%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU530^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 08:29:56 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU530^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n017.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 13:43:52 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.27 % (359929)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.27 % (359937)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3991352729:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.19/0.27 % (359937) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-359929-359937"...
% 0.19/0.27 % (359937)...printing done.
% 0.19/0.27 % (359937)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% 0.19/0.27 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.27 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.19/0.27 thf(func_def_2, type, setadjoin: ($i > $i > $i)).
% 0.19/0.27 thf(func_def_3, type, uniqinunit: $o).
% 0.19/0.27 thf(func_def_5, type, eqinunit: $o).
% 0.19/0.27 thf(f1,axiom,(
% 0.19/0.27 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)) = uniqinunit)),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit)).
% 0.19/0.27 thf(f3,conjecture,(
% 0.19/0.27 uniqinunit => (eqinunit => ! [X1 : $i,X0 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (in @ X1 @ (setadjoin @ X0 @ emptyset))))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch)).
% 0.19/0.27 thf(f4,negated_conjecture,(
% 0.19/0.27 ~(uniqinunit => (eqinunit => ! [X1 : $i,X0 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (in @ X1 @ (setadjoin @ X0 @ emptyset)))))),
% 0.19/0.27 inference(negated_conjecture,[status(cth)],[f3])).
% 0.19/0.27 thf(f5,plain,(
% 0.19/0.27 ~(uniqinunit => (eqinunit => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X0 @ emptyset)) => (in @ X0 @ (setadjoin @ X1 @ emptyset)))))),
% 0.19/0.27 inference(rectify,[],[f4])).
% 0.19/0.27 thf(f6,plain,(
% 0.19/0.27 ~((uniqinunit = $true) => ((eqinunit = $true) => ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (setadjoin @ X0 @ emptyset))) = $true) => (((in @ X0 @ (setadjoin @ X1 @ emptyset))) = $true))))),
% 0.19/0.27 inference(fool_elimination,[],[f5])).
% 0.19/0.27 thf(f9,plain,(
% 0.19/0.27 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)) = uniqinunit)),
% 0.19/0.27 inference(rectify,[],[f1])).
% 0.19/0.27 thf(f10,plain,(
% 0.19/0.27 ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (setadjoin @ X1 @ emptyset))) = $true) => (X0 = X1)) <=> (uniqinunit = $true)),
% 0.19/0.27 inference(fool_elimination,[],[f9])).
% 0.19/0.27 thf(f12,plain,(
% 0.19/0.27 (? [X0 : $i,X1 : $i] : ((((in @ X1 @ (setadjoin @ X0 @ emptyset))) = $true) & (((in @ X0 @ (setadjoin @ X1 @ emptyset))) != $true)) & (eqinunit = $true)) & (uniqinunit = $true)),
% 0.19/0.27 inference(ennf_transformation,[],[f6])).
% 0.19/0.27 thf(f13,plain,(
% 0.19/0.27 (uniqinunit = $true) & ? [X0 : $i,X1 : $i] : ((((in @ X1 @ (setadjoin @ X0 @ emptyset))) = $true) & (((in @ X0 @ (setadjoin @ X1 @ emptyset))) != $true)) & (eqinunit = $true)),
% 0.19/0.27 inference(flattening,[],[f12])).
% 0.19/0.27 thf(f14,plain,(
% 0.19/0.27 (uniqinunit = $true) <=> ! [X1 : $i,X0 : $i] : ((X0 = X1) | (((in @ X0 @ (setadjoin @ X1 @ emptyset))) != $true))),
% 0.19/0.27 inference(ennf_transformation,[],[f10])).
% 0.19/0.27 thf(f15,plain,(
% 0.19/0.27 ((uniqinunit = $true) | ? [X1 : $i,X0 : $i] : ((X0 != X1) & (((in @ X0 @ (setadjoin @ X1 @ emptyset))) = $true))) & (! [X1 : $i,X0 : $i] : ((X0 = X1) | (((in @ X0 @ (setadjoin @ X1 @ emptyset))) != $true)) | (uniqinunit != $true))),
% 0.19/0.27 inference(nnf_transformation,[],[f14])).
% 0.19/0.27 thf(f16,plain,(
% 0.19/0.27 ((uniqinunit = $true) | ? [X0 : $i,X1 : $i] : ((X0 != X1) & (((in @ X1 @ (setadjoin @ X0 @ emptyset))) = $true))) & (! [X2 : $i,X3 : $i] : ((X2 = X3) | ($true != ((in @ X3 @ (setadjoin @ X2 @ emptyset))))) | (uniqinunit != $true))),
% 0.19/0.27 inference(rectify,[],[f15])).
% 0.19/0.27 thf(f17,plain,(
% 0.19/0.27 ((uniqinunit = $true) | ((sK0 != sK1) & ($true = ((in @ sK1 @ (setadjoin @ sK0 @ emptyset)))))) & (! [X2 : $i,X3 : $i] : ((X2 = X3) | ($true != ((in @ X3 @ (setadjoin @ X2 @ emptyset))))) | (uniqinunit != $true))),
% 0.19/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16])).
% 0.19/0.27 thf(f18,plain,(
% 0.19/0.27 (uniqinunit = $true) & (($true = ((in @ sK3 @ (setadjoin @ sK2 @ emptyset)))) & ($true != ((in @ sK2 @ (setadjoin @ sK3 @ emptyset))))) & (eqinunit = $true)),
% 0.19/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f13])).
% 0.19/0.27 thf(f22,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i] : ((uniqinunit != $true) | (X2 = X3) | ($true != ((in @ X3 @ (setadjoin @ X2 @ emptyset))))) )),
% 0.19/0.27 inference(cnf_transformation,[],[f17])).
% 0.19/0.27 thf(f26,plain,(
% 0.19/0.27 ($true != ((in @ sK2 @ (setadjoin @ sK3 @ emptyset))))),
% 0.19/0.27 inference(cnf_transformation,[],[f18])).
% 0.19/0.27 thf(f27,plain,(
% 0.19/0.27 ($true = ((in @ sK3 @ (setadjoin @ sK2 @ emptyset))))),
% 0.19/0.27 inference(cnf_transformation,[],[f18])).
% 0.19/0.27 thf(f28,plain,(
% 0.19/0.27 (uniqinunit = $true)),
% 0.19/0.27 inference(cnf_transformation,[],[f18])).
% 0.19/0.27 thf(f48,definition,(
% 0.19/0.27 spl6_4 <=> (uniqinunit = $true)),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition])).
% 0.19/0.27 thf(f52,definition,(
% 0.19/0.27 spl6_5 <=> ! [X2 : $i,X3 : $i] : ((X2 = X3) | ($true != ((in @ X3 @ (setadjoin @ X2 @ emptyset)))))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition])).
% 0.19/0.27 thf(f53,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i] : (($true != ((in @ X3 @ (setadjoin @ X2 @ emptyset)))) | (X2 = X3)) ) | ~spl6_5),
% 0.19/0.27 inference(avatar_component_clause,[],[f52])).
% 0.19/0.27 thf(f54,plain,(
% 0.19/0.27 ~spl6_4 | spl6_5),
% 0.19/0.27 inference(avatar_split_clause,[],[f22,f52,f48])).
% 0.19/0.27 thf(f65,plain,(
% 0.19/0.27 spl6_4),
% 0.19/0.27 inference(avatar_split_clause,[],[f28,f48])).
% 0.19/0.27 thf(f68,definition,(
% 0.19/0.27 spl6_8 <=> ($true = ((in @ sK2 @ (setadjoin @ sK3 @ emptyset))))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition])).
% 0.19/0.27 thf(f71,plain,(
% 0.19/0.27 ~spl6_8),
% 0.19/0.27 inference(avatar_split_clause,[],[f26,f68])).
% 0.19/0.27 thf(f73,definition,(
% 0.19/0.27 spl6_9 <=> ($true = ((in @ sK3 @ (setadjoin @ sK2 @ emptyset))))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition])).
% 0.19/0.27 thf(f75,plain,(
% 0.19/0.27 ($true = ((in @ sK3 @ (setadjoin @ sK2 @ emptyset)))) | ~spl6_9),
% 0.19/0.27 inference(avatar_component_clause,[],[f73])).
% 0.19/0.27 thf(f76,plain,(
% 0.19/0.27 spl6_9),
% 0.19/0.27 inference(avatar_split_clause,[],[f27,f73])).
% 0.19/0.27 thf(f84,plain,(
% 0.19/0.27 ($true != $true) | (sK3 = sK2) | (~spl6_5 | ~spl6_9)),
% 0.19/0.27 inference(superposition,[],[f53,f75])).
% 0.19/0.27 thf(f85,plain,(
% 0.19/0.27 (sK3 = sK2) | (~spl6_5 | ~spl6_9)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f84])).
% 0.19/0.27 thf(f87,definition,(
% 0.19/0.27 spl6_11 <=> (sK3 = sK2)),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl6_11])],[avatar_definition])).
% 0.19/0.27 thf(f90,plain,(
% 0.19/0.27 spl6_11 | ~spl6_5 | ~spl6_9),
% 0.19/0.27 inference(avatar_split_clause,[],[f85,f73,f52,f87])).
% 0.19/0.27 thf(f91,definition,(
% 0.19/0.27 (sK3 != sK2) | ($true != ((in @ sK3 @ (setadjoin @ sK2 @ emptyset)))) | ($true = ((in @ sK2 @ (setadjoin @ sK3 @ emptyset))))),
% 0.19/0.27 introduced(theory,[theory_tautology_sat_conflict])).
% 0.19/0.27 cnf(s3, plain, ~spl6_4 | spl6_5, inference(sat_conversion,[],[f54])).
% 0.19/0.27 cnf(s6, plain, spl6_4, inference(sat_conversion,[],[f65])).
% 0.19/0.27 cnf(s8, plain, ~spl6_8, inference(sat_conversion,[],[f71])).
% 0.19/0.27 cnf(s9, plain, spl6_9, inference(sat_conversion,[],[f76])).
% 0.19/0.27 cnf(s11, plain, ~spl6_5 | ~spl6_9 | spl6_11, inference(sat_conversion,[],[f90])).
% 0.19/0.27 cnf(s12, plain, spl6_8 | ~spl6_9 | ~spl6_11, inference(sat_conversion,[],[f91])).
% 0.19/0.27 cnf(s13, plain, ~spl6_11, inference(rat,[],[s12,s9,s8])).
% 0.19/0.27 cnf(s14, plain, ~spl6_5, inference(rat,[],[s11,s9,s13])).
% 0.19/0.27 cnf(s15, plain, $false, inference(rat,[],[s3,s14,s6])).
% 0.19/0.27 thf(f92,plain,(
% 0.19/0.27 $false),
% 0.19/0.27 inference(avatar_sat_refutation,[],[s15])).
% 0.19/0.27 % SZS output end Proof for theBenchmark
% 0.19/0.27 % (359937)------------------------------
% 0.19/0.27 % (359937)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (359937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (359937)CaDiCaL version: 2.1.3
% 0.19/0.27 % (359937)Termination reason: Refutation
% 0.19/0.27 % (359937)Time elapsed: 0.002 s
% 0.19/0.27 % (359937)Peak memory usage: 13 MB
% 0.19/0.27 % (359937)Instructions burned: 4 (million)
% 0.19/0.27 % (359929)Success in time 0.038 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------