%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU526^2 : 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 : 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 08:32:18 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU526^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n014.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:48:00 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.20/0.27 % (2687513)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (2687528)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=147801171_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.27 % Exception at run slice level
% 0.20/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.27 % (2687530)% WARNING: option uhcvi not known.
% 0.20/0.27 % (2687531)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=572952546:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.27 % (2687530)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2417601217:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.27 % (2687532)dis+10_1_sil=32000:sp=arity:random_seed=3474880412:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.27 % (2687534)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3620698095:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.27 % (2687533)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2434245598:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.27 % (2687530)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.27 % (2687535)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3071852699:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.27 % (2687530)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.27 % (2687533)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.27 % (2687542)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1383365008:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.27 % (2687534) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2687513-2687534"...
% 0.20/0.27 % (2687532) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2687513-2687532"...
% 0.20/0.27 % Exception at run slice level
% 0.20/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.27 % (2687533) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2687513-2687533"...
% 0.20/0.27 % (2687535) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2687513-2687535"...
% 0.20/0.27 % (2687531) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2687513-2687531"...
% 0.20/0.27 % (2687530) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2687513-2687530"...
% 0.20/0.27 % (2687534)...printing done.
% 0.20/0.27 % (2687533)...printing done.
% 0.20/0.27 % (2687532)...printing done.
% 0.20/0.27 % (2687535)...printing done.
% 0.20/0.27 % (2687531)...printing done.
% 0.20/0.27 % (2687530)...printing done.
% 0.20/0.27 % (2687534)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% 0.20/0.27 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.27 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.20/0.27 thf(func_def_2, type, emptysetE: $o).
% 0.20/0.27 thf(func_def_4, type, setext: $o).
% 0.20/0.27 thf(func_def_5, type, nonempty: ($i > $o)).
% 0.20/0.27 thf(func_def_6, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.27 thf(func_def_7, type, vIMP: ($o > $o > $o)).
% 0.20/0.27 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.27 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.27 thf(func_def_10, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.27 thf(func_def_11, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.27 thf(func_def_12, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.27 thf(func_def_13, type, vNOT: ($o > $o)).
% 0.20/0.27 thf(func_def_17, type, sK1: ($i > $i > $i)).
% 0.20/0.27 thf(func_def_18, type, sK2: ($i > $i > $i)).
% 0.20/0.27 thf(f1,axiom,(
% 0.20/0.27 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 0.20/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE)).
% 0.20/0.27 thf(f2,axiom,(
% 0.20/0.27 (setext = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (X0 = X1))))),
% 0.20/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext)).
% 0.20/0.27 thf(f3,axiom,(
% 0.20/0.27 (nonempty = (^[X0 : $i] : ((X0 != emptyset))))),
% 0.20/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty)).
% 0.20/0.27 thf(f4,conjecture,(
% 0.20/0.27 emptysetE => (setext => ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ($true & (in @ X1 @ X0))))),
% 0.20/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness)).
% 0.20/0.28 thf(f5,negated_conjecture,(
% 0.20/0.28 ~(emptysetE => (setext => ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ($true & (in @ X1 @ X0)))))),
% 0.20/0.28 inference(negated_conjecture,[status(cth)],[f4])).
% 0.20/0.28 thf(f6,plain,(
% 0.20/0.28 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 0.20/0.28 inference(rectify,[],[f1])).
% 0.20/0.28 thf(f7,plain,(
% 0.20/0.28 (emptysetE = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))))))),
% 0.20/0.28 inference(fool_elimination,[],[f6])).
% 0.20/0.28 thf(f8,plain,(
% 0.20/0.28 (setext = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => (in @ X3 @ X0)) => (X0 = X1))))),
% 0.20/0.28 inference(rectify,[],[f2])).
% 0.20/0.28 thf(f9,plain,(
% 0.20/0.28 (setext = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0)))))))))),
% 0.20/0.28 inference(fool_elimination,[],[f8])).
% 0.20/0.28 thf(f10,plain,(
% 0.20/0.28 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 0.20/0.28 inference(fool_elimination,[],[f3])).
% 0.20/0.28 thf(f11,plain,(
% 0.20/0.28 ~(emptysetE => (setext => ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ($true & (in @ X1 @ X0)))))),
% 0.20/0.28 inference(rectify,[],[f5])).
% 0.20/0.28 thf(f12,plain,(
% 0.20/0.28 ~((emptysetE = $true) => ((setext = $true) => ! [X0 : $i] : ((((nonempty @ X0)) = $true) => ? [X1 : $i] : ($true & (((in @ X1 @ X0)) = $true)))))),
% 0.20/0.28 inference(fool_elimination,[],[f11])).
% 0.20/0.28 thf(f13,plain,(
% 0.20/0.28 ~((emptysetE = $true) => ((setext = $true) => ! [X0 : $i] : ((((nonempty @ X0)) = $true) => ? [X1 : $i] : (((in @ X1 @ X0)) = $true))))),
% 0.20/0.28 inference(true_and_false_elimination,[],[f12])).
% 0.20/0.28 thf(f14,plain,(
% 0.20/0.28 (? [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0)) != $true) & (((nonempty @ X0)) = $true)) & (setext = $true)) & (emptysetE = $true)),
% 0.20/0.28 inference(ennf_transformation,[],[f13])).
% 0.20/0.28 thf(f15,plain,(
% 0.20/0.28 ? [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0)) != $true) & (((nonempty @ X0)) = $true)) & (setext = $true) & (emptysetE = $true)),
% 0.20/0.28 inference(flattening,[],[f14])).
% 0.20/0.28 thf(f16,plain,(
% 0.20/0.28 (! [X1 : $i] : ($true != ((in @ X1 @ sK0))) & ($true = ((nonempty @ sK0)))) & (setext = $true) & (emptysetE = $true)),
% 0.20/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f15])).
% 0.20/0.28 thf(f17,plain,(
% 0.20/0.28 (emptysetE = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))))))),
% 0.20/0.28 inference(cnf_transformation,[],[f7])).
% 0.20/0.28 thf(f18,plain,(
% 0.20/0.28 (setext = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0)))))))))),
% 0.20/0.28 inference(cnf_transformation,[],[f9])).
% 0.20/0.28 thf(f19,plain,(
% 0.20/0.28 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 0.20/0.28 inference(cnf_transformation,[],[f10])).
% 0.20/0.28 thf(f20,plain,(
% 0.20/0.28 (emptysetE = $true)),
% 0.20/0.28 inference(cnf_transformation,[],[f16])).
% 0.20/0.28 thf(f21,plain,(
% 0.20/0.28 (setext = $true)),
% 0.20/0.28 inference(cnf_transformation,[],[f16])).
% 0.20/0.28 thf(f22,plain,(
% 0.20/0.28 ($true = ((nonempty @ sK0)))),
% 0.20/0.28 inference(cnf_transformation,[],[f16])).
% 0.20/0.28 thf(f23,plain,(
% 0.20/0.28 ( ! [X1 : $i] : (($true != ((in @ X1 @ sK0)))) )),
% 0.20/0.28 inference(cnf_transformation,[],[f16])).
% 0.20/0.28 thf(f25,definition,(
% 0.20/0.28 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.28 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.28 thf(f26,plain,(
% 0.20/0.28 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))))) = $true)),
% 0.20/0.28 inference(definition_unfolding,[],[f17,f20])).
% 0.20/0.28 thf(f27,plain,(
% 0.20/0.28 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0)))))))) = $true)),
% 0.20/0.28 inference(definition_unfolding,[],[f18,f21])).
% 0.20/0.28 thf(f28,plain,(
% 0.20/0.28 ($true = (((^[Y0 : $i]: (~ (emptyset = Y0))) @ sK0)))),
% 0.20/0.28 inference(definition_unfolding,[],[f22,f19])).
% 0.20/0.28 thf(f29,plain,(
% 0.20/0.28 ($true = ((~ (emptyset = sK0))))),
% 0.20/0.28 inference(beta-eta_normalization,[],[f28])).
% 0.20/0.28 thf(f30,plain,(
% 0.20/0.28 ($false = ((emptyset = sK0)))),
% 0.20/0.28 inference(not_proxy_clausification,[],[f29])).
% 0.20/0.28 thf(f31,plain,(
% 0.20/0.28 (emptyset != sK0)),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f30])).
% 0.20/0.28 thf(f32,plain,(
% 0.20/0.28 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) @ X1)))) )),
% 0.20/0.28 inference(pi_proxy_clausification,[],[f27])).
% 0.20/0.28 thf(f33,plain,(
% 0.20/0.28 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (Y0 = X1)))))))) )),
% 0.20/0.28 inference(beta-eta_normalization,[],[f32])).
% 0.20/0.28 thf(f34,plain,(
% 0.20/0.28 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (Y0 = X1)))) @ X2)))) )),
% 0.20/0.28 inference(pi_proxy_clausification,[],[f33])).
% 0.20/0.28 thf(f35,plain,(
% 0.20/0.28 ( ! [X2 : $i,X1 : $i] : (($true = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (X2 = X1)))))) )),
% 0.20/0.28 inference(beta-eta_normalization,[],[f34])).
% 0.20/0.28 thf(f36,plain,(
% 0.20/0.28 ( ! [X2 : $i,X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))))) | ($true = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (X2 = X1))))) )),
% 0.20/0.28 inference(imp_proxy_clausification,[],[f35])).
% 0.20/0.28 thf(f37,plain,(
% 0.20/0.28 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1))) @ (sK1 @ X1 @ X2)))) | ($true = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (X2 = X1))))) )),
% 0.20/0.28 inference(sigma_proxy_clausification,[],[f36])).
% 0.20/0.28 thf(f38,plain,(
% 0.20/0.28 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1))) @ (sK1 @ X1 @ X2)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))))) | ($true = ((X2 = X1)))) )),
% 0.20/0.28 inference(imp_proxy_clausification,[],[f37])).
% 0.20/0.28 thf(f39,plain,(
% 0.20/0.28 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1))) @ (sK1 @ X1 @ X2)))) | ($false = (((^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2))) @ (sK2 @ X1 @ X2)))) | ($true = ((X2 = X1)))) )),
% 0.20/0.28 inference(sigma_proxy_clausification,[],[f38])).
% 0.20/0.28 thf(f40,plain,(
% 0.20/0.28 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1))) @ (sK1 @ X1 @ X2)))) | ($false = (((^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2))) @ (sK2 @ X1 @ X2)))) | (X1 = X2)) )),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f39])).
% 0.20/0.28 thf(f41,plain,(
% 0.20/0.28 ( ! [X2 : $i,X1 : $i] : (($false = (((in @ (sK1 @ X1 @ X2) @ X2) => (in @ (sK1 @ X1 @ X2) @ X1)))) | ($false = (((in @ (sK2 @ X1 @ X2) @ X1) => (in @ (sK2 @ X1 @ X2) @ X2)))) | (X1 = X2)) )),
% 0.20/0.28 inference(beta-eta_normalization,[],[f40])).
% 0.20/0.28 thf(f43,plain,(
% 0.20/0.28 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ (sK1 @ X1 @ X2) @ X2))) | ($false = (((in @ (sK2 @ X1 @ X2) @ X1) => (in @ (sK2 @ X1 @ X2) @ X2)))) | (X1 = X2)) )),
% 0.20/0.28 inference(imp_proxy_clausification,[],[f41])).
% 0.20/0.28 thf(f45,plain,(
% 0.20/0.28 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ (sK2 @ X1 @ X2) @ X1))) | ($true = ((in @ (sK1 @ X1 @ X2) @ X2))) | (X1 = X2)) )),
% 0.20/0.28 inference(imp_proxy_clausification,[],[f43])).
% 0.20/0.28 thf(f48,plain,(
% 0.20/0.28 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))) @ X1)))) )),
% 0.20/0.28 inference(pi_proxy_clausification,[],[f26])).
% 0.20/0.28 thf(f49,plain,(
% 0.20/0.28 ( ! [X1 : $i] : (($true = (((in @ X1 @ emptyset) => (!! @ $o @ (^[Y0 : $o]: (Y0))))))) )),
% 0.20/0.28 inference(beta-eta_normalization,[],[f48])).
% 0.20/0.28 thf(f50,plain,(
% 0.20/0.28 ( ! [X1 : $i] : (($false = ((in @ X1 @ emptyset))) | (((!! @ $o @ (^[Y0 : $o]: (Y0)))) = $true)) )),
% 0.20/0.28 inference(imp_proxy_clausification,[],[f49])).
% 0.20/0.28 thf(f51,plain,(
% 0.20/0.28 ( ! [X2 : $o,X1 : $i] : (($false = ((in @ X1 @ emptyset))) | ($true = (((^[Y0 : $o]: (Y0)) @ X2)))) )),
% 0.20/0.28 inference(pi_proxy_clausification,[],[f50])).
% 0.20/0.28 thf(f52,plain,(
% 0.20/0.28 ( ! [X2 : $o,X1 : $i] : (($false = ((in @ X1 @ emptyset))) | ($true = X2)) )),
% 0.20/0.28 inference(beta-eta_normalization,[],[f51])).
% 0.20/0.28 thf(f54,definition,(
% 0.20/0.28 spl3_1 <=> ! [X2 : $o] : ($true = X2)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.20/0.28 thf(f55,plain,(
% 0.20/0.28 ( ! [X2 : $o] : (($true = X2)) ) | ~spl3_1),
% 0.20/0.28 inference(avatar_component_clause,[],[f54])).
% 0.20/0.28 thf(f57,definition,(
% 0.20/0.28 spl3_2 <=> ! [X1 : $i] : ($false = ((in @ X1 @ emptyset)))),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 0.20/0.28 thf(f58,plain,(
% 0.20/0.28 ( ! [X1 : $i] : (($false = ((in @ X1 @ emptyset)))) ) | ~spl3_2),
% 0.20/0.28 inference(avatar_component_clause,[],[f57])).
% 0.20/0.28 thf(f59,plain,(
% 0.20/0.28 spl3_1 | spl3_2),
% 0.20/0.28 inference(avatar_split_clause,[],[f52,f57,f54])).
% 0.20/0.28 thf(f63,plain,(
% 0.20/0.28 ( ! [X0 : $i] : (($true != $true) | ($false = ((in @ X0 @ sK0)))) )),
% 0.20/0.28 inference(constrained_superposition,[],[f23,f25])).
% 0.20/0.28 thf(f69,plain,(
% 0.20/0.28 ( ! [X0 : $i] : (($false = ((in @ X0 @ sK0)))) )),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f63])).
% 0.20/0.28 thf(f81,plain,(
% 0.20/0.28 ( ! [X0 : $i] : (($true = $false) | ($true = ((in @ (sK1 @ emptyset @ X0) @ X0))) | (emptyset = X0)) ) | ~spl3_2),
% 0.20/0.28 inference(constrained_superposition,[],[f58,f45])).
% 0.20/0.28 thf(f82,plain,(
% 0.20/0.28 ( ! [X0 : $i] : (($true = ((in @ (sK1 @ emptyset @ X0) @ X0))) | (emptyset = X0)) ) | ~spl3_2),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f81])).
% 0.20/0.28 thf(f87,plain,(
% 0.20/0.28 ($true = $false) | (emptyset = sK0) | ~spl3_2),
% 0.20/0.28 inference(constrained_superposition,[],[f82,f69])).
% 0.20/0.28 thf(f92,plain,(
% 0.20/0.28 (emptyset = sK0) | ~spl3_2),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f87])).
% 0.20/0.28 thf(f97,plain,(
% 0.20/0.28 $false | ~spl3_2),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f92,f31])).
% 0.20/0.28 thf(f98,plain,(
% 0.20/0.28 ~spl3_2),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f97])).
% 0.20/0.28 thf(f103,plain,(
% 0.20/0.28 ($true = $false) | ~spl3_1),
% 0.20/0.28 inference(constrained_superposition,[],[f69,f55])).
% 0.20/0.28 thf(f109,plain,(
% 0.20/0.28 $false | ~spl3_1),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f103])).
% 0.20/0.28 thf(f110,plain,(
% 0.20/0.28 ~spl3_1),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f109])).
% 0.20/0.28 cnf(s1, plain, spl3_1 | spl3_2, inference(sat_conversion,[],[f59])).
% 0.20/0.28 cnf(s4, plain, ~spl3_2, inference(sat_conversion,[],[f98])).
% 0.20/0.28 cnf(s6, plain, ~spl3_1, inference(sat_conversion,[],[f110])).
% 0.20/0.28 cnf(s7, plain, $false, inference(rat,[],[s1,s4,s6])).
% 0.20/0.28 thf(f119,plain,(
% 0.20/0.28 $false),
% 0.20/0.28 inference(avatar_sat_refutation,[],[s7])).
% 0.20/0.28 % SZS output end Proof for theBenchmark
% 0.20/0.28 % (2687534)------------------------------
% 0.20/0.28 % (2687534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (2687534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (2687534)CaDiCaL version: 2.1.3
% 0.20/0.28 % (2687534)Termination reason: Refutation
% 0.20/0.28 % (2687534)Time elapsed: 0.006 s
% 0.20/0.28 % (2687534)Peak memory usage: 12 MB
% 0.20/0.28 % (2687534)Instructions burned: 8 (million)
% 0.20/0.28 % (2687513)Success in time 0.045 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------