%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU855^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 08:34:18 AM UTC 2026
% Result : Theorem 0.12s 0.27s
% Output : Refutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU855^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.18 % Computer : n013.cluster.edu
% 0.12/0.18 % Model : x86_64 x86_64
% 0.12/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.18 % Memory : 8046.5625MB
% 0.12/0.18 % OS : Linux 6.8.0-71-generic
% 0.12/0.18 % CPULimit : 300
% 0.12/0.18 % WCLimit : 300
% 0.12/0.18 % DateTime : Tue Sep 29 14:39:36 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.21 Running first-order model finding
% 0.12/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.27 % (2208000)Will run a generic schedule for satisfiability detection.
% 0.12/0.27 % (2208007)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2285549766_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.27 % Exception at run slice level
% 0.12/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.27 % (2208008)% WARNING: option uhcvi not known.
% 0.12/0.27 % (2208008)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2368173825:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.27 % (2208010)dis+10_1_sil=32000:sp=arity:random_seed=3345675965:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.27 % (2208011)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1403638672:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.27 % (2208008)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.12/0.27 % (2208009)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3085471012:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.27 % (2208012)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1094901772:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.27 % (2208008)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.12/0.27 % (2208011)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.12/0.27 % (2208011) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2208000-2208011"...
% 0.12/0.27 % (2208010) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2208000-2208010"...
% 0.12/0.27 % (2208008) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2208000-2208008"...
% 0.12/0.27 % (2208012) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2208000-2208012"...
% 0.12/0.27 % (2208009) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2208000-2208009"...
% 0.12/0.27 % (2208011)...printing done.
% 0.12/0.27 % (2208010)...printing done.
% 0.12/0.27 % (2208008)...printing done.
% 0.12/0.27 % (2208012)...printing done.
% 0.12/0.27 % (2208015)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=382794779:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.12/0.27 % Exception at run slice level% (2208011)Refutation found. Thanks to Tanya!
% 0.12/0.27 % SZS status Theorem for theBenchmark
% 0.12/0.27 % SZS output start Proof for theBenchmark
% 0.12/0.27 thf(type_def_5, type, a: $tType).
% 0.12/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.12/0.27 thf(func_def_3, type, vAND: ($o > $o > $o)).
% 0.12/0.27 thf(func_def_4, type, db0: !>[X0: $tType]:(X0)).
% 0.12/0.27 thf(func_def_5, type, vNOT: ($o > $o)).
% 0.12/0.27 thf(func_def_6, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.12/0.27 thf(func_def_7, type, sK0: (a > $o)).
% 0.12/0.27 thf(func_def_8, type, sK1: (a > $o)).
% 0.12/0.27 thf(func_def_9, type, sK2: (a > $o)).
% 0.12/0.27 thf(func_def_10, type, sK3: a).
% 0.12/0.27 thf(func_def_12, type, sK5: a).
% 0.12/0.27 thf(f1,conjecture,(
% 0.12/0.27 ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((! [X3 : a] : ((X1 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X0 @ X3) => (X2 @ X3))) => (! [X3 : a] : ((X0 @ X3) => (X1 @ X3)) <=> ((^[X3 : a] : (~(X1 @ X3) & (X2 @ X3) & (X0 @ X3))) = (^[X3 : a] : ($false)))))),
% 0.12/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGAZING_THM33_pme)).
% 0.12/0.27 thf(f2,negated_conjecture,(
% 0.12/0.27 ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((! [X3 : a] : ((X1 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X0 @ X3) => (X2 @ X3))) => (! [X3 : a] : ((X0 @ X3) => (X1 @ X3)) <=> ((^[X3 : a] : (~(X1 @ X3) & (X2 @ X3) & (X0 @ X3))) = (^[X3 : a] : ($false)))))),
% 0.12/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.12/0.27 thf(f3,plain,(
% 0.12/0.27 ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((! [X3 : a] : ((X1 @ X3) => (X2 @ X3)) & ! [X4 : a] : ((X0 @ X4) => (X2 @ X4))) => (! [X5 : a] : ((X0 @ X5) => (X1 @ X5)) <=> ((^[X6 : a] : (~(X1 @ X6) & (X2 @ X6) & (X0 @ X6))) = (^[X7 : a] : ($false)))))),
% 0.12/0.27 inference(rectify,[],[f2])).
% 0.12/0.27 thf(f4,plain,(
% 0.12/0.27 ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((! [X3 : a] : ((((X1 @ X3)) = $true) => (((X2 @ X3)) = $true)) & ! [X4 : a] : ((((X0 @ X4)) = $true) => (((X2 @ X4)) = $true))) => (! [X5 : a] : ((((X0 @ X5)) = $true) => (((X1 @ X5)) = $true)) <=> ((^[Y0 : a]: (((X0 @ Y0) & (X2 @ Y0)) & (~ (X1 @ Y0)))) = (^[Y0 : a]: ($false)))))),
% 0.12/0.27 inference(fool_elimination,[],[f3])).
% 0.12/0.27 thf(f5,plain,(
% 0.12/0.27 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((! [X5 : a] : ((((X1 @ X5)) = $true) | (((X0 @ X5)) != $true)) <~> ((^[Y0 : a]: (((X0 @ Y0) & (X2 @ Y0)) & (~ (X1 @ Y0)))) = (^[Y0 : a]: ($false)))) & (! [X3 : a] : ((((X2 @ X3)) = $true) | (((X1 @ X3)) != $true)) & ! [X4 : a] : ((((X2 @ X4)) = $true) | (((X0 @ X4)) != $true))))),
% 0.12/0.27 inference(ennf_transformation,[],[f4])).
% 0.12/0.27 thf(f6,plain,(
% 0.12/0.27 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((! [X5 : a] : ((((X1 @ X5)) = $true) | (((X0 @ X5)) != $true)) <~> ((^[Y0 : a]: (((X0 @ Y0) & (X2 @ Y0)) & (~ (X1 @ Y0)))) = (^[Y0 : a]: ($false)))) & ! [X3 : a] : ((((X2 @ X3)) = $true) | (((X1 @ X3)) != $true)) & ! [X4 : a] : ((((X2 @ X4)) = $true) | (((X0 @ X4)) != $true)))),
% 0.12/0.27 inference(flattening,[],[f5])).
% 0.12/0.27 thf(f7,plain,(
% 0.12/0.27 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (((((^[Y0 : a]: (((X0 @ Y0) & (X2 @ Y0)) & (~ (X1 @ Y0)))) != (^[Y0 : a]: ($false))) | ? [X5 : a] : ((((X1 @ X5)) != $true) & (((X0 @ X5)) = $true))) & (((^[Y0 : a]: (((X0 @ Y0) & (X2 @ Y0)) & (~ (X1 @ Y0)))) = (^[Y0 : a]: ($false))) | ! [X5 : a] : ((((X1 @ X5)) = $true) | (((X0 @ X5)) != $true)))) & ! [X3 : a] : ((((X2 @ X3)) = $true) | (((X1 @ X3)) != $true)) & ! [X4 : a] : ((((X2 @ X4)) = $true) | (((X0 @ X4)) != $true)))),
% 0.12/0.27 inference(nnf_transformation,[],[f6])).
% 0.12/0.27 thf(f8,plain,(
% 0.12/0.27 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((((^[Y0 : a]: (((X0 @ Y0) & (X2 @ Y0)) & (~ (X1 @ Y0)))) != (^[Y0 : a]: ($false))) | ? [X5 : a] : ((((X1 @ X5)) != $true) & (((X0 @ X5)) = $true))) & (((^[Y0 : a]: (((X0 @ Y0) & (X2 @ Y0)) & (~ (X1 @ Y0)))) = (^[Y0 : a]: ($false))) | ! [X5 : a] : ((((X1 @ X5)) = $true) | (((X0 @ X5)) != $true))) & ! [X3 : a] : ((((X2 @ X3)) = $true) | (((X1 @ X3)) != $true)) & ! [X4 : a] : ((((X2 @ X4)) = $true) | (((X0 @ X4)) != $true)))),
% 0.12/0.27 inference(flattening,[],[f7])).
% 0.12/0.27 thf(f9,plain,(
% 0.12/0.27 ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((((^[Y0 : a]: (((X0 @ Y0) & (X2 @ Y0)) & (~ (X1 @ Y0)))) != (^[Y0 : a]: ($false))) | ? [X3 : a] : ((((X1 @ X3)) != $true) & (((X0 @ X3)) = $true))) & (((^[Y0 : a]: (((X0 @ Y0) & (X2 @ Y0)) & (~ (X1 @ Y0)))) = (^[Y0 : a]: ($false))) | ! [X4 : a] : (($true = ((X1 @ X4))) | (((X0 @ X4)) != $true))) & ! [X5 : a] : (($true = ((X2 @ X5))) | (((X1 @ X5)) != $true)) & ! [X6 : a] : ((((X2 @ X6)) = $true) | (((X0 @ X6)) != $true)))),
% 0.12/0.27 inference(rectify,[],[f8])).
% 0.12/0.27 thf(f10,plain,(
% 0.12/0.27 (((^[Y0 : a]: ($false)) != (^[Y0 : a]: (((sK0 @ Y0) & (sK2 @ Y0)) & (~ (sK1 @ Y0))))) | (($true != ((sK1 @ sK3))) & ($true = ((sK0 @ sK3))))) & (((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((sK0 @ Y0) & (sK2 @ Y0)) & (~ (sK1 @ Y0))))) | ! [X4 : a] : (($true = ((sK1 @ X4))) | ($true != ((sK0 @ X4))))) & ! [X5 : a] : (($true = ((sK2 @ X5))) | ($true != ((sK1 @ X5)))) & ! [X6 : a] : (($true = ((sK2 @ X6))) | ($true != ((sK0 @ X6))))),
% 0.12/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f9])).
% 0.12/0.27 thf(f11,plain,(
% 0.12/0.27 ( ! [X6 : a] : (($true = ((sK2 @ X6))) | ($true != ((sK0 @ X6)))) )),
% 0.12/0.27 inference(cnf_transformation,[],[f10])).
% 0.12/0.27 thf(f13,plain,(
% 0.12/0.27 ( ! [X4 : a] : (((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((sK0 @ Y0) & (sK2 @ Y0)) & (~ (sK1 @ Y0))))) | ($true = ((sK1 @ X4))) | ($true != ((sK0 @ X4)))) )),
% 0.12/0.27 inference(cnf_transformation,[],[f10])).
% 0.12/0.27 thf(f14,plain,(
% 0.12/0.27 ((^[Y0 : a]: ($false)) != (^[Y0 : a]: (((sK0 @ Y0) & (sK2 @ Y0)) & (~ (sK1 @ Y0))))) | ($true = ((sK0 @ sK3)))),
% 0.12/0.27 inference(cnf_transformation,[],[f10])).
% 0.12/0.27 thf(f15,plain,(
% 0.12/0.27 ((^[Y0 : a]: ($false)) != (^[Y0 : a]: (((sK0 @ Y0) & (sK2 @ Y0)) & (~ (sK1 @ Y0))))) | ($true != ((sK1 @ sK3)))),
% 0.12/0.27 inference(cnf_transformation,[],[f10])).
% 0.12/0.27 thf(f17,definition,(
% 0.12/0.27 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.12/0.27 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.12/0.27 thf(f19,definition,(
% 0.12/0.27 spl4_1 <=> ! [X4 : a] : (($true = ((sK1 @ X4))) | ($true != ((sK0 @ X4))))),
% 0.12/0.27 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.12/0.27 thf(f20,plain,(
% 0.12/0.27 ( ! [X4 : a] : (($true = ((sK1 @ X4))) | ($true != ((sK0 @ X4)))) ) | ~spl4_1),
% 0.12/0.27 inference(avatar_component_clause,[],[f19])).
% 0.12/0.27 thf(f22,definition,(
% 0.12/0.27 spl4_2 <=> ((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((sK0 @ Y0) & (sK2 @ Y0)) & (~ (sK1 @ Y0)))))),
% 0.12/0.27 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.12/0.27 thf(f23,plain,(
% 0.12/0.27 ((^[Y0 : a]: ($false)) != (^[Y0 : a]: (((sK0 @ Y0) & (sK2 @ Y0)) & (~ (sK1 @ Y0))))) | spl4_2),
% 0.12/0.27 inference(avatar_component_clause,[],[f22])).
% 0.12/0.27 thf(f24,plain,(
% 0.12/0.27 ((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((sK0 @ Y0) & (sK2 @ Y0)) & (~ (sK1 @ Y0))))) | ~spl4_2),
% 0.12/0.27 inference(avatar_component_clause,[],[f22])).
% 0.12/0.27 thf(f25,plain,(
% 0.12/0.27 spl4_1 | spl4_2),
% 0.12/0.27 inference(avatar_split_clause,[],[f13,f22,f19])).
% 0.12/0.27 thf(f27,definition,(
% 0.12/0.27 spl4_3 <=> ($true = ((sK0 @ sK3)))),
% 0.12/0.27 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
% 0.12/0.27 thf(f29,plain,(
% 0.12/0.27 ($true = ((sK0 @ sK3))) | ~spl4_3),
% 0.12/0.27 inference(avatar_component_clause,[],[f27])).
% 0.12/0.27 thf(f30,plain,(
% 0.12/0.27 spl4_3 | ~spl4_2),
% 0.12/0.27 inference(avatar_split_clause,[],[f14,f22,f27])).
% 0.12/0.27 thf(f32,definition,(
% 0.12/0.27 spl4_4 <=> ($true = ((sK1 @ sK3)))),
% 0.12/0.27 introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
% 0.12/0.27 thf(f34,plain,(
% 0.12/0.27 ($true != ((sK1 @ sK3))) | spl4_4),
% 0.12/0.27 inference(avatar_component_clause,[],[f32])).
% 0.12/0.27 thf(f35,plain,(
% 0.12/0.27 ~spl4_4 | ~spl4_2),
% 0.12/0.27 inference(avatar_split_clause,[],[f15,f22,f32])).
% 0.12/0.27 thf(f36,plain,(
% 0.12/0.27 ( ! [X1 : a] : (((((^[Y0 : a]: ($false)) @ X1)) = (((^[Y0 : a]: (((sK0 @ Y0) & (sK2 @ Y0)) & (~ (sK1 @ Y0)))) @ X1)))) ) | ~spl4_2),
% 0.12/0.27 inference(argument_congruence,[],[f24])).
% 0.12/0.27 thf(f37,plain,(
% 0.12/0.27 ( ! [X1 : a] : (($true = (((^[Y0 : a]: ($false)) @ X1))) | ($false = (((^[Y0 : a]: (((sK0 @ Y0) & (sK2 @ Y0)) & (~ (sK1 @ Y0)))) @ X1)))) ) | ~spl4_2),
% 0.12/0.27 inference(iff_proxy_clausification,[],[f36])).
% 0.12/0.27 thf(f45,plain,(
% 0.12/0.27 ( ! [X1 : a] : (($true = $false) | ($false = ((((sK0 @ X1) & (sK2 @ X1)) & (~ (sK1 @ X1)))))) ) | ~spl4_2),
% 0.12/0.27 inference(beta-eta_normalization,[],[f37])).
% 0.12/0.27 thf(f46,plain,(
% 0.12/0.27 ( ! [X1 : a] : (($true = $false) | ($false = ((~ (sK1 @ X1)))) | ($false = (((sK0 @ X1) & (sK2 @ X1))))) ) | ~spl4_2),
% 0.12/0.27 inference(and_proxy_clausification,[],[f45])).
% 0.12/0.27 thf(f47,plain,(
% 0.12/0.27 ( ! [X1 : a] : (($true = $false) | ($true = ((sK1 @ X1))) | ($false = (((sK0 @ X1) & (sK2 @ X1))))) ) | ~spl4_2),
% 0.12/0.27 inference(not_proxy_clausification,[],[f46])).
% 0.12/0.27 thf(f48,plain,(
% 0.12/0.27 ( ! [X1 : a] : (($true = $false) | ($true = ((sK1 @ X1))) | ($false = ((sK2 @ X1))) | ($false = ((sK0 @ X1)))) ) | ~spl4_2),
% 0.12/0.27 inference(and_proxy_clausification,[],[f47])).
% 0.12/0.27 thf(f49,plain,(
% 0.12/0.27 ( ! [X1 : a] : (($false = ((sK2 @ X1))) | ($true = ((sK1 @ X1))) | ($false = ((sK0 @ X1)))) ) | ~spl4_2),
% 0.12/0.27 inference(trivial_inequality_removal,[],[f48])).
% 0.12/0.27 thf(f53,plain,(
% 0.12/0.27 ( ! [X0 : a] : (($true = $false) | ($true != ((sK0 @ X0))) | ($true = ((sK1 @ X0))) | ($false = ((sK0 @ X0)))) ) | ~spl4_2),
% 0.12/0.27 inference(constrained_superposition,[],[f11,f49])).
% 0.12/0.27 thf(f54,plain,(
% 0.12/0.27 ( ! [X0 : a] : (($true != ((sK0 @ X0))) | ($true = ((sK1 @ X0))) | ($false = ((sK0 @ X0)))) ) | ~spl4_2),
% 0.12/0.27 inference(trivial_inequality_removal,[],[f53])).
% 0.12/0.27 thf(f56,plain,(
% 0.12/0.27 ( ! [X0 : a] : (($true = ((sK1 @ X0))) | ($false = ((sK0 @ X0)))) ) | ~spl4_2),
% 0.12/0.27 inference(forward_subsumption_resolution,[],[f54,f17])).
% 0.12/0.27 thf(f74,plain,(
% 0.12/0.27 ($true != $true) | ($false = ((sK0 @ sK3))) | (~spl4_2 | spl4_4)),
% 0.12/0.27 inference(constrained_superposition,[],[f34,f56])).
% 0.12/0.27 thf(f75,plain,(
% 0.12/0.27 ($false = ((sK0 @ sK3))) | (~spl4_2 | spl4_4)),
% 0.12/0.27 inference(trivial_inequality_removal,[],[f74])).
% 0.12/0.27 thf(f79,plain,(
% 0.12/0.27 ($true = $false) | (~spl4_2 | ~spl4_3 | spl4_4)),
% 0.12/0.27 inference(constrained_superposition,[],[f75,f29])).
% 0.12/0.27 thf(f83,plain,(
% 0.12/0.27 $false | (~spl4_2 | ~spl4_3 | spl4_4)),
% 0.12/0.27 inference(trivial_inequality_removal,[],[f79])).
% 0.12/0.27 thf(f84,plain,(
% 0.12/0.27 ~spl4_2 | ~spl4_3 | spl4_4),
% 0.12/0.27 inference(avatar_contradiction_clause,[],[f83])).
% 0.12/0.27 thf(f98,plain,(
% 0.12/0.27 ((((^[Y0 : a]: ($false)) @ sK5)) != (((^[Y0 : a]: (((sK0 @ Y0) & (sK2 @ Y0)) & (~ (sK1 @ Y0)))) @ sK5))) | spl4_2),
% 0.12/0.27 inference(negative_extensionality,[],[f23])).
% 0.12/0.27 thf(f99,plain,(
% 0.12/0.27 ($true = (((^[Y0 : a]: ($false)) @ sK5))) | ($true = (((^[Y0 : a]: (((sK0 @ Y0) & (sK2 @ Y0)) & (~ (sK1 @ Y0)))) @ sK5))) | spl4_2),
% 0.12/0.27 inference(xor_proxy_clausification,[],[f98])).
% 0.12/0.27 thf(f105,plain,(
% 0.12/0.27 ($true = $false) | ($true = ((((sK0 @ sK5) & (sK2 @ sK5)) & (~ (sK1 @ sK5))))) | spl4_2),
% 0.12/0.27 inference(beta-eta_normalization,[],[f99])).
% 0.12/0.27 thf(f106,plain,(
% 0.12/0.27 ($true = $false) | ($true = ((~ (sK1 @ sK5)))) | spl4_2),
% 0.12/0.27 inference(and_proxy_clausification,[],[f105])).
% 0.12/0.27 thf(f107,plain,(
% 0.12/0.27 ($true = $false) | ($true = (((sK0 @ sK5) & (sK2 @ sK5)))) | spl4_2),
% 0.12/0.27 inference(and_proxy_clausification,[],[f105])).
% 0.12/0.27 thf(f109,plain,(
% 0.12/0.27 ($true = $false) | ($true = ((sK0 @ sK5))) | spl4_2),
% 0.12/0.27 inference(and_proxy_clausification,[],[f107])).
% 0.12/0.27 thf(f110,plain,(
% 0.12/0.27 ($true = ((sK0 @ sK5))) | spl4_2),
% 0.12/0.27 inference(trivial_inequality_removal,[],[f109])).
% 0.12/0.27 thf(f112,plain,(
% 0.12/0.27 ($true = $false) | ($false = ((sK1 @ sK5))) | spl4_2),
% 0.12/0.27 inference(not_proxy_clausification,[],[f106])).
% 0.12/0.27 thf(f113,plain,(
% 0.12/0.27 ($false = ((sK1 @ sK5))) | spl4_2),
% 0.12/0.27 inference(trivial_inequality_removal,[],[f112])).
% 0.12/0.27 thf(f115,plain,(
% 0.12/0.27 ($true = $false) | ($true != ((sK0 @ sK5))) | (~spl4_1 | spl4_2)),
% 0.12/0.27 inference(constrained_superposition,[],[f113,f20])).
% 0.12/0.27 thf(f118,plain,(
% 0.12/0.27 ($true != ((sK0 @ sK5))) | (~spl4_1 | spl4_2)),
% 0.12/0.27 inference(trivial_inequality_removal,[],[f115])).
% 0.12/0.27 thf(f122,plain,(
% 0.12/0.27 $false | (~spl4_1 | spl4_2)),
% 0.12/0.27 inference(forward_subsumption_resolution,[],[f118,f110])).
% 0.12/0.27 thf(f123,plain,(
% 0.12/0.27 ~spl4_1 | spl4_2),
% 0.12/0.27 inference(avatar_contradiction_clause,[],[f122])).
% 0.12/0.27 cnf(s1, plain, spl4_1 | spl4_2, inference(sat_conversion,[],[f25])).
% 0.12/0.27 cnf(s2, plain, ~spl4_2 | spl4_3, inference(sat_conversion,[],[f30])).
% 0.12/0.27 cnf(s3, plain, ~spl4_2 | ~spl4_4, inference(sat_conversion,[],[f35])).
% 0.12/0.27 cnf(s5, plain, ~spl4_2 | ~spl4_3 | spl4_4, inference(sat_conversion,[],[f84])).
% 0.12/0.27 cnf(s10, plain, ~spl4_1 | spl4_2, inference(sat_conversion,[],[f123])).
% 0.12/0.27 cnf(s11, plain, ~spl4_2, inference(rat,[],[s5,s2,s3])).
% 0.12/0.27 cnf(s12, plain, ~spl4_1, inference(rat,[],[s10,s11])).
% 0.12/0.27 cnf(s13, plain, $false, inference(rat,[],[s1,s11,s12])).
% 0.12/0.27 thf(f124,plain,(
% 0.12/0.27 $false),
% 0.12/0.27 inference(avatar_sat_refutation,[],[s13])).
% 0.12/0.27 % SZS output end Proof for theBenchmark
% 0.12/0.27 % (2208011)------------------------------
% 0.12/0.27 % (2208011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.27 % (2208011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.27 % (2208011)CaDiCaL version: 2.1.3
% 0.12/0.27 % (2208011)Termination reason: Refutation
% 0.12/0.27 % (2208011)Time elapsed: 0.006 s
% 0.12/0.27 % (2208011)Peak memory usage: 12 MB
% 0.12/0.27 % (2208011)Instructions burned: 7 (million)
% 0.12/0.27 % (2208000)Success in time 0.049 s
% 0.12/0.27 % Vampire exiting
%------------------------------------------------------------------------------