%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU768^2 : 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 : n007.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 08:31:14 AM UTC 2026
% Result : Theorem 0.24s 0.33s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU768^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 % Computer : n007.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 14:21:41 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 Running higher-order theorem proving
% 0.11/0.27 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
% 0.24/0.33 % (3436680)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.33 % (3436688)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2596140975:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.33 % (3436688)Instruction limit reached!
% 0.24/0.33 % (3436688)------------------------------
% 0.24/0.33 % (3436688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.33 % (3436688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.33 % (3436688)CaDiCaL version: 2.1.3
% 0.24/0.33 % (3436688)Termination reason: Instruction limit
% 0.24/0.33 % (3436688)Termination phase: Saturation
% 0.24/0.33 % (3436688)Time elapsed: 0.002 s
% 0.24/0.33 % (3436688)Peak memory usage: 12 MB
% 0.24/0.33 % (3436688)Instructions burned: 3 (million)
% 0.24/0.33 % (3436687)lrs+10_16_si=on:nwc=1.5:random_seed=765282950:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.33 % (3436692)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.33 % (3436692)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
% 0.24/0.33 % (3436686)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1580044980:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.33 % (3436690)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2902504420:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.24/0.33 % (3436691)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3345260307:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.33 % (3436689)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=1997816827: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)
% 0.24/0.33 % (3436692)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=658527654:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.24/0.33 % (3436687)Instruction limit reached!
% 0.24/0.33 % (3436687)------------------------------
% 0.24/0.33 % (3436687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.33 % (3436687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.33 % (3436687)CaDiCaL version: 2.1.3
% 0.24/0.33 % (3436687)Termination reason: Instruction limit
% 0.24/0.33 % (3436687)Termination phase: Saturation
% 0.24/0.33 % (3436687)Time elapsed: 0.012 s
% 0.24/0.33 % (3436687)Peak memory usage: 12 MB
% 0.24/0.33 % (3436687)Instructions burned: 19 (million)
% 0.24/0.33 % (3436695)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2519870197:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.24/0.33 % (3436695)Instruction limit reached!
% 0.24/0.33 % (3436695)------------------------------
% 0.24/0.33 % (3436695)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.33 % (3436695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.33 % (3436695)CaDiCaL version: 2.1.3
% 0.24/0.33 % (3436695)Termination reason: Instruction limit
% 0.24/0.33 % (3436695)Termination phase: Saturation
% 0.24/0.33 % (3436695)Time elapsed: 0.001 s
% 0.24/0.33 % (3436695)Peak memory usage: 12 MB
% 0.24/0.33 % (3436695)Instructions burned: 2 (million)
% 0.24/0.33 % (3436686) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3436680-3436686"...
% 0.24/0.33 % (3436686)...printing done.
% 0.24/0.33 % (3436686)Refutation found. Thanks to Tanya!
% 0.24/0.33 % SZS status Theorem for theBenchmark
% 0.24/0.33 % SZS output start Proof for theBenchmark
% 0.24/0.33 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.24/0.33 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.24/0.33 thf(func_def_1, type, subset: ($i > $i > $o)).
% 0.24/0.33 thf(func_def_2, type, kpair: ($i > $i > $i)).
% 0.24/0.33 thf(func_def_3, type, cartprod: ($i > $i > $i)).
% 0.24/0.33 thf(func_def_4, type, breln: ($i > $i > $i > $o)).
% 0.24/0.33 thf(func_def_6, type, brelnall2: $o).
% 0.24/0.33 thf(func_def_7, type, breln1: ($i > $i > $o)).
% 0.24/0.33 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.24/0.33 thf(func_def_11, type, db2: !>[X0: $tType]:(X0)).
% 0.24/0.33 thf(func_def_12, type, db1: !>[X0: $tType]:(X0)).
% 0.24/0.33 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.24/0.33 thf(func_def_16, type, sK2: ($i > $o)).
% 0.24/0.33 thf(func_def_21, type, sK7: ($i > $o)).
% 0.24/0.33 thf(func_def_23, type, sK9: (($i > $o) > $i > $i > $i > $i)).
% 0.24/0.33 thf(func_def_24, type, sK10: (($i > $o) > $i > $i > $i > $i)).
% 0.24/0.33 thf(func_def_25, type, vNOT: ($o > $o)).
% 0.24/0.33 thf(func_def_26, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.24/0.33 thf(f1,axiom,(
% 0.24/0.33 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : ((subset @ X2 @ (cartprod @ X0 @ X1)))))),
% 0.24/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln)).
% 0.24/0.33 thf(f2,axiom,(
% 0.24/0.33 (! [X0 : $i,X2 : $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)))) = brelnall2)),
% 0.24/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall2)).
% 0.24/0.33 thf(f3,axiom,(
% 0.24/0.33 (breln1 = (^[X0 : $i, X1 : $i] : ((breln @ X0 @ X0 @ X1))))),
% 0.24/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1)).
% 0.24/0.33 thf(f4,conjecture,(
% 0.24/0.33 brelnall2 => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : ($i > $o)] : (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (X2 @ (kpair @ X3 @ X4))))) => ! [X3 : $i] : ((in @ X3 @ X1) => (X2 @ X3))))),
% 0.24/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1all2)).
% 0.24/0.33 thf(f5,negated_conjecture,(
% 0.24/0.33 ~(brelnall2 => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : ($i > $o)] : (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (X2 @ (kpair @ X3 @ X4))))) => ! [X3 : $i] : ((in @ X3 @ X1) => (X2 @ X3)))))),
% 0.24/0.33 inference(negated_conjecture,[status(cth)],[f4])).
% 0.24/0.33 thf(f6,plain,(
% 0.24/0.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X0 @ X2 @ X1) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X2) => ((in @ (kpair @ X4 @ X5) @ X1) => (X3 @ (kpair @ X4 @ X5))))) => ! [X6 : $i] : ((in @ X6 @ X1) => (X3 @ X6)))) = brelnall2)),
% 0.24/0.33 inference(rectify,[],[f2])).
% 0.24/0.33 thf(f7,plain,(
% 0.24/0.33 ! [X2 : $i,X1 : $i,X0 : $i] : ((((breln @ X0 @ X2 @ X1)) = $true) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((((in @ X4 @ X0)) = $true) => ! [X5 : $i] : ((((in @ X5 @ X2)) = $true) => ((((in @ (kpair @ X4 @ X5) @ X1)) = $true) => (((X3 @ (kpair @ X4 @ X5))) = $true)))) => ! [X6 : $i] : ((((in @ X6 @ X1)) = $true) => ($true = ((X3 @ X6)))))) <=> (brelnall2 = $true)),
% 0.24/0.33 inference(fool_elimination,[],[f6])).
% 0.24/0.33 thf(f8,plain,(
% 0.24/0.33 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.24/0.33 inference(fool_elimination,[],[f1])).
% 0.24/0.33 thf(f9,plain,(
% 0.24/0.33 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 0.24/0.33 inference(fool_elimination,[],[f3])).
% 0.24/0.33 thf(f10,plain,(
% 0.24/0.33 ~(brelnall2 => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : ($i > $o)] : (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (X2 @ (kpair @ X3 @ X4))))) => ! [X5 : $i] : ((in @ X5 @ X1) => (X2 @ X5)))))),
% 0.24/0.33 inference(rectify,[],[f5])).
% 0.24/0.33 thf(f11,plain,(
% 0.24/0.33 ~((brelnall2 = $true) => ! [X0 : $i,X1 : $i] : ((((breln1 @ X0 @ X1)) = $true) => ! [X2 : ($i > $o)] : (! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => ! [X4 : $i] : ((((in @ X4 @ X0)) = $true) => ((((in @ (kpair @ X3 @ X4) @ X1)) = $true) => (((X2 @ (kpair @ X3 @ X4))) = $true)))) => ! [X5 : $i] : ((((in @ X5 @ X1)) = $true) => ($true = ((X2 @ X5)))))))),
% 0.24/0.33 inference(fool_elimination,[],[f10])).
% 0.24/0.33 thf(f12,plain,(
% 0.24/0.33 ! [X2 : $i,X1 : $i,X0 : $i] : (! [X3 : ($i > $o)] : (! [X6 : $i] : ((((in @ X6 @ X1)) != $true) | ($true = ((X3 @ X6)))) | ? [X4 : $i] : (? [X5 : $i] : (((((X3 @ (kpair @ X4 @ X5))) != $true) & (((in @ (kpair @ X4 @ X5) @ X1)) = $true)) & (((in @ X5 @ X2)) = $true)) & (((in @ X4 @ X0)) = $true))) | (((breln @ X0 @ X2 @ X1)) != $true)) <=> (brelnall2 = $true)),
% 0.24/0.33 inference(ennf_transformation,[],[f7])).
% 0.24/0.33 thf(f13,plain,(
% 0.24/0.33 (brelnall2 = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : ((((breln @ X0 @ X2 @ X1)) != $true) | ! [X3 : ($i > $o)] : (! [X6 : $i] : ((((in @ X6 @ X1)) != $true) | ($true = ((X3 @ X6)))) | ? [X4 : $i] : (? [X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ X1)) = $true) & (((in @ X5 @ X2)) = $true) & (((X3 @ (kpair @ X4 @ X5))) != $true)) & (((in @ X4 @ X0)) = $true))))),
% 0.24/0.33 inference(flattening,[],[f12])).
% 0.24/0.33 thf(f14,plain,(
% 0.24/0.33 ? [X0 : $i,X1 : $i] : (? [X2 : ($i > $o)] : (? [X5 : $i] : ((((in @ X5 @ X1)) = $true) & ($true != ((X2 @ X5)))) & ! [X3 : $i] : (! [X4 : $i] : (((((X2 @ (kpair @ X3 @ X4))) = $true) | (((in @ (kpair @ X3 @ X4) @ X1)) != $true)) | (((in @ X4 @ X0)) != $true)) | (((in @ X3 @ X0)) != $true))) & (((breln1 @ X0 @ X1)) = $true)) & (brelnall2 = $true)),
% 0.24/0.33 inference(ennf_transformation,[],[f11])).
% 0.24/0.33 thf(f15,plain,(
% 0.24/0.33 ? [X1 : $i,X0 : $i] : (? [X2 : ($i > $o)] : (! [X3 : $i] : ((((in @ X3 @ X0)) != $true) | ! [X4 : $i] : ((((X2 @ (kpair @ X3 @ X4))) = $true) | (((in @ X4 @ X0)) != $true) | (((in @ (kpair @ X3 @ X4) @ X1)) != $true))) & ? [X5 : $i] : ((((in @ X5 @ X1)) = $true) & ($true != ((X2 @ X5))))) & (((breln1 @ X0 @ X1)) = $true)) & (brelnall2 = $true)),
% 0.24/0.33 inference(flattening,[],[f14])).
% 0.24/0.33 thf(f16,plain,(
% 0.24/0.33 ? [X0 : $i,X1 : $i] : (? [X2 : ($i > $o)] : (! [X3 : $i] : ((((in @ X3 @ X1)) != $true) | ! [X4 : $i] : ((((X2 @ (kpair @ X3 @ X4))) = $true) | (((in @ X4 @ X1)) != $true) | ($true != ((in @ (kpair @ X3 @ X4) @ X0))))) & ? [X5 : $i] : ((((in @ X5 @ X0)) = $true) & ($true != ((X2 @ X5))))) & ($true = ((breln1 @ X1 @ X0)))) & (brelnall2 = $true)),
% 0.24/0.33 inference(rectify,[],[f15])).
% 0.24/0.33 thf(f17,plain,(
% 0.24/0.33 ((! [X3 : $i] : ((((in @ X3 @ sK1)) != $true) | ! [X4 : $i] : ((((sK2 @ (kpair @ X3 @ X4))) = $true) | (((in @ X4 @ sK1)) != $true) | (((in @ (kpair @ X3 @ X4) @ sK0)) != $true))) & (($true = ((in @ sK3 @ sK0))) & (((sK2 @ sK3)) != $true))) & ($true = ((breln1 @ sK1 @ sK0)))) & (brelnall2 = $true)),
% 0.24/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X5,sK3)],[f16])).
% 0.24/0.33 thf(f18,plain,(
% 0.24/0.33 ((brelnall2 = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : ((((breln @ X0 @ X2 @ X1)) = $true) & ? [X3 : ($i > $o)] : (? [X6 : $i] : ((((in @ X6 @ X1)) = $true) & ($true != ((X3 @ X6)))) & ! [X4 : $i] : (! [X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ X1)) != $true) | (((in @ X5 @ X2)) != $true) | (((X3 @ (kpair @ X4 @ X5))) = $true)) | (((in @ X4 @ X0)) != $true))))) & (! [X0 : $i,X2 : $i,X1 : $i] : ((((breln @ X0 @ X2 @ X1)) != $true) | ! [X3 : ($i > $o)] : (! [X6 : $i] : ((((in @ X6 @ X1)) != $true) | ($true = ((X3 @ X6)))) | ? [X4 : $i] : (? [X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ X1)) = $true) & (((in @ X5 @ X2)) = $true) & (((X3 @ (kpair @ X4 @ X5))) != $true)) & (((in @ X4 @ X0)) = $true)))) | (brelnall2 != $true))),
% 0.24/0.33 inference(nnf_transformation,[],[f13])).
% 0.24/0.33 thf(f19,plain,(
% 0.24/0.33 ((brelnall2 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((breln @ X0 @ X1 @ X2)) = $true) & ? [X3 : ($i > $o)] : (? [X4 : $i] : ((((in @ X4 @ X2)) = $true) & (((X3 @ X4)) != $true)) & ! [X5 : $i] : (! [X6 : $i] : (($true != ((in @ (kpair @ X5 @ X6) @ X2))) | (((in @ X6 @ X1)) != $true) | (((X3 @ (kpair @ X5 @ X6))) = $true)) | (((in @ X5 @ X0)) != $true))))) & (! [X7 : $i,X8 : $i,X9 : $i] : ((((breln @ X7 @ X8 @ X9)) != $true) | ! [X10 : ($i > $o)] : (! [X11 : $i] : (($true != ((in @ X11 @ X9))) | ($true = ((X10 @ X11)))) | ? [X12 : $i] : (? [X13 : $i] : (($true = ((in @ (kpair @ X12 @ X13) @ X9))) & (((in @ X13 @ X8)) = $true) & ($true != ((X10 @ (kpair @ X12 @ X13))))) & (((in @ X12 @ X7)) = $true)))) | (brelnall2 != $true))),
% 0.24/0.33 inference(rectify,[],[f18])).
% 0.24/0.33 thf(f20,plain,(
% 0.24/0.33 ((brelnall2 = $true) | (($true = ((breln @ sK4 @ sK5 @ sK6))) & (((((in @ sK8 @ sK6)) = $true) & ($true != ((sK7 @ sK8)))) & ! [X5 : $i] : (! [X6 : $i] : ((((in @ (kpair @ X5 @ X6) @ sK6)) != $true) | ($true != ((in @ X6 @ sK5))) | ($true = ((sK7 @ (kpair @ X5 @ X6))))) | ($true != ((in @ X5 @ sK4))))))) & (! [X7 : $i,X8 : $i,X9 : $i] : ((((breln @ X7 @ X8 @ X9)) != $true) | ! [X10 : ($i > $o)] : (! [X11 : $i] : (($true != ((in @ X11 @ X9))) | ($true = ((X10 @ X11)))) | ((($true = ((in @ (kpair @ (sK9 @ X10 @ X9 @ X8 @ X7) @ (sK10 @ X10 @ X9 @ X8 @ X7)) @ X9))) & ($true = ((in @ (sK10 @ X10 @ X9 @ X8 @ X7) @ X8))) & (((X10 @ (kpair @ (sK9 @ X10 @ X9 @ X8 @ X7) @ (sK10 @ X10 @ X9 @ X8 @ X7)))) != $true)) & ($true = ((in @ (sK9 @ X10 @ X9 @ X8 @ X7) @ X7)))))) | (brelnall2 != $true))),
% 0.24/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8,vAPP,vAPP]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7),skolemize(X4,sK8),skolemize(X13,sK10 @ X10 @ X9 @ X8 @ X7),skolemize(X13,sK10 @ X10 @ X9 @ X8 @ X7)],[f19])).
% 0.24/0.33 thf(f21,plain,(
% 0.24/0.33 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.24/0.33 inference(cnf_transformation,[],[f8])).
% 0.24/0.33 thf(f22,plain,(
% 0.24/0.33 (brelnall2 = $true)),
% 0.24/0.33 inference(cnf_transformation,[],[f17])).
% 0.24/0.33 thf(f23,plain,(
% 0.24/0.33 ($true = ((breln1 @ sK1 @ sK0)))),
% 0.24/0.33 inference(cnf_transformation,[],[f17])).
% 0.24/0.33 thf(f24,plain,(
% 0.24/0.33 (((sK2 @ sK3)) != $true)),
% 0.24/0.33 inference(cnf_transformation,[],[f17])).
% 0.24/0.33 thf(f25,plain,(
% 0.24/0.33 ($true = ((in @ sK3 @ sK0)))),
% 0.24/0.33 inference(cnf_transformation,[],[f17])).
% 0.24/0.33 thf(f26,plain,(
% 0.24/0.33 ( ! [X3 : $i,X4 : $i] : ((((in @ (kpair @ X3 @ X4) @ sK0)) != $true) | (((in @ X3 @ sK1)) != $true) | (((sK2 @ (kpair @ X3 @ X4))) = $true) | (((in @ X4 @ sK1)) != $true)) )),
% 0.24/0.33 inference(cnf_transformation,[],[f17])).
% 0.24/0.33 thf(f27,plain,(
% 0.24/0.33 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : ((((breln @ X7 @ X8 @ X9)) != $true) | ($true != ((in @ X11 @ X9))) | ($true = ((X10 @ X11))) | ($true = ((in @ (sK9 @ X10 @ X9 @ X8 @ X7) @ X7))) | (brelnall2 != $true)) )),
% 0.24/0.33 inference(cnf_transformation,[],[f20])).
% 0.24/0.33 thf(f28,plain,(
% 0.24/0.33 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : ((((breln @ X7 @ X8 @ X9)) != $true) | ($true != ((in @ X11 @ X9))) | ($true = ((X10 @ X11))) | (((X10 @ (kpair @ (sK9 @ X10 @ X9 @ X8 @ X7) @ (sK10 @ X10 @ X9 @ X8 @ X7)))) != $true) | (brelnall2 != $true)) )),
% 0.24/0.33 inference(cnf_transformation,[],[f20])).
% 0.24/0.33 thf(f29,plain,(
% 0.24/0.33 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : ((((breln @ X7 @ X8 @ X9)) != $true) | ($true != ((in @ X11 @ X9))) | ($true = ((X10 @ X11))) | ($true = ((in @ (sK10 @ X10 @ X9 @ X8 @ X7) @ X8))) | (brelnall2 != $true)) )),
% 0.24/0.33 inference(cnf_transformation,[],[f20])).
% 0.24/0.33 thf(f30,plain,(
% 0.24/0.33 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : ((((breln @ X7 @ X8 @ X9)) != $true) | ($true != ((in @ X11 @ X9))) | ($true = ((X10 @ X11))) | ($true = ((in @ (kpair @ (sK9 @ X10 @ X9 @ X8 @ X7) @ (sK10 @ X10 @ X9 @ X8 @ X7)) @ X9))) | (brelnall2 != $true)) )),
% 0.24/0.33 inference(cnf_transformation,[],[f20])).
% 0.24/0.33 thf(f35,plain,(
% 0.24/0.33 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 0.24/0.33 inference(cnf_transformation,[],[f9])).
% 0.24/0.33 thf(f38,plain,(
% 0.24/0.33 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))))),
% 0.24/0.33 inference(definition_unfolding,[],[f35,f21])).
% 0.24/0.33 thf(f39,plain,(
% 0.24/0.33 ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ sK1 @ sK0)))),
% 0.24/0.33 inference(definition_unfolding,[],[f23,f38])).
% 0.24/0.33 thf(f44,plain,(
% 0.24/0.33 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : (((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X7 @ X8 @ X9)) != $true) | ($true != ((in @ X11 @ X9))) | ($true = ((X10 @ X11))) | ($true = ((in @ (kpair @ (sK9 @ X10 @ X9 @ X8 @ X7) @ (sK10 @ X10 @ X9 @ X8 @ X7)) @ X9))) | ($true != $true)) )),
% 0.24/0.33 inference(definition_unfolding,[],[f30,f21,f22])).
% 0.24/0.33 thf(f45,plain,(
% 0.24/0.33 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : (($true = ((in @ (sK10 @ X10 @ X9 @ X8 @ X7) @ X8))) | ($true = ((X10 @ X11))) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X7 @ X8 @ X9)) != $true) | ($true != $true) | ($true != ((in @ X11 @ X9)))) )),
% 0.24/0.33 inference(definition_unfolding,[],[f29,f21,f22])).
% 0.24/0.33 thf(f46,plain,(
% 0.24/0.33 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : (($true != $true) | (((X10 @ (kpair @ (sK9 @ X10 @ X9 @ X8 @ X7) @ (sK10 @ X10 @ X9 @ X8 @ X7)))) != $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X7 @ X8 @ X9)) != $true) | ($true != ((in @ X11 @ X9))) | ($true = ((X10 @ X11)))) )),
% 0.24/0.33 inference(definition_unfolding,[],[f28,f21,f22])).
% 0.24/0.33 thf(f47,plain,(
% 0.24/0.33 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : (($true != $true) | ($true = ((in @ (sK9 @ X10 @ X9 @ X8 @ X7) @ X7))) | ($true != ((in @ X11 @ X9))) | ($true = ((X10 @ X11))) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X7 @ X8 @ X9)) != $true)) )),
% 0.24/0.33 inference(definition_unfolding,[],[f27,f21,f22])).
% 0.24/0.33 thf(f48,plain,(
% 0.24/0.33 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : (($true = ((X10 @ X11))) | ($true != ((in @ X11 @ X9))) | (((X10 @ (kpair @ (sK9 @ X10 @ X9 @ X8 @ X7) @ (sK10 @ X10 @ X9 @ X8 @ X7)))) != $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X7 @ X8 @ X9)) != $true)) )),
% 0.24/0.33 inference(trivial_inequality_removal,[],[f46])).
% 0.24/0.33 thf(f49,plain,(
% 0.24/0.33 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : ((((X10 @ (kpair @ (sK9 @ X10 @ X9 @ X8 @ X7) @ (sK10 @ X10 @ X9 @ X8 @ X7)))) != $true) | ($true = ((X10 @ X11))) | ($true != ((subset @ X9 @ (cartprod @ X7 @ X8)))) | ($true != ((in @ X11 @ X9)))) )),
% 0.24/0.33 inference(beta-eta_normalization,[],[f48])).
% 0.24/0.33 thf(f50,plain,(
% 0.24/0.33 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : (((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X7 @ X8 @ X9)) != $true) | ($true = ((X10 @ X11))) | ($true = ((in @ (sK10 @ X10 @ X9 @ X8 @ X7) @ X8))) | ($true != ((in @ X11 @ X9)))) )),
% 0.24/0.33 inference(trivial_inequality_removal,[],[f45])).
% 0.24/0.33 thf(f51,plain,(
% 0.24/0.33 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : (($true != ((subset @ X9 @ (cartprod @ X7 @ X8)))) | ($true != ((in @ X11 @ X9))) | ($true = ((in @ (sK10 @ X10 @ X9 @ X8 @ X7) @ X8))) | ($true = ((X10 @ X11)))) )),
% 0.24/0.33 inference(beta-eta_normalization,[],[f50])).
% 0.24/0.33 thf(f52,plain,(
% 0.24/0.33 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : (($true = ((in @ (kpair @ (sK9 @ X10 @ X9 @ X8 @ X7) @ (sK10 @ X10 @ X9 @ X8 @ X7)) @ X9))) | ($true != ((in @ X11 @ X9))) | ($true = ((X10 @ X11))) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X7 @ X8 @ X9)) != $true)) )),
% 0.24/0.33 inference(trivial_inequality_removal,[],[f44])).
% 0.24/0.33 thf(f53,plain,(
% 0.24/0.33 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : (($true != ((subset @ X9 @ (cartprod @ X7 @ X8)))) | ($true = ((X10 @ X11))) | ($true != ((in @ X11 @ X9))) | ($true = ((in @ (kpair @ (sK9 @ X10 @ X9 @ X8 @ X7) @ (sK10 @ X10 @ X9 @ X8 @ X7)) @ X9)))) )),
% 0.24/0.33 inference(beta-eta_normalization,[],[f52])).
% 0.24/0.33 thf(f54,plain,(
% 0.24/0.33 (((subset @ sK0 @ (cartprod @ sK1 @ sK1))) = $true)),
% 0.24/0.33 inference(beta-eta_normalization,[],[f39])).
% 0.24/0.33 thf(f55,plain,(
% 0.24/0.33 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : (($true = ((in @ (sK9 @ X10 @ X9 @ X8 @ X7) @ X7))) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X7 @ X8 @ X9)) != $true) | ($true = ((X10 @ X11))) | ($true != ((in @ X11 @ X9)))) )),
% 0.24/0.33 inference(trivial_inequality_removal,[],[f47])).
% 0.24/0.33 thf(f56,plain,(
% 0.24/0.33 ( ! [X10 : ($i > $o),X11 : $i,X8 : $i,X9 : $i,X7 : $i] : (($true != ((subset @ X9 @ (cartprod @ X7 @ X8)))) | ($true = ((X10 @ X11))) | ($true != ((in @ X11 @ X9))) | ($true = ((in @ (sK9 @ X10 @ X9 @ X8 @ X7) @ X7)))) )),
% 0.24/0.33 inference(beta-eta_normalization,[],[f55])).
% 0.24/0.33 thf(f57,plain,(
% 0.24/0.33 ( ! [X0 : $i,X1 : ($i > $o)] : (($true != $true) | ($true = ((X1 @ X0))) | ($true != ((in @ X0 @ sK0))) | (((in @ (sK10 @ X1 @ sK0 @ sK1 @ sK1) @ sK1)) = $true)) )),
% 0.24/0.33 inference(constrained_superposition,[],[f51,f54])).
% 0.24/0.33 thf(f58,plain,(
% 0.24/0.33 ( ! [X0 : $i,X1 : ($i > $o)] : (($true != ((in @ X0 @ sK0))) | (((in @ (sK10 @ X1 @ sK0 @ sK1 @ sK1) @ sK1)) = $true) | ($true = ((X1 @ X0)))) )),
% 0.24/0.33 inference(trivial_inequality_removal,[],[f57])).
% 0.24/0.33 thf(f59,plain,(
% 0.24/0.33 ( ! [X0 : ($i > $o)] : ((((in @ (sK10 @ X0 @ sK0 @ sK1 @ sK1) @ sK1)) = $true) | (((X0 @ sK3)) = $true) | ($true != $true)) )),
% 0.24/0.33 inference(constrained_superposition,[],[f58,f25])).
% 0.24/0.33 thf(f60,plain,(
% 0.24/0.33 ( ! [X0 : ($i > $o)] : ((((in @ (sK10 @ X0 @ sK0 @ sK1 @ sK1) @ sK1)) = $true) | (((X0 @ sK3)) = $true)) )),
% 0.24/0.33 inference(trivial_inequality_removal,[],[f59])).
% 0.24/0.33 thf(f61,plain,(
% 0.24/0.33 ( ! [X0 : ($i > $o),X1 : $i] : ((((in @ X1 @ sK0)) != $true) | ($true != $true) | (((in @ (sK9 @ X0 @ sK0 @ sK1 @ sK1) @ sK1)) = $true) | (((X0 @ X1)) = $true)) )),
% 0.24/0.33 inference(constrained_superposition,[],[f56,f54])).
% 0.24/0.33 thf(f62,plain,(
% 0.24/0.33 ( ! [X0 : ($i > $o),X1 : $i] : ((((in @ X1 @ sK0)) != $true) | (((X0 @ X1)) = $true) | (((in @ (sK9 @ X0 @ sK0 @ sK1 @ sK1) @ sK1)) = $true)) )),
% 0.24/0.33 inference(trivial_inequality_removal,[],[f61])).
% 0.24/0.33 thf(f63,plain,(
% 0.24/0.33 ( ! [X0 : ($i > $o)] : ((((in @ (sK9 @ X0 @ sK0 @ sK1 @ sK1) @ sK1)) = $true) | ($true != $true) | (((X0 @ sK3)) = $true)) )),
% 0.24/0.33 inference(constrained_superposition,[],[f62,f25])).
% 0.24/0.33 thf(f64,plain,(
% 0.24/0.33 ( ! [X0 : ($i > $o)] : ((((in @ (sK9 @ X0 @ sK0 @ sK1 @ sK1) @ sK1)) = $true) | (((X0 @ sK3)) = $true)) )),
% 0.24/0.33 inference(trivial_inequality_removal,[],[f63])).
% 0.24/0.33 thf(f76,plain,(
% 0.24/0.33 ( ! [X0 : ($i > $o),X1 : $i] : ((((in @ (kpair @ (sK9 @ X0 @ sK0 @ sK1 @ sK1) @ (sK10 @ X0 @ sK0 @ sK1 @ sK1)) @ sK0)) = $true) | (((in @ X1 @ sK0)) != $true) | (((X0 @ X1)) = $true) | ($true != $true)) )),
% 0.24/0.33 inference(constrained_superposition,[],[f53,f54])).
% 0.24/0.33 thf(f77,plain,(
% 0.24/0.33 ( ! [X0 : ($i > $o),X1 : $i] : ((((in @ X1 @ sK0)) != $true) | (((in @ (kpair @ (sK9 @ X0 @ sK0 @ sK1 @ sK1) @ (sK10 @ X0 @ sK0 @ sK1 @ sK1)) @ sK0)) = $true) | (((X0 @ X1)) = $true)) )),
% 0.24/0.33 inference(trivial_inequality_removal,[],[f76])).
% 0.24/0.33 thf(f78,plain,(
% 0.24/0.33 ( ! [X0 : ($i > $o)] : ((((in @ (kpair @ (sK9 @ X0 @ sK0 @ sK1 @ sK1) @ (sK10 @ X0 @ sK0 @ sK1 @ sK1)) @ sK0)) = $true) | ($true != $true) | (((X0 @ sK3)) = $true)) )),
% 0.24/0.33 inference(constrained_superposition,[],[f77,f25])).
% 0.24/0.33 thf(f79,plain,(
% 0.24/0.33 ( ! [X0 : ($i > $o)] : ((((in @ (kpair @ (sK9 @ X0 @ sK0 @ sK1 @ sK1) @ (sK10 @ X0 @ sK0 @ sK1 @ sK1)) @ sK0)) = $true) | (((X0 @ sK3)) = $true)) )),
% 0.24/0.33 inference(trivial_inequality_removal,[],[f78])).
% 0.24/0.33 thf(f80,plain,(
% 0.24/0.33 ( ! [X0 : ($i > $o)] : ((((in @ (sK10 @ X0 @ sK0 @ sK1 @ sK1) @ sK1)) != $true) | (((in @ (sK9 @ X0 @ sK0 @ sK1 @ sK1) @ sK1)) != $true) | ($true != $true) | (((sK2 @ (kpair @ (sK9 @ X0 @ sK0 @ sK1 @ sK1) @ (sK10 @ X0 @ sK0 @ sK1 @ sK1)))) = $true) | (((X0 @ sK3)) = $true)) )),
% 0.24/0.33 inference(constrained_superposition,[],[f26,f79])).
% 0.24/0.33 thf(f84,plain,(
% 0.24/0.33 ( ! [X0 : ($i > $o)] : ((((in @ (sK10 @ X0 @ sK0 @ sK1 @ sK1) @ sK1)) != $true) | (((sK2 @ (kpair @ (sK9 @ X0 @ sK0 @ sK1 @ sK1) @ (sK10 @ X0 @ sK0 @ sK1 @ sK1)))) = $true) | (((in @ (sK9 @ X0 @ sK0 @ sK1 @ sK1) @ sK1)) != $true) | (((X0 @ sK3)) = $true)) )),
% 0.24/0.33 inference(trivial_inequality_removal,[],[f80])).
% 0.24/0.33 thf(f88,plain,(
% 0.24/0.33 ( ! [X0 : ($i > $o)] : ((((X0 @ sK3)) = $true) | (((sK2 @ (kpair @ (sK9 @ X0 @ sK0 @ sK1 @ sK1) @ (sK10 @ X0 @ sK0 @ sK1 @ sK1)))) = $true) | (((in @ (sK9 @ X0 @ sK0 @ sK1 @ sK1) @ sK1)) != $true)) )),
% 0.24/0.33 inference(forward_subsumption_resolution,[],[f84,f60])).
% 0.24/0.33 thf(f89,plain,(
% 0.24/0.33 ( ! [X0 : ($i > $o)] : ((((sK2 @ (kpair @ (sK9 @ X0 @ sK0 @ sK1 @ sK1) @ (sK10 @ X0 @ sK0 @ sK1 @ sK1)))) = $true) | (((X0 @ sK3)) = $true)) )),
% 0.24/0.33 inference(forward_subsumption_resolution,[],[f88,f64])).
% 0.24/0.33 thf(f90,plain,(
% 0.24/0.33 ( ! [X0 : $i] : ((((sK2 @ X0)) = $true) | (((sK2 @ sK3)) = $true) | ($true != $true) | (((subset @ sK0 @ (cartprod @ sK1 @ sK1))) != $true) | ($true != ((in @ X0 @ sK0)))) )),
% 0.24/0.33 inference(constrained_superposition,[],[f49,f89])).
% 0.24/0.33 thf(f91,plain,(
% 0.24/0.33 ( ! [X0 : $i] : ((((sK2 @ sK3)) = $true) | (((subset @ sK0 @ (cartprod @ sK1 @ sK1))) != $true) | ($true != ((in @ X0 @ sK0))) | (((sK2 @ X0)) = $true)) )),
% 0.24/0.33 inference(trivial_inequality_removal,[],[f90])).
% 0.24/0.33 thf(f92,plain,(
% 0.24/0.33 ( ! [X0 : $i] : ((((subset @ sK0 @ (cartprod @ sK1 @ sK1))) != $true) | (((sK2 @ X0)) = $true) | ($true != ((in @ X0 @ sK0)))) )),
% 0.24/0.33 inference(forward_subsumption_resolution,[],[f91,f24])).
% 0.24/0.33 thf(f93,plain,(
% 0.24/0.33 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK0))) | (((sK2 @ X0)) = $true)) )),
% 0.24/0.33 inference(forward_subsumption_resolution,[],[f92,f54])).
% 0.24/0.33 thf(f94,plain,(
% 0.24/0.33 (((sK2 @ sK3)) = $true) | ($true != $true)),
% 0.24/0.33 inference(constrained_superposition,[],[f93,f25])).
% 0.24/0.33 thf(f96,plain,(
% 0.24/0.33 (((sK2 @ sK3)) = $true)),
% 0.24/0.33 inference(trivial_inequality_removal,[],[f94])).
% 0.24/0.33 thf(f98,plain,(
% 0.24/0.33 $false),
% 0.24/0.33 inference(forward_subsumption_resolution,[],[f96,f24])).
% 0.24/0.33 % SZS output end Proof for theBenchmark
% 0.24/0.33 % (3436686)------------------------------
% 0.24/0.33 % (3436686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.33 % (3436686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.33 % (3436686)CaDiCaL version: 2.1.3
% 0.24/0.33 % (3436686)Termination reason: Refutation
% 0.24/0.33 % (3436686)Time elapsed: 0.016 s
% 0.24/0.33 % (3436686)Peak memory usage: 12 MB
% 0.24/0.33 % (3436686)Instructions burned: 15 (million)
% 0.24/0.33 % (3436680)Success in time 0.055 s
% 0.24/0.33 % Vampire exiting
%------------------------------------------------------------------------------