%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU519^2 : 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 : n012.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 08:32:17 AM UTC 2026
% Result : Theorem 0.09s 0.17s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU519^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.00/0.12 % Computer : n012.cluster.edu
% 0.00/0.12 % Model : x86_64 x86_64
% 0.00/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.12 % Memory : 8046.5625MB
% 0.00/0.12 % OS : Linux 6.8.0-71-generic
% 0.00/0.12 % CPULimit : 300
% 0.00/0.12 % WCLimit : 300
% 0.00/0.12 % DateTime : Tue Sep 29 13:47:19 UTC 2026
% 0.09/0.12 % CPUTime :
% 0.09/0.12 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.13 Running first-order model finding
% 0.09/0.13 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
% 0.09/0.17 % (126822)Will run a generic schedule for satisfiability detection.
% 0.09/0.17 % (126828)% WARNING: option uhcvi not known.
% 0.09/0.17 % (126831)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2311779008:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.17 % (126830)dis+10_1_sil=32000:sp=arity:random_seed=2978200504:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.17 % (126829)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1594640786:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.17 % (126827)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2613584532_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.17 % (126828)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3678756172:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.17 % (126833)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=10829743:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.17 % (126828)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.17 % (126831)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.17 % (126832)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3816157323:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.17 % (126828)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.09/0.17 % Exception at run slice level
% 0.09/0.17 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.17 % (126833) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-126822-126833"...
% 0.09/0.17 % (126831) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-126822-126831"...
% 0.09/0.17 % (126828) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-126822-126828"...
% 0.09/0.17 % (126829) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-126822-126829"...
% 0.09/0.17 % (126832) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-126822-126832"...
% 0.09/0.17 % (126830) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-126822-126830"...
% 0.09/0.17 % (126831)...printing done.
% 0.09/0.17 % (126833)...printing done.
% 0.09/0.17 % (126828)...printing done.
% 0.09/0.17 % (126829)...printing done.
% 0.09/0.17 % (126832)...printing done.
% 0.09/0.17 % (126831)Refutation found. Thanks to Tanya!
% 0.09/0.17 % SZS status Theorem for theBenchmark
% 0.09/0.17 % SZS output start Proof for theBenchmark
% 0.09/0.17 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.17 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.09/0.17 thf(func_def_2, type, powerset: ($i > $i)).
% 0.09/0.17 thf(func_def_3, type, emptysetE: $o).
% 0.09/0.17 thf(func_def_5, type, powersetI: $o).
% 0.09/0.17 thf(func_def_6, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.09/0.17 thf(func_def_7, type, vIMP: ($o > $o > $o)).
% 0.09/0.17 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.09/0.17 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.09/0.17 thf(func_def_10, type, db2: !>[X0: $tType]:(X0)).
% 0.09/0.17 thf(func_def_11, type, db1: !>[X0: $tType]:(X0)).
% 0.09/0.17 thf(func_def_15, type, vNOT: ($o > $o)).
% 0.09/0.17 thf(func_def_16, type, sK1: ($i > $i > $i)).
% 0.09/0.17 thf(f1,axiom,(
% 0.09/0.17 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 0.09/0.17 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE)).
% 0.09/0.17 thf(f2,axiom,(
% 0.09/0.17 (powersetI = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 0.09/0.17 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI)).
% 0.09/0.17 thf(f3,conjecture,(
% 0.09/0.17 emptysetE => (powersetI => ! [X0 : $i] : (in @ emptyset @ (powerset @ X0)))),
% 0.09/0.17 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset)).
% 0.09/0.17 thf(f4,negated_conjecture,(
% 0.09/0.17 ~(emptysetE => (powersetI => ! [X0 : $i] : (in @ emptyset @ (powerset @ X0))))),
% 0.09/0.17 inference(negated_conjecture,[status(cth)],[f3])).
% 0.09/0.17 thf(f5,plain,(
% 0.09/0.17 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 0.09/0.17 inference(rectify,[],[f1])).
% 0.09/0.17 thf(f6,plain,(
% 0.09/0.17 (emptysetE = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))))))),
% 0.09/0.17 inference(fool_elimination,[],[f5])).
% 0.09/0.17 thf(f7,plain,(
% 0.09/0.17 (powersetI = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 0.09/0.17 inference(rectify,[],[f2])).
% 0.09/0.17 thf(f8,plain,(
% 0.09/0.17 (powersetI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1)))))))))),
% 0.09/0.17 inference(fool_elimination,[],[f7])).
% 0.09/0.17 thf(f9,plain,(
% 0.09/0.17 ~(emptysetE => (powersetI => ! [X0 : $i] : (in @ emptyset @ (powerset @ X0))))),
% 0.09/0.17 inference(rectify,[],[f4])).
% 0.09/0.17 thf(f10,plain,(
% 0.09/0.17 ~((emptysetE = $true) => ((powersetI = $true) => ! [X0 : $i] : (((in @ emptyset @ (powerset @ X0))) = $true)))),
% 0.09/0.17 inference(fool_elimination,[],[f9])).
% 0.09/0.17 thf(f11,plain,(
% 0.09/0.17 (? [X0 : $i] : (((in @ emptyset @ (powerset @ X0))) != $true) & (powersetI = $true)) & (emptysetE = $true)),
% 0.09/0.17 inference(ennf_transformation,[],[f10])).
% 0.09/0.17 thf(f12,plain,(
% 0.09/0.17 ? [X0 : $i] : (((in @ emptyset @ (powerset @ X0))) != $true) & (powersetI = $true) & (emptysetE = $true)),
% 0.09/0.17 inference(flattening,[],[f11])).
% 0.09/0.17 thf(f13,plain,(
% 0.09/0.17 ($true != ((in @ emptyset @ (powerset @ sK0)))) & (powersetI = $true) & (emptysetE = $true)),
% 0.09/0.17 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f12])).
% 0.09/0.17 thf(f14,plain,(
% 0.09/0.17 (emptysetE = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))))))),
% 0.09/0.17 inference(cnf_transformation,[],[f6])).
% 0.09/0.17 thf(f15,plain,(
% 0.09/0.17 (powersetI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1)))))))))),
% 0.09/0.17 inference(cnf_transformation,[],[f8])).
% 0.09/0.17 thf(f16,plain,(
% 0.09/0.17 (emptysetE = $true)),
% 0.09/0.17 inference(cnf_transformation,[],[f13])).
% 0.09/0.17 thf(f17,plain,(
% 0.09/0.17 (powersetI = $true)),
% 0.09/0.17 inference(cnf_transformation,[],[f13])).
% 0.09/0.17 thf(f18,plain,(
% 0.09/0.17 ($true != ((in @ emptyset @ (powerset @ sK0))))),
% 0.09/0.17 inference(cnf_transformation,[],[f13])).
% 0.09/0.17 thf(f20,definition,(
% 0.09/0.17 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.09/0.17 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.09/0.17 thf(f21,plain,(
% 0.09/0.17 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))))) = $true)),
% 0.09/0.17 inference(definition_unfolding,[],[f14,f16])).
% 0.09/0.17 thf(f22,plain,(
% 0.09/0.17 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1)))))))) = $true)),
% 0.09/0.17 inference(definition_unfolding,[],[f15,f17])).
% 0.09/0.17 thf(f23,plain,(
% 0.09/0.17 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1)))))) @ X1)))) )),
% 0.09/0.17 inference(pi_proxy_clausification,[],[f22])).
% 0.09/0.17 thf(f24,plain,(
% 0.09/0.17 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (in @ X1 @ (powerset @ Y0)))))))) )),
% 0.09/0.17 inference(beta-eta_normalization,[],[f23])).
% 0.09/0.17 thf(f25,plain,(
% 0.09/0.17 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (in @ X1 @ (powerset @ Y0)))) @ X2)))) )),
% 0.09/0.17 inference(pi_proxy_clausification,[],[f24])).
% 0.09/0.17 thf(f26,plain,(
% 0.09/0.17 ( ! [X2 : $i,X1 : $i] : (($true = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (in @ X1 @ (powerset @ X2)))))) )),
% 0.09/0.17 inference(beta-eta_normalization,[],[f25])).
% 0.09/0.17 thf(f27,plain,(
% 0.09/0.17 ( ! [X2 : $i,X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))))) | ($true = ((in @ X1 @ (powerset @ X2))))) )),
% 0.09/0.17 inference(imp_proxy_clausification,[],[f26])).
% 0.09/0.17 thf(f28,plain,(
% 0.09/0.17 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2))) @ (sK1 @ X1 @ X2)))) | ($true = ((in @ X1 @ (powerset @ X2))))) )),
% 0.09/0.17 inference(sigma_proxy_clausification,[],[f27])).
% 0.09/0.17 thf(f29,plain,(
% 0.09/0.17 ( ! [X2 : $i,X1 : $i] : (($false = (((in @ (sK1 @ X1 @ X2) @ X1) => (in @ (sK1 @ X1 @ X2) @ X2)))) | ($true = ((in @ X1 @ (powerset @ X2))))) )),
% 0.09/0.17 inference(beta-eta_normalization,[],[f28])).
% 0.09/0.17 thf(f31,plain,(
% 0.09/0.17 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ (sK1 @ X1 @ X2) @ X1))) | ($true = ((in @ X1 @ (powerset @ X2))))) )),
% 0.09/0.17 inference(imp_proxy_clausification,[],[f29])).
% 0.09/0.17 thf(f32,plain,(
% 0.09/0.17 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))) @ X1)))) )),
% 0.09/0.17 inference(pi_proxy_clausification,[],[f21])).
% 0.09/0.17 thf(f33,plain,(
% 0.09/0.17 ( ! [X1 : $i] : (($true = (((in @ X1 @ emptyset) => (!! @ $o @ (^[Y0 : $o]: (Y0))))))) )),
% 0.09/0.17 inference(beta-eta_normalization,[],[f32])).
% 0.09/0.17 thf(f34,plain,(
% 0.09/0.17 ( ! [X1 : $i] : (($false = ((in @ X1 @ emptyset))) | (((!! @ $o @ (^[Y0 : $o]: (Y0)))) = $true)) )),
% 0.09/0.17 inference(imp_proxy_clausification,[],[f33])).
% 0.09/0.17 thf(f35,plain,(
% 0.09/0.17 ( ! [X2 : $o,X1 : $i] : (($false = ((in @ X1 @ emptyset))) | ($true = (((^[Y0 : $o]: (Y0)) @ X2)))) )),
% 0.09/0.17 inference(pi_proxy_clausification,[],[f34])).
% 0.09/0.17 thf(f36,plain,(
% 0.09/0.17 ( ! [X2 : $o,X1 : $i] : (($false = ((in @ X1 @ emptyset))) | ($true = X2)) )),
% 0.09/0.17 inference(beta-eta_normalization,[],[f35])).
% 0.09/0.17 thf(f38,definition,(
% 0.09/0.17 spl2_1 <=> ! [X2 : $o] : ($true = X2)),
% 0.09/0.17 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.09/0.17 thf(f39,plain,(
% 0.09/0.17 ( ! [X2 : $o] : (($true = X2)) ) | ~spl2_1),
% 0.09/0.17 inference(avatar_component_clause,[],[f38])).
% 0.09/0.17 thf(f41,definition,(
% 0.09/0.17 spl2_2 <=> ! [X1 : $i] : ($false = ((in @ X1 @ emptyset)))),
% 0.09/0.17 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.09/0.17 thf(f42,plain,(
% 0.09/0.17 ( ! [X1 : $i] : (($false = ((in @ X1 @ emptyset)))) ) | ~spl2_2),
% 0.09/0.17 inference(avatar_component_clause,[],[f41])).
% 0.09/0.17 thf(f43,plain,(
% 0.09/0.17 spl2_1 | spl2_2),
% 0.09/0.17 inference(avatar_split_clause,[],[f36,f41,f38])).
% 0.09/0.17 thf(f47,plain,(
% 0.09/0.17 ($true != $true) | (((in @ emptyset @ (powerset @ sK0))) = $false)),
% 0.09/0.17 inference(constrained_superposition,[],[f18,f20])).
% 0.09/0.17 thf(f49,plain,(
% 0.09/0.17 (((in @ emptyset @ (powerset @ sK0))) = $false)),
% 0.09/0.17 inference(trivial_inequality_removal,[],[f47])).
% 0.09/0.17 thf(f63,plain,(
% 0.09/0.17 ( ! [X0 : $i] : (($true = $false) | (((in @ emptyset @ (powerset @ X0))) = $true)) ) | ~spl2_2),
% 0.09/0.17 inference(constrained_superposition,[],[f42,f31])).
% 0.09/0.17 thf(f64,plain,(
% 0.09/0.17 ( ! [X0 : $i] : ((((in @ emptyset @ (powerset @ X0))) = $true)) ) | ~spl2_2),
% 0.09/0.17 inference(trivial_inequality_removal,[],[f63])).
% 0.09/0.17 thf(f70,plain,(
% 0.09/0.17 ($true = $false) | ~spl2_2),
% 0.09/0.17 inference(constrained_superposition,[],[f64,f49])).
% 0.09/0.17 thf(f77,plain,(
% 0.09/0.17 $false | ~spl2_2),
% 0.09/0.17 inference(trivial_inequality_removal,[],[f70])).
% 0.09/0.17 thf(f78,plain,(
% 0.09/0.17 ~spl2_2),
% 0.09/0.17 inference(avatar_contradiction_clause,[],[f77])).
% 0.09/0.17 thf(f84,plain,(
% 0.09/0.17 ($true = $false) | ~spl2_1),
% 0.09/0.17 inference(constrained_superposition,[],[f49,f39])).
% 0.09/0.17 thf(f88,plain,(
% 0.09/0.17 $false | ~spl2_1),
% 0.09/0.17 inference(trivial_inequality_removal,[],[f84])).
% 0.09/0.17 thf(f89,plain,(
% 0.09/0.17 ~spl2_1),
% 0.09/0.17 inference(avatar_contradiction_clause,[],[f88])).
% 0.09/0.17 cnf(s1, plain, spl2_1 | spl2_2, inference(sat_conversion,[],[f43])).
% 0.09/0.17 cnf(s4, plain, ~spl2_2, inference(sat_conversion,[],[f78])).
% 0.09/0.17 cnf(s6, plain, ~spl2_1, inference(sat_conversion,[],[f89])).
% 0.09/0.17 cnf(s7, plain, $false, inference(rat,[],[s1,s4,s6])).
% 0.09/0.17 thf(f99,plain,(
% 0.09/0.17 $false),
% 0.09/0.17 inference(avatar_sat_refutation,[],[s7])).
% 0.09/0.17 % SZS output end Proof for theBenchmark
% 0.09/0.17 % (126831)------------------------------
% 0.09/0.17 % (126831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.17 % (126831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.17 % (126831)CaDiCaL version: 2.1.3
% 0.09/0.17 % (126831)Termination reason: Refutation
% 0.09/0.17 % (126831)Time elapsed: 0.002 s
% 0.09/0.17 % (126831)Peak memory usage: 12 MB
% 0.09/0.17 % (126831)Instructions burned: 5 (million)
% 0.09/0.17 % (126822)Success in time 0.032 s
% 0.09/0.17 % Vampire exiting
%------------------------------------------------------------------------------