3))))) = X2)))))),
% 0.18/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta2)).
% 0.18/0.28 thf(f6,negated_conjecture,(
% 0.18/0.28 ~(ap2p => (lam2p => (funcext2 => (beta2 => ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => (((lam @ X0 @ X1 @ (^[X3 : $i] : ((ap @ X0 @ X1 @ X2 @ X3))))) = X2))))))),
% 0.18/0.28 inference(negated_conjecture,[status(cth)],[f5])).
% 0.18/0.28 thf(f7,plain,(
% 0.18/0.28 (! [X0 : $i,X1 : $i,X2 : ($i > $i)] : (! [X3 : $i] : ((in @ X3 @ X0) => (in @ (X2 @ X3) @ X1)) => ! [X4 : $i] : ((in @ X4 @ X0) => (((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X5 : $i] : ((X2 @ X5)))) @ X4)) = ((X2 @ X4))))) = beta2)),
% 0.18/0.28 inference(rectify,[],[f4])).
% 0.18/0.28 thf(f8,plain,(
% 0.18/0.28 (beta2 = $true) <=> ! [X2 : ($i > $i),X0 : $i,X1 : $i] : (! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => (((in @ (X2 @ X3) @ X1)) = $true)) => ! [X4 : $i] : ((((in @ X4 @ X0)) = $true) => (((X2 @ X4)) = ((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[Y0 : $i]: (X2 @ Y0))) @ X4)))))),
% 0.18/0.28 inference(fool_elimination,[],[f7])).
% 0.18/0.28 thf(f9,plain,(
% 0.18/0.28 (ap2p = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (funcSet @ X1 @ X2)) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (ap @ X1 @ X2 @ X0 @ X3) @ X2))))),
% 0.18/0.28 inference(rectify,[],[f1])).
% 0.18/0.28 thf(f10,plain,(
% 0.18/0.28 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X0 @ (funcSet @ X1 @ X2)))) => ! [X3 : $i] : ((((in @ X3 @ X1)) = $true) => (((in @ (ap @ X1 @ X2 @ X0 @ X3) @ X2)) = $true))) <=> (ap2p = $true)),
% 0.18/0.28 inference(fool_elimination,[],[f9])).
% 0.18/0.28 thf(f11,plain,(
% 0.18/0.28 ~(ap2p => (lam2p => (funcext2 => (beta2 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (funcSet @ X0 @ X2)) => (((lam @ X0 @ X2 @ (^[X3 : $i] : ((ap @ X0 @ X2 @ X1 @ X3))))) = X1))))))),
% 0.18/0.28 inference(rectify,[],[f6])).
% 0.18/0.28 thf(f12,plain,(
% 0.18/0.28 ~((ap2p = $true) => ((lam2p = $true) => ((funcext2 = $true) => ((beta2 = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ (funcSet @ X0 @ X2))) = $true) => (((lam @ X0 @ X2 @ (^[Y0 : $i]: (ap @ X0 @ X2 @ X1 @ Y0)))) = X1))))))),
% 0.18/0.28 inference(fool_elimination,[],[f11])).
% 0.18/0.28 thf(f13,plain,(
% 0.18/0.28 (funcext2 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X3 : $i] : ((in @ X3 @ (funcSet @ X0 @ X1)) => (! [X4 : $i] : ((in @ X4 @ X0) => (((ap @ X0 @ X1 @ X2 @ X4)) = ((ap @ X0 @ X1 @ X3 @ X4)))) => (X2 = X3)))))),
% 0.18/0.28 inference(rectify,[],[f3])).
% 0.18/0.28 thf(f14,plain,(
% 0.18/0.28 (funcext2 = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X2 @ (funcSet @ X0 @ X1))) = $true) => ! [X3 : $i] : ((((in @ X3 @ (funcSet @ X0 @ X1))) = $true) => (! [X4 : $i] : ((((in @ X4 @ X0)) = $true) => (((ap @ X0 @ X1 @ X2 @ X4)) = ((ap @ X0 @ X1 @ X3 @ X4)))) => (X2 = X3))))),
% 0.18/0.28 inference(fool_elimination,[],[f13])).
% 0.18/0.28 thf(f15,plain,(
% 0.18/0.28 (! [X0 : ($i > $i),X1 : $i,X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X2) => (in @ (X0 @ X3) @ X1)) => (in @ (lam @ X2 @ X1 @ (^[X4 : $i] : ((X0 @ X4)))) @ (funcSet @ X2 @ X1))) = lam2p)),
% 0.18/0.28 inference(rectify,[],[f2])).
% 0.18/0.28 thf(f16,plain,(
% 0.18/0.28 (lam2p = $true) <=> ! [X0 : ($i > $i),X1 : $i,X2 : $i] : (! [X3 : $i] : (($true = ((in @ X3 @ X2))) => (((in @ (X0 @ X3) @ X1)) = $true)) => ($true = ((in @ (lam @ X2 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) @ (funcSet @ X2 @ X1)))))),
% 0.18/0.28 inference(fool_elimination,[],[f15])).
% 0.18/0.28 thf(f17,plain,(
% 0.18/0.28 (funcext2 = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (! [X3 : $i] : (((X2 = X3) | ? [X4 : $i] : ((((in @ X4 @ X0)) = $true) & (((ap @ X0 @ X1 @ X2 @ X4)) != ((ap @ X0 @ X1 @ X3 @ X4))))) | (((in @ X3 @ (funcSet @ X0 @ X1))) != $true)) | (((in @ X2 @ (funcSet @ X0 @ X1))) != $true))),
% 0.18/0.28 inference(ennf_transformation,[],[f14])).
% 0.18/0.28 thf(f18,plain,(
% 0.18/0.28 ! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X2 @ (funcSet @ X0 @ X1))) != $true) | ! [X3 : $i] : ((X2 = X3) | ? [X4 : $i] : ((((in @ X4 @ X0)) = $true) & (((ap @ X0 @ X1 @ X2 @ X4)) != ((ap @ X0 @ X1 @ X3 @ X4)))) | (((in @ X3 @ (funcSet @ X0 @ X1))) != $true))) <=> (funcext2 = $true)),
% 0.18/0.28 inference(flattening,[],[f17])).
% 0.18/0.28 thf(f19,plain,(
% 0.18/0.28 (((? [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X1 @ (funcSet @ X0 @ X2))) = $true) & (((lam @ X0 @ X2 @ (^[Y0 : $i]: (ap @ X0 @ X2 @ X1 @ Y0)))) != X1)) & (beta2 = $true)) & (funcext2 = $true)) & (lam2p = $true)) & (ap2p = $true)),
% 0.18/0.28 inference(ennf_transformation,[],[f12])).
% 0.18/0.28 thf(f20,plain,(
% 0.18/0.28 (lam2p = $true) & ? [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X1 @ (funcSet @ X0 @ X2))) = $true) & (((lam @ X0 @ X2 @ (^[Y0 : $i]: (ap @ X0 @ X2 @ X1 @ Y0)))) != X1)) & (beta2 = $true) & (funcext2 = $true) & (ap2p = $true)),
% 0.18/0.28 inference(flattening,[],[f19])).
% 0.18/0.28 thf(f21,plain,(
% 0.18/0.28 ! [X1 : $i,X2 : $i,X0 : ($i > $i)] : (? [X3 : $i] : ((((in @ (X0 @ X3) @ X1)) != $true) & ($true = ((in @ X3 @ X2)))) | ($true = ((in @ (lam @ X2 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) @ (funcSet @ X2 @ X1))))) <=> (lam2p = $true)),
% 0.18/0.28 inference(ennf_transformation,[],[f16])).
% 0.18/0.28 thf(f22,plain,(
% 0.18/0.28 ! [X2 : ($i > $i),X1 : $i,X0 : $i] : (! [X4 : $i] : ((((X2 @ X4)) = ((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[Y0 : $i]: (X2 @ Y0))) @ X4))) | (((in @ X4 @ X0)) != $true)) | ? [X3 : $i] : ((((in @ (X2 @ X3) @ X1)) != $true) & (((in @ X3 @ X0)) = $true))) <=> (beta2 = $true)),
% 0.18/0.28 inference(ennf_transformation,[],[f8])).
% 0.18/0.28 thf(f23,plain,(
% 0.18/0.28 ! [X1 : $i,X0 : $i,X2 : $i] : (($true != ((in @ X0 @ (funcSet @ X1 @ X2)))) | ! [X3 : $i] : ((((in @ X3 @ X1)) != $true) | (((in @ (ap @ X1 @ X2 @ X0 @ X3) @ X2)) = $true))) <=> (ap2p = $true)),
% 0.18/0.28 inference(ennf_transformation,[],[f10])).
% 0.18/0.28 thf(f24,plain,(
% 0.18/0.28 (! [X1 : $i,X0 : $i,X2 : $i] : (($true != ((in @ X0 @ (funcSet @ X1 @ X2)))) | ! [X3 : $i] : ((((in @ X3 @ X1)) != $true) | (((in @ (ap @ X1 @ X2 @ X0 @ X3) @ X2)) = $true))) | (ap2p != $true)) & ((ap2p = $true) | ? [X1 : $i,X0 : $i,X2 : $i] : (($true = ((in @ X0 @ (funcSet @ X1 @ X2)))) & ? [X3 : $i] : ((((in @ X3 @ X1)) = $true) & (((in @ (ap @ X1 @ X2 @ X0 @ X3) @ X2)) != $true))))),
% 0.18/0.28 inference(nnf_transformation,[],[f23])).
% 0.18/0.28 thf(f25,plain,(
% 0.18/0.28 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ (funcSet @ X0 @ X2))) != $true) | ! [X3 : $i] : ((((in @ X3 @ X0)) != $true) | ($true = ((in @ (ap @ X0 @ X2 @ X1 @ X3) @ X2))))) | (ap2p != $true)) & ((ap2p = $true) | ? [X4 : $i,X5 : $i,X6 : $i] : ((((in @ X5 @ (funcSet @ X4 @ X6))) = $true) & ? [X7 : $i] : ((((in @ X7 @ X4)) = $true) & (((in @ (ap @ X4 @ X6 @ X5 @ X7) @ X6)) != $true))))),
% 0.18/0.28 inference(rectify,[],[f24])).
% 0.18/0.28 thf(f26,plain,(
% 0.18/0.28 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ (funcSet @ X0 @ X2))) != $true) | ! [X3 : $i] : ((((in @ X3 @ X0)) != $true) | ($true = ((in @ (ap @ X0 @ X2 @ X1 @ X3) @ X2))))) | (ap2p != $true)) & ((ap2p = $true) | ((((in @ sK1 @ (funcSet @ sK0 @ sK2))) = $true) & (($true = ((in @ sK3 @ sK0))) & (((in @ (ap @ sK0 @ sK2 @ sK1 @ sK3) @ sK2)) != $true))))),
% 0.18/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X4,sK0),skolemize(X5,sK1),skolemize(X6,sK2),skolemize(X7,sK3)],[f25])).
% 0.18/0.28 thf(f27,plain,(
% 0.18/0.28 (! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X2 @ (funcSet @ X0 @ X1))) != $true) | ! [X3 : $i] : ((X2 = X3) | ? [X4 : $i] : ((((in @ X4 @ X0)) = $true) & (((ap @ X0 @ X1 @ X2 @ X4)) != ((ap @ X0 @ X1 @ X3 @ X4)))) | (((in @ X3 @ (funcSet @ X0 @ X1))) != $true))) | (funcext2 != $true)) & ((funcext2 = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X2 @ (funcSet @ X0 @ X1))) = $true) & ? [X3 : $i] : ((X2 != X3) & ! [X4 : $i] : ((((in @ X4 @ X0)) != $true) | (((ap @ X0 @ X1 @ X2 @ X4)) = ((ap @ X0 @ X1 @ X3 @ X4)))) & (((in @ X3 @ (funcSet @ X0 @ X1))) = $true))))),
% 0.18/0.28 inference(nnf_transformation,[],[f18])).
% 0.18/0.28 thf(f28,plain,(
% 0.18/0.28 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X0 @ (funcSet @ X2 @ X1)))) | ! [X3 : $i] : ((X0 = X3) | ? [X4 : $i] : ((((in @ X4 @ X2)) = $true) & (((ap @ X2 @ X1 @ X3 @ X4)) != ((ap @ X2 @ X1 @ X0 @ X4)))) | (((in @ X3 @ (funcSet @ X2 @ X1))) != $true))) | (funcext2 != $true)) & ((funcext2 = $true) | ? [X5 : $i,X6 : $i,X7 : $i] : (($true = ((in @ X5 @ (funcSet @ X7 @ X6)))) & ? [X8 : $i] : ((X5 != X8) & ! [X9 : $i] : ((((in @ X9 @ X7)) != $true) | (((ap @ X7 @ X6 @ X5 @ X9)) = ((ap @ X7 @ X6 @ X8 @ X9)))) & (((in @ X8 @ (funcSet @ X7 @ X6))) = $true))))),
% 0.18/0.28 inference(rectify,[],[f27])).
% 0.18/0.28 thf(f29,plain,(
% 0.18/0.28 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X0 @ (funcSet @ X2 @ X1)))) | ! [X3 : $i] : ((X0 = X3) | ((((in @ (sK4 @ X3 @ X2 @ X1 @ X0) @ X2)) = $true) & (((ap @ X2 @ X1 @ X0 @ (sK4 @ X3 @ X2 @ X1 @ X0))) != ((ap @ X2 @ X1 @ X3 @ (sK4 @ X3 @ X2 @ X1 @ X0))))) | (((in @ X3 @ (funcSet @ X2 @ X1))) != $true))) | (funcext2 != $true)) & ((funcext2 = $true) | (($true = ((in @ sK5 @ (funcSet @ sK7 @ sK6)))) & ((sK8 != sK5) & ! [X9 : $i] : ((((in @ X9 @ sK7)) != $true) | (((ap @ sK7 @ sK6 @ sK5 @ X9)) = ((ap @ sK7 @ sK6 @ sK8 @ X9)))) & (((in @ sK8 @ (funcSet @ sK7 @ sK6))) = $true))))),
% 0.18/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK5,sK6,sK7,sK8]),skolemize(X4,sK4 @ X3 @ X2 @ X1 @ X0),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X7,sK7),skolemize(X8,sK8)],[f28])).
% 0.18/0.28 thf(f30,plain,(
% 0.18/0.28 (! [X2 : ($i > $i),X1 : $i,X0 : $i] : (! [X4 : $i] : ((((X2 @ X4)) = ((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[Y0 : $i]: (X2 @ Y0))) @ X4))) | (((in @ X4 @ X0)) != $true)) | ? [X3 : $i] : ((((in @ (X2 @ X3) @ X1)) != $true) & (((in @ X3 @ X0)) = $true))) | (beta2 != $true)) & ((beta2 = $true) | ? [X2 : ($i > $i),X1 : $i,X0 : $i] : (? [X4 : $i] : ((((X2 @ X4)) != ((ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[Y0 : $i]: (X2 @ Y0))) @ X4))) & (((in @ X4 @ X0)) = $true)) & ! [X3 : $i] : ((((in @ (X2 @ X3) @ X1)) = $true) | (((in @ X3 @ X0)) != $true))))),
% 0.18/0.28 inference(nnf_transformation,[],[f22])).
% 0.18/0.28 thf(f31,plain,(
% 0.18/0.28 (! [X0 : ($i > $i),X1 : $i,X2 : $i] : (! [X3 : $i] : ((((X0 @ X3)) = ((ap @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) @ X3))) | ($true != ((in @ X3 @ X2)))) | ? [X4 : $i] : ((((in @ (X0 @ X4) @ X1)) != $true) & (((in @ X4 @ X2)) = $true))) | (beta2 != $true)) & ((beta2 = $true) | ? [X5 : ($i > $i),X6 : $i,X7 : $i] : (? [X8 : $i] : ((((X5 @ X8)) != ((ap @ X7 @ X6 @ (lam @ X7 @ X6 @ (^[Y0 : $i]: (X5 @ Y0))) @ X8))) & (((in @ X8 @ X7)) = $true)) & ! [X9 : $i] : (($true = ((in @ (X5 @ X9) @ X6))) | (((in @ X9 @ X7)) != $true))))),
% 0.18/0.28 inference(rectify,[],[f30])).
% 0.18/0.28 thf(f32,plain,(
% 0.18/0.28 (! [X0 : ($i > $i),X1 : $i,X2 : $i] : (! [X3 : $i] : ((((X0 @ X3)) = ((ap @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) @ X3))) | ($true != ((in @ X3 @ X2)))) | ((((in @ (X0 @ (sK9 @ X2 @ X1 @ X0)) @ X1)) != $true) & (((in @ (sK9 @ X2 @ X1 @ X0) @ X2)) = $true))) | (beta2 != $true)) & ((beta2 = $true) | (((((ap @ sK12 @ sK11 @ (lam @ sK12 @ sK11 @ (^[Y0 : $i]: (sK10 @ Y0))) @ sK13)) != ((sK10 @ sK13))) & ($true = ((in @ sK13 @ sK12)))) & ! [X9 : $i] : ((((in @ (sK10 @ X9) @ sK11)) = $true) | (((in @ X9 @ sK12)) != $true))))),
% 0.18/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK10,sK11,sK12,sK13]),skolemize(X4,sK4 @ X3 @ X2 @ X1 @ X0),skolemize(X5,sK10),skolemize(X6,sK11),skolemize(X7,sK12),skolemize(X8,sK13)],[f31])).
% 0.18/0.28 thf(f33,plain,(
% 0.18/0.28 (lam2p = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ (funcSet @ X0 @ X1))) = $true) & (((lam @ X0 @ X1 @ (^[Y0 : $i]: (ap @ X0 @ X1 @ X2 @ Y0)))) != X2)) & (beta2 = $true) & (funcext2 = $true) & (ap2p = $true)),
% 0.18/0.28 inference(rectify,[],[f20])).
% 0.18/0.28 thf(f34,plain,(
% 0.18/0.28 (lam2p = $true) & ((((in @ sK16 @ (funcSet @ sK14 @ sK15))) = $true) & (sK16 != ((lam @ sK14 @ sK15 @ (^[Y0 : $i]: (ap @ sK14 @ sK15 @ sK16 @ Y0)))))) & (beta2 = $true) & (funcext2 = $true) & (ap2p = $true)),
% 0.18/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X0,sK14),skolemize(X1,sK15),skolemize(X2,sK16)],[f33])).
% 0.18/0.28 thf(f35,plain,(
% 0.18/0.28 (! [X1 : $i,X2 : $i,X0 : ($i > $i)] : (? [X3 : $i] : ((((in @ (X0 @ X3) @ X1)) != $true) & ($true = ((in @ X3 @ X2)))) | ($true = ((in @ (lam @ X2 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) @ (funcSet @ X2 @ X1))))) | (lam2p != $true)) & ((lam2p = $true) | ? [X1 : $i,X2 : $i,X0 : ($i > $i)] : (! [X3 : $i] : ((((in @ (X0 @ X3) @ X1)) = $true) | ($true != ((in @ X3 @ X2)))) & ($true != ((in @ (lam @ X2 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) @ (funcSet @ X2 @ X1))))))),
% 0.18/0.28 inference(nnf_transformation,[],[f21])).
% 0.18/0.28 thf(f36,plain,(
% 0.18/0.28 (! [X0 : $i,X1 : $i,X2 : ($i > $i)] : (? [X3 : $i] : (($true != ((in @ (X2 @ X3) @ X0))) & (((in @ X3 @ X1)) = $true)) | ($true = ((in @ (lam @ X1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))) @ (funcSet @ X1 @ X0))))) | (lam2p != $true)) & ((lam2p = $true) | ? [X4 : $i,X5 : $i,X6 : ($i > $i)] : (! [X7 : $i] : ((((in @ (X6 @ X7) @ X4)) = $true) | (((in @ X7 @ X5)) != $true)) & ($true != ((in @ (lam @ X5 @ X4 @ (^[Y0 : $i]: (X6 @ Y0))) @ (funcSet @ X5 @ X4))))))),
% 0.18/0.28 inference(rectify,[],[f35])).
% 0.18/0.28 thf(f37,plain,(
% 0.18/0.28 (! [X0 : $i,X1 : $i,X2 : ($i > $i)] : (((((in @ (X2 @ (sK17 @ X2 @ X1 @ X0)) @ X0)) != $true) & (((in @ (sK17 @ X2 @ X1 @ X0) @ X1)) = $true)) | ($true = ((in @ (lam @ X1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))) @ (funcSet @ X1 @ X0))))) | (lam2p != $true)) & ((lam2p = $true) | (! [X7 : $i] : ((((in @ (sK20 @ X7) @ sK18)) = $true) | (((in @ X7 @ sK19)) != $true)) & (((in @ (lam @ sK19 @ sK18 @ (^[Y0 : $i]: (sK20 @ Y0))) @ (funcSet @ sK19 @ sK18))) != $true)))),
% 0.18/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK18,sK19,sK20]),skolemize(X4,sK4 @ X3 @ X2 @ X1 @ X0),skolemize(X4,sK18),skolemize(X5,sK19),skolemize(X6,sK20)],[f36])).
% 0.18/0.28 thf(f41,plain,(
% 0.18/0.28 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((ap2p != $true) | (((in @ X1 @ (funcSet @ X0 @ X2))) != $true) | (((in @ X3 @ X0)) != $true) | ($true = ((in @ (ap @ X0 @ X2 @ X1 @ X3) @ X2)))) )),
% 0.18/0.28 inference(cnf_transformation,[],[f26])).
% 0.18/0.28 thf(f46,plain,(
% 0.18/0.28 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((X0 = X3) | (funcext2 != $true) | (((in @ X3 @ (funcSet @ X2 @ X1))) != $true) | (((ap @ X2 @ X1 @ X0 @ (sK4 @ X3 @ X2 @ X1 @ X0))) != ((ap @ X2 @ X1 @ X3 @ (sK4 @ X3 @ X2 @ X1 @ X0)))) | ($true != ((in @ X0 @ (funcSet @ X2 @ X1))))) )),
% 0.18/0.28 inference(cnf_transformation,[],[f29])).
% 0.18/0.28 thf(f47,plain,(
% 0.18/0.28 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((funcext2 != $true) | (((in @ (sK4 @ X3 @ X2 @ X1 @ X0) @ X2)) = $true) | ($true != ((in @ X0 @ (funcSet @ X2 @ X1)))) | (X0 = X3) | (((in @ X3 @ (funcSet @ X2 @ X1))) != $true)) )),
% 0.18/0.28 inference(cnf_transformation,[],[f29])).
% 0.18/0.28 thf(f51,plain,(
% 0.18/0.28 ( ! [X2 : $i,X3 : $i,X0 : ($i > $i),X1 : $i] : ((((in @ (sK9 @ X2 @ X1 @ X0) @ X2)) = $true) | (beta2 != $true) | (((X0 @ X3)) = ((ap @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) @ X3))) | ($true != ((in @ X3 @ X2)))) )),
% 0.18/0.28 inference(cnf_transformation,[],[f32])).
% 0.18/0.28 thf(f52,plain,(
% 0.18/0.28 ( ! [X2 : $i,X3 : $i,X0 : ($i > $i),X1 : $i] : ((((X0 @ X3)) = ((ap @ X2 @ X1 @ (lam @ X2 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) @ X3))) | (((in @ (X0 @ (sK9 @ X2 @ X1 @ X0)) @ X1)) != $true) | (beta2 != $true) | ($true != ((in @ X3 @ X2)))) )),
% 0.18/0.28 inference(cnf_transformation,[],[f32])).
% 0.18/0.28 thf(f53,plain,(
% 0.18/0.28 (ap2p = $true)),
% 0.18/0.28 inference(cnf_transformation,[],[f34])).
% 0.18/0.28 thf(f54,plain,(
% 0.18/0.28 (funcext2 = $true)),
% 0.18/0.28 inference(cnf_transformation,[],[f34])).
% 0.18/0.28 thf(f55,plain,(
% 0.18/0.28 (beta2 = $true)),
% 0.18/0.28 inference(cnf_transformation,[],[f34])).
% 0.18/0.28 thf(f56,plain,(
% 0.18/0.28 (sK16 != ((lam @ sK14 @ sK15 @ (^[Y0 : $i]: (ap @ sK14 @ sK15 @ sK16 @ Y0)))))),
% 0.18/0.28 inference(cnf_transformation,[],[f34])).
% 0.18/0.28 thf(f57,plain,(
% 0.18/0.28 (((in @ sK16 @ (funcSet @ sK14 @ sK15))) = $true)),
% 0.18/0.28 inference(cnf_transformation,[],[f34])).
% 0.18/0.28 thf(f58,plain,(
% 0.18/0.28 (lam2p = $true)),
% 0.18/0.28 inference(cnf_transformation,[],[f34])).
% 0.18/0.28 thf(f61,plain,(
% 0.18/0.28 ( ! [X2 : ($i > $i),X0 : $i,X1 : $i] : ((((in @ (sK17 @ X2 @ X1 @ X0) @ X1)) = $true) | ($true = ((in @ (lam @ X1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))) @ (funcSet @ X1 @ X0)))) | (lam2p != $true)) )),
% 0.18/0.28 inference(cnf_transformation,[],[f37])).
% 0.18/0.28 thf(f62,plain,(
% 0.18/0.28 ( ! [X2 : ($i > $i),X0 : $i,X1 : $i] : (($true = ((in @ (lam @ X1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))) @ (funcSet @ X1 @ X0)))) | (((in @ (X2 @ (sK17 @ X2 @ X1 @ X0)) @ X0)) != $true) | (lam2p != $true)) )),
% 0.18/0.28 inference(cnf_transformation,[],[f37])).
% 0.18/0.28 thf(f65,plain,(
% 0.18/0.28 ( ! [X2 : $i,X3 : $i,X0 : ($i > $i),X1 : $i] : ((beta2 != $true) | (((ap @ X2 @ X1 @ (lam @ X2 @ X1 @ X0) @ X3)) = ((X0 @ X3))) | ($true != ((in @ X3 @ X2))) | (((in @ (X0 @ (sK9 @ X2 @ X1 @ X0)) @ X1)) != $true)) )),
% 0.18/0.28 inference(beta-eta_normalization,[],[f52])).
% 0.18/0.28 thf(f66,plain,(
% 0.18/0.28 ( ! [X2 : ($i > $i),X0 : $i,X1 : $i] : ((lam2p != $true) | (((in @ (lam @ X1 @ X0 @ X2) @ (funcSet @ X1 @ X0))) = $true) | (((in @ (sK17 @ X2 @ X1 @ X0) @ X1)) = $true)) )),
% 0.18/0.28 inference(beta-eta_normalization,[],[f61])).
% 0.18/0.28 thf(f67,plain,(
% 0.18/0.28 ( ! [X2 : $i,X3 : $i,X0 : ($i > $i),X1 : $i] : (($true != ((in @ X3 @ X2))) | (((in @ (sK9 @ X2 @ X1 @ X0) @ X2)) = $true) | (((ap @ X2 @ X1 @ (lam @ X2 @ X1 @ X0) @ X3)) = ((X0 @ X3))) | (beta2 != $true)) )),
% 0.18/0.28 inference(beta-eta_normalization,[],[f51])).
% 0.18/0.28 thf(f68,plain,(
% 0.18/0.28 (sK16 != ((lam @ sK14 @ sK15 @ (ap @ sK14 @ sK15 @ sK16))))),
% 0.18/0.28 inference(beta-eta_normalization,[],[f56])).
% 0.18/0.28 thf(f70,plain,(
% 0.18/0.28 ( ! [X2 : ($i > $i),X0 : $i,X1 : $i] : ((lam2p != $true) | (((in @ (X2 @ (sK17 @ X2 @ X1 @ X0)) @ X0)) != $true) | (((in @ (lam @ X1 @ X0 @ X2) @ (funcSet @ X1 @ X0))) = $true)) )),
% 0.18/0.28 inference(beta-eta_normalization,[],[f62])).
% 0.18/0.28 thf(f72,definition,(
% 0.18/0.28 spl21_1 <=> (funcext2 = $true)),
% 0.18/0.28 introduced(definition,[new_symbols(definition,[spl21_1])],[avatar_definition])).
% 0.18/0.28 thf(f81,definition,(
% 0.18/0.28 spl21_3 <=> (((in @ sK16 @ (funcSet @ sK14 @ sK15))) = $true)),
% 0.18/0.28 introduced(definition,[new_symbols(definition,[spl21_3])],[avatar_definition])).
% 0.18/0.28 thf(f83,plain,(
% 0.18/0.28 (((in @ sK16 @ (funcSet @ sK14 @ sK15))) = $true) | ~spl21_3),
% 0.18/0.28 inference(avatar_component_clause,[],[f81])).
% 0.18/0.28 thf(f84,plain,(
% 0.18/0.28 spl21_3),
% 0.18/0.28 inference(avatar_split_clause,[],[f57,f81])).
% 0.18/0.28 thf(f86,definition,(
% 0.18/0.28 spl21_4 <=> (beta2 = $true)),
% 0.18/0.28 introduced(definition,[new_symbols(definition,[spl21_4])],[avatar_definition])).
% 0.18/0.28 thf(f100,definition,(
% 0.18/0.28 spl21_7 <=> (ap2p = $true)),
% 0.18/0.28 introduced(definition,[new_symbols(definition,[spl21_7])],[avatar_definition])).
% 0.18/0.28 thf(f103,plain,(
% 0.18/0.28 spl21_7),
% 0.18/0.28 inference(avatar_split_clause,[],[f53,f100])).
% 0.18/0.28 thf(f105,definition,(
% 0.18/0.28 spl21_8 <=> (lam2p = $true)),
% 0.18/0.28 introduced(definition,[new_symbols(definition,[spl21_8])],[avatar_definition])).
% 0.18/0.28 thf(f117,plain,(
% 0.18/0.28 spl21_1),
% 0.18/0.28 inference(avatar_split_clause,[],[f54,f72])).
% 0.18/0.28 thf(f124,definition,(
% 0.18/0.28 spl21_12 <=> ! [X0 : ($i > $i),X3 : $i,X2 : $i,X1 : $i] : ((((ap @ X2 @ X1 @ (lam @ X2 @ X1 @ X0) @ X3)) = ((X0 @ X3))) | (((in @ (X0 @ (sK9 @ X2 @ X1 @ X0)) @ X1)) != $true) | ($true != ((in @ X3 @ X2))))),
% 0.18/0.28 introduced(definition,[new_symbols(definition,[spl21_12])],[avatar_definition])).
% 0.18/0.28 thf(f125,plain,(
% 0.18/0.28 ( ! [X2 : $i,X3 : $i,X0 : ($i > $i),X1 : $i] : ((((ap @ X2 @ X1 @ (lam @ X2 @ X1 @ X0) @ X3)) = ((X0 @ X3))) | ($true != ((in @ X3 @ X2))) | (((in @ (X0 @ (sK9 @ X2 @ X1 @ X0)) @ X1)) != $true)) ) | ~spl21_12),
% 0.18/0.28 inference(avatar_component_clause,[],[f124])).
% 0.18/0.28 thf(f126,plain,(
% 0.18/0.28 ~spl21_4 | spl21_12),
% 0.18/0.28 inference(avatar_split_clause,[],[f65,f124,f86])).
% 0.18/0.28 thf(f128,definition,(
% 0.18/0.28 spl21_13 <=> ! [X0 : $i,X3 : $i,X2 : $i,X1 : $i] : ((X0 = X3) | ($true != ((in @ X0 @ (funcSet @ X2 @ X1)))) | (((ap @ X2 @ X1 @ X0 @ (sK4 @ X3 @ X2 @ X1 @ X0))) != ((ap @ X2 @ X1 @ X3 @ (sK4 @ X3 @ X2 @ X1 @ X0)))) | (((in @ X3 @ (funcSet @ X2 @ X1))) != $true))),
% 0.18/0.28 introduced(definition,[new_symbols(definition,[spl21_13])],[avatar_definition])).
% 0.18/0.28 thf(f129,plain,(
% 0.18/0.28 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((ap @ X2 @ X1 @ X0 @ (sK4 @ X3 @ X2 @ X1 @ X0))) != ((ap @ X2 @ X1 @ X3 @ (sK4 @ X3 @ X2 @ X1 @ X0)))) | (((in @ X3 @ (funcSet @ X2 @ X1))) != $true) | ($true != ((in @ X0 @ (funcSet @ X2 @ X1)))) | (X0 = X3)) ) | ~spl21_13),
% 0.18/0.28 inference(avatar_component_clause,[],[f128])).
% 0.18/0.28 thf(f130,plain,(
% 0.18/0.28 ~spl21_1 | spl21_13),
% 0.18/0.28 inference(avatar_split_clause,[],[f46,f128,f72])).
% 0.18/0.28 thf(f132,definition,(
% 0.18/0.28 spl21_14 <=> ! [X2 : ($i > $i),X0 : $i,X1 : $i] : ((((in @ (lam @ X1 @ X0 @ X2) @ (funcSet @ X1 @ X0))) = $true) | (((in @ (sK17 @ X2 @ X1 @ X0) @ X1)) = $true))),
% 0.18/0.28 introduced(definition,[new_symbols(definition,[spl21_14])],[avatar_definition])).
% 0.18/0.28 thf(f133,plain,(
% 0.18/0.28 ( ! [X2 : ($i > $i),X0 : $i,X1 : $i] : ((((in @ (lam @ X1 @ X0 @ X2) @ (funcSet @ X1 @ X0))) = $true) | (((in @ (sK17 @ X2 @ X1 @ X0) @ X1)) = $true)) ) | ~spl21_14),
% 0.18/0.28 inference(avatar_component_clause,[],[f132])).
% 0.18/0.28 thf(f134,plain,(
% 0.18/0.28 spl21_14 | ~spl21_8),
% 0.18/0.28 inference(avatar_split_clause,[],[f66,f105,f132])).
% 0.18/0.28 thf(f136,definition,(
% 0.18/0.28 spl21_15 <=> ! [X0 : $i,X3 : $i,X2 : $i,X1 : $i] : ((((in @ (sK4 @ X3 @ X2 @ X1 @ X0) @ X2)) = $true) | (((in @ X3 @ (funcSet @ X2 @ X1))) != $true) | (X0 = X3) | ($true != ((in @ X0 @ (funcSet @ X2 @ X1)))))),
% 0.18/0.28 introduced(definition,[new_symbols(definition,[spl21_15])],[avatar_definition])).
% 0.18/0.28 thf(f137,plain,(
% 0.18/0.28 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ (sK4 @ X3 @ X2 @ X1 @ X0) @ X2)) = $true) | ($true != ((in @ X0 @ (funcSet @ X2 @ X1)))) | (X0 = X3) | (((in @ X3 @ (funcSet @ X2 @ X1))) != $true)) ) | ~spl21_15),
% 0.18/0.28 inference(avatar_component_clause,[],[f136])).
% 0.18/0.28 thf(f138,plain,(
% 0.18/0.28 spl21_15 | ~spl21_1),
% 0.18/0.28 inference(avatar_split_clause,[],[f47,f72,f136])).
% 0.18/0.28 thf(f140,definition,(
% 0.18/0.28 spl21_16 <=> ! [X0 : ($i > $i),X3 : $i,X2 : $i,X1 : $i] : (($true != ((in @ X3 @ X2))) | (((ap @ X2 @ X1 @ (lam @ X2 @ X1 @ X0) @ X3)) = ((X0 @ X3))) | (((in @ (sK9 @ X2 @ X1 @ X0) @ X2)) = $true))),
% 0.18/0.28 introduced(definition,[new_symbols(definition,[spl21_16])],[avatar_definition])).
% 0.18/0.28 thf(f141,plain,(
% 0.18/0.28 ( ! [X2 : $i,X3 : $i,X0 : ($i > $i),X1 : $i] : ((((ap @ X2 @ X1 @ (lam @ X2 @ X1 @ X0) @ X3)) = ((X0 @ X3))) | ($true != ((in @ X3 @ X2))) | (((in @ (sK9 @ X2 @ X1 @ X0) @ X2)) = $true)) ) | ~spl21_16),
% 0.18/0.28 inference(avatar_component_clause,[],[f140])).
% 0.18/0.28 thf(f142,plain,(
% 0.18/0.28 ~spl21_4 | spl21_16),
% 0.18/0.28 inference(avatar_split_clause,[],[f67,f140,f86])).
% 0.18/0.28 thf(f144,definition,(
% 0.18/0.28 spl21_17 <=> (sK16 = ((lam @ sK14 @ sK15 @ (ap @ sK14 @ sK15 @ sK16))))),
% 0.18/0.28 introduced(definition,[new_symbols(definition,[spl21_17])],[avatar_definition])).
% 0.18/0.28 thf(f146,plain,(
% 0.18/0.28 (sK16 != ((lam @ sK14 @ sK15 @ (ap @ sK14 @ sK15 @ sK16)))) | spl21_17),
% 0.18/0.28 inference(avatar_component_clause,[],[f144])).
% 0.18/0.28 thf(f147,plain,(
% 0.18/0.28 ~spl21_17),
% 0.18/0.28 inference(avatar_split_clause,[],[f68,f144])).
% 0.18/0.28 thf(f149,definition,(
% 0.18/0.28 spl21_18 <=> ! [X0 : $i,X3 : $i,X2 : $i,X1 : $i] : ((((in @ X1 @ (funcSet @ X0 @ X2))) != $true) | ($true = ((in @ (ap @ X0 @ X2 @ X1 @ X3) @ X2))) | (((in @ X3 @ X0)) != $true))),
% 0.18/0.28 introduced(definition,[new_symbols(definition,[spl21_18])],[avatar_definition])).
% 0.18/0.28 thf(f150,plain,(
% 0.18/0.28 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (ap @ X0 @ X2 @ X1 @ X3) @ X2))) | (((in @ X1 @ (funcSet @ X0 @ X2))) != $true) | (((in @ X3 @ X0)) != $true)) ) | ~spl21_18),
% 0.18/0.28 inference(avatar_component_clause,[],[f149])).
% 0.18/0.28 thf(f151,plain,(
% 0.18/0.28 ~spl21_7 | spl21_18),
% 0.18/0.28 inference(avatar_split_clause,[],[f41,f149,f100])).
% 0.18/0.28 thf(f158,definition,(
% 0.18/0.28 spl21_20 <=> ! [X2 : ($i > $i),X0 : $i,X1 : $i] : ((((in @ (X2 @ (sK17 @ X2 @ X1 @ X0)) @ X0)) != $true) | (((in @ (lam @ X1 @ X0 @ X2) @ (funcSet @ X1 @ X0))) = $true))),
% 0.18/0.28 introduced(definition,[new_symbols(definition,[spl21_20])],[avatar_definition])).
% 0.18/0.28 thf(f159,plain,(
% 0.18/0.28 ( ! [X2 : ($i > $i),X0 : $i,X1 : $i] : ((((in @ (lam @ X1 @ X0 @ X2) @ (funcSet @ X1 @ X0))) = $true) | (((in @ (X2 @ (sK17 @ X2 @ X1 @ X0)) @ X0)) != $true)) ) | ~spl21_20),
% 0.18/0.28 inference(avatar_component_clause,[],[f158])).
% 0.18/0.28 thf(f160,plain,(
% 0.18/0.28 ~spl21_8 | spl21_20),
% 0.18/0.28 inference(avatar_split_clause,[],[f70,f158,f105])).
% 0.18/0.28 thf(f174,plain,(
% 0.18/0.28 spl21_8),
% 0.18/0.28 inference(avatar_split_clause,[],[f58,f105])).
% 0.18/0.28 thf(f175,plain,(
% 0.18/0.28 spl21_4),
% 0.18/0.28 inference(avatar_split_clause,[],[f55,f86])).
% 0.18/0.28 thf(f193,plain,(
% 0.18/0.28 ( ! [X2 : $i,X3 : $i,X0 : ($i > $i),X1 : $i] : ((((in @ (sK4 @ X1 @ X2 @ X3 @ (lam @ X2 @ X3 @ X0)) @ X2)) != $true) | (((lam @ X2 @ X3 @ X0)) = X1) | ($true != ((in @ X1 @ (funcSet @ X2 @ X3)))) | (((in @ (sK9 @ X2 @ X3 @ X0) @ X2)) = $true) | (((ap @ X2 @ X3 @ X1 @ (sK4 @ X1 @ X2 @ X3 @ (lam @ X2 @ X3 @ X0)))) != ((X0 @ (sK4 @ X1 @ X2 @ X3 @ (lam @ X2 @ X3 @ X0))))) | (((in @ (lam @ X2 @ X3 @ X0) @ (funcSet @ X2 @ X3))) != $true)) ) | (~spl21_13 | ~spl21_16)),
% 0.18/0.28 inference(superposition,[],[f129,f141])).
% 0.18/0.28 thf(f196,plain,(
% 0.18/0.28 ( ! [X2 : $i,X3 : $i,X0 : ($i > $i),X1 : $i] : ((((ap @ X2 @ X3 @ X1 @ (sK4 @ X1 @ X2 @ X3 @ (lam @ X2 @ X3 @ X0)))) != ((X0 @ (sK4 @ X1 @ X2 @ X3 @ (lam @ X2 @ X3 @ X0))))) | ($true != ((in @ X1 @ (funcSet @ X2 @ X3)))) | (((in @ (sK9 @ X2 @ X3 @ X0) @ X2)) = $true) | (((in @ (lam @ X2 @ X3 @ X0) @ (funcSet @ X2 @ X3))) != $true) | (((lam @ X2 @ X3 @ X0)) = X1)) ) | (~spl21_13 | ~spl21_15 | ~spl21_16)),
% 0.18/0.28 inference(forward_subsumption_resolution,[],[f193,f137])).
% 0.18/0.28 thf(f200,plain,(
% 0.18/0.28 ( ! [X2 : $i,X3 : $i,X0 : ($i > $i),X1 : $i] : ((((in @ X3 @ (funcSet @ X1 @ X2))) != $true) | (((in @ (sK4 @ (lam @ X1 @ X2 @ X0) @ X1 @ X2 @ X3) @ X1)) != $true) | (((in @ (lam @ X1 @ X2 @ X0) @ (funcSet @ X1 @ X2))) != $true) | (((in @ (X0 @ (sK9 @ X1 @ X2 @ X0)) @ X2)) != $true) | (((lam @ X1 @ X2 @ X0)) = X3) | (((X0 @ (sK4 @ (lam @ X1 @ X2 @ X0) @ X1 @ X2 @ X3))) != ((ap @ X1 @ X2 @ X3 @ (sK4 @ (lam @ X1 @ X2 @ X0) @ X1 @ X2 @ X3))))) ) | (~spl21_12 | ~spl21_13)),
% 0.18/0.28 inference(superposition,[],[f129,f125])).
% 0.18/0.28 thf(f202,plain,(
% 0.18/0.28 ( ! [X2 : $i,X3 : $i,X0 : ($i > $i),X1 : $i] : ((((X0 @ (sK4 @ (lam @ X1 @ X2 @ X0) @ X1 @ X2 @ X3))) != ((ap @ X1 @ X2 @ X3 @ (sK4 @ (lam @ X1 @ X2 @ X0) @ X1 @ X2 @ X3)))) | (((lam @ X1 @ X2 @ X0)) = X3) | (((in @ (lam @ X1 @ X2 @ X0) @ (funcSet @ X1 @ X2))) != $true) | (((in @ X3 @ (funcSet @ X1 @ X2))) != $true) | (((in @ (X0 @ (sK9 @ X1 @ X2 @ X0)) @ X2)) != $true)) ) | (~spl21_12 | ~spl21_13 | ~spl21_15)),
% 0.18/0.28 inference(forward_subsumption_resolution,[],[f200,f137])).
% 0.18/0.28 thf(f217,plain,(
% 0.18/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (lam @ X1 @ X2 @ (ap @ X1 @ X2 @ X0)) @ (funcSet @ X1 @ X2))) != $true) | (((in @ (sK9 @ X1 @ X2 @ (ap @ X1 @ X2 @ X0)) @ X1)) = $true) | ($true != ((in @ X0 @ (funcSet @ X1 @ X2)))) | (((lam @ X1 @ X2 @ (ap @ X1 @ X2 @ X0))) = X0)) ) | (~spl21_13 | ~spl21_15 | ~spl21_16)),
% 0.18/0.28 inference(equality_resolution,[],[f196])).
% 0.18/0.28 thf(f248,plain,(
% 0.18/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (ap @ X0 @ X1 @ X2 @ (sK9 @ X0 @ X1 @ (ap @ X0 @ X1 @ X2))) @ X1)) != $true) | (((lam @ X0 @ X1 @ (ap @ X0 @ X1 @ X2))) = X2) | (((in @ (lam @ X0 @ X1 @ (ap @ X0 @ X1 @ X2)) @ (funcSet @ X0 @ X1))) != $true) | (((in @ X2 @ (funcSet @ X0 @ X1))) != $true)) ) | (~spl21_12 | ~spl21_13 | ~spl21_15)),
% 0.18/0.28 inference(equality_resolution,[],[f202])).
% 0.18/0.28 thf(f260,plain,(
% 0.18/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (funcSet @ X0 @ X1))) != $true) | ($true != $true) | (((in @ (sK9 @ X0 @ X1 @ (ap @ X0 @ X1 @ X2)) @ X0)) != $true) | (((lam @ X0 @ X1 @ (ap @ X0 @ X1 @ X2))) = X2) | (((in @ X2 @ (funcSet @ X0 @ X1))) != $true) | (((in @ (lam @ X0 @ X1 @ (ap @ X0 @ X1 @ X2)) @ (funcSet @ X0 @ X1))) != $true)) ) | (~spl21_12 | ~spl21_13 | ~spl21_15 | ~spl21_18)),
% 0.18/0.28 inference(superposition,[],[f248,f150])).
% 0.18/0.28 thf(f261,plain,(
% 0.18/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (lam @ X0 @ X1 @ (ap @ X0 @ X1 @ X2)) @ (funcSet @ X0 @ X1))) != $true) | (((lam @ X0 @ X1 @ (ap @ X0 @ X1 @ X2))) = X2) | (((in @ (sK9 @ X0 @ X1 @ (ap @ X0 @ X1 @ X2)) @ X0)) != $true) | ($true != $true) | (((in @ X2 @ (funcSet @ X0 @ X1))) != $true)) ) | (~spl21_12 | ~spl21_13 | ~spl21_15 | ~spl21_18)),
% 0.18/0.28 inference(duplicate_literal_removal,[],[f260])).
% 0.18/0.28 thf(f262,plain,(
% 0.18/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK9 @ X0 @ X1 @ (ap @ X0 @ X1 @ X2)) @ X0)) != $true) | (((in @ (lam @ X0 @ X1 @ (ap @ X0 @ X1 @ X2)) @ (funcSet @ X0 @ X1))) != $true) | (((lam @ X0 @ X1 @ (ap @ X0 @ X1 @ X2))) = X2) | (((in @ X2 @ (funcSet @ X0 @ X1))) != $true)) ) | (~spl21_12 | ~spl21_13 | ~spl21_15 | ~spl21_18)),
% 0.18/0.28 inference(trivial_inequality_removal,[],[f261])).
% 0.18/0.28 thf(f263,plain,(
% 0.18/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (lam @ X0 @ X1 @ (ap @ X0 @ X1 @ X2)) @ (funcSet @ X0 @ X1))) != $true) | (((in @ X2 @ (funcSet @ X0 @ X1))) != $true) | (((lam @ X0 @ X1 @ (ap @ X0 @ X1 @ X2))) = X2)) ) | (~spl21_12 | ~spl21_13 | ~spl21_15 | ~spl21_16 | ~spl21_18)),
% 0.18/0.28 inference(forward_subsumption_resolution,[],[f262,f217])).
% 0.18/0.28 thf(f267,plain,(
% 0.18/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((lam @ X0 @ X1 @ (ap @ X0 @ X1 @ X2))) = X2) | (((in @ (ap @ X0 @ X1 @ X2 @ (sK17 @ (ap @ X0 @ X1 @ X2) @ X0 @ X1)) @ X1)) != $true) | ($true != $true) | (((in @ X2 @ (funcSet @ X0 @ X1))) != $true)) ) | (~spl21_12 | ~spl21_13 | ~spl21_15 | ~spl21_16 | ~spl21_18 | ~spl21_20)),
% 0.18/0.28 inference(superposition,[],[f263,f159])).
% 0.18/0.28 thf(f268,plain,(
% 0.18/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK17 @ (ap @ X0 @ X1 @ X2) @ X0 @ X1) @ X0)) = $true) | (((in @ X2 @ (funcSet @ X0 @ X1))) != $true) | ($true != $true) | (((lam @ X0 @ X1 @ (ap @ X0 @ X1 @ X2))) = X2)) ) | (~spl21_12 | ~spl21_13 | ~spl21_14 | ~spl21_15 | ~spl21_16 | ~spl21_18)),
% 0.18/0.28 inference(superposition,[],[f263,f133])).
% 0.18/0.28 thf(f269,plain,(
% 0.18/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK17 @ (ap @ X0 @ X1 @ X2) @ X0 @ X1) @ X0)) = $true) | (((in @ X2 @ (funcSet @ X0 @ X1))) != $true) | (((lam @ X0 @ X1 @ (ap @ X0 @ X1 @ X2))) = X2)) ) | (~spl21_12 | ~spl21_13 | ~spl21_14 | ~spl21_15 | ~spl21_16 | ~spl21_18)),
% 0.18/0.28 inference(trivial_inequality_removal,[],[f268])).
% 0.18/0.28 thf(f270,plain,(
% 0.18/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (ap @ X0 @ X1 @ X2 @ (sK17 @ (ap @ X0 @ X1 @ X2) @ X0 @ X1)) @ X1)) != $true) | (((lam @ X0 @ X1 @ (ap @ X0 @ X1 @ X2))) = X2) | (((in @ X2 @ (funcSet @ X0 @ X1))) != $true)) ) | (~spl21_12 | ~spl21_13 | ~spl21_15 | ~spl21_16 | ~spl21_18 | ~spl21_20)),
% 0.18/0.28 inference(trivial_inequality_removal,[],[f267])).
% 0.18/0.28 thf(f289,plain,(
% 0.18/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | (((lam @ X0 @ X1 @ (ap @ X0 @ X1 @ X2))) = X2) | (((in @ X2 @ (funcSet @ X0 @ X1))) != $true) | (((in @ X2 @ (funcSet @ X0 @ X1))) != $true) | (((in @ (sK17 @ (ap @ X0 @ X1 @ X2) @ X0 @ X1) @ X0)) != $true)) ) | (~spl21_12 | ~spl21_13 | ~spl21_15 | ~spl21_16 | ~spl21_18 | ~spl21_20)),
% 0.18/0.28 inference(superposition,[],[f270,f150])).
% 0.18/0.28 thf(f290,plain,(
% 0.18/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((lam @ X0 @ X1 @ (ap @ X0 @ X1 @ X2))) = X2) | (((in @ X2 @ (funcSet @ X0 @ X1))) != $true) | (((in @ (sK17 @ (ap @ X0 @ X1 @ X2) @ X0 @ X1) @ X0)) != $true) | ($true != $true)) ) | (~spl21_12 | ~spl21_13 | ~spl21_15 | ~spl21_16 | ~spl21_18 | ~spl21_20)),
% 0.18/0.28 inference(duplicate_literal_removal,[],[f289])).
% 0.18/0.28 thf(f291,plain,(
% 0.18/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (funcSet @ X0 @ X1))) != $true) | (((lam @ X0 @ X1 @ (ap @ X0 @ X1 @ X2))) = X2) | (((in @ (sK17 @ (ap @ X0 @ X1 @ X2) @ X0 @ X1) @ X0)) != $true)) ) | (~spl21_12 | ~spl21_13 | ~spl21_15 | ~spl21_16 | ~spl21_18 | ~spl21_20)),
% 0.18/0.28 inference(trivial_inequality_removal,[],[f290])).
% 0.18/0.28 thf(f292,plain,(
% 0.18/0.28 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((lam @ X0 @ X1 @ (ap @ X0 @ X1 @ X2))) = X2) | (((in @ X2 @ (funcSet @ X0 @ X1))) != $true)) ) | (~spl21_12 | ~spl21_13 | ~spl21_14 | ~spl21_15 | ~spl21_16 | ~spl21_18 | ~spl21_20)),
% 0.18/0.28 inference(forward_subsumption_resolution,[],[f291,f269])).
% 0.18/0.28 thf(f303,plain,(
% 0.18/0.28 (((in @ sK16 @ (funcSet @ sK14 @ sK15))) != $true) | (sK16 != sK16) | (~spl21_12 | ~spl21_13 | ~spl21_14 | ~spl21_15 | ~spl21_16 | spl21_17 | ~spl21_18 | ~spl21_20)),
% 0.18/0.28 inference(superposition,[],[f146,f292])).
% 0.18/0.28 thf(f309,plain,(
% 0.18/0.28 (((in @ sK16 @ (funcSet @ sK14 @ sK15))) != $true) | (~spl21_12 | ~spl21_13 | ~spl21_14 | ~spl21_15 | ~spl21_16 | spl21_17 | ~spl21_18 | ~spl21_20)),
% 0.18/0.28 inference(trivial_inequality_removal,[],[f303])).
% 0.18/0.28 thf(f310,plain,(
% 0.18/0.28 $false | (~spl21_3 | ~spl21_12 | ~spl21_13 | ~spl21_14 | ~spl21_15 | ~spl21_16 | spl21_17 | ~spl21_18 | ~spl21_20)),
% 0.18/0.28 inference(forward_subsumption_resolution,[],[f309,f83])).
% 0.18/0.28 thf(f311,plain,(
% 0.18/0.28 ~spl21_3 | ~spl21_12 | ~spl21_13 | ~spl21_14 | ~spl21_15 | ~spl21_16 | spl21_17 | ~spl21_18 | ~spl21_20),
% 0.18/0.28 inference(avatar_contradiction_clause,[],[f310])).
% 0.18/0.28 cnf(s2, plain, spl21_3, inference(sat_conversion,[],[f84])).
% 0.18/0.28 cnf(s5, plain, spl21_7, inference(sat_conversion,[],[f103])).
% 0.18/0.28 cnf(s8, plain, spl21_1, inference(sat_conversion,[],[f117])).
% 0.18/0.28 cnf(s10, plain, ~spl21_4 | spl21_12, inference(sat_conversion,[],[f126])).
% 0.18/0.28 cnf(s11, plain, ~spl21_1 | spl21_13, inference(sat_conversion,[],[f130])).
% 0.18/0.28 cnf(s12, plain, ~spl21_8 | spl21_14, inference(sat_conversion,[],[f134])).
% 0.18/0.28 cnf(s13, plain, ~spl21_1 | spl21_15, inference(sat_conversion,[],[f138])).
% 0.18/0.28 cnf(s14, plain, ~spl21_4 | spl21_16, inference(sat_conversion,[],[f142])).
% 0.18/0.28 cnf(s15, plain, ~spl21_17, inference(sat_conversion,[],[f147])).
% 0.18/0.28 cnf(s16, plain, ~spl21_7 | spl21_18, inference(sat_conversion,[],[f151])).
% 0.18/0.28 cnf(s18, plain, ~spl21_8 | spl21_20, inference(sat_conversion,[],[f160])).
% 0.18/0.28 cnf(s22, plain, spl21_8, inference(sat_conversion,[],[f174])).
% 0.18/0.28 cnf(s23, plain, spl21_4, inference(sat_conversion,[],[f175])).
% 0.18/0.28 cnf(s26, plain, ~spl21_3 | ~spl21_12 | ~spl21_13 | ~spl21_14 | ~spl21_15 | ~spl21_16 | spl21_17 | ~spl21_18 | ~spl21_20, inference(sat_conversion,[],[f311])).
% 0.18/0.28 cnf(s27, plain, spl21_20, inference(rat,[],[s18,s22])).
% 0.18/0.28 cnf(s28, plain, spl21_16, inference(rat,[],[s14,s23])).
% 0.18/0.28 cnf(s29, plain, spl21_14, inference(rat,[],[s12,s22])).
% 0.18/0.28 cnf(s30, plain, spl21_12, inference(rat,[],[s10,s23])).
% 0.18/0.28 cnf(s31, plain, spl21_15, inference(rat,[],[s13,s8])).
% 0.18/0.28 cnf(s32, plain, spl21_13, inference(rat,[],[s11,s8])).
% 0.18/0.28 cnf(s33, plain, spl21_18, inference(rat,[],[s16,s5])).
% 0.18/0.28 cnf(s34, plain, ~spl21_3, inference(rat,[],[s26,s27,s32,s15,s28,s31,s29,s30,s33])).
% 0.18/0.28 cnf(s35, plain, $false, inference(rat,[],[s2,s34])).
% 0.18/0.28 thf(f312,plain,(
% 0.18/0.28 $false),
% 0.18/0.28 inference(avatar_sat_refutation,[],[s35])).
% 0.18/0.28 % SZS output end Proof for theBenchmark
% 0.18/0.28 % (1725828)------------------------------
% 0.18/0.28 % (1725828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.28 % (1725828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.28 % (1725828)CaDiCaL version: 2.1.3
% 0.18/0.28 % (1725828)Termination reason: Refutation
% 0.18/0.28 % (1725828)Time elapsed: 0.016 s
% 0.18/0.28 % (1725828)Peak memory usage: 13 MB
% 0.18/0.28 % (1725828)Instructions burned: 54 (million)
% 0.18/0.28 % (1725820)Success in time 0.043 s
% 0.18/0.28 % Vampire exiting
%------------------------------------------------------------------------------