%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU646^2 : 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 : n006.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 08:30:30 AM UTC 2026
% Result : Theorem 0.24s 0.32s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU646^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n006.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 14:01:24 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.25 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
% 0.24/0.32 % (763301)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.32 % (763306)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=139048872:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.32 % (763312)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.32 % (763312)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
% 0.24/0.32 % (763306) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-763301-763306"...
% 0.24/0.32 % (763312)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=2109966380:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.24/0.32 % (763311)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4152219372:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.32 % (763306)...printing done.
% 0.24/0.32 % (763306)Refutation found. Thanks to Tanya!
% 0.24/0.32 % SZS status Theorem for theBenchmark
% 0.24/0.32 % SZS output start Proof for theBenchmark
% 0.24/0.32 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.24/0.32 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.24/0.32 thf(func_def_2, type, setadjoin: ($i > $i > $i)).
% 0.24/0.32 thf(func_def_3, type, kpair: ($i > $i > $i)).
% 0.24/0.32 thf(func_def_5, type, cartprod: ($i > $i > $i)).
% 0.24/0.32 thf(func_def_6, type, cartprodmempair1: $o).
% 0.24/0.32 thf(func_def_7, type, kfst: ($i > $i)).
% 0.24/0.32 thf(func_def_8, type, kfstpairEq: $o).
% 0.24/0.32 thf(func_def_11, type, db1: !>[X0: $tType]:(X0)).
% 0.24/0.32 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.24/0.32 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.24/0.32 thf(func_def_19, type, sK5: ($i > $i > $i > $i)).
% 0.24/0.32 thf(func_def_20, type, sK6: ($i > $i > $i > $i)).
% 0.24/0.32 thf(func_def_24, type, vNOT: ($o > $o)).
% 0.24/0.32 thf(f1,axiom,(
% 0.24/0.32 ((^[X0 : $i, X1 : $i] : ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) = kpair)),
% 0.24/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpair)).
% 0.24/0.32 thf(f2,axiom,(
% 0.24/0.32 (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => ? [X3 : $i] : ((in @ X3 @ X0) & ? [X4 : $i] : ((X2 = ((kpair @ X3 @ X4))) & (in @ X4 @ X1)))) = cartprodmempair1)),
% 0.24/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1)).
% 0.24/0.32 thf(f3,axiom,(
% 0.24/0.32 (kfstpairEq = ! [X0 : $i,X1 : $i] : (((kfst @ (kpair @ X0 @ X1))) = X0))),
% 0.24/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq)).
% 0.24/0.32 thf(f4,conjecture,(
% 0.24/0.32 cartprodmempair1 => (kfstpairEq => ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (in @ (kfst @ X2) @ X0)))),
% 0.24/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstin)).
% 0.24/0.32 thf(f5,negated_conjecture,(
% 0.24/0.32 ~(cartprodmempair1 => (kfstpairEq => ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (in @ (kfst @ X2) @ X0))))),
% 0.24/0.32 inference(negated_conjecture,[status(cth)],[f4])).
% 0.24/0.32 thf(f6,plain,(
% 0.24/0.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (cartprod @ X2 @ X0)) => ? [X3 : $i] : ((in @ X3 @ X2) & ? [X4 : $i] : ((((kpair @ X3 @ X4)) = X1) & (in @ X4 @ X0)))) = cartprodmempair1)),
% 0.24/0.32 inference(rectify,[],[f2])).
% 0.24/0.32 thf(f7,plain,(
% 0.24/0.32 ! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X1 @ (cartprod @ X2 @ X0))) = $true) => ? [X3 : $i] : ((((in @ X3 @ X2)) = $true) & ? [X4 : $i] : ((((kpair @ X3 @ X4)) = X1) & ($true = ((in @ X4 @ X0)))))) <=> (cartprodmempair1 = $true)),
% 0.24/0.32 inference(fool_elimination,[],[f6])).
% 0.24/0.32 thf(f8,plain,(
% 0.24/0.32 ~(cartprodmempair1 => (kfstpairEq => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (cartprod @ X2 @ X0)) => (in @ (kfst @ X1) @ X2))))),
% 0.24/0.32 inference(rectify,[],[f5])).
% 0.24/0.32 thf(f9,plain,(
% 0.24/0.32 ~((cartprodmempair1 = $true) => ((kfstpairEq = $true) => ! [X1 : $i,X2 : $i,X0 : $i] : ((((in @ X1 @ (cartprod @ X2 @ X0))) = $true) => ($true = ((in @ (kfst @ X1) @ X2))))))),
% 0.24/0.32 inference(fool_elimination,[],[f8])).
% 0.24/0.32 thf(f10,plain,(
% 0.24/0.32 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 0.24/0.32 inference(fool_elimination,[],[f1])).
% 0.24/0.32 thf(f11,plain,(
% 0.24/0.32 ! [X1 : $i,X0 : $i] : (((kfst @ (kpair @ X0 @ X1))) = X0) <=> (kfstpairEq = $true)),
% 0.24/0.32 inference(fool_elimination,[],[f3])).
% 0.24/0.32 thf(f12,plain,(
% 0.24/0.32 ! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X1 @ (cartprod @ X2 @ X0))) != $true) | ? [X3 : $i] : ((((in @ X3 @ X2)) = $true) & ? [X4 : $i] : ((((kpair @ X3 @ X4)) = X1) & ($true = ((in @ X4 @ X0)))))) <=> (cartprodmempair1 = $true)),
% 0.24/0.32 inference(ennf_transformation,[],[f7])).
% 0.24/0.32 thf(f13,plain,(
% 0.24/0.32 (? [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X1 @ (cartprod @ X2 @ X0))) = $true) & ($true != ((in @ (kfst @ X1) @ X2)))) & (kfstpairEq = $true)) & (cartprodmempair1 = $true)),
% 0.24/0.32 inference(ennf_transformation,[],[f9])).
% 0.24/0.32 thf(f14,plain,(
% 0.24/0.32 ? [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X1 @ (cartprod @ X2 @ X0))) = $true) & ($true != ((in @ (kfst @ X1) @ X2)))) & (kfstpairEq = $true) & (cartprodmempair1 = $true)),
% 0.24/0.32 inference(flattening,[],[f13])).
% 0.24/0.32 thf(f15,plain,(
% 0.24/0.32 (! [X1 : $i,X0 : $i] : (((kfst @ (kpair @ X0 @ X1))) = X0) | (kfstpairEq != $true)) & ((kfstpairEq = $true) | ? [X1 : $i,X0 : $i] : (((kfst @ (kpair @ X0 @ X1))) != X0))),
% 0.24/0.32 inference(nnf_transformation,[],[f11])).
% 0.24/0.32 thf(f16,plain,(
% 0.24/0.32 (! [X0 : $i,X1 : $i] : (((kfst @ (kpair @ X1 @ X0))) = X1) | (kfstpairEq != $true)) & ((kfstpairEq = $true) | ? [X2 : $i,X3 : $i] : (((kfst @ (kpair @ X3 @ X2))) != X3))),
% 0.24/0.32 inference(rectify,[],[f15])).
% 0.24/0.32 thf(f17,plain,(
% 0.24/0.32 (! [X0 : $i,X1 : $i] : (((kfst @ (kpair @ X1 @ X0))) = X1) | (kfstpairEq != $true)) & ((kfstpairEq = $true) | (((kfst @ (kpair @ sK1 @ sK0))) != sK1))),
% 0.24/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0),skolemize(X3,sK1)],[f16])).
% 0.24/0.32 thf(f18,plain,(
% 0.24/0.32 ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ (cartprod @ X1 @ X0))) = $true) & (((in @ (kfst @ X2) @ X1)) != $true)) & (kfstpairEq = $true) & (cartprodmempair1 = $true)),
% 0.24/0.32 inference(rectify,[],[f14])).
% 0.24/0.32 thf(f19,plain,(
% 0.24/0.32 ((((in @ sK4 @ (cartprod @ sK3 @ sK2))) = $true) & ($true != ((in @ (kfst @ sK4) @ sK3)))) & (kfstpairEq = $true) & (cartprodmempair1 = $true)),
% 0.24/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f18])).
% 0.24/0.32 thf(f20,plain,(
% 0.24/0.32 (! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X1 @ (cartprod @ X2 @ X0))) != $true) | ? [X3 : $i] : ((((in @ X3 @ X2)) = $true) & ? [X4 : $i] : ((((kpair @ X3 @ X4)) = X1) & ($true = ((in @ X4 @ X0)))))) | (cartprodmempair1 != $true)) & ((cartprodmempair1 = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X1 @ (cartprod @ X2 @ X0))) = $true) & ! [X3 : $i] : ((((in @ X3 @ X2)) != $true) | ! [X4 : $i] : ((((kpair @ X3 @ X4)) != X1) | ($true != ((in @ X4 @ X0)))))))),
% 0.24/0.32 inference(nnf_transformation,[],[f12])).
% 0.24/0.32 thf(f21,plain,(
% 0.24/0.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ (cartprod @ X0 @ X2))) != $true) | ? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & ? [X4 : $i] : ((((kpair @ X3 @ X4)) = X1) & (((in @ X4 @ X2)) = $true)))) | (cartprodmempair1 != $true)) & ((cartprodmempair1 = $true) | ? [X5 : $i,X6 : $i,X7 : $i] : ((((in @ X6 @ (cartprod @ X5 @ X7))) = $true) & ! [X8 : $i] : ((((in @ X8 @ X5)) != $true) | ! [X9 : $i] : ((((kpair @ X8 @ X9)) != X6) | (((in @ X9 @ X7)) != $true)))))),
% 0.24/0.32 inference(rectify,[],[f20])).
% 0.24/0.32 thf(f22,plain,(
% 0.24/0.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ (cartprod @ X0 @ X2))) != $true) | ((((in @ (sK5 @ X2 @ X1 @ X0) @ X0)) = $true) & ((((kpair @ (sK5 @ X2 @ X1 @ X0) @ (sK6 @ X2 @ X1 @ X0))) = X1) & (((in @ (sK6 @ X2 @ X1 @ X0) @ X2)) = $true)))) | (cartprodmempair1 != $true)) & ((cartprodmempair1 = $true) | (($true = ((in @ sK8 @ (cartprod @ sK7 @ sK9)))) & ! [X8 : $i] : ((((in @ X8 @ sK7)) != $true) | ! [X9 : $i] : ((((kpair @ X8 @ X9)) != sK8) | (((in @ X9 @ sK9)) != $true)))))),
% 0.24/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,sK7,sK8,sK9]),skolemize(X4,sK6 @ X2 @ X1 @ X0),skolemize(X4,sK6 @ X2 @ X1 @ X0),skolemize(X5,sK7),skolemize(X6,sK8),skolemize(X7,sK9)],[f21])).
% 0.24/0.32 thf(f24,plain,(
% 0.24/0.32 ( ! [X0 : $i,X1 : $i] : ((((kfst @ (kpair @ X1 @ X0))) = X1) | (kfstpairEq != $true)) )),
% 0.24/0.32 inference(cnf_transformation,[],[f17])).
% 0.24/0.32 thf(f25,plain,(
% 0.24/0.32 (cartprodmempair1 = $true)),
% 0.24/0.32 inference(cnf_transformation,[],[f19])).
% 0.24/0.32 thf(f26,plain,(
% 0.24/0.32 (kfstpairEq = $true)),
% 0.24/0.32 inference(cnf_transformation,[],[f19])).
% 0.24/0.32 thf(f27,plain,(
% 0.24/0.32 ($true != ((in @ (kfst @ sK4) @ sK3)))),
% 0.24/0.32 inference(cnf_transformation,[],[f19])).
% 0.24/0.32 thf(f28,plain,(
% 0.24/0.32 (((in @ sK4 @ (cartprod @ sK3 @ sK2))) = $true)),
% 0.24/0.32 inference(cnf_transformation,[],[f19])).
% 0.24/0.32 thf(f29,plain,(
% 0.24/0.32 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 0.24/0.32 inference(cnf_transformation,[],[f10])).
% 0.24/0.32 thf(f33,plain,(
% 0.24/0.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (cartprod @ X0 @ X2))) != $true) | (((kpair @ (sK5 @ X2 @ X1 @ X0) @ (sK6 @ X2 @ X1 @ X0))) = X1) | (cartprodmempair1 != $true)) )),
% 0.24/0.32 inference(cnf_transformation,[],[f22])).
% 0.24/0.32 thf(f34,plain,(
% 0.24/0.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (cartprod @ X0 @ X2))) != $true) | (((in @ (sK5 @ X2 @ X1 @ X0) @ X0)) = $true) | (cartprodmempair1 != $true)) )),
% 0.24/0.32 inference(cnf_transformation,[],[f22])).
% 0.24/0.32 thf(f37,plain,(
% 0.24/0.32 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((kfst @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ X1 @ X0))) = X1)) )),
% 0.24/0.32 inference(definition_unfolding,[],[f24,f29,f26])).
% 0.24/0.32 thf(f39,plain,(
% 0.24/0.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (cartprod @ X0 @ X2))) != $true) | (((in @ (sK5 @ X2 @ X1 @ X0) @ X0)) = $true) | ($true != $true)) )),
% 0.24/0.32 inference(definition_unfolding,[],[f34,f25])).
% 0.24/0.32 thf(f40,plain,(
% 0.24/0.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | (((in @ X1 @ (cartprod @ X0 @ X2))) != $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ (sK5 @ X2 @ X1 @ X0) @ (sK6 @ X2 @ X1 @ X0))) = X1)) )),
% 0.24/0.32 inference(definition_unfolding,[],[f33,f29,f25])).
% 0.24/0.32 thf(f45,plain,(
% 0.24/0.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ (sK5 @ X2 @ X1 @ X0) @ (sK6 @ X2 @ X1 @ X0))) = X1) | (((in @ X1 @ (cartprod @ X0 @ X2))) != $true)) )),
% 0.24/0.32 inference(trivial_inequality_removal,[],[f40])).
% 0.24/0.32 thf(f46,plain,(
% 0.24/0.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (cartprod @ X0 @ X2))) != $true) | (((setadjoin @ (setadjoin @ (sK5 @ X2 @ X1 @ X0) @ emptyset) @ (setadjoin @ (setadjoin @ (sK5 @ X2 @ X1 @ X0) @ (setadjoin @ (sK6 @ X2 @ X1 @ X0) @ emptyset)) @ emptyset))) = X1)) )),
% 0.24/0.32 inference(beta-eta_normalization,[],[f45])).
% 0.24/0.32 thf(f47,plain,(
% 0.24/0.32 ( ! [X0 : $i,X1 : $i] : ((((kfst @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ X1 @ X0))) = X1)) )),
% 0.24/0.32 inference(trivial_inequality_removal,[],[f37])).
% 0.24/0.32 thf(f48,plain,(
% 0.24/0.32 ( ! [X0 : $i,X1 : $i] : ((((kfst @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))) = X1)) )),
% 0.24/0.32 inference(beta-eta_normalization,[],[f47])).
% 0.24/0.32 thf(f49,plain,(
% 0.24/0.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (cartprod @ X0 @ X2))) != $true) | (((in @ (sK5 @ X2 @ X1 @ X0) @ X0)) = $true)) )),
% 0.24/0.32 inference(trivial_inequality_removal,[],[f39])).
% 0.24/0.32 thf(f52,plain,(
% 0.24/0.32 (((in @ (sK5 @ sK2 @ sK4 @ sK3) @ sK3)) = $true) | ($true != $true)),
% 0.24/0.32 inference(constrained_superposition,[],[f49,f28])).
% 0.24/0.32 thf(f53,plain,(
% 0.24/0.32 (((in @ (sK5 @ sK2 @ sK4 @ sK3) @ sK3)) = $true)),
% 0.24/0.32 inference(trivial_inequality_removal,[],[f52])).
% 0.24/0.32 thf(f54,plain,(
% 0.24/0.32 ($true != $true) | (((setadjoin @ (setadjoin @ (sK5 @ sK2 @ sK4 @ sK3) @ emptyset) @ (setadjoin @ (setadjoin @ (sK5 @ sK2 @ sK4 @ sK3) @ (setadjoin @ (sK6 @ sK2 @ sK4 @ sK3) @ emptyset)) @ emptyset))) = sK4)),
% 0.24/0.32 inference(constrained_superposition,[],[f46,f28])).
% 0.24/0.32 thf(f55,plain,(
% 0.24/0.32 (((setadjoin @ (setadjoin @ (sK5 @ sK2 @ sK4 @ sK3) @ emptyset) @ (setadjoin @ (setadjoin @ (sK5 @ sK2 @ sK4 @ sK3) @ (setadjoin @ (sK6 @ sK2 @ sK4 @ sK3) @ emptyset)) @ emptyset))) = sK4)),
% 0.24/0.32 inference(trivial_inequality_removal,[],[f54])).
% 0.24/0.32 thf(f57,plain,(
% 0.24/0.32 (((kfst @ sK4)) = ((sK5 @ sK2 @ sK4 @ sK3)))),
% 0.24/0.32 inference(constrained_superposition,[],[f48,f55])).
% 0.24/0.32 thf(f60,plain,(
% 0.24/0.32 ($true = ((in @ (kfst @ sK4) @ sK3)))),
% 0.24/0.32 inference(constrained_superposition,[],[f53,f57])).
% 0.24/0.32 thf(f61,plain,(
% 0.24/0.32 $false),
% 0.24/0.32 inference(forward_subsumption_resolution,[],[f60,f27])).
% 0.24/0.32 % SZS output end Proof for theBenchmark
% 0.24/0.32 % (763306)------------------------------
% 0.24/0.32 % (763306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.32 % (763306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.32 % (763306)CaDiCaL version: 2.1.3
% 0.24/0.32 % (763306)Termination reason: Refutation
% 0.24/0.32 % (763306)Time elapsed: 0.006 s
% 0.24/0.32 % (763306)Peak memory usage: 12 MB
% 0.24/0.32 % (763306)Instructions burned: 8 (million)
% 0.24/0.32 % (763301)Success in time 0.053 s
% 0.24/0.32 % Vampire exiting
%------------------------------------------------------------------------------