%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU682^2 : 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 : n014.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 08:30:45 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU682^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n014.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:09:30 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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
% 0.22/0.30 % (2721092)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (2721118)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1020312085:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.30 % (2721119)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.30 % (2721119)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.30 % (2721112)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3562626441:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (2721114)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3036955890:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (2721113)lrs+10_16_si=on:nwc=1.5:random_seed=487594397:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (2721116)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=596411328:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.30 % (2721115)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=3269529172:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.30 % (2721119)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=784739962:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.30 % (2721114)Instruction limit reached!
% 0.22/0.30 % (2721114)------------------------------
% 0.22/0.30 % (2721114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (2721114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (2721114)CaDiCaL version: 2.1.3
% 0.22/0.30 % (2721114)Termination reason: Instruction limit
% 0.22/0.30 % (2721114)Termination phase: Saturation
% 0.22/0.30 % (2721114)Time elapsed: 0.002 s
% 0.22/0.30 % (2721114)Peak memory usage: 12 MB
% 0.22/0.30 % (2721114)Instructions burned: 3 (million)
% 0.22/0.30 % (2721112) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2721092-2721112"...
% 0.22/0.30 % (2721112)...printing done.
% 0.22/0.30 % (2721112)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% 0.22/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.30 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.22/0.30 thf(func_def_1, type, subset: ($i > $i > $o)).
% 0.22/0.30 thf(func_def_2, type, kpair: ($i > $i > $i)).
% 0.22/0.30 thf(func_def_3, type, cartprod: ($i > $i > $i)).
% 0.22/0.30 thf(func_def_4, type, breln: ($i > $i > $i > $o)).
% 0.22/0.30 thf(func_def_6, type, brelnall1: $o).
% 0.22/0.30 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.30 thf(func_def_10, type, db2: !>[X0: $tType]:(X0)).
% 0.22/0.30 thf(func_def_11, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.30 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.30 thf(func_def_16, type, sK3: ($i > $o)).
% 0.22/0.30 thf(func_def_21, type, sK8: ($i > $o)).
% 0.22/0.30 thf(func_def_23, type, sK10: (($i > $o) > $i > $i > $i > $i)).
% 0.22/0.30 thf(func_def_24, type, sK11: (($i > $o) > $i > $i > $i > $i)).
% 0.22/0.30 thf(func_def_25, type, vNOT: ($o > $o)).
% 0.22/0.30 thf(func_def_26, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.30 thf(f1,axiom,(
% 0.22/0.30 ((^[X0 : $i, X1 : $i, X2 : $i] : ((subset @ X2 @ (cartprod @ X0 @ X1)))) = breln)),
% 0.22/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln)).
% 0.22/0.30 thf(f2,axiom,(
% 0.22/0.30 (brelnall1 = ! [X1 : $i,X0 : $i,X2 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (X3 @ (kpair @ X4 @ X5))))) => ! [X4 : $i] : ((in @ X4 @ X2) => (X3 @ X4)))))),
% 0.22/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall1)).
% 0.22/0.30 thf(f3,conjecture,(
% 0.22/0.30 brelnall1 => ! [X2 : $i,X0 : $i,X1 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (X3 @ (kpair @ X4 @ X5))))) => ! [X4 : $i] : ((in @ X4 @ X2) => (X3 @ X4))))),
% 0.22/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall2)).
% 0.22/0.30 thf(f4,negated_conjecture,(
% 0.22/0.30 ~(brelnall1 => ! [X2 : $i,X0 : $i,X1 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (X3 @ (kpair @ X4 @ X5))))) => ! [X4 : $i] : ((in @ X4 @ X2) => (X3 @ X4)))))),
% 0.22/0.30 inference(negated_conjecture,[status(cth)],[f3])).
% 0.22/0.30 thf(f5,plain,(
% 0.22/0.30 ~(brelnall1 => ! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X1 @ X2 @ X0) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((in @ X4 @ X1) => ! [X5 : $i] : ((in @ X5 @ X2) => ((in @ (kpair @ X4 @ X5) @ X0) => (X3 @ (kpair @ X4 @ X5))))) => ! [X6 : $i] : ((in @ X6 @ X0) => (X3 @ X6)))))),
% 0.22/0.30 inference(rectify,[],[f4])).
% 0.22/0.30 thf(f6,plain,(
% 0.22/0.30 ~((brelnall1 = $true) => ! [X1 : $i,X2 : $i,X0 : $i] : ((((breln @ X1 @ X2 @ X0)) = $true) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((((in @ X4 @ X1)) = $true) => ! [X5 : $i] : ((((in @ X5 @ X2)) = $true) => ((((in @ (kpair @ X4 @ X5) @ X0)) = $true) => (((X3 @ (kpair @ X4 @ X5))) = $true)))) => ! [X6 : $i] : ((((in @ X6 @ X0)) = $true) => (((X3 @ X6)) = $true)))))),
% 0.22/0.30 inference(fool_elimination,[],[f5])).
% 0.22/0.30 thf(f7,plain,(
% 0.22/0.30 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.22/0.30 inference(fool_elimination,[],[f1])).
% 0.22/0.30 thf(f8,plain,(
% 0.22/0.30 (brelnall1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X1 @ X0 @ X2) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((in @ X4 @ X1) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ (kpair @ X4 @ X5) @ X2) => (X3 @ (kpair @ X4 @ X5))))) => ! [X6 : $i] : ((in @ X6 @ X2) => (X3 @ X6)))))),
% 0.22/0.30 inference(rectify,[],[f2])).
% 0.22/0.30 thf(f9,plain,(
% 0.22/0.30 ! [X0 : $i,X1 : $i,X2 : $i] : ((((breln @ X1 @ X0 @ X2)) = $true) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((((in @ X4 @ X1)) = $true) => ! [X5 : $i] : ((((in @ X5 @ X0)) = $true) => ((((in @ (kpair @ X4 @ X5) @ X2)) = $true) => (((X3 @ (kpair @ X4 @ X5))) = $true)))) => ! [X6 : $i] : ((((in @ X6 @ X2)) = $true) => (((X3 @ X6)) = $true)))) <=> (brelnall1 = $true)),
% 0.22/0.30 inference(fool_elimination,[],[f8])).
% 0.22/0.30 thf(f10,plain,(
% 0.22/0.30 ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : ($i > $o)] : (! [X6 : $i] : ((((in @ X6 @ X2)) != $true) | (((X3 @ X6)) = $true)) | ? [X4 : $i] : (? [X5 : $i] : (((((X3 @ (kpair @ X4 @ X5))) != $true) & (((in @ (kpair @ X4 @ X5) @ X2)) = $true)) & (((in @ X5 @ X0)) = $true)) & (((in @ X4 @ X1)) = $true))) | (((breln @ X1 @ X0 @ X2)) != $true)) <=> (brelnall1 = $true)),
% 0.22/0.30 inference(ennf_transformation,[],[f9])).
% 0.22/0.30 thf(f11,plain,(
% 0.22/0.30 (brelnall1 = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : ((((breln @ X1 @ X0 @ X2)) != $true) | ! [X3 : ($i > $o)] : (! [X6 : $i] : ((((in @ X6 @ X2)) != $true) | (((X3 @ X6)) = $true)) | ? [X4 : $i] : ((((in @ X4 @ X1)) = $true) & ? [X5 : $i] : ((((in @ X5 @ X0)) = $true) & (((X3 @ (kpair @ X4 @ X5))) != $true) & (((in @ (kpair @ X4 @ X5) @ X2)) = $true)))))),
% 0.22/0.30 inference(flattening,[],[f10])).
% 0.22/0.30 thf(f12,plain,(
% 0.22/0.30 ? [X1 : $i,X2 : $i,X0 : $i] : (? [X3 : ($i > $o)] : (? [X6 : $i] : ((((X3 @ X6)) != $true) & (((in @ X6 @ X0)) = $true)) & ! [X4 : $i] : (! [X5 : $i] : (((((X3 @ (kpair @ X4 @ X5))) = $true) | (((in @ (kpair @ X4 @ X5) @ X0)) != $true)) | (((in @ X5 @ X2)) != $true)) | (((in @ X4 @ X1)) != $true))) & (((breln @ X1 @ X2 @ X0)) = $true)) & (brelnall1 = $true)),
% 0.22/0.30 inference(ennf_transformation,[],[f6])).
% 0.22/0.30 thf(f13,plain,(
% 0.22/0.30 ? [X1 : $i,X2 : $i,X0 : $i] : (? [X3 : ($i > $o)] : (? [X6 : $i] : ((((X3 @ X6)) != $true) & (((in @ X6 @ X0)) = $true)) & ! [X4 : $i] : (! [X5 : $i] : ((((X3 @ (kpair @ X4 @ X5))) = $true) | (((in @ X5 @ X2)) != $true) | (((in @ (kpair @ X4 @ X5) @ X0)) != $true)) | (((in @ X4 @ X1)) != $true))) & (((breln @ X1 @ X2 @ X0)) = $true)) & (brelnall1 = $true)),
% 0.22/0.30 inference(flattening,[],[f12])).
% 0.22/0.30 thf(f14,plain,(
% 0.22/0.30 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : ($i > $o)] : (? [X4 : $i] : ((((X3 @ X4)) != $true) & (((in @ X4 @ X2)) = $true)) & ! [X5 : $i] : (! [X6 : $i] : (($true = ((X3 @ (kpair @ X5 @ X6)))) | (((in @ X6 @ X1)) != $true) | (((in @ (kpair @ X5 @ X6) @ X2)) != $true)) | (((in @ X5 @ X0)) != $true))) & (((breln @ X0 @ X1 @ X2)) = $true)) & (brelnall1 = $true)),
% 0.22/0.30 inference(rectify,[],[f13])).
% 0.22/0.30 thf(f15,plain,(
% 0.22/0.30 ((((((sK3 @ sK4)) != $true) & (((in @ sK4 @ sK2)) = $true)) & ! [X5 : $i] : (! [X6 : $i] : ((((sK3 @ (kpair @ X5 @ X6))) = $true) | (((in @ X6 @ sK1)) != $true) | ($true != ((in @ (kpair @ X5 @ X6) @ sK2)))) | (((in @ X5 @ sK0)) != $true))) & (((breln @ sK0 @ sK1 @ sK2)) = $true)) & (brelnall1 = $true)),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f14])).
% 0.22/0.30 thf(f16,plain,(
% 0.22/0.30 ((brelnall1 = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : ((((breln @ X1 @ X0 @ X2)) = $true) & ? [X3 : ($i > $o)] : (? [X6 : $i] : ((((in @ X6 @ X2)) = $true) & (((X3 @ X6)) != $true)) & ! [X4 : $i] : ((((in @ X4 @ X1)) != $true) | ! [X5 : $i] : ((((in @ X5 @ X0)) != $true) | (((X3 @ (kpair @ X4 @ X5))) = $true) | (((in @ (kpair @ X4 @ X5) @ X2)) != $true)))))) & (! [X1 : $i,X2 : $i,X0 : $i] : ((((breln @ X1 @ X0 @ X2)) != $true) | ! [X3 : ($i > $o)] : (! [X6 : $i] : ((((in @ X6 @ X2)) != $true) | (((X3 @ X6)) = $true)) | ? [X4 : $i] : ((((in @ X4 @ X1)) = $true) & ? [X5 : $i] : ((((in @ X5 @ X0)) = $true) & (((X3 @ (kpair @ X4 @ X5))) != $true) & (((in @ (kpair @ X4 @ X5) @ X2)) = $true))))) | (brelnall1 != $true))),
% 0.22/0.30 inference(nnf_transformation,[],[f11])).
% 0.22/0.30 thf(f17,plain,(
% 0.22/0.30 ((brelnall1 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((breln @ X0 @ X2 @ X1)) = $true) & ? [X3 : ($i > $o)] : (? [X4 : $i] : ((((in @ X4 @ X1)) = $true) & (((X3 @ X4)) != $true)) & ! [X5 : $i] : ((((in @ X5 @ X0)) != $true) | ! [X6 : $i] : ((((in @ X6 @ X2)) != $true) | ($true = ((X3 @ (kpair @ X5 @ X6)))) | (((in @ (kpair @ X5 @ X6) @ X1)) != $true)))))) & (! [X7 : $i,X8 : $i,X9 : $i] : ((((breln @ X7 @ X9 @ X8)) != $true) | ! [X10 : ($i > $o)] : (! [X11 : $i] : ((((in @ X11 @ X8)) != $true) | (((X10 @ X11)) = $true)) | ? [X12 : $i] : (($true = ((in @ X12 @ X7))) & ? [X13 : $i] : ((((in @ X13 @ X9)) = $true) & (((X10 @ (kpair @ X12 @ X13))) != $true) & (((in @ (kpair @ X12 @ X13) @ X8)) = $true))))) | (brelnall1 != $true))),
% 0.22/0.30 inference(rectify,[],[f16])).
% 0.22/0.30 thf(f18,plain,(
% 0.22/0.30 ((brelnall1 = $true) | ((((breln @ sK5 @ sK7 @ sK6)) = $true) & (((((in @ sK9 @ sK6)) = $true) & (((sK8 @ sK9)) != $true)) & ! [X5 : $i] : ((((in @ X5 @ sK5)) != $true) | ! [X6 : $i] : ((((in @ X6 @ sK7)) != $true) | (((sK8 @ (kpair @ X5 @ X6))) = $true) | (((in @ (kpair @ X5 @ X6) @ sK6)) != $true)))))) & (! [X7 : $i,X8 : $i,X9 : $i] : ((((breln @ X7 @ X9 @ X8)) != $true) | ! [X10 : ($i > $o)] : (! [X11 : $i] : ((((in @ X11 @ X8)) != $true) | (((X10 @ X11)) = $true)) | ((((in @ (sK10 @ X10 @ X9 @ X8 @ X7) @ X7)) = $true) & ((((in @ (sK11 @ X10 @ X9 @ X8 @ X7) @ X9)) = $true) & (((X10 @ (kpair @ (sK10 @ X10 @ X9 @ X8 @ X7) @ (sK11 @ X10 @ X9 @ X8 @ X7)))) != $true) & (((in @ (kpair @ (sK10 @ X10 @ X9 @ X8 @ X7) @ (sK11 @ X10 @ X9 @ X8 @ X7)) @ X8)) = $true))))) | (brelnall1 != $true))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9,vAPP,vAPP]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7),skolemize(X3,sK8),skolemize(X4,sK9),skolemize(X13,sK11 @ X10 @ X9 @ X8 @ X7),skolemize(X13,sK11 @ X10 @ X9 @ X8 @ X7)],[f17])).
% 0.22/0.30 thf(f19,plain,(
% 0.22/0.30 (brelnall1 = $true)),
% 0.22/0.30 inference(cnf_transformation,[],[f15])).
% 0.22/0.30 thf(f20,plain,(
% 0.22/0.30 (((breln @ sK0 @ sK1 @ sK2)) = $true)),
% 0.22/0.30 inference(cnf_transformation,[],[f15])).
% 0.22/0.30 thf(f21,plain,(
% 0.22/0.30 ( ! [X6 : $i,X5 : $i] : (($true != ((in @ (kpair @ X5 @ X6) @ sK2))) | (((in @ X5 @ sK0)) != $true) | (((sK3 @ (kpair @ X5 @ X6))) = $true) | (((in @ X6 @ sK1)) != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f15])).
% 0.22/0.30 thf(f22,plain,(
% 0.22/0.30 (((in @ sK4 @ sK2)) = $true)),
% 0.22/0.30 inference(cnf_transformation,[],[f15])).
% 0.22/0.30 thf(f23,plain,(
% 0.22/0.30 (((sK3 @ sK4)) != $true)),
% 0.22/0.30 inference(cnf_transformation,[],[f15])).
% 0.22/0.30 thf(f24,plain,(
% 0.22/0.30 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.22/0.30 inference(cnf_transformation,[],[f7])).
% 0.22/0.30 thf(f25,plain,(
% 0.22/0.30 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : ((((breln @ X7 @ X9 @ X8)) != $true) | (((in @ X11 @ X8)) != $true) | (((X10 @ X11)) = $true) | (((in @ (kpair @ (sK10 @ X10 @ X9 @ X8 @ X7) @ (sK11 @ X10 @ X9 @ X8 @ X7)) @ X8)) = $true) | (brelnall1 != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f18])).
% 0.22/0.30 thf(f26,plain,(
% 0.22/0.30 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : ((((breln @ X7 @ X9 @ X8)) != $true) | (((in @ X11 @ X8)) != $true) | (((X10 @ X11)) = $true) | (((X10 @ (kpair @ (sK10 @ X10 @ X9 @ X8 @ X7) @ (sK11 @ X10 @ X9 @ X8 @ X7)))) != $true) | (brelnall1 != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f18])).
% 0.22/0.30 thf(f27,plain,(
% 0.22/0.30 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : ((((breln @ X7 @ X9 @ X8)) != $true) | (((in @ X11 @ X8)) != $true) | (((X10 @ X11)) = $true) | (((in @ (sK11 @ X10 @ X9 @ X8 @ X7) @ X9)) = $true) | (brelnall1 != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f18])).
% 0.22/0.30 thf(f28,plain,(
% 0.22/0.30 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : ((((breln @ X7 @ X9 @ X8)) != $true) | (((in @ X11 @ X8)) != $true) | (((X10 @ X11)) = $true) | (((in @ (sK10 @ X10 @ X9 @ X8 @ X7) @ X7)) = $true) | (brelnall1 != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f18])).
% 0.22/0.30 thf(f35,plain,(
% 0.22/0.30 ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ sK0 @ sK1 @ sK2)) = $true)),
% 0.22/0.30 inference(definition_unfolding,[],[f20,f24])).
% 0.22/0.30 thf(f40,plain,(
% 0.22/0.30 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : ((((in @ (sK10 @ X10 @ X9 @ X8 @ X7) @ X7)) = $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X7 @ X9 @ X8)) != $true) | ($true != $true) | (((X10 @ X11)) = $true) | (((in @ X11 @ X8)) != $true)) )),
% 0.22/0.30 inference(definition_unfolding,[],[f28,f24,f19])).
% 0.22/0.30 thf(f41,plain,(
% 0.22/0.30 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : ((((X10 @ X11)) = $true) | ($true != $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X7 @ X9 @ X8)) != $true) | (((in @ (sK11 @ X10 @ X9 @ X8 @ X7) @ X9)) = $true) | (((in @ X11 @ X8)) != $true)) )),
% 0.22/0.30 inference(definition_unfolding,[],[f27,f24,f19])).
% 0.22/0.30 thf(f42,plain,(
% 0.22/0.30 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : (((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X7 @ X9 @ X8)) != $true) | (((in @ X11 @ X8)) != $true) | ($true != $true) | (((X10 @ X11)) = $true) | (((X10 @ (kpair @ (sK10 @ X10 @ X9 @ X8 @ X7) @ (sK11 @ X10 @ X9 @ X8 @ X7)))) != $true)) )),
% 0.22/0.30 inference(definition_unfolding,[],[f26,f24,f19])).
% 0.22/0.30 thf(f43,plain,(
% 0.22/0.30 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : ((((X10 @ X11)) = $true) | (((in @ (kpair @ (sK10 @ X10 @ X9 @ X8 @ X7) @ (sK11 @ X10 @ X9 @ X8 @ X7)) @ X8)) = $true) | (((in @ X11 @ X8)) != $true) | ($true != $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X7 @ X9 @ X8)) != $true)) )),
% 0.22/0.30 inference(definition_unfolding,[],[f25,f24,f19])).
% 0.22/0.30 thf(f44,plain,(
% 0.22/0.30 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : ((((X10 @ (kpair @ (sK10 @ X10 @ X9 @ X8 @ X7) @ (sK11 @ X10 @ X9 @ X8 @ X7)))) != $true) | (((in @ X11 @ X8)) != $true) | (((X10 @ X11)) = $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X7 @ X9 @ X8)) != $true)) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f42])).
% 0.22/0.30 thf(f45,plain,(
% 0.22/0.30 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : ((((X10 @ (kpair @ (sK10 @ X10 @ X9 @ X8 @ X7) @ (sK11 @ X10 @ X9 @ X8 @ X7)))) != $true) | (((X10 @ X11)) = $true) | (((in @ X11 @ X8)) != $true) | (((subset @ X8 @ (cartprod @ X7 @ X9))) != $true)) )),
% 0.22/0.30 inference(beta-eta_normalization,[],[f44])).
% 0.22/0.30 thf(f46,plain,(
% 0.22/0.30 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : ((((X10 @ X11)) = $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X7 @ X9 @ X8)) != $true) | (((in @ X11 @ X8)) != $true) | (((in @ (kpair @ (sK10 @ X10 @ X9 @ X8 @ X7) @ (sK11 @ X10 @ X9 @ X8 @ X7)) @ X8)) = $true)) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f43])).
% 0.22/0.30 thf(f47,plain,(
% 0.22/0.30 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : ((((subset @ X8 @ (cartprod @ X7 @ X9))) != $true) | (((in @ (kpair @ (sK10 @ X10 @ X9 @ X8 @ X7) @ (sK11 @ X10 @ X9 @ X8 @ X7)) @ X8)) = $true) | (((in @ X11 @ X8)) != $true) | (((X10 @ X11)) = $true)) )),
% 0.22/0.30 inference(beta-eta_normalization,[],[f46])).
% 0.22/0.30 thf(f48,plain,(
% 0.22/0.30 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : ((((X10 @ X11)) = $true) | (((in @ (sK11 @ X10 @ X9 @ X8 @ X7) @ X9)) = $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X7 @ X9 @ X8)) != $true) | (((in @ X11 @ X8)) != $true)) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f41])).
% 0.22/0.30 thf(f49,plain,(
% 0.22/0.30 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : ((((subset @ X8 @ (cartprod @ X7 @ X9))) != $true) | (((X10 @ X11)) = $true) | (((in @ (sK11 @ X10 @ X9 @ X8 @ X7) @ X9)) = $true) | (((in @ X11 @ X8)) != $true)) )),
% 0.22/0.30 inference(beta-eta_normalization,[],[f48])).
% 0.22/0.30 thf(f50,plain,(
% 0.22/0.30 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : ((((in @ (sK10 @ X10 @ X9 @ X8 @ X7) @ X7)) = $true) | (((X10 @ X11)) = $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X7 @ X9 @ X8)) != $true) | (((in @ X11 @ X8)) != $true)) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f40])).
% 0.22/0.30 thf(f51,plain,(
% 0.22/0.30 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : ((((subset @ X8 @ (cartprod @ X7 @ X9))) != $true) | (((X10 @ X11)) = $true) | (((in @ X11 @ X8)) != $true) | (((in @ (sK10 @ X10 @ X9 @ X8 @ X7) @ X7)) = $true)) )),
% 0.22/0.30 inference(beta-eta_normalization,[],[f50])).
% 0.22/0.30 thf(f52,plain,(
% 0.22/0.30 (((subset @ sK2 @ (cartprod @ sK0 @ sK1))) = $true)),
% 0.22/0.30 inference(beta-eta_normalization,[],[f35])).
% 0.22/0.30 thf(f53,plain,(
% 0.22/0.30 ( ! [X0 : ($i > $o),X1 : $i] : ((((in @ X1 @ sK2)) != $true) | (((in @ (sK11 @ X0 @ sK1 @ sK2 @ sK0) @ sK1)) = $true) | ($true != $true) | (((X0 @ X1)) = $true)) )),
% 0.22/0.30 inference(constrained_superposition,[],[f49,f52])).
% 0.22/0.30 thf(f54,plain,(
% 0.22/0.30 ( ! [X0 : ($i > $o),X1 : $i] : ((((in @ X1 @ sK2)) != $true) | (((in @ (sK11 @ X0 @ sK1 @ sK2 @ sK0) @ sK1)) = $true) | (((X0 @ X1)) = $true)) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f53])).
% 0.22/0.30 thf(f55,plain,(
% 0.22/0.30 ( ! [X0 : ($i > $o)] : (($true != $true) | (((in @ (sK11 @ X0 @ sK1 @ sK2 @ sK0) @ sK1)) = $true) | (((X0 @ sK4)) = $true)) )),
% 0.22/0.30 inference(constrained_superposition,[],[f54,f22])).
% 0.22/0.30 thf(f56,plain,(
% 0.22/0.30 ( ! [X0 : ($i > $o)] : ((((in @ (sK11 @ X0 @ sK1 @ sK2 @ sK0) @ sK1)) = $true) | (((X0 @ sK4)) = $true)) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f55])).
% 0.22/0.30 thf(f57,plain,(
% 0.22/0.30 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ X1)) = $true) | (((in @ (sK10 @ X0 @ sK1 @ sK2 @ sK0) @ sK0)) = $true) | (((in @ X1 @ sK2)) != $true) | ($true != $true)) )),
% 0.22/0.30 inference(constrained_superposition,[],[f51,f52])).
% 0.22/0.30 thf(f58,plain,(
% 0.22/0.30 ( ! [X0 : ($i > $o),X1 : $i] : ((((in @ X1 @ sK2)) != $true) | (((in @ (sK10 @ X0 @ sK1 @ sK2 @ sK0) @ sK0)) = $true) | (((X0 @ X1)) = $true)) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f57])).
% 0.22/0.30 thf(f59,plain,(
% 0.22/0.30 ( ! [X0 : ($i > $o)] : ((((in @ (sK10 @ X0 @ sK1 @ sK2 @ sK0) @ sK0)) = $true) | ($true != $true) | (((X0 @ sK4)) = $true)) )),
% 0.22/0.31 inference(constrained_superposition,[],[f58,f22])).
% 0.22/0.31 thf(f60,plain,(
% 0.22/0.31 ( ! [X0 : ($i > $o)] : ((((in @ (sK10 @ X0 @ sK1 @ sK2 @ sK0) @ sK0)) = $true) | (((X0 @ sK4)) = $true)) )),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f59])).
% 0.22/0.31 thf(f72,plain,(
% 0.22/0.31 ( ! [X0 : ($i > $o),X1 : $i] : (($true != $true) | (((X0 @ X1)) = $true) | (((in @ (kpair @ (sK10 @ X0 @ sK1 @ sK2 @ sK0) @ (sK11 @ X0 @ sK1 @ sK2 @ sK0)) @ sK2)) = $true) | (((in @ X1 @ sK2)) != $true)) )),
% 0.22/0.31 inference(constrained_superposition,[],[f47,f52])).
% 0.22/0.31 thf(f73,plain,(
% 0.22/0.31 ( ! [X0 : ($i > $o),X1 : $i] : ((((in @ X1 @ sK2)) != $true) | (((X0 @ X1)) = $true) | (((in @ (kpair @ (sK10 @ X0 @ sK1 @ sK2 @ sK0) @ (sK11 @ X0 @ sK1 @ sK2 @ sK0)) @ sK2)) = $true)) )),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f72])).
% 0.22/0.31 thf(f74,plain,(
% 0.22/0.31 ( ! [X0 : ($i > $o)] : (($true != $true) | (((X0 @ sK4)) = $true) | (((in @ (kpair @ (sK10 @ X0 @ sK1 @ sK2 @ sK0) @ (sK11 @ X0 @ sK1 @ sK2 @ sK0)) @ sK2)) = $true)) )),
% 0.22/0.31 inference(constrained_superposition,[],[f73,f22])).
% 0.22/0.31 thf(f75,plain,(
% 0.22/0.31 ( ! [X0 : ($i > $o)] : ((((in @ (kpair @ (sK10 @ X0 @ sK1 @ sK2 @ sK0) @ (sK11 @ X0 @ sK1 @ sK2 @ sK0)) @ sK2)) = $true) | (((X0 @ sK4)) = $true)) )),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f74])).
% 0.22/0.31 thf(f76,plain,(
% 0.22/0.31 ( ! [X0 : ($i > $o)] : ((((sK3 @ (kpair @ (sK10 @ X0 @ sK1 @ sK2 @ sK0) @ (sK11 @ X0 @ sK1 @ sK2 @ sK0)))) = $true) | (((in @ (sK10 @ X0 @ sK1 @ sK2 @ sK0) @ sK0)) != $true) | ($true != $true) | (((in @ (sK11 @ X0 @ sK1 @ sK2 @ sK0) @ sK1)) != $true) | (((X0 @ sK4)) = $true)) )),
% 0.22/0.31 inference(constrained_superposition,[],[f21,f75])).
% 0.22/0.31 thf(f82,plain,(
% 0.22/0.31 ( ! [X0 : ($i > $o)] : ((((sK3 @ (kpair @ (sK10 @ X0 @ sK1 @ sK2 @ sK0) @ (sK11 @ X0 @ sK1 @ sK2 @ sK0)))) = $true) | (((in @ (sK10 @ X0 @ sK1 @ sK2 @ sK0) @ sK0)) != $true) | (((X0 @ sK4)) = $true) | (((in @ (sK11 @ X0 @ sK1 @ sK2 @ sK0) @ sK1)) != $true)) )),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f76])).
% 0.22/0.31 thf(f84,plain,(
% 0.22/0.31 ( ! [X0 : ($i > $o)] : ((((in @ (sK11 @ X0 @ sK1 @ sK2 @ sK0) @ sK1)) != $true) | (((sK3 @ (kpair @ (sK10 @ X0 @ sK1 @ sK2 @ sK0) @ (sK11 @ X0 @ sK1 @ sK2 @ sK0)))) = $true) | (((X0 @ sK4)) = $true)) )),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f82,f60])).
% 0.22/0.31 thf(f85,plain,(
% 0.22/0.31 ( ! [X0 : ($i > $o)] : ((((sK3 @ (kpair @ (sK10 @ X0 @ sK1 @ sK2 @ sK0) @ (sK11 @ X0 @ sK1 @ sK2 @ sK0)))) = $true) | (((X0 @ sK4)) = $true)) )),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f84,f56])).
% 0.22/0.31 thf(f86,plain,(
% 0.22/0.31 ( ! [X0 : $i] : ((((sK3 @ X0)) = $true) | ($true != $true) | (((in @ X0 @ sK2)) != $true) | (((subset @ sK2 @ (cartprod @ sK0 @ sK1))) != $true) | (((sK3 @ sK4)) = $true)) )),
% 0.22/0.31 inference(constrained_superposition,[],[f45,f85])).
% 0.22/0.31 thf(f87,plain,(
% 0.22/0.31 ( ! [X0 : $i] : ((((sK3 @ sK4)) = $true) | (((sK3 @ X0)) = $true) | (((in @ X0 @ sK2)) != $true) | (((subset @ sK2 @ (cartprod @ sK0 @ sK1))) != $true)) )),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f86])).
% 0.22/0.31 thf(f88,plain,(
% 0.22/0.31 ( ! [X0 : $i] : ((((sK3 @ X0)) = $true) | (((in @ X0 @ sK2)) != $true) | (((subset @ sK2 @ (cartprod @ sK0 @ sK1))) != $true)) )),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f87,f23])).
% 0.22/0.31 thf(f89,plain,(
% 0.22/0.31 ( ! [X0 : $i] : ((((in @ X0 @ sK2)) != $true) | (((sK3 @ X0)) = $true)) )),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f88,f52])).
% 0.22/0.31 thf(f90,plain,(
% 0.22/0.31 (((sK3 @ sK4)) = $true) | ($true != $true)),
% 0.22/0.31 inference(constrained_superposition,[],[f89,f22])).
% 0.22/0.31 thf(f93,plain,(
% 0.22/0.31 (((sK3 @ sK4)) = $true)),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f90])).
% 0.22/0.31 thf(f94,plain,(
% 0.22/0.31 $false),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f93,f23])).
% 0.22/0.31 % SZS output end Proof for theBenchmark
% 0.22/0.31 % (2721112)------------------------------
% 0.22/0.31 % (2721112)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (2721112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (2721112)CaDiCaL version: 2.1.3
% 0.22/0.31 % (2721112)Termination reason: Refutation
% 0.22/0.31 % (2721112)Time elapsed: 0.009 s
% 0.22/0.31 % (2721112)Peak memory usage: 12 MB
% 0.22/0.31 % (2721112)Instructions burned: 15 (million)
% 0.22/0.31 % (2721092)Success in time 0.048 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------