%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU776^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 08:33:22 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : Refutation 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU776^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n015.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:31:19 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.26 % (3603817)Will run a generic schedule for satisfiability detection.
% 0.07/0.26 % (3603828)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1729399846:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.26 % (3603823)% WARNING: option uhcvi not known.
% 0.07/0.26 % (3603826)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4122537863:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.26 % (3603823)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=209182664:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.26 % (3603824)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4043113164:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.26 % (3603822)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2885236393_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.26 % (3603827)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3837193535:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.26 % (3603828) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3603817-3603828"...
% 0.07/0.26 % (3603826)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.26 % (3603823)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.26 % Exception at run slice level% (3603823)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.07/0.26
% 0.07/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.07/0.26 % (3603828)...printing done.
% 0.07/0.26 % (3603828)Refutation found. Thanks to Tanya!
% 0.07/0.26 % SZS status Theorem for theBenchmark
% 0.07/0.26 % SZS output start Proof for theBenchmark
% 0.07/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.07/0.26 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.07/0.26 thf(func_def_1, type, subset: ($i > $i > $o)).
% 0.07/0.26 thf(func_def_2, type, kpair: ($i > $i > $i)).
% 0.07/0.26 thf(func_def_3, type, cartprod: ($i > $i > $i)).
% 0.07/0.26 thf(func_def_4, type, breln: ($i > $i > $i > $o)).
% 0.07/0.26 thf(func_def_6, type, dpsetconstr: ($i > $i > ($i > $i > $o) > $i)).
% 0.07/0.26 thf(func_def_7, type, dpsetconstrI: $o).
% 0.07/0.26 thf(func_def_8, type, breln1: ($i > $i > $o)).
% 0.07/0.26 thf(func_def_9, type, breln1invset: ($i > $i > $i)).
% 0.07/0.26 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.07/0.26 thf(func_def_11, type, db2: !>[X0: $tType]:(X0)).
% 0.07/0.26 thf(func_def_12, type, db1: !>[X0: $tType]:(X0)).
% 0.07/0.26 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.07/0.26 thf(func_def_14, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.07/0.26 thf(func_def_15, type, vIMP: ($o > $o > $o)).
% 0.07/0.26 thf(func_def_16, type, db3: !>[X0: $tType]:(X0)).
% 0.07/0.26 thf(func_def_17, type, db4: !>[X0: $tType]:(X0)).
% 0.07/0.26 thf(func_def_18, type, db5: !>[X0: $tType]:(X0)).
% 0.07/0.26 thf(func_def_25, type, vNOT: ($o > $o)).
% 0.07/0.26 thf(func_def_26, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.07/0.26 thf(f2,axiom,(
% 0.07/0.26 (dpsetconstrI = ! [X0 : $i,X1 : $i,X2 : ($i > $i > $o),X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X1) => ((X2 @ X3 @ X4) => (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6)))))))))),
% 0.07/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrI)).
% 0.07/0.26 thf(f4,axiom,(
% 0.07/0.26 (breln1invset = (^[X0 : $i, X1 : $i] : ((dpsetconstr @ X0 @ X0 @ (^[X2 : $i, X3 : $i] : ((in @ (kpair @ X3 @ X2) @ X1)))))))),
% 0.07/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1invset)).
% 0.07/0.26 thf(f5,conjecture,(
% 0.07/0.26 dpsetconstrI => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ (kpair @ X2 @ X3) @ X1) => (in @ (kpair @ X3 @ X2) @ (breln1invset @ X0 @ X1))))))),
% 0.07/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1invI)).
% 0.07/0.26 thf(f6,negated_conjecture,(
% 0.07/0.26 ~(dpsetconstrI => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ (kpair @ X2 @ X3) @ X1) => (in @ (kpair @ X3 @ X2) @ (breln1invset @ X0 @ X1)))))))),
% 0.07/0.26 inference(negated_conjecture,[status(cth)],[f5])).
% 0.07/0.26 thf(f8,plain,(
% 0.07/0.26 (dpsetconstrI = ! [X0 : $i,X1 : $i,X2 : ($i > $i > $o),X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X1) => ((X2 @ X3 @ X4) => (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : ((X2 @ X5 @ X6)))))))))),
% 0.07/0.26 inference(rectify,[],[f2])).
% 0.07/0.26 thf(f9,plain,(
% 0.07/0.26 (dpsetconstrI = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y1 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y3 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y1 @ Y5 @ Y6)))))))))))))))))))))),
% 0.07/0.26 inference(fool_elimination,[],[f8])).
% 0.07/0.26 thf(f11,plain,(
% 0.07/0.26 (breln1invset = (^[X0 : $i, X1 : $i] : ((dpsetconstr @ X0 @ X0 @ (^[X2 : $i, X3 : $i] : ((in @ (kpair @ X3 @ X2) @ X1)))))))),
% 0.07/0.26 inference(rectify,[],[f4])).
% 0.07/0.26 thf(f12,plain,(
% 0.07/0.26 (breln1invset = (^[Y0 : $i]: ((^[Y1 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (in @ (kpair @ Y3 @ Y2) @ Y1)))))))))),
% 0.07/0.26 inference(fool_elimination,[],[f11])).
% 0.07/0.26 thf(f13,plain,(
% 0.07/0.26 ~(dpsetconstrI => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ (kpair @ X2 @ X3) @ X1) => (in @ (kpair @ X3 @ X2) @ (breln1invset @ X0 @ X1)))))))),
% 0.07/0.26 inference(rectify,[],[f6])).
% 0.07/0.26 thf(f14,plain,(
% 0.07/0.26 ~((dpsetconstrI = $true) => ! [X0 : $i,X1 : $i] : ((((breln1 @ X0 @ X1)) = $true) => ! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => ! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => ((((in @ (kpair @ X2 @ X3) @ X1)) = $true) => (((in @ (kpair @ X3 @ X2) @ (breln1invset @ X0 @ X1))) = $true))))))),
% 0.07/0.26 inference(fool_elimination,[],[f13])).
% 0.07/0.26 thf(f15,plain,(
% 0.07/0.26 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((((in @ (kpair @ X3 @ X2) @ (breln1invset @ X0 @ X1))) != $true) & (((in @ (kpair @ X2 @ X3) @ X1)) = $true)) & (((in @ X3 @ X0)) = $true)) & (((in @ X2 @ X0)) = $true)) & (((breln1 @ X0 @ X1)) = $true)) & (dpsetconstrI = $true)),
% 0.07/0.26 inference(ennf_transformation,[],[f14])).
% 0.07/0.26 thf(f16,plain,(
% 0.07/0.26 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((((in @ (kpair @ X3 @ X2) @ (breln1invset @ X0 @ X1))) != $true) & (((in @ (kpair @ X2 @ X3) @ X1)) = $true) & (((in @ X3 @ X0)) = $true)) & (((in @ X2 @ X0)) = $true)) & (((breln1 @ X0 @ X1)) = $true)) & (dpsetconstrI = $true)),
% 0.07/0.26 inference(flattening,[],[f15])).
% 0.07/0.26 thf(f17,plain,(
% 0.07/0.26 (((($true != ((in @ (kpair @ sK3 @ sK2) @ (breln1invset @ sK0 @ sK1)))) & ($true = ((in @ (kpair @ sK2 @ sK3) @ sK1))) & ($true = ((in @ sK3 @ sK0)))) & ($true = ((in @ sK2 @ sK0)))) & ($true = ((breln1 @ sK0 @ sK1)))) & (dpsetconstrI = $true)),
% 0.07/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f16])).
% 0.07/0.26 thf(f19,plain,(
% 0.07/0.26 (dpsetconstrI = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y1 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y3 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y1 @ Y5 @ Y6)))))))))))))))))))))),
% 0.07/0.26 inference(cnf_transformation,[],[f9])).
% 0.07/0.26 thf(f21,plain,(
% 0.07/0.26 (breln1invset = (^[Y0 : $i]: ((^[Y1 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (in @ (kpair @ Y3 @ Y2) @ Y1)))))))))),
% 0.07/0.26 inference(cnf_transformation,[],[f12])).
% 0.07/0.26 thf(f22,plain,(
% 0.07/0.26 (dpsetconstrI = $true)),
% 0.07/0.26 inference(cnf_transformation,[],[f17])).
% 0.07/0.26 thf(f24,plain,(
% 0.07/0.26 ($true = ((in @ sK2 @ sK0)))),
% 0.07/0.26 inference(cnf_transformation,[],[f17])).
% 0.07/0.26 thf(f25,plain,(
% 0.07/0.26 ($true = ((in @ sK3 @ sK0)))),
% 0.07/0.26 inference(cnf_transformation,[],[f17])).
% 0.07/0.26 thf(f26,plain,(
% 0.07/0.26 ($true = ((in @ (kpair @ sK2 @ sK3) @ sK1)))),
% 0.07/0.26 inference(cnf_transformation,[],[f17])).
% 0.07/0.26 thf(f27,plain,(
% 0.07/0.26 ($true != ((in @ (kpair @ sK3 @ sK2) @ (breln1invset @ sK0 @ sK1))))),
% 0.07/0.26 inference(cnf_transformation,[],[f17])).
% 0.07/0.26 thf(f29,definition,(
% 0.07/0.26 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.07/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.07/0.26 thf(f31,plain,(
% 0.07/0.26 (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y1 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y3 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y1 @ Y5 @ Y6)))))))))))))))))))) = $true)),
% 0.07/0.26 inference(definition_unfolding,[],[f19,f22])).
% 0.07/0.26 thf(f32,plain,(
% 0.07/0.26 ($true != ((in @ (kpair @ sK3 @ sK2) @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (in @ (kpair @ Y3 @ Y2) @ Y1)))))))) @ sK0 @ sK1))))),
% 0.07/0.26 inference(definition_unfolding,[],[f27,f21])).
% 0.07/0.26 thf(f35,plain,(
% 0.07/0.26 ($true != ((in @ (kpair @ sK3 @ sK2) @ (dpsetconstr @ sK0 @ sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (in @ (kpair @ Y1 @ Y0) @ sK1))))))))),
% 0.07/0.26 inference(beta-eta_normalization,[],[f32])).
% 0.07/0.26 thf(f36,plain,(
% 0.07/0.26 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y1 @ Y0 @ Y4) => (in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y3 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y1 @ Y5 @ Y6)))))))))))))))))) @ X1)))) )),
% 0.07/0.26 inference(pi_proxy_clausification,[],[f31])).
% 0.07/0.26 thf(f37,plain,(
% 0.07/0.26 ( ! [X1 : $i] : (($true = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ X1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ X1 @ Y3) => (in @ (kpair @ X1 @ Y3) @ (dpsetconstr @ Y2 @ Y1 @ Y0)))))))))))))))) )),
% 0.07/0.26 inference(beta-eta_normalization,[],[f36])).
% 0.07/0.26 thf(f38,plain,(
% 0.07/0.26 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ X1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ X1 @ Y3) => (in @ (kpair @ X1 @ Y3) @ (dpsetconstr @ Y2 @ Y1 @ Y0)))))))))))) @ X2)))) )),
% 0.07/0.26 inference(pi_proxy_clausification,[],[f37])).
% 0.07/0.26 thf(f39,plain,(
% 0.07/0.26 ( ! [X2 : ($i > $i > $o),X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((X2 @ X1 @ Y2) => (in @ (kpair @ X1 @ Y2) @ (dpsetconstr @ Y1 @ Y0 @ X2)))))))))))))) )),
% 0.07/0.26 inference(beta-eta_normalization,[],[f38])).
% 0.07/0.26 thf(f40,plain,(
% 0.07/0.26 ( ! [X2 : ($i > $i > $o),X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((X2 @ X1 @ Y2) => (in @ (kpair @ X1 @ Y2) @ (dpsetconstr @ Y1 @ Y0 @ X2)))))))))) @ X3)))) )),
% 0.07/0.26 inference(pi_proxy_clausification,[],[f39])).
% 0.07/0.26 thf(f41,plain,(
% 0.07/0.26 ( ! [X2 : ($i > $i > $o),X3 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => ((X2 @ X1 @ Y1) => (in @ (kpair @ X1 @ Y1) @ (dpsetconstr @ Y0 @ X3 @ X2)))))))))))) )),
% 0.07/0.26 inference(beta-eta_normalization,[],[f40])).
% 0.07/0.26 thf(f42,plain,(
% 0.07/0.26 ( ! [X2 : ($i > $i > $o),X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => ((X2 @ X1 @ Y1) => (in @ (kpair @ X1 @ Y1) @ (dpsetconstr @ Y0 @ X3 @ X2)))))))) @ X4)))) )),
% 0.07/0.26 inference(pi_proxy_clausification,[],[f41])).
% 0.07/0.26 thf(f43,plain,(
% 0.07/0.26 ( ! [X2 : ($i > $i > $o),X3 : $i,X1 : $i,X4 : $i] : (($true = (((in @ X1 @ X4) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => ((X2 @ X1 @ Y0) => (in @ (kpair @ X1 @ Y0) @ (dpsetconstr @ X4 @ X3 @ X2)))))))))) )),
% 0.07/0.26 inference(beta-eta_normalization,[],[f42])).
% 0.07/0.26 thf(f44,plain,(
% 0.07/0.26 ( ! [X2 : ($i > $i > $o),X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ X4))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => ((X2 @ X1 @ Y0) => (in @ (kpair @ X1 @ Y0) @ (dpsetconstr @ X4 @ X3 @ X2))))))))) )),
% 0.07/0.26 inference(imp_proxy_clausification,[],[f43])).
% 0.07/0.26 thf(f45,plain,(
% 0.07/0.26 ( ! [X2 : ($i > $i > $o),X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((in @ X1 @ X4))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X3) => ((X2 @ X1 @ Y0) => (in @ (kpair @ X1 @ Y0) @ (dpsetconstr @ X4 @ X3 @ X2))))) @ X5)))) )),
% 0.07/0.26 inference(pi_proxy_clausification,[],[f44])).
% 0.07/0.26 thf(f46,plain,(
% 0.07/0.26 ( ! [X2 : ($i > $i > $o),X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((in @ X1 @ X4))) | ($true = (((in @ X5 @ X3) => ((X2 @ X1 @ X5) => (in @ (kpair @ X1 @ X5) @ (dpsetconstr @ X4 @ X3 @ X2))))))) )),
% 0.07/0.26 inference(beta-eta_normalization,[],[f45])).
% 0.07/0.26 thf(f47,plain,(
% 0.07/0.26 ( ! [X2 : ($i > $i > $o),X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((in @ X1 @ X4))) | ($false = ((in @ X5 @ X3))) | ($true = (((X2 @ X1 @ X5) => (in @ (kpair @ X1 @ X5) @ (dpsetconstr @ X4 @ X3 @ X2)))))) )),
% 0.07/0.26 inference(imp_proxy_clausification,[],[f46])).
% 0.07/0.26 thf(f48,plain,(
% 0.07/0.26 ( ! [X2 : ($i > $i > $o),X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((X2 @ X1 @ X5))) | ($true = ((in @ (kpair @ X1 @ X5) @ (dpsetconstr @ X4 @ X3 @ X2)))) | ($false = ((in @ X5 @ X3))) | ($false = ((in @ X1 @ X4)))) )),
% 0.07/0.26 inference(imp_proxy_clausification,[],[f47])).
% 0.07/0.26 thf(f56,plain,(
% 0.07/0.26 ($true != $true) | ($false = ((in @ (kpair @ sK3 @ sK2) @ (dpsetconstr @ sK0 @ sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (in @ (kpair @ Y1 @ Y0) @ sK1))))))))),
% 0.07/0.26 inference(constrained_superposition,[],[f35,f29])).
% 0.07/0.26 thf(f57,plain,(
% 0.07/0.26 ($false = ((in @ (kpair @ sK3 @ sK2) @ (dpsetconstr @ sK0 @ sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (in @ (kpair @ Y1 @ Y0) @ sK1))))))))),
% 0.07/0.26 inference(trivial_inequality_removal,[],[f56])).
% 0.07/0.26 thf(f83,plain,(
% 0.07/0.26 ($true = $false) | ($false = (((^[Y0 : $i]: ((^[Y1 : $i]: (in @ (kpair @ Y1 @ Y0) @ sK1)))) @ sK3 @ sK2))) | (((in @ sK2 @ sK0)) = $false) | (((in @ sK3 @ sK0)) = $false)),
% 0.07/0.26 inference(constrained_superposition,[],[f48,f57])).
% 0.07/0.26 thf(f168,plain,(
% 0.07/0.26 ($false = (((^[Y0 : $i]: ((^[Y1 : $i]: (in @ (kpair @ Y1 @ Y0) @ sK1)))) @ sK3 @ sK2))) | (((in @ sK2 @ sK0)) = $false) | (((in @ sK3 @ sK0)) = $false)),
% 0.07/0.26 inference(trivial_inequality_removal,[],[f83])).
% 0.07/0.26 thf(f169,plain,(
% 0.07/0.26 (((in @ (kpair @ sK2 @ sK3) @ sK1)) = $false) | (((in @ sK2 @ sK0)) = $false) | (((in @ sK3 @ sK0)) = $false)),
% 0.07/0.26 inference(beta-eta_normalization,[],[f168])).
% 0.07/0.26 thf(f213,definition,(
% 0.07/0.26 spl4_1 <=> (((in @ sK3 @ sK0)) = $false)),
% 0.07/0.26 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.07/0.26 thf(f215,plain,(
% 0.07/0.26 (((in @ sK3 @ sK0)) = $false) | ~spl4_1),
% 0.07/0.26 inference(avatar_component_clause,[],[f213])).
% 0.07/0.26 thf(f217,definition,(
% 0.07/0.26 spl4_2 <=> (((in @ sK2 @ sK0)) = $false)),
% 0.07/0.26 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.07/0.26 thf(f219,plain,(
% 0.07/0.26 (((in @ sK2 @ sK0)) = $false) | ~spl4_2),
% 0.07/0.26 inference(avatar_component_clause,[],[f217])).
% 0.07/0.26 thf(f221,definition,(
% 0.07/0.26 spl4_3 <=> (((in @ (kpair @ sK2 @ sK3) @ sK1)) = $false)),
% 0.07/0.26 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
% 0.07/0.26 thf(f223,plain,(
% 0.07/0.26 (((in @ (kpair @ sK2 @ sK3) @ sK1)) = $false) | ~spl4_3),
% 0.07/0.26 inference(avatar_component_clause,[],[f221])).
% 0.07/0.26 thf(f226,plain,(
% 0.07/0.26 spl4_1 | spl4_2 | spl4_3),
% 0.07/0.26 inference(avatar_split_clause,[],[f169,f221,f217,f213])).
% 0.07/0.26 thf(f238,plain,(
% 0.07/0.26 ($true = $false) | ~spl4_2),
% 0.07/0.26 inference(constrained_superposition,[],[f219,f24])).
% 0.07/0.26 thf(f244,plain,(
% 0.07/0.26 $false | ~spl4_2),
% 0.07/0.26 inference(trivial_inequality_removal,[],[f238])).
% 0.07/0.26 thf(f245,plain,(
% 0.07/0.26 ~spl4_2),
% 0.07/0.26 inference(avatar_contradiction_clause,[],[f244])).
% 0.07/0.26 thf(f257,plain,(
% 0.07/0.26 ($true = $false) | ~spl4_3),
% 0.07/0.26 inference(constrained_superposition,[],[f223,f26])).
% 0.07/0.26 thf(f263,plain,(
% 0.07/0.26 $false | ~spl4_3),
% 0.07/0.26 inference(trivial_inequality_removal,[],[f257])).
% 0.07/0.26 thf(f264,plain,(
% 0.07/0.26 ~spl4_3),
% 0.07/0.26 inference(avatar_contradiction_clause,[],[f263])).
% 0.07/0.26 thf(f265,plain,(
% 0.07/0.26 ($true = $false) | ~spl4_1),
% 0.07/0.26 inference(constrained_superposition,[],[f215,f25])).
% 0.07/0.26 thf(f271,plain,(
% 0.07/0.26 $false | ~spl4_1),
% 0.07/0.26 inference(trivial_inequality_removal,[],[f265])).
% 0.07/0.26 thf(f272,plain,(
% 0.07/0.26 ~spl4_1),
% 0.07/0.26 inference(avatar_contradiction_clause,[],[f271])).
% 0.07/0.26 cnf(s3, plain, spl4_1 | spl4_2 | spl4_3, inference(sat_conversion,[],[f226])).
% 0.07/0.26 cnf(s5, plain, ~spl4_2, inference(sat_conversion,[],[f245])).
% 0.07/0.26 cnf(s7, plain, ~spl4_3, inference(sat_conversion,[],[f264])).
% 0.07/0.26 cnf(s9, plain, ~spl4_1, inference(sat_conversion,[],[f272])).
% 0.07/0.26 cnf(s10, plain, $false, inference(rat,[],[s3,s7,s5,s9])).
% 0.07/0.26 thf(f273,plain,(
% 0.07/0.26 $false),
% 0.07/0.26 inference(avatar_sat_refutation,[],[s10])).
% 0.07/0.26 % SZS output end Proof for theBenchmark
% 0.07/0.26 % (3603828)------------------------------
% 0.07/0.26 % (3603828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (3603828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (3603828)CaDiCaL version: 2.1.3
% 0.07/0.26 % (3603828)Termination reason: Refutation
% 0.07/0.26 % (3603828)Time elapsed: 0.009 s
% 0.07/0.26 % (3603828)Peak memory usage: 13 MB
% 0.07/0.26 % (3603828)Instructions burned: 30 (million)
% 0.07/0.26 % (3603817)Success in time 0.037 s
% 0.07/0.26 % Vampire exiting
%------------------------------------------------------------------------------