%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET600^5 : 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 : n005.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 08:23:19 AM UTC 2026
% Result : Theorem 0.23s 0.27s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET600^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n005.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 13:38:02 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.25 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
% 0.23/0.27 % (1672580)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.27 % (1672588)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=1351454925: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)
% 0.23/0.27 % (1672588) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1672580-1672588"...
% 0.23/0.27 % (1672588)...printing done.
% 0.23/0.27 % (1672588)Refutation found. Thanks to Tanya!
% 0.23/0.27 % SZS status Theorem for theBenchmark
% 0.23/0.27 % SZS output start Proof for theBenchmark
% 0.23/0.27 thf(type_def_5, type, a: $tType).
% 0.23/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.27 thf(func_def_1, type, vOR: ($o > $o > $o)).
% 0.23/0.27 thf(func_def_2, type, db0: !>[X0: $tType]:(X0)).
% 0.23/0.27 thf(func_def_3, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.23/0.27 thf(func_def_6, type, sK0: (a > $o)).
% 0.23/0.27 thf(func_def_7, type, sK1: (a > $o)).
% 0.23/0.27 thf(func_def_9, type, sK3: a).
% 0.23/0.27 thf(func_def_10, type, sK4: a).
% 0.23/0.27 thf(f1,conjecture,(
% 0.23/0.27 ! [X0 : (a > $o),X1 : (a > $o)] : (((^[X2 : a] : ((X0 @ X2) | (X1 @ X2))) = (^[X3 : a] : ($false))) <=> ((X1 = (^[X3 : a] : ($false))) & ((^[X3 : a] : ($false)) = X0)))),
% 0.23/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_59_pme)).
% 0.23/0.27 thf(f2,negated_conjecture,(
% 0.23/0.27 ~ ! [X0 : (a > $o),X1 : (a > $o)] : (((^[X2 : a] : ((X0 @ X2) | (X1 @ X2))) = (^[X3 : a] : ($false))) <=> ((X1 = (^[X3 : a] : ($false))) & ((^[X3 : a] : ($false)) = X0)))),
% 0.23/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.23/0.27 thf(f3,plain,(
% 0.23/0.27 ~ ! [X0 : (a > $o),X1 : (a > $o)] : (((^[X2 : a] : ((X0 @ X2) | (X1 @ X2))) = (^[X3 : a] : ($false))) <=> ((X1 = (^[X4 : a] : ($false))) & ((^[X5 : a] : ($false)) = X0)))),
% 0.23/0.27 inference(rectify,[],[f2])).
% 0.23/0.27 thf(f4,plain,(
% 0.23/0.27 ~ ! [X1 : (a > $o),X0 : (a > $o)] : ((((^[Y0 : a]: ($false)) = X0) & ((^[Y0 : a]: ($false)) = X1)) <=> ((^[Y0 : a]: ((X1 @ Y0) | (X0 @ Y0))) = (^[Y0 : a]: ($false))))),
% 0.23/0.27 inference(fool_elimination,[],[f3])).
% 0.23/0.27 thf(f5,plain,(
% 0.23/0.27 ? [X0 : (a > $o),X1 : (a > $o)] : (((^[Y0 : a]: ((X1 @ Y0) | (X0 @ Y0))) = (^[Y0 : a]: ($false))) <~> (((^[Y0 : a]: ($false)) = X0) & ((^[Y0 : a]: ($false)) = X1)))),
% 0.23/0.27 inference(ennf_transformation,[],[f4])).
% 0.23/0.27 thf(f6,plain,(
% 0.23/0.27 ? [X0 : (a > $o),X1 : (a > $o)] : (((((^[Y0 : a]: ($false)) != X0) | ((^[Y0 : a]: ($false)) != X1)) | ((^[Y0 : a]: ((X1 @ Y0) | (X0 @ Y0))) != (^[Y0 : a]: ($false)))) & ((((^[Y0 : a]: ($false)) = X0) & ((^[Y0 : a]: ($false)) = X1)) | ((^[Y0 : a]: ((X1 @ Y0) | (X0 @ Y0))) = (^[Y0 : a]: ($false)))))),
% 0.23/0.27 inference(nnf_transformation,[],[f5])).
% 0.23/0.27 thf(f7,plain,(
% 0.23/0.27 ? [X0 : (a > $o),X1 : (a > $o)] : ((((^[Y0 : a]: ($false)) != X0) | ((^[Y0 : a]: ($false)) != X1) | ((^[Y0 : a]: ((X1 @ Y0) | (X0 @ Y0))) != (^[Y0 : a]: ($false)))) & ((((^[Y0 : a]: ($false)) = X0) & ((^[Y0 : a]: ($false)) = X1)) | ((^[Y0 : a]: ((X1 @ Y0) | (X0 @ Y0))) = (^[Y0 : a]: ($false)))))),
% 0.23/0.27 inference(flattening,[],[f6])).
% 0.23/0.27 thf(f8,plain,(
% 0.23/0.27 ((sK0 != (^[Y0 : a]: ($false))) | (sK1 != (^[Y0 : a]: ($false))) | ((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) != (^[Y0 : a]: ($false)))) & (((sK0 = (^[Y0 : a]: ($false))) & (sK1 = (^[Y0 : a]: ($false)))) | ((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) = (^[Y0 : a]: ($false))))),
% 0.23/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f7])).
% 0.23/0.27 thf(f9,plain,(
% 0.23/0.27 (sK1 = (^[Y0 : a]: ($false))) | ((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) = (^[Y0 : a]: ($false)))),
% 0.23/0.27 inference(cnf_transformation,[],[f8])).
% 0.23/0.27 thf(f10,plain,(
% 0.23/0.27 ((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) = (^[Y0 : a]: ($false))) | (sK0 = (^[Y0 : a]: ($false)))),
% 0.23/0.27 inference(cnf_transformation,[],[f8])).
% 0.23/0.27 thf(f11,plain,(
% 0.23/0.27 (sK0 != (^[Y0 : a]: ($false))) | (sK1 != (^[Y0 : a]: ($false))) | ((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) != (^[Y0 : a]: ($false)))),
% 0.23/0.27 inference(cnf_transformation,[],[f8])).
% 0.23/0.27 thf(f14,definition,(
% 0.23/0.27 spl2_1 <=> ((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) = (^[Y0 : a]: ($false)))),
% 0.23/0.27 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.23/0.27 thf(f15,plain,(
% 0.23/0.27 ((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) = (^[Y0 : a]: ($false))) | ~spl2_1),
% 0.23/0.28 inference(avatar_component_clause,[],[f14])).
% 0.23/0.28 thf(f16,plain,(
% 0.23/0.28 ((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) != (^[Y0 : a]: ($false))) | spl2_1),
% 0.23/0.28 inference(avatar_component_clause,[],[f14])).
% 0.23/0.28 thf(f18,definition,(
% 0.23/0.28 spl2_2 <=> (sK0 = (^[Y0 : a]: ($false)))),
% 0.23/0.28 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.23/0.28 thf(f19,plain,(
% 0.23/0.28 (sK0 = (^[Y0 : a]: ($false))) | ~spl2_2),
% 0.23/0.28 inference(avatar_component_clause,[],[f18])).
% 0.23/0.28 thf(f22,definition,(
% 0.23/0.28 spl2_3 <=> (sK1 = (^[Y0 : a]: ($false)))),
% 0.23/0.28 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.23/0.28 thf(f24,plain,(
% 0.23/0.28 (sK1 != (^[Y0 : a]: ($false))) | spl2_3),
% 0.23/0.28 inference(avatar_component_clause,[],[f22])).
% 0.23/0.28 thf(f25,plain,(
% 0.23/0.28 ~spl2_1 | ~spl2_2 | ~spl2_3),
% 0.23/0.28 inference(avatar_split_clause,[],[f11,f22,f18,f14])).
% 0.23/0.28 thf(f26,plain,(
% 0.23/0.28 spl2_2 | spl2_1),
% 0.23/0.28 inference(avatar_split_clause,[],[f10,f14,f18])).
% 0.23/0.28 thf(f27,plain,(
% 0.23/0.28 spl2_3 | spl2_1),
% 0.23/0.28 inference(avatar_split_clause,[],[f9,f14,f22])).
% 0.23/0.28 thf(f28,plain,(
% 0.23/0.28 ( ! [X1 : a] : (((((^[Y0 : a]: ($false)) @ X1)) = ((sK0 @ X1)))) ) | ~spl2_2),
% 0.23/0.28 inference(argument_congruence,[],[f19])).
% 0.23/0.28 thf(f29,plain,(
% 0.23/0.28 ( ! [X1 : a] : (((((^[Y0 : a]: ($false)) @ X1)) = $true) | (((sK0 @ X1)) = $false)) ) | ~spl2_2),
% 0.23/0.28 inference(iff_proxy_clausification,[],[f28])).
% 0.23/0.28 thf(f32,plain,(
% 0.23/0.28 ( ! [X1 : a] : ((((sK0 @ X1)) = $false) | ($true = $false)) ) | ~spl2_2),
% 0.23/0.28 inference(beta-eta_normalization,[],[f29])).
% 0.23/0.28 thf(f33,plain,(
% 0.23/0.28 ( ! [X1 : a] : ((((sK0 @ X1)) = $false)) ) | ~spl2_2),
% 0.23/0.28 inference(trivial_inequality_removal,[],[f32])).
% 0.23/0.28 thf(f34,plain,(
% 0.23/0.28 (sK0 != (^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0)))) | (spl2_1 | ~spl2_2)),
% 0.23/0.28 inference(forward_demodulation,[],[f16,f19])).
% 0.23/0.28 thf(f36,definition,(
% 0.23/0.28 spl2_4 <=> (sK0 = (^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))))),
% 0.23/0.28 introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition])).
% 0.23/0.28 thf(f38,plain,(
% 0.23/0.28 (sK0 != (^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0)))) | spl2_4),
% 0.23/0.28 inference(avatar_component_clause,[],[f36])).
% 0.23/0.28 thf(f39,plain,(
% 0.23/0.28 ~spl2_4 | spl2_1 | ~spl2_2),
% 0.23/0.28 inference(avatar_split_clause,[],[f34,f18,f14,f36])).
% 0.23/0.28 thf(f40,plain,(
% 0.23/0.28 ((((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) @ sK3)) != ((sK0 @ sK3))) | spl2_4),
% 0.23/0.28 inference(negative_extensionality,[],[f38])).
% 0.23/0.28 thf(f41,plain,(
% 0.23/0.28 (((sK0 @ sK3)) = $true) | ((((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) @ sK3)) = $true) | spl2_4),
% 0.23/0.28 inference(xor_proxy_clausification,[],[f40])).
% 0.23/0.28 thf(f42,plain,(
% 0.23/0.28 ((((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) @ sK3)) = $false) | (((sK0 @ sK3)) = $false) | spl2_4),
% 0.23/0.28 inference(xor_proxy_clausification,[],[f40])).
% 0.23/0.28 thf(f43,plain,(
% 0.23/0.28 ((((sK1 @ sK3) | (sK0 @ sK3))) = $false) | (((sK0 @ sK3)) = $false) | spl2_4),
% 0.23/0.28 inference(beta-eta_normalization,[],[f42])).
% 0.23/0.28 thf(f44,plain,(
% 0.23/0.28 (((sK0 @ sK3)) = $false) | (((sK0 @ sK3)) = $false) | spl2_4),
% 0.23/0.28 inference(or_proxy_clausification,[],[f43])).
% 0.23/0.28 thf(f46,plain,(
% 0.23/0.28 (((sK0 @ sK3)) = $false) | spl2_4),
% 0.23/0.28 inference(duplicate_literal_removal,[],[f44])).
% 0.23/0.28 thf(f47,plain,(
% 0.23/0.28 ($true = (((sK1 @ sK3) | (sK0 @ sK3)))) | (((sK0 @ sK3)) = $true) | spl2_4),
% 0.23/0.28 inference(beta-eta_normalization,[],[f41])).
% 0.23/0.28 thf(f48,plain,(
% 0.23/0.28 ($true = ((sK1 @ sK3))) | (((sK0 @ sK3)) = $true) | (((sK0 @ sK3)) = $true) | spl2_4),
% 0.23/0.28 inference(or_proxy_clausification,[],[f47])).
% 0.23/0.28 thf(f49,plain,(
% 0.23/0.28 ($true = ((sK1 @ sK3))) | (((sK0 @ sK3)) = $true) | spl2_4),
% 0.23/0.28 inference(duplicate_literal_removal,[],[f48])).
% 0.23/0.28 thf(f51,definition,(
% 0.23/0.28 spl2_5 <=> (((sK0 @ sK3)) = $false)),
% 0.23/0.28 introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition])).
% 0.23/0.28 thf(f53,plain,(
% 0.23/0.28 (((sK0 @ sK3)) = $false) | ~spl2_5),
% 0.23/0.28 inference(avatar_component_clause,[],[f51])).
% 0.23/0.28 thf(f59,plain,(
% 0.23/0.28 spl2_5 | spl2_4),
% 0.23/0.28 inference(avatar_split_clause,[],[f46,f36,f51])).
% 0.23/0.28 thf(f61,definition,(
% 0.23/0.28 spl2_7 <=> ($true = ((sK1 @ sK3)))),
% 0.23/0.28 introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition])).
% 0.23/0.28 thf(f63,plain,(
% 0.23/0.28 ($true = ((sK1 @ sK3))) | ~spl2_7),
% 0.23/0.28 inference(avatar_component_clause,[],[f61])).
% 0.23/0.28 thf(f65,definition,(
% 0.23/0.28 spl2_8 <=> (((sK0 @ sK3)) = $true)),
% 0.23/0.28 introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition])).
% 0.23/0.28 thf(f67,plain,(
% 0.23/0.28 (((sK0 @ sK3)) = $true) | ~spl2_8),
% 0.23/0.28 inference(avatar_component_clause,[],[f65])).
% 0.23/0.28 thf(f68,plain,(
% 0.23/0.28 spl2_7 | spl2_8 | spl2_4),
% 0.23/0.28 inference(avatar_split_clause,[],[f49,f36,f65,f61])).
% 0.23/0.28 thf(f70,plain,(
% 0.23/0.28 (sK0 != sK1) | (~spl2_2 | spl2_3)),
% 0.23/0.28 inference(forward_demodulation,[],[f24,f19])).
% 0.23/0.28 thf(f73,definition,(
% 0.23/0.28 spl2_9 <=> (sK0 = sK1)),
% 0.23/0.28 introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition])).
% 0.23/0.28 thf(f75,plain,(
% 0.23/0.28 (sK0 != sK1) | spl2_9),
% 0.23/0.28 inference(avatar_component_clause,[],[f73])).
% 0.23/0.28 thf(f76,plain,(
% 0.23/0.28 ~spl2_9 | ~spl2_2 | spl2_3),
% 0.23/0.28 inference(avatar_split_clause,[],[f70,f22,f18,f73])).
% 0.23/0.28 thf(f77,plain,(
% 0.23/0.28 (((sK1 @ sK4)) != ((sK0 @ sK4))) | spl2_9),
% 0.23/0.28 inference(negative_extensionality,[],[f75])).
% 0.23/0.28 thf(f78,plain,(
% 0.23/0.28 ($true = ((sK0 @ sK4))) | ($true = ((sK1 @ sK4))) | spl2_9),
% 0.23/0.28 inference(xor_proxy_clausification,[],[f77])).
% 0.23/0.28 thf(f80,plain,(
% 0.23/0.28 ($true = ((sK1 @ sK4))) | ($true = $false) | (~spl2_2 | spl2_9)),
% 0.23/0.28 inference(forward_demodulation,[],[f78,f33])).
% 0.23/0.28 thf(f81,plain,(
% 0.23/0.28 ($true = ((sK1 @ sK4))) | (~spl2_2 | spl2_9)),
% 0.23/0.28 inference(trivial_inequality_removal,[],[f80])).
% 0.23/0.28 thf(f83,definition,(
% 0.23/0.28 spl2_10 <=> ($true = ((sK1 @ sK4)))),
% 0.23/0.28 introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition])).
% 0.23/0.28 thf(f85,plain,(
% 0.23/0.28 ($true = ((sK1 @ sK4))) | ~spl2_10),
% 0.23/0.28 inference(avatar_component_clause,[],[f83])).
% 0.23/0.28 thf(f86,plain,(
% 0.23/0.28 spl2_10 | ~spl2_2 | spl2_9),
% 0.23/0.28 inference(avatar_split_clause,[],[f81,f73,f18,f83])).
% 0.23/0.28 thf(f87,definition,(
% 0.23/0.28 (sK0 != (^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0)))) | ((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) != (^[Y0 : a]: ($false))) | (sK0 = (^[Y0 : a]: ($false)))),
% 0.23/0.28 introduced(theory,[theory_tautology_sat_conflict])).
% 0.23/0.28 thf(f88,plain,(
% 0.23/0.28 ($true = $false) | (~spl2_5 | ~spl2_8)),
% 0.23/0.28 inference(superposition,[],[f53,f67])).
% 0.23/0.28 thf(f89,plain,(
% 0.23/0.28 ($true = $false) | (~spl2_5 | ~spl2_8)),
% 0.23/0.28 inference(superposition,[],[f67,f53])).
% 0.23/0.28 thf(f90,plain,(
% 0.23/0.28 $false | (~spl2_5 | ~spl2_8)),
% 0.23/0.28 inference(trivial_inequality_removal,[],[f88])).
% 0.23/0.28 thf(f91,plain,(
% 0.23/0.28 ~spl2_5 | ~spl2_8),
% 0.23/0.28 inference(avatar_contradiction_clause,[],[f90])).
% 0.23/0.28 thf(f92,plain,(
% 0.23/0.28 $false | (~spl2_5 | ~spl2_8)),
% 0.23/0.28 inference(trivial_inequality_removal,[],[f89])).
% 0.23/0.28 thf(f93,plain,(
% 0.23/0.28 ~spl2_5 | ~spl2_8),
% 0.23/0.28 inference(avatar_contradiction_clause,[],[f92])).
% 0.23/0.28 thf(f95,plain,(
% 0.23/0.28 ( ! [X1 : a] : (((((^[Y0 : a]: ($false)) @ X1)) = (((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) @ X1)))) ) | ~spl2_1),
% 0.23/0.28 inference(argument_congruence,[],[f15])).
% 0.23/0.28 thf(f96,plain,(
% 0.23/0.28 ( ! [X1 : a] : (((((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) @ X1)) = $false) | ((((^[Y0 : a]: ($false)) @ X1)) = $true)) ) | ~spl2_1),
% 0.23/0.28 inference(iff_proxy_clausification,[],[f95])).
% 0.23/0.28 thf(f100,plain,(
% 0.23/0.28 ( ! [X1 : a] : (((((sK1 @ X1) | (sK0 @ X1))) = $false) | ($true = $false)) ) | ~spl2_1),
% 0.23/0.28 inference(beta-eta_normalization,[],[f96])).
% 0.23/0.28 thf(f102,plain,(
% 0.23/0.28 ( ! [X1 : a] : (($true = $false) | (((sK1 @ X1)) = $false)) ) | ~spl2_1),
% 0.23/0.28 inference(or_proxy_clausification,[],[f100])).
% 0.23/0.28 thf(f103,plain,(
% 0.23/0.28 ( ! [X1 : a] : ((((sK1 @ X1)) = $false)) ) | ~spl2_1),
% 0.23/0.28 inference(trivial_inequality_removal,[],[f102])).
% 0.23/0.28 thf(f105,plain,(
% 0.23/0.28 ($true = $false) | (~spl2_1 | ~spl2_7)),
% 0.23/0.28 inference(superposition,[],[f103,f63])).
% 0.23/0.28 thf(f109,plain,(
% 0.23/0.28 $false | (~spl2_1 | ~spl2_7)),
% 0.23/0.28 inference(trivial_inequality_removal,[],[f105])).
% 0.23/0.28 thf(f110,plain,(
% 0.23/0.28 ~spl2_1 | ~spl2_7),
% 0.23/0.28 inference(avatar_contradiction_clause,[],[f109])).
% 0.23/0.28 thf(f111,definition,(
% 0.23/0.28 (sK0 != (^[Y0 : a]: ($false))) | (sK1 != (^[Y0 : a]: ($false))) | ($true != ((sK1 @ sK3))) | (((sK0 @ sK3)) = $true)),
% 0.23/0.28 introduced(theory,[theory_tautology_sat_conflict])).
% 0.23/0.28 thf(f112,plain,(
% 0.23/0.28 ($true = $false) | (~spl2_1 | ~spl2_10)),
% 0.23/0.28 inference(forward_demodulation,[],[f85,f103])).
% 0.23/0.28 thf(f113,plain,(
% 0.23/0.28 $false | (~spl2_1 | ~spl2_10)),
% 0.23/0.28 inference(trivial_inequality_removal,[],[f112])).
% 0.23/0.28 thf(f114,plain,(
% 0.23/0.28 ~spl2_1 | ~spl2_10),
% 0.23/0.28 inference(avatar_contradiction_clause,[],[f113])).
% 0.23/0.28 cnf(s1, plain, ~spl2_1 | ~spl2_2 | ~spl2_3, inference(sat_conversion,[],[f25])).
% 0.23/0.28 cnf(s2, plain, spl2_1 | spl2_2, inference(sat_conversion,[],[f26])).
% 0.23/0.28 cnf(s3, plain, spl2_1 | spl2_3, inference(sat_conversion,[],[f27])).
% 0.23/0.28 cnf(s4, plain, spl2_1 | ~spl2_2 | ~spl2_4, inference(sat_conversion,[],[f39])).
% 0.23/0.28 cnf(s6, plain, spl2_4 | spl2_5, inference(sat_conversion,[],[f59])).
% 0.23/0.28 cnf(s7, plain, spl2_4 | spl2_7 | spl2_8, inference(sat_conversion,[],[f68])).
% 0.23/0.28 cnf(s9, plain, ~spl2_2 | spl2_3 | ~spl2_9, inference(sat_conversion,[],[f76])).
% 0.23/0.28 cnf(s10, plain, ~spl2_2 | spl2_9 | spl2_10, inference(sat_conversion,[],[f86])).
% 0.23/0.28 cnf(s11, plain, ~spl2_1 | spl2_2 | ~spl2_4, inference(sat_conversion,[],[f87])).
% 0.23/0.28 cnf(s12, plain, ~spl2_5 | ~spl2_8, inference(sat_conversion,[],[f91])).
% 0.23/0.28 cnf(s13, plain, ~spl2_5 | ~spl2_8, inference(sat_conversion,[],[f93])).
% 0.23/0.28 cnf(s15, plain, ~spl2_1 | ~spl2_7, inference(sat_conversion,[],[f110])).
% 0.23/0.28 cnf(s16, plain, ~spl2_2 | ~spl2_3 | ~spl2_7 | spl2_8, inference(sat_conversion,[],[f111])).
% 0.23/0.28 cnf(s17, plain, ~spl2_1 | ~spl2_10, inference(sat_conversion,[],[f114])).
% 0.23/0.28 cnf(s18, plain, spl2_1, inference(rat,[],[s16,s7,s13,s6,s4,s2,s3])).
% 0.23/0.28 cnf(s19, plain, ~spl2_10, inference(rat,[],[s17,s18])).
% 0.23/0.28 cnf(s20, plain, ~spl2_7, inference(rat,[],[s15,s18])).
% 0.23/0.28 cnf(s21, plain, ~spl2_2, inference(rat,[],[s9,s10,s1,s19,s18])).
% 0.23/0.28 cnf(s22, plain, ~spl2_4, inference(rat,[],[s11,s18,s21])).
% 0.23/0.28 cnf(s23, plain, spl2_5, inference(rat,[],[s6,s22])).
% 0.23/0.28 cnf(s24, plain, spl2_8, inference(rat,[],[s7,s20,s22])).
% 0.23/0.28 cnf(s25, plain, $false, inference(rat,[],[s12,s24,s23])).
% 0.23/0.28 thf(f116,plain,(
% 0.23/0.28 $false),
% 0.23/0.28 inference(avatar_sat_refutation,[],[s25])).
% 0.23/0.28 % SZS output end Proof for theBenchmark
% 0.23/0.28 % (1672588)------------------------------
% 0.23/0.28 % (1672588)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.28 % (1672588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.28 % (1672588)CaDiCaL version: 2.1.3
% 0.23/0.28 % (1672588)Termination reason: Refutation
% 0.23/0.28 % (1672588)Time elapsed: 0.003 s
% 0.23/0.28 % (1672588)Peak memory usage: 13 MB
% 0.23/0.28 % (1672588)Instructions burned: 5 (million)
% 0.23/0.28 % (1672580)Success in time 0.019 s
% 0.23/0.28 % Vampire exiting
%------------------------------------------------------------------------------