%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU632^2 : 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 : n004.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 08:30:26 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU632^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n004.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:00:18 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.22/0.29 % (1330768)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (1330779)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.29 % (1330779)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
% 0.22/0.29 % (1330775)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3660626239:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.29 % (1330773)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1908460328:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.29 % (1330774)lrs+10_16_si=on:nwc=1.5:random_seed=149300741:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.29 % (1330778)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2273831001:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.29 % (1330776)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=2897904005: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)
% 0.22/0.29 % (1330777)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4177331706:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.29 % (1330779)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=3997363180:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.29 % (1330775)Instruction limit reached!
% 0.22/0.29 % (1330775)------------------------------
% 0.22/0.29 % (1330775)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (1330775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (1330775)CaDiCaL version: 2.1.3
% 0.22/0.29 % (1330775)Termination reason: Instruction limit
% 0.22/0.29 % (1330775)Termination phase: Saturation
% 0.22/0.29 % (1330775)Time elapsed: 0.003 s
% 0.22/0.29 % (1330775)Peak memory usage: 11 MB
% 0.22/0.29 % (1330775)Instructions burned: 4 (million)
% 0.22/0.29 % (1330777) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1330768-1330777"...
% 0.22/0.29 % (1330776) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1330768-1330776"...
% 0.22/0.29 % (1330777)...printing done.
% 0.22/0.29 % (1330777)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% 0.22/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.29 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.22/0.29 thf(func_def_2, type, setadjoin: ($i > $i > $i)).
% 0.22/0.29 thf(func_def_3, type, setunion: ($i > $i)).
% 0.22/0.29 thf(func_def_4, type, iskpair: ($i > $o)).
% 0.22/0.29 thf(func_def_6, type, kpair: ($i > $i > $i)).
% 0.22/0.29 thf(func_def_7, type, kpairp: $o).
% 0.22/0.29 thf(func_def_8, type, cartprod: ($i > $i > $i)).
% 0.22/0.29 thf(func_def_9, type, cartprodmempair1: $o).
% 0.22/0.29 thf(func_def_12, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.29 thf(func_def_13, type, vAND: ($o > $o > $o)).
% 0.22/0.29 thf(func_def_14, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.29 thf(func_def_15, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.29 thf(func_def_16, type, db2: !>[X0: $tType]:(X0)).
% 0.22/0.29 thf(func_def_17, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.29 thf(func_def_18, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.29 thf(func_def_22, type, sK3: ($i > $i > $i > $i)).
% 0.22/0.29 thf(func_def_23, type, sK4: ($i > $i > $i > $i)).
% 0.22/0.29 thf(f3,axiom,(
% 0.22/0.29 (kpairp = ! [X1 : $i,X0 : $i] : (iskpair @ (kpair @ X0 @ X1)))),
% 0.22/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp)).
% 0.22/0.29 thf(f4,axiom,(
% 0.22/0.29 (! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => ? [X3 : $i] : ((in @ X3 @ X0) & ? [X4 : $i] : ((X2 = ((kpair @ X3 @ X4))) & (in @ X4 @ X1)))) = cartprodmempair1)),
% 0.22/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1)).
% 0.22/0.29 thf(f5,conjecture,(
% 0.22/0.29 kpairp => (cartprodmempair1 => ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (iskpair @ X2)))),
% 0.22/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair)).
% 0.22/0.29 thf(f6,negated_conjecture,(
% 0.22/0.29 ~(kpairp => (cartprodmempair1 => ! [X0 : $i,X2 : $i,X1 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (iskpair @ X2))))),
% 0.22/0.29 inference(negated_conjecture,[status(cth)],[f5])).
% 0.22/0.29 thf(f7,plain,(
% 0.22/0.29 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (cartprod @ X1 @ X2)) => ? [X3 : $i] : ((in @ X3 @ X1) & ? [X4 : $i] : ((((kpair @ X3 @ X4)) = X0) & (in @ X4 @ X2)))) = cartprodmempair1)),
% 0.22/0.29 inference(rectify,[],[f4])).
% 0.22/0.29 thf(f8,plain,(
% 0.22/0.29 ! [X0 : $i,X2 : $i,X1 : $i] : (($true = ((in @ X0 @ (cartprod @ X1 @ X2)))) => ? [X3 : $i] : (? [X4 : $i] : ((((kpair @ X3 @ X4)) = X0) & ($true = ((in @ X4 @ X2)))) & (((in @ X3 @ X1)) = $true))) <=> (cartprodmempair1 = $true)),
% 0.22/0.29 inference(fool_elimination,[],[f7])).
% 0.22/0.29 thf(f9,plain,(
% 0.22/0.29 (kpairp = ! [X0 : $i,X1 : $i] : (iskpair @ (kpair @ X1 @ X0)))),
% 0.22/0.29 inference(rectify,[],[f3])).
% 0.22/0.29 thf(f10,plain,(
% 0.22/0.29 (kpairp = $true) <=> ! [X0 : $i,X1 : $i] : ($true = ((iskpair @ (kpair @ X1 @ X0))))),
% 0.22/0.29 inference(fool_elimination,[],[f9])).
% 0.22/0.29 thf(f11,plain,(
% 0.22/0.29 ~(kpairp => (cartprodmempair1 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (cartprod @ X0 @ X2)) => (iskpair @ X1))))),
% 0.22/0.29 inference(rectify,[],[f6])).
% 0.22/0.29 thf(f12,plain,(
% 0.22/0.29 ~((kpairp = $true) => ((cartprodmempair1 = $true) => ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X1 @ (cartprod @ X0 @ X2)))) => (((iskpair @ X1)) = $true))))),
% 0.22/0.29 inference(fool_elimination,[],[f11])).
% 0.22/0.29 thf(f16,plain,(
% 0.22/0.29 (cartprodmempair1 = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : (? [X3 : $i] : (? [X4 : $i] : ((((kpair @ X3 @ X4)) = X0) & ($true = ((in @ X4 @ X2)))) & (((in @ X3 @ X1)) = $true)) | ($true != ((in @ X0 @ (cartprod @ X1 @ X2)))))),
% 0.22/0.29 inference(ennf_transformation,[],[f8])).
% 0.22/0.29 thf(f17,plain,(
% 0.22/0.29 (? [X0 : $i,X2 : $i,X1 : $i] : (($true = ((in @ X1 @ (cartprod @ X0 @ X2)))) & (((iskpair @ X1)) != $true)) & (cartprodmempair1 = $true)) & (kpairp = $true)),
% 0.22/0.29 inference(ennf_transformation,[],[f12])).
% 0.22/0.29 thf(f18,plain,(
% 0.22/0.29 (kpairp = $true) & (cartprodmempair1 = $true) & ? [X0 : $i,X2 : $i,X1 : $i] : (($true = ((in @ X1 @ (cartprod @ X0 @ X2)))) & (((iskpair @ X1)) != $true))),
% 0.22/0.29 inference(flattening,[],[f17])).
% 0.22/0.29 thf(f19,plain,(
% 0.22/0.29 ((cartprodmempair1 = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (! [X3 : $i] : (! [X4 : $i] : ((((kpair @ X3 @ X4)) != X0) | ($true != ((in @ X4 @ X2)))) | (((in @ X3 @ X1)) != $true)) & ($true = ((in @ X0 @ (cartprod @ X1 @ X2)))))) & (! [X1 : $i,X2 : $i,X0 : $i] : (? [X3 : $i] : (? [X4 : $i] : ((((kpair @ X3 @ X4)) = X0) & ($true = ((in @ X4 @ X2)))) & (((in @ X3 @ X1)) = $true)) | ($true != ((in @ X0 @ (cartprod @ X1 @ X2))))) | (cartprodmempair1 != $true))),
% 0.22/0.29 inference(nnf_transformation,[],[f16])).
% 0.22/0.29 thf(f20,plain,(
% 0.22/0.29 ((cartprodmempair1 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : ((((kpair @ X3 @ X4)) != X2) | (((in @ X4 @ X1)) != $true)) | (((in @ X3 @ X0)) != $true)) & (((in @ X2 @ (cartprod @ X0 @ X1))) = $true))) & (! [X5 : $i,X6 : $i,X7 : $i] : (? [X8 : $i] : (? [X9 : $i] : ((((kpair @ X8 @ X9)) = X7) & (((in @ X9 @ X6)) = $true)) & ($true = ((in @ X8 @ X5)))) | ($true != ((in @ X7 @ (cartprod @ X5 @ X6))))) | (cartprodmempair1 != $true))),
% 0.22/0.29 inference(rectify,[],[f19])).
% 0.22/0.29 thf(f21,plain,(
% 0.22/0.29 ((cartprodmempair1 = $true) | (! [X3 : $i] : (! [X4 : $i] : ((((kpair @ X3 @ X4)) != sK2) | (((in @ X4 @ sK1)) != $true)) | ($true != ((in @ X3 @ sK0)))) & ($true = ((in @ sK2 @ (cartprod @ sK0 @ sK1)))))) & (! [X5 : $i,X6 : $i,X7 : $i] : ((((((kpair @ (sK3 @ X7 @ X6 @ X5) @ (sK4 @ X7 @ X6 @ X5))) = X7) & (((in @ (sK4 @ X7 @ X6 @ X5) @ X6)) = $true)) & ($true = ((in @ (sK3 @ X7 @ X6 @ X5) @ X5)))) | ($true != ((in @ X7 @ (cartprod @ X5 @ X6))))) | (cartprodmempair1 != $true))),
% 0.22/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X9,sK4 @ X7 @ X6 @ X5),skolemize(X9,sK4 @ X7 @ X6 @ X5)],[f20])).
% 0.22/0.29 thf(f22,plain,(
% 0.22/0.29 ((kpairp = $true) | ? [X0 : $i,X1 : $i] : ($true != ((iskpair @ (kpair @ X1 @ X0))))) & (! [X0 : $i,X1 : $i] : ($true = ((iskpair @ (kpair @ X1 @ X0)))) | (kpairp != $true))),
% 0.22/0.29 inference(nnf_transformation,[],[f10])).
% 0.22/0.29 thf(f23,plain,(
% 0.22/0.29 ((kpairp = $true) | ? [X0 : $i,X1 : $i] : ($true != ((iskpair @ (kpair @ X1 @ X0))))) & (! [X2 : $i,X3 : $i] : (((iskpair @ (kpair @ X3 @ X2))) = $true) | (kpairp != $true))),
% 0.22/0.29 inference(rectify,[],[f22])).
% 0.22/0.29 thf(f24,plain,(
% 0.22/0.29 ((kpairp = $true) | (((iskpair @ (kpair @ sK6 @ sK5))) != $true)) & (! [X2 : $i,X3 : $i] : (((iskpair @ (kpair @ X3 @ X2))) = $true) | (kpairp != $true))),
% 0.22/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X1,sK6)],[f23])).
% 0.22/0.29 thf(f25,plain,(
% 0.22/0.29 (kpairp = $true) & (cartprodmempair1 = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ (cartprod @ X0 @ X1))) = $true) & (((iskpair @ X2)) != $true))),
% 0.22/0.29 inference(rectify,[],[f18])).
% 0.22/0.29 thf(f26,plain,(
% 0.22/0.29 (kpairp = $true) & (cartprodmempair1 = $true) & ((((in @ sK9 @ (cartprod @ sK7 @ sK8))) = $true) & ($true != ((iskpair @ sK9))))),
% 0.22/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9)],[f25])).
% 0.22/0.29 thf(f29,plain,(
% 0.22/0.29 ( ! [X6 : $i,X7 : $i,X5 : $i] : ((((kpair @ (sK3 @ X7 @ X6 @ X5) @ (sK4 @ X7 @ X6 @ X5))) = X7) | ($true != ((in @ X7 @ (cartprod @ X5 @ X6)))) | (cartprodmempair1 != $true)) )),
% 0.22/0.29 inference(cnf_transformation,[],[f21])).
% 0.22/0.29 thf(f32,plain,(
% 0.22/0.29 ( ! [X2 : $i,X3 : $i] : ((kpairp != $true) | (((iskpair @ (kpair @ X3 @ X2))) = $true)) )),
% 0.22/0.29 inference(cnf_transformation,[],[f24])).
% 0.22/0.29 thf(f36,plain,(
% 0.22/0.29 ($true != ((iskpair @ sK9)))),
% 0.22/0.29 inference(cnf_transformation,[],[f26])).
% 0.22/0.29 thf(f37,plain,(
% 0.22/0.29 (((in @ sK9 @ (cartprod @ sK7 @ sK8))) = $true)),
% 0.22/0.29 inference(cnf_transformation,[],[f26])).
% 0.22/0.29 thf(f38,plain,(
% 0.22/0.29 (cartprodmempair1 = $true)),
% 0.22/0.29 inference(cnf_transformation,[],[f26])).
% 0.22/0.29 thf(f39,plain,(
% 0.22/0.29 (kpairp = $true)),
% 0.22/0.29 inference(cnf_transformation,[],[f26])).
% 0.22/0.29 thf(f43,plain,(
% 0.22/0.29 ( ! [X2 : $i,X3 : $i] : ((((iskpair @ (kpair @ X3 @ X2))) = $true)) )),
% 0.22/0.29 inference(forward_subsumption_resolution,[],[f32,f39])).
% 0.22/0.29 thf(f50,plain,(
% 0.22/0.29 ( ! [X6 : $i,X7 : $i,X5 : $i] : ((((kpair @ (sK3 @ X7 @ X6 @ X5) @ (sK4 @ X7 @ X6 @ X5))) = X7) | ($true != ((in @ X7 @ (cartprod @ X5 @ X6))))) )),
% 0.22/0.29 inference(forward_subsumption_resolution,[],[f29,f38])).
% 0.22/0.29 thf(f51,plain,(
% 0.22/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (cartprod @ X2 @ X1)))) | ($true = ((iskpair @ X0)))) )),
% 0.22/0.29 inference(superposition,[],[f43,f50])).
% 0.22/0.29 thf(f52,plain,(
% 0.22/0.29 ($true != $true) | ($true = ((iskpair @ sK9)))),
% 0.22/0.29 inference(superposition,[],[f51,f37])).
% 0.22/0.29 thf(f55,plain,(
% 0.22/0.29 ($true = ((iskpair @ sK9)))),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f52])).
% 0.22/0.29 thf(f58,plain,(
% 0.22/0.29 $false),
% 0.22/0.29 inference(forward_subsumption_resolution,[],[f55,f36])).
% 0.22/0.29 % SZS output end Proof for theBenchmark
% 0.22/0.29 % (1330777)------------------------------
% 0.22/0.29 % (1330777)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (1330777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (1330777)CaDiCaL version: 2.1.3
% 0.22/0.29 % (1330777)Termination reason: Refutation
% 0.22/0.29 % (1330777)Time elapsed: 0.005 s
% 0.22/0.29 % (1330777)Peak memory usage: 12 MB
% 0.22/0.29 % (1330777)Instructions burned: 6 (million)
% 0.22/0.29 % (1330768)Success in time 0.036 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------