%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV084^5 : 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 : n014.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 08:37:36 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV084^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n014.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 15:09:32 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.22/0.28 % (2783180)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (2783188)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=399023764: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)
% 0.22/0.28 % (2783188) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2783180-2783188"...
% 0.22/0.28 % (2783188)...printing done.
% 0.22/0.28 % (2783188)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% 0.22/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.28 thf(func_def_0, type, cP: $o).
% 0.22/0.28 thf(func_def_4, type, vOR: ($o > $o > $o)).
% 0.22/0.28 thf(func_def_5, type, vNOT: ($o > $o)).
% 0.22/0.28 thf(func_def_6, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.28 thf(func_def_7, type, vAND: ($o > $o > $o)).
% 0.22/0.28 thf(func_def_8, type, sK0: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.22/0.28 thf(func_def_9, type, sK1: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.22/0.28 thf(func_def_10, type, sK2: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.22/0.28 thf(func_def_11, type, sK3: ((($i > $o) > ($i > $o) > $o) > $i > $o)).
% 0.22/0.28 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.28 thf(func_def_13, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.28 thf(func_def_14, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.28 thf(f1,conjecture,(
% 0.22/0.28 ? [X0 : (($i > $o) > ($i > $o) > $o)] : (~(X0 @ (^[X1 : $i] : (cP | ~cP)) @ (^[X1 : $i] : (cP & ~cP))) & ! [X1 : ($i > $o)] : (X0 @ X1 @ X1) & ! [X1 : ($i > $o),X3 : ($i > $o),X2 : ($i > $o)] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)))),
% 0.22/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120J_pme)).
% 0.22/0.28 thf(f2,negated_conjecture,(
% 0.22/0.28 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (~(X0 @ (^[X1 : $i] : (cP | ~cP)) @ (^[X1 : $i] : (cP & ~cP))) & ! [X1 : ($i > $o)] : (X0 @ X1 @ X1) & ! [X1 : ($i > $o),X3 : ($i > $o),X2 : ($i > $o)] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)))),
% 0.22/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.28 thf(f3,plain,(
% 0.22/0.28 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (~(X0 @ (^[X1 : $i] : (cP | ~cP)) @ (^[X2 : $i] : (cP & ~cP))) & ! [X3 : ($i > $o)] : (X0 @ X3 @ X3) & ! [X4 : ($i > $o),X5 : ($i > $o),X6 : ($i > $o)] : (((X0 @ X4 @ X6) & (X0 @ X6 @ X5)) => (X0 @ X4 @ X5)))),
% 0.22/0.28 inference(rectify,[],[f2])).
% 0.22/0.28 thf(f4,plain,(
% 0.22/0.28 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (~ (((X0 @ (^[Y0 : $i]: ((~ cP) | cP)) @ (^[Y0 : $i]: ((~ cP) & cP)))) = $true) & ! [X3 : ($i > $o)] : (((X0 @ X3 @ X3)) = $true) & ! [X4 : ($i > $o),X5 : ($i > $o),X6 : ($i > $o)] : (((((X0 @ X4 @ X6)) = $true) & (((X0 @ X6 @ X5)) = $true)) => (((X0 @ X4 @ X5)) = $true)))),
% 0.22/0.28 inference(fool_elimination,[],[f3])).
% 0.22/0.28 thf(f5,plain,(
% 0.22/0.28 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (~ (((X0 @ (^[Y0 : $i]: ((~ cP) | cP)) @ (^[Y0 : $i]: ((~ cP) & cP)))) = $true) & ! [X1 : ($i > $o)] : (((X0 @ X1 @ X1)) = $true) & ! [X3 : ($i > $o),X4 : ($i > $o),X2 : ($i > $o)] : (((((X0 @ X2 @ X4)) = $true) & (((X0 @ X4 @ X3)) = $true)) => (((X0 @ X2 @ X3)) = $true)))),
% 0.22/0.28 inference(rectify,[],[f4])).
% 0.22/0.28 thf(f6,plain,(
% 0.22/0.28 ~ ? [X0 : (($i > $o) > ($i > $o) > $o)] : (! [X3 : ($i > $o),X4 : ($i > $o),X2 : ($i > $o)] : (((((X0 @ X2 @ X4)) = $true) & (((X0 @ X4 @ X3)) = $true)) => (((X0 @ X2 @ X3)) = $true)) & ! [X1 : ($i > $o)] : (((X0 @ X1 @ X1)) = $true) & (((X0 @ (^[Y0 : $i]: ((~ cP) | cP)) @ (^[Y0 : $i]: ((~ cP) & cP)))) != $true))),
% 0.22/0.28 inference(flattening,[],[f5])).
% 0.22/0.28 thf(f7,plain,(
% 0.22/0.28 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X3 : ($i > $o),X4 : ($i > $o),X2 : ($i > $o)] : ((((X0 @ X2 @ X3)) != $true) & ((((X0 @ X2 @ X4)) = $true) & (((X0 @ X4 @ X3)) = $true))) | ? [X1 : ($i > $o)] : (((X0 @ X1 @ X1)) != $true) | (((X0 @ (^[Y0 : $i]: ((~ cP) | cP)) @ (^[Y0 : $i]: ((~ cP) & cP)))) = $true))),
% 0.22/0.28 inference(ennf_transformation,[],[f6])).
% 0.22/0.28 thf(f8,plain,(
% 0.22/0.28 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X2 : ($i > $o),X3 : ($i > $o),X4 : ($i > $o)] : ((((X0 @ X2 @ X4)) = $true) & (((X0 @ X4 @ X3)) = $true) & (((X0 @ X2 @ X3)) != $true)) | (((X0 @ (^[Y0 : $i]: ((~ cP) | cP)) @ (^[Y0 : $i]: ((~ cP) & cP)))) = $true) | ? [X1 : ($i > $o)] : (((X0 @ X1 @ X1)) != $true))),
% 0.22/0.28 inference(flattening,[],[f7])).
% 0.22/0.28 thf(f9,plain,(
% 0.22/0.28 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (? [X1 : ($i > $o),X2 : ($i > $o),X3 : ($i > $o)] : ((((X0 @ X1 @ X3)) = $true) & (((X0 @ X3 @ X2)) = $true) & (((X0 @ X1 @ X2)) != $true)) | (((X0 @ (^[Y0 : $i]: ((~ cP) | cP)) @ (^[Y0 : $i]: ((~ cP) & cP)))) = $true) | ? [X4 : ($i > $o)] : ($true != ((X0 @ X4 @ X4))))),
% 0.22/0.28 inference(rectify,[],[f8])).
% 0.22/0.28 thf(f10,plain,(
% 0.22/0.28 ! [X0 : (($i > $o) > ($i > $o) > $o)] : (((((X0 @ (sK0 @ X0) @ (sK2 @ X0))) = $true) & (((X0 @ (sK2 @ X0) @ (sK1 @ X0))) = $true) & ($true != ((X0 @ (sK0 @ X0) @ (sK1 @ X0))))) | (((X0 @ (^[Y0 : $i]: ((~ cP) | cP)) @ (^[Y0 : $i]: ((~ cP) & cP)))) = $true) | (((X0 @ (sK3 @ X0) @ (sK3 @ X0))) != $true))),
% 0.22/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP]),skolemize(X4,sK3 @ X0),skolemize(X4,sK3 @ X0),skolemize(X4,sK3 @ X0),skolemize(X4,sK3 @ X0)],[f9])).
% 0.22/0.28 thf(f11,plain,(
% 0.22/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (sK3 @ X0) @ (sK3 @ X0))) != $true) | ($true != ((X0 @ (sK0 @ X0) @ (sK1 @ X0)))) | (((X0 @ (^[Y0 : $i]: ((~ cP) | cP)) @ (^[Y0 : $i]: ((~ cP) & cP)))) = $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f10])).
% 0.22/0.28 thf(f12,plain,(
% 0.22/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (sK3 @ X0) @ (sK3 @ X0))) != $true) | (((X0 @ (^[Y0 : $i]: ((~ cP) | cP)) @ (^[Y0 : $i]: ((~ cP) & cP)))) = $true) | (((X0 @ (sK2 @ X0) @ (sK1 @ X0))) = $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f10])).
% 0.22/0.28 thf(f13,plain,(
% 0.22/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (sK3 @ X0) @ (sK3 @ X0))) != $true) | (((X0 @ (sK0 @ X0) @ (sK2 @ X0))) = $true) | (((X0 @ (^[Y0 : $i]: ((~ cP) | cP)) @ (^[Y0 : $i]: ((~ cP) & cP)))) = $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f10])).
% 0.22/0.28 thf(f15,plain,(
% 0.22/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (^[Y0 : $i]: ((~ cP) | cP)) @ (^[Y0 : $i]: ($false)))) = $true) | (((X0 @ (sK3 @ X0) @ (sK3 @ X0))) != $true) | (((X0 @ (sK2 @ X0) @ (sK1 @ X0))) = $true)) )),
% 0.22/0.28 inference(boolean_simplification,[],[f12])).
% 0.22/0.28 thf(f16,plain,(
% 0.22/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (sK2 @ X0) @ (sK1 @ X0))) = $true) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true) | (((X0 @ (sK3 @ X0) @ (sK3 @ X0))) != $true)) )),
% 0.22/0.28 inference(boolean_simplification,[],[f15])).
% 0.22/0.28 thf(f17,plain,(
% 0.22/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (sK3 @ X0) @ (sK3 @ X0))) != $true) | ($true != ((X0 @ (sK0 @ X0) @ (sK1 @ X0)))) | (((X0 @ (^[Y0 : $i]: ((~ cP) | cP)) @ (^[Y0 : $i]: ($false)))) = $true)) )),
% 0.22/0.28 inference(boolean_simplification,[],[f11])).
% 0.22/0.28 thf(f18,plain,(
% 0.22/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : (($true != ((X0 @ (sK0 @ X0) @ (sK1 @ X0)))) | (((X0 @ (sK3 @ X0) @ (sK3 @ X0))) != $true) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true)) )),
% 0.22/0.28 inference(boolean_simplification,[],[f17])).
% 0.22/0.28 thf(f19,plain,(
% 0.22/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (^[Y0 : $i]: ((~ cP) | cP)) @ (^[Y0 : $i]: ($false)))) = $true) | (((X0 @ (sK3 @ X0) @ (sK3 @ X0))) != $true) | (((X0 @ (sK0 @ X0) @ (sK2 @ X0))) = $true)) )),
% 0.22/0.28 inference(boolean_simplification,[],[f13])).
% 0.22/0.28 thf(f20,plain,(
% 0.22/0.28 ( ! [X0 : (($i > $o) > ($i > $o) > $o)] : ((((X0 @ (sK0 @ X0) @ (sK2 @ X0))) = $true) | (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true) | (((X0 @ (sK3 @ X0) @ (sK3 @ X0))) != $true)) )),
% 0.22/0.28 inference(boolean_simplification,[],[f19])).
% 0.22/0.28 thf(f21,plain,(
% 0.22/0.28 ($true = (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))))))) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true)),
% 0.22/0.28 inference(primitive_instantiation,[],[f16])).
% 0.22/0.28 thf(f33,plain,(
% 0.22/0.28 ((((sK2 @ =) = (sK1 @ =))) = $true) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | ((((sK3 @ =) = (sK3 @ =))) != $true)),
% 0.22/0.28 inference(beta-eta_normalization,[],[f21])).
% 0.22/0.28 thf(f34,plain,(
% 0.22/0.28 ((((sK3 @ =) = (sK3 @ =))) != $true) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | (((sK2 @ =)) = ((sK1 @ =)))),
% 0.22/0.28 inference(equality_proxy_clausification,[],[f33])).
% 0.22/0.28 thf(f35,plain,(
% 0.22/0.28 ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | (((sK2 @ =)) = ((sK1 @ =))) | (((sK3 @ =)) != ((sK3 @ =)))),
% 0.22/0.28 inference(equality_proxy_clausification,[],[f34])).
% 0.22/0.28 thf(f36,plain,(
% 0.22/0.28 (((sK3 @ =)) != ((sK3 @ =))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((sK2 @ =)) = ((sK1 @ =)))),
% 0.22/0.28 inference(equality_proxy_clausification,[],[f35])).
% 0.22/0.28 thf(f37,plain,(
% 0.22/0.28 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((sK2 @ =)) = ((sK1 @ =)))),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f36])).
% 0.22/0.28 thf(f47,definition,(
% 0.22/0.28 spl4_1 <=> (((sK2 @ =)) = ((sK1 @ =)))),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.22/0.28 thf(f51,definition,(
% 0.22/0.28 spl4_2 <=> ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.22/0.28 thf(f53,plain,(
% 0.22/0.28 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ~spl4_2),
% 0.22/0.28 inference(avatar_component_clause,[],[f51])).
% 0.22/0.28 thf(f54,plain,(
% 0.22/0.28 spl4_1 | spl4_2),
% 0.22/0.28 inference(avatar_split_clause,[],[f37,f51,f47])).
% 0.22/0.28 thf(f55,plain,(
% 0.22/0.28 ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true)),
% 0.22/0.28 inference(primitive_instantiation,[],[f18])).
% 0.22/0.28 thf(f65,plain,(
% 0.22/0.28 ((((sK0 @ =) = (sK1 @ =))) != $true) | ((((sK3 @ =) = (sK3 @ =))) != $true) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true)),
% 0.22/0.28 inference(beta-eta_normalization,[],[f55])).
% 0.22/0.28 thf(f66,plain,(
% 0.22/0.28 ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | ((((sK3 @ =) = (sK3 @ =))) != $true) | (((sK0 @ =)) != ((sK1 @ =)))),
% 0.22/0.28 inference(equality_proxy_clausification,[],[f65])).
% 0.22/0.28 thf(f67,plain,(
% 0.22/0.28 (((sK0 @ =)) != ((sK1 @ =))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((((sK3 @ =) = (sK3 @ =))) != $true)),
% 0.22/0.28 inference(equality_proxy_clausification,[],[f66])).
% 0.22/0.28 thf(f68,plain,(
% 0.22/0.28 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((sK0 @ =)) != ((sK1 @ =))) | (((sK3 @ =)) != ((sK3 @ =)))),
% 0.22/0.28 inference(equality_proxy_clausification,[],[f67])).
% 0.22/0.28 thf(f69,plain,(
% 0.22/0.28 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((sK0 @ =)) != ((sK1 @ =)))),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f68])).
% 0.22/0.28 thf(f84,definition,(
% 0.22/0.28 spl4_3 <=> (((sK0 @ =)) = ((sK1 @ =)))),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
% 0.22/0.28 thf(f87,plain,(
% 0.22/0.28 ~spl4_3 | spl4_2),
% 0.22/0.28 inference(avatar_split_clause,[],[f69,f51,f84])).
% 0.22/0.28 thf(f88,plain,(
% 0.22/0.28 ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) = $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)))) = $true) | ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y0 = Y1))))))) != $true)),
% 0.22/0.28 inference(primitive_instantiation,[],[f20])).
% 0.22/0.28 thf(f97,plain,(
% 0.22/0.28 ((((sK3 @ =) = (sK3 @ =))) != $true) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | ((((sK0 @ =) = (sK2 @ =))) = $true)),
% 0.22/0.28 inference(beta-eta_normalization,[],[f88])).
% 0.22/0.28 thf(f98,plain,(
% 0.22/0.28 (((sK3 @ =)) != ((sK3 @ =))) | ((((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) = $true) | ((((sK0 @ =) = (sK2 @ =))) = $true)),
% 0.22/0.28 inference(equality_proxy_clausification,[],[f97])).
% 0.22/0.28 thf(f99,plain,(
% 0.22/0.28 ((((sK0 @ =) = (sK2 @ =))) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((sK3 @ =)) != ((sK3 @ =)))),
% 0.22/0.28 inference(equality_proxy_clausification,[],[f98])).
% 0.22/0.28 thf(f100,plain,(
% 0.22/0.28 (((sK0 @ =)) = ((sK2 @ =))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((sK3 @ =)) != ((sK3 @ =)))),
% 0.22/0.28 inference(equality_proxy_clausification,[],[f99])).
% 0.22/0.28 thf(f101,plain,(
% 0.22/0.28 (((sK0 @ =)) = ((sK2 @ =))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f100])).
% 0.22/0.28 thf(f114,definition,(
% 0.22/0.28 spl4_4 <=> (((sK0 @ =)) = ((sK2 @ =)))),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
% 0.22/0.28 thf(f117,plain,(
% 0.22/0.28 spl4_4 | spl4_2),
% 0.22/0.28 inference(avatar_split_clause,[],[f101,f51,f114])).
% 0.22/0.28 thf(f118,plain,(
% 0.22/0.28 ( ! [X1 : $i] : (((((^[Y0 : $i]: ($true)) @ X1)) = (((^[Y0 : $i]: ($false)) @ X1)))) ) | ~spl4_2),
% 0.22/0.28 inference(argument_congruence,[],[f53])).
% 0.22/0.28 thf(f120,plain,(
% 0.22/0.28 ( ! [X1 : $i] : (((((^[Y0 : $i]: ($true)) @ X1)) = $false) | ($true = (((^[Y0 : $i]: ($false)) @ X1)))) ) | ~spl4_2),
% 0.22/0.28 inference(iff_proxy_clausification,[],[f118])).
% 0.22/0.28 thf(f121,plain,(
% 0.22/0.28 ($true = $false) | ($true = $false) | ~spl4_2),
% 0.22/0.28 inference(beta-eta_normalization,[],[f120])).
% 0.22/0.28 thf(f122,plain,(
% 0.22/0.28 ($true = $false) | ~spl4_2),
% 0.22/0.28 inference(duplicate_literal_removal,[],[f121])).
% 0.22/0.28 thf(f123,plain,(
% 0.22/0.28 $false | ~spl4_2),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f122])).
% 0.22/0.28 thf(f124,plain,(
% 0.22/0.28 ~spl4_2),
% 0.22/0.28 inference(avatar_contradiction_clause,[],[f123])).
% 0.22/0.28 thf(f126,definition,(
% 0.22/0.28 (((sK0 @ =)) != ((sK2 @ =))) | (((sK2 @ =)) != ((sK1 @ =))) | (((sK0 @ =)) = ((sK1 @ =)))),
% 0.22/0.28 introduced(theory,[theory_tautology_sat_conflict])).
% 0.22/0.28 cnf(s1, plain, spl4_1 | spl4_2, inference(sat_conversion,[],[f54])).
% 0.22/0.28 cnf(s2, plain, spl4_2 | ~spl4_3, inference(sat_conversion,[],[f87])).
% 0.22/0.28 cnf(s3, plain, spl4_2 | spl4_4, inference(sat_conversion,[],[f117])).
% 0.22/0.28 cnf(s4, plain, ~spl4_2, inference(sat_conversion,[],[f124])).
% 0.22/0.28 cnf(s5, plain, ~spl4_1 | spl4_3 | ~spl4_4, inference(sat_conversion,[],[f126])).
% 0.22/0.28 cnf(s6, plain, spl4_4, inference(rat,[],[s3,s4])).
% 0.22/0.28 cnf(s7, plain, ~spl4_3, inference(rat,[],[s2,s4])).
% 0.22/0.28 cnf(s8, plain, ~spl4_1, inference(rat,[],[s5,s6,s7])).
% 0.22/0.28 cnf(s9, plain, $false, inference(rat,[],[s1,s4,s8])).
% 0.22/0.28 thf(f127,plain,(
% 0.22/0.28 $false),
% 0.22/0.28 inference(avatar_sat_refutation,[],[s9])).
% 0.22/0.28 % SZS output end Proof for theBenchmark
% 0.22/0.28 % (2783188)------------------------------
% 0.22/0.28 % (2783188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (2783188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (2783188)CaDiCaL version: 2.1.3
% 0.22/0.28 % (2783188)Termination reason: Refutation
% 0.22/0.28 % (2783188)Time elapsed: 0.003 s
% 0.22/0.28 % (2783188)Peak memory usage: 13 MB
% 0.22/0.28 % (2783188)Instructions burned: 9 (million)
% 0.22/0.28 % (2783180)Success in time 0.04 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------