%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU717^2 : 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 : n002.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 08:33:06 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU717^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 % Computer : n002.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Sep 29 14:17:30 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.24 Running first-order model finding
% 0.07/0.24 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
% 0.23/0.29 % (1353719)Will run a generic schedule for satisfiability detection.
% 0.23/0.29 % (1353730)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2021584234:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.23/0.29 % (1353725)% WARNING: option uhcvi not known.
% 0.23/0.29 % (1353724)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=760705167_2999 on theBenchmark for (2999ds/0Mi)
% 0.23/0.29 % (1353725)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1856761246:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.23/0.29 % (1353726)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3242367572:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.23/0.29 % (1353727)dis+10_1_sil=32000:sp=arity:random_seed=1110246686:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.23/0.29 % (1353725)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.23/0.29 % (1353728)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=946332449:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.23/0.29 % (1353729)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2036661874:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.23/0.29 % Exception at run slice level
% 0.23/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.29 % (1353725)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.23/0.29 % (1353728)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.23/0.29 % (1353730) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1353719-1353730"...
% 0.23/0.29 % (1353730)...printing done.
% 0.23/0.29 % (1353730)Refutation found. Thanks to Tanya!
% 0.23/0.29 % SZS status Theorem for theBenchmark
% 0.23/0.29 % SZS output start Proof for theBenchmark
% 0.23/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.29 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.23/0.29 thf(func_def_1, type, powerset: ($i > $i)).
% 0.23/0.29 thf(func_def_2, type, subset: ($i > $i > $o)).
% 0.23/0.29 thf(func_def_3, type, powersetI1: $o).
% 0.23/0.29 thf(func_def_5, type, subsetTI: $o).
% 0.23/0.29 thf(func_def_6, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.23/0.29 thf(func_def_7, type, vIMP: ($o > $o > $o)).
% 0.23/0.29 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.23/0.29 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.23/0.29 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.23/0.29 thf(func_def_11, type, db2: !>[X0: $tType]:(X0)).
% 0.23/0.29 thf(func_def_12, type, db3: !>[X0: $tType]:(X0)).
% 0.23/0.29 thf(func_def_18, type, vNOT: ($o > $o)).
% 0.23/0.29 thf(func_def_19, type, sK3: ($i > $i > $i > $i)).
% 0.23/0.29 thf(f1,axiom,(
% 0.23/0.29 (powersetI1 = ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))))),
% 0.23/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1)).
% 0.23/0.29 thf(f2,axiom,(
% 0.23/0.29 (subsetTI = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (subset @ X1 @ X2)))))),
% 0.23/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTI)).
% 0.23/0.29 thf(f3,conjecture,(
% 0.23/0.29 powersetI1 => (subsetTI => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (in @ X1 @ (powerset @ X2))))))),
% 0.23/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetTI1)).
% 0.23/0.29 thf(f4,negated_conjecture,(
% 0.23/0.29 ~(powersetI1 => (subsetTI => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (in @ X1 @ (powerset @ X2)))))))),
% 0.23/0.29 inference(negated_conjecture,[status(cth)],[f3])).
% 0.23/0.29 thf(f5,plain,(
% 0.23/0.29 (powersetI1 = ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))))),
% 0.23/0.29 inference(rectify,[],[f1])).
% 0.23/0.29 thf(f6,plain,(
% 0.23/0.29 (powersetI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1)))))))))),
% 0.23/0.29 inference(fool_elimination,[],[f5])).
% 0.23/0.29 thf(f7,plain,(
% 0.23/0.29 (subsetTI = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (subset @ X1 @ X2)))))),
% 0.23/0.29 inference(rectify,[],[f2])).
% 0.23/0.29 thf(f8,plain,(
% 0.23/0.29 (subsetTI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ Y0) => (in @ Y3 @ Y2))))) => (subset @ Y0 @ Y2))))))))))))),
% 0.23/0.29 inference(fool_elimination,[],[f7])).
% 0.23/0.29 thf(f9,plain,(
% 0.23/0.29 ~(powersetI1 => (subsetTI => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (in @ X1 @ (powerset @ X2)))))))),
% 0.23/0.29 inference(rectify,[],[f4])).
% 0.23/0.29 thf(f10,plain,(
% 0.23/0.29 ~((powersetI1 = $true) => ((subsetTI = $true) => ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) => (! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => ((((in @ X3 @ X1)) = $true) => (((in @ X3 @ X2)) = $true))) => (((in @ X1 @ (powerset @ X2))) = $true))))))),
% 0.23/0.29 inference(fool_elimination,[],[f9])).
% 0.23/0.29 thf(f11,plain,(
% 0.23/0.29 (? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((((in @ X1 @ (powerset @ X2))) != $true) & ! [X3 : $i] : (((((in @ X3 @ X2)) = $true) | (((in @ X3 @ X1)) != $true)) | (((in @ X3 @ X0)) != $true))) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (subsetTI = $true)) & (powersetI1 = $true)),
% 0.23/0.29 inference(ennf_transformation,[],[f10])).
% 0.23/0.29 thf(f12,plain,(
% 0.23/0.29 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X1 @ (powerset @ X2))) != $true) & ! [X3 : $i] : ((((in @ X3 @ X2)) = $true) | (((in @ X3 @ X1)) != $true) | (((in @ X3 @ X0)) != $true)) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (subsetTI = $true) & (powersetI1 = $true)),
% 0.23/0.29 inference(flattening,[],[f11])).
% 0.23/0.29 thf(f13,plain,(
% 0.23/0.29 ((($true != ((in @ sK1 @ (powerset @ sK2)))) & ! [X3 : $i] : (($true = ((in @ X3 @ sK2))) | ($true != ((in @ X3 @ sK1))) | ($true != ((in @ X3 @ sK0)))) & ($true = ((in @ sK2 @ (powerset @ sK0))))) & ($true = ((in @ sK1 @ (powerset @ sK0))))) & (subsetTI = $true) & (powersetI1 = $true)),
% 0.23/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f12])).
% 0.23/0.29 thf(f14,plain,(
% 0.23/0.29 (powersetI1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1)))))))))),
% 0.23/0.29 inference(cnf_transformation,[],[f6])).
% 0.23/0.29 thf(f15,plain,(
% 0.23/0.29 (subsetTI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ Y0) => (in @ Y3 @ Y2))))) => (subset @ Y0 @ Y2))))))))))))),
% 0.23/0.29 inference(cnf_transformation,[],[f8])).
% 0.23/0.29 thf(f16,plain,(
% 0.23/0.29 (powersetI1 = $true)),
% 0.23/0.29 inference(cnf_transformation,[],[f13])).
% 0.23/0.29 thf(f17,plain,(
% 0.23/0.29 (subsetTI = $true)),
% 0.23/0.29 inference(cnf_transformation,[],[f13])).
% 0.23/0.29 thf(f18,plain,(
% 0.23/0.29 ($true = ((in @ sK1 @ (powerset @ sK0))))),
% 0.23/0.29 inference(cnf_transformation,[],[f13])).
% 0.23/0.29 thf(f19,plain,(
% 0.23/0.29 ($true = ((in @ sK2 @ (powerset @ sK0))))),
% 0.23/0.29 inference(cnf_transformation,[],[f13])).
% 0.23/0.29 thf(f20,plain,(
% 0.23/0.29 ( ! [X3 : $i] : (($true != ((in @ X3 @ sK1))) | ($true = ((in @ X3 @ sK2))) | ($true != ((in @ X3 @ sK0)))) )),
% 0.23/0.29 inference(cnf_transformation,[],[f13])).
% 0.23/0.29 thf(f21,plain,(
% 0.23/0.29 ($true != ((in @ sK1 @ (powerset @ sK2))))),
% 0.23/0.29 inference(cnf_transformation,[],[f13])).
% 0.23/0.29 thf(f23,definition,(
% 0.23/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.23/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.23/0.29 thf(f24,plain,(
% 0.23/0.29 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1)))))))) = $true)),
% 0.23/0.29 inference(definition_unfolding,[],[f14,f16])).
% 0.23/0.29 thf(f25,plain,(
% 0.23/0.29 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ Y0) => (in @ Y3 @ Y2))))) => (subset @ Y0 @ Y2))))))))))) = $true)),
% 0.23/0.29 inference(definition_unfolding,[],[f15,f17])).
% 0.23/0.29 thf(f26,plain,(
% 0.23/0.29 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ Y0) => (in @ Y3 @ Y2))))) => (subset @ Y0 @ Y2))))))))) @ X1)))) )),
% 0.23/0.29 inference(pi_proxy_clausification,[],[f25])).
% 0.23/0.29 thf(f27,plain,(
% 0.23/0.29 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ X1) => (in @ Y2 @ Y1))))) => (subset @ X1 @ Y1))))))))))) )),
% 0.23/0.29 inference(beta-eta_normalization,[],[f26])).
% 0.23/0.29 thf(f28,plain,(
% 0.23/0.29 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ X1) => (in @ Y2 @ Y1))))) => (subset @ X1 @ Y1))))))) @ X2)))) )),
% 0.23/0.29 inference(pi_proxy_clausification,[],[f27])).
% 0.23/0.29 thf(f29,plain,(
% 0.23/0.29 ( ! [X2 : $i,X1 : $i] : (($true = (((in @ X1 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ Y1 @ X1) => (in @ Y1 @ Y0))))) => (subset @ X1 @ Y0))))))))) )),
% 0.23/0.29 inference(beta-eta_normalization,[],[f28])).
% 0.23/0.29 thf(f30,plain,(
% 0.23/0.29 ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ Y1 @ X1) => (in @ Y1 @ Y0))))) => (subset @ X1 @ Y0)))))))) )),
% 0.23/0.29 inference(imp_proxy_clausification,[],[f29])).
% 0.23/0.29 thf(f31,plain,(
% 0.23/0.29 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ Y1 @ X1) => (in @ Y1 @ Y0))))) => (subset @ X1 @ Y0)))) @ X3)))) )),
% 0.23/0.29 inference(pi_proxy_clausification,[],[f30])).
% 0.23/0.29 thf(f32,plain,(
% 0.23/0.29 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($true = (((in @ X3 @ (powerset @ X2)) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ X1) => (in @ Y0 @ X3))))) => (subset @ X1 @ X3)))))) )),
% 0.23/0.29 inference(beta-eta_normalization,[],[f31])).
% 0.23/0.29 thf(f33,plain,(
% 0.23/0.29 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ X1) => (in @ Y0 @ X3))))) => (subset @ X1 @ X3))))) )),
% 0.23/0.29 inference(imp_proxy_clausification,[],[f32])).
% 0.23/0.29 thf(f34,plain,(
% 0.23/0.29 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ X1) => (in @ Y0 @ X3))))))) | ($true = ((subset @ X1 @ X3)))) )),
% 0.23/0.29 inference(imp_proxy_clausification,[],[f33])).
% 0.23/0.29 thf(f35,plain,(
% 0.23/0.29 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = (((^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ X1) => (in @ Y0 @ X3)))) @ (sK3 @ X3 @ X1 @ X2)))) | ($true = ((subset @ X1 @ X3)))) )),
% 0.23/0.29 inference(sigma_proxy_clausification,[],[f34])).
% 0.23/0.29 thf(f36,plain,(
% 0.23/0.29 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = (((in @ (sK3 @ X3 @ X1 @ X2) @ X2) => ((in @ (sK3 @ X3 @ X1 @ X2) @ X1) => (in @ (sK3 @ X3 @ X1 @ X2) @ X3))))) | ($true = ((subset @ X1 @ X3)))) )),
% 0.23/0.29 inference(beta-eta_normalization,[],[f35])).
% 0.23/0.29 thf(f37,plain,(
% 0.23/0.29 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = (((in @ (sK3 @ X3 @ X1 @ X2) @ X1) => (in @ (sK3 @ X3 @ X1 @ X2) @ X3)))) | ($true = ((subset @ X1 @ X3)))) )),
% 0.23/0.29 inference(imp_proxy_clausification,[],[f36])).
% 0.23/0.29 thf(f38,plain,(
% 0.23/0.29 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((subset @ X1 @ X3))) | ($true = ((in @ (sK3 @ X3 @ X1 @ X2) @ X2))) | ($false = ((in @ X3 @ (powerset @ X2)))) | (((in @ X1 @ (powerset @ X2))) = $false)) )),
% 0.23/0.29 inference(imp_proxy_clausification,[],[f36])).
% 0.23/0.29 thf(f39,plain,(
% 0.23/0.29 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((subset @ X1 @ X3))) | ($false = ((in @ (sK3 @ X3 @ X1 @ X2) @ X3))) | ($false = ((in @ X3 @ (powerset @ X2)))) | (((in @ X1 @ (powerset @ X2))) = $false)) )),
% 0.23/0.29 inference(imp_proxy_clausification,[],[f37])).
% 0.23/0.29 thf(f40,plain,(
% 0.23/0.29 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((subset @ X1 @ X3))) | ($true = ((in @ (sK3 @ X3 @ X1 @ X2) @ X1))) | ($false = ((in @ X3 @ (powerset @ X2)))) | (((in @ X1 @ (powerset @ X2))) = $false)) )),
% 0.23/0.29 inference(imp_proxy_clausification,[],[f37])).
% 0.23/0.29 thf(f41,plain,(
% 0.23/0.29 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1)))))) @ X1)))) )),
% 0.23/0.29 inference(pi_proxy_clausification,[],[f24])).
% 0.23/0.29 thf(f42,plain,(
% 0.23/0.29 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((subset @ X1 @ Y0) => (in @ X1 @ (powerset @ Y0)))))))) )),
% 0.23/0.29 inference(beta-eta_normalization,[],[f41])).
% 0.23/0.29 thf(f43,plain,(
% 0.23/0.29 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((subset @ X1 @ Y0) => (in @ X1 @ (powerset @ Y0)))) @ X2)))) )),
% 0.23/0.29 inference(pi_proxy_clausification,[],[f42])).
% 0.23/0.29 thf(f44,plain,(
% 0.23/0.29 ( ! [X2 : $i,X1 : $i] : (($true = (((subset @ X1 @ X2) => (in @ X1 @ (powerset @ X2)))))) )),
% 0.23/0.29 inference(beta-eta_normalization,[],[f43])).
% 0.23/0.29 thf(f45,plain,(
% 0.23/0.29 ( ! [X2 : $i,X1 : $i] : ((((subset @ X1 @ X2)) = $false) | (((in @ X1 @ (powerset @ X2))) = $true)) )),
% 0.23/0.29 inference(imp_proxy_clausification,[],[f44])).
% 0.23/0.29 thf(f48,plain,(
% 0.23/0.29 ($true != $true) | (((in @ sK1 @ (powerset @ sK2))) = $false)),
% 0.23/0.29 inference(constrained_superposition,[],[f21,f23])).
% 0.23/0.29 thf(f50,plain,(
% 0.23/0.29 ( ! [X0 : $i] : (($true != $true) | ($true = ((in @ X0 @ sK2))) | ($true != ((in @ X0 @ sK0))) | ($false = ((in @ X0 @ sK1)))) )),
% 0.23/0.29 inference(constrained_superposition,[],[f20,f23])).
% 0.23/0.29 thf(f52,plain,(
% 0.23/0.29 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK0))) | ($true = ((in @ X0 @ sK2))) | ($false = ((in @ X0 @ sK1)))) )),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f50])).
% 0.23/0.29 thf(f54,plain,(
% 0.23/0.29 (((in @ sK1 @ (powerset @ sK2))) = $false)),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f48])).
% 0.23/0.29 thf(f66,plain,(
% 0.23/0.29 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = ((in @ (sK3 @ X0 @ X1 @ sK0) @ sK2))) | ($false = ((in @ (sK3 @ X0 @ X1 @ sK0) @ sK1))) | (((subset @ X1 @ X0)) = $true) | ($false = ((in @ X0 @ (powerset @ sK0)))) | ($false = ((in @ X1 @ (powerset @ sK0))))) )),
% 0.23/0.29 inference(constrained_superposition,[],[f52,f38])).
% 0.23/0.29 thf(f69,plain,(
% 0.23/0.29 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK3 @ X0 @ X1 @ sK0) @ sK2))) | (((subset @ X1 @ X0)) = $true) | ($false = ((in @ (sK3 @ X0 @ X1 @ sK0) @ sK1))) | ($false = ((in @ X0 @ (powerset @ sK0)))) | ($false = ((in @ X1 @ (powerset @ sK0))))) )),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f66])).
% 0.23/0.29 thf(f98,plain,(
% 0.23/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | ($true = ((in @ X0 @ (powerset @ X1)))) | ($true = ((in @ (sK3 @ X1 @ X0 @ X2) @ X0))) | (((in @ X1 @ (powerset @ X2))) = $false) | ($false = ((in @ X0 @ (powerset @ X2))))) )),
% 0.23/0.29 inference(constrained_superposition,[],[f45,f40])).
% 0.23/0.29 thf(f106,plain,(
% 0.23/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK3 @ X1 @ X0 @ X2) @ X0))) | ($true = ((in @ X0 @ (powerset @ X1)))) | (((in @ X1 @ (powerset @ X2))) = $false) | ($false = ((in @ X0 @ (powerset @ X2))))) )),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f98])).
% 0.23/0.29 thf(f285,plain,(
% 0.23/0.29 ( ! [X0 : $i] : (($true = $false) | ($true = ((subset @ X0 @ sK2))) | ($false = ((in @ (sK3 @ sK2 @ X0 @ sK0) @ sK1))) | (((in @ sK2 @ (powerset @ sK0))) = $false) | ($false = ((in @ X0 @ (powerset @ sK0)))) | ($true = ((subset @ X0 @ sK2))) | (((in @ sK2 @ (powerset @ sK0))) = $false) | ($false = ((in @ X0 @ (powerset @ sK0))))) )),
% 0.23/0.29 inference(constrained_superposition,[],[f69,f39])).
% 0.23/0.29 thf(f296,plain,(
% 0.23/0.29 ( ! [X0 : $i] : (($true = $false) | ($true = ((subset @ X0 @ sK2))) | ($false = ((in @ (sK3 @ sK2 @ X0 @ sK0) @ sK1))) | (((in @ sK2 @ (powerset @ sK0))) = $false) | ($false = ((in @ X0 @ (powerset @ sK0))))) )),
% 0.23/0.29 inference(duplicate_literal_removal,[],[f285])).
% 0.23/0.29 thf(f297,plain,(
% 0.23/0.29 ( ! [X0 : $i] : (($true = ((subset @ X0 @ sK2))) | ($false = ((in @ (sK3 @ sK2 @ X0 @ sK0) @ sK1))) | (((in @ sK2 @ (powerset @ sK0))) = $false) | ($false = ((in @ X0 @ (powerset @ sK0))))) )),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f296])).
% 0.23/0.29 thf(f301,definition,(
% 0.23/0.29 spl4_8 <=> (((in @ sK2 @ (powerset @ sK0))) = $false)),
% 0.23/0.29 introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition])).
% 0.23/0.29 thf(f303,plain,(
% 0.23/0.29 (((in @ sK2 @ (powerset @ sK0))) = $false) | ~spl4_8),
% 0.23/0.29 inference(avatar_component_clause,[],[f301])).
% 0.23/0.29 thf(f305,definition,(
% 0.23/0.29 spl4_9 <=> ! [X0 : $i] : (($true = ((subset @ X0 @ sK2))) | ($false = ((in @ (sK3 @ sK2 @ X0 @ sK0) @ sK1))) | ($false = ((in @ X0 @ (powerset @ sK0)))))),
% 0.23/0.29 introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition])).
% 0.23/0.29 thf(f306,plain,(
% 0.23/0.29 ( ! [X0 : $i] : (($true = ((subset @ X0 @ sK2))) | ($false = ((in @ (sK3 @ sK2 @ X0 @ sK0) @ sK1))) | ($false = ((in @ X0 @ (powerset @ sK0))))) ) | ~spl4_9),
% 0.23/0.29 inference(avatar_component_clause,[],[f305])).
% 0.23/0.29 thf(f312,plain,(
% 0.23/0.29 spl4_8 | spl4_9),
% 0.23/0.29 inference(avatar_split_clause,[],[f297,f305,f301])).
% 0.23/0.29 thf(f314,plain,(
% 0.23/0.29 ($true = $false) | ~spl4_8),
% 0.23/0.29 inference(constrained_superposition,[],[f303,f19])).
% 0.23/0.29 thf(f320,plain,(
% 0.23/0.29 $false | ~spl4_8),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f314])).
% 0.23/0.29 thf(f321,plain,(
% 0.23/0.29 ~spl4_8),
% 0.23/0.29 inference(avatar_contradiction_clause,[],[f320])).
% 0.23/0.29 thf(f325,plain,(
% 0.23/0.29 ($true = $false) | ($true = ((subset @ sK1 @ sK2))) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ($true = ((in @ sK1 @ (powerset @ sK2)))) | (((in @ sK2 @ (powerset @ sK0))) = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl4_9),
% 0.23/0.29 inference(constrained_superposition,[],[f306,f106])).
% 0.23/0.29 thf(f340,plain,(
% 0.23/0.29 ($true = $false) | ($true = ((subset @ sK1 @ sK2))) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ($true = ((in @ sK1 @ (powerset @ sK2)))) | (((in @ sK2 @ (powerset @ sK0))) = $false) | ~spl4_9),
% 0.23/0.29 inference(duplicate_literal_removal,[],[f325])).
% 0.23/0.29 thf(f341,plain,(
% 0.23/0.29 ($true = ((subset @ sK1 @ sK2))) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ($true = ((in @ sK1 @ (powerset @ sK2)))) | (((in @ sK2 @ (powerset @ sK0))) = $false) | ~spl4_9),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f340])).
% 0.23/0.29 thf(f344,definition,(
% 0.23/0.29 spl4_11 <=> (((in @ sK1 @ (powerset @ sK0))) = $false)),
% 0.23/0.29 introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition])).
% 0.23/0.29 thf(f346,plain,(
% 0.23/0.29 (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl4_11),
% 0.23/0.29 inference(avatar_component_clause,[],[f344])).
% 0.23/0.29 thf(f348,definition,(
% 0.23/0.29 spl4_12 <=> ($true = ((subset @ sK1 @ sK2)))),
% 0.23/0.29 introduced(definition,[new_symbols(definition,[spl4_12])],[avatar_definition])).
% 0.23/0.29 thf(f350,plain,(
% 0.23/0.29 ($true = ((subset @ sK1 @ sK2))) | ~spl4_12),
% 0.23/0.29 inference(avatar_component_clause,[],[f348])).
% 0.23/0.29 thf(f353,definition,(
% 0.23/0.29 spl4_13 <=> ($true = ((in @ sK1 @ (powerset @ sK2))))),
% 0.23/0.29 introduced(definition,[new_symbols(definition,[spl4_13])],[avatar_definition])).
% 0.23/0.29 thf(f355,plain,(
% 0.23/0.29 ($true = ((in @ sK1 @ (powerset @ sK2)))) | ~spl4_13),
% 0.23/0.29 inference(avatar_component_clause,[],[f353])).
% 0.23/0.29 thf(f358,plain,(
% 0.23/0.29 spl4_8 | spl4_13 | spl4_11 | spl4_12 | ~spl4_9),
% 0.23/0.29 inference(avatar_split_clause,[],[f341,f305,f348,f344,f353,f301])).
% 0.23/0.29 thf(f377,plain,(
% 0.23/0.29 ($true = $false) | ~spl4_11),
% 0.23/0.29 inference(constrained_superposition,[],[f346,f18])).
% 0.23/0.29 thf(f383,plain,(
% 0.23/0.29 $false | ~spl4_11),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f377])).
% 0.23/0.29 thf(f384,plain,(
% 0.23/0.29 ~spl4_11),
% 0.23/0.29 inference(avatar_contradiction_clause,[],[f383])).
% 0.23/0.29 thf(f386,plain,(
% 0.23/0.29 ($true = $false) | ($true = ((in @ sK1 @ (powerset @ sK2)))) | ~spl4_12),
% 0.23/0.29 inference(constrained_superposition,[],[f45,f350])).
% 0.23/0.29 thf(f387,plain,(
% 0.23/0.29 ($true = ((in @ sK1 @ (powerset @ sK2)))) | ~spl4_12),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f386])).
% 0.23/0.29 thf(f389,plain,(
% 0.23/0.29 spl4_13 | ~spl4_12),
% 0.23/0.29 inference(avatar_split_clause,[],[f387,f348,f353])).
% 0.23/0.29 thf(f393,plain,(
% 0.23/0.29 ($true = $false) | ~spl4_13),
% 0.23/0.29 inference(constrained_superposition,[],[f355,f54])).
% 0.23/0.29 thf(f402,plain,(
% 0.23/0.29 $false | ~spl4_13),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f393])).
% 0.23/0.29 thf(f403,plain,(
% 0.23/0.29 ~spl4_13),
% 0.23/0.29 inference(avatar_contradiction_clause,[],[f402])).
% 0.23/0.30 cnf(s8, plain, spl4_8 | spl4_9, inference(sat_conversion,[],[f312])).
% 0.23/0.30 cnf(s11, plain, ~spl4_8, inference(sat_conversion,[],[f321])).
% 0.23/0.30 cnf(s15, plain, spl4_8 | ~spl4_9 | spl4_11 | spl4_12 | spl4_13, inference(sat_conversion,[],[f358])).
% 0.23/0.30 cnf(s17, plain, ~spl4_11, inference(sat_conversion,[],[f384])).
% 0.23/0.30 cnf(s18, plain, ~spl4_12 | spl4_13, inference(sat_conversion,[],[f389])).
% 0.23/0.30 cnf(s22, plain, ~spl4_13, inference(sat_conversion,[],[f403])).
% 0.23/0.30 cnf(s23, plain, ~spl4_12, inference(rat,[],[s18,s22])).
% 0.23/0.30 cnf(s24, plain, spl4_8 | ~spl4_9, inference(rat,[],[s15,s22,s23,s17])).
% 0.23/0.30 cnf(s28, plain, ~spl4_9, inference(rat,[],[s24,s11])).
% 0.23/0.30 cnf(s30, plain, $false, inference(rat,[],[s8,s28,s11])).
% 0.23/0.30 thf(f405,plain,(
% 0.23/0.30 $false),
% 0.23/0.30 inference(avatar_sat_refutation,[],[s30])).
% 0.23/0.30 % SZS output end Proof for theBenchmark
% 0.23/0.30 % (1353730)------------------------------
% 0.23/0.30 % (1353730)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (1353730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (1353730)CaDiCaL version: 2.1.3
% 0.23/0.30 % (1353730)Termination reason: Refutation
% 0.23/0.30 % (1353730)Time elapsed: 0.021 s
% 0.23/0.30 % (1353730)Peak memory usage: 12 MB
% 0.23/0.30 % (1353730)Instructions burned: 41 (million)
% 0.23/0.30 % (1353719)Success in time 0.046 s
% 0.23/0.30 % Vampire exiting
%------------------------------------------------------------------------------