%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU511^2 : 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 : n003.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 08:32:15 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU511^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n003.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 13:49:14 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 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
% 0.21/0.28 % (2526003)Will run a generic schedule for satisfiability detection.
% 0.21/0.28 % (2526011)dis+10_1_sil=32000:sp=arity:random_seed=2062508040:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.28 % (2526011) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2526003-2526011"...
% 0.21/0.28 % (2526011)...printing done.
% 0.21/0.28 % (2526011)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% 0.21/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.28 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.21/0.28 thf(func_def_2, type, emptysetE: $o).
% 0.21/0.28 thf(func_def_4, type, nonempty: ($i > $o)).
% 0.21/0.28 thf(func_def_5, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.28 thf(func_def_6, type, vIMP: ($o > $o > $o)).
% 0.21/0.28 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.28 thf(func_def_8, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.28 thf(func_def_9, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.28 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.21/0.28 thf(f1,axiom,(
% 0.21/0.28 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE)).
% 0.21/0.28 thf(f2,axiom,(
% 0.21/0.28 (nonempty = (^[X0 : $i] : ((X0 != emptyset))))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty)).
% 0.21/0.28 thf(f3,conjecture,(
% 0.21/0.28 emptysetE => ! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => (nonempty @ X0))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1)).
% 0.21/0.28 thf(f4,negated_conjecture,(
% 0.21/0.28 ~(emptysetE => ! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => (nonempty @ X0)))),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f3])).
% 0.21/0.28 thf(f5,plain,(
% 0.21/0.28 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 0.21/0.28 inference(rectify,[],[f1])).
% 0.21/0.28 thf(f6,plain,(
% 0.21/0.28 (emptysetE = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))))))),
% 0.21/0.28 inference(fool_elimination,[],[f5])).
% 0.21/0.28 thf(f7,plain,(
% 0.21/0.28 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 0.21/0.28 inference(fool_elimination,[],[f2])).
% 0.21/0.28 thf(f8,plain,(
% 0.21/0.28 ~(emptysetE => ! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => (nonempty @ X0)))),
% 0.21/0.28 inference(rectify,[],[f4])).
% 0.21/0.28 thf(f9,plain,(
% 0.21/0.28 ~((emptysetE = $true) => ! [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0)) = $true) => (((nonempty @ X0)) = $true)))),
% 0.21/0.28 inference(fool_elimination,[],[f8])).
% 0.21/0.28 thf(f10,plain,(
% 0.21/0.28 ? [X0 : $i] : ((((nonempty @ X0)) != $true) & ? [X1 : $i] : (((in @ X1 @ X0)) = $true)) & (emptysetE = $true)),
% 0.21/0.28 inference(ennf_transformation,[],[f9])).
% 0.21/0.28 thf(f11,plain,(
% 0.21/0.28 (($true != ((nonempty @ sK0))) & ($true = ((in @ sK1 @ sK0)))) & (emptysetE = $true)),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f10])).
% 0.21/0.28 thf(f12,plain,(
% 0.21/0.28 (emptysetE = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))))))),
% 0.21/0.28 inference(cnf_transformation,[],[f6])).
% 0.21/0.28 thf(f13,plain,(
% 0.21/0.28 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 0.21/0.28 inference(cnf_transformation,[],[f7])).
% 0.21/0.28 thf(f14,plain,(
% 0.21/0.28 (emptysetE = $true)),
% 0.21/0.28 inference(cnf_transformation,[],[f11])).
% 0.21/0.28 thf(f15,plain,(
% 0.21/0.28 ($true = ((in @ sK1 @ sK0)))),
% 0.21/0.28 inference(cnf_transformation,[],[f11])).
% 0.21/0.28 thf(f16,plain,(
% 0.21/0.28 ($true != ((nonempty @ sK0)))),
% 0.21/0.28 inference(cnf_transformation,[],[f11])).
% 0.21/0.28 thf(f17,definition,(
% 0.21/0.28 ($true != $false)),
% 0.21/0.28 introduced(theory,[fool_distinctness_axiom])).
% 0.21/0.28 thf(f19,plain,(
% 0.21/0.28 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))))) = $true)),
% 0.21/0.28 inference(definition_unfolding,[],[f12,f14])).
% 0.21/0.28 thf(f20,plain,(
% 0.21/0.28 ($true != (((^[Y0 : $i]: (~ (emptyset = Y0))) @ sK0)))),
% 0.21/0.28 inference(definition_unfolding,[],[f16,f13])).
% 0.21/0.28 thf(f21,plain,(
% 0.21/0.28 ($true != ((~ (emptyset = sK0))))),
% 0.21/0.28 inference(beta-eta_normalization,[],[f20])).
% 0.21/0.28 thf(f22,plain,(
% 0.21/0.28 ($true = ((emptyset = sK0)))),
% 0.21/0.28 inference(not_proxy_clausification,[],[f21])).
% 0.21/0.28 thf(f23,plain,(
% 0.21/0.28 (emptyset = sK0)),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f22])).
% 0.21/0.28 thf(f24,plain,(
% 0.21/0.28 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))) @ X1)))) )),
% 0.21/0.28 inference(pi_proxy_clausification,[],[f19])).
% 0.21/0.28 thf(f25,plain,(
% 0.21/0.28 ( ! [X1 : $i] : (($true = (((in @ X1 @ emptyset) => (!! @ $o @ (^[Y0 : $o]: (Y0))))))) )),
% 0.21/0.28 inference(beta-eta_normalization,[],[f24])).
% 0.21/0.28 thf(f26,plain,(
% 0.21/0.28 ( ! [X1 : $i] : (($false = ((in @ X1 @ emptyset))) | (((!! @ $o @ (^[Y0 : $o]: (Y0)))) = $true)) )),
% 0.21/0.28 inference(imp_proxy_clausification,[],[f25])).
% 0.21/0.28 thf(f27,plain,(
% 0.21/0.28 ( ! [X2 : $o,X1 : $i] : (($false = ((in @ X1 @ emptyset))) | ($true = (((^[Y0 : $o]: (Y0)) @ X2)))) )),
% 0.21/0.28 inference(pi_proxy_clausification,[],[f26])).
% 0.21/0.28 thf(f28,plain,(
% 0.21/0.28 ( ! [X2 : $o,X1 : $i] : (($false = ((in @ X1 @ emptyset))) | ($true = X2)) )),
% 0.21/0.28 inference(beta-eta_normalization,[],[f27])).
% 0.21/0.28 thf(f30,definition,(
% 0.21/0.28 spl2_1 <=> ! [X2 : $o] : ($true = X2)),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.21/0.28 thf(f31,plain,(
% 0.21/0.28 ( ! [X2 : $o] : (($true = X2)) ) | ~spl2_1),
% 0.21/0.28 inference(avatar_component_clause,[],[f30])).
% 0.21/0.28 thf(f33,definition,(
% 0.21/0.28 spl2_2 <=> ! [X1 : $i] : ($false = ((in @ X1 @ emptyset)))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.21/0.28 thf(f34,plain,(
% 0.21/0.28 ( ! [X1 : $i] : (($false = ((in @ X1 @ emptyset)))) ) | ~spl2_2),
% 0.21/0.28 inference(avatar_component_clause,[],[f33])).
% 0.21/0.28 thf(f35,plain,(
% 0.21/0.28 spl2_1 | spl2_2),
% 0.21/0.28 inference(avatar_split_clause,[],[f28,f33,f30])).
% 0.21/0.28 thf(f36,plain,(
% 0.21/0.28 ($true = ((in @ sK1 @ emptyset)))),
% 0.21/0.28 inference(forward_demodulation,[],[f15,f23])).
% 0.21/0.28 thf(f37,plain,(
% 0.21/0.28 ($true = $false) | ~spl2_2),
% 0.21/0.28 inference(forward_demodulation,[],[f36,f34])).
% 0.21/0.28 thf(f38,plain,(
% 0.21/0.28 $false | ~spl2_2),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f37])).
% 0.21/0.28 thf(f39,plain,(
% 0.21/0.28 ~spl2_2),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f38])).
% 0.21/0.28 thf(f43,plain,(
% 0.21/0.28 $false | ~spl2_1),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f17,f31])).
% 0.21/0.28 thf(f44,plain,(
% 0.21/0.28 ~spl2_1),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f43])).
% 0.21/0.28 cnf(s1, plain, spl2_1 | spl2_2, inference(sat_conversion,[],[f35])).
% 0.21/0.28 cnf(s2, plain, ~spl2_2, inference(sat_conversion,[],[f39])).
% 0.21/0.28 cnf(s3, plain, ~spl2_1, inference(sat_conversion,[],[f44])).
% 0.21/0.28 cnf(s4, plain, $false, inference(rat,[],[s1,s2,s3])).
% 0.21/0.28 thf(f45,plain,(
% 0.21/0.28 $false),
% 0.21/0.28 inference(avatar_sat_refutation,[],[s4])).
% 0.21/0.28 % SZS output end Proof for theBenchmark
% 0.21/0.28 % (2526011)------------------------------
% 0.21/0.28 % (2526011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (2526011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (2526011)CaDiCaL version: 2.1.3
% 0.21/0.28 % (2526011)Termination reason: Refutation
% 0.21/0.28 % (2526011)Time elapsed: 0.002 s
% 0.21/0.28 % (2526011)Peak memory usage: 12 MB
% 0.21/0.28 % (2526011)Instructions burned: 2 (million)
% 0.21/0.28 % (2526003)Success in time 0.03 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------