%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET580^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 08:23:38 AM UTC 2026
% Result : Theorem 0.18s 0.27s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET580^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n019.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:38:03 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.18/0.27 % (773135)Will run a generic schedule for satisfiability detection.
% 0.18/0.27 % (773141)% WARNING: option uhcvi not known.
% 0.18/0.27 % (773142)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1616045622:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.27 % (773146)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3567225455:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.27 % (773141)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1242627317:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.27 % (773141)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.27 % (773141)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.18/0.27 % (773140)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=931041577_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.27 % Exception at run slice level
% 0.18/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.27 % (773141) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-773135-773141"...
% 0.18/0.27 % (773141)...printing done.
% 0.18/0.27 % (773145)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2493143708:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.27 % (773146) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-773135-773146"...
% 0.18/0.27 % (773141)Refutation found. Thanks to Tanya!
% 0.18/0.27 % SZS status Theorem for theBenchmark
% 0.18/0.27 % SZS output start Proof for theBenchmark
% 0.18/0.27 thf(type_def_5, type, a: $tType).
% 0.18/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.18/0.27 thf(func_def_3, type, sP0: ((a > $o) > (a > $o) > a > $o)).
% 0.18/0.27 thf(func_def_4, type, sK1: a).
% 0.18/0.27 thf(func_def_5, type, sK2: (a > $o)).
% 0.18/0.27 thf(func_def_6, type, sK3: (a > $o)).
% 0.18/0.27 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.18/0.27 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.18/0.27 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.18/0.27 thf(f1,conjecture,(
% 0.18/0.27 ! [X0 : a,X1 : (a > $o),X2 : (a > $o)] : ((((~(X1 @ X0) & (X2 @ X0)) | (~(X2 @ X0) & (X1 @ X0))) <=> (X1 @ X0)) <=> ~(X2 @ X0))),
% 0.18/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_23_pme)).
% 0.18/0.27 thf(f2,negated_conjecture,(
% 0.18/0.27 ~ ! [X0 : a,X1 : (a > $o),X2 : (a > $o)] : ((((~(X1 @ X0) & (X2 @ X0)) | (~(X2 @ X0) & (X1 @ X0))) <=> (X1 @ X0)) <=> ~(X2 @ X0))),
% 0.18/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.18/0.27 thf(f3,plain,(
% 0.18/0.27 ~ ! [X0 : a,X1 : (a > $o),X2 : (a > $o)] : ((((~(X1 @ X0) & (X2 @ X0)) | (~(X2 @ X0) & (X1 @ X0))) <=> (X1 @ X0)) <=> ~(X2 @ X0))),
% 0.18/0.27 inference(rectify,[],[f2])).
% 0.18/0.27 thf(f4,plain,(
% 0.18/0.27 ~ ! [X0 : a,X1 : (a > $o),X2 : (a > $o)] : ((((~ (((X1 @ X0)) = $true) & (((X2 @ X0)) = $true)) | (~ (((X2 @ X0)) = $true) & (((X1 @ X0)) = $true))) <=> (((X1 @ X0)) = $true)) <=> ~ (((X2 @ X0)) = $true))),
% 0.18/0.27 inference(fool_elimination,[],[f3])).
% 0.18/0.27 thf(f5,plain,(
% 0.18/0.27 ~ ! [X0 : a,X1 : (a > $o),X2 : (a > $o)] : (((((((X1 @ X0)) != $true) & (((X2 @ X0)) = $true)) | ((((X2 @ X0)) != $true) & (((X1 @ X0)) = $true))) <=> (((X1 @ X0)) = $true)) <=> (((X2 @ X0)) != $true))),
% 0.18/0.27 inference(flattening,[],[f4])).
% 0.18/0.27 thf(f6,plain,(
% 0.18/0.27 ? [X0 : a,X1 : (a > $o),X2 : (a > $o)] : (((((((X1 @ X0)) != $true) & (((X2 @ X0)) = $true)) | ((((X2 @ X0)) != $true) & (((X1 @ X0)) = $true))) <=> (((X1 @ X0)) = $true)) <~> (((X2 @ X0)) != $true))),
% 0.18/0.27 inference(ennf_transformation,[],[f5])).
% 0.18/0.27 thf(f7,definition,(
% 0.18/0.27 ! [X0 : a,X1 : (a > $o),X2 : (a > $o)] : (($true = ((sP0 @ X2 @ X1 @ X0))) <=> ((((((X1 @ X0)) != $true) & (((X2 @ X0)) = $true)) | ((((X2 @ X0)) != $true) & (((X1 @ X0)) = $true))) <=> (((X1 @ X0)) = $true)))),
% 0.18/0.27 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.18/0.27 thf(f8,plain,(
% 0.18/0.27 ? [X0 : a,X1 : (a > $o),X2 : (a > $o)] : (($true = ((sP0 @ X2 @ X1 @ X0))) <~> (((X2 @ X0)) != $true))),
% 0.18/0.27 inference(definition_folding,[],[f6,f7])).
% 0.18/0.27 thf(f9,plain,(
% 0.18/0.27 ! [X0 : a,X1 : (a > $o),X2 : (a > $o)] : ((($true = ((sP0 @ X2 @ X1 @ X0))) | (((((X1 @ X0)) != $true) | (((((X1 @ X0)) = $true) | (((X2 @ X0)) != $true)) & ((((X2 @ X0)) = $true) | (((X1 @ X0)) != $true)))) & ((((X1 @ X0)) = $true) | (((((X1 @ X0)) != $true) & (((X2 @ X0)) = $true)) | ((((X2 @ X0)) != $true) & (((X1 @ X0)) = $true)))))) & ((((((((X1 @ X0)) != $true) & (((X2 @ X0)) = $true)) | ((((X2 @ X0)) != $true) & (((X1 @ X0)) = $true))) | (((X1 @ X0)) != $true)) & ((((X1 @ X0)) = $true) | (((((X1 @ X0)) = $true) | (((X2 @ X0)) != $true)) & ((((X2 @ X0)) = $true) | (((X1 @ X0)) != $true))))) | ($true != ((sP0 @ X2 @ X1 @ X0)))))),
% 0.18/0.27 inference(nnf_transformation,[],[f7])).
% 0.18/0.27 thf(f10,plain,(
% 0.18/0.27 ! [X0 : a,X1 : (a > $o),X2 : (a > $o)] : ((($true = ((sP0 @ X2 @ X1 @ X0))) | (((((X1 @ X0)) != $true) | (((((X1 @ X0)) = $true) | (((X2 @ X0)) != $true)) & ((((X2 @ X0)) = $true) | (((X1 @ X0)) != $true)))) & ((((X1 @ X0)) = $true) | ((((X1 @ X0)) != $true) & (((X2 @ X0)) = $true)) | ((((X2 @ X0)) != $true) & (((X1 @ X0)) = $true))))) & (((((((X1 @ X0)) != $true) & (((X2 @ X0)) = $true)) | ((((X2 @ X0)) != $true) & (((X1 @ X0)) = $true)) | (((X1 @ X0)) != $true)) & ((((X1 @ X0)) = $true) | (((((X1 @ X0)) = $true) | (((X2 @ X0)) != $true)) & ((((X2 @ X0)) = $true) | (((X1 @ X0)) != $true))))) | ($true != ((sP0 @ X2 @ X1 @ X0)))))),
% 0.18/0.27 inference(flattening,[],[f9])).
% 0.18/0.27 thf(f11,plain,(
% 0.18/0.27 ? [X0 : a,X1 : (a > $o),X2 : (a > $o)] : (((((X2 @ X0)) = $true) | ($true != ((sP0 @ X2 @ X1 @ X0)))) & ((((X2 @ X0)) != $true) | ($true = ((sP0 @ X2 @ X1 @ X0)))))),
% 0.18/0.27 inference(nnf_transformation,[],[f8])).
% 0.18/0.27 thf(f12,plain,(
% 0.18/0.27 (($true = ((sK3 @ sK1))) | ($true != ((sP0 @ sK3 @ sK2 @ sK1)))) & (($true != ((sK3 @ sK1))) | ($true = ((sP0 @ sK3 @ sK2 @ sK1))))),
% 0.18/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f11])).
% 0.18/0.27 thf(f14,plain,(
% 0.18/0.27 ( ! [X2 : (a > $o),X0 : a,X1 : (a > $o)] : ((((X1 @ X0)) = $true) | (((X1 @ X0)) = $true) | (((X2 @ X0)) != $true) | ($true != ((sP0 @ X2 @ X1 @ X0)))) )),
% 0.18/0.27 inference(cnf_transformation,[],[f10])).
% 0.18/0.27 thf(f18,plain,(
% 0.18/0.27 ( ! [X2 : (a > $o),X0 : a,X1 : (a > $o)] : ((((X1 @ X0)) != $true) | (((X2 @ X0)) != $true) | (((X1 @ X0)) != $true) | ($true != ((sP0 @ X2 @ X1 @ X0)))) )),
% 0.18/0.27 inference(cnf_transformation,[],[f10])).
% 0.18/0.27 thf(f19,plain,(
% 0.18/0.27 ( ! [X2 : (a > $o),X0 : a,X1 : (a > $o)] : (($true = ((sP0 @ X2 @ X1 @ X0))) | (((X1 @ X0)) = $true) | (((X2 @ X0)) = $true) | (((X1 @ X0)) = $true)) )),
% 0.18/0.27 inference(cnf_transformation,[],[f10])).
% 0.18/0.27 thf(f23,plain,(
% 0.18/0.27 ( ! [X2 : (a > $o),X0 : a,X1 : (a > $o)] : (($true = ((sP0 @ X2 @ X1 @ X0))) | (((X1 @ X0)) != $true) | (((X2 @ X0)) = $true) | (((X1 @ X0)) != $true)) )),
% 0.18/0.27 inference(cnf_transformation,[],[f10])).
% 0.18/0.27 thf(f25,plain,(
% 0.18/0.27 ($true != ((sK3 @ sK1))) | ($true = ((sP0 @ sK3 @ sK2 @ sK1)))),
% 0.18/0.27 inference(cnf_transformation,[],[f12])).
% 0.18/0.27 thf(f26,plain,(
% 0.18/0.27 ($true = ((sK3 @ sK1))) | ($true != ((sP0 @ sK3 @ sK2 @ sK1)))),
% 0.18/0.27 inference(cnf_transformation,[],[f12])).
% 0.18/0.27 thf(f28,definition,(
% 0.18/0.27 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.18/0.27 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.18/0.27 thf(f29,plain,(
% 0.18/0.27 ( ! [X2 : (a > $o),X0 : a,X1 : (a > $o)] : (($true != ((sP0 @ X2 @ X1 @ X0))) | (((X2 @ X0)) != $true) | (((X1 @ X0)) = $true)) )),
% 0.18/0.27 inference(duplicate_literal_removal,[],[f14])).
% 0.18/0.27 thf(f31,plain,(
% 0.18/0.27 ( ! [X2 : (a > $o),X0 : a,X1 : (a > $o)] : ((((X1 @ X0)) != $true) | (((X2 @ X0)) != $true) | ($true != ((sP0 @ X2 @ X1 @ X0)))) )),
% 0.18/0.27 inference(duplicate_literal_removal,[],[f18])).
% 0.18/0.27 thf(f32,plain,(
% 0.18/0.27 ( ! [X2 : (a > $o),X0 : a,X1 : (a > $o)] : (($true = ((sP0 @ X2 @ X1 @ X0))) | (((X1 @ X0)) = $true) | (((X2 @ X0)) = $true)) )),
% 0.18/0.27 inference(duplicate_literal_removal,[],[f19])).
% 0.18/0.27 thf(f34,plain,(
% 0.18/0.27 ( ! [X2 : (a > $o),X0 : a,X1 : (a > $o)] : (($true = ((sP0 @ X2 @ X1 @ X0))) | (((X1 @ X0)) != $true) | (((X2 @ X0)) = $true)) )),
% 0.18/0.27 inference(duplicate_literal_removal,[],[f23])).
% 0.18/0.27 thf(f36,definition,(
% 0.18/0.27 spl4_1 <=> ($true = ((sP0 @ sK3 @ sK2 @ sK1)))),
% 0.18/0.27 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.18/0.27 thf(f37,plain,(
% 0.18/0.27 ($true != ((sP0 @ sK3 @ sK2 @ sK1))) | spl4_1),
% 0.18/0.27 inference(avatar_component_clause,[],[f36])).
% 0.18/0.27 thf(f38,plain,(
% 0.18/0.27 ($true = ((sP0 @ sK3 @ sK2 @ sK1))) | ~spl4_1),
% 0.18/0.27 inference(avatar_component_clause,[],[f36])).
% 0.18/0.27 thf(f40,definition,(
% 0.18/0.27 spl4_2 <=> ($true = ((sK3 @ sK1)))),
% 0.18/0.27 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.18/0.27 thf(f41,plain,(
% 0.18/0.27 ($true = ((sK3 @ sK1))) | ~spl4_2),
% 0.18/0.27 inference(avatar_component_clause,[],[f40])).
% 0.18/0.27 thf(f42,plain,(
% 0.18/0.27 ($true != ((sK3 @ sK1))) | spl4_2),
% 0.18/0.27 inference(avatar_component_clause,[],[f40])).
% 0.18/0.27 thf(f43,plain,(
% 0.18/0.27 spl4_1 | ~spl4_2),
% 0.18/0.27 inference(avatar_split_clause,[],[f25,f40,f36])).
% 0.18/0.27 thf(f44,plain,(
% 0.18/0.27 ~spl4_1 | spl4_2),
% 0.18/0.27 inference(avatar_split_clause,[],[f26,f40,f36])).
% 0.18/0.27 thf(f48,plain,(
% 0.18/0.27 ($true != $true) | (((sP0 @ sK3 @ sK2 @ sK1)) = $false) | spl4_1),
% 0.18/0.27 inference(constrained_superposition,[],[f37,f28])).
% 0.18/0.27 thf(f50,plain,(
% 0.18/0.27 (((sP0 @ sK3 @ sK2 @ sK1)) = $false) | spl4_1),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f48])).
% 0.18/0.27 thf(f61,plain,(
% 0.18/0.27 ( ! [X2 : (a > $o),X0 : a,X1 : (a > $o)] : (($true != ((sP0 @ X2 @ X1 @ X0))) | (((X2 @ X0)) != $true)) )),
% 0.18/0.27 inference(forward_subsumption_resolution,[],[f31,f29])).
% 0.18/0.27 thf(f151,plain,(
% 0.18/0.27 ( ! [X2 : (a > $o),X0 : a,X1 : (a > $o)] : (($true = ((sP0 @ X2 @ X1 @ X0))) | (((X2 @ X0)) = $true)) )),
% 0.18/0.27 inference(forward_subsumption_resolution,[],[f34,f32])).
% 0.18/0.27 thf(f152,plain,(
% 0.18/0.27 ($true = $false) | ($true = ((sK3 @ sK1))) | spl4_1),
% 0.18/0.27 inference(constrained_superposition,[],[f151,f50])).
% 0.18/0.27 thf(f167,plain,(
% 0.18/0.27 ($true = ((sK3 @ sK1))) | spl4_1),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f152])).
% 0.18/0.27 thf(f172,plain,(
% 0.18/0.27 $false | (spl4_1 | spl4_2)),
% 0.18/0.27 inference(forward_subsumption_resolution,[],[f167,f42])).
% 0.18/0.27 thf(f173,plain,(
% 0.18/0.27 spl4_1 | spl4_2),
% 0.18/0.27 inference(avatar_contradiction_clause,[],[f172])).
% 0.18/0.27 thf(f182,plain,(
% 0.18/0.27 ($true != $true) | ($true != ((sK3 @ sK1))) | ~spl4_1),
% 0.18/0.27 inference(constrained_superposition,[],[f61,f38])).
% 0.18/0.27 thf(f185,plain,(
% 0.18/0.27 ($true != ((sK3 @ sK1))) | ~spl4_1),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f182])).
% 0.18/0.27 thf(f191,plain,(
% 0.18/0.27 $false | (~spl4_1 | ~spl4_2)),
% 0.18/0.27 inference(forward_subsumption_resolution,[],[f185,f41])).
% 0.18/0.27 thf(f192,plain,(
% 0.18/0.27 ~spl4_1 | ~spl4_2),
% 0.18/0.27 inference(avatar_contradiction_clause,[],[f191])).
% 0.18/0.27 cnf(s1, plain, spl4_1 | ~spl4_2, inference(sat_conversion,[],[f43])).
% 0.18/0.27 cnf(s2, plain, ~spl4_1 | spl4_2, inference(sat_conversion,[],[f44])).
% 0.18/0.27 cnf(s11, plain, spl4_1 | spl4_2, inference(sat_conversion,[],[f173])).
% 0.18/0.27 cnf(s12, plain, ~spl4_1 | ~spl4_2, inference(sat_conversion,[],[f192])).
% 0.18/0.27 cnf(s14, plain, spl4_1, inference(rat,[],[s1,s11])).
% 0.18/0.27 cnf(s15, plain, ~spl4_2, inference(rat,[],[s12,s14])).
% 0.18/0.27 cnf(s16, plain, $false, inference(rat,[],[s2,s15,s14])).
% 0.18/0.27 thf(f193,plain,(
% 0.18/0.27 $false),
% 0.18/0.27 inference(avatar_sat_refutation,[],[s16])).
% 0.18/0.27 % SZS output end Proof for theBenchmark
% 0.18/0.27 % (773141)------------------------------
% 0.18/0.27 % (773141)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (773141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (773141)CaDiCaL version: 2.1.3
% 0.18/0.27 % (773141)Termination reason: Refutation
% 0.18/0.27 % (773141)Time elapsed: 0.008 s
% 0.18/0.27 % (773141)Peak memory usage: 13 MB
% 0.18/0.27 % (773141)Instructions burned: 10 (million)
% 0.18/0.27 % (773135)Success in time 0.043 s
% 0.18/0.27 % Vampire exiting
%------------------------------------------------------------------------------