%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU630^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 08:32:45 AM UTC 2026
% Result : Theorem 0.34s 0.42s
% Output : Refutation 0.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU630^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.30 % Computer : n001.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8046.5625MB
% 0.12/0.30 % OS : Linux 6.8.0-71-generic
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Sep 29 14:06:17 UTC 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.30/0.35 Running first-order model finding
% 0.30/0.35 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.34/0.42 % (1290151)Will run a generic schedule for satisfiability detection.
% 0.34/0.42 % (1290157)% WARNING: option uhcvi not known.
% 0.34/0.42 % (1290157)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2377145718:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.34/0.42 % (1290157)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.34/0.42 % (1290157)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.34/0.42 % (1290162)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3316169541:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.34/0.42 % (1290157) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1290151-1290157"...
% 0.34/0.42 % (1290156)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3648208628_2999 on theBenchmark for (2999ds/0Mi)
% 0.34/0.42 % (1290157)...printing done.
% 0.34/0.42 % (1290158)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2720670611:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.34/0.42 % (1290157)Refutation found. Thanks to Tanya!
% 0.34/0.42 % SZS status Theorem for theBenchmark
% 0.34/0.42 % SZS output start Proof for theBenchmark
% 0.34/0.42 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.34/0.42 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.34/0.42 thf(func_def_2, type, setadjoin: ($i > $i > $i)).
% 0.34/0.42 thf(func_def_3, type, powerset: ($i > $i)).
% 0.34/0.42 thf(func_def_4, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.34/0.42 thf(func_def_5, type, dsetconstrI: $o).
% 0.34/0.42 thf(func_def_7, type, binunion: ($i > $i > $i)).
% 0.34/0.42 thf(func_def_8, type, kpair: ($i > $i > $i)).
% 0.34/0.42 thf(func_def_9, type, cartprod: ($i > $i > $i)).
% 0.34/0.42 thf(func_def_10, type, ubforcartprodlem3: $o).
% 0.34/0.42 thf(func_def_11, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.34/0.42 thf(func_def_12, type, vIMP: ($o > $o > $o)).
% 0.34/0.42 thf(func_def_13, type, db2: !>[X0: $tType]:(X0)).
% 0.34/0.42 thf(func_def_14, type, db0: !>[X0: $tType]:(X0)).
% 0.34/0.42 thf(func_def_15, type, db1: !>[X0: $tType]:(X0)).
% 0.34/0.42 thf(func_def_16, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.34/0.42 thf(func_def_17, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.34/0.42 thf(func_def_18, type, vAND: ($o > $o > $o)).
% 0.34/0.42 thf(func_def_19, type, db3: !>[X0: $tType]:(X0)).
% 0.34/0.42 thf(func_def_20, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.34/0.42 thf(func_def_27, type, vNOT: ($o > $o)).
% 0.34/0.42 thf(f1,axiom,(
% 0.34/0.42 (dsetconstrI = ! [X0 : $i,X1 : ($i > $o),X2 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))))))),
% 0.34/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI)).
% 0.34/0.42 thf(f2,axiom,(
% 0.34/0.42 (kpair = (^[X0 : $i, X1 : $i] : ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))))),
% 0.34/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpair)).
% 0.34/0.42 thf(f3,axiom,(
% 0.34/0.42 (cartprod = (^[X0 : $i, X1 : $i] : ((dsetconstr @ (powerset @ (powerset @ (binunion @ X0 @ X1))) @ (^[X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : ((X2 = ((kpair @ X3 @ X4))) & (in @ X4 @ X1)) & (in @ X3 @ X0))))))))),
% 0.34/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprod)).
% 0.34/0.42 thf(f4,axiom,(
% 0.34/0.42 (ubforcartprodlem3 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X0 @ X1)))))))),
% 0.34/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3)).
% 0.34/0.42 thf(f5,conjecture,(
% 0.34/0.42 dsetconstrI => (ubforcartprodlem3 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1)))))),
% 0.34/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairin)).
% 0.34/0.42 thf(f6,negated_conjecture,(
% 0.34/0.42 ~(dsetconstrI => (ubforcartprodlem3 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1))))))),
% 0.34/0.42 inference(negated_conjecture,[status(cth)],[f5])).
% 0.34/0.42 thf(f7,plain,(
% 0.34/0.42 (dsetconstrI = ! [X0 : $i,X1 : ($i > $o),X2 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : ((X1 @ X3))))))))),
% 0.34/0.42 inference(rectify,[],[f1])).
% 0.34/0.42 thf(f8,plain,(
% 0.34/0.42 (dsetconstrI = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3))))))))))))))),
% 0.34/0.42 inference(fool_elimination,[],[f7])).
% 0.34/0.42 thf(f9,plain,(
% 0.34/0.42 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 0.34/0.42 inference(fool_elimination,[],[f2])).
% 0.34/0.42 thf(f10,plain,(
% 0.34/0.42 (cartprod = (^[X0 : $i, X1 : $i] : ((dsetconstr @ (powerset @ (powerset @ (binunion @ X0 @ X1))) @ (^[X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : ((X2 = ((kpair @ X3 @ X4))) & (in @ X4 @ X1)) & (in @ X3 @ X0))))))))),
% 0.34/0.42 inference(rectify,[],[f3])).
% 0.34/0.42 thf(f11,plain,(
% 0.34/0.42 (cartprod = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))),
% 0.34/0.42 inference(fool_elimination,[],[f10])).
% 0.34/0.42 thf(f12,plain,(
% 0.34/0.42 (ubforcartprodlem3 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X0 @ X1)))))))),
% 0.34/0.42 inference(rectify,[],[f4])).
% 0.34/0.42 thf(f13,plain,(
% 0.34/0.42 (ubforcartprodlem3 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1))))))))))))))))),
% 0.34/0.42 inference(fool_elimination,[],[f12])).
% 0.34/0.42 thf(f14,plain,(
% 0.34/0.42 ~(dsetconstrI => (ubforcartprodlem3 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1))))))),
% 0.34/0.42 inference(rectify,[],[f6])).
% 0.34/0.42 thf(f15,plain,(
% 0.34/0.42 ~((dsetconstrI = $true) => ((ubforcartprodlem3 = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) = $true) => ! [X3 : $i] : ((((in @ X3 @ X1)) = $true) => (((in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1))) = $true)))))),
% 0.34/0.42 inference(fool_elimination,[],[f14])).
% 0.34/0.42 thf(f16,plain,(
% 0.34/0.42 (? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : ((((in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1))) != $true) & (((in @ X3 @ X1)) = $true)) & (((in @ X2 @ X0)) = $true)) & (ubforcartprodlem3 = $true)) & (dsetconstrI = $true)),
% 0.34/0.42 inference(ennf_transformation,[],[f15])).
% 0.34/0.42 thf(f17,plain,(
% 0.34/0.42 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : ((((in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1))) != $true) & (((in @ X3 @ X1)) = $true)) & (((in @ X2 @ X0)) = $true)) & (ubforcartprodlem3 = $true) & (dsetconstrI = $true)),
% 0.34/0.42 inference(flattening,[],[f16])).
% 0.34/0.42 thf(f18,plain,(
% 0.34/0.42 ((($true != ((in @ (kpair @ sK2 @ sK3) @ (cartprod @ sK0 @ sK1)))) & ($true = ((in @ sK3 @ sK1)))) & ($true = ((in @ sK2 @ sK0)))) & (ubforcartprodlem3 = $true) & (dsetconstrI = $true)),
% 0.34/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f17])).
% 0.34/0.42 thf(f19,plain,(
% 0.34/0.42 (dsetconstrI = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3))))))))))))))),
% 0.34/0.42 inference(cnf_transformation,[],[f8])).
% 0.34/0.42 thf(f20,plain,(
% 0.34/0.42 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 0.34/0.42 inference(cnf_transformation,[],[f9])).
% 0.34/0.42 thf(f21,plain,(
% 0.34/0.42 (cartprod = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))),
% 0.34/0.42 inference(cnf_transformation,[],[f11])).
% 0.34/0.42 thf(f22,plain,(
% 0.34/0.42 (ubforcartprodlem3 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1))))))))))))))))),
% 0.34/0.42 inference(cnf_transformation,[],[f13])).
% 0.34/0.42 thf(f23,plain,(
% 0.34/0.42 (dsetconstrI = $true)),
% 0.34/0.42 inference(cnf_transformation,[],[f18])).
% 0.34/0.42 thf(f24,plain,(
% 0.34/0.42 (ubforcartprodlem3 = $true)),
% 0.34/0.42 inference(cnf_transformation,[],[f18])).
% 0.34/0.42 thf(f25,plain,(
% 0.34/0.42 ($true = ((in @ sK2 @ sK0)))),
% 0.34/0.42 inference(cnf_transformation,[],[f18])).
% 0.34/0.42 thf(f26,plain,(
% 0.34/0.42 ($true = ((in @ sK3 @ sK1)))),
% 0.34/0.42 inference(cnf_transformation,[],[f18])).
% 0.34/0.42 thf(f27,plain,(
% 0.34/0.42 ($true != ((in @ (kpair @ sK2 @ sK3) @ (cartprod @ sK0 @ sK1))))),
% 0.34/0.42 inference(cnf_transformation,[],[f18])).
% 0.34/0.42 thf(f29,definition,(
% 0.34/0.42 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.34/0.42 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.34/0.42 thf(f30,plain,(
% 0.34/0.42 (cartprod = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & (((^[Y5 : $i]: ((^[Y6 : $i]: (setadjoin @ (setadjoin @ Y5 @ emptyset) @ (setadjoin @ (setadjoin @ Y5 @ (setadjoin @ Y6 @ emptyset)) @ emptyset))))) @ Y3 @ Y4) = Y2)))))))))))))),
% 0.34/0.42 inference(definition_unfolding,[],[f21,f20])).
% 0.34/0.42 thf(f31,plain,(
% 0.34/0.42 (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3))))))))))))) = $true)),
% 0.34/0.42 inference(definition_unfolding,[],[f19,f23])).
% 0.34/0.42 thf(f32,plain,(
% 0.34/0.42 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ ((^[Y4 : $i]: ((^[Y5 : $i]: (setadjoin @ (setadjoin @ Y4 @ emptyset) @ (setadjoin @ (setadjoin @ Y4 @ (setadjoin @ Y5 @ emptyset)) @ emptyset))))) @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1))))))))))))))))),
% 0.34/0.42 inference(definition_unfolding,[],[f22,f24,f20])).
% 0.34/0.42 thf(f33,plain,(
% 0.34/0.42 ($true != ((in @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ sK2 @ sK3) @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) & (((^[Y5 : $i]: ((^[Y6 : $i]: (setadjoin @ (setadjoin @ Y5 @ emptyset) @ (setadjoin @ (setadjoin @ Y5 @ (setadjoin @ Y6 @ emptyset)) @ emptyset))))) @ Y3 @ Y4) = Y2)))))))))))) @ sK0 @ sK1))))),
% 0.34/0.42 inference(definition_unfolding,[],[f27,f20,f30])).
% 0.34/0.42 thf(f34,plain,(
% 0.34/0.42 ($true != ((in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (dsetconstr @ (powerset @ (powerset @ (binunion @ sK0 @ sK1))) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) & (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK1) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0))))))))))))),
% 0.34/0.42 inference(beta-eta_normalization,[],[f33])).
% 0.34/0.42 thf(f35,plain,(
% 0.34/0.42 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ ((^[Y4 : $i]: ((^[Y5 : $i]: (setadjoin @ (setadjoin @ Y4 @ emptyset) @ (setadjoin @ (setadjoin @ Y4 @ (setadjoin @ Y5 @ emptyset)) @ emptyset))))) @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) @ X1)))) )),
% 0.34/0.42 inference(pi_proxy_clausification,[],[f32])).
% 0.34/0.42 thf(f36,plain,(
% 0.34/0.42 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y1 @ Y0))))))))))))))) )),
% 0.34/0.42 inference(beta-eta_normalization,[],[f35])).
% 0.34/0.42 thf(f37,plain,(
% 0.34/0.42 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y1 @ Y0))))))))))) @ X2)))) )),
% 0.34/0.42 inference(pi_proxy_clausification,[],[f36])).
% 0.34/0.42 thf(f38,plain,(
% 0.34/0.42 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ X2))))))))))))) )),
% 0.34/0.42 inference(beta-eta_normalization,[],[f37])).
% 0.34/0.42 thf(f39,plain,(
% 0.34/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ X2))))))))) @ X3)))) )),
% 0.34/0.42 inference(pi_proxy_clausification,[],[f38])).
% 0.34/0.42 thf(f40,plain,(
% 0.34/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((in @ X1 @ X3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X3 @ X2))))))))))) )),
% 0.34/0.42 inference(beta-eta_normalization,[],[f39])).
% 0.34/0.42 thf(f41,plain,(
% 0.34/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X3 @ X2)))))))))) )),
% 0.34/0.42 inference(imp_proxy_clausification,[],[f40])).
% 0.34/0.42 thf(f42,plain,(
% 0.34/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ X3))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X3 @ X2)))))) @ X4)))) )),
% 0.34/0.42 inference(pi_proxy_clausification,[],[f41])).
% 0.34/0.42 thf(f43,plain,(
% 0.34/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ X3))) | ($true = (((in @ X4 @ X2) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X4 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X3 @ X2)))))))) )),
% 0.34/0.42 inference(beta-eta_normalization,[],[f42])).
% 0.34/0.42 thf(f44,plain,(
% 0.34/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X4 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X3 @ X2)))))) | ($false = ((in @ X4 @ X2))) | ($false = ((in @ X1 @ X3)))) )),
% 0.34/0.42 inference(imp_proxy_clausification,[],[f43])).
% 0.34/0.42 thf(f45,plain,(
% 0.34/0.42 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3))))))))))) @ X1)))) )),
% 0.34/0.42 inference(pi_proxy_clausification,[],[f31])).
% 0.34/0.42 thf(f46,plain,(
% 0.34/0.42 ( ! [X1 : $i] : (($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => ((Y0 @ X1) => (in @ X1 @ (dsetconstr @ Y1 @ Y0))))))))))) )),
% 0.34/0.42 inference(beta-eta_normalization,[],[f45])).
% 0.34/0.42 thf(f47,plain,(
% 0.34/0.42 ( ! [X2 : ($i > $o),X1 : $i] : (($true = (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => ((Y0 @ X1) => (in @ X1 @ (dsetconstr @ Y1 @ Y0))))))) @ X2)))) )),
% 0.34/0.42 inference(pi_proxy_clausification,[],[f46])).
% 0.34/0.42 thf(f48,plain,(
% 0.34/0.42 ( ! [X2 : ($i > $o),X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ Y0) => ((X2 @ X1) => (in @ X1 @ (dsetconstr @ Y0 @ X2))))))))) )),
% 0.34/0.42 inference(beta-eta_normalization,[],[f47])).
% 0.34/0.42 thf(f49,plain,(
% 0.34/0.42 ( ! [X2 : ($i > $o),X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ Y0) => ((X2 @ X1) => (in @ X1 @ (dsetconstr @ Y0 @ X2))))) @ X3)))) )),
% 0.34/0.42 inference(pi_proxy_clausification,[],[f48])).
% 0.34/0.42 thf(f50,plain,(
% 0.34/0.42 ( ! [X2 : ($i > $o),X3 : $i,X1 : $i] : (($true = (((in @ X1 @ X3) => ((X2 @ X1) => (in @ X1 @ (dsetconstr @ X3 @ X2))))))) )),
% 0.34/0.42 inference(beta-eta_normalization,[],[f49])).
% 0.34/0.42 thf(f51,plain,(
% 0.34/0.42 ( ! [X2 : ($i > $o),X3 : $i,X1 : $i] : (($false = ((in @ X1 @ X3))) | ($true = (((X2 @ X1) => (in @ X1 @ (dsetconstr @ X3 @ X2)))))) )),
% 0.34/0.42 inference(imp_proxy_clausification,[],[f50])).
% 0.34/0.42 thf(f52,plain,(
% 0.34/0.42 ( ! [X2 : ($i > $o),X3 : $i,X1 : $i] : (($true = ((in @ X1 @ (dsetconstr @ X3 @ X2)))) | ($false = ((X2 @ X1))) | ($false = ((in @ X1 @ X3)))) )),
% 0.34/0.42 inference(imp_proxy_clausification,[],[f51])).
% 0.34/0.42 thf(f65,plain,(
% 0.34/0.42 ($true != $true) | ($false = ((in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (dsetconstr @ (powerset @ (powerset @ (binunion @ sK0 @ sK1))) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) & (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK1) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0))))))))))))),
% 0.34/0.42 inference(constrained_superposition,[],[f34,f29])).
% 0.34/0.42 thf(f66,plain,(
% 0.34/0.42 ($false = ((in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (dsetconstr @ (powerset @ (powerset @ (binunion @ sK0 @ sK1))) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) & (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK1) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0))))))))))))),
% 0.34/0.42 inference(trivial_inequality_removal,[],[f65])).
% 0.34/0.42 thf(f77,definition,(
% 0.34/0.42 spl4_1 <=> ($false = ((in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1))))))),
% 0.34/0.42 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.34/0.42 thf(f79,plain,(
% 0.34/0.42 ($false = ((in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1)))))) | ~spl4_1),
% 0.34/0.42 inference(avatar_component_clause,[],[f77])).
% 0.34/0.42 thf(f81,definition,(
% 0.34/0.42 spl4_2 <=> ! [X2 : $i,X1 : $i] : ((((setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) != ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) | ($false = ((in @ X2 @ sK1))) | ($false = ((in @ X1 @ sK0))))),
% 0.34/0.42 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.34/0.42 thf(f82,plain,(
% 0.34/0.42 ( ! [X2 : $i,X1 : $i] : ((((setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) != ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) | ($false = ((in @ X2 @ sK1))) | ($false = ((in @ X1 @ sK0)))) ) | ~spl4_2),
% 0.34/0.42 inference(avatar_component_clause,[],[f81])).
% 0.34/0.42 thf(f84,plain,(
% 0.34/0.42 (((in @ sK3 @ sK1)) = $false) | (((in @ sK2 @ sK0)) = $false) | ~spl4_2),
% 0.34/0.42 inference(equality_resolution,[],[f82])).
% 0.34/0.42 thf(f85,plain,(
% 0.34/0.42 ($true = $false) | (((in @ sK3 @ sK1)) = $false) | ~spl4_2),
% 0.34/0.42 inference(forward_demodulation,[],[f84,f25])).
% 0.34/0.42 thf(f86,plain,(
% 0.34/0.42 (((in @ sK3 @ sK1)) = $false) | ~spl4_2),
% 0.34/0.42 inference(trivial_inequality_removal,[],[f85])).
% 0.34/0.42 thf(f87,plain,(
% 0.34/0.42 ($true = $false) | ($false = (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) & (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK1) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))))))) @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))))) | ($false = ((in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1))))))),
% 0.34/0.42 inference(constrained_superposition,[],[f66,f52])).
% 0.34/0.42 thf(f101,plain,(
% 0.34/0.42 ($false = (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) & (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK1) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))))))) @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))))) | ($false = ((in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1))))))),
% 0.34/0.42 inference(trivial_inequality_removal,[],[f87])).
% 0.34/0.42 thf(f102,plain,(
% 0.34/0.42 ($false = ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) & (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK1) & ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))))))))))) | ($false = ((in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1))))))),
% 0.34/0.42 inference(beta-eta_normalization,[],[f101])).
% 0.34/0.42 thf(f103,plain,(
% 0.34/0.42 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((in @ Y0 @ sK0) & (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK1) & ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)))))))) @ X1))) | ($false = ((in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1))))))) )),
% 0.34/0.42 inference(pi_proxy_clausification,[],[f102])).
% 0.34/0.42 thf(f104,plain,(
% 0.34/0.42 ( ! [X1 : $i] : (($false = (((in @ X1 @ sK0) & (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))))))))) | ($false = ((in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1))))))) )),
% 0.34/0.42 inference(beta-eta_normalization,[],[f103])).
% 0.34/0.42 thf(f105,plain,(
% 0.34/0.42 ( ! [X1 : $i] : (($false = ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)))))))) | ($false = ((in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1)))))) | ($false = ((in @ X1 @ sK0)))) )),
% 0.34/0.42 inference(and_proxy_clausification,[],[f104])).
% 0.34/0.42 thf(f106,plain,(
% 0.34/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ((in @ Y0 @ sK1) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))))) @ X2))) | ($false = ((in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1)))))) | ($false = ((in @ X1 @ sK0)))) )),
% 0.34/0.42 inference(pi_proxy_clausification,[],[f105])).
% 0.34/0.42 thf(f107,plain,(
% 0.34/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (((in @ X2 @ sK1) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)))))) | ($false = ((in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1)))))) | ($false = ((in @ X1 @ sK0)))) )),
% 0.34/0.42 inference(beta-eta_normalization,[],[f106])).
% 0.34/0.42 thf(f108,plain,(
% 0.34/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))))) | ($false = ((in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1)))))) | ($false = ((in @ X1 @ sK0))) | ($false = ((in @ X2 @ sK1)))) )),
% 0.34/0.42 inference(and_proxy_clausification,[],[f107])).
% 0.34/0.42 thf(f109,plain,(
% 0.34/0.42 ( ! [X2 : $i,X1 : $i] : ((((setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) != ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) | ($false = ((in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1)))))) | ($false = ((in @ X1 @ sK0))) | ($false = ((in @ X2 @ sK1)))) )),
% 0.34/0.42 inference(equality_proxy_clausification,[],[f108])).
% 0.34/0.42 thf(f110,plain,(
% 0.34/0.42 ($true = $false) | ~spl4_2),
% 0.34/0.42 inference(constrained_superposition,[],[f86,f26])).
% 0.34/0.42 thf(f116,plain,(
% 0.34/0.42 $false | ~spl4_2),
% 0.34/0.42 inference(trivial_inequality_removal,[],[f110])).
% 0.34/0.42 thf(f117,plain,(
% 0.34/0.42 ~spl4_2),
% 0.34/0.42 inference(avatar_contradiction_clause,[],[f116])).
% 0.34/0.42 thf(f119,plain,(
% 0.34/0.42 spl4_1 | spl4_2),
% 0.34/0.42 inference(avatar_split_clause,[],[f109,f81,f77])).
% 0.34/0.42 thf(f122,plain,(
% 0.34/0.42 ($true = $false) | (((in @ sK3 @ sK1)) = $false) | (((in @ sK2 @ sK0)) = $false) | ~spl4_1),
% 0.34/0.42 inference(constrained_superposition,[],[f44,f79])).
% 0.34/0.42 thf(f123,plain,(
% 0.34/0.42 (((in @ sK3 @ sK1)) = $false) | (((in @ sK2 @ sK0)) = $false) | ~spl4_1),
% 0.34/0.42 inference(trivial_inequality_removal,[],[f122])).
% 0.34/0.42 thf(f126,plain,(
% 0.34/0.42 ($true = $false) | (((in @ sK3 @ sK1)) = $false) | ~spl4_1),
% 0.34/0.42 inference(forward_demodulation,[],[f123,f25])).
% 0.34/0.42 thf(f127,plain,(
% 0.34/0.42 (((in @ sK3 @ sK1)) = $false) | ~spl4_1),
% 0.34/0.42 inference(trivial_inequality_removal,[],[f126])).
% 0.34/0.42 thf(f130,plain,(
% 0.34/0.42 ($true = $false) | ~spl4_1),
% 0.34/0.42 inference(constrained_superposition,[],[f127,f26])).
% 0.34/0.42 thf(f136,plain,(
% 0.34/0.42 $false | ~spl4_1),
% 0.34/0.42 inference(trivial_inequality_removal,[],[f130])).
% 0.34/0.42 thf(f137,plain,(
% 0.34/0.42 ~spl4_1),
% 0.34/0.42 inference(avatar_contradiction_clause,[],[f136])).
% 0.34/0.42 cnf(s3, plain, ~spl4_2, inference(sat_conversion,[],[f117])).
% 0.34/0.42 cnf(s5, plain, spl4_1 | spl4_2, inference(sat_conversion,[],[f119])).
% 0.34/0.42 cnf(s7, plain, ~spl4_1, inference(sat_conversion,[],[f137])).
% 0.34/0.42 cnf(s8, plain, spl4_2, inference(rat,[],[s5,s7])).
% 0.34/0.42 cnf(s9, plain, $false, inference(rat,[],[s3,s8])).
% 0.34/0.42 thf(f138,plain,(
% 0.34/0.42 $false),
% 0.34/0.42 inference(avatar_sat_refutation,[],[s9])).
% 0.34/0.42 % SZS output end Proof for theBenchmark
% 0.34/0.42 % (1290157)------------------------------
% 0.34/0.42 % (1290157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.42 % (1290157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.42 % (1290157)CaDiCaL version: 2.1.3
% 0.34/0.42 % (1290157)Termination reason: Refutation
% 0.34/0.42 % (1290157)Time elapsed: 0.010 s
% 0.34/0.42 % (1290157)Peak memory usage: 13 MB
% 0.34/0.42 % (1290157)Instructions burned: 18 (million)
% 0.34/0.42 % (1290151)Success in time 0.055 s
% 0.34/0.42 % Vampire exiting
%------------------------------------------------------------------------------