%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU670^2 : 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 : 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 08:30:39 AM UTC 2026
% Result : Theorem 0.22s 0.26s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU670^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n014.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:06:45 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 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
% 0.22/0.26 % (2713867)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.26 % (2713884)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1972373726:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.26 % (2713884) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2713867-2713884"...
% 0.22/0.26 % (2713884)...printing done.
% 0.22/0.26 % (2713885)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.26 % (2713885)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
% 0.22/0.26 % (2713884)Refutation found. Thanks to Tanya!
% 0.22/0.26 % SZS status Theorem for theBenchmark
% 0.22/0.26 % SZS output start Proof for theBenchmark
% 0.22/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.26 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.22/0.26 thf(func_def_1, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.22/0.26 thf(func_def_2, type, dsetconstrEL: $o).
% 0.22/0.26 thf(func_def_4, type, kpair: ($i > $i > $i)).
% 0.22/0.26 thf(func_def_5, type, cartprod: ($i > $i > $i)).
% 0.22/0.26 thf(func_def_6, type, cartprodpairmemER: $o).
% 0.22/0.26 thf(func_def_7, type, dpsetconstr: ($i > $i > ($i > $i > $o) > $i)).
% 0.22/0.26 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.26 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.26 thf(func_def_12, type, db2: !>[X0: $tType]:(X0)).
% 0.22/0.26 thf(func_def_13, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.26 thf(func_def_14, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.26 thf(func_def_15, type, vAND: ($o > $o > $o)).
% 0.22/0.26 thf(func_def_16, type, db4: !>[X0: $tType]:(X0)).
% 0.22/0.26 thf(func_def_17, type, db3: !>[X0: $tType]:(X0)).
% 0.22/0.26 thf(func_def_18, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.26 thf(func_def_20, type, sK1: ($i > $i > $o)).
% 0.22/0.26 thf(func_def_26, type, sK7: ($i > $o)).
% 0.22/0.26 thf(func_def_31, type, vNOT: ($o > $o)).
% 0.22/0.26 thf(f1,axiom,(
% 0.22/0.26 (! [X1 : ($i > $o),X0 : $i,X2 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))) => (in @ X2 @ X0)) = dsetconstrEL)),
% 0.22/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL)).
% 0.22/0.26 thf(f2,axiom,(
% 0.22/0.26 (cartprodpairmemER = ! [X2 : $i,X1 : $i,X3 : $i,X0 : $i] : ((in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1)) => (in @ X3 @ X1)))),
% 0.22/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemER)).
% 0.22/0.26 thf(f3,axiom,(
% 0.22/0.26 ((^[X0 : $i, X1 : $i, X2 : ($i > $i > $o)] : ((dsetconstr @ (cartprod @ X0 @ X1) @ (^[X3 : $i] : (? [X4 : $i] : (? [X5 : $i] : ((X3 = ((kpair @ X4 @ X5))) & (in @ X5 @ X1) & (X2 @ X4 @ X5)) & (in @ X4 @ X0))))))) = dpsetconstr)),
% 0.22/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstr)).
% 0.22/0.26 thf(f4,conjecture,(
% 0.22/0.26 dsetconstrEL => (cartprodpairmemER => ! [X4 : $i,X3 : $i,X1 : $i,X2 : ($i > $i > $o),X0 : $i] : ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6))))) => (in @ X4 @ X1)))),
% 0.22/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL2)).
% 0.22/0.26 thf(f5,negated_conjecture,(
% 0.22/0.26 ~(dsetconstrEL => (cartprodpairmemER => ! [X4 : $i,X3 : $i,X1 : $i,X2 : ($i > $i > $o),X0 : $i] : ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6))))) => (in @ X4 @ X1))))),
% 0.22/0.26 inference(negated_conjecture,[status(cth)],[f4])).
% 0.22/0.26 thf(f6,plain,(
% 0.22/0.26 (! [X0 : ($i > $o),X1 : $i,X2 : $i] : ((in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : ((X0 @ X3))))) => (in @ X2 @ X1)) = dsetconstrEL)),
% 0.22/0.26 inference(rectify,[],[f1])).
% 0.22/0.26 thf(f7,plain,(
% 0.22/0.26 ! [X1 : $i,X0 : ($i > $o),X2 : $i] : ((((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true) => (((in @ X2 @ X1)) = $true)) <=> (dsetconstrEL = $true)),
% 0.22/0.26 inference(fool_elimination,[],[f6])).
% 0.22/0.26 thf(f8,plain,(
% 0.22/0.26 ((^[X0 : $i, X1 : $i, X2 : ($i > $i > $o)] : ((dsetconstr @ (cartprod @ X0 @ X1) @ (^[X3 : $i] : (? [X4 : $i] : (? [X5 : $i] : ((X3 = ((kpair @ X4 @ X5))) & (in @ X5 @ X1) & (X2 @ X4 @ X5)) & (in @ X4 @ X0))))))) = dpsetconstr)),
% 0.22/0.26 inference(rectify,[],[f3])).
% 0.22/0.26 thf(f9,plain,(
% 0.22/0.26 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (?? @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) & (in @ Y5 @ Y1)) & ((kpair @ Y4 @ Y5) = Y3)))))))))))))))),
% 0.22/0.26 inference(fool_elimination,[],[f8])).
% 0.22/0.26 thf(f10,plain,(
% 0.22/0.26 ~(dsetconstrEL => (cartprodpairmemER => ! [X0 : $i,X1 : $i,X2 : $i,X3 : ($i > $i > $o),X4 : $i] : ((in @ (kpair @ X1 @ X0) @ (dpsetconstr @ X4 @ X2 @ (^[X5 : $i, X6 : $i] : ((X3 @ X5 @ X6))))) => (in @ X0 @ X2))))),
% 0.22/0.26 inference(rectify,[],[f5])).
% 0.22/0.26 thf(f11,plain,(
% 0.22/0.26 ~((dsetconstrEL = $true) => ((cartprodpairmemER = $true) => ! [X4 : $i,X2 : $i,X3 : ($i > $i > $o),X0 : $i,X1 : $i] : ((((in @ (kpair @ X1 @ X0) @ (dpsetconstr @ X4 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1))))))) = $true) => (((in @ X0 @ X2)) = $true))))),
% 0.22/0.26 inference(fool_elimination,[],[f10])).
% 0.22/0.26 thf(f12,plain,(
% 0.22/0.26 (cartprodpairmemER = ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((in @ (kpair @ X0 @ X2) @ (cartprod @ X3 @ X1)) => (in @ X2 @ X1)))),
% 0.22/0.26 inference(rectify,[],[f2])).
% 0.22/0.26 thf(f13,plain,(
% 0.22/0.26 ! [X2 : $i,X1 : $i,X0 : $i,X3 : $i] : ((((in @ (kpair @ X0 @ X2) @ (cartprod @ X3 @ X1))) = $true) => (((in @ X2 @ X1)) = $true)) <=> (cartprodpairmemER = $true)),
% 0.22/0.26 inference(fool_elimination,[],[f12])).
% 0.22/0.26 thf(f14,plain,(
% 0.22/0.26 (dsetconstrEL = $true) <=> ! [X1 : $i,X2 : $i,X0 : ($i > $o)] : ((((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) != $true) | (((in @ X2 @ X1)) = $true))),
% 0.22/0.26 inference(ennf_transformation,[],[f7])).
% 0.22/0.26 thf(f15,plain,(
% 0.22/0.26 (? [X0 : $i,X3 : ($i > $i > $o),X2 : $i,X4 : $i,X1 : $i] : ((((in @ X0 @ X2)) != $true) & (((in @ (kpair @ X1 @ X0) @ (dpsetconstr @ X4 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1))))))) = $true)) & (cartprodpairmemER = $true)) & (dsetconstrEL = $true)),
% 0.22/0.26 inference(ennf_transformation,[],[f11])).
% 0.22/0.26 thf(f16,plain,(
% 0.22/0.26 (dsetconstrEL = $true) & (cartprodpairmemER = $true) & ? [X0 : $i,X3 : ($i > $i > $o),X2 : $i,X4 : $i,X1 : $i] : ((((in @ X0 @ X2)) != $true) & (((in @ (kpair @ X1 @ X0) @ (dpsetconstr @ X4 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1))))))) = $true))),
% 0.22/0.26 inference(flattening,[],[f15])).
% 0.22/0.26 thf(f17,plain,(
% 0.22/0.26 (cartprodpairmemER = $true) <=> ! [X1 : $i,X0 : $i,X3 : $i,X2 : $i] : ((((in @ (kpair @ X0 @ X2) @ (cartprod @ X3 @ X1))) != $true) | (((in @ X2 @ X1)) = $true))),
% 0.22/0.26 inference(ennf_transformation,[],[f13])).
% 0.22/0.26 thf(f18,plain,(
% 0.22/0.26 (dsetconstrEL = $true) & (cartprodpairmemER = $true) & ? [X0 : $i,X1 : ($i > $i > $o),X2 : $i,X3 : $i,X4 : $i] : ((((in @ X0 @ X2)) != $true) & (((in @ (kpair @ X4 @ X0) @ (dpsetconstr @ X3 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1))))))) = $true))),
% 0.22/0.26 inference(rectify,[],[f16])).
% 0.22/0.26 thf(f19,plain,(
% 0.22/0.26 (dsetconstrEL = $true) & (cartprodpairmemER = $true) & (($true != ((in @ sK0 @ sK2))) & (((in @ (kpair @ sK4 @ sK0) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1))))))) = $true))),
% 0.22/0.26 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)],[f18])).
% 0.22/0.26 thf(f20,plain,(
% 0.22/0.26 ((dsetconstrEL = $true) | ? [X1 : $i,X2 : $i,X0 : ($i > $o)] : ((((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true) & (((in @ X2 @ X1)) != $true))) & (! [X1 : $i,X2 : $i,X0 : ($i > $o)] : ((((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0))))) != $true) | (((in @ X2 @ X1)) = $true)) | (dsetconstrEL != $true))),
% 0.22/0.26 inference(nnf_transformation,[],[f14])).
% 0.22/0.26 thf(f21,plain,(
% 0.22/0.26 ((dsetconstrEL = $true) | ? [X0 : $i,X1 : $i,X2 : ($i > $o)] : (($true = ((in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))))) & (((in @ X1 @ X0)) != $true))) & (! [X3 : $i,X4 : $i,X5 : ($i > $o)] : (($true != ((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))))) | (((in @ X4 @ X3)) = $true)) | (dsetconstrEL != $true))),
% 0.22/0.26 inference(rectify,[],[f20])).
% 0.22/0.26 thf(f22,plain,(
% 0.22/0.26 ((dsetconstrEL = $true) | ((((in @ sK6 @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (sK7 @ Y0))))) = $true) & ($true != ((in @ sK6 @ sK5))))) & (! [X3 : $i,X4 : $i,X5 : ($i > $o)] : (($true != ((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))))) | (((in @ X4 @ X3)) = $true)) | (dsetconstrEL != $true))),
% 0.22/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f21])).
% 0.22/0.26 thf(f23,plain,(
% 0.22/0.26 ((cartprodpairmemER = $true) | ? [X1 : $i,X0 : $i,X3 : $i,X2 : $i] : ((((in @ (kpair @ X0 @ X2) @ (cartprod @ X3 @ X1))) = $true) & (((in @ X2 @ X1)) != $true))) & (! [X1 : $i,X0 : $i,X3 : $i,X2 : $i] : ((((in @ (kpair @ X0 @ X2) @ (cartprod @ X3 @ X1))) != $true) | (((in @ X2 @ X1)) = $true)) | (cartprodpairmemER != $true))),
% 0.22/0.26 inference(nnf_transformation,[],[f17])).
% 0.22/0.26 thf(f24,plain,(
% 0.22/0.26 ((cartprodpairmemER = $true) | ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((((in @ (kpair @ X1 @ X3) @ (cartprod @ X2 @ X0))) = $true) & (((in @ X3 @ X0)) != $true))) & (! [X4 : $i,X5 : $i,X6 : $i,X7 : $i] : ((((in @ (kpair @ X5 @ X7) @ (cartprod @ X6 @ X4))) != $true) | (((in @ X7 @ X4)) = $true)) | (cartprodpairmemER != $true))),
% 0.22/0.26 inference(rectify,[],[f23])).
% 0.22/0.26 thf(f25,plain,(
% 0.22/0.26 ((cartprodpairmemER = $true) | ((((in @ (kpair @ sK9 @ sK11) @ (cartprod @ sK10 @ sK8))) = $true) & (((in @ sK11 @ sK8)) != $true))) & (! [X4 : $i,X5 : $i,X6 : $i,X7 : $i] : ((((in @ (kpair @ X5 @ X7) @ (cartprod @ X6 @ X4))) != $true) | (((in @ X7 @ X4)) = $true)) | (cartprodpairmemER != $true))),
% 0.22/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10),skolemize(X3,sK11)],[f24])).
% 0.22/0.26 thf(f26,plain,(
% 0.22/0.26 (((in @ (kpair @ sK4 @ sK0) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1))))))) = $true)),
% 0.22/0.26 inference(cnf_transformation,[],[f19])).
% 0.22/0.26 thf(f27,plain,(
% 0.22/0.26 ($true != ((in @ sK0 @ sK2)))),
% 0.22/0.26 inference(cnf_transformation,[],[f19])).
% 0.22/0.26 thf(f28,plain,(
% 0.22/0.26 (cartprodpairmemER = $true)),
% 0.22/0.26 inference(cnf_transformation,[],[f19])).
% 0.22/0.26 thf(f29,plain,(
% 0.22/0.26 (dsetconstrEL = $true)),
% 0.22/0.26 inference(cnf_transformation,[],[f19])).
% 0.22/0.26 thf(f30,plain,(
% 0.22/0.26 ( ! [X3 : $i,X4 : $i,X5 : ($i > $o)] : (($true != ((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))))) | (((in @ X4 @ X3)) = $true) | (dsetconstrEL != $true)) )),
% 0.22/0.26 inference(cnf_transformation,[],[f22])).
% 0.22/0.26 thf(f33,plain,(
% 0.22/0.26 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (?? @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) & (in @ Y5 @ Y1)) & ((kpair @ Y4 @ Y5) = Y3)))))))))))))))),
% 0.22/0.26 inference(cnf_transformation,[],[f9])).
% 0.22/0.26 thf(f34,plain,(
% 0.22/0.26 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((in @ (kpair @ X5 @ X7) @ (cartprod @ X6 @ X4))) != $true) | (((in @ X7 @ X4)) = $true) | (cartprodpairmemER != $true)) )),
% 0.22/0.26 inference(cnf_transformation,[],[f25])).
% 0.22/0.26 thf(f38,definition,(
% 0.22/0.26 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.22/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.22/0.26 thf(f39,plain,(
% 0.22/0.26 (((in @ (kpair @ sK4 @ sK0) @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (?? @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) & (in @ Y5 @ Y1)) & ((kpair @ Y4 @ Y5) = Y3)))))))))))))) @ sK3 @ sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1))))))) = $true)),
% 0.22/0.26 inference(definition_unfolding,[],[f26,f33])).
% 0.22/0.26 thf(f42,plain,(
% 0.22/0.26 ( ! [X3 : $i,X4 : $i,X5 : ($i > $o)] : ((((in @ X4 @ X3)) = $true) | ($true != $true) | ($true != ((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0))))))) )),
% 0.22/0.26 inference(definition_unfolding,[],[f30,f29])).
% 0.22/0.26 thf(f45,plain,(
% 0.22/0.26 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != $true) | (((in @ X7 @ X4)) = $true) | (((in @ (kpair @ X5 @ X7) @ (cartprod @ X6 @ X4))) != $true)) )),
% 0.22/0.26 inference(definition_unfolding,[],[f34,f28])).
% 0.22/0.26 thf(f46,plain,(
% 0.22/0.26 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((in @ (kpair @ X5 @ X7) @ (cartprod @ X6 @ X4))) != $true) | (((in @ X7 @ X4)) = $true)) )),
% 0.22/0.26 inference(trivial_inequality_removal,[],[f45])).
% 0.22/0.26 thf(f47,plain,(
% 0.22/0.26 (((in @ (kpair @ sK4 @ sK0) @ (dsetconstr @ (cartprod @ sK3 @ sK2) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) & (?? @ $i @ (^[Y2 : $i]: (((sK1 @ Y1 @ Y2) & (in @ Y2 @ sK2)) & ((kpair @ Y1 @ Y2) = Y0))))))))))) = $true)),
% 0.22/0.26 inference(beta-eta_normalization,[],[f39])).
% 0.22/0.26 thf(f48,plain,(
% 0.22/0.26 ( ! [X3 : $i,X4 : $i,X5 : ($i > $o)] : ((((in @ X4 @ X3)) = $true) | ($true != ((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0))))))) )),
% 0.22/0.26 inference(trivial_inequality_removal,[],[f42])).
% 0.22/0.26 thf(f49,plain,(
% 0.22/0.26 ( ! [X3 : $i,X4 : $i,X5 : ($i > $o)] : ((((in @ X4 @ (dsetconstr @ X3 @ X5))) != $true) | (((in @ X4 @ X3)) = $true)) )),
% 0.22/0.26 inference(beta-eta_normalization,[],[f48])).
% 0.22/0.26 thf(f52,plain,(
% 0.22/0.26 ($false = ((in @ sK0 @ sK2))) | ($true != $true)),
% 0.22/0.26 inference(constrained_superposition,[],[f27,f38])).
% 0.22/0.26 thf(f57,plain,(
% 0.22/0.26 ($false = ((in @ sK0 @ sK2)))),
% 0.22/0.26 inference(trivial_inequality_removal,[],[f52])).
% 0.22/0.26 thf(f64,plain,(
% 0.22/0.26 (((in @ (kpair @ sK4 @ sK0) @ (cartprod @ sK3 @ sK2))) = $true) | ($true != $true)),
% 0.22/0.26 inference(constrained_superposition,[],[f49,f47])).
% 0.22/0.26 thf(f65,plain,(
% 0.22/0.26 (((in @ (kpair @ sK4 @ sK0) @ (cartprod @ sK3 @ sK2))) = $true)),
% 0.22/0.26 inference(trivial_inequality_removal,[],[f64])).
% 0.22/0.26 thf(f68,plain,(
% 0.22/0.26 ($true = ((in @ sK0 @ sK2))) | ($true != $true)),
% 0.22/0.26 inference(constrained_superposition,[],[f46,f65])).
% 0.22/0.26 thf(f69,plain,(
% 0.22/0.26 ($true = ((in @ sK0 @ sK2)))),
% 0.22/0.26 inference(trivial_inequality_removal,[],[f68])).
% 0.22/0.26 thf(f70,plain,(
% 0.22/0.26 ($false = $true)),
% 0.22/0.26 inference(forward_demodulation,[],[f69,f57])).
% 0.22/0.26 thf(f71,plain,(
% 0.22/0.26 $false),
% 0.22/0.26 inference(trivial_inequality_removal,[],[f70])).
% 0.22/0.26 % SZS output end Proof for theBenchmark
% 0.22/0.26 % (2713884)------------------------------
% 0.22/0.26 % (2713884)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.26 % (2713884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.26 % (2713884)CaDiCaL version: 2.1.3
% 0.22/0.26 % (2713884)Termination reason: Refutation
% 0.22/0.26 % (2713884)Time elapsed: 0.003 s
% 0.22/0.26 % (2713884)Peak memory usage: 12 MB
% 0.22/0.26 % (2713884)Instructions burned: 8 (million)
% 0.22/0.26 % (2713867)Success in time 0.026 s
% 0.22/0.26 % Vampire exiting
%------------------------------------------------------------------------------