%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU640^2 : 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 : n020.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 08:30:28 AM UTC 2026
% Result : Theorem 0.26s 0.38s
% Output : Refutation 0.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU640^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.26 % Computer : n020.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 14:02:05 UTC 2026
% 0.11/0.26 % CPUTime :
% 0.11/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.31 Running higher-order theorem proving
% 0.26/0.32 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
% 0.26/0.38 % (1100935)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.26/0.38 % (1100943)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=3839340824: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)
% 0.26/0.38 % (1100942)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3699292636:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.26/0.38 % (1100942)Refutation not found, incomplete strategy
% 0.26/0.38 % (1100942)------------------------------
% 0.26/0.38 % (1100942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.38 % (1100942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.38 % (1100942)CaDiCaL version: 2.1.3
% 0.26/0.38 % (1100942)Termination reason: Refutation not found, incomplete strategy
% 0.26/0.38 % (1100942)Time elapsed: 0.003 s
% 0.26/0.38 % (1100942)Peak memory usage: 12 MB
% 0.26/0.38 % (1100942)Instructions burned: 4 (million)
% 0.26/0.38 % (1100942)------------------------------
% 0.26/0.38 % (1100942)------------------------------
% 0.26/0.38 % (1100946)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.26/0.38 % (1100946)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
% 0.26/0.38 % (1100941)lrs+10_16_si=on:nwc=1.5:random_seed=1574382363:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.26/0.38 % (1100940)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3964541825:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.26/0.38 % (1100946)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=1104696926:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.26/0.38 % (1100944)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2314396217:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.26/0.38 % (1100945)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1102907626:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.26/0.38 % (1100943) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1100935-1100943"...
% 0.26/0.38 % (1100943)...printing done.
% 0.26/0.38 % (1100943)Refutation found. Thanks to Tanya!
% 0.26/0.38 % SZS status Theorem for theBenchmark
% 0.26/0.38 % SZS output start Proof for theBenchmark
% 0.26/0.38 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.26/0.38 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.26/0.38 thf(func_def_2, type, setadjoin: ($i > $i > $i)).
% 0.26/0.38 thf(func_def_3, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.26/0.38 thf(func_def_4, type, singleton: ($i > $o)).
% 0.26/0.38 thf(func_def_6, type, singletonprop: $o).
% 0.26/0.38 thf(func_def_7, type, ex1: ($i > ($i > $o) > $o)).
% 0.26/0.38 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.26/0.38 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.26/0.38 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.26/0.38 thf(func_def_13, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.26/0.38 thf(func_def_14, type, vAND: ($o > $o > $o)).
% 0.26/0.38 thf(func_def_15, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.26/0.38 thf(func_def_16, type, sK0: ($i > $o)).
% 0.26/0.38 thf(func_def_19, type, sK3: ($i > ($i > $o) > $i)).
% 0.26/0.38 thf(func_def_20, type, sK4: ($i > ($i > $o) > $i)).
% 0.26/0.38 thf(func_def_21, type, sK5: ($i > $o)).
% 0.26/0.38 thf(func_def_24, type, vNOT: ($o > $o)).
% 0.26/0.38 thf(func_def_26, type, sK9: ($i > $i)).
% 0.26/0.38 thf(f2,axiom,(
% 0.26/0.38 (singletonprop = ! [X1 : ($i > $o),X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0)) => (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))))),
% 0.26/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonprop)).
% 0.26/0.38 thf(f3,axiom,(
% 0.26/0.38 (ex1 = (^[X0 : $i, X1 : ($i > $o)] : ((singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))))),
% 0.26/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1)).
% 0.26/0.38 thf(f4,conjecture,(
% 0.26/0.38 singletonprop => ! [X1 : ($i > $o),X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0)) => (ex1 @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))),
% 0.26/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I2)).
% 0.26/0.38 thf(f5,negated_conjecture,(
% 0.26/0.38 ~(singletonprop => ! [X1 : ($i > $o),X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X2 : $i] : ((X1 @ X2) & (in @ X2 @ X0)) => (ex1 @ X0 @ (^[X2 : $i] : ((X1 @ X2)))))))),
% 0.26/0.38 inference(negated_conjecture,[status(cth)],[f4])).
% 0.26/0.38 thf(f6,plain,(
% 0.26/0.38 (ex1 = (^[X0 : $i, X1 : ($i > $o)] : ((singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))))),
% 0.26/0.38 inference(rectify,[],[f3])).
% 0.26/0.38 thf(f7,plain,(
% 0.26/0.38 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 0.26/0.38 inference(fool_elimination,[],[f6])).
% 0.26/0.38 thf(f8,plain,(
% 0.26/0.38 (singletonprop = ! [X0 : ($i > $o),X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X1) => ((X0 @ X2) => ((X0 @ X3) => (X2 = X3))))) => (? [X4 : $i] : ((X0 @ X4) & (in @ X4 @ X1)) => (singleton @ (dsetconstr @ X1 @ (^[X5 : $i] : ((X0 @ X5))))))))),
% 0.26/0.38 inference(rectify,[],[f2])).
% 0.26/0.38 thf(f9,plain,(
% 0.26/0.38 (singletonprop = $true) <=> ! [X0 : ($i > $o),X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => ! [X3 : $i] : (($true = ((in @ X3 @ X1))) => ((((X0 @ X2)) = $true) => (($true = ((X0 @ X3))) => (X2 = X3))))) => (? [X4 : $i] : ((((in @ X4 @ X1)) = $true) & ($true = ((X0 @ X4)))) => (((singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true)))),
% 0.26/0.38 inference(fool_elimination,[],[f8])).
% 0.26/0.38 thf(f10,plain,(
% 0.26/0.38 ~(singletonprop => ! [X0 : ($i > $o),X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X1) => ((X0 @ X2) => ((X0 @ X3) => (X2 = X3))))) => (? [X4 : $i] : ((X0 @ X4) & (in @ X4 @ X1)) => (ex1 @ X1 @ (^[X5 : $i] : ((X0 @ X5)))))))),
% 0.26/0.38 inference(rectify,[],[f5])).
% 0.26/0.38 thf(f11,plain,(
% 0.26/0.38 ~((singletonprop = $true) => ! [X0 : ($i > $o),X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => ! [X3 : $i] : (($true = ((in @ X3 @ X1))) => ((((X0 @ X2)) = $true) => (($true = ((X0 @ X3))) => (X2 = X3))))) => (? [X4 : $i] : (($true = ((X0 @ X4))) & (((in @ X4 @ X1)) = $true)) => (((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true))))),
% 0.26/0.38 inference(fool_elimination,[],[f10])).
% 0.26/0.38 thf(f14,plain,(
% 0.26/0.38 ? [X0 : ($i > $o),X1 : $i] : (((((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) & ? [X4 : $i] : (($true = ((X0 @ X4))) & (((in @ X4 @ X1)) = $true))) & ! [X2 : $i] : (! [X3 : $i] : ((((X2 = X3) | ($true != ((X0 @ X3)))) | (((X0 @ X2)) != $true)) | ($true != ((in @ X3 @ X1)))) | (((in @ X2 @ X1)) != $true))) & (singletonprop = $true)),
% 0.26/0.38 inference(ennf_transformation,[],[f11])).
% 0.26/0.38 thf(f15,plain,(
% 0.26/0.38 ? [X0 : ($i > $o),X1 : $i] : (? [X4 : $i] : (($true = ((X0 @ X4))) & (((in @ X4 @ X1)) = $true)) & (((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) & ! [X2 : $i] : (! [X3 : $i] : ((((X0 @ X2)) != $true) | ($true != ((X0 @ X3))) | (X2 = X3) | ($true != ((in @ X3 @ X1)))) | (((in @ X2 @ X1)) != $true))) & (singletonprop = $true)),
% 0.26/0.38 inference(flattening,[],[f14])).
% 0.26/0.38 thf(f16,plain,(
% 0.26/0.38 (singletonprop = $true) <=> ! [X0 : ($i > $o),X1 : $i] : (((((singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true) | ! [X4 : $i] : ((((in @ X4 @ X1)) != $true) | ($true != ((X0 @ X4))))) | ? [X2 : $i] : (? [X3 : $i] : ((((X2 != X3) & ($true = ((X0 @ X3)))) & (((X0 @ X2)) = $true)) & ($true = ((in @ X3 @ X1)))) & (((in @ X2 @ X1)) = $true)))),
% 0.26/0.38 inference(ennf_transformation,[],[f9])).
% 0.26/0.38 thf(f17,plain,(
% 0.26/0.38 (singletonprop = $true) <=> ! [X0 : ($i > $o),X1 : $i] : ((((singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & ? [X3 : $i] : ((X2 != X3) & ($true = ((X0 @ X3))) & ($true = ((in @ X3 @ X1))) & (((X0 @ X2)) = $true))) | ! [X4 : $i] : ((((in @ X4 @ X1)) != $true) | ($true != ((X0 @ X4)))))),
% 0.26/0.38 inference(flattening,[],[f16])).
% 0.26/0.38 thf(f18,plain,(
% 0.26/0.38 ((singletonprop = $true) | ? [X0 : ($i > $o),X1 : $i] : ((((singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | ! [X3 : $i] : ((X2 = X3) | ($true != ((X0 @ X3))) | ($true != ((in @ X3 @ X1))) | (((X0 @ X2)) != $true))) & ? [X4 : $i] : ((((in @ X4 @ X1)) = $true) & ($true = ((X0 @ X4)))))) & (! [X0 : ($i > $o),X1 : $i] : ((((singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & ? [X3 : $i] : ((X2 != X3) & ($true = ((X0 @ X3))) & ($true = ((in @ X3 @ X1))) & (((X0 @ X2)) = $true))) | ! [X4 : $i] : ((((in @ X4 @ X1)) != $true) | ($true != ((X0 @ X4))))) | (singletonprop != $true))),
% 0.26/0.38 inference(nnf_transformation,[],[f17])).
% 0.26/0.38 thf(f19,plain,(
% 0.26/0.38 ((singletonprop = $true) | ? [X0 : ($i > $o),X1 : $i] : ((((singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | ! [X3 : $i] : ((X2 = X3) | ($true != ((X0 @ X3))) | ($true != ((in @ X3 @ X1))) | (((X0 @ X2)) != $true))) & ? [X4 : $i] : ((((in @ X4 @ X1)) = $true) & ($true = ((X0 @ X4)))))) & (! [X5 : ($i > $o),X6 : $i] : (($true = ((singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (X5 @ Y0)))))) | ? [X7 : $i] : ((((in @ X7 @ X6)) = $true) & ? [X8 : $i] : ((X7 != X8) & (((X5 @ X8)) = $true) & ($true = ((in @ X8 @ X6))) & (((X5 @ X7)) = $true))) | ! [X9 : $i] : ((((in @ X9 @ X6)) != $true) | ($true != ((X5 @ X9))))) | (singletonprop != $true))),
% 0.26/0.38 inference(rectify,[],[f18])).
% 0.26/0.38 thf(f20,plain,(
% 0.26/0.38 ((singletonprop = $true) | ((((singleton @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (sK0 @ Y0))))) != $true) & ! [X2 : $i] : (($true != ((in @ X2 @ sK1))) | ! [X3 : $i] : ((X2 = X3) | ($true != ((sK0 @ X3))) | (((in @ X3 @ sK1)) != $true) | ($true != ((sK0 @ X2))))) & ((((in @ sK2 @ sK1)) = $true) & (((sK0 @ sK2)) = $true)))) & (! [X5 : ($i > $o),X6 : $i] : (($true = ((singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (X5 @ Y0)))))) | (($true = ((in @ (sK3 @ X6 @ X5) @ X6))) & ((((sK4 @ X6 @ X5)) != ((sK3 @ X6 @ X5))) & ($true = ((X5 @ (sK4 @ X6 @ X5)))) & ($true = ((in @ (sK4 @ X6 @ X5) @ X6))) & (((X5 @ (sK3 @ X6 @ X5))) = $true))) | ! [X9 : $i] : ((((in @ X9 @ X6)) != $true) | ($true != ((X5 @ X9))))) | (singletonprop != $true))),
% 0.26/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X4,sK2),skolemize(X8,sK4 @ X6 @ X5),skolemize(X8,sK4 @ X6 @ X5)],[f19])).
% 0.26/0.38 thf(f21,plain,(
% 0.26/0.38 ? [X0 : ($i > $o),X1 : $i] : (? [X2 : $i] : ((((X0 @ X2)) = $true) & (((in @ X2 @ X1)) = $true)) & (((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) & ! [X3 : $i] : (! [X4 : $i] : (($true != ((X0 @ X3))) | ($true != ((X0 @ X4))) | (X3 = X4) | (((in @ X4 @ X1)) != $true)) | ($true != ((in @ X3 @ X1))))) & (singletonprop = $true)),
% 0.26/0.38 inference(rectify,[],[f15])).
% 0.26/0.38 thf(f22,plain,(
% 0.26/0.38 ((($true = ((sK5 @ sK7))) & (((in @ sK7 @ sK6)) = $true)) & ($true != ((ex1 @ sK6 @ (^[Y0 : $i]: (sK5 @ Y0))))) & ! [X3 : $i] : (! [X4 : $i] : (($true != ((sK5 @ X3))) | ($true != ((sK5 @ X4))) | (X3 = X4) | ($true != ((in @ X4 @ sK6)))) | ($true != ((in @ X3 @ sK6))))) & (singletonprop = $true)),
% 0.26/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f21])).
% 0.26/0.38 thf(f23,plain,(
% 0.26/0.38 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 0.26/0.38 inference(cnf_transformation,[],[f7])).
% 0.26/0.38 thf(f24,plain,(
% 0.26/0.38 ( ! [X6 : $i,X9 : $i,X5 : ($i > $o)] : ((((X5 @ (sK3 @ X6 @ X5))) = $true) | (((in @ X9 @ X6)) != $true) | ($true = ((singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (X5 @ Y0)))))) | ($true != ((X5 @ X9))) | (singletonprop != $true)) )),
% 0.26/0.38 inference(cnf_transformation,[],[f20])).
% 0.26/0.38 thf(f25,plain,(
% 0.26/0.38 ( ! [X6 : $i,X9 : $i,X5 : ($i > $o)] : ((singletonprop != $true) | (((in @ X9 @ X6)) != $true) | ($true = ((singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (X5 @ Y0)))))) | ($true != ((X5 @ X9))) | ($true = ((in @ (sK4 @ X6 @ X5) @ X6)))) )),
% 0.26/0.38 inference(cnf_transformation,[],[f20])).
% 0.26/0.38 thf(f26,plain,(
% 0.26/0.38 ( ! [X6 : $i,X9 : $i,X5 : ($i > $o)] : (($true != ((X5 @ X9))) | ($true = ((singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (X5 @ Y0)))))) | (singletonprop != $true) | ($true = ((X5 @ (sK4 @ X6 @ X5)))) | (((in @ X9 @ X6)) != $true)) )),
% 0.26/0.38 inference(cnf_transformation,[],[f20])).
% 0.26/0.38 thf(f27,plain,(
% 0.26/0.38 ( ! [X6 : $i,X9 : $i,X5 : ($i > $o)] : ((singletonprop != $true) | ($true = ((singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (X5 @ Y0)))))) | (((in @ X9 @ X6)) != $true) | (((sK4 @ X6 @ X5)) != ((sK3 @ X6 @ X5))) | ($true != ((X5 @ X9)))) )),
% 0.26/0.38 inference(cnf_transformation,[],[f20])).
% 0.26/0.38 thf(f28,plain,(
% 0.26/0.38 ( ! [X6 : $i,X9 : $i,X5 : ($i > $o)] : ((singletonprop != $true) | (((in @ X9 @ X6)) != $true) | ($true = ((singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (X5 @ Y0)))))) | ($true != ((X5 @ X9))) | ($true = ((in @ (sK3 @ X6 @ X5) @ X6)))) )),
% 0.26/0.38 inference(cnf_transformation,[],[f20])).
% 0.26/0.38 thf(f33,plain,(
% 0.26/0.38 (singletonprop = $true)),
% 0.26/0.38 inference(cnf_transformation,[],[f22])).
% 0.26/0.38 thf(f34,plain,(
% 0.26/0.38 ( ! [X3 : $i,X4 : $i] : (($true != ((in @ X4 @ sK6))) | (X3 = X4) | ($true != ((in @ X3 @ sK6))) | ($true != ((sK5 @ X3))) | ($true != ((sK5 @ X4)))) )),
% 0.26/0.38 inference(cnf_transformation,[],[f22])).
% 0.26/0.38 thf(f35,plain,(
% 0.26/0.38 ($true != ((ex1 @ sK6 @ (^[Y0 : $i]: (sK5 @ Y0)))))),
% 0.26/0.38 inference(cnf_transformation,[],[f22])).
% 0.26/0.38 thf(f36,plain,(
% 0.26/0.38 (((in @ sK7 @ sK6)) = $true)),
% 0.26/0.38 inference(cnf_transformation,[],[f22])).
% 0.26/0.38 thf(f37,plain,(
% 0.26/0.38 ($true = ((sK5 @ sK7)))),
% 0.26/0.38 inference(cnf_transformation,[],[f22])).
% 0.26/0.38 thf(f40,plain,(
% 0.26/0.38 ( ! [X6 : $i,X9 : $i,X5 : ($i > $o)] : (($true = ((singleton @ (dsetconstr @ X6 @ X5)))) | ($true = ((in @ (sK4 @ X6 @ X5) @ X6))) | ($true != ((X5 @ X9))) | (((in @ X9 @ X6)) != $true) | (singletonprop != $true)) )),
% 0.26/0.38 inference(beta-eta_normalization,[],[f25])).
% 0.26/0.38 thf(f41,plain,(
% 0.26/0.38 ( ! [X6 : $i,X9 : $i,X5 : ($i > $o)] : ((singletonprop != $true) | (((in @ X9 @ X6)) != $true) | ($true = ((in @ (sK3 @ X6 @ X5) @ X6))) | ($true = ((singleton @ (dsetconstr @ X6 @ X5)))) | ($true != ((X5 @ X9)))) )),
% 0.26/0.38 inference(beta-eta_normalization,[],[f28])).
% 0.26/0.38 thf(f42,plain,(
% 0.26/0.38 ($true != ((ex1 @ sK6 @ sK5)))),
% 0.26/0.38 inference(beta-eta_normalization,[],[f35])).
% 0.26/0.38 thf(f43,plain,(
% 0.26/0.38 ( ! [X6 : $i,X9 : $i,X5 : ($i > $o)] : (($true != ((X5 @ X9))) | (singletonprop != $true) | (((sK4 @ X6 @ X5)) != ((sK3 @ X6 @ X5))) | (((in @ X9 @ X6)) != $true) | ($true = ((singleton @ (dsetconstr @ X6 @ X5))))) )),
% 0.26/0.38 inference(beta-eta_normalization,[],[f27])).
% 0.26/0.38 thf(f44,plain,(
% 0.26/0.38 ( ! [X6 : $i,X9 : $i,X5 : ($i > $o)] : ((((in @ X9 @ X6)) != $true) | (singletonprop != $true) | (((X5 @ (sK3 @ X6 @ X5))) = $true) | ($true = ((singleton @ (dsetconstr @ X6 @ X5)))) | ($true != ((X5 @ X9)))) )),
% 0.26/0.38 inference(beta-eta_normalization,[],[f24])).
% 0.26/0.38 thf(f46,plain,(
% 0.26/0.38 ( ! [X6 : $i,X9 : $i,X5 : ($i > $o)] : ((singletonprop != $true) | ($true = ((singleton @ (dsetconstr @ X6 @ X5)))) | ($true != ((X5 @ X9))) | ($true = ((X5 @ (sK4 @ X6 @ X5)))) | (((in @ X9 @ X6)) != $true)) )),
% 0.26/0.38 inference(beta-eta_normalization,[],[f26])).
% 0.26/0.38 thf(f47,plain,(
% 0.26/0.38 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ Y1))))))),
% 0.26/0.38 inference(beta-eta_normalization,[],[f23])).
% 0.26/0.38 thf(f53,definition,(
% 0.26/0.38 spl8_2 <=> (singletonprop = $true)),
% 0.26/0.38 introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition])).
% 0.26/0.38 thf(f62,definition,(
% 0.26/0.38 spl8_4 <=> (((in @ sK7 @ sK6)) = $true)),
% 0.26/0.38 introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition])).
% 0.26/0.38 thf(f64,plain,(
% 0.26/0.38 (((in @ sK7 @ sK6)) = $true) | ~spl8_4),
% 0.26/0.38 inference(avatar_component_clause,[],[f62])).
% 0.26/0.38 thf(f65,plain,(
% 0.26/0.38 spl8_4),
% 0.26/0.38 inference(avatar_split_clause,[],[f36,f62])).
% 0.26/0.38 thf(f67,definition,(
% 0.26/0.38 spl8_5 <=> ! [X6 : $i,X9 : $i,X5 : ($i > $o)] : (($true = ((singleton @ (dsetconstr @ X6 @ X5)))) | (((in @ X9 @ X6)) != $true) | ($true != ((X5 @ X9))) | ($true = ((in @ (sK4 @ X6 @ X5) @ X6))))),
% 0.26/0.38 introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition])).
% 0.26/0.38 thf(f68,plain,(
% 0.26/0.38 ( ! [X6 : $i,X9 : $i,X5 : ($i > $o)] : (($true = ((in @ (sK4 @ X6 @ X5) @ X6))) | (((in @ X9 @ X6)) != $true) | ($true = ((singleton @ (dsetconstr @ X6 @ X5)))) | ($true != ((X5 @ X9)))) ) | ~spl8_5),
% 0.26/0.38 inference(avatar_component_clause,[],[f67])).
% 0.26/0.38 thf(f69,plain,(
% 0.26/0.38 spl8_5 | ~spl8_2),
% 0.26/0.38 inference(avatar_split_clause,[],[f40,f53,f67])).
% 0.26/0.38 thf(f81,definition,(
% 0.26/0.38 spl8_8 <=> ! [X6 : $i,X9 : $i,X5 : ($i > $o)] : ((((in @ X9 @ X6)) != $true) | ($true != ((X5 @ X9))) | ($true = ((singleton @ (dsetconstr @ X6 @ X5)))) | ($true = ((in @ (sK3 @ X6 @ X5) @ X6))))),
% 0.26/0.38 introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition])).
% 0.26/0.38 thf(f82,plain,(
% 0.26/0.38 ( ! [X6 : $i,X9 : $i,X5 : ($i > $o)] : (($true = ((in @ (sK3 @ X6 @ X5) @ X6))) | ($true = ((singleton @ (dsetconstr @ X6 @ X5)))) | (((in @ X9 @ X6)) != $true) | ($true != ((X5 @ X9)))) ) | ~spl8_8),
% 0.26/0.38 inference(avatar_component_clause,[],[f81])).
% 0.26/0.38 thf(f83,plain,(
% 0.26/0.38 spl8_8 | ~spl8_2),
% 0.26/0.38 inference(avatar_split_clause,[],[f41,f53,f81])).
% 0.26/0.38 thf(f85,definition,(
% 0.26/0.38 spl8_9 <=> ($true = ((ex1 @ sK6 @ sK5)))),
% 0.26/0.38 introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition])).
% 0.26/0.38 thf(f87,plain,(
% 0.26/0.38 ($true != ((ex1 @ sK6 @ sK5))) | spl8_9),
% 0.26/0.38 inference(avatar_component_clause,[],[f85])).
% 0.26/0.38 thf(f88,plain,(
% 0.26/0.38 ~spl8_9),
% 0.26/0.38 inference(avatar_split_clause,[],[f42,f85])).
% 0.26/0.38 thf(f89,plain,(
% 0.26/0.38 spl8_2),
% 0.26/0.38 inference(avatar_split_clause,[],[f33,f53])).
% 0.26/0.38 thf(f91,definition,(
% 0.26/0.38 spl8_10 <=> ! [X6 : $i,X9 : $i,X5 : ($i > $o)] : (($true != ((X5 @ X9))) | ($true = ((singleton @ (dsetconstr @ X6 @ X5)))) | (((in @ X9 @ X6)) != $true) | (((sK4 @ X6 @ X5)) != ((sK3 @ X6 @ X5))))),
% 0.26/0.38 introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition])).
% 0.26/0.38 thf(f92,plain,(
% 0.26/0.38 ( ! [X6 : $i,X9 : $i,X5 : ($i > $o)] : ((((sK4 @ X6 @ X5)) != ((sK3 @ X6 @ X5))) | ($true = ((singleton @ (dsetconstr @ X6 @ X5)))) | ($true != ((X5 @ X9))) | (((in @ X9 @ X6)) != $true)) ) | ~spl8_10),
% 0.26/0.38 inference(avatar_component_clause,[],[f91])).
% 0.26/0.38 thf(f93,plain,(
% 0.26/0.38 ~spl8_2 | spl8_10),
% 0.26/0.38 inference(avatar_split_clause,[],[f43,f91,f53])).
% 0.26/0.38 thf(f95,definition,(
% 0.26/0.38 spl8_11 <=> ($true = ((sK5 @ sK7)))),
% 0.26/0.38 introduced(definition,[new_symbols(definition,[spl8_11])],[avatar_definition])).
% 0.26/0.38 thf(f97,plain,(
% 0.26/0.38 ($true = ((sK5 @ sK7))) | ~spl8_11),
% 0.26/0.38 inference(avatar_component_clause,[],[f95])).
% 0.26/0.38 thf(f98,plain,(
% 0.26/0.38 spl8_11),
% 0.26/0.38 inference(avatar_split_clause,[],[f37,f95])).
% 0.26/0.38 thf(f100,definition,(
% 0.26/0.38 spl8_12 <=> ! [X6 : $i,X9 : $i,X5 : ($i > $o)] : ((((in @ X9 @ X6)) != $true) | ($true != ((X5 @ X9))) | ($true = ((singleton @ (dsetconstr @ X6 @ X5)))) | (((X5 @ (sK3 @ X6 @ X5))) = $true))),
% 0.26/0.38 introduced(definition,[new_symbols(definition,[spl8_12])],[avatar_definition])).
% 0.26/0.38 thf(f101,plain,(
% 0.26/0.38 ( ! [X6 : $i,X9 : $i,X5 : ($i > $o)] : (($true = ((singleton @ (dsetconstr @ X6 @ X5)))) | (((X5 @ (sK3 @ X6 @ X5))) = $true) | (((in @ X9 @ X6)) != $true) | ($true != ((X5 @ X9)))) ) | ~spl8_12),
% 0.26/0.38 inference(avatar_component_clause,[],[f100])).
% 0.26/0.38 thf(f102,plain,(
% 0.26/0.38 ~spl8_2 | spl8_12),
% 0.26/0.38 inference(avatar_split_clause,[],[f44,f100,f53])).
% 0.26/0.38 thf(f109,definition,(
% 0.26/0.38 spl8_14 <=> ! [X6 : $i,X9 : $i,X5 : ($i > $o)] : (($true = ((singleton @ (dsetconstr @ X6 @ X5)))) | (((in @ X9 @ X6)) != $true) | ($true = ((X5 @ (sK4 @ X6 @ X5)))) | ($true != ((X5 @ X9))))),
% 0.26/0.38 introduced(definition,[new_symbols(definition,[spl8_14])],[avatar_definition])).
% 0.26/0.38 thf(f110,plain,(
% 0.26/0.38 ( ! [X6 : $i,X9 : $i,X5 : ($i > $o)] : (($true = ((singleton @ (dsetconstr @ X6 @ X5)))) | (((in @ X9 @ X6)) != $true) | ($true = ((X5 @ (sK4 @ X6 @ X5)))) | ($true != ((X5 @ X9)))) ) | ~spl8_14),
% 0.26/0.38 inference(avatar_component_clause,[],[f109])).
% 0.26/0.38 thf(f111,plain,(
% 0.26/0.38 spl8_14 | ~spl8_2),
% 0.26/0.38 inference(avatar_split_clause,[],[f46,f53,f109])).
% 0.26/0.38 thf(f113,definition,(
% 0.26/0.38 spl8_15 <=> (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ Y1))))))),
% 0.26/0.38 introduced(definition,[new_symbols(definition,[spl8_15])],[avatar_definition])).
% 0.26/0.38 thf(f115,plain,(
% 0.26/0.38 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ Y1)))))) | ~spl8_15),
% 0.26/0.38 inference(avatar_component_clause,[],[f113])).
% 0.26/0.38 thf(f116,plain,(
% 0.26/0.38 spl8_15),
% 0.26/0.38 inference(avatar_split_clause,[],[f47,f113])).
% 0.26/0.38 thf(f117,plain,(
% 0.26/0.38 ( ! [X0 : $i] : (($true != ((sK5 @ X0))) | ($true != ((sK5 @ sK7))) | ($true != ((in @ X0 @ sK6))) | (sK7 = X0) | ($true != $true)) ) | ~spl8_4),
% 0.26/0.38 inference(superposition,[],[f34,f64])).
% 0.26/0.38 thf(f118,plain,(
% 0.26/0.38 ( ! [X0 : $i] : (($true != ((sK5 @ X0))) | (sK7 = X0) | ($true != ((in @ X0 @ sK6))) | ($true != ((sK5 @ sK7)))) ) | ~spl8_4),
% 0.26/0.38 inference(trivial_inequality_removal,[],[f117])).
% 0.26/0.38 thf(f119,plain,(
% 0.26/0.38 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK6))) | ($true != ((sK5 @ X0))) | (sK7 = X0)) ) | (~spl8_4 | ~spl8_11)),
% 0.26/0.38 inference(forward_subsumption_resolution,[],[f118,f97])).
% 0.26/0.38 thf(f121,plain,(
% 0.26/0.38 ( ! [X1 : $i] : ((((ex1 @ X1)) = (((^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ Y1))))) @ X1)))) ) | ~spl8_15),
% 0.26/0.38 inference(argument_congruence,[],[f115])).
% 0.26/0.38 thf(f122,plain,(
% 0.26/0.38 ( ! [X1 : $i] : (((^[Y0 : $i > $o]: (singleton @ (dsetconstr @ X1 @ Y0))) = ((ex1 @ X1)))) ) | ~spl8_15),
% 0.26/0.38 inference(beta-eta_normalization,[],[f121])).
% 0.26/0.38 thf(f179,plain,(
% 0.26/0.38 ( ! [X0 : ($i > $o),X1 : $i] : (($true != $true) | (((sK4 @ sK6 @ X0)) = sK7) | ($true != ((in @ X1 @ sK6))) | ($true = ((singleton @ (dsetconstr @ sK6 @ X0)))) | (((X0 @ X1)) != $true) | ($true != ((sK5 @ (sK4 @ sK6 @ X0))))) ) | (~spl8_4 | ~spl8_5 | ~spl8_11)),
% 0.26/0.38 inference(superposition,[],[f119,f68])).
% 0.26/0.38 thf(f184,plain,(
% 0.26/0.38 ( ! [X0 : ($i > $o),X1 : $i] : (($true = ((singleton @ (dsetconstr @ sK6 @ X0)))) | ($true != ((in @ X1 @ sK6))) | ($true != ((sK5 @ (sK4 @ sK6 @ X0)))) | (((X0 @ X1)) != $true) | (((sK4 @ sK6 @ X0)) = sK7)) ) | (~spl8_4 | ~spl8_5 | ~spl8_11)),
% 0.26/0.38 inference(trivial_inequality_removal,[],[f179])).
% 0.26/0.38 thf(f187,plain,(
% 0.26/0.38 ( ! [X0 : ($i > $o),X1 : $i] : (($true != $true) | (((X0 @ X1)) != $true) | (((sK3 @ sK6 @ X0)) = sK7) | ($true != ((in @ X1 @ sK6))) | (((sK5 @ (sK3 @ sK6 @ X0))) != $true) | ($true = ((singleton @ (dsetconstr @ sK6 @ X0))))) ) | (~spl8_4 | ~spl8_8 | ~spl8_11)),
% 0.26/0.38 inference(superposition,[],[f119,f82])).
% 0.26/0.38 thf(f190,plain,(
% 0.26/0.38 ( ! [X0 : ($i > $o),X1 : $i] : (($true = ((singleton @ (dsetconstr @ sK6 @ X0)))) | (((sK5 @ (sK3 @ sK6 @ X0))) != $true) | (((X0 @ X1)) != $true) | ($true != ((in @ X1 @ sK6))) | (((sK3 @ sK6 @ X0)) = sK7)) ) | (~spl8_4 | ~spl8_8 | ~spl8_11)),
% 0.26/0.38 inference(trivial_inequality_removal,[],[f187])).
% 0.26/0.38 thf(f194,plain,(
% 0.26/0.38 ( ! [X2 : ($i > $o),X1 : $i] : ((((ex1 @ X1 @ X2)) = (((^[Y0 : $i > $o]: (singleton @ (dsetconstr @ X1 @ Y0))) @ X2)))) ) | ~spl8_15),
% 0.26/0.38 inference(argument_congruence,[],[f122])).
% 0.26/0.38 thf(f195,plain,(
% 0.26/0.38 ( ! [X2 : ($i > $o),X1 : $i] : (($false = (((^[Y0 : $i > $o]: (singleton @ (dsetconstr @ X1 @ Y0))) @ X2))) | (((ex1 @ X1 @ X2)) = $true)) ) | ~spl8_15),
% 0.26/0.38 inference(iff_proxy_clausification,[],[f194])).
% 0.26/0.38 thf(f198,plain,(
% 0.26/0.38 ( ! [X2 : ($i > $o),X1 : $i] : (($false = ((singleton @ (dsetconstr @ X1 @ X2)))) | (((ex1 @ X1 @ X2)) = $true)) ) | ~spl8_15),
% 0.26/0.38 inference(beta-eta_normalization,[],[f195])).
% 0.26/0.38 thf(f200,plain,(
% 0.26/0.38 ( ! [X2 : $i,X0 : $i,X1 : ($i > $o)] : ((((ex1 @ X0 @ X1)) = $true) | (((X1 @ X2)) != $true) | (((X1 @ (sK4 @ X0 @ X1))) = $true) | (((in @ X2 @ X0)) != $true) | ($false = $true)) ) | (~spl8_14 | ~spl8_15)),
% 0.26/0.38 inference(superposition,[],[f198,f110])).
% 0.26/0.38 thf(f201,plain,(
% 0.26/0.38 ( ! [X2 : $i,X0 : $i,X1 : ($i > $o)] : ((((in @ X2 @ X0)) != $true) | (((X1 @ X2)) != $true) | ($false = $true) | (((ex1 @ X0 @ X1)) = $true) | ($true = ((X1 @ (sK3 @ X0 @ X1))))) ) | (~spl8_12 | ~spl8_15)),
% 0.26/0.38 inference(superposition,[],[f198,f101])).
% 0.26/0.38 thf(f206,plain,(
% 0.26/0.38 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ X1)) != $true) | ($false = $true) | (((sK3 @ sK6 @ X0)) = sK7) | ($true != ((in @ X1 @ sK6))) | ($true = ((ex1 @ sK6 @ X0))) | (((sK5 @ (sK3 @ sK6 @ X0))) != $true)) ) | (~spl8_4 | ~spl8_8 | ~spl8_11 | ~spl8_15)),
% 0.26/0.38 inference(superposition,[],[f198,f190])).
% 0.26/0.38 thf(f216,plain,(
% 0.26/0.38 ( ! [X0 : ($i > $o),X1 : $i] : ((((sK4 @ sK6 @ X0)) = sK7) | (((X0 @ X1)) != $true) | ($true != ((sK5 @ (sK4 @ sK6 @ X0)))) | ($true = ((ex1 @ sK6 @ X0))) | ($false = $true) | ($true != ((in @ X1 @ sK6)))) ) | (~spl8_4 | ~spl8_5 | ~spl8_11 | ~spl8_15)),
% 0.26/0.38 inference(superposition,[],[f184,f198])).
% 0.26/0.38 thf(f217,plain,(
% 0.26/0.38 ( ! [X0 : ($i > $o),X1 : $i] : (($true != ((sK5 @ (sK4 @ sK6 @ X0)))) | ($true = ((ex1 @ sK6 @ X0))) | (((sK4 @ sK6 @ X0)) = sK7) | ($true != ((in @ X1 @ sK6))) | (((X0 @ X1)) != $true)) ) | (~spl8_4 | ~spl8_5 | ~spl8_11 | ~spl8_15)),
% 0.26/0.38 inference(trivial_inequality_removal,[],[f216])).
% 0.26/0.38 thf(f221,plain,(
% 0.26/0.38 ( ! [X0 : ($i > $o),X1 : $i] : ((((sK5 @ (sK3 @ sK6 @ X0))) != $true) | (((sK3 @ sK6 @ X0)) = sK7) | ($true = ((ex1 @ sK6 @ X0))) | ($true != ((in @ X1 @ sK6))) | (((X0 @ X1)) != $true)) ) | (~spl8_4 | ~spl8_8 | ~spl8_11 | ~spl8_15)),
% 0.26/0.38 inference(trivial_inequality_removal,[],[f206])).
% 0.26/0.38 thf(f222,plain,(
% 0.26/0.38 ( ! [X2 : $i,X0 : $i,X1 : ($i > $o)] : (($true = ((X1 @ (sK3 @ X0 @ X1)))) | (((in @ X2 @ X0)) != $true) | (((ex1 @ X0 @ X1)) = $true) | (((X1 @ X2)) != $true)) ) | (~spl8_12 | ~spl8_15)),
% 0.26/0.38 inference(trivial_inequality_removal,[],[f201])).
% 0.26/0.38 thf(f226,plain,(
% 0.26/0.38 ( ! [X2 : $i,X0 : $i,X1 : ($i > $o)] : ((((X1 @ (sK4 @ X0 @ X1))) = $true) | (((X1 @ X2)) != $true) | (((ex1 @ X0 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)) ) | (~spl8_14 | ~spl8_15)),
% 0.26/0.38 inference(trivial_inequality_removal,[],[f200])).
% 0.26/0.38 thf(f242,plain,(
% 0.26/0.38 ( ! [X0 : $i,X1 : $i] : ((((sK5 @ X1)) != $true) | ($true != ((in @ X0 @ sK6))) | ($true != ((sK5 @ X0))) | (((sK3 @ sK6 @ sK5)) = sK7) | ($true = ((ex1 @ sK6 @ sK5))) | ($true = ((ex1 @ sK6 @ sK5))) | ($true != $true) | ($true != ((in @ X1 @ sK6)))) ) | (~spl8_4 | ~spl8_8 | ~spl8_11 | ~spl8_12 | ~spl8_15)),
% 0.26/0.38 inference(superposition,[],[f221,f222])).
% 0.26/0.38 thf(f252,plain,(
% 0.26/0.38 ( ! [X0 : $i,X1 : $i] : ((((sK5 @ X1)) != $true) | ($true != $true) | ($true != ((in @ X1 @ sK6))) | ($true != ((in @ X0 @ sK6))) | ($true = ((ex1 @ sK6 @ sK5))) | ($true != ((sK5 @ X0))) | (((sK3 @ sK6 @ sK5)) = sK7)) ) | (~spl8_4 | ~spl8_8 | ~spl8_11 | ~spl8_12 | ~spl8_15)),
% 0.26/0.38 inference(duplicate_literal_removal,[],[f242])).
% 0.26/0.38 thf(f253,plain,(
% 0.26/0.38 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ sK6))) | ($true != ((sK5 @ X0))) | (((sK5 @ X1)) != $true) | ($true = ((ex1 @ sK6 @ sK5))) | ($true != ((in @ X1 @ sK6))) | (((sK3 @ sK6 @ sK5)) = sK7)) ) | (~spl8_4 | ~spl8_8 | ~spl8_11 | ~spl8_12 | ~spl8_15)),
% 0.26/0.38 inference(trivial_inequality_removal,[],[f252])).
% 0.26/0.38 thf(f255,plain,(
% 0.26/0.38 ( ! [X0 : $i,X1 : $i] : ((((sK5 @ X1)) != $true) | (((sK3 @ sK6 @ sK5)) = sK7) | ($true != ((sK5 @ X0))) | ($true != ((in @ X1 @ sK6))) | ($true != ((in @ X0 @ sK6)))) ) | (~spl8_4 | ~spl8_8 | spl8_9 | ~spl8_11 | ~spl8_12 | ~spl8_15)),
% 0.26/0.38 inference(forward_subsumption_resolution,[],[f253,f87])).
% 0.26/0.38 thf(f260,definition,(
% 0.26/0.38 spl8_23 <=> ! [X0 : $i] : (($true != ((in @ X0 @ sK6))) | ($true != ((sK5 @ X0))))),
% 0.26/0.38 introduced(definition,[new_symbols(definition,[spl8_23])],[avatar_definition])).
% 0.26/0.38 thf(f261,plain,(
% 0.26/0.38 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK6))) | ($true != ((sK5 @ X0)))) ) | ~spl8_23),
% 0.26/0.38 inference(avatar_component_clause,[],[f260])).
% 0.26/0.38 thf(f264,definition,(
% 0.26/0.38 spl8_24 <=> (((sK3 @ sK6 @ sK5)) = sK7)),
% 0.26/0.38 introduced(definition,[new_symbols(definition,[spl8_24])],[avatar_definition])).
% 0.26/0.38 thf(f266,plain,(
% 0.26/0.38 (((sK3 @ sK6 @ sK5)) = sK7) | ~spl8_24),
% 0.26/0.38 inference(avatar_component_clause,[],[f264])).
% 0.26/0.38 thf(f267,plain,(
% 0.26/0.38 spl8_23 | spl8_24 | spl8_23 | ~spl8_4 | ~spl8_8 | spl8_9 | ~spl8_11 | ~spl8_12 | ~spl8_15),
% 0.26/0.38 inference(avatar_split_clause,[],[f255,f113,f100,f95,f85,f81,f62,f260,f264,f260])).
% 0.26/0.38 thf(f268,plain,(
% 0.26/0.38 ($true != $true) | ($true != ((sK5 @ sK7))) | (~spl8_4 | ~spl8_23)),
% 0.26/0.38 inference(superposition,[],[f261,f64])).
% 0.26/0.38 thf(f275,plain,(
% 0.26/0.38 ($true != ((sK5 @ sK7))) | (~spl8_4 | ~spl8_23)),
% 0.26/0.38 inference(trivial_inequality_removal,[],[f268])).
% 0.26/0.38 thf(f277,plain,(
% 0.26/0.38 $false | (~spl8_4 | ~spl8_11 | ~spl8_23)),
% 0.26/0.38 inference(forward_subsumption_resolution,[],[f275,f97])).
% 0.26/0.38 thf(f278,plain,(
% 0.26/0.38 ~spl8_4 | ~spl8_11 | ~spl8_23),
% 0.26/0.38 inference(avatar_contradiction_clause,[],[f277])).
% 0.26/0.38 thf(f291,plain,(
% 0.26/0.38 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ X1 @ sK6))) | ($true != $true) | (((sK4 @ sK6 @ sK5)) = sK7) | ($true != ((sK5 @ X0))) | (((sK5 @ X1)) != $true) | ($true != ((in @ X0 @ sK6))) | ($true = ((ex1 @ sK6 @ sK5))) | ($true = ((ex1 @ sK6 @ sK5)))) ) | (~spl8_4 | ~spl8_5 | ~spl8_11 | ~spl8_14 | ~spl8_15)),
% 0.26/0.38 inference(superposition,[],[f217,f226])).
% 0.26/0.38 thf(f293,plain,(
% 0.26/0.38 ( ! [X0 : $i,X1 : $i] : (($true != ((sK5 @ X0))) | ($true != $true) | ($true = ((ex1 @ sK6 @ sK5))) | (((sK4 @ sK6 @ sK5)) = sK7) | (((sK5 @ X1)) != $true) | ($true != ((in @ X1 @ sK6))) | ($true != ((in @ X0 @ sK6)))) ) | (~spl8_4 | ~spl8_5 | ~spl8_11 | ~spl8_14 | ~spl8_15)),
% 0.26/0.38 inference(duplicate_literal_removal,[],[f291])).
% 0.26/0.38 thf(f294,plain,(
% 0.26/0.38 ( ! [X0 : $i,X1 : $i] : (($true != ((sK5 @ X0))) | ($true != ((in @ X0 @ sK6))) | ($true = ((ex1 @ sK6 @ sK5))) | (((sK5 @ X1)) != $true) | ($true != ((in @ X1 @ sK6))) | (((sK4 @ sK6 @ sK5)) = sK7)) ) | (~spl8_4 | ~spl8_5 | ~spl8_11 | ~spl8_14 | ~spl8_15)),
% 0.26/0.38 inference(trivial_inequality_removal,[],[f293])).
% 0.26/0.38 thf(f303,plain,(
% 0.26/0.38 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ sK6))) | ($true != ((sK5 @ X0))) | (((sK5 @ X1)) != $true) | (((sK4 @ sK6 @ sK5)) = sK7) | ($true != ((in @ X1 @ sK6)))) ) | (~spl8_4 | ~spl8_5 | spl8_9 | ~spl8_11 | ~spl8_14 | ~spl8_15)),
% 0.26/0.38 inference(forward_subsumption_resolution,[],[f294,f87])).
% 0.26/0.38 thf(f306,definition,(
% 0.26/0.38 spl8_25 <=> (((sK4 @ sK6 @ sK5)) = sK7)),
% 0.26/0.38 introduced(definition,[new_symbols(definition,[spl8_25])],[avatar_definition])).
% 0.26/0.38 thf(f308,plain,(
% 0.26/0.38 (((sK4 @ sK6 @ sK5)) = sK7) | ~spl8_25),
% 0.26/0.38 inference(avatar_component_clause,[],[f306])).
% 0.26/0.38 thf(f309,plain,(
% 0.26/0.38 spl8_25 | spl8_23 | spl8_23 | ~spl8_4 | ~spl8_5 | spl8_9 | ~spl8_11 | ~spl8_14 | ~spl8_15),
% 0.26/0.38 inference(avatar_split_clause,[],[f303,f113,f109,f95,f85,f67,f62,f260,f260,f306])).
% 0.26/0.38 thf(f317,plain,(
% 0.26/0.38 ( ! [X0 : $i] : (($true = ((singleton @ (dsetconstr @ sK6 @ sK5)))) | (((sK3 @ sK6 @ sK5)) != sK7) | ($true != ((in @ X0 @ sK6))) | ($true != ((sK5 @ X0)))) ) | (~spl8_10 | ~spl8_25)),
% 0.26/0.38 inference(superposition,[],[f92,f308])).
% 0.26/0.38 thf(f319,plain,(
% 0.26/0.38 ( ! [X0 : $i] : (($true = ((singleton @ (dsetconstr @ sK6 @ sK5)))) | ($true != ((in @ X0 @ sK6))) | ($true != ((sK5 @ X0)))) ) | (~spl8_10 | ~spl8_24 | ~spl8_25)),
% 0.26/0.38 inference(forward_subsumption_resolution,[],[f317,f266])).
% 0.26/0.38 thf(f321,definition,(
% 0.26/0.38 spl8_27 <=> ($true = ((singleton @ (dsetconstr @ sK6 @ sK5))))),
% 0.26/0.38 introduced(definition,[new_symbols(definition,[spl8_27])],[avatar_definition])).
% 0.26/0.38 thf(f323,plain,(
% 0.26/0.38 ($true = ((singleton @ (dsetconstr @ sK6 @ sK5)))) | ~spl8_27),
% 0.26/0.38 inference(avatar_component_clause,[],[f321])).
% 0.26/0.38 thf(f324,plain,(
% 0.26/0.38 spl8_23 | spl8_27 | ~spl8_10 | ~spl8_24 | ~spl8_25),
% 0.26/0.38 inference(avatar_split_clause,[],[f319,f306,f264,f91,f321,f260])).
% 0.26/0.38 thf(f326,plain,(
% 0.26/0.38 ($true = ((ex1 @ sK6 @ sK5))) | ($false = $true) | (~spl8_15 | ~spl8_27)),
% 0.26/0.38 inference(superposition,[],[f323,f198])).
% 0.26/0.38 thf(f329,plain,(
% 0.26/0.38 ($true = ((ex1 @ sK6 @ sK5))) | (~spl8_15 | ~spl8_27)),
% 0.26/0.38 inference(trivial_inequality_removal,[],[f326])).
% 0.26/0.38 thf(f332,plain,(
% 0.26/0.38 $false | (spl8_9 | ~spl8_15 | ~spl8_27)),
% 0.26/0.38 inference(forward_subsumption_resolution,[],[f329,f87])).
% 0.26/0.38 thf(f333,plain,(
% 0.26/0.38 spl8_9 | ~spl8_15 | ~spl8_27),
% 0.26/0.38 inference(avatar_contradiction_clause,[],[f332])).
% 0.26/0.38 cnf(s3, plain, spl8_4, inference(sat_conversion,[],[f65])).
% 0.26/0.38 cnf(s4, plain, ~spl8_2 | spl8_5, inference(sat_conversion,[],[f69])).
% 0.26/0.38 cnf(s7, plain, ~spl8_2 | spl8_8, inference(sat_conversion,[],[f83])).
% 0.26/0.38 cnf(s8, plain, ~spl8_9, inference(sat_conversion,[],[f88])).
% 0.26/0.38 cnf(s9, plain, spl8_2, inference(sat_conversion,[],[f89])).
% 0.26/0.38 cnf(s10, plain, ~spl8_2 | spl8_10, inference(sat_conversion,[],[f93])).
% 0.26/0.38 cnf(s11, plain, spl8_11, inference(sat_conversion,[],[f98])).
% 0.26/0.38 cnf(s12, plain, ~spl8_2 | spl8_12, inference(sat_conversion,[],[f102])).
% 0.26/0.38 cnf(s14, plain, ~spl8_2 | spl8_14, inference(sat_conversion,[],[f111])).
% 0.26/0.38 cnf(s15, plain, spl8_15, inference(sat_conversion,[],[f116])).
% 0.26/0.38 cnf(s22, plain, spl8_23 | ~spl8_8 | spl8_9 | ~spl8_11 | ~spl8_12 | ~spl8_15 | ~spl8_4 | spl8_23 | spl8_24, inference(sat_conversion,[],[f267])).
% 0.26/0.38 cnf(s23, plain, ~spl8_4 | ~spl8_8 | spl8_9 | ~spl8_11 | ~spl8_12 | ~spl8_15 | spl8_23 | spl8_24, inference(rat,[],[s22])).
% 0.26/0.38 cnf(s24, plain, ~spl8_4 | ~spl8_11 | ~spl8_23, inference(sat_conversion,[],[f278])).
% 0.26/0.38 cnf(s25, plain, spl8_23 | ~spl8_5 | spl8_9 | ~spl8_11 | ~spl8_14 | ~spl8_15 | ~spl8_4 | spl8_23 | spl8_25, inference(sat_conversion,[],[f309])).
% 0.26/0.38 cnf(s26, plain, ~spl8_4 | ~spl8_5 | spl8_9 | ~spl8_11 | ~spl8_14 | ~spl8_15 | spl8_23 | spl8_25, inference(rat,[],[s25])).
% 0.26/0.38 cnf(s29, plain, ~spl8_10 | spl8_23 | ~spl8_24 | ~spl8_25 | spl8_27, inference(sat_conversion,[],[f324])).
% 0.26/0.38 cnf(s31, plain, spl8_9 | ~spl8_15 | ~spl8_27, inference(sat_conversion,[],[f333])).
% 0.26/0.38 cnf(s32, plain, spl8_14, inference(rat,[],[s14,s9])).
% 0.26/0.38 cnf(s33, plain, spl8_12, inference(rat,[],[s12,s9])).
% 0.26/0.38 cnf(s34, plain, spl8_10, inference(rat,[],[s10,s9])).
% 0.26/0.38 cnf(s35, plain, ~spl8_27, inference(rat,[],[s31,s15,s8])).
% 0.26/0.38 cnf(s36, plain, spl8_8, inference(rat,[],[s7,s9])).
% 0.26/0.38 cnf(s37, plain, spl8_5, inference(rat,[],[s4,s9])).
% 0.26/0.38 cnf(s38, plain, ~spl8_23, inference(rat,[],[s24,s11,s3])).
% 0.26/0.38 cnf(s40, plain, spl8_24, inference(rat,[],[s23,s3,s36,s15,s33,s11,s8,s38])).
% 0.26/0.38 cnf(s42, plain, spl8_25, inference(rat,[],[s26,s3,s37,s15,s32,s11,s8,s38])).
% 0.26/0.38 cnf(s43, plain, $false, inference(rat,[],[s29,s35,s38,s34,s42,s40])).
% 0.26/0.38 thf(f334,plain,(
% 0.26/0.38 $false),
% 0.26/0.38 inference(avatar_sat_refutation,[],[s43])).
% 0.26/0.38 % SZS output end Proof for theBenchmark
% 0.26/0.38 % (1100943)------------------------------
% 0.26/0.38 % (1100943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.38 % (1100943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.38 % (1100943)CaDiCaL version: 2.1.3
% 0.26/0.38 % (1100943)Termination reason: Refutation
% 0.26/0.38 % (1100943)Time elapsed: 0.019 s
% 0.26/0.38 % (1100943)Peak memory usage: 13 MB
% 0.26/0.38 % (1100943)Instructions burned: 33 (million)
% 0.26/0.38 % (1100935)Success in time 0.045 s
% 0.26/0.38 % Vampire exiting
%------------------------------------------------------------------------------