%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU545^2 : 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 : n016.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 08:32:23 AM UTC 2026
% Result : Theorem 0.22s 0.26s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU545^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n016.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:54:35 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.22/0.26 % (386761)Will run a generic schedule for satisfiability detection.
% 0.22/0.26 % (386772)% WARNING: option uhcvi not known.
% 0.22/0.26 % (386772)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1794213089:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.22/0.26 % (386772)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.26 % (386772)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.26 % (386773)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1643880223:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.22/0.26 % (386771)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2373864446_3000 on theBenchmark for (3000ds/0Mi)
% 0.22/0.26 % (386774)dis+10_1_sil=32000:sp=arity:random_seed=4241426099:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.22/0.26 % (386775)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1202079444:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.22/0.26 % (386776)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3898955431:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.22/0.26 % Exception at run slice level
% 0.22/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.26 % (386777)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1951005172:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.22/0.26 % (386775)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.26 % (386772) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-386761-386772"...
% 0.22/0.26 % (386772)...printing done.
% 0.22/0.26 % (386775) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-386761-386775"...
% 0.22/0.26 % (386773) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-386761-386773"...
% 0.22/0.26 % (386777) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-386761-386777"...
% 0.22/0.26 % (386776) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-386761-386776"...
% 0.22/0.26 % (386775)...printing done.
% 0.22/0.26 % (386773)...printing done.
% 0.22/0.26 % (386776)...printing done.
% 0.22/0.26 % (386772)Refutation found. Thanks to Tanya!
% 0.22/0.26 % SZS status Theorem for theBenchmark
% 0.22/0.26 % SZS output start Proof for theBenchmark
% 0.22/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.26 thf(func_def_0, type, exu: (($i > $o) > $o)).
% 0.22/0.26 thf(func_def_2, type, exuI1: $o).
% 0.22/0.26 thf(func_def_3, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.26 thf(func_def_4, type, vAND: ($o > $o > $o)).
% 0.22/0.26 thf(func_def_5, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.26 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.26 thf(func_def_7, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.26 thf(func_def_8, type, vIMP: ($o > $o > $o)).
% 0.22/0.26 thf(func_def_9, type, db2: !>[X0: $tType]:(X0)).
% 0.22/0.26 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.26 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.26 thf(func_def_14, type, sK0: ($i > $o)).
% 0.22/0.26 thf(func_def_16, type, vNOT: ($o > $o)).
% 0.22/0.26 thf(func_def_17, type, sK2: ($i > $i)).
% 0.22/0.26 thf(func_def_18, type, sK3: (($i > $o) > $i)).
% 0.22/0.26 thf(func_def_19, type, sK4: (($i > $o) > $i > $i)).
% 0.22/0.26 thf(f1,axiom,(
% 0.22/0.26 (exu = (^[X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 0.22/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu)).
% 0.22/0.26 thf(f3,conjecture,(
% 0.22/0.26 exuI1 => ! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (! [X1 : $i,X2 : $i] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X1 : $i] : ((X0 @ X1))))))),
% 0.22/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI3)).
% 0.22/0.26 thf(f4,negated_conjecture,(
% 0.22/0.26 ~(exuI1 => ! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (! [X1 : $i,X2 : $i] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X1 : $i] : ((X0 @ X1)))))))),
% 0.22/0.26 inference(negated_conjecture,[status(cth)],[f3])).
% 0.22/0.26 thf(f5,plain,(
% 0.22/0.26 (exu = (^[X0 : ($i > $o)] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 0.22/0.26 inference(rectify,[],[f1])).
% 0.22/0.26 thf(f6,plain,(
% 0.22/0.26 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 0.22/0.26 inference(fool_elimination,[],[f5])).
% 0.22/0.26 thf(f9,plain,(
% 0.22/0.26 ~(exuI1 => ! [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) => (! [X2 : $i,X3 : $i] : ((X0 @ X2) => ((X0 @ X3) => (X2 = X3))) => (exu @ (^[X4 : $i] : ((X0 @ X4)))))))),
% 0.22/0.26 inference(rectify,[],[f4])).
% 0.22/0.26 thf(f10,plain,(
% 0.22/0.26 ~((exuI1 = $true) => ! [X0 : ($i > $o)] : (? [X1 : $i] : (((X0 @ X1)) = $true) => (! [X2 : $i,X3 : $i] : ((((X0 @ X2)) = $true) => ((((X0 @ X3)) = $true) => (X2 = X3))) => ($true = ((exu @ (^[Y0 : $i]: (X0 @ Y0))))))))),
% 0.22/0.26 inference(fool_elimination,[],[f9])).
% 0.22/0.26 thf(f11,plain,(
% 0.22/0.26 ? [X0 : ($i > $o)] : ((($true != ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) & ! [X2 : $i,X3 : $i] : (((X2 = X3) | (((X0 @ X3)) != $true)) | (((X0 @ X2)) != $true))) & ? [X1 : $i] : (((X0 @ X1)) = $true)) & (exuI1 = $true)),
% 0.22/0.26 inference(ennf_transformation,[],[f10])).
% 0.22/0.26 thf(f12,plain,(
% 0.22/0.26 ? [X0 : ($i > $o)] : (($true != ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) & ! [X2 : $i,X3 : $i] : ((X2 = X3) | (((X0 @ X3)) != $true) | (((X0 @ X2)) != $true)) & ? [X1 : $i] : (((X0 @ X1)) = $true)) & (exuI1 = $true)),
% 0.22/0.26 inference(flattening,[],[f11])).
% 0.22/0.26 thf(f13,plain,(
% 0.22/0.26 ? [X0 : ($i > $o)] : (($true != ((exu @ (^[Y0 : $i]: (X0 @ Y0))))) & ! [X1 : $i,X2 : $i] : ((X1 = X2) | (((X0 @ X2)) != $true) | (((X0 @ X1)) != $true)) & ? [X3 : $i] : (((X0 @ X3)) = $true)) & (exuI1 = $true)),
% 0.22/0.26 inference(rectify,[],[f12])).
% 0.22/0.26 thf(f14,plain,(
% 0.22/0.26 (($true != ((exu @ (^[Y0 : $i]: (sK0 @ Y0))))) & ! [X1 : $i,X2 : $i] : ((X1 = X2) | ($true != ((sK0 @ X2))) | ($true != ((sK0 @ X1)))) & ($true = ((sK0 @ sK1)))) & (exuI1 = $true)),
% 0.22/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X3,sK1)],[f13])).
% 0.22/0.26 thf(f15,plain,(
% 0.22/0.26 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 0.22/0.26 inference(cnf_transformation,[],[f6])).
% 0.22/0.26 thf(f18,plain,(
% 0.22/0.26 ($true = ((sK0 @ sK1)))),
% 0.22/0.26 inference(cnf_transformation,[],[f14])).
% 0.22/0.26 thf(f19,plain,(
% 0.22/0.26 ( ! [X2 : $i,X1 : $i] : (($true != ((sK0 @ X2))) | (X1 = X2) | ($true != ((sK0 @ X1)))) )),
% 0.22/0.26 inference(cnf_transformation,[],[f14])).
% 0.22/0.26 thf(f20,plain,(
% 0.22/0.26 ($true != ((exu @ (^[Y0 : $i]: (sK0 @ Y0)))))),
% 0.22/0.26 inference(cnf_transformation,[],[f14])).
% 0.22/0.26 thf(f22,definition,(
% 0.22/0.26 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.22/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.22/0.26 thf(f24,plain,(
% 0.22/0.26 ($true != (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))) @ (^[Y0 : $i]: (sK0 @ Y0)))))),
% 0.22/0.26 inference(definition_unfolding,[],[f20,f15])).
% 0.22/0.26 thf(f25,plain,(
% 0.22/0.26 ($true != ((?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))))))),
% 0.22/0.26 inference(beta-eta_normalization,[],[f24])).
% 0.22/0.26 thf(f26,plain,(
% 0.22/0.26 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))) @ X1)))) )),
% 0.22/0.26 inference(pi_proxy_clausification,[],[f25])).
% 0.22/0.26 thf(f27,plain,(
% 0.22/0.26 ( ! [X1 : $i] : (($false = (((sK0 @ X1) & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X1 = Y0)))))))) )),
% 0.22/0.26 inference(beta-eta_normalization,[],[f26])).
% 0.22/0.26 thf(f28,plain,(
% 0.22/0.26 ( ! [X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X1 = Y0)))))) | (((sK0 @ X1)) = $false)) )),
% 0.22/0.26 inference(and_proxy_clausification,[],[f27])).
% 0.22/0.26 thf(f29,plain,(
% 0.22/0.26 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((sK0 @ Y0) => (X1 = Y0))) @ (sK2 @ X1)))) | (((sK0 @ X1)) = $false)) )),
% 0.22/0.26 inference(sigma_proxy_clausification,[],[f28])).
% 0.22/0.26 thf(f30,plain,(
% 0.22/0.26 ( ! [X1 : $i] : (($false = (((sK0 @ (sK2 @ X1)) => (X1 = (sK2 @ X1))))) | (((sK0 @ X1)) = $false)) )),
% 0.22/0.26 inference(beta-eta_normalization,[],[f29])).
% 0.22/0.26 thf(f31,plain,(
% 0.22/0.26 ( ! [X1 : $i] : (($false = ((X1 = (sK2 @ X1)))) | (((sK0 @ X1)) = $false)) )),
% 0.22/0.26 inference(imp_proxy_clausification,[],[f30])).
% 0.22/0.26 thf(f32,plain,(
% 0.22/0.26 ( ! [X1 : $i] : (($true = ((sK0 @ (sK2 @ X1)))) | (((sK0 @ X1)) = $false)) )),
% 0.22/0.26 inference(imp_proxy_clausification,[],[f30])).
% 0.22/0.26 thf(f33,plain,(
% 0.22/0.26 ( ! [X1 : $i] : ((((sK2 @ X1)) != X1) | (((sK0 @ X1)) = $false)) )),
% 0.22/0.26 inference(equality_proxy_clausification,[],[f31])).
% 0.22/0.26 thf(f66,plain,(
% 0.22/0.26 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (X0 = X1) | ($true != ((sK0 @ X1))) | ($false = ((sK0 @ X0)))) )),
% 0.22/0.26 inference(constrained_superposition,[],[f19,f22])).
% 0.22/0.26 thf(f68,plain,(
% 0.22/0.26 ( ! [X0 : $i,X1 : $i] : (($true != ((sK0 @ X1))) | (X0 = X1) | ($false = ((sK0 @ X0)))) )),
% 0.22/0.26 inference(trivial_inequality_removal,[],[f66])).
% 0.22/0.26 thf(f84,plain,(
% 0.22/0.26 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((sK2 @ X0)) = X1) | (((sK0 @ X1)) = $false) | ($false = ((sK0 @ X0)))) )),
% 0.22/0.26 inference(constrained_superposition,[],[f68,f32])).
% 0.22/0.26 thf(f88,plain,(
% 0.22/0.26 ( ! [X0 : $i,X1 : $i] : ((((sK2 @ X0)) = X1) | (((sK0 @ X1)) = $false) | ($false = ((sK0 @ X0)))) )),
% 0.22/0.26 inference(trivial_inequality_removal,[],[f84])).
% 0.22/0.26 thf(f163,plain,(
% 0.22/0.26 ( ! [X0 : $i] : (($false != $false) | (((sK2 @ X0)) = X0) | ($false = ((sK0 @ X0)))) )),
% 0.22/0.26 inference(equality_factoring,[],[f88])).
% 0.22/0.26 thf(f164,plain,(
% 0.22/0.26 ( ! [X0 : $i] : ((((sK2 @ X0)) = X0) | ($false = ((sK0 @ X0)))) )),
% 0.22/0.26 inference(trivial_inequality_removal,[],[f163])).
% 0.22/0.26 thf(f179,plain,(
% 0.22/0.26 ( ! [X0 : $i] : (($false = ((sK0 @ X0)))) )),
% 0.22/0.26 inference(forward_subsumption_resolution,[],[f164,f33])).
% 0.22/0.26 thf(f183,definition,(
% 0.22/0.26 spl5_1 <=> ! [X0 : $i] : ($false = ((sK0 @ X0)))),
% 0.22/0.26 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.22/0.26 thf(f184,plain,(
% 0.22/0.26 ( ! [X0 : $i] : (($false = ((sK0 @ X0)))) ) | ~spl5_1),
% 0.22/0.26 inference(avatar_component_clause,[],[f183])).
% 0.22/0.26 thf(f190,plain,(
% 0.22/0.26 spl5_1),
% 0.22/0.26 inference(avatar_split_clause,[],[f179,f183])).
% 0.22/0.26 thf(f445,plain,(
% 0.22/0.26 ($true = $false) | ~spl5_1),
% 0.22/0.26 inference(constrained_superposition,[],[f184,f18])).
% 0.22/0.26 thf(f471,plain,(
% 0.22/0.26 $false | ~spl5_1),
% 0.22/0.26 inference(trivial_inequality_removal,[],[f445])).
% 0.22/0.26 thf(f472,plain,(
% 0.22/0.26 ~spl5_1),
% 0.22/0.26 inference(avatar_contradiction_clause,[],[f471])).
% 0.22/0.26 cnf(s3, plain, spl5_1, inference(sat_conversion,[],[f190])).
% 0.22/0.26 cnf(s10, plain, ~spl5_1, inference(sat_conversion,[],[f472])).
% 0.22/0.26 cnf(s11, plain, $false, inference(rat,[],[s3,s10])).
% 0.22/0.26 thf(f473,plain,(
% 0.22/0.26 $false),
% 0.22/0.26 inference(avatar_sat_refutation,[],[s11])).
% 0.22/0.26 % SZS output end Proof for theBenchmark
% 0.22/0.26 % (386772)------------------------------
% 0.22/0.26 % (386772)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.26 % (386772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.26 % (386772)CaDiCaL version: 2.1.3
% 0.22/0.26 % (386772)Termination reason: Refutation
% 0.22/0.26 % (386772)Time elapsed: 0.010 s
% 0.22/0.26 % (386772)Peak memory usage: 13 MB
% 0.22/0.26 % (386772)Instructions burned: 31 (million)
% 0.22/0.26 % (386761)Success in time 0.03 s
% 0.22/0.26 % Vampire exiting
%------------------------------------------------------------------------------