%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO331^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 08:49:44 AM UTC 2026
% Result : Theorem 0.26s 0.38s
% Output : Refutation 0.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO331^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 % Computer : n016.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 16:51:20 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.27 Running first-order model finding
% 0.09/0.27 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.26/0.38 % (604229)Will run a generic schedule for satisfiability detection.
% 0.26/0.38 % (604234)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2464359490_2999 on theBenchmark for (2999ds/0Mi)
% 0.26/0.38 % Exception at run slice level
% 0.26/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.26/0.38 % (604239)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=630935886:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.26/0.38 % (604235)% WARNING: option uhcvi not known.
% 0.26/0.38 % (604235)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2158741802:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.26/0.38 % (604238)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1287705616:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.26/0.38 % (604235)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.26/0.38 % (604235)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.26/0.38 % (604238)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.26/0.38 % (604237)dis+10_1_sil=32000:sp=arity:random_seed=2572038921:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.26/0.38 % (604236)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4000533832:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.26/0.38 % (604240)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3606560623:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.26/0.38 % (604242)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=564123305:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.26/0.38 % Exception at run slice level
% 0.26/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.26/0.38 % (604235) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-604229-604235"...
% 0.26/0.38 % (604235)...printing done.
% 0.26/0.38 % (604235)Refutation found. Thanks to Tanya!
% 0.26/0.38 % SZS status Theorem for theBenchmark
% 0.26/0.38 % SZS output start Proof for theBenchmark
% 0.26/0.38 thf(type_def_5, type, a: $tType).
% 0.26/0.38 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.26/0.38 thf(func_def_0, type, cK: ((a > $o) > a > $o)).
% 0.26/0.38 thf(func_def_4, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.26/0.38 thf(func_def_5, type, vAND: ($o > $o > $o)).
% 0.26/0.38 thf(func_def_6, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.26/0.38 thf(func_def_7, type, vIMP: ($o > $o > $o)).
% 0.26/0.38 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.26/0.38 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.26/0.38 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.26/0.38 thf(func_def_11, type, sK0: a).
% 0.26/0.38 thf(func_def_12, type, sK1: (a > $o)).
% 0.26/0.38 thf(func_def_13, type, sK2: ((a > $o) > a)).
% 0.26/0.38 thf(func_def_14, type, sK3: ((a > $o) > a)).
% 0.26/0.38 thf(func_def_15, type, vNOT: ($o > $o)).
% 0.26/0.38 thf(func_def_17, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.26/0.38 thf(func_def_18, type, sK5: (a > $o)).
% 0.26/0.38 thf(func_def_19, type, sK6: ((a > $o) > a)).
% 0.26/0.38 thf(func_def_20, type, sK7: ((a > $o) > a)).
% 0.26/0.38 thf(f1,conjecture,(
% 0.26/0.38 ! [X0 : (a > $o)] : (! [X1 : a] : ((X0 @ X1) => ? [X2 : (a > $o)] : ((X2 @ X1) & ! [X3 : a] : ((X2 @ X3) => (cK @ X2 @ X3)))) => ! [X1 : a] : ((cK @ X0 @ X1) => (cK @ (^[X3 : a] : (? [X2 : (a > $o)] : ((X2 @ X3) & ! [X4 : a] : ((X2 @ X4) => (cK @ X2 @ X4))))) @ X1))) => ! [X1 : a] : (? [X2 : (a > $o)] : ((X2 @ X1) & ! [X3 : a] : ((X2 @ X3) => (cK @ X2 @ X3))) => (cK @ (^[X3 : a] : (? [X2 : (a > $o)] : ((X2 @ X3) & ! [X4 : a] : ((X2 @ X4) => (cK @ X2 @ X4))))) @ X1))),
% 0.26/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM116_2SS_pme)).
% 0.26/0.38 thf(f2,negated_conjecture,(
% 0.26/0.38 ~(! [X0 : (a > $o)] : (! [X1 : a] : ((X0 @ X1) => ? [X2 : (a > $o)] : ((X2 @ X1) & ! [X3 : a] : ((X2 @ X3) => (cK @ X2 @ X3)))) => ! [X1 : a] : ((cK @ X0 @ X1) => (cK @ (^[X3 : a] : (? [X2 : (a > $o)] : ((X2 @ X3) & ! [X4 : a] : ((X2 @ X4) => (cK @ X2 @ X4))))) @ X1))) => ! [X1 : a] : (? [X2 : (a > $o)] : ((X2 @ X1) & ! [X3 : a] : ((X2 @ X3) => (cK @ X2 @ X3))) => (cK @ (^[X3 : a] : (? [X2 : (a > $o)] : ((X2 @ X3) & ! [X4 : a] : ((X2 @ X4) => (cK @ X2 @ X4))))) @ X1)))),
% 0.26/0.38 inference(negated_conjecture,[status(cth)],[f1])).
% 0.26/0.38 thf(f3,plain,(
% 0.26/0.38 ~(! [X0 : (a > $o)] : (! [X1 : a] : ((X0 @ X1) => ? [X2 : (a > $o)] : ((X2 @ X1) & ! [X3 : a] : ((X2 @ X3) => (cK @ X2 @ X3)))) => ! [X4 : a] : ((cK @ X0 @ X4) => (cK @ (^[X5 : a] : (? [X6 : (a > $o)] : ((X6 @ X5) & ! [X7 : a] : ((X6 @ X7) => (cK @ X6 @ X7))))) @ X4))) => ! [X8 : a] : (? [X9 : (a > $o)] : ((X9 @ X8) & ! [X10 : a] : ((X9 @ X10) => (cK @ X9 @ X10))) => (cK @ (^[X11 : a] : (? [X12 : (a > $o)] : ((X12 @ X11) & ! [X13 : a] : ((X12 @ X13) => (cK @ X12 @ X13))))) @ X8)))),
% 0.26/0.38 inference(rectify,[],[f2])).
% 0.26/0.38 thf(f4,plain,(
% 0.26/0.38 ~(! [X0 : (a > $o)] : (! [X1 : a] : ((((X0 @ X1)) = $true) => ? [X2 : (a > $o)] : ((((X2 @ X1)) = $true) & ! [X3 : a] : ((((X2 @ X3)) = $true) => (((cK @ X2 @ X3)) = $true)))) => ! [X4 : a] : ((((cK @ X0 @ X4)) = $true) => ($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4))))) => ! [X8 : a] : (? [X9 : (a > $o)] : ((((X9 @ X8)) = $true) & ! [X10 : a] : ((((X9 @ X10)) = $true) => (((cK @ X9 @ X10)) = $true))) => ($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X8)))))),
% 0.26/0.38 inference(fool_elimination,[],[f3])).
% 0.26/0.38 thf(f5,plain,(
% 0.26/0.38 ~(! [X0 : (a > $o)] : (! [X1 : a] : ((((X0 @ X1)) = $true) => ? [X2 : (a > $o)] : ((((X2 @ X1)) = $true) & ! [X3 : a] : ((((X2 @ X3)) = $true) => (((cK @ X2 @ X3)) = $true)))) => ! [X4 : a] : ((((cK @ X0 @ X4)) = $true) => ($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4))))) => ! [X5 : a] : (? [X6 : (a > $o)] : ((((X6 @ X5)) = $true) & ! [X7 : a] : ((((X6 @ X7)) = $true) => (((cK @ X6 @ X7)) = $true))) => ($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X5)))))),
% 0.26/0.38 inference(rectify,[],[f4])).
% 0.26/0.38 thf(f6,plain,(
% 0.26/0.38 ? [X5 : a] : (($true != ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X5))) & ? [X6 : (a > $o)] : ((((X6 @ X5)) = $true) & ! [X7 : a] : ((((cK @ X6 @ X7)) = $true) | (((X6 @ X7)) != $true)))) & ! [X0 : (a > $o)] : (! [X4 : a] : (($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4))) | (((cK @ X0 @ X4)) != $true)) | ? [X1 : a] : (! [X2 : (a > $o)] : ((((X2 @ X1)) != $true) | ? [X3 : a] : ((((cK @ X2 @ X3)) != $true) & (((X2 @ X3)) = $true))) & (((X0 @ X1)) = $true)))),
% 0.26/0.38 inference(ennf_transformation,[],[f5])).
% 0.26/0.38 thf(f7,plain,(
% 0.26/0.38 ? [X0 : a] : (($true != ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X0))) & ? [X1 : (a > $o)] : (($true = ((X1 @ X0))) & ! [X2 : a] : (($true = ((cK @ X1 @ X2))) | ($true != ((X1 @ X2)))))) & ! [X3 : (a > $o)] : (! [X4 : a] : (($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4))) | ($true != ((cK @ X3 @ X4)))) | ? [X5 : a] : (! [X6 : (a > $o)] : ((((X6 @ X5)) != $true) | ? [X7 : a] : ((((cK @ X6 @ X7)) != $true) & (((X6 @ X7)) = $true))) & ($true = ((X3 @ X5)))))),
% 0.26/0.38 inference(rectify,[],[f6])).
% 0.26/0.38 thf(f8,plain,(
% 0.26/0.38 (($true != ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK0))) & (($true = ((sK1 @ sK0))) & ! [X2 : a] : (($true = ((cK @ sK1 @ X2))) | ($true != ((sK1 @ X2)))))) & ! [X3 : (a > $o)] : (! [X4 : a] : (($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4))) | ($true != ((cK @ X3 @ X4)))) | (! [X6 : (a > $o)] : (($true != ((X6 @ (sK2 @ X3)))) | (($true != ((cK @ X6 @ (sK3 @ X6)))) & ($true = ((X6 @ (sK3 @ X6)))))) & ($true = ((X3 @ (sK2 @ X3))))))),
% 0.26/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X7,sK3 @ X6),skolemize(X7,sK3 @ X6)],[f7])).
% 0.31/0.38 thf(f9,plain,(
% 0.31/0.38 ( ! [X3 : (a > $o),X4 : a] : (($true != ((cK @ X3 @ X4))) | ($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4))) | ($true = ((X3 @ (sK2 @ X3))))) )),
% 0.31/0.38 inference(cnf_transformation,[],[f8])).
% 0.31/0.38 thf(f10,plain,(
% 0.31/0.38 ( ! [X3 : (a > $o),X6 : (a > $o),X4 : a] : (($true != ((cK @ X3 @ X4))) | ($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4))) | ($true != ((X6 @ (sK2 @ X3)))) | ($true = ((X6 @ (sK3 @ X6))))) )),
% 0.31/0.38 inference(cnf_transformation,[],[f8])).
% 0.31/0.38 thf(f11,plain,(
% 0.31/0.38 ( ! [X3 : (a > $o),X6 : (a > $o),X4 : a] : (($true != ((cK @ X6 @ (sK3 @ X6)))) | ($true != ((cK @ X3 @ X4))) | ($true != ((X6 @ (sK2 @ X3)))) | ($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X4)))) )),
% 0.31/0.38 inference(cnf_transformation,[],[f8])).
% 0.31/0.38 thf(f12,plain,(
% 0.31/0.38 ( ! [X2 : a] : (($true != ((sK1 @ X2))) | ($true = ((cK @ sK1 @ X2)))) )),
% 0.31/0.38 inference(cnf_transformation,[],[f8])).
% 0.31/0.38 thf(f13,plain,(
% 0.31/0.38 ($true = ((sK1 @ sK0)))),
% 0.31/0.38 inference(cnf_transformation,[],[f8])).
% 0.31/0.38 thf(f14,plain,(
% 0.31/0.38 ($true != ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK0)))),
% 0.31/0.38 inference(cnf_transformation,[],[f8])).
% 0.31/0.38 thf(f16,definition,(
% 0.31/0.38 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.31/0.38 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.31/0.38 thf(f17,plain,(
% 0.31/0.38 ($true != $true) | ($true = ((cK @ sK1 @ sK0)))),
% 0.31/0.38 inference(constrained_superposition,[],[f12,f13])).
% 0.31/0.38 thf(f18,plain,(
% 0.31/0.38 ($true = ((cK @ sK1 @ sK0)))),
% 0.31/0.38 inference(trivial_inequality_removal,[],[f17])).
% 0.31/0.38 thf(f21,plain,(
% 0.31/0.38 ( ! [X0 : a] : (($true != $true) | ($true = ((cK @ sK1 @ X0))) | ($false = ((sK1 @ X0)))) )),
% 0.31/0.38 inference(constrained_superposition,[],[f12,f16])).
% 0.31/0.38 thf(f23,plain,(
% 0.31/0.38 ( ! [X0 : a] : (($true = ((cK @ sK1 @ X0))) | ($false = ((sK1 @ X0)))) )),
% 0.31/0.38 inference(trivial_inequality_removal,[],[f21])).
% 0.31/0.38 thf(f30,plain,(
% 0.31/0.38 ($true != $true) | ($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK0))) | ($true = ((sK1 @ (sK2 @ sK1))))),
% 0.31/0.38 inference(constrained_superposition,[],[f9,f18])).
% 0.31/0.38 thf(f35,plain,(
% 0.31/0.38 ($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK0))) | ($true = ((sK1 @ (sK2 @ sK1))))),
% 0.31/0.38 inference(trivial_inequality_removal,[],[f30])).
% 0.31/0.38 thf(f37,definition,(
% 0.31/0.38 spl4_1 <=> ($true = ((sK1 @ (sK2 @ sK1))))),
% 0.31/0.38 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.31/0.38 thf(f39,plain,(
% 0.31/0.38 ($true = ((sK1 @ (sK2 @ sK1)))) | ~spl4_1),
% 0.31/0.38 inference(avatar_component_clause,[],[f37])).
% 0.31/0.38 thf(f44,plain,(
% 0.31/0.38 ($true = ((sK1 @ (sK2 @ sK1))))),
% 0.31/0.38 inference(forward_subsumption_resolution,[],[f35,f14])).
% 0.31/0.38 thf(f45,plain,(
% 0.31/0.38 spl4_1),
% 0.31/0.38 inference(avatar_split_clause,[],[f44,f37])).
% 0.31/0.38 thf(f49,plain,(
% 0.31/0.38 ( ! [X0 : (a > $o)] : (($true != $true) | ($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK0))) | ($true != ((X0 @ (sK2 @ sK1)))) | ($true = ((X0 @ (sK3 @ X0))))) )),
% 0.31/0.38 inference(constrained_superposition,[],[f10,f18])).
% 0.31/0.38 thf(f54,plain,(
% 0.31/0.38 ( ! [X0 : (a > $o)] : (($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK0))) | ($true != ((X0 @ (sK2 @ sK1)))) | ($true = ((X0 @ (sK3 @ X0))))) )),
% 0.31/0.38 inference(trivial_inequality_removal,[],[f49])).
% 0.31/0.38 thf(f56,definition,(
% 0.31/0.38 spl4_3 <=> ! [X1 : (a > $o)] : (($true != ((X1 @ (sK2 @ sK1)))) | ($true = ((X1 @ (sK3 @ X1)))))),
% 0.31/0.38 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
% 0.31/0.38 thf(f57,plain,(
% 0.31/0.38 ( ! [X1 : (a > $o)] : (($true != ((X1 @ (sK2 @ sK1)))) | ($true = ((X1 @ (sK3 @ X1))))) ) | ~spl4_3),
% 0.31/0.38 inference(avatar_component_clause,[],[f56])).
% 0.31/0.38 thf(f59,plain,(
% 0.31/0.38 ( ! [X0 : (a > $o)] : (($true != ((X0 @ (sK2 @ sK1)))) | ($true = ((X0 @ (sK3 @ X0))))) )),
% 0.31/0.38 inference(forward_subsumption_resolution,[],[f54,f14])).
% 0.31/0.38 thf(f60,plain,(
% 0.31/0.38 spl4_3),
% 0.31/0.38 inference(avatar_split_clause,[],[f59,f56])).
% 0.31/0.38 thf(f77,plain,(
% 0.31/0.38 ($true != $true) | ($true = (((^[Y0 : a]: (sK1 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK3 @ (^[Y0 : a]: (sK1 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | (~spl4_1 | ~spl4_3)),
% 0.31/0.38 inference(constrained_superposition,[],[f57,f39])).
% 0.31/0.38 thf(f93,plain,(
% 0.31/0.38 ($true = (((^[Y0 : a]: (sK1 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK3 @ (^[Y0 : a]: (sK1 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | (~spl4_1 | ~spl4_3)),
% 0.31/0.38 inference(trivial_inequality_removal,[],[f77])).
% 0.31/0.38 thf(f94,plain,(
% 0.31/0.38 ($true = ((sK1 @ (sK3 @ sK1)))) | (~spl4_1 | ~spl4_3)),
% 0.31/0.38 inference(beta-eta_normalization,[],[f93])).
% 0.31/0.38 thf(f106,plain,(
% 0.31/0.38 ( ! [X0 : (a > $o),X1 : a] : (($true != $true) | (((cK @ X0 @ X1)) != $true) | ($true != ((sK1 @ (sK2 @ X0)))) | ($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1))) | ($false = ((sK1 @ (sK3 @ sK1))))) )),
% 0.31/0.38 inference(constrained_superposition,[],[f11,f23])).
% 0.31/0.38 thf(f109,plain,(
% 0.31/0.38 ( ! [X0 : (a > $o),X1 : a] : ((((cK @ X0 @ X1)) != $true) | ($true != ((sK1 @ (sK2 @ X0)))) | ($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1))) | ($false = ((sK1 @ (sK3 @ sK1))))) )),
% 0.31/0.38 inference(trivial_inequality_removal,[],[f106])).
% 0.31/0.38 thf(f111,definition,(
% 0.31/0.38 spl4_5 <=> ($false = ((sK1 @ (sK3 @ sK1))))),
% 0.31/0.38 introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition])).
% 0.31/0.38 thf(f113,plain,(
% 0.31/0.38 ($false = ((sK1 @ (sK3 @ sK1)))) | ~spl4_5),
% 0.31/0.38 inference(avatar_component_clause,[],[f111])).
% 0.31/0.38 thf(f115,definition,(
% 0.31/0.38 spl4_6 <=> ! [X0 : (a > $o),X1 : a] : ((((cK @ X0 @ X1)) != $true) | ($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1))) | ($true != ((sK1 @ (sK2 @ X0)))))),
% 0.31/0.38 introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition])).
% 0.31/0.38 thf(f116,plain,(
% 0.31/0.38 ( ! [X0 : (a > $o),X1 : a] : ((((cK @ X0 @ X1)) != $true) | ($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X1))) | ($true != ((sK1 @ (sK2 @ X0))))) ) | ~spl4_6),
% 0.31/0.38 inference(avatar_component_clause,[],[f115])).
% 0.31/0.38 thf(f117,plain,(
% 0.31/0.38 spl4_5 | spl4_6),
% 0.31/0.38 inference(avatar_split_clause,[],[f109,f115,f111])).
% 0.31/0.38 thf(f249,plain,(
% 0.31/0.38 ($true = $false) | (~spl4_1 | ~spl4_3 | ~spl4_5)),
% 0.31/0.38 inference(forward_demodulation,[],[f94,f113])).
% 0.31/0.38 thf(f250,plain,(
% 0.31/0.38 $false | (~spl4_1 | ~spl4_3 | ~spl4_5)),
% 0.31/0.38 inference(trivial_inequality_removal,[],[f249])).
% 0.31/0.38 thf(f251,plain,(
% 0.31/0.38 ~spl4_1 | ~spl4_3 | ~spl4_5),
% 0.31/0.38 inference(avatar_contradiction_clause,[],[f250])).
% 0.31/0.38 thf(f491,plain,(
% 0.31/0.38 ($true != $true) | ($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK0))) | ($true != ((sK1 @ (sK2 @ sK1)))) | ~spl4_6),
% 0.31/0.38 inference(constrained_superposition,[],[f116,f18])).
% 0.31/0.38 thf(f496,plain,(
% 0.31/0.38 ($true = ((cK @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cK @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK0))) | ($true != ((sK1 @ (sK2 @ sK1)))) | ~spl4_6),
% 0.31/0.38 inference(trivial_inequality_removal,[],[f491])).
% 0.31/0.38 thf(f502,plain,(
% 0.31/0.38 ($true != ((sK1 @ (sK2 @ sK1)))) | ~spl4_6),
% 0.31/0.38 inference(forward_subsumption_resolution,[],[f496,f14])).
% 0.31/0.38 thf(f505,plain,(
% 0.31/0.38 $false | (~spl4_1 | ~spl4_6)),
% 0.31/0.38 inference(forward_subsumption_resolution,[],[f502,f39])).
% 0.31/0.38 thf(f506,plain,(
% 0.31/0.38 ~spl4_1 | ~spl4_6),
% 0.31/0.38 inference(avatar_contradiction_clause,[],[f505])).
% 0.31/0.38 cnf(s2, plain, spl4_1, inference(sat_conversion,[],[f45])).
% 0.31/0.38 cnf(s4, plain, spl4_3, inference(sat_conversion,[],[f60])).
% 0.31/0.38 cnf(s6, plain, spl4_5 | spl4_6, inference(sat_conversion,[],[f117])).
% 0.31/0.38 cnf(s10, plain, ~spl4_1 | ~spl4_3 | ~spl4_5, inference(sat_conversion,[],[f251])).
% 0.31/0.38 cnf(s24, plain, ~spl4_1 | ~spl4_6, inference(sat_conversion,[],[f506])).
% 0.31/0.38 cnf(s27, plain, ~spl4_6, inference(rat,[],[s24,s2])).
% 0.31/0.38 cnf(s29, plain, ~spl4_5, inference(rat,[],[s10,s4,s2])).
% 0.31/0.38 cnf(s30, plain, $false, inference(rat,[],[s6,s27,s29])).
% 0.31/0.38 thf(f509,plain,(
% 0.31/0.38 $false),
% 0.31/0.38 inference(avatar_sat_refutation,[],[s30])).
% 0.31/0.38 % SZS output end Proof for theBenchmark
% 0.31/0.38 % (604235)------------------------------
% 0.31/0.38 % (604235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.38 % (604235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.38 % (604235)CaDiCaL version: 2.1.3
% 0.31/0.38 % (604235)Termination reason: Refutation
% 0.31/0.38 % (604235)Time elapsed: 0.055 s
% 0.31/0.38 % (604235)Peak memory usage: 13 MB
% 0.31/0.38 % (604235)Instructions burned: 60 (million)
% 0.31/0.38 % (604229)Success in time 0.092 s
% 0.31/0.38 % Vampire exiting
%------------------------------------------------------------------------------