%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV221^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:38:03 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV221^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n026.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 15:25:27 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.29 % (729089)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (729096)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1028093127:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.29 % (729094)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2447997326:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.29 % (729095)lrs+10_16_si=on:nwc=1.5:random_seed=4057560530:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.29 % (729097)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=828696548: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)
% 0.22/0.29 % (729096)Refutation not found, incomplete strategy
% 0.22/0.29 % (729096)------------------------------
% 0.22/0.29 % (729096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (729096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (729096)CaDiCaL version: 2.1.3
% 0.22/0.29 % (729096)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.29 % (729096)Time elapsed: 0.003 s
% 0.22/0.29 % (729096)Peak memory usage: 12 MB
% 0.22/0.29 % (729096)Instructions burned: 3 (million)
% 0.22/0.29 % (729097) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-729089-729097"...
% 0.22/0.29 % (729094) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-729089-729094"...
% 0.22/0.29 % (729096)------------------------------
% 0.22/0.29 % (729096)------------------------------
% 0.22/0.29 % (729095) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-729089-729095"...
% 0.22/0.29 % (729097)...printing done.
% 0.22/0.29 % (729097)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% 0.22/0.29 thf(type_def_5, type, a: $tType).
% 0.22/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.29 thf(func_def_0, type, cZ: (a > $o)).
% 0.22/0.29 thf(func_def_1, type, cW: ((a > $o) > $o)).
% 0.22/0.29 thf(func_def_5, type, vAND: ($o > $o > $o)).
% 0.22/0.29 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.29 thf(func_def_7, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.29 thf(func_def_8, type, sK0: a).
% 0.22/0.29 thf(func_def_9, type, sK1: (a > $o)).
% 0.22/0.29 thf(func_def_10, type, sK2: (a > $o)).
% 0.22/0.29 thf(func_def_11, type, sK3: (a > $o)).
% 0.22/0.29 thf(func_def_12, type, vNOT: ($o > $o)).
% 0.22/0.29 thf(f1,conjecture,(
% 0.22/0.29 ! [X0 : a] : (((cZ @ X0) & ? [X1 : (a > $o)] : ((X1 @ X0) & (cW @ X1))) <=> ? [X1 : (a > $o)] : ((X1 @ X0) & ? [X2 : (a > $o)] : ((X1 = (^[X3 : a] : ((X2 @ X3) & (cZ @ X3)))) & (cW @ X2))))),
% 0.22/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM61_pme)).
% 0.22/0.29 thf(f2,negated_conjecture,(
% 0.22/0.29 ~ ! [X0 : a] : (((cZ @ X0) & ? [X1 : (a > $o)] : ((X1 @ X0) & (cW @ X1))) <=> ? [X1 : (a > $o)] : ((X1 @ X0) & ? [X2 : (a > $o)] : ((X1 = (^[X3 : a] : ((X2 @ X3) & (cZ @ X3)))) & (cW @ X2))))),
% 0.22/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.29 thf(f3,plain,(
% 0.22/0.29 ~ ! [X0 : a] : (((cZ @ X0) & ? [X1 : (a > $o)] : ((X1 @ X0) & (cW @ X1))) <=> ? [X2 : (a > $o)] : ((X2 @ X0) & ? [X3 : (a > $o)] : ((X2 = (^[X4 : a] : ((X3 @ X4) & (cZ @ X4)))) & (cW @ X3))))),
% 0.22/0.29 inference(rectify,[],[f2])).
% 0.22/0.29 thf(f4,plain,(
% 0.22/0.29 ~ ! [X0 : a] : ((? [X1 : (a > $o)] : ((((cW @ X1)) = $true) & (((X1 @ X0)) = $true)) & (((cZ @ X0)) = $true)) <=> ? [X2 : (a > $o)] : (? [X3 : (a > $o)] : (((^[Y0 : a]: ((cZ @ Y0) & (X3 @ Y0))) = X2) & ($true = ((cW @ X3)))) & ($true = ((X2 @ X0)))))),
% 0.22/0.29 inference(fool_elimination,[],[f3])).
% 0.22/0.29 thf(f5,plain,(
% 0.22/0.29 ? [X0 : a] : ((? [X1 : (a > $o)] : ((((cW @ X1)) = $true) & (((X1 @ X0)) = $true)) & (((cZ @ X0)) = $true)) <~> ? [X2 : (a > $o)] : (? [X3 : (a > $o)] : (((^[Y0 : a]: ((cZ @ Y0) & (X3 @ Y0))) = X2) & ($true = ((cW @ X3)))) & ($true = ((X2 @ X0)))))),
% 0.22/0.29 inference(ennf_transformation,[],[f4])).
% 0.22/0.29 thf(f6,plain,(
% 0.22/0.29 ? [X0 : a] : ((! [X2 : (a > $o)] : (! [X3 : (a > $o)] : (((^[Y0 : a]: ((cZ @ Y0) & (X3 @ Y0))) != X2) | ($true != ((cW @ X3)))) | ($true != ((X2 @ X0)))) | (! [X1 : (a > $o)] : ((((cW @ X1)) != $true) | (((X1 @ X0)) != $true)) | (((cZ @ X0)) != $true))) & (? [X2 : (a > $o)] : (? [X3 : (a > $o)] : (((^[Y0 : a]: ((cZ @ Y0) & (X3 @ Y0))) = X2) & ($true = ((cW @ X3)))) & ($true = ((X2 @ X0)))) | (? [X1 : (a > $o)] : ((((cW @ X1)) = $true) & (((X1 @ X0)) = $true)) & (((cZ @ X0)) = $true))))),
% 0.22/0.29 inference(nnf_transformation,[],[f5])).
% 0.22/0.29 thf(f7,plain,(
% 0.22/0.29 ? [X0 : a] : ((! [X2 : (a > $o)] : (! [X3 : (a > $o)] : (((^[Y0 : a]: ((cZ @ Y0) & (X3 @ Y0))) != X2) | ($true != ((cW @ X3)))) | ($true != ((X2 @ X0)))) | ! [X1 : (a > $o)] : ((((cW @ X1)) != $true) | (((X1 @ X0)) != $true)) | (((cZ @ X0)) != $true)) & (? [X2 : (a > $o)] : (? [X3 : (a > $o)] : (((^[Y0 : a]: ((cZ @ Y0) & (X3 @ Y0))) = X2) & ($true = ((cW @ X3)))) & ($true = ((X2 @ X0)))) | (? [X1 : (a > $o)] : ((((cW @ X1)) = $true) & (((X1 @ X0)) = $true)) & (((cZ @ X0)) = $true))))),
% 0.22/0.29 inference(flattening,[],[f6])).
% 0.22/0.29 thf(f8,plain,(
% 0.22/0.29 ? [X0 : a] : ((! [X1 : (a > $o)] : (! [X2 : (a > $o)] : (((^[Y0 : a]: ((cZ @ Y0) & (X2 @ Y0))) != X1) | (((cW @ X2)) != $true)) | (((X1 @ X0)) != $true)) | ! [X3 : (a > $o)] : (($true != ((cW @ X3))) | ($true != ((X3 @ X0)))) | (((cZ @ X0)) != $true)) & (? [X4 : (a > $o)] : (? [X5 : (a > $o)] : (((^[Y0 : a]: ((cZ @ Y0) & (X5 @ Y0))) = X4) & ($true = ((cW @ X5)))) & ($true = ((X4 @ X0)))) | (? [X6 : (a > $o)] : ((((cW @ X6)) = $true) & ($true = ((X6 @ X0)))) & (((cZ @ X0)) = $true))))),
% 0.22/0.29 inference(rectify,[],[f7])).
% 0.22/0.29 thf(f9,plain,(
% 0.22/0.29 (! [X1 : (a > $o)] : (! [X2 : (a > $o)] : (((^[Y0 : a]: ((cZ @ Y0) & (X2 @ Y0))) != X1) | (((cW @ X2)) != $true)) | ($true != ((X1 @ sK0)))) | ! [X3 : (a > $o)] : (($true != ((cW @ X3))) | ($true != ((X3 @ sK0)))) | ($true != ((cZ @ sK0)))) & (((((^[Y0 : a]: ((cZ @ Y0) & (sK2 @ Y0))) = sK1) & ($true = ((cW @ sK2)))) & (((sK1 @ sK0)) = $true)) | ((($true = ((cW @ sK3))) & ($true = ((sK3 @ sK0)))) & ($true = ((cZ @ sK0)))))),
% 0.22/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X4,sK1),skolemize(X5,sK2),skolemize(X6,sK3)],[f8])).
% 0.22/0.29 thf(f10,plain,(
% 0.22/0.29 (((sK1 @ sK0)) = $true) | ($true = ((cZ @ sK0)))),
% 0.22/0.29 inference(cnf_transformation,[],[f9])).
% 0.22/0.29 thf(f11,plain,(
% 0.22/0.29 ($true = ((sK3 @ sK0))) | (((sK1 @ sK0)) = $true)),
% 0.22/0.29 inference(cnf_transformation,[],[f9])).
% 0.22/0.29 thf(f12,plain,(
% 0.22/0.29 (((sK1 @ sK0)) = $true) | ($true = ((cW @ sK3)))),
% 0.22/0.29 inference(cnf_transformation,[],[f9])).
% 0.22/0.29 thf(f14,plain,(
% 0.22/0.29 ($true = ((sK3 @ sK0))) | ($true = ((cW @ sK2)))),
% 0.22/0.29 inference(cnf_transformation,[],[f9])).
% 0.22/0.29 thf(f15,plain,(
% 0.22/0.29 ($true = ((cW @ sK3))) | ($true = ((cW @ sK2)))),
% 0.22/0.29 inference(cnf_transformation,[],[f9])).
% 0.22/0.29 thf(f16,plain,(
% 0.22/0.29 ($true = ((cZ @ sK0))) | ((^[Y0 : a]: ((cZ @ Y0) & (sK2 @ Y0))) = sK1)),
% 0.22/0.29 inference(cnf_transformation,[],[f9])).
% 0.22/0.29 thf(f17,plain,(
% 0.22/0.29 ($true = ((sK3 @ sK0))) | ((^[Y0 : a]: ((cZ @ Y0) & (sK2 @ Y0))) = sK1)),
% 0.22/0.29 inference(cnf_transformation,[],[f9])).
% 0.22/0.29 thf(f18,plain,(
% 0.22/0.29 ($true = ((cW @ sK3))) | ((^[Y0 : a]: ((cZ @ Y0) & (sK2 @ Y0))) = sK1)),
% 0.22/0.29 inference(cnf_transformation,[],[f9])).
% 0.22/0.29 thf(f19,plain,(
% 0.22/0.29 ( ! [X2 : (a > $o),X3 : (a > $o),X1 : (a > $o)] : (((^[Y0 : a]: ((cZ @ Y0) & (X2 @ Y0))) != X1) | (((cW @ X2)) != $true) | ($true != ((X1 @ sK0))) | ($true != ((cW @ X3))) | ($true != ((X3 @ sK0))) | ($true != ((cZ @ sK0)))) )),
% 0.22/0.29 inference(cnf_transformation,[],[f9])).
% 0.22/0.29 thf(f21,plain,(
% 0.22/0.29 ( ! [X2 : (a > $o),X3 : (a > $o)] : (($true != ((X3 @ sK0))) | ($true != (((^[Y0 : a]: ((cZ @ Y0) & (X2 @ Y0))) @ sK0))) | ($true != ((cZ @ sK0))) | (((cW @ X2)) != $true) | ($true != ((cW @ X3)))) )),
% 0.22/0.29 inference(equality_resolution,[],[f19])).
% 0.22/0.29 thf(f22,plain,(
% 0.22/0.29 ( ! [X2 : (a > $o),X3 : (a > $o)] : (($true != (((cZ @ sK0) & (X2 @ sK0)))) | (((cW @ X2)) != $true) | ($true != ((X3 @ sK0))) | ($true != ((cW @ X3))) | ($true != ((cZ @ sK0)))) )),
% 0.22/0.29 inference(beta-eta_normalization,[],[f21])).
% 0.22/0.29 thf(f23,plain,(
% 0.22/0.29 ( ! [X2 : (a > $o),X3 : (a > $o)] : (($false = ((cZ @ sK0))) | (((X2 @ sK0)) = $false) | ($true != ((cZ @ sK0))) | ($true != ((cW @ X3))) | (((cW @ X2)) != $true) | ($true != ((X3 @ sK0)))) )),
% 0.22/0.29 inference(and_proxy_clausification,[],[f22])).
% 0.22/0.29 thf(f25,definition,(
% 0.22/0.29 spl4_1 <=> ! [X3 : (a > $o)] : (($true != ((cW @ X3))) | ($true != ((X3 @ sK0))))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.22/0.29 thf(f26,plain,(
% 0.22/0.29 ( ! [X3 : (a > $o)] : (($true != ((cW @ X3))) | ($true != ((X3 @ sK0)))) ) | ~spl4_1),
% 0.22/0.29 inference(avatar_component_clause,[],[f25])).
% 0.22/0.29 thf(f28,definition,(
% 0.22/0.29 spl4_2 <=> ($true = ((cZ @ sK0)))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.22/0.29 thf(f29,plain,(
% 0.22/0.29 ($true = ((cZ @ sK0))) | ~spl4_2),
% 0.22/0.29 inference(avatar_component_clause,[],[f28])).
% 0.22/0.29 thf(f30,plain,(
% 0.22/0.29 ($true != ((cZ @ sK0))) | spl4_2),
% 0.22/0.29 inference(avatar_component_clause,[],[f28])).
% 0.22/0.29 thf(f32,definition,(
% 0.22/0.29 spl4_3 <=> ! [X2 : (a > $o)] : ((((X2 @ sK0)) = $false) | (((cW @ X2)) != $true))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
% 0.22/0.29 thf(f33,plain,(
% 0.22/0.29 ( ! [X2 : (a > $o)] : ((((cW @ X2)) != $true) | (((X2 @ sK0)) = $false)) ) | ~spl4_3),
% 0.22/0.29 inference(avatar_component_clause,[],[f32])).
% 0.22/0.29 thf(f35,definition,(
% 0.22/0.29 spl4_4 <=> ($false = ((cZ @ sK0)))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
% 0.22/0.29 thf(f37,plain,(
% 0.22/0.29 ($false = ((cZ @ sK0))) | ~spl4_4),
% 0.22/0.29 inference(avatar_component_clause,[],[f35])).
% 0.22/0.29 thf(f38,plain,(
% 0.22/0.29 spl4_1 | ~spl4_2 | spl4_3 | spl4_4),
% 0.22/0.29 inference(avatar_split_clause,[],[f23,f35,f32,f28,f25])).
% 0.22/0.29 thf(f40,definition,(
% 0.22/0.29 spl4_5 <=> ($true = ((cW @ sK2)))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition])).
% 0.22/0.29 thf(f42,plain,(
% 0.22/0.29 ($true = ((cW @ sK2))) | ~spl4_5),
% 0.22/0.29 inference(avatar_component_clause,[],[f40])).
% 0.22/0.29 thf(f45,definition,(
% 0.22/0.29 spl4_6 <=> ($true = ((cW @ sK3)))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition])).
% 0.22/0.29 thf(f47,plain,(
% 0.22/0.29 ($true = ((cW @ sK3))) | ~spl4_6),
% 0.22/0.29 inference(avatar_component_clause,[],[f45])).
% 0.22/0.29 thf(f48,plain,(
% 0.22/0.29 spl4_6 | spl4_5),
% 0.22/0.29 inference(avatar_split_clause,[],[f15,f40,f45])).
% 0.22/0.29 thf(f50,definition,(
% 0.22/0.29 spl4_7 <=> ((^[Y0 : a]: ((cZ @ Y0) & (sK2 @ Y0))) = sK1)),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition])).
% 0.22/0.29 thf(f52,plain,(
% 0.22/0.29 ((^[Y0 : a]: ((cZ @ Y0) & (sK2 @ Y0))) = sK1) | ~spl4_7),
% 0.22/0.29 inference(avatar_component_clause,[],[f50])).
% 0.22/0.29 thf(f53,plain,(
% 0.22/0.29 spl4_7 | spl4_6),
% 0.22/0.29 inference(avatar_split_clause,[],[f18,f45,f50])).
% 0.22/0.29 thf(f55,definition,(
% 0.22/0.29 spl4_8 <=> (((sK1 @ sK0)) = $true)),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition])).
% 0.22/0.29 thf(f57,plain,(
% 0.22/0.29 (((sK1 @ sK0)) = $true) | ~spl4_8),
% 0.22/0.29 inference(avatar_component_clause,[],[f55])).
% 0.22/0.29 thf(f58,plain,(
% 0.22/0.29 spl4_8 | spl4_2),
% 0.22/0.29 inference(avatar_split_clause,[],[f10,f28,f55])).
% 0.22/0.29 thf(f59,plain,(
% 0.22/0.29 spl4_6 | spl4_8),
% 0.22/0.29 inference(avatar_split_clause,[],[f12,f55,f45])).
% 0.22/0.29 thf(f60,plain,(
% 0.22/0.29 spl4_2 | spl4_7),
% 0.22/0.29 inference(avatar_split_clause,[],[f16,f50,f28])).
% 0.22/0.29 thf(f62,definition,(
% 0.22/0.29 spl4_9 <=> ($true = ((sK3 @ sK0)))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition])).
% 0.22/0.29 thf(f64,plain,(
% 0.22/0.29 ($true = ((sK3 @ sK0))) | ~spl4_9),
% 0.22/0.29 inference(avatar_component_clause,[],[f62])).
% 0.22/0.29 thf(f65,plain,(
% 0.22/0.29 spl4_9 | spl4_7),
% 0.22/0.29 inference(avatar_split_clause,[],[f17,f50,f62])).
% 0.22/0.29 thf(f66,plain,(
% 0.22/0.29 spl4_5 | spl4_9),
% 0.22/0.29 inference(avatar_split_clause,[],[f14,f62,f40])).
% 0.22/0.29 thf(f67,plain,(
% 0.22/0.29 spl4_9 | spl4_8),
% 0.22/0.29 inference(avatar_split_clause,[],[f11,f55,f62])).
% 0.22/0.29 thf(f68,plain,(
% 0.22/0.29 ( ! [X1 : a] : ((((sK1 @ X1)) = (((^[Y0 : a]: ((cZ @ Y0) & (sK2 @ Y0))) @ X1)))) ) | ~spl4_7),
% 0.22/0.29 inference(argument_congruence,[],[f52])).
% 0.22/0.29 thf(f70,plain,(
% 0.22/0.29 ( ! [X1 : a] : ((((sK1 @ X1)) = $false) | ($true = (((^[Y0 : a]: ((cZ @ Y0) & (sK2 @ Y0))) @ X1)))) ) | ~spl4_7),
% 0.22/0.29 inference(iff_proxy_clausification,[],[f68])).
% 0.22/0.29 thf(f71,plain,(
% 0.22/0.29 ( ! [X1 : a] : ((((sK1 @ X1)) = $false) | ($true = (((cZ @ X1) & (sK2 @ X1))))) ) | ~spl4_7),
% 0.22/0.29 inference(beta-eta_normalization,[],[f70])).
% 0.22/0.29 thf(f72,plain,(
% 0.22/0.29 ( ! [X1 : a] : (($true = ((sK2 @ X1))) | (((sK1 @ X1)) = $false)) ) | ~spl4_7),
% 0.22/0.29 inference(and_proxy_clausification,[],[f71])).
% 0.22/0.29 thf(f73,plain,(
% 0.22/0.29 ( ! [X1 : a] : (($true = ((cZ @ X1))) | (((sK1 @ X1)) = $false)) ) | ~spl4_7),
% 0.22/0.29 inference(and_proxy_clausification,[],[f71])).
% 0.22/0.29 thf(f78,plain,(
% 0.22/0.29 (((sK1 @ sK0)) = $false) | ($true != $true) | (spl4_2 | ~spl4_7)),
% 0.22/0.29 inference(superposition,[],[f30,f73])).
% 0.22/0.29 thf(f79,plain,(
% 0.22/0.29 (((sK1 @ sK0)) = $false) | (spl4_2 | ~spl4_7)),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f78])).
% 0.22/0.29 thf(f81,definition,(
% 0.22/0.29 spl4_10 <=> (((sK1 @ sK0)) = $false)),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl4_10])],[avatar_definition])).
% 0.22/0.29 thf(f83,plain,(
% 0.22/0.29 (((sK1 @ sK0)) = $false) | ~spl4_10),
% 0.22/0.29 inference(avatar_component_clause,[],[f81])).
% 0.22/0.29 thf(f84,plain,(
% 0.22/0.29 spl4_10 | spl4_2 | ~spl4_7),
% 0.22/0.29 inference(avatar_split_clause,[],[f79,f50,f28,f81])).
% 0.22/0.29 thf(f85,plain,(
% 0.22/0.29 ($true = $false) | (~spl4_8 | ~spl4_10)),
% 0.22/0.29 inference(superposition,[],[f83,f57])).
% 0.22/0.29 thf(f86,plain,(
% 0.22/0.29 ($true = $false) | (~spl4_8 | ~spl4_10)),
% 0.22/0.29 inference(superposition,[],[f57,f83])).
% 0.22/0.29 thf(f87,plain,(
% 0.22/0.29 $false | (~spl4_8 | ~spl4_10)),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f86])).
% 0.22/0.29 thf(f88,plain,(
% 0.22/0.29 ~spl4_8 | ~spl4_10),
% 0.22/0.29 inference(avatar_contradiction_clause,[],[f87])).
% 0.22/0.29 thf(f89,plain,(
% 0.22/0.29 $false | (~spl4_8 | ~spl4_10)),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f85])).
% 0.22/0.29 thf(f90,plain,(
% 0.22/0.29 ~spl4_8 | ~spl4_10),
% 0.22/0.29 inference(avatar_contradiction_clause,[],[f89])).
% 0.22/0.29 thf(f92,plain,(
% 0.22/0.29 ($true != ((sK2 @ sK0))) | ($true != $true) | (~spl4_1 | ~spl4_5)),
% 0.22/0.29 inference(superposition,[],[f26,f42])).
% 0.22/0.29 thf(f93,plain,(
% 0.22/0.29 ($true != ((sK2 @ sK0))) | (~spl4_1 | ~spl4_5)),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f92])).
% 0.22/0.29 thf(f95,definition,(
% 0.22/0.29 spl4_11 <=> ($true = ((sK2 @ sK0)))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition])).
% 0.22/0.29 thf(f97,plain,(
% 0.22/0.29 ($true != ((sK2 @ sK0))) | spl4_11),
% 0.22/0.29 inference(avatar_component_clause,[],[f95])).
% 0.22/0.29 thf(f98,plain,(
% 0.22/0.29 ~spl4_11 | ~spl4_1 | ~spl4_5),
% 0.22/0.29 inference(avatar_split_clause,[],[f93,f40,f25,f95])).
% 0.22/0.29 thf(f99,plain,(
% 0.22/0.29 ($true != ((sK3 @ sK0))) | ($true != $true) | (~spl4_1 | ~spl4_6)),
% 0.22/0.29 inference(superposition,[],[f26,f47])).
% 0.22/0.29 thf(f100,plain,(
% 0.22/0.29 ($true != ((sK3 @ sK0))) | (~spl4_1 | ~spl4_6)),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f99])).
% 0.22/0.29 thf(f101,plain,(
% 0.22/0.29 $false | (~spl4_1 | ~spl4_6 | ~spl4_9)),
% 0.22/0.29 inference(forward_subsumption_resolution,[],[f100,f64])).
% 0.22/0.29 thf(f102,plain,(
% 0.22/0.29 ~spl4_1 | ~spl4_6 | ~spl4_9),
% 0.22/0.29 inference(avatar_contradiction_clause,[],[f101])).
% 0.22/0.29 thf(f103,plain,(
% 0.22/0.29 ($true != $true) | ($false = ((sK2 @ sK0))) | (~spl4_3 | ~spl4_5)),
% 0.22/0.29 inference(superposition,[],[f33,f42])).
% 0.22/0.29 thf(f104,plain,(
% 0.22/0.29 ($true != $true) | ($false = ((sK3 @ sK0))) | (~spl4_3 | ~spl4_6)),
% 0.22/0.29 inference(superposition,[],[f33,f47])).
% 0.22/0.29 thf(f105,plain,(
% 0.22/0.29 ($false = ((sK3 @ sK0))) | (~spl4_3 | ~spl4_6)),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f104])).
% 0.22/0.29 thf(f106,plain,(
% 0.22/0.29 ($false = ((sK2 @ sK0))) | (~spl4_3 | ~spl4_5)),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f103])).
% 0.22/0.29 thf(f108,definition,(
% 0.22/0.29 spl4_12 <=> ($false = ((sK3 @ sK0)))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl4_12])],[avatar_definition])).
% 0.22/0.29 thf(f111,plain,(
% 0.22/0.29 spl4_12 | ~spl4_3 | ~spl4_6),
% 0.22/0.29 inference(avatar_split_clause,[],[f105,f45,f32,f108])).
% 0.22/0.29 thf(f113,definition,(
% 0.22/0.29 spl4_13 <=> ($false = ((sK2 @ sK0)))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl4_13])],[avatar_definition])).
% 0.22/0.29 thf(f115,plain,(
% 0.22/0.29 ($false = ((sK2 @ sK0))) | ~spl4_13),
% 0.22/0.29 inference(avatar_component_clause,[],[f113])).
% 0.22/0.29 thf(f116,plain,(
% 0.22/0.29 spl4_13 | ~spl4_3 | ~spl4_5),
% 0.22/0.29 inference(avatar_split_clause,[],[f106,f40,f32,f113])).
% 0.22/0.29 thf(f122,plain,(
% 0.22/0.29 ($true = $false) | (~spl4_2 | ~spl4_4)),
% 0.22/0.29 inference(superposition,[],[f29,f37])).
% 0.22/0.29 thf(f126,plain,(
% 0.22/0.29 $false | (~spl4_2 | ~spl4_4)),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f122])).
% 0.22/0.29 thf(f127,plain,(
% 0.22/0.29 ~spl4_2 | ~spl4_4),
% 0.22/0.29 inference(avatar_contradiction_clause,[],[f126])).
% 0.22/0.29 thf(f131,definition,(
% 0.22/0.29 ($false != ((sK3 @ sK0))) | ($true != ((sK3 @ sK0))) | ($true != ((cZ @ sK0))) | ($false = ((cZ @ sK0)))),
% 0.22/0.29 introduced(theory,[theory_tautology_sat_conflict])).
% 0.22/0.29 thf(f134,plain,(
% 0.22/0.29 (((sK1 @ sK0)) = $false) | ($true = $false) | (~spl4_7 | ~spl4_13)),
% 0.22/0.29 inference(superposition,[],[f115,f72])).
% 0.22/0.29 thf(f136,plain,(
% 0.22/0.29 (((sK1 @ sK0)) = $false) | (~spl4_7 | ~spl4_13)),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f134])).
% 0.22/0.29 thf(f138,plain,(
% 0.22/0.29 spl4_10 | ~spl4_7 | ~spl4_13),
% 0.22/0.29 inference(avatar_split_clause,[],[f136,f113,f50,f81])).
% 0.22/0.29 thf(f139,plain,(
% 0.22/0.29 (((sK1 @ sK0)) = $false) | ($true != $true) | (~spl4_7 | spl4_11)),
% 0.22/0.29 inference(superposition,[],[f97,f72])).
% 0.22/0.29 thf(f141,plain,(
% 0.22/0.29 (((sK1 @ sK0)) = $false) | (~spl4_7 | spl4_11)),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f139])).
% 0.22/0.29 thf(f142,plain,(
% 0.22/0.29 spl4_10 | ~spl4_7 | spl4_11),
% 0.22/0.29 inference(avatar_split_clause,[],[f141,f95,f50,f81])).
% 0.22/0.29 cnf(s1, plain, spl4_1 | ~spl4_2 | spl4_3 | spl4_4, inference(sat_conversion,[],[f38])).
% 0.22/0.29 cnf(s3, plain, spl4_5 | spl4_6, inference(sat_conversion,[],[f48])).
% 0.22/0.29 cnf(s4, plain, spl4_6 | spl4_7, inference(sat_conversion,[],[f53])).
% 0.22/0.29 cnf(s5, plain, spl4_2 | spl4_8, inference(sat_conversion,[],[f58])).
% 0.22/0.29 cnf(s6, plain, spl4_6 | spl4_8, inference(sat_conversion,[],[f59])).
% 0.22/0.29 cnf(s7, plain, spl4_2 | spl4_7, inference(sat_conversion,[],[f60])).
% 0.22/0.29 cnf(s8, plain, spl4_7 | spl4_9, inference(sat_conversion,[],[f65])).
% 0.22/0.29 cnf(s9, plain, spl4_5 | spl4_9, inference(sat_conversion,[],[f66])).
% 0.22/0.29 cnf(s10, plain, spl4_8 | spl4_9, inference(sat_conversion,[],[f67])).
% 0.22/0.29 cnf(s11, plain, spl4_2 | ~spl4_7 | spl4_10, inference(sat_conversion,[],[f84])).
% 0.22/0.29 cnf(s12, plain, ~spl4_8 | ~spl4_10, inference(sat_conversion,[],[f88])).
% 0.22/0.29 cnf(s13, plain, ~spl4_8 | ~spl4_10, inference(sat_conversion,[],[f90])).
% 0.22/0.29 cnf(s14, plain, ~spl4_1 | ~spl4_5 | ~spl4_11, inference(sat_conversion,[],[f98])).
% 0.22/0.29 cnf(s15, plain, ~spl4_1 | ~spl4_6 | ~spl4_9, inference(sat_conversion,[],[f102])).
% 0.22/0.29 cnf(s16, plain, ~spl4_3 | ~spl4_6 | spl4_12, inference(sat_conversion,[],[f111])).
% 0.22/0.29 cnf(s17, plain, ~spl4_3 | ~spl4_5 | spl4_13, inference(sat_conversion,[],[f116])).
% 0.22/0.29 cnf(s22, plain, ~spl4_2 | ~spl4_4, inference(sat_conversion,[],[f127])).
% 0.22/0.29 cnf(s25, plain, ~spl4_2 | spl4_4 | ~spl4_9 | ~spl4_12, inference(sat_conversion,[],[f131])).
% 0.22/0.29 cnf(s26, plain, ~spl4_7 | spl4_10 | ~spl4_13, inference(sat_conversion,[],[f138])).
% 0.22/0.29 cnf(s28, plain, ~spl4_7 | spl4_10 | spl4_11, inference(sat_conversion,[],[f142])).
% 0.22/0.29 cnf(s29, plain, spl4_2, inference(rat,[],[s12,s11,s5,s7])).
% 0.22/0.29 cnf(s30, plain, ~spl4_4, inference(rat,[],[s22,s29])).
% 0.22/0.29 cnf(s31, plain, spl4_6 | ~spl4_13, inference(rat,[],[s26,s13,s4,s6])).
% 0.22/0.29 cnf(s32, plain, ~spl4_13 | ~spl4_3, inference(rat,[],[s26,s13,s8,s10,s25,s16,s31,s29,s30])).
% 0.22/0.29 cnf(s33, plain, spl4_13 | ~spl4_3, inference(rat,[],[s16,s25,s3,s9,s17,s30,s29])).
% 0.22/0.29 cnf(s34, plain, ~spl4_3, inference(rat,[],[s33,s32])).
% 0.22/0.29 cnf(s35, plain, spl4_1, inference(rat,[],[s1,s30,s29,s34])).
% 0.22/0.29 cnf(s36, plain, spl4_6 | spl4_11, inference(rat,[],[s28,s13,s4,s6])).
% 0.22/0.29 cnf(s37, plain, spl4_11, inference(rat,[],[s28,s13,s8,s10,s15,s36,s35])).
% 0.22/0.29 cnf(s38, plain, ~spl4_5, inference(rat,[],[s14,s35,s37])).
% 0.22/0.29 cnf(s39, plain, spl4_9, inference(rat,[],[s9,s38])).
% 0.22/0.29 cnf(s40, plain, spl4_6, inference(rat,[],[s3,s38])).
% 0.22/0.29 cnf(s42, plain, $false, inference(rat,[],[s15,s35,s39,s40])).
% 0.22/0.29 thf(f143,plain,(
% 0.22/0.29 $false),
% 0.22/0.29 inference(avatar_sat_refutation,[],[s42])).
% 0.22/0.29 % SZS output end Proof for theBenchmark
% 0.22/0.29 % (729097)------------------------------
% 0.22/0.29 % (729097)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (729097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (729097)CaDiCaL version: 2.1.3
% 0.22/0.29 % (729097)Termination reason: Refutation
% 0.22/0.29 % (729097)Time elapsed: 0.004 s
% 0.22/0.29 % (729097)Peak memory usage: 13 MB
% 0.22/0.29 % (729097)Instructions burned: 9 (million)
% 0.22/0.29 % (729089)Success in time 0.042 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------