%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU849^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 08:31:48 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU849^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n010.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 14:40:18 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.27 % (2947996)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (2948004)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=1414277277: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)
% 0.20/0.27 % (2948004) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2947996-2948004"...
% 0.20/0.27 % (2948004)...printing done.
% 0.20/0.27 % (2948004)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% 0.20/0.27 thf(type_def_5, type, a: $tType).
% 0.20/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.27 thf(func_def_1, type, vAND: ($o > $o > $o)).
% 0.20/0.27 thf(func_def_2, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.27 thf(func_def_3, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.27 thf(func_def_6, type, sK0: (a > $o)).
% 0.20/0.27 thf(func_def_7, type, sK1: (a > $o)).
% 0.20/0.27 thf(func_def_8, type, sK2: a).
% 0.20/0.27 thf(func_def_10, type, sK4: a).
% 0.20/0.27 thf(f1,conjecture,(
% 0.20/0.27 ! [X0 : (a > $o),X1 : (a > $o)] : (((^[X2 : a] : ((X1 @ X2) & (X0 @ X2))) = X0) <=> ! [X2 : a] : ((X0 @ X2) => (X1 @ X2)))),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGAZING_THM39_pme)).
% 0.20/0.27 thf(f2,negated_conjecture,(
% 0.20/0.27 ~ ! [X0 : (a > $o),X1 : (a > $o)] : (((^[X2 : a] : ((X1 @ X2) & (X0 @ X2))) = X0) <=> ! [X2 : a] : ((X0 @ X2) => (X1 @ X2)))),
% 0.20/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.27 thf(f3,plain,(
% 0.20/0.27 ~ ! [X0 : (a > $o),X1 : (a > $o)] : (((^[X2 : a] : ((X1 @ X2) & (X0 @ X2))) = X0) <=> ! [X3 : a] : ((X0 @ X3) => (X1 @ X3)))),
% 0.20/0.27 inference(rectify,[],[f2])).
% 0.20/0.27 thf(f4,plain,(
% 0.20/0.27 ~ ! [X0 : (a > $o),X1 : (a > $o)] : (((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = X0) <=> ! [X3 : a] : (($true = ((X0 @ X3))) => ($true = ((X1 @ X3)))))),
% 0.20/0.27 inference(fool_elimination,[],[f3])).
% 0.20/0.27 thf(f5,plain,(
% 0.20/0.27 ~ ! [X1 : (a > $o),X0 : (a > $o)] : (! [X2 : a] : ((((X0 @ X2)) = $true) => (((X1 @ X2)) = $true)) <=> ((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = X0))),
% 0.20/0.27 inference(rectify,[],[f4])).
% 0.20/0.27 thf(f6,plain,(
% 0.20/0.27 ? [X1 : (a > $o),X0 : (a > $o)] : (! [X2 : a] : ((((X1 @ X2)) = $true) | (((X0 @ X2)) != $true)) <~> ((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = X0))),
% 0.20/0.27 inference(ennf_transformation,[],[f5])).
% 0.20/0.27 thf(f7,plain,(
% 0.20/0.27 ? [X1 : (a > $o),X0 : (a > $o)] : ((((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) != X0) | ? [X2 : a] : ((((X1 @ X2)) != $true) & (((X0 @ X2)) = $true))) & (((^[Y0 : a]: ((X0 @ Y0) & (X1 @ Y0))) = X0) | ! [X2 : a] : ((((X1 @ X2)) = $true) | (((X0 @ X2)) != $true))))),
% 0.20/0.27 inference(nnf_transformation,[],[f6])).
% 0.20/0.27 thf(f8,plain,(
% 0.20/0.27 ? [X0 : (a > $o),X1 : (a > $o)] : ((((^[Y0 : a]: ((X1 @ Y0) & (X0 @ Y0))) != X1) | ? [X2 : a] : ((((X0 @ X2)) != $true) & (((X1 @ X2)) = $true))) & (((^[Y0 : a]: ((X1 @ Y0) & (X0 @ Y0))) = X1) | ! [X3 : a] : (($true = ((X0 @ X3))) | ($true != ((X1 @ X3))))))),
% 0.20/0.27 inference(rectify,[],[f7])).
% 0.20/0.27 thf(f9,plain,(
% 0.20/0.27 (((^[Y0 : a]: ((sK1 @ Y0) & (sK0 @ Y0))) != sK1) | (($true != ((sK0 @ sK2))) & ($true = ((sK1 @ sK2))))) & (((^[Y0 : a]: ((sK1 @ Y0) & (sK0 @ Y0))) = sK1) | ! [X3 : a] : (($true = ((sK0 @ X3))) | ($true != ((sK1 @ X3)))))),
% 0.20/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f8])).
% 0.20/0.27 thf(f10,plain,(
% 0.20/0.27 ( ! [X3 : a] : (($true = ((sK0 @ X3))) | ($true != ((sK1 @ X3))) | ((^[Y0 : a]: ((sK1 @ Y0) & (sK0 @ Y0))) = sK1)) )),
% 0.20/0.27 inference(cnf_transformation,[],[f9])).
% 0.20/0.27 thf(f11,plain,(
% 0.20/0.27 ($true = ((sK1 @ sK2))) | ((^[Y0 : a]: ((sK1 @ Y0) & (sK0 @ Y0))) != sK1)),
% 0.20/0.27 inference(cnf_transformation,[],[f9])).
% 0.20/0.27 thf(f12,plain,(
% 0.20/0.27 ((^[Y0 : a]: ((sK1 @ Y0) & (sK0 @ Y0))) != sK1) | ($true != ((sK0 @ sK2)))),
% 0.20/0.27 inference(cnf_transformation,[],[f9])).
% 0.20/0.27 thf(f15,definition,(
% 0.20/0.27 spl3_1 <=> ($true = ((sK0 @ sK2)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.20/0.27 thf(f17,plain,(
% 0.20/0.27 ($true != ((sK0 @ sK2))) | spl3_1),
% 0.20/0.27 inference(avatar_component_clause,[],[f15])).
% 0.20/0.27 thf(f19,definition,(
% 0.20/0.27 spl3_2 <=> ((^[Y0 : a]: ((sK1 @ Y0) & (sK0 @ Y0))) = sK1)),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 0.20/0.27 thf(f20,plain,(
% 0.20/0.27 ((^[Y0 : a]: ((sK1 @ Y0) & (sK0 @ Y0))) = sK1) | ~spl3_2),
% 0.20/0.27 inference(avatar_component_clause,[],[f19])).
% 0.20/0.27 thf(f21,plain,(
% 0.20/0.27 ((^[Y0 : a]: ((sK1 @ Y0) & (sK0 @ Y0))) != sK1) | spl3_2),
% 0.20/0.27 inference(avatar_component_clause,[],[f19])).
% 0.20/0.27 thf(f22,plain,(
% 0.20/0.27 ~spl3_1 | ~spl3_2),
% 0.20/0.27 inference(avatar_split_clause,[],[f12,f19,f15])).
% 0.20/0.27 thf(f24,definition,(
% 0.20/0.27 spl3_3 <=> ($true = ((sK1 @ sK2)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition])).
% 0.20/0.27 thf(f26,plain,(
% 0.20/0.27 ($true = ((sK1 @ sK2))) | ~spl3_3),
% 0.20/0.27 inference(avatar_component_clause,[],[f24])).
% 0.20/0.27 thf(f27,plain,(
% 0.20/0.27 spl3_3 | ~spl3_2),
% 0.20/0.27 inference(avatar_split_clause,[],[f11,f19,f24])).
% 0.20/0.27 thf(f29,definition,(
% 0.20/0.27 spl3_4 <=> ! [X3 : a] : (($true = ((sK0 @ X3))) | ($true != ((sK1 @ X3))))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition])).
% 0.20/0.27 thf(f30,plain,(
% 0.20/0.27 ( ! [X3 : a] : (($true = ((sK0 @ X3))) | ($true != ((sK1 @ X3)))) ) | ~spl3_4),
% 0.20/0.27 inference(avatar_component_clause,[],[f29])).
% 0.20/0.27 thf(f31,plain,(
% 0.20/0.27 spl3_2 | spl3_4),
% 0.20/0.27 inference(avatar_split_clause,[],[f10,f29,f19])).
% 0.20/0.27 thf(f32,plain,(
% 0.20/0.27 ( ! [X1 : a] : (((((^[Y0 : a]: ((sK1 @ Y0) & (sK0 @ Y0))) @ X1)) = ((sK1 @ X1)))) ) | ~spl3_2),
% 0.20/0.27 inference(argument_congruence,[],[f20])).
% 0.20/0.27 thf(f33,plain,(
% 0.20/0.27 ( ! [X1 : a] : ((((sK1 @ X1)) = $false) | ($true = (((^[Y0 : a]: ((sK1 @ Y0) & (sK0 @ Y0))) @ X1)))) ) | ~spl3_2),
% 0.20/0.27 inference(iff_proxy_clausification,[],[f32])).
% 0.20/0.27 thf(f37,plain,(
% 0.20/0.27 ( ! [X1 : a] : ((((sK1 @ X1)) = $false) | ($true = (((sK1 @ X1) & (sK0 @ X1))))) ) | ~spl3_2),
% 0.20/0.27 inference(beta-eta_normalization,[],[f33])).
% 0.20/0.27 thf(f38,plain,(
% 0.20/0.27 ( ! [X1 : a] : (($true = ((sK0 @ X1))) | (((sK1 @ X1)) = $false)) ) | ~spl3_2),
% 0.20/0.27 inference(and_proxy_clausification,[],[f37])).
% 0.20/0.27 thf(f40,plain,(
% 0.20/0.27 ($false = ((sK1 @ sK2))) | ($true != $true) | (spl3_1 | ~spl3_2)),
% 0.20/0.27 inference(superposition,[],[f17,f38])).
% 0.20/0.27 thf(f41,plain,(
% 0.20/0.27 ($false = ((sK1 @ sK2))) | (spl3_1 | ~spl3_2)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f40])).
% 0.20/0.27 thf(f43,definition,(
% 0.20/0.27 spl3_5 <=> ($false = ((sK1 @ sK2)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition])).
% 0.20/0.27 thf(f45,plain,(
% 0.20/0.27 ($false = ((sK1 @ sK2))) | ~spl3_5),
% 0.20/0.27 inference(avatar_component_clause,[],[f43])).
% 0.20/0.27 thf(f46,plain,(
% 0.20/0.27 spl3_5 | spl3_1 | ~spl3_2),
% 0.20/0.27 inference(avatar_split_clause,[],[f41,f19,f15,f43])).
% 0.20/0.27 thf(f51,plain,(
% 0.20/0.27 ((((^[Y0 : a]: ((sK1 @ Y0) & (sK0 @ Y0))) @ sK4)) != ((sK1 @ sK4))) | spl3_2),
% 0.20/0.27 inference(negative_extensionality,[],[f21])).
% 0.20/0.27 thf(f52,plain,(
% 0.20/0.27 ($true = ((sK1 @ sK4))) | ($true = (((^[Y0 : a]: ((sK1 @ Y0) & (sK0 @ Y0))) @ sK4))) | spl3_2),
% 0.20/0.27 inference(xor_proxy_clausification,[],[f51])).
% 0.20/0.27 thf(f53,plain,(
% 0.20/0.27 ($false = ((sK1 @ sK4))) | ((((^[Y0 : a]: ((sK1 @ Y0) & (sK0 @ Y0))) @ sK4)) = $false) | spl3_2),
% 0.20/0.27 inference(xor_proxy_clausification,[],[f51])).
% 0.20/0.27 thf(f54,plain,(
% 0.20/0.27 ((((sK1 @ sK4) & (sK0 @ sK4))) = $false) | ($false = ((sK1 @ sK4))) | spl3_2),
% 0.20/0.27 inference(beta-eta_normalization,[],[f53])).
% 0.20/0.27 thf(f55,plain,(
% 0.20/0.27 ($false = ((sK1 @ sK4))) | ($false = ((sK1 @ sK4))) | (((sK0 @ sK4)) = $false) | spl3_2),
% 0.20/0.27 inference(and_proxy_clausification,[],[f54])).
% 0.20/0.27 thf(f56,plain,(
% 0.20/0.27 (((sK0 @ sK4)) = $false) | ($false = ((sK1 @ sK4))) | spl3_2),
% 0.20/0.27 inference(duplicate_literal_removal,[],[f55])).
% 0.20/0.27 thf(f57,plain,(
% 0.20/0.27 ($true = (((sK1 @ sK4) & (sK0 @ sK4)))) | ($true = ((sK1 @ sK4))) | spl3_2),
% 0.20/0.27 inference(beta-eta_normalization,[],[f52])).
% 0.20/0.27 thf(f58,plain,(
% 0.20/0.27 ($true = ((sK0 @ sK4))) | ($true = ((sK1 @ sK4))) | spl3_2),
% 0.20/0.27 inference(and_proxy_clausification,[],[f57])).
% 0.20/0.27 thf(f59,plain,(
% 0.20/0.27 ($true = ((sK1 @ sK4))) | ($true = ((sK1 @ sK4))) | spl3_2),
% 0.20/0.27 inference(and_proxy_clausification,[],[f57])).
% 0.20/0.27 thf(f60,plain,(
% 0.20/0.27 ($true = ((sK1 @ sK4))) | spl3_2),
% 0.20/0.27 inference(duplicate_literal_removal,[],[f59])).
% 0.20/0.27 thf(f62,definition,(
% 0.20/0.27 spl3_6 <=> (((sK0 @ sK4)) = $false)),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition])).
% 0.20/0.27 thf(f66,definition,(
% 0.20/0.27 spl3_7 <=> ($false = ((sK1 @ sK4)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition])).
% 0.20/0.27 thf(f68,plain,(
% 0.20/0.27 ($false = ((sK1 @ sK4))) | ~spl3_7),
% 0.20/0.27 inference(avatar_component_clause,[],[f66])).
% 0.20/0.27 thf(f69,plain,(
% 0.20/0.27 spl3_6 | spl3_7 | spl3_2),
% 0.20/0.27 inference(avatar_split_clause,[],[f56,f19,f66,f62])).
% 0.20/0.27 thf(f71,definition,(
% 0.20/0.27 spl3_8 <=> ($true = ((sK1 @ sK4)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition])).
% 0.20/0.27 thf(f73,plain,(
% 0.20/0.27 ($true = ((sK1 @ sK4))) | ~spl3_8),
% 0.20/0.27 inference(avatar_component_clause,[],[f71])).
% 0.20/0.27 thf(f74,plain,(
% 0.20/0.27 spl3_8 | spl3_2),
% 0.20/0.27 inference(avatar_split_clause,[],[f60,f19,f71])).
% 0.20/0.27 thf(f75,plain,(
% 0.20/0.27 ($true = ((sK0 @ sK4))) | (spl3_2 | ~spl3_4)),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f58,f30])).
% 0.20/0.27 thf(f77,definition,(
% 0.20/0.27 spl3_9 <=> ($true = ((sK0 @ sK4)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition])).
% 0.20/0.27 thf(f80,plain,(
% 0.20/0.27 spl3_9 | spl3_2 | ~spl3_4),
% 0.20/0.27 inference(avatar_split_clause,[],[f75,f29,f19,f77])).
% 0.20/0.27 thf(f81,plain,(
% 0.20/0.27 ($true = $false) | (~spl3_7 | ~spl3_8)),
% 0.20/0.27 inference(forward_demodulation,[],[f73,f68])).
% 0.20/0.27 thf(f82,plain,(
% 0.20/0.27 $false | (~spl3_7 | ~spl3_8)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f81])).
% 0.20/0.27 thf(f83,plain,(
% 0.20/0.27 ~spl3_7 | ~spl3_8),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f82])).
% 0.20/0.27 thf(f84,definition,(
% 0.20/0.27 ($true != ((sK1 @ sK4))) | ($true != ((sK0 @ sK4))) | (((sK0 @ sK4)) != $false) | ($false = ((sK1 @ sK4)))),
% 0.20/0.27 introduced(theory,[theory_tautology_sat_conflict])).
% 0.20/0.27 thf(f88,plain,(
% 0.20/0.27 ($true = $false) | (~spl3_3 | ~spl3_5)),
% 0.20/0.27 inference(superposition,[],[f26,f45])).
% 0.20/0.27 thf(f89,plain,(
% 0.20/0.27 $false | (~spl3_3 | ~spl3_5)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f88])).
% 0.20/0.27 thf(f90,plain,(
% 0.20/0.27 ~spl3_3 | ~spl3_5),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f89])).
% 0.20/0.27 cnf(s1, plain, ~spl3_1 | ~spl3_2, inference(sat_conversion,[],[f22])).
% 0.20/0.27 cnf(s2, plain, ~spl3_2 | spl3_3, inference(sat_conversion,[],[f27])).
% 0.20/0.27 cnf(s3, plain, spl3_2 | spl3_4, inference(sat_conversion,[],[f31])).
% 0.20/0.27 cnf(s4, plain, spl3_1 | ~spl3_2 | spl3_5, inference(sat_conversion,[],[f46])).
% 0.20/0.27 cnf(s6, plain, spl3_2 | spl3_6 | spl3_7, inference(sat_conversion,[],[f69])).
% 0.20/0.27 cnf(s7, plain, spl3_2 | spl3_8, inference(sat_conversion,[],[f74])).
% 0.20/0.27 cnf(s8, plain, spl3_2 | ~spl3_4 | spl3_9, inference(sat_conversion,[],[f80])).
% 0.20/0.27 cnf(s9, plain, ~spl3_7 | ~spl3_8, inference(sat_conversion,[],[f83])).
% 0.20/0.27 cnf(s10, plain, ~spl3_6 | spl3_7 | ~spl3_8 | ~spl3_9, inference(sat_conversion,[],[f84])).
% 0.20/0.27 cnf(s13, plain, ~spl3_3 | ~spl3_5, inference(sat_conversion,[],[f90])).
% 0.20/0.27 cnf(s15, plain, spl3_2, inference(rat,[],[s6,s10,s8,s9,s3,s7])).
% 0.20/0.27 cnf(s16, plain, spl3_3, inference(rat,[],[s2,s15])).
% 0.20/0.27 cnf(s17, plain, ~spl3_5, inference(rat,[],[s13,s16])).
% 0.20/0.27 cnf(s18, plain, ~spl3_1, inference(rat,[],[s1,s15])).
% 0.20/0.27 cnf(s19, plain, $false, inference(rat,[],[s4,s18,s15,s17])).
% 0.20/0.27 thf(f93,plain,(
% 0.20/0.27 $false),
% 0.20/0.27 inference(avatar_sat_refutation,[],[s19])).
% 0.20/0.27 % SZS output end Proof for theBenchmark
% 0.20/0.27 % (2948004)------------------------------
% 0.20/0.27 % (2948004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (2948004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (2948004)CaDiCaL version: 2.1.3
% 0.20/0.27 % (2948004)Termination reason: Refutation
% 0.20/0.27 % (2948004)Time elapsed: 0.003 s
% 0.20/0.27 % (2948004)Peak memory usage: 13 MB
% 0.20/0.27 % (2948004)Instructions burned: 5 (million)
% 0.20/0.27 % (2947996)Success in time 0.031 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------