%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU856^5 : 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 : 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 08:31:49 AM UTC 2026
% Result : Theorem 0.20s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU856^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n017.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:35:37 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 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
% 0.20/0.26 % (422267)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.26 % (422281)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.26 % (422281)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.26 % (422281)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3347449415:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.26 % (422281) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-422267-422281"...
% 0.20/0.26 % (422281)...printing done.
% 0.20/0.26 % (422281)Refutation found. Thanks to Tanya!
% 0.20/0.26 % SZS status Theorem for theBenchmark
% 0.20/0.26 % SZS output start Proof for theBenchmark
% 0.20/0.26 thf(type_def_5, type, a: $tType).
% 0.20/0.26 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.26 thf(func_def_3, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.26 thf(func_def_4, type, vOR: ($o > $o > $o)).
% 0.20/0.26 thf(func_def_5, type, vAND: ($o > $o > $o)).
% 0.20/0.26 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.26 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.20/0.26 thf(func_def_8, type, sK0: (a > $o)).
% 0.20/0.26 thf(func_def_9, type, sK1: (a > $o)).
% 0.20/0.26 thf(func_def_11, type, sK3: a).
% 0.20/0.26 thf(func_def_12, type, sK4: a).
% 0.20/0.26 thf(func_def_13, type, sK5: a).
% 0.20/0.26 thf(f1,conjecture,(
% 0.20/0.26 ! [X0 : (a > $o),X1 : (a > $o)] : ((X0 = X1) <=> ((^[X3 : a] : ($false)) = (^[X2 : a] : ((~(X1 @ X2) & (X0 @ X2)) | (~(X0 @ X2) & (X1 @ X2))))))),
% 0.20/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGAZING_THM46_pme)).
% 0.20/0.26 thf(f2,negated_conjecture,(
% 0.20/0.26 ~ ! [X0 : (a > $o),X1 : (a > $o)] : ((X0 = X1) <=> ((^[X3 : a] : ($false)) = (^[X2 : a] : ((~(X1 @ X2) & (X0 @ X2)) | (~(X0 @ X2) & (X1 @ X2))))))),
% 0.20/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.26 thf(f3,plain,(
% 0.20/0.26 ~ ! [X0 : (a > $o),X1 : (a > $o)] : ((X0 = X1) <=> ((^[X2 : a] : ($false)) = (^[X3 : a] : ((~(X1 @ X3) & (X0 @ X3)) | (~(X0 @ X3) & (X1 @ X3))))))),
% 0.20/0.26 inference(rectify,[],[f2])).
% 0.20/0.26 thf(f4,plain,(
% 0.20/0.26 ~ ! [X0 : (a > $o),X1 : (a > $o)] : ((X0 = X1) <=> ((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((X1 @ Y0) & (~ (X0 @ Y0))) | ((X0 @ Y0) & (~ (X1 @ Y0)))))))),
% 0.20/0.26 inference(fool_elimination,[],[f3])).
% 0.20/0.26 thf(f5,plain,(
% 0.20/0.26 ? [X0 : (a > $o),X1 : (a > $o)] : ((X0 = X1) <~> ((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((X1 @ Y0) & (~ (X0 @ Y0))) | ((X0 @ Y0) & (~ (X1 @ Y0)))))))),
% 0.20/0.26 inference(ennf_transformation,[],[f4])).
% 0.20/0.26 thf(f6,plain,(
% 0.20/0.26 ? [X0 : (a > $o),X1 : (a > $o)] : ((((^[Y0 : a]: ($false)) != (^[Y0 : a]: (((X1 @ Y0) & (~ (X0 @ Y0))) | ((X0 @ Y0) & (~ (X1 @ Y0)))))) | (X0 != X1)) & (((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((X1 @ Y0) & (~ (X0 @ Y0))) | ((X0 @ Y0) & (~ (X1 @ Y0)))))) | (X0 = X1)))),
% 0.20/0.26 inference(nnf_transformation,[],[f5])).
% 0.20/0.26 thf(f7,plain,(
% 0.20/0.26 (((^[Y0 : a]: ($false)) != (^[Y0 : a]: (((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK1 @ Y0)))))) | (sK1 != sK0)) & (((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK1 @ Y0)))))) | (sK1 = sK0))),
% 0.20/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f6])).
% 0.20/0.26 thf(f8,plain,(
% 0.20/0.26 ((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK1 @ Y0)))))) | (sK1 = sK0)),
% 0.20/0.26 inference(cnf_transformation,[],[f7])).
% 0.20/0.26 thf(f9,plain,(
% 0.20/0.26 (sK1 != sK0) | ((^[Y0 : a]: ($false)) != (^[Y0 : a]: (((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK1 @ Y0))))))),
% 0.20/0.26 inference(cnf_transformation,[],[f7])).
% 0.20/0.26 thf(f11,definition,(
% 0.20/0.26 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.26 thf(f13,definition,(
% 0.20/0.26 spl2_1 <=> ((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK1 @ Y0))))))),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.20/0.26 thf(f14,plain,(
% 0.20/0.26 ((^[Y0 : a]: ($false)) != (^[Y0 : a]: (((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK1 @ Y0)))))) | spl2_1),
% 0.20/0.26 inference(avatar_component_clause,[],[f13])).
% 0.20/0.26 thf(f15,plain,(
% 0.20/0.26 ((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK1 @ Y0)))))) | ~spl2_1),
% 0.20/0.26 inference(avatar_component_clause,[],[f13])).
% 0.20/0.26 thf(f17,definition,(
% 0.20/0.26 spl2_2 <=> (sK1 = sK0)),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.20/0.26 thf(f18,plain,(
% 0.20/0.26 (sK1 != sK0) | spl2_2),
% 0.20/0.26 inference(avatar_component_clause,[],[f17])).
% 0.20/0.26 thf(f19,plain,(
% 0.20/0.26 (sK1 = sK0) | ~spl2_2),
% 0.20/0.26 inference(avatar_component_clause,[],[f17])).
% 0.20/0.26 thf(f20,plain,(
% 0.20/0.26 spl2_1 | spl2_2),
% 0.20/0.26 inference(avatar_split_clause,[],[f8,f17,f13])).
% 0.20/0.26 thf(f21,plain,(
% 0.20/0.26 ~spl2_1 | ~spl2_2),
% 0.20/0.26 inference(avatar_split_clause,[],[f9,f17,f13])).
% 0.20/0.26 thf(f22,plain,(
% 0.20/0.26 ( ! [X1 : a] : ((((sK1 @ X1)) = ((sK0 @ X1)))) ) | ~spl2_2),
% 0.20/0.26 inference(argument_congruence,[],[f19])).
% 0.20/0.26 thf(f23,plain,(
% 0.20/0.26 ( ! [X1 : a] : ((((sK1 @ X1)) = $true) | (((sK0 @ X1)) = $false)) ) | ~spl2_2),
% 0.20/0.26 inference(iff_proxy_clausification,[],[f22])).
% 0.20/0.26 thf(f32,plain,(
% 0.20/0.26 ((((^[Y0 : a]: (((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK1 @ Y0))))) @ sK3)) != (((^[Y0 : a]: ($false)) @ sK3))) | spl2_1),
% 0.20/0.26 inference(negative_extensionality,[],[f14])).
% 0.20/0.26 thf(f33,plain,(
% 0.20/0.26 ($true = (((^[Y0 : a]: ($false)) @ sK3))) | ($true = (((^[Y0 : a]: (((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK1 @ Y0))))) @ sK3))) | spl2_1),
% 0.20/0.26 inference(xor_proxy_clausification,[],[f32])).
% 0.20/0.26 thf(f42,plain,(
% 0.20/0.26 ($true = $false) | ($true = ((((sK1 @ sK3) & (~ (sK0 @ sK3))) | ((sK0 @ sK3) & (~ (sK1 @ sK3)))))) | spl2_1),
% 0.20/0.26 inference(beta-eta_normalization,[],[f33])).
% 0.20/0.26 thf(f43,plain,(
% 0.20/0.26 ((((sK1 @ sK3) & (~ (sK0 @ sK3)))) = $true) | ($true = (((sK0 @ sK3) & (~ (sK1 @ sK3))))) | ($true = $false) | spl2_1),
% 0.20/0.26 inference(or_proxy_clausification,[],[f42])).
% 0.20/0.26 thf(f44,plain,(
% 0.20/0.26 (((~ (sK0 @ sK3))) = $true) | ($true = (((sK0 @ sK3) & (~ (sK1 @ sK3))))) | ($true = $false) | spl2_1),
% 0.20/0.26 inference(and_proxy_clausification,[],[f43])).
% 0.20/0.26 thf(f45,plain,(
% 0.20/0.26 ($true = (((sK0 @ sK3) & (~ (sK1 @ sK3))))) | ($true = $false) | ($true = ((sK1 @ sK3))) | spl2_1),
% 0.20/0.26 inference(and_proxy_clausification,[],[f43])).
% 0.20/0.26 thf(f47,plain,(
% 0.20/0.26 ($true = $false) | ($true = ((sK1 @ sK3))) | ($true = ((sK0 @ sK3))) | spl2_1),
% 0.20/0.26 inference(and_proxy_clausification,[],[f45])).
% 0.20/0.26 thf(f48,plain,(
% 0.20/0.26 ($true = ((sK0 @ sK3))) | ($true = ((sK1 @ sK3))) | spl2_1),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f47])).
% 0.20/0.26 thf(f51,plain,(
% 0.20/0.26 ($true = $false) | (((sK0 @ sK3)) = $false) | ($true = (((sK0 @ sK3) & (~ (sK1 @ sK3))))) | spl2_1),
% 0.20/0.26 inference(not_proxy_clausification,[],[f44])).
% 0.20/0.26 thf(f52,plain,(
% 0.20/0.26 (((sK0 @ sK3)) = $false) | ($true = $false) | ($true = ((~ (sK1 @ sK3)))) | spl2_1),
% 0.20/0.26 inference(and_proxy_clausification,[],[f51])).
% 0.20/0.26 thf(f55,plain,(
% 0.20/0.26 (((sK0 @ sK3)) = $false) | (((sK1 @ sK3)) = $false) | ($true = $false) | spl2_1),
% 0.20/0.26 inference(not_proxy_clausification,[],[f52])).
% 0.20/0.26 thf(f56,plain,(
% 0.20/0.26 (((sK0 @ sK3)) = $false) | (((sK1 @ sK3)) = $false) | spl2_1),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f55])).
% 0.20/0.26 thf(f58,definition,(
% 0.20/0.26 spl2_3 <=> ($true = ((sK0 @ sK3)))),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.20/0.26 thf(f59,plain,(
% 0.20/0.26 ($true != ((sK0 @ sK3))) | spl2_3),
% 0.20/0.26 inference(avatar_component_clause,[],[f58])).
% 0.20/0.26 thf(f60,plain,(
% 0.20/0.26 ($true = ((sK0 @ sK3))) | ~spl2_3),
% 0.20/0.26 inference(avatar_component_clause,[],[f58])).
% 0.20/0.26 thf(f62,definition,(
% 0.20/0.26 spl2_4 <=> ($true = ((sK1 @ sK3)))),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition])).
% 0.20/0.26 thf(f64,plain,(
% 0.20/0.26 ($true = ((sK1 @ sK3))) | ~spl2_4),
% 0.20/0.26 inference(avatar_component_clause,[],[f62])).
% 0.20/0.26 thf(f65,plain,(
% 0.20/0.26 spl2_3 | spl2_4 | spl2_1),
% 0.20/0.26 inference(avatar_split_clause,[],[f48,f13,f62,f58])).
% 0.20/0.26 thf(f67,definition,(
% 0.20/0.26 spl2_5 <=> (((sK0 @ sK3)) = $false)),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition])).
% 0.20/0.26 thf(f69,plain,(
% 0.20/0.26 (((sK0 @ sK3)) = $false) | ~spl2_5),
% 0.20/0.26 inference(avatar_component_clause,[],[f67])).
% 0.20/0.26 thf(f71,definition,(
% 0.20/0.26 spl2_6 <=> (((sK1 @ sK3)) = $false)),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition])).
% 0.20/0.26 thf(f73,plain,(
% 0.20/0.26 (((sK1 @ sK3)) = $false) | ~spl2_6),
% 0.20/0.26 inference(avatar_component_clause,[],[f71])).
% 0.20/0.26 thf(f74,plain,(
% 0.20/0.26 spl2_5 | spl2_6 | spl2_1),
% 0.20/0.26 inference(avatar_split_clause,[],[f56,f13,f71,f67])).
% 0.20/0.26 thf(f75,plain,(
% 0.20/0.26 ($true = $false) | (~spl2_3 | ~spl2_5)),
% 0.20/0.26 inference(forward_demodulation,[],[f69,f60])).
% 0.20/0.26 thf(f76,plain,(
% 0.20/0.26 $false | (~spl2_3 | ~spl2_5)),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f75])).
% 0.20/0.26 thf(f77,plain,(
% 0.20/0.26 ~spl2_3 | ~spl2_5),
% 0.20/0.26 inference(avatar_contradiction_clause,[],[f76])).
% 0.20/0.26 thf(f79,plain,(
% 0.20/0.26 (((sK0 @ sK3)) = $false) | ($true = $false) | (~spl2_2 | ~spl2_6)),
% 0.20/0.26 inference(constrained_superposition,[],[f73,f23])).
% 0.20/0.26 thf(f83,plain,(
% 0.20/0.26 (((sK0 @ sK3)) = $false) | (~spl2_2 | ~spl2_6)),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f79])).
% 0.20/0.26 thf(f88,plain,(
% 0.20/0.26 ($true = $false) | (~spl2_2 | ~spl2_3 | ~spl2_6)),
% 0.20/0.26 inference(forward_demodulation,[],[f83,f60])).
% 0.20/0.26 thf(f89,plain,(
% 0.20/0.26 $false | (~spl2_2 | ~spl2_3 | ~spl2_6)),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f88])).
% 0.20/0.26 thf(f90,plain,(
% 0.20/0.26 ~spl2_2 | ~spl2_3 | ~spl2_6),
% 0.20/0.26 inference(avatar_contradiction_clause,[],[f89])).
% 0.20/0.26 thf(f91,plain,(
% 0.20/0.26 (((sK0 @ sK4)) != ((sK1 @ sK4))) | spl2_2),
% 0.20/0.26 inference(negative_extensionality,[],[f18])).
% 0.20/0.26 thf(f92,plain,(
% 0.20/0.26 ($true = ((sK1 @ sK4))) | (((sK0 @ sK4)) = $true) | spl2_2),
% 0.20/0.26 inference(xor_proxy_clausification,[],[f91])).
% 0.20/0.26 thf(f93,plain,(
% 0.20/0.26 (((sK1 @ sK4)) = $false) | (((sK0 @ sK4)) = $false) | spl2_2),
% 0.20/0.26 inference(xor_proxy_clausification,[],[f91])).
% 0.20/0.26 thf(f95,definition,(
% 0.20/0.26 spl2_7 <=> (((sK1 @ sK4)) = $false)),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition])).
% 0.20/0.26 thf(f97,plain,(
% 0.20/0.26 (((sK1 @ sK4)) = $false) | ~spl2_7),
% 0.20/0.26 inference(avatar_component_clause,[],[f95])).
% 0.20/0.26 thf(f99,definition,(
% 0.20/0.26 spl2_8 <=> (((sK0 @ sK4)) = $false)),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition])).
% 0.20/0.26 thf(f101,plain,(
% 0.20/0.26 (((sK0 @ sK4)) = $false) | ~spl2_8),
% 0.20/0.26 inference(avatar_component_clause,[],[f99])).
% 0.20/0.26 thf(f102,plain,(
% 0.20/0.26 spl2_7 | spl2_8 | spl2_2),
% 0.20/0.26 inference(avatar_split_clause,[],[f93,f17,f99,f95])).
% 0.20/0.26 thf(f104,definition,(
% 0.20/0.26 spl2_9 <=> (((sK0 @ sK4)) = $true)),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition])).
% 0.20/0.26 thf(f106,plain,(
% 0.20/0.26 (((sK0 @ sK4)) = $true) | ~spl2_9),
% 0.20/0.26 inference(avatar_component_clause,[],[f104])).
% 0.20/0.26 thf(f108,definition,(
% 0.20/0.26 spl2_10 <=> ($true = ((sK1 @ sK4)))),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition])).
% 0.20/0.26 thf(f109,plain,(
% 0.20/0.26 ($true != ((sK1 @ sK4))) | spl2_10),
% 0.20/0.26 inference(avatar_component_clause,[],[f108])).
% 0.20/0.26 thf(f110,plain,(
% 0.20/0.26 ($true = ((sK1 @ sK4))) | ~spl2_10),
% 0.20/0.26 inference(avatar_component_clause,[],[f108])).
% 0.20/0.26 thf(f111,plain,(
% 0.20/0.26 spl2_9 | spl2_10 | spl2_2),
% 0.20/0.26 inference(avatar_split_clause,[],[f92,f17,f108,f104])).
% 0.20/0.26 thf(f112,plain,(
% 0.20/0.26 ( ! [X1 : a] : (((((^[Y0 : a]: ($false)) @ X1)) = (((^[Y0 : a]: (((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK1 @ Y0))))) @ X1)))) ) | ~spl2_1),
% 0.20/0.26 inference(argument_congruence,[],[f15])).
% 0.20/0.26 thf(f113,plain,(
% 0.20/0.26 ( ! [X1 : a] : (((((^[Y0 : a]: (((sK1 @ Y0) & (~ (sK0 @ Y0))) | ((sK0 @ Y0) & (~ (sK1 @ Y0))))) @ X1)) = $false) | ((((^[Y0 : a]: ($false)) @ X1)) = $true)) ) | ~spl2_1),
% 0.20/0.26 inference(iff_proxy_clausification,[],[f112])).
% 0.20/0.26 thf(f126,plain,(
% 0.20/0.26 ( ! [X1 : a] : (($true = $false) | (((((sK1 @ X1) & (~ (sK0 @ X1))) | ((sK0 @ X1) & (~ (sK1 @ X1))))) = $false)) ) | ~spl2_1),
% 0.20/0.26 inference(beta-eta_normalization,[],[f113])).
% 0.20/0.26 thf(f127,plain,(
% 0.20/0.26 ( ! [X1 : a] : (((((sK0 @ X1) & (~ (sK1 @ X1)))) = $false) | ($true = $false)) ) | ~spl2_1),
% 0.20/0.26 inference(or_proxy_clausification,[],[f126])).
% 0.20/0.26 thf(f128,plain,(
% 0.20/0.26 ( ! [X1 : a] : (($true = $false) | ((((sK1 @ X1) & (~ (sK0 @ X1)))) = $false)) ) | ~spl2_1),
% 0.20/0.26 inference(or_proxy_clausification,[],[f126])).
% 0.20/0.26 thf(f129,plain,(
% 0.20/0.26 ( ! [X1 : a] : ((((sK1 @ X1)) = $false) | (((~ (sK0 @ X1))) = $false) | ($true = $false)) ) | ~spl2_1),
% 0.20/0.26 inference(and_proxy_clausification,[],[f128])).
% 0.20/0.26 thf(f130,plain,(
% 0.20/0.26 ( ! [X1 : a] : ((((sK1 @ X1)) = $false) | ($true = $false) | ($true = ((sK0 @ X1)))) ) | ~spl2_1),
% 0.20/0.26 inference(not_proxy_clausification,[],[f129])).
% 0.20/0.26 thf(f131,plain,(
% 0.20/0.26 ( ! [X1 : a] : (($true = ((sK0 @ X1))) | (((sK1 @ X1)) = $false)) ) | ~spl2_1),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f130])).
% 0.20/0.26 thf(f132,plain,(
% 0.20/0.26 ( ! [X1 : a] : ((((sK0 @ X1)) = $false) | (((~ (sK1 @ X1))) = $false) | ($true = $false)) ) | ~spl2_1),
% 0.20/0.26 inference(and_proxy_clausification,[],[f127])).
% 0.20/0.26 thf(f133,plain,(
% 0.20/0.26 ( ! [X1 : a] : ((((sK0 @ X1)) = $false) | (((sK1 @ X1)) = $true) | ($true = $false)) ) | ~spl2_1),
% 0.20/0.26 inference(not_proxy_clausification,[],[f132])).
% 0.20/0.26 thf(f134,plain,(
% 0.20/0.26 ( ! [X1 : a] : ((((sK1 @ X1)) = $true) | (((sK0 @ X1)) = $false)) ) | ~spl2_1),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f133])).
% 0.20/0.26 thf(f138,plain,(
% 0.20/0.26 (((sK1 @ sK4)) = $false) | ($true = $false) | (~spl2_1 | ~spl2_8)),
% 0.20/0.26 inference(constrained_superposition,[],[f101,f131])).
% 0.20/0.26 thf(f140,plain,(
% 0.20/0.26 (((sK1 @ sK4)) = $false) | (~spl2_1 | ~spl2_8)),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f138])).
% 0.20/0.26 thf(f144,plain,(
% 0.20/0.26 ($true = $false) | (~spl2_1 | ~spl2_8 | ~spl2_10)),
% 0.20/0.26 inference(forward_demodulation,[],[f140,f110])).
% 0.20/0.26 thf(f145,plain,(
% 0.20/0.26 $false | (~spl2_1 | ~spl2_8 | ~spl2_10)),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f144])).
% 0.20/0.26 thf(f146,plain,(
% 0.20/0.26 ~spl2_1 | ~spl2_8 | ~spl2_10),
% 0.20/0.26 inference(avatar_contradiction_clause,[],[f145])).
% 0.20/0.26 thf(f147,plain,(
% 0.20/0.26 ($true = $false) | (~spl2_7 | ~spl2_10)),
% 0.20/0.26 inference(forward_demodulation,[],[f97,f110])).
% 0.20/0.26 thf(f148,plain,(
% 0.20/0.26 $false | (~spl2_7 | ~spl2_10)),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f147])).
% 0.20/0.26 thf(f149,plain,(
% 0.20/0.26 ~spl2_7 | ~spl2_10),
% 0.20/0.26 inference(avatar_contradiction_clause,[],[f148])).
% 0.20/0.26 thf(f156,plain,(
% 0.20/0.26 ($true = $false) | (((sK0 @ sK4)) = $false) | (~spl2_1 | ~spl2_7)),
% 0.20/0.26 inference(constrained_superposition,[],[f134,f97])).
% 0.20/0.26 thf(f159,plain,(
% 0.20/0.26 (((sK0 @ sK4)) = $false) | (~spl2_1 | ~spl2_7)),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f156])).
% 0.20/0.26 thf(f167,plain,(
% 0.20/0.26 ($true = $false) | (~spl2_1 | ~spl2_7 | ~spl2_9)),
% 0.20/0.26 inference(forward_demodulation,[],[f159,f106])).
% 0.20/0.26 thf(f168,plain,(
% 0.20/0.26 $false | (~spl2_1 | ~spl2_7 | ~spl2_9)),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f167])).
% 0.20/0.26 thf(f169,plain,(
% 0.20/0.26 ~spl2_1 | ~spl2_7 | ~spl2_9),
% 0.20/0.26 inference(avatar_contradiction_clause,[],[f168])).
% 0.20/0.26 thf(f173,plain,(
% 0.20/0.26 ( ! [X1 : a] : ((((sK1 @ X1)) = ((sK0 @ X1)))) ) | ~spl2_2),
% 0.20/0.26 inference(argument_congruence,[],[f19])).
% 0.20/0.26 thf(f175,plain,(
% 0.20/0.26 ( ! [X1 : a] : (($true = ((sK0 @ X1))) | (((sK1 @ X1)) = $false)) ) | ~spl2_2),
% 0.20/0.26 inference(iff_proxy_clausification,[],[f173])).
% 0.20/0.26 thf(f179,plain,(
% 0.20/0.26 (((sK1 @ sK4)) = $false) | ($true != $true) | spl2_10),
% 0.20/0.26 inference(constrained_superposition,[],[f109,f11])).
% 0.20/0.26 thf(f180,plain,(
% 0.20/0.26 (((sK1 @ sK4)) = $false) | spl2_10),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f179])).
% 0.20/0.26 thf(f181,plain,(
% 0.20/0.26 spl2_7 | spl2_10),
% 0.20/0.26 inference(avatar_split_clause,[],[f180,f108,f95])).
% 0.20/0.26 thf(f244,plain,(
% 0.20/0.26 (((sK1 @ sK3)) = $false) | ($true != $true) | (~spl2_2 | spl2_3)),
% 0.20/0.26 inference(constrained_superposition,[],[f59,f175])).
% 0.20/0.26 thf(f248,plain,(
% 0.20/0.26 (((sK1 @ sK3)) = $false) | (~spl2_2 | spl2_3)),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f244])).
% 0.20/0.26 thf(f257,plain,(
% 0.20/0.26 ($true = $false) | (~spl2_2 | spl2_3 | ~spl2_4)),
% 0.20/0.26 inference(forward_demodulation,[],[f248,f64])).
% 0.20/0.26 thf(f258,plain,(
% 0.20/0.26 $false | (~spl2_2 | spl2_3 | ~spl2_4)),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f257])).
% 0.20/0.26 thf(f259,plain,(
% 0.20/0.26 ~spl2_2 | spl2_3 | ~spl2_4),
% 0.20/0.26 inference(avatar_contradiction_clause,[],[f258])).
% 0.20/0.26 cnf(s1, plain, spl2_1 | spl2_2, inference(sat_conversion,[],[f20])).
% 0.20/0.26 cnf(s2, plain, ~spl2_1 | ~spl2_2, inference(sat_conversion,[],[f21])).
% 0.20/0.26 cnf(s3, plain, spl2_1 | spl2_3 | spl2_4, inference(sat_conversion,[],[f65])).
% 0.20/0.26 cnf(s4, plain, spl2_1 | spl2_5 | spl2_6, inference(sat_conversion,[],[f74])).
% 0.20/0.26 cnf(s5, plain, ~spl2_3 | ~spl2_5, inference(sat_conversion,[],[f77])).
% 0.20/0.26 cnf(s7, plain, ~spl2_2 | ~spl2_3 | ~spl2_6, inference(sat_conversion,[],[f90])).
% 0.20/0.26 cnf(s8, plain, spl2_2 | spl2_7 | spl2_8, inference(sat_conversion,[],[f102])).
% 0.20/0.26 cnf(s9, plain, spl2_2 | spl2_9 | spl2_10, inference(sat_conversion,[],[f111])).
% 0.20/0.26 cnf(s11, plain, ~spl2_1 | ~spl2_8 | ~spl2_10, inference(sat_conversion,[],[f146])).
% 0.20/0.26 cnf(s12, plain, ~spl2_7 | ~spl2_10, inference(sat_conversion,[],[f149])).
% 0.20/0.26 cnf(s16, plain, ~spl2_1 | ~spl2_7 | ~spl2_9, inference(sat_conversion,[],[f169])).
% 0.20/0.26 cnf(s18, plain, spl2_7 | spl2_10, inference(sat_conversion,[],[f181])).
% 0.20/0.27 cnf(s24, plain, ~spl2_2 | spl2_3 | ~spl2_4, inference(sat_conversion,[],[f259])).
% 0.20/0.27 cnf(s30, plain, spl2_3 | spl2_1, inference(rat,[],[s3,s24,s1])).
% 0.20/0.27 cnf(s31, plain, spl2_1, inference(rat,[],[s4,s5,s7,s30,s1])).
% 0.20/0.27 cnf(s32, plain, ~spl2_2, inference(rat,[],[s2,s31])).
% 0.20/0.27 cnf(s33, plain, spl2_7, inference(rat,[],[s11,s8,s18,s31,s32])).
% 0.20/0.27 cnf(s34, plain, ~spl2_9, inference(rat,[],[s16,s31,s33])).
% 0.20/0.27 cnf(s36, plain, ~spl2_10, inference(rat,[],[s12,s33])).
% 0.20/0.27 cnf(s37, plain, $false, inference(rat,[],[s9,s32,s36,s34])).
% 0.20/0.27 thf(f273,plain,(
% 0.20/0.27 $false),
% 0.20/0.27 inference(avatar_sat_refutation,[],[s37])).
% 0.20/0.27 % SZS output end Proof for theBenchmark
% 0.20/0.27 % (422281)------------------------------
% 0.20/0.27 % (422281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (422281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (422281)CaDiCaL version: 2.1.3
% 0.20/0.27 % (422281)Termination reason: Refutation
% 0.20/0.27 % (422281)Time elapsed: 0.004 s
% 0.20/0.27 % (422281)Peak memory usage: 13 MB
% 0.20/0.27 % (422281)Instructions burned: 10 (million)
% 0.20/0.27 % (422267)Success in time 0.035 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------