%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU523^2 : 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 : n010.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 0.12s 0.25s
% Output : Refutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU523^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.17 % Computer : n010.cluster.edu
% 0.12/0.17 % Model : x86_64 x86_64
% 0.12/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.17 % Memory : 8046.5625MB
% 0.12/0.17 % OS : Linux 6.8.0-71-generic
% 0.12/0.17 % CPULimit : 300
% 0.12/0.17 % WCLimit : 300
% 0.12/0.17 % DateTime : Tue Sep 29 13:48:33 UTC 2026
% 0.12/0.17 % CPUTime :
% 0.12/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.20 Running first-order model finding
% 0.12/0.20 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
% 0.12/0.25 % (2882038)Will run a generic schedule for satisfiability detection.
% 0.12/0.25 % (2882050)% WARNING: option uhcvi not known.
% 0.12/0.25 % (2882050)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2445753997:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.25 % (2882050)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.12/0.25 % (2882050)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.12/0.25 % (2882050) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2882038-2882050"...
% 0.12/0.25 % (2882050)...printing done.
% 0.12/0.25 % (2882050)Refutation found. Thanks to Tanya!
% 0.12/0.25 % SZS status Theorem for theBenchmark
% 0.12/0.25 % SZS output start Proof for theBenchmark
% 0.12/0.25 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.12/0.25 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.12/0.25 thf(func_def_1, type, setunion: ($i > $i)).
% 0.12/0.25 thf(func_def_2, type, setunionAx: $o).
% 0.12/0.25 thf(func_def_4, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.12/0.25 thf(func_def_5, type, vIFF: ($o > $o > $o)).
% 0.12/0.25 thf(func_def_6, type, db1: !>[X0: $tType]:(X0)).
% 0.12/0.25 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 0.12/0.25 thf(func_def_8, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.12/0.25 thf(func_def_9, type, vAND: ($o > $o > $o)).
% 0.12/0.25 thf(func_def_10, type, db2: !>[X0: $tType]:(X0)).
% 0.12/0.25 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.12/0.25 thf(func_def_16, type, sK2: $o).
% 0.12/0.25 thf(func_def_17, type, vNOT: ($o > $o)).
% 0.12/0.25 thf(func_def_18, type, sK3: ($i > $i > $i)).
% 0.12/0.25 thf(f1,axiom,(
% 0.12/0.25 (setunionAx = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) <=> ? [X2 : $i] : ((in @ X2 @ X0) & (in @ X1 @ X2))))),
% 0.12/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx)).
% 0.12/0.25 thf(f2,conjecture,(
% 0.12/0.25 setunionAx => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2))),
% 0.12/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE)).
% 0.12/0.25 thf(f3,negated_conjecture,(
% 0.12/0.25 ~(setunionAx => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2)))),
% 0.12/0.25 inference(negated_conjecture,[status(cth)],[f2])).
% 0.12/0.25 thf(f4,plain,(
% 0.12/0.25 (setunionAx = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) <=> ? [X2 : $i] : ((in @ X2 @ X0) & (in @ X1 @ X2))))),
% 0.12/0.25 inference(rectify,[],[f1])).
% 0.12/0.25 thf(f5,plain,(
% 0.12/0.25 (setunionAx = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))))))))))),
% 0.12/0.25 inference(fool_elimination,[],[f4])).
% 0.12/0.25 thf(f6,plain,(
% 0.12/0.25 ~(setunionAx => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3 : $i] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2)))),
% 0.12/0.25 inference(rectify,[],[f3])).
% 0.12/0.25 thf(f7,plain,(
% 0.12/0.25 ~((setunionAx = $true) => ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (setunion @ X0))) = $true) => ! [X2 : $o] : (! [X3 : $i] : ((((in @ X1 @ X3)) = $true) => ((((in @ X3 @ X0)) = $true) => ($true = X2))) => ($true = X2))))),
% 0.12/0.25 inference(fool_elimination,[],[f6])).
% 0.12/0.25 thf(f8,plain,(
% 0.12/0.25 ? [X0 : $i,X1 : $i] : (? [X2 : $o] : (($true != X2) & ! [X3 : $i] : ((($true = X2) | (((in @ X3 @ X0)) != $true)) | (((in @ X1 @ X3)) != $true))) & (((in @ X1 @ (setunion @ X0))) = $true)) & (setunionAx = $true)),
% 0.12/0.25 inference(ennf_transformation,[],[f7])).
% 0.12/0.25 thf(f9,plain,(
% 0.12/0.25 ? [X0 : $i,X1 : $i] : (? [X2 : $o] : (($true != X2) & ! [X3 : $i] : (($true = X2) | (((in @ X3 @ X0)) != $true) | (((in @ X1 @ X3)) != $true))) & (((in @ X1 @ (setunion @ X0))) = $true)) & (setunionAx = $true)),
% 0.12/0.25 inference(flattening,[],[f8])).
% 0.12/0.25 thf(f10,plain,(
% 0.12/0.25 ((($true != sK2) & ! [X3 : $i] : (($true = sK2) | ($true != ((in @ X3 @ sK0))) | ($true != ((in @ sK1 @ X3))))) & ($true = ((in @ sK1 @ (setunion @ sK0))))) & (setunionAx = $true)),
% 0.12/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f9])).
% 0.12/0.25 thf(f11,plain,(
% 0.12/0.25 (setunionAx = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))))))))))),
% 0.12/0.25 inference(cnf_transformation,[],[f5])).
% 0.12/0.25 thf(f12,plain,(
% 0.12/0.25 (setunionAx = $true)),
% 0.12/0.25 inference(cnf_transformation,[],[f10])).
% 0.12/0.25 thf(f13,plain,(
% 0.12/0.25 ($true = ((in @ sK1 @ (setunion @ sK0))))),
% 0.12/0.25 inference(cnf_transformation,[],[f10])).
% 0.12/0.25 thf(f14,plain,(
% 0.12/0.25 ( ! [X3 : $i] : (($true = sK2) | ($true != ((in @ X3 @ sK0))) | ($true != ((in @ sK1 @ X3)))) )),
% 0.12/0.25 inference(cnf_transformation,[],[f10])).
% 0.12/0.25 thf(f15,plain,(
% 0.12/0.25 ($true != sK2)),
% 0.12/0.25 inference(cnf_transformation,[],[f10])).
% 0.12/0.25 thf(f17,definition,(
% 0.12/0.25 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.12/0.25 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.12/0.25 thf(f18,plain,(
% 0.12/0.25 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))))))))) = $true)),
% 0.12/0.25 inference(definition_unfolding,[],[f11,f12])).
% 0.12/0.25 thf(f19,plain,(
% 0.12/0.25 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))))))) @ X1)))) )),
% 0.12/0.25 inference(pi_proxy_clausification,[],[f18])).
% 0.12/0.25 thf(f20,plain,(
% 0.12/0.25 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) & (in @ Y1 @ Y0)))))))))) )),
% 0.12/0.25 inference(beta-eta_normalization,[],[f19])).
% 0.12/0.25 thf(f21,plain,(
% 0.12/0.25 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) & (in @ Y1 @ Y0)))))) @ X2)))) )),
% 0.12/0.25 inference(pi_proxy_clausification,[],[f20])).
% 0.12/0.25 thf(f22,plain,(
% 0.12/0.25 ( ! [X2 : $i,X1 : $i] : (($true = (((in @ X1 @ (setunion @ X2)) = (?? @ $i @ (^[Y0 : $i]: ((in @ X1 @ Y0) & (in @ Y0 @ X2)))))))) )),
% 0.12/0.25 inference(beta-eta_normalization,[],[f21])).
% 0.12/0.25 thf(f23,plain,(
% 0.12/0.25 ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ (setunion @ X2))) = ((?? @ $i @ (^[Y0 : $i]: ((in @ X1 @ Y0) & (in @ Y0 @ X2))))))) )),
% 0.12/0.25 inference(iff_proxy_clausification,[],[f22])).
% 0.12/0.25 thf(f25,plain,(
% 0.12/0.25 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ X1 @ (setunion @ X2)))) | ($true = ((?? @ $i @ (^[Y0 : $i]: ((in @ X1 @ Y0) & (in @ Y0 @ X2))))))) )),
% 0.12/0.25 inference(iff_proxy_clausification,[],[f23])).
% 0.12/0.25 thf(f26,plain,(
% 0.12/0.25 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ X1 @ (setunion @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ X1 @ Y0) & (in @ Y0 @ X2))) @ (sK3 @ X1 @ X2))))) )),
% 0.12/0.25 inference(sigma_proxy_clausification,[],[f25])).
% 0.12/0.25 thf(f27,plain,(
% 0.12/0.25 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ X1 @ (setunion @ X2)))) | ($true = (((in @ X1 @ (sK3 @ X1 @ X2)) & (in @ (sK3 @ X1 @ X2) @ X2))))) )),
% 0.12/0.25 inference(beta-eta_normalization,[],[f26])).
% 0.12/0.25 thf(f28,plain,(
% 0.12/0.25 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ (sK3 @ X1 @ X2) @ X2))) | ($false = ((in @ X1 @ (setunion @ X2))))) )),
% 0.12/0.25 inference(and_proxy_clausification,[],[f27])).
% 0.12/0.25 thf(f29,plain,(
% 0.12/0.25 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X1 @ (sK3 @ X1 @ X2)))) | ($false = ((in @ X1 @ (setunion @ X2))))) )),
% 0.12/0.25 inference(and_proxy_clausification,[],[f27])).
% 0.12/0.25 thf(f34,definition,(
% 0.12/0.25 spl4_1 <=> ! [X3 : $i] : (($true != ((in @ X3 @ sK0))) | ($true != ((in @ sK1 @ X3))))),
% 0.12/0.25 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.12/0.25 thf(f35,plain,(
% 0.12/0.25 ( ! [X3 : $i] : (($true != ((in @ sK1 @ X3))) | ($true != ((in @ X3 @ sK0)))) ) | ~spl4_1),
% 0.12/0.25 inference(avatar_component_clause,[],[f34])).
% 0.12/0.25 thf(f37,definition,(
% 0.12/0.25 spl4_2 <=> ($true = sK2)),
% 0.12/0.25 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.12/0.25 thf(f40,plain,(
% 0.12/0.25 spl4_1 | spl4_2),
% 0.12/0.25 inference(avatar_split_clause,[],[f14,f37,f34])).
% 0.12/0.25 thf(f41,plain,(
% 0.12/0.25 ~spl4_2),
% 0.12/0.25 inference(avatar_split_clause,[],[f15,f37])).
% 0.12/0.25 thf(f46,plain,(
% 0.12/0.25 ( ! [X0 : $i] : (($true != $true) | ($true != ((in @ X0 @ sK0))) | ($false = ((in @ sK1 @ X0)))) ) | ~spl4_1),
% 0.12/0.25 inference(constrained_superposition,[],[f35,f17])).
% 0.12/0.25 thf(f50,plain,(
% 0.12/0.25 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK0))) | ($false = ((in @ sK1 @ X0)))) ) | ~spl4_1),
% 0.12/0.25 inference(trivial_inequality_removal,[],[f46])).
% 0.12/0.25 thf(f97,plain,(
% 0.12/0.25 ( ! [X0 : $i] : (($true != $true) | ($false = ((in @ sK1 @ (sK3 @ X0 @ sK0)))) | ($false = ((in @ X0 @ (setunion @ sK0))))) ) | ~spl4_1),
% 0.12/0.25 inference(constrained_superposition,[],[f50,f28])).
% 0.12/0.25 thf(f102,plain,(
% 0.12/0.25 ( ! [X0 : $i] : (($false = ((in @ sK1 @ (sK3 @ X0 @ sK0)))) | ($false = ((in @ X0 @ (setunion @ sK0))))) ) | ~spl4_1),
% 0.12/0.25 inference(trivial_inequality_removal,[],[f97])).
% 0.12/0.25 thf(f120,plain,(
% 0.12/0.25 ($true = $false) | (((in @ sK1 @ (setunion @ sK0))) = $false) | (((in @ sK1 @ (setunion @ sK0))) = $false) | ~spl4_1),
% 0.12/0.25 inference(constrained_superposition,[],[f29,f102])).
% 0.12/0.25 thf(f121,plain,(
% 0.12/0.25 ($true = $false) | (((in @ sK1 @ (setunion @ sK0))) = $false) | ~spl4_1),
% 0.12/0.25 inference(duplicate_literal_removal,[],[f120])).
% 0.12/0.25 thf(f122,plain,(
% 0.12/0.25 (((in @ sK1 @ (setunion @ sK0))) = $false) | ~spl4_1),
% 0.12/0.25 inference(trivial_inequality_removal,[],[f121])).
% 0.12/0.25 thf(f127,plain,(
% 0.12/0.25 ($true = $false) | ~spl4_1),
% 0.12/0.25 inference(constrained_superposition,[],[f122,f13])).
% 0.12/0.25 thf(f136,plain,(
% 0.12/0.25 $false | ~spl4_1),
% 0.12/0.25 inference(trivial_inequality_removal,[],[f127])).
% 0.12/0.25 thf(f137,plain,(
% 0.12/0.25 ~spl4_1),
% 0.12/0.25 inference(avatar_contradiction_clause,[],[f136])).
% 0.12/0.25 cnf(s1, plain, spl4_1 | spl4_2, inference(sat_conversion,[],[f40])).
% 0.12/0.25 cnf(s2, plain, ~spl4_2, inference(sat_conversion,[],[f41])).
% 0.12/0.25 cnf(s4, plain, ~spl4_1, inference(sat_conversion,[],[f137])).
% 0.12/0.25 cnf(s5, plain, $false, inference(rat,[],[s1,s2,s4])).
% 0.12/0.25 thf(f139,plain,(
% 0.12/0.25 $false),
% 0.12/0.25 inference(avatar_sat_refutation,[],[s5])).
% 0.12/0.25 % SZS output end Proof for theBenchmark
% 0.12/0.25 % (2882050)------------------------------
% 0.12/0.25 % (2882050)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.25 % (2882050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.25 % (2882050)CaDiCaL version: 2.1.3
% 0.12/0.25 % (2882050)Termination reason: Refutation
% 0.12/0.25 % (2882050)Time elapsed: 0.004 s
% 0.12/0.25 % (2882050)Peak memory usage: 13 MB
% 0.12/0.25 % (2882050)Instructions burned: 11 (million)
% 0.12/0.25 % (2882038)Success in time 0.038 s
% 0.12/0.25 % Vampire exiting
%------------------------------------------------------------------------------