%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU899^5 : 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 08:31:54 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU899^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n005.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:44:17 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.22/0.27 % (1758889)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.27 % (1758900)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.27 % (1758900)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
% 0.22/0.27 % (1758900)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=795731513:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.27 % (1758900) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1758889-1758900"...
% 0.22/0.27 % (1758900)...printing done.
% 0.22/0.27 % (1758900)Refutation found. Thanks to Tanya!
% 0.22/0.27 % SZS status Theorem for theBenchmark
% 0.22/0.27 % SZS output start Proof for theBenchmark
% 0.22/0.27 thf(type_def_5, type, b: $tType).
% 0.22/0.27 thf(type_def_6, type, a: $tType).
% 0.22/0.27 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.27 thf(func_def_0, type, cF: (b > a)).
% 0.22/0.27 thf(func_def_1, type, cS: (b > $o)).
% 0.22/0.27 thf(func_def_2, type, cR: (b > $o)).
% 0.22/0.27 thf(func_def_6, type, sP0: (a > $o)).
% 0.22/0.27 thf(func_def_7, type, sP1: (a > $o)).
% 0.22/0.27 thf(func_def_8, type, sP2: (a > $o)).
% 0.22/0.27 thf(func_def_9, type, sK3: (a > b)).
% 0.22/0.27 thf(func_def_10, type, sK4: (a > b)).
% 0.22/0.27 thf(func_def_11, type, sK5: (a > b)).
% 0.22/0.27 thf(func_def_12, type, sK6: a).
% 0.22/0.27 thf(func_def_13, type, sF7: $o).
% 0.22/0.27 thf(func_def_14, type, sF8: $o).
% 0.22/0.27 thf(f1,conjecture,(
% 0.22/0.27 ! [X0 : a] : ((? [X1 : b] : ((cS @ X1) & (X0 = ((cF @ X1)))) | ? [X1 : b] : ((X0 = ((cF @ X1))) & (cR @ X1))) <=> ? [X1 : b] : ((X0 = ((cF @ X1))) & ((cS @ X1) | (cR @ X1))))),
% 0.22/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM34_pme)).
% 0.22/0.27 thf(f2,negated_conjecture,(
% 0.22/0.27 ~ ! [X0 : a] : ((? [X1 : b] : ((cS @ X1) & (X0 = ((cF @ X1)))) | ? [X1 : b] : ((X0 = ((cF @ X1))) & (cR @ X1))) <=> ? [X1 : b] : ((X0 = ((cF @ X1))) & ((cS @ X1) | (cR @ X1))))),
% 0.22/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.27 thf(f3,plain,(
% 0.22/0.27 ~ ! [X0 : a] : ((? [X1 : b] : ((cS @ X1) & (X0 = ((cF @ X1)))) | ? [X2 : b] : ((((cF @ X2)) = X0) & (cR @ X2))) <=> ? [X3 : b] : ((((cF @ X3)) = X0) & ((cS @ X3) | (cR @ X3))))),
% 0.22/0.27 inference(rectify,[],[f2])).
% 0.22/0.27 thf(f4,plain,(
% 0.22/0.27 ~ ! [X0 : a] : ((? [X2 : b] : ((((cR @ X2)) = $true) & (((cF @ X2)) = X0)) | ? [X1 : b] : ((((cS @ X1)) = $true) & (((cF @ X1)) = X0))) <=> ? [X3 : b] : ((((cF @ X3)) = X0) & (($true = ((cS @ X3))) | ($true = ((cR @ X3))))))),
% 0.22/0.27 inference(fool_elimination,[],[f3])).
% 0.22/0.27 thf(f5,plain,(
% 0.22/0.27 ? [X0 : a] : (? [X3 : b] : ((((cF @ X3)) = X0) & (($true = ((cS @ X3))) | ($true = ((cR @ X3))))) <~> (? [X2 : b] : ((((cR @ X2)) = $true) & (((cF @ X2)) = X0)) | ? [X1 : b] : ((((cS @ X1)) = $true) & (((cF @ X1)) = X0))))),
% 0.22/0.27 inference(ennf_transformation,[],[f4])).
% 0.22/0.27 thf(f6,definition,(
% 0.22/0.27 ! [X0 : a] : (($true = ((sP0 @ X0))) <=> ? [X1 : b] : ((((cS @ X1)) = $true) & (((cF @ X1)) = X0)))),
% 0.22/0.27 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.22/0.27 thf(f7,definition,(
% 0.22/0.27 ! [X0 : a] : (($true = ((sP1 @ X0))) <=> ? [X3 : b] : ((((cF @ X3)) = X0) & (($true = ((cS @ X3))) | ($true = ((cR @ X3))))))),
% 0.22/0.27 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.22/0.27 thf(f8,definition,(
% 0.22/0.27 ! [X0 : a] : (($true = ((sP2 @ X0))) <=> (? [X2 : b] : ((((cR @ X2)) = $true) & (((cF @ X2)) = X0)) | ($true = ((sP0 @ X0)))))),
% 0.22/0.27 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.22/0.27 thf(f9,plain,(
% 0.22/0.27 ? [X0 : a] : (($true = ((sP1 @ X0))) <~> ($true = ((sP2 @ X0))))),
% 0.22/0.27 inference(definition_folding,[],[f5,f8,f7,f6])).
% 0.22/0.27 thf(f10,plain,(
% 0.22/0.27 ! [X0 : a] : ((($true = ((sP2 @ X0))) | (! [X2 : b] : ((((cR @ X2)) != $true) | (((cF @ X2)) != X0)) & ($true != ((sP0 @ X0))))) & ((? [X2 : b] : ((((cR @ X2)) = $true) & (((cF @ X2)) = X0)) | ($true = ((sP0 @ X0)))) | ($true != ((sP2 @ X0)))))),
% 0.22/0.27 inference(nnf_transformation,[],[f8])).
% 0.22/0.27 thf(f11,plain,(
% 0.22/0.27 ! [X0 : a] : ((($true = ((sP2 @ X0))) | (! [X2 : b] : ((((cR @ X2)) != $true) | (((cF @ X2)) != X0)) & ($true != ((sP0 @ X0))))) & (? [X2 : b] : ((((cR @ X2)) = $true) & (((cF @ X2)) = X0)) | ($true = ((sP0 @ X0))) | ($true != ((sP2 @ X0)))))),
% 0.22/0.27 inference(flattening,[],[f10])).
% 0.22/0.27 thf(f12,plain,(
% 0.22/0.27 ! [X0 : a] : ((($true = ((sP2 @ X0))) | (! [X1 : b] : ((((cR @ X1)) != $true) | (((cF @ X1)) != X0)) & ($true != ((sP0 @ X0))))) & (? [X2 : b] : ((((cR @ X2)) = $true) & (((cF @ X2)) = X0)) | ($true = ((sP0 @ X0))) | ($true != ((sP2 @ X0)))))),
% 0.22/0.27 inference(rectify,[],[f11])).
% 0.22/0.27 thf(f13,plain,(
% 0.22/0.27 ! [X0 : a] : ((($true = ((sP2 @ X0))) | (! [X1 : b] : ((((cR @ X1)) != $true) | (((cF @ X1)) != X0)) & ($true != ((sP0 @ X0))))) & (((((cR @ (sK3 @ X0))) = $true) & (((cF @ (sK3 @ X0))) = X0)) | ($true = ((sP0 @ X0))) | ($true != ((sP2 @ X0)))))),
% 0.22/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK3 @ X0)],[f12])).
% 0.22/0.27 thf(f14,plain,(
% 0.22/0.27 ! [X0 : a] : ((($true = ((sP1 @ X0))) | ! [X3 : b] : ((((cF @ X3)) != X0) | (($true != ((cS @ X3))) & ($true != ((cR @ X3)))))) & (? [X3 : b] : ((((cF @ X3)) = X0) & (($true = ((cS @ X3))) | ($true = ((cR @ X3))))) | ($true != ((sP1 @ X0)))))),
% 0.22/0.27 inference(nnf_transformation,[],[f7])).
% 0.22/0.27 thf(f15,plain,(
% 0.22/0.27 ! [X0 : a] : ((($true = ((sP1 @ X0))) | ! [X1 : b] : ((((cF @ X1)) != X0) | ((((cS @ X1)) != $true) & (((cR @ X1)) != $true)))) & (? [X2 : b] : ((((cF @ X2)) = X0) & (($true = ((cS @ X2))) | (((cR @ X2)) = $true))) | ($true != ((sP1 @ X0)))))),
% 0.22/0.27 inference(rectify,[],[f14])).
% 0.22/0.27 thf(f16,plain,(
% 0.22/0.27 ! [X0 : a] : ((($true = ((sP1 @ X0))) | ! [X1 : b] : ((((cF @ X1)) != X0) | ((((cS @ X1)) != $true) & (((cR @ X1)) != $true)))) & (((((cF @ (sK4 @ X0))) = X0) & (($true = ((cS @ (sK4 @ X0)))) | ($true = ((cR @ (sK4 @ X0)))))) | ($true != ((sP1 @ X0)))))),
% 0.22/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK3 @ X0)],[f15])).
% 0.22/0.27 thf(f17,plain,(
% 0.22/0.27 ! [X0 : a] : ((($true = ((sP0 @ X0))) | ! [X1 : b] : ((((cS @ X1)) != $true) | (((cF @ X1)) != X0))) & (? [X1 : b] : ((((cS @ X1)) = $true) & (((cF @ X1)) = X0)) | ($true != ((sP0 @ X0)))))),
% 0.22/0.27 inference(nnf_transformation,[],[f6])).
% 0.22/0.27 thf(f18,plain,(
% 0.22/0.27 ! [X0 : a] : ((($true = ((sP0 @ X0))) | ! [X1 : b] : ((((cS @ X1)) != $true) | (((cF @ X1)) != X0))) & (? [X2 : b] : (($true = ((cS @ X2))) & (((cF @ X2)) = X0)) | ($true != ((sP0 @ X0)))))),
% 0.22/0.27 inference(rectify,[],[f17])).
% 0.22/0.27 thf(f19,plain,(
% 0.22/0.27 ! [X0 : a] : ((($true = ((sP0 @ X0))) | ! [X1 : b] : ((((cS @ X1)) != $true) | (((cF @ X1)) != X0))) & (((((cS @ (sK5 @ X0))) = $true) & (((cF @ (sK5 @ X0))) = X0)) | ($true != ((sP0 @ X0)))))),
% 0.22/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK3 @ X0)],[f18])).
% 0.22/0.27 thf(f20,plain,(
% 0.22/0.27 ? [X0 : a] : ((($true != ((sP2 @ X0))) | ($true != ((sP1 @ X0)))) & (($true = ((sP2 @ X0))) | ($true = ((sP1 @ X0)))))),
% 0.22/0.27 inference(nnf_transformation,[],[f9])).
% 0.22/0.27 thf(f21,plain,(
% 0.22/0.27 ((((sP2 @ sK6)) != $true) | (((sP1 @ sK6)) != $true)) & ((((sP2 @ sK6)) = $true) | (((sP1 @ sK6)) = $true))),
% 0.22/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f20])).
% 0.22/0.27 thf(f22,plain,(
% 0.22/0.27 ( ! [X0 : a] : ((((cF @ (sK3 @ X0))) = X0) | ($true != ((sP2 @ X0))) | ($true = ((sP0 @ X0)))) )),
% 0.22/0.27 inference(cnf_transformation,[],[f13])).
% 0.22/0.27 thf(f23,plain,(
% 0.22/0.27 ( ! [X0 : a] : ((((cR @ (sK3 @ X0))) = $true) | ($true = ((sP0 @ X0))) | ($true != ((sP2 @ X0)))) )),
% 0.22/0.27 inference(cnf_transformation,[],[f13])).
% 0.22/0.27 thf(f24,plain,(
% 0.22/0.27 ( ! [X0 : a] : (($true = ((sP2 @ X0))) | ($true != ((sP0 @ X0)))) )),
% 0.22/0.27 inference(cnf_transformation,[],[f13])).
% 0.22/0.27 thf(f25,plain,(
% 0.22/0.27 ( ! [X0 : a,X1 : b] : (($true = ((sP2 @ X0))) | (((cR @ X1)) != $true) | (((cF @ X1)) != X0)) )),
% 0.22/0.27 inference(cnf_transformation,[],[f13])).
% 0.22/0.27 thf(f26,plain,(
% 0.22/0.27 ( ! [X0 : a] : (($true = ((cR @ (sK4 @ X0)))) | ($true = ((cS @ (sK4 @ X0)))) | ($true != ((sP1 @ X0)))) )),
% 0.22/0.27 inference(cnf_transformation,[],[f16])).
% 0.22/0.27 thf(f27,plain,(
% 0.22/0.27 ( ! [X0 : a] : ((((cF @ (sK4 @ X0))) = X0) | ($true != ((sP1 @ X0)))) )),
% 0.22/0.27 inference(cnf_transformation,[],[f16])).
% 0.22/0.27 thf(f28,plain,(
% 0.22/0.27 ( ! [X0 : a,X1 : b] : (($true = ((sP1 @ X0))) | (((cF @ X1)) != X0) | (((cR @ X1)) != $true)) )),
% 0.22/0.27 inference(cnf_transformation,[],[f16])).
% 0.22/0.27 thf(f29,plain,(
% 0.22/0.27 ( ! [X0 : a,X1 : b] : (($true = ((sP1 @ X0))) | (((cF @ X1)) != X0) | (((cS @ X1)) != $true)) )),
% 0.22/0.27 inference(cnf_transformation,[],[f16])).
% 0.22/0.27 thf(f30,plain,(
% 0.22/0.27 ( ! [X0 : a] : ((((cF @ (sK5 @ X0))) = X0) | ($true != ((sP0 @ X0)))) )),
% 0.22/0.27 inference(cnf_transformation,[],[f19])).
% 0.22/0.27 thf(f31,plain,(
% 0.22/0.27 ( ! [X0 : a] : ((((cS @ (sK5 @ X0))) = $true) | ($true != ((sP0 @ X0)))) )),
% 0.22/0.27 inference(cnf_transformation,[],[f19])).
% 0.22/0.27 thf(f32,plain,(
% 0.22/0.27 ( ! [X0 : a,X1 : b] : (($true = ((sP0 @ X0))) | (((cS @ X1)) != $true) | (((cF @ X1)) != X0)) )),
% 0.22/0.27 inference(cnf_transformation,[],[f19])).
% 0.22/0.27 thf(f33,plain,(
% 0.22/0.27 (((sP2 @ sK6)) = $true) | (((sP1 @ sK6)) = $true)),
% 0.22/0.27 inference(cnf_transformation,[],[f21])).
% 0.22/0.27 thf(f34,plain,(
% 0.22/0.27 (((sP2 @ sK6)) != $true) | (((sP1 @ sK6)) != $true)),
% 0.22/0.27 inference(cnf_transformation,[],[f21])).
% 0.22/0.27 thf(f36,definition,(
% 0.22/0.27 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.22/0.27 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.22/0.27 thf(f37,plain,(
% 0.22/0.27 ( ! [X1 : b] : (($true = ((sP2 @ (cF @ X1)))) | (((cR @ X1)) != $true)) )),
% 0.22/0.27 inference(equality_resolution,[],[f25])).
% 0.22/0.27 thf(f38,plain,(
% 0.22/0.27 ( ! [X1 : b] : ((((sP1 @ (cF @ X1))) = $true) | (((cS @ X1)) != $true)) )),
% 0.22/0.27 inference(equality_resolution,[],[f29])).
% 0.22/0.27 thf(f39,plain,(
% 0.22/0.27 ( ! [X1 : b] : ((((sP1 @ (cF @ X1))) = $true) | (((cR @ X1)) != $true)) )),
% 0.22/0.27 inference(equality_resolution,[],[f28])).
% 0.22/0.27 thf(f40,plain,(
% 0.22/0.27 ( ! [X1 : b] : (($true = ((sP0 @ (cF @ X1)))) | (((cS @ X1)) != $true)) )),
% 0.22/0.27 inference(equality_resolution,[],[f32])).
% 0.22/0.27 thf(f41,definition,(
% 0.22/0.27 (sF7 = ((sP2 @ sK6)))),
% 0.22/0.27 introduced(definition,[new_symbols(definition,[sF7])],[function_definition])).
% 0.22/0.27 thf(f42,plain,(
% 0.22/0.27 (((sP2 @ sK6)) = sF7)),
% 0.22/0.27 inference(reorient_equations,[],[f41])).
% 0.22/0.27 thf(f43,definition,(
% 0.22/0.27 (sF8 = ((sP1 @ sK6)))),
% 0.22/0.27 introduced(definition,[new_symbols(definition,[sF8])],[function_definition])).
% 0.22/0.27 thf(f44,plain,(
% 0.22/0.27 (((sP1 @ sK6)) = sF8)),
% 0.22/0.27 inference(reorient_equations,[],[f43])).
% 0.22/0.27 thf(f45,plain,(
% 0.22/0.27 (sF7 != $true) | ($true != sF8)),
% 0.22/0.27 inference(definition_folding,[],[f34,f44,f42])).
% 0.22/0.27 thf(f46,plain,(
% 0.22/0.27 ($true = sF8) | (sF7 = $true)),
% 0.22/0.27 inference(definition_folding,[],[f33,f44,f42])).
% 0.22/0.27 thf(f47,plain,(
% 0.22/0.27 (((sP1 @ sK6)) = $true) | ($false = sF8)),
% 0.22/0.27 inference(iff_proxy_clausification,[],[f44])).
% 0.22/0.27 thf(f48,plain,(
% 0.22/0.27 (((sP1 @ sK6)) = $false) | ($true = sF8)),
% 0.22/0.27 inference(iff_proxy_clausification,[],[f44])).
% 0.22/0.27 thf(f49,plain,(
% 0.22/0.27 (((sP2 @ sK6)) = $true) | (sF7 = $false)),
% 0.22/0.27 inference(iff_proxy_clausification,[],[f42])).
% 0.22/0.27 thf(f50,plain,(
% 0.22/0.27 (sF7 = $true) | (((sP2 @ sK6)) = $false)),
% 0.22/0.27 inference(iff_proxy_clausification,[],[f42])).
% 0.22/0.27 thf(f52,definition,(
% 0.22/0.27 spl9_1 <=> ($true = sF8)),
% 0.22/0.27 introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition])).
% 0.22/0.27 thf(f54,plain,(
% 0.22/0.27 ($true = sF8) | ~spl9_1),
% 0.22/0.27 inference(avatar_component_clause,[],[f52])).
% 0.22/0.27 thf(f56,definition,(
% 0.22/0.27 spl9_2 <=> (((sP1 @ sK6)) = $false)),
% 0.22/0.27 introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition])).
% 0.22/0.27 thf(f58,plain,(
% 0.22/0.27 (((sP1 @ sK6)) = $false) | ~spl9_2),
% 0.22/0.27 inference(avatar_component_clause,[],[f56])).
% 0.22/0.27 thf(f59,plain,(
% 0.22/0.27 spl9_1 | spl9_2),
% 0.22/0.27 inference(avatar_split_clause,[],[f48,f56,f52])).
% 0.22/0.27 thf(f61,definition,(
% 0.22/0.27 spl9_3 <=> ($false = sF8)),
% 0.22/0.27 introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition])).
% 0.22/0.27 thf(f63,plain,(
% 0.22/0.27 ($false = sF8) | ~spl9_3),
% 0.22/0.27 inference(avatar_component_clause,[],[f61])).
% 0.22/0.27 thf(f65,definition,(
% 0.22/0.27 spl9_4 <=> (((sP1 @ sK6)) = $true)),
% 0.22/0.27 introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition])).
% 0.22/0.27 thf(f67,plain,(
% 0.22/0.27 (((sP1 @ sK6)) = $true) | ~spl9_4),
% 0.22/0.27 inference(avatar_component_clause,[],[f65])).
% 0.22/0.27 thf(f68,plain,(
% 0.22/0.27 spl9_3 | spl9_4),
% 0.22/0.27 inference(avatar_split_clause,[],[f47,f65,f61])).
% 0.22/0.27 thf(f70,definition,(
% 0.22/0.27 spl9_5 <=> (sF7 = $true)),
% 0.22/0.27 introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition])).
% 0.22/0.27 thf(f72,plain,(
% 0.22/0.27 (sF7 = $true) | ~spl9_5),
% 0.22/0.27 inference(avatar_component_clause,[],[f70])).
% 0.22/0.27 thf(f73,plain,(
% 0.22/0.27 spl9_1 | spl9_5),
% 0.22/0.27 inference(avatar_split_clause,[],[f46,f70,f52])).
% 0.22/0.27 thf(f74,plain,(
% 0.22/0.27 ~spl9_5 | ~spl9_1),
% 0.22/0.27 inference(avatar_split_clause,[],[f45,f52,f70])).
% 0.22/0.27 thf(f76,definition,(
% 0.22/0.27 spl9_6 <=> (((sP2 @ sK6)) = $false)),
% 0.22/0.27 introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition])).
% 0.22/0.27 thf(f78,plain,(
% 0.22/0.27 (((sP2 @ sK6)) = $false) | ~spl9_6),
% 0.22/0.27 inference(avatar_component_clause,[],[f76])).
% 0.22/0.27 thf(f79,plain,(
% 0.22/0.27 spl9_5 | spl9_6),
% 0.22/0.27 inference(avatar_split_clause,[],[f50,f76,f70])).
% 0.22/0.27 thf(f81,definition,(
% 0.22/0.27 spl9_7 <=> (((sP2 @ sK6)) = $true)),
% 0.22/0.27 introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition])).
% 0.22/0.27 thf(f85,definition,(
% 0.22/0.27 spl9_8 <=> (sF7 = $false)),
% 0.22/0.27 introduced(definition,[new_symbols(definition,[spl9_8])],[avatar_definition])).
% 0.22/0.27 thf(f87,plain,(
% 0.22/0.27 (sF7 = $false) | ~spl9_8),
% 0.22/0.27 inference(avatar_component_clause,[],[f85])).
% 0.22/0.27 thf(f88,plain,(
% 0.22/0.27 spl9_7 | spl9_8),
% 0.22/0.27 inference(avatar_split_clause,[],[f49,f85,f81])).
% 0.22/0.27 thf(f103,plain,(
% 0.22/0.27 ( ! [X0 : a] : (($true != ((cR @ (sK4 @ X0)))) | ($true = ((sP2 @ X0))) | ($true != ((sP1 @ X0)))) )),
% 0.22/0.27 inference(constrained_superposition,[],[f37,f27])).
% 0.22/0.27 thf(f106,plain,(
% 0.22/0.27 ( ! [X0 : a] : (($true = ((sP1 @ X0))) | ($true != ((sP0 @ X0))) | (((cS @ (sK5 @ X0))) != $true)) )),
% 0.22/0.27 inference(constrained_superposition,[],[f38,f30])).
% 0.22/0.27 thf(f107,plain,(
% 0.22/0.27 ( ! [X0 : a] : (($true = ((sP1 @ X0))) | ($true != ((sP0 @ X0)))) )),
% 0.22/0.27 inference(forward_subsumption_resolution,[],[f106,f31])).
% 0.22/0.27 thf(f119,plain,(
% 0.22/0.27 ( ! [X0 : a] : (($true != ((cS @ (sK4 @ X0)))) | ($true = ((sP0 @ X0))) | ($true != ((sP1 @ X0)))) )),
% 0.22/0.27 inference(constrained_superposition,[],[f40,f27])).
% 0.22/0.27 thf(f122,plain,(
% 0.22/0.27 ( ! [X0 : a] : ((((cR @ (sK3 @ X0))) != $true) | ($true = ((sP0 @ X0))) | ($true != ((sP2 @ X0))) | ($true = ((sP1 @ X0)))) )),
% 0.22/0.27 inference(constrained_superposition,[],[f39,f22])).
% 0.22/0.27 thf(f126,plain,(
% 0.22/0.27 ( ! [X0 : a] : ((((cR @ (sK3 @ X0))) != $true) | ($true = ((sP1 @ X0))) | ($true != ((sP2 @ X0)))) )),
% 0.22/0.27 inference(forward_subsumption_resolution,[],[f122,f107])).
% 0.22/0.27 thf(f130,plain,(
% 0.22/0.27 ( ! [X0 : a] : (($false = ((cS @ (sK4 @ X0)))) | ($true = ((sP0 @ X0))) | ($true != $true) | ($true != ((sP1 @ X0)))) )),
% 0.22/0.27 inference(constrained_superposition,[],[f119,f36])).
% 0.22/0.27 thf(f131,plain,(
% 0.22/0.27 ( ! [X0 : a] : (($false = ((cS @ (sK4 @ X0)))) | ($true = ((sP0 @ X0))) | ($true != ((sP1 @ X0)))) )),
% 0.22/0.27 inference(trivial_inequality_removal,[],[f130])).
% 0.22/0.27 thf(f134,plain,(
% 0.22/0.27 ( ! [X0 : a] : (($true = ((sP0 @ X0))) | ($true != $true) | ($true != ((sP2 @ X0))) | ($true != ((sP2 @ X0))) | ($true = ((sP1 @ X0)))) )),
% 0.22/0.27 inference(constrained_superposition,[],[f126,f23])).
% 0.22/0.27 thf(f136,plain,(
% 0.22/0.27 ( ! [X0 : a] : (($true != ((sP2 @ X0))) | ($true != $true) | ($true = ((sP0 @ X0))) | ($true = ((sP1 @ X0)))) )),
% 0.22/0.27 inference(duplicate_literal_removal,[],[f134])).
% 0.22/0.27 thf(f137,plain,(
% 0.22/0.27 ( ! [X0 : a] : (($true = ((sP0 @ X0))) | ($true = ((sP1 @ X0))) | ($true != ((sP2 @ X0)))) )),
% 0.22/0.27 inference(trivial_inequality_removal,[],[f136])).
% 0.22/0.27 thf(f139,plain,(
% 0.22/0.27 ( ! [X0 : a] : (($true = ((sP1 @ X0))) | ($true != ((sP2 @ X0)))) )),
% 0.22/0.27 inference(forward_subsumption_resolution,[],[f137,f107])).
% 0.22/0.27 thf(f140,plain,(
% 0.22/0.27 (((sP2 @ sK6)) != $true) | ($false = $true) | ~spl9_2),
% 0.22/0.27 inference(constrained_superposition,[],[f139,f58])).
% 0.22/0.27 thf(f143,plain,(
% 0.22/0.27 (((sP2 @ sK6)) != $true) | ~spl9_2),
% 0.22/0.27 inference(trivial_inequality_removal,[],[f140])).
% 0.22/0.27 thf(f148,plain,(
% 0.22/0.27 ($false = $true) | (~spl9_5 | ~spl9_8)),
% 0.22/0.27 inference(forward_demodulation,[],[f87,f72])).
% 0.22/0.27 thf(f149,plain,(
% 0.22/0.27 $false | (~spl9_5 | ~spl9_8)),
% 0.22/0.27 inference(trivial_inequality_removal,[],[f148])).
% 0.22/0.27 thf(f150,plain,(
% 0.22/0.27 ~spl9_5 | ~spl9_8),
% 0.22/0.27 inference(avatar_contradiction_clause,[],[f149])).
% 0.22/0.27 thf(f151,plain,(
% 0.22/0.27 ~spl9_7 | ~spl9_2),
% 0.22/0.27 inference(avatar_split_clause,[],[f143,f56,f81])).
% 0.22/0.27 thf(f152,plain,(
% 0.22/0.27 ($false = $true) | (~spl9_1 | ~spl9_3)),
% 0.22/0.27 inference(forward_demodulation,[],[f54,f63])).
% 0.22/0.27 thf(f153,plain,(
% 0.22/0.27 $false | (~spl9_1 | ~spl9_3)),
% 0.22/0.27 inference(trivial_inequality_removal,[],[f152])).
% 0.22/0.27 thf(f154,plain,(
% 0.22/0.27 ~spl9_1 | ~spl9_3),
% 0.22/0.27 inference(avatar_contradiction_clause,[],[f153])).
% 0.22/0.27 thf(f161,plain,(
% 0.22/0.27 ( ! [X0 : a] : (($true != ((sP1 @ X0))) | ($true != ((sP1 @ X0))) | ($true != $true) | ($true = ((cS @ (sK4 @ X0)))) | ($true = ((sP2 @ X0)))) )),
% 0.22/0.27 inference(constrained_superposition,[],[f103,f26])).
% 0.22/0.27 thf(f162,plain,(
% 0.22/0.27 ( ! [X0 : a] : (($true = ((sP2 @ X0))) | ($true != $true) | ($true != ((sP1 @ X0))) | ($true = ((cS @ (sK4 @ X0))))) )),
% 0.22/0.27 inference(duplicate_literal_removal,[],[f161])).
% 0.22/0.27 thf(f163,plain,(
% 0.22/0.27 ( ! [X0 : a] : (($true = ((cS @ (sK4 @ X0)))) | ($true != ((sP1 @ X0))) | ($true = ((sP2 @ X0)))) )),
% 0.22/0.27 inference(trivial_inequality_removal,[],[f162])).
% 0.22/0.27 thf(f202,plain,(
% 0.22/0.27 ( ! [X0 : a] : (($true != ((sP1 @ X0))) | ($false = $true) | ($true != ((sP1 @ X0))) | ($true = ((sP0 @ X0))) | ($true = ((sP2 @ X0)))) )),
% 0.22/0.27 inference(constrained_superposition,[],[f163,f131])).
% 0.22/0.27 thf(f205,plain,(
% 0.22/0.27 ( ! [X0 : a] : (($true = ((sP2 @ X0))) | ($true != ((sP1 @ X0))) | ($true = ((sP0 @ X0))) | ($false = $true)) )),
% 0.22/0.27 inference(duplicate_literal_removal,[],[f202])).
% 0.22/0.27 thf(f206,plain,(
% 0.22/0.27 ( ! [X0 : a] : (($true = ((sP2 @ X0))) | ($true != ((sP1 @ X0))) | ($true = ((sP0 @ X0)))) )),
% 0.22/0.27 inference(trivial_inequality_removal,[],[f205])).
% 0.22/0.27 thf(f211,plain,(
% 0.22/0.27 ( ! [X0 : a] : (($true = ((sP2 @ X0))) | ($true != ((sP1 @ X0)))) )),
% 0.22/0.27 inference(forward_subsumption_resolution,[],[f206,f24])).
% 0.22/0.27 thf(f214,plain,(
% 0.22/0.27 (((sP1 @ sK6)) != $true) | ($false = $true) | ~spl9_6),
% 0.22/0.27 inference(constrained_superposition,[],[f211,f78])).
% 0.22/0.27 thf(f216,plain,(
% 0.22/0.27 (((sP1 @ sK6)) != $true) | ~spl9_6),
% 0.22/0.27 inference(trivial_inequality_removal,[],[f214])).
% 0.22/0.27 thf(f218,plain,(
% 0.22/0.27 $false | (~spl9_4 | ~spl9_6)),
% 0.22/0.27 inference(forward_subsumption_resolution,[],[f216,f67])).
% 0.22/0.27 thf(f219,plain,(
% 0.22/0.27 ~spl9_4 | ~spl9_6),
% 0.22/0.27 inference(avatar_contradiction_clause,[],[f218])).
% 0.22/0.27 cnf(s1, plain, spl9_1 | spl9_2, inference(sat_conversion,[],[f59])).
% 0.22/0.27 cnf(s2, plain, spl9_3 | spl9_4, inference(sat_conversion,[],[f68])).
% 0.22/0.27 cnf(s3, plain, spl9_1 | spl9_5, inference(sat_conversion,[],[f73])).
% 0.22/0.27 cnf(s4, plain, ~spl9_1 | ~spl9_5, inference(sat_conversion,[],[f74])).
% 0.22/0.27 cnf(s5, plain, spl9_5 | spl9_6, inference(sat_conversion,[],[f79])).
% 0.22/0.27 cnf(s6, plain, spl9_7 | spl9_8, inference(sat_conversion,[],[f88])).
% 0.22/0.27 cnf(s9, plain, ~spl9_5 | ~spl9_8, inference(sat_conversion,[],[f150])).
% 0.22/0.27 cnf(s10, plain, ~spl9_2 | ~spl9_7, inference(sat_conversion,[],[f151])).
% 0.22/0.27 cnf(s12, plain, ~spl9_1 | ~spl9_3, inference(sat_conversion,[],[f154])).
% 0.22/0.27 cnf(s15, plain, ~spl9_4 | ~spl9_6, inference(sat_conversion,[],[f219])).
% 0.22/0.27 cnf(s17, plain, spl9_1, inference(rat,[],[s6,s10,s9,s1,s3])).
% 0.22/0.27 cnf(s18, plain, ~spl9_3, inference(rat,[],[s12,s17])).
% 0.22/0.27 cnf(s19, plain, ~spl9_5, inference(rat,[],[s4,s17])).
% 0.22/0.27 cnf(s20, plain, spl9_4, inference(rat,[],[s2,s18])).
% 0.22/0.27 cnf(s22, plain, spl9_6, inference(rat,[],[s5,s19])).
% 0.22/0.27 cnf(s24, plain, $false, inference(rat,[],[s15,s22,s20])).
% 0.22/0.27 thf(f222,plain,(
% 0.22/0.27 $false),
% 0.22/0.27 inference(avatar_sat_refutation,[],[s24])).
% 0.22/0.27 % SZS output end Proof for theBenchmark
% 0.22/0.27 % (1758900)------------------------------
% 0.22/0.27 % (1758900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.27 % (1758900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.27 % (1758900)CaDiCaL version: 2.1.3
% 0.22/0.27 % (1758900)Termination reason: Refutation
% 0.22/0.27 % (1758900)Time elapsed: 0.005 s
% 0.22/0.27 % (1758900)Peak memory usage: 13 MB
% 0.22/0.27 % (1758900)Instructions burned: 14 (million)
% 0.22/0.27 % (1758889)Success in time 0.033 s
% 0.22/0.27 % Vampire exiting
%------------------------------------------------------------------------------