%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU810^2 : 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 : n006.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 08:33:30 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU810^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n006.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:33:09 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.08/0.26 % (809127)Will run a generic schedule for satisfiability detection.
% 0.08/0.26 % (809134)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2250605177:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.26 % (809134) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-809127-809134"...
% 0.08/0.26 % (809133)% WARNING: option uhcvi not known.
% 0.08/0.26 % (809134)...printing done.
% 0.08/0.26 % (809134)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% 0.08/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.26 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.08/0.26 thf(func_def_2, type, setadjoin: ($i > $i > $i)).
% 0.08/0.26 thf(func_def_4, type, emptysetE: $o).
% 0.08/0.26 thf(func_def_6, type, setadjoinIL: $o).
% 0.08/0.26 thf(func_def_7, type, in__Cong: $o).
% 0.08/0.26 thf(func_def_8, type, omegaS: ($i > $i)).
% 0.08/0.26 thf(func_def_9, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.08/0.26 thf(func_def_10, type, vIMP: ($o > $o > $o)).
% 0.08/0.26 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.08/0.26 thf(func_def_13, type, db1: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_14, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.08/0.26 thf(func_def_15, type, vIFF: ($o > $o > $o)).
% 0.08/0.26 thf(func_def_16, type, db2: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_17, type, db3: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_21, type, vNOT: ($o > $o)).
% 0.08/0.26 thf(f1,axiom,(
% 0.08/0.26 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 0.08/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE)).
% 0.08/0.26 thf(f2,axiom,(
% 0.08/0.26 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 0.08/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL)).
% 0.08/0.26 thf(f4,axiom,(
% 0.08/0.26 (omegaS = (^[X0 : $i] : ((setadjoin @ X0 @ X0))))),
% 0.08/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaS)).
% 0.08/0.26 thf(f5,conjecture,(
% 0.08/0.26 emptysetE => (setadjoinIL => (in__Cong => ! [X0 : $i] : ((in @ X0 @ omega) => (((omegaS @ X0)) != emptyset))))),
% 0.08/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',peano0notS)).
% 0.08/0.26 thf(f6,negated_conjecture,(
% 0.08/0.26 ~(emptysetE => (setadjoinIL => (in__Cong => ! [X0 : $i] : ((in @ X0 @ omega) => (((omegaS @ X0)) != emptyset)))))),
% 0.08/0.26 inference(negated_conjecture,[status(cth)],[f5])).
% 0.08/0.26 thf(f7,plain,(
% 0.08/0.26 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 0.08/0.26 inference(rectify,[],[f1])).
% 0.08/0.26 thf(f8,plain,(
% 0.08/0.26 (emptysetE = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))))))),
% 0.08/0.26 inference(fool_elimination,[],[f7])).
% 0.08/0.26 thf(f9,plain,(
% 0.08/0.26 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 0.08/0.26 inference(rectify,[],[f2])).
% 0.08/0.26 thf(f10,plain,(
% 0.08/0.26 (setadjoinIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0))))))))),
% 0.08/0.26 inference(fool_elimination,[],[f9])).
% 0.08/0.26 thf(f13,plain,(
% 0.08/0.26 (omegaS = (^[Y0 : $i]: (setadjoin @ Y0 @ Y0)))),
% 0.08/0.26 inference(fool_elimination,[],[f4])).
% 0.08/0.26 thf(f14,plain,(
% 0.08/0.26 ~(emptysetE => (setadjoinIL => (in__Cong => ! [X0 : $i] : ((in @ X0 @ omega) => (((omegaS @ X0)) != emptyset)))))),
% 0.08/0.26 inference(rectify,[],[f6])).
% 0.08/0.26 thf(f15,plain,(
% 0.08/0.26 ~((emptysetE = $true) => ((setadjoinIL = $true) => ((in__Cong = $true) => ! [X0 : $i] : ((((in @ X0 @ omega)) = $true) => (emptyset != ((omegaS @ X0)))))))),
% 0.08/0.26 inference(fool_elimination,[],[f14])).
% 0.08/0.26 thf(f16,plain,(
% 0.08/0.26 ((? [X0 : $i] : ((emptyset = ((omegaS @ X0))) & (((in @ X0 @ omega)) = $true)) & (in__Cong = $true)) & (setadjoinIL = $true)) & (emptysetE = $true)),
% 0.08/0.26 inference(ennf_transformation,[],[f15])).
% 0.08/0.26 thf(f17,plain,(
% 0.08/0.26 ? [X0 : $i] : ((emptyset = ((omegaS @ X0))) & (((in @ X0 @ omega)) = $true)) & (in__Cong = $true) & (setadjoinIL = $true) & (emptysetE = $true)),
% 0.08/0.26 inference(flattening,[],[f16])).
% 0.08/0.26 thf(f18,plain,(
% 0.08/0.26 ((emptyset = ((omegaS @ sK0))) & ($true = ((in @ sK0 @ omega)))) & (in__Cong = $true) & (setadjoinIL = $true) & (emptysetE = $true)),
% 0.08/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f17])).
% 0.08/0.26 thf(f19,plain,(
% 0.08/0.26 (emptysetE = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))))))),
% 0.08/0.26 inference(cnf_transformation,[],[f8])).
% 0.08/0.26 thf(f20,plain,(
% 0.08/0.26 (setadjoinIL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0))))))))),
% 0.08/0.26 inference(cnf_transformation,[],[f10])).
% 0.08/0.26 thf(f22,plain,(
% 0.08/0.26 (omegaS = (^[Y0 : $i]: (setadjoin @ Y0 @ Y0)))),
% 0.08/0.26 inference(cnf_transformation,[],[f13])).
% 0.08/0.26 thf(f23,plain,(
% 0.08/0.26 (emptysetE = $true)),
% 0.08/0.26 inference(cnf_transformation,[],[f18])).
% 0.08/0.26 thf(f24,plain,(
% 0.08/0.26 (setadjoinIL = $true)),
% 0.08/0.26 inference(cnf_transformation,[],[f18])).
% 0.08/0.26 thf(f27,plain,(
% 0.08/0.26 (emptyset = ((omegaS @ sK0)))),
% 0.08/0.26 inference(cnf_transformation,[],[f18])).
% 0.08/0.26 thf(f28,definition,(
% 0.08/0.26 ($true != $false)),
% 0.08/0.26 introduced(theory,[fool_distinctness_axiom])).
% 0.08/0.26 thf(f30,plain,(
% 0.08/0.26 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))))) = $true)),
% 0.08/0.26 inference(definition_unfolding,[],[f19,f23])).
% 0.08/0.26 thf(f31,plain,(
% 0.08/0.26 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0))))))) = $true)),
% 0.08/0.26 inference(definition_unfolding,[],[f20,f24])).
% 0.08/0.26 thf(f33,plain,(
% 0.08/0.26 (emptyset = (((^[Y0 : $i]: (setadjoin @ Y0 @ Y0)) @ sK0)))),
% 0.08/0.26 inference(definition_unfolding,[],[f27,f22])).
% 0.08/0.26 thf(f34,plain,(
% 0.08/0.26 (emptyset = ((setadjoin @ sK0 @ sK0)))),
% 0.08/0.26 inference(beta-eta_normalization,[],[f33])).
% 0.08/0.26 thf(f50,plain,(
% 0.08/0.26 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0))))) @ X1)))) )),
% 0.08/0.26 inference(pi_proxy_clausification,[],[f31])).
% 0.08/0.26 thf(f51,plain,(
% 0.08/0.26 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ X1))))))) )),
% 0.08/0.26 inference(beta-eta_normalization,[],[f50])).
% 0.08/0.26 thf(f52,plain,(
% 0.08/0.26 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ X1))) @ X2)))) )),
% 0.08/0.26 inference(pi_proxy_clausification,[],[f51])).
% 0.08/0.26 thf(f53,plain,(
% 0.08/0.26 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X2 @ (setadjoin @ X2 @ X1))))) )),
% 0.08/0.26 inference(beta-eta_normalization,[],[f52])).
% 0.08/0.26 thf(f54,plain,(
% 0.08/0.26 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))) @ X1)))) )),
% 0.08/0.26 inference(pi_proxy_clausification,[],[f30])).
% 0.08/0.26 thf(f55,plain,(
% 0.08/0.26 ( ! [X1 : $i] : (($true = (((in @ X1 @ emptyset) => (!! @ $o @ (^[Y0 : $o]: (Y0))))))) )),
% 0.08/0.26 inference(beta-eta_normalization,[],[f54])).
% 0.08/0.26 thf(f56,plain,(
% 0.08/0.26 ( ! [X1 : $i] : (($false = ((in @ X1 @ emptyset))) | (((!! @ $o @ (^[Y0 : $o]: (Y0)))) = $true)) )),
% 0.08/0.26 inference(imp_proxy_clausification,[],[f55])).
% 0.08/0.26 thf(f57,plain,(
% 0.08/0.26 ( ! [X2 : $o,X1 : $i] : (($false = ((in @ X1 @ emptyset))) | ($true = (((^[Y0 : $o]: (Y0)) @ X2)))) )),
% 0.08/0.26 inference(pi_proxy_clausification,[],[f56])).
% 0.08/0.26 thf(f58,plain,(
% 0.08/0.26 ( ! [X2 : $o,X1 : $i] : (($false = ((in @ X1 @ emptyset))) | ($true = X2)) )),
% 0.08/0.26 inference(beta-eta_normalization,[],[f57])).
% 0.08/0.26 thf(f60,definition,(
% 0.08/0.26 spl1_1 <=> ! [X2 : $o] : ($true = X2)),
% 0.08/0.26 introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition])).
% 0.08/0.26 thf(f61,plain,(
% 0.08/0.26 ( ! [X2 : $o] : (($true = X2)) ) | ~spl1_1),
% 0.08/0.26 inference(avatar_component_clause,[],[f60])).
% 0.08/0.26 thf(f63,definition,(
% 0.08/0.26 spl1_2 <=> ! [X1 : $i] : ($false = ((in @ X1 @ emptyset)))),
% 0.08/0.26 introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition])).
% 0.08/0.26 thf(f64,plain,(
% 0.08/0.26 ( ! [X1 : $i] : (($false = ((in @ X1 @ emptyset)))) ) | ~spl1_2),
% 0.08/0.26 inference(avatar_component_clause,[],[f63])).
% 0.08/0.26 thf(f65,plain,(
% 0.08/0.26 spl1_1 | spl1_2),
% 0.08/0.26 inference(avatar_split_clause,[],[f58,f63,f60])).
% 0.08/0.26 thf(f67,plain,(
% 0.08/0.26 ( ! [X0 : $o] : (($false != X0)) ) | ~spl1_1),
% 0.08/0.26 inference(constrained_superposition,[],[f28,f61])).
% 0.08/0.26 thf(f70,plain,(
% 0.08/0.26 $false | ~spl1_1),
% 0.08/0.26 inference(equality_resolution,[],[f67])).
% 0.08/0.26 thf(f71,plain,(
% 0.08/0.26 ~spl1_1),
% 0.08/0.26 inference(avatar_contradiction_clause,[],[f70])).
% 0.08/0.26 thf(f72,plain,(
% 0.08/0.26 ($true = ((in @ sK0 @ emptyset)))),
% 0.08/0.26 inference(constrained_superposition,[],[f53,f34])).
% 0.08/0.26 thf(f73,plain,(
% 0.08/0.26 ($true = $false) | ~spl1_2),
% 0.08/0.26 inference(forward_demodulation,[],[f72,f64])).
% 0.08/0.26 thf(f74,plain,(
% 0.08/0.26 $false | ~spl1_2),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f73])).
% 0.08/0.26 thf(f75,plain,(
% 0.08/0.26 ~spl1_2),
% 0.08/0.26 inference(avatar_contradiction_clause,[],[f74])).
% 0.08/0.26 cnf(s13, plain, spl1_1 | spl1_2, inference(sat_conversion,[],[f65])).
% 0.08/0.26 cnf(s18, plain, ~spl1_1, inference(sat_conversion,[],[f71])).
% 0.08/0.26 cnf(s22, plain, ~spl1_2, inference(sat_conversion,[],[f75])).
% 0.08/0.26 cnf(s23, plain, $false, inference(rat,[],[s13,s22,s18])).
% 0.08/0.26 thf(f76,plain,(
% 0.08/0.26 $false),
% 0.08/0.26 inference(avatar_sat_refutation,[],[s23])).
% 0.08/0.26 % SZS output end Proof for theBenchmark
% 0.08/0.26 % (809134)------------------------------
% 0.08/0.26 % (809134)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (809134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (809134)CaDiCaL version: 2.1.3
% 0.08/0.26 % (809134)Termination reason: Refutation
% 0.08/0.26 % (809134)Time elapsed: 0.003 s
% 0.08/0.26 % (809134)Peak memory usage: 13 MB
% 0.08/0.26 % (809134)Instructions burned: 5 (million)
% 0.08/0.26 % (809127)Success in time 0.039 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------