%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PUZ104^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 08:21:03 AM UTC 2026
% Result : Theorem 0.09s 0.28s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ104^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n009.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:24:15 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.09/0.28 % (3971843)Will run a generic schedule for satisfiability detection.
% 0.09/0.28 % (3971851)dis+10_1_sil=32000:sp=arity:random_seed=1336645851:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.28 % (3971849)% WARNING: option uhcvi not known.
% 0.09/0.28 % (3971848)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3723541251_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.28 % (3971849)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3097384178:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.28 % (3971850)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2532624893:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.28 % (3971852)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=947092089:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.28 % (3971854)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3867453502:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.28 % (3971849)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.28 % Exception at run slice level
% 0.09/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.28 % (3971853)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2389183824:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.28 % (3971852)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.28 % (3971849)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.09/0.28 % (3971851) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3971843-3971851"...
% 0.09/0.28 % (3971851)...printing done.
% 0.09/0.28 % (3971851)Refutation found. Thanks to Tanya!
% 0.09/0.28 % SZS status Theorem for theBenchmark
% 0.09/0.28 % SZS output start Proof for theBenchmark
% 0.09/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.28 thf(func_def_1, type, s: ($i > $i)).
% 0.09/0.28 thf(func_def_2, type, cCKB6_NUM: ($i > $o)).
% 0.09/0.28 thf(func_def_4, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.09/0.28 thf(func_def_5, type, vIMP: ($o > $o > $o)).
% 0.09/0.28 thf(func_def_6, type, vAND: ($o > $o > $o)).
% 0.09/0.28 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 0.09/0.28 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.09/0.28 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.09/0.28 thf(func_def_13, type, vNOT: ($o > $o)).
% 0.09/0.28 thf(func_def_14, type, sK1: (($i > $o) > $i)).
% 0.09/0.28 thf(func_def_15, type, sK2: ($i > $o)).
% 0.09/0.28 thf(func_def_16, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.09/0.28 thf(f1,axiom,(
% 0.09/0.28 (cCKB6_NUM = (^[X0 : $i] : (! [X1 : ($i > $o)] : ((! [X2 : $i] : ((X1 @ X2) => (X1 @ (s @ X2))) & (X1 @ c1)) => (X1 @ X0)))))),
% 0.09/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCKB6_NUM_def)).
% 0.09/0.28 thf(f2,conjecture,(
% 0.09/0.28 ! [X0 : $i] : ((cCKB6_NUM @ X0) => (cCKB6_NUM @ (s @ (s @ X0))))),
% 0.09/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCKB6_L4000)).
% 0.09/0.28 thf(f3,negated_conjecture,(
% 0.09/0.28 ~ ! [X0 : $i] : ((cCKB6_NUM @ X0) => (cCKB6_NUM @ (s @ (s @ X0))))),
% 0.09/0.28 inference(negated_conjecture,[status(cth)],[f2])).
% 0.09/0.28 thf(f4,plain,(
% 0.09/0.28 (cCKB6_NUM = (^[X0 : $i] : (! [X1 : ($i > $o)] : ((! [X2 : $i] : ((X1 @ X2) => (X1 @ (s @ X2))) & (X1 @ c1)) => (X1 @ X0)))))),
% 0.09/0.28 inference(rectify,[],[f1])).
% 0.09/0.28 thf(f5,plain,(
% 0.09/0.28 (cCKB6_NUM = (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((Y1 @ c1) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (s @ Y2)))))) => (Y1 @ Y0))))))),
% 0.09/0.28 inference(fool_elimination,[],[f4])).
% 0.09/0.28 thf(f6,plain,(
% 0.09/0.28 ~ ! [X0 : $i] : ((cCKB6_NUM @ X0) => (cCKB6_NUM @ (s @ (s @ X0))))),
% 0.09/0.28 inference(rectify,[],[f3])).
% 0.09/0.28 thf(f7,plain,(
% 0.09/0.28 ~ ! [X0 : $i] : ((((cCKB6_NUM @ X0)) = $true) => (((cCKB6_NUM @ (s @ (s @ X0)))) = $true))),
% 0.09/0.28 inference(fool_elimination,[],[f6])).
% 0.09/0.28 thf(f8,plain,(
% 0.09/0.28 ? [X0 : $i] : ((((cCKB6_NUM @ (s @ (s @ X0)))) != $true) & (((cCKB6_NUM @ X0)) = $true))),
% 0.09/0.28 inference(ennf_transformation,[],[f7])).
% 0.09/0.28 thf(f9,plain,(
% 0.09/0.28 ($true != ((cCKB6_NUM @ (s @ (s @ sK0))))) & ($true = ((cCKB6_NUM @ sK0)))),
% 0.09/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f8])).
% 0.09/0.28 thf(f10,plain,(
% 0.09/0.28 (cCKB6_NUM = (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((Y1 @ c1) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (s @ Y2)))))) => (Y1 @ Y0))))))),
% 0.09/0.28 inference(cnf_transformation,[],[f5])).
% 0.09/0.28 thf(f11,plain,(
% 0.09/0.28 ($true = ((cCKB6_NUM @ sK0)))),
% 0.09/0.28 inference(cnf_transformation,[],[f9])).
% 0.09/0.28 thf(f12,plain,(
% 0.09/0.28 ($true != ((cCKB6_NUM @ (s @ (s @ sK0)))))),
% 0.09/0.28 inference(cnf_transformation,[],[f9])).
% 0.09/0.28 thf(f14,definition,(
% 0.09/0.28 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.09/0.28 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.09/0.28 thf(f15,plain,(
% 0.09/0.28 ($true != (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((Y1 @ c1) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (s @ Y2)))))) => (Y1 @ Y0))))) @ (s @ (s @ sK0)))))),
% 0.09/0.28 inference(definition_unfolding,[],[f12,f10])).
% 0.09/0.28 thf(f16,plain,(
% 0.09/0.28 ($true = (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((Y1 @ c1) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (Y1 @ (s @ Y2)))))) => (Y1 @ Y0))))) @ sK0)))),
% 0.09/0.28 inference(definition_unfolding,[],[f11,f10])).
% 0.09/0.28 thf(f17,plain,(
% 0.09/0.28 ($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c1) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1)))))) => (Y0 @ sK0))))))),
% 0.09/0.28 inference(beta-eta_normalization,[],[f16])).
% 0.09/0.28 thf(f18,plain,(
% 0.09/0.28 ( ! [X1 : ($i > $o)] : (($true = (((^[Y0 : $i > $o]: (((Y0 @ c1) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1)))))) => (Y0 @ sK0))) @ X1)))) )),
% 0.09/0.28 inference(pi_proxy_clausification,[],[f17])).
% 0.09/0.28 thf(f19,plain,(
% 0.09/0.28 ( ! [X1 : ($i > $o)] : (($true = ((((X1 @ c1) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ Y0)))))) => (X1 @ sK0))))) )),
% 0.09/0.28 inference(beta-eta_normalization,[],[f18])).
% 0.09/0.28 thf(f20,plain,(
% 0.09/0.28 ( ! [X1 : ($i > $o)] : (($false = (((X1 @ c1) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ Y0)))))))) | ($true = ((X1 @ sK0)))) )),
% 0.09/0.28 inference(imp_proxy_clausification,[],[f19])).
% 0.09/0.28 thf(f21,plain,(
% 0.09/0.28 ( ! [X1 : ($i > $o)] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ Y0))))))) | ($true = ((X1 @ sK0))) | (((X1 @ c1)) = $false)) )),
% 0.09/0.28 inference(and_proxy_clausification,[],[f20])).
% 0.09/0.28 thf(f22,plain,(
% 0.09/0.28 ( ! [X1 : ($i > $o)] : (($false = (((^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ Y0)))) @ (sK1 @ X1)))) | ($true = ((X1 @ sK0))) | (((X1 @ c1)) = $false)) )),
% 0.09/0.28 inference(sigma_proxy_clausification,[],[f21])).
% 0.09/0.28 thf(f23,plain,(
% 0.09/0.28 ( ! [X1 : ($i > $o)] : (($false = (((X1 @ (sK1 @ X1)) => (X1 @ (s @ (sK1 @ X1)))))) | ($true = ((X1 @ sK0))) | (((X1 @ c1)) = $false)) )),
% 0.09/0.28 inference(beta-eta_normalization,[],[f22])).
% 0.09/0.28 thf(f24,plain,(
% 0.09/0.28 ( ! [X1 : ($i > $o)] : (($false = ((X1 @ (s @ (sK1 @ X1))))) | ($true = ((X1 @ sK0))) | (((X1 @ c1)) = $false)) )),
% 0.09/0.28 inference(imp_proxy_clausification,[],[f23])).
% 0.09/0.28 thf(f25,plain,(
% 0.09/0.28 ( ! [X1 : ($i > $o)] : (($true = ((X1 @ (sK1 @ X1)))) | ($true = ((X1 @ sK0))) | (((X1 @ c1)) = $false)) )),
% 0.09/0.28 inference(imp_proxy_clausification,[],[f23])).
% 0.09/0.28 thf(f26,plain,(
% 0.09/0.28 ($true != ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c1) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1)))))) => (Y0 @ (s @ (s @ sK0))))))))),
% 0.09/0.28 inference(beta-eta_normalization,[],[f15])).
% 0.09/0.28 thf(f27,plain,(
% 0.09/0.28 ($false = (((^[Y0 : $i > $o]: (((Y0 @ c1) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ Y1)))))) => (Y0 @ (s @ (s @ sK0))))) @ sK2)))),
% 0.09/0.28 inference(sigma_proxy_clausification,[],[f26])).
% 0.09/0.28 thf(f28,plain,(
% 0.09/0.28 ($false = ((((sK2 @ c1) & (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (s @ Y0)))))) => (sK2 @ (s @ (s @ sK0))))))),
% 0.09/0.28 inference(beta-eta_normalization,[],[f27])).
% 0.09/0.28 thf(f29,plain,(
% 0.09/0.28 ($false = ((sK2 @ (s @ (s @ sK0)))))),
% 0.09/0.28 inference(imp_proxy_clausification,[],[f28])).
% 0.09/0.28 thf(f30,plain,(
% 0.09/0.28 ($true = (((sK2 @ c1) & (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (s @ Y0))))))))),
% 0.09/0.28 inference(imp_proxy_clausification,[],[f28])).
% 0.09/0.28 thf(f31,plain,(
% 0.09/0.28 ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (s @ Y0)))))))),
% 0.09/0.28 inference(and_proxy_clausification,[],[f30])).
% 0.09/0.28 thf(f32,plain,(
% 0.09/0.28 ($true = ((sK2 @ c1)))),
% 0.09/0.28 inference(and_proxy_clausification,[],[f30])).
% 0.09/0.28 thf(f33,plain,(
% 0.09/0.28 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((sK2 @ Y0) => (sK2 @ (s @ Y0)))) @ X1)))) )),
% 0.09/0.28 inference(pi_proxy_clausification,[],[f31])).
% 0.09/0.28 thf(f34,plain,(
% 0.09/0.28 ( ! [X1 : $i] : (($true = (((sK2 @ X1) => (sK2 @ (s @ X1)))))) )),
% 0.09/0.28 inference(beta-eta_normalization,[],[f33])).
% 0.09/0.28 thf(f35,plain,(
% 0.09/0.28 ( ! [X1 : $i] : (($true = ((sK2 @ (s @ X1)))) | ($false = ((sK2 @ X1)))) )),
% 0.09/0.28 inference(imp_proxy_clausification,[],[f34])).
% 0.09/0.28 thf(f46,plain,(
% 0.09/0.28 ($true = $false) | ($false = ((sK2 @ (s @ sK0))))),
% 0.09/0.28 inference(constrained_superposition,[],[f29,f35])).
% 0.09/0.28 thf(f47,plain,(
% 0.09/0.28 ($false = ((sK2 @ (s @ sK0))))),
% 0.09/0.28 inference(trivial_inequality_removal,[],[f46])).
% 0.09/0.28 thf(f59,plain,(
% 0.09/0.28 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ c1))) | ($true = ((X0 @ sK0))) | ($false = ((X0 @ c1))) | ($false != ((X0 @ (sK1 @ X0))))) )),
% 0.09/0.28 inference(equality_factoring,[],[f25])).
% 0.09/0.28 thf(f82,plain,(
% 0.09/0.28 ( ! [X0 : ($i > $o)] : (($false != ((X0 @ (sK1 @ X0)))) | ($false = ((X0 @ c1))) | ($true = ((X0 @ sK0)))) )),
% 0.09/0.28 inference(forward_subsumption_resolution,[],[f59,f14])).
% 0.09/0.28 thf(f95,plain,(
% 0.09/0.28 ($true = $false) | ($false = ((sK2 @ sK0)))),
% 0.09/0.28 inference(constrained_superposition,[],[f35,f47])).
% 0.09/0.28 thf(f99,plain,(
% 0.09/0.28 ($false = ((sK2 @ sK0)))),
% 0.09/0.28 inference(trivial_inequality_removal,[],[f95])).
% 0.09/0.28 thf(f120,plain,(
% 0.09/0.28 ( ! [X0 : ($i > $o)] : (($false != ((X0 @ sK0))) | ($true = ((X0 @ sK0))) | ($false = ((X0 @ c1))) | ($true != ((X0 @ (s @ (sK1 @ X0)))))) )),
% 0.09/0.28 inference(equality_factoring,[],[f24])).
% 0.09/0.28 thf(f170,plain,(
% 0.09/0.28 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ (s @ (sK1 @ X0))))) | ($false = ((X0 @ c1))) | ($true = ((X0 @ sK0)))) )),
% 0.09/0.28 inference(forward_subsumption_resolution,[],[f120,f14])).
% 0.09/0.28 thf(f185,definition,(
% 0.09/0.28 spl3_5 <=> ! [X0 : $i] : (($false = ((sK2 @ X0))) | (((sK1 @ sK2)) != X0))),
% 0.09/0.28 introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition])).
% 0.09/0.28 thf(f186,plain,(
% 0.09/0.28 ( ! [X0 : $i] : ((((sK1 @ sK2)) != X0) | ($false = ((sK2 @ X0)))) ) | ~spl3_5),
% 0.09/0.28 inference(avatar_component_clause,[],[f185])).
% 0.09/0.28 thf(f278,plain,(
% 0.09/0.28 ( ! [X0 : $i] : (($true != $true) | ($false = (((^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ c1))) | ($true = (((^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK0))) | ($false = ((sK2 @ X0))) | (((sK1 @ sK2)) != X0)) )),
% 0.09/0.28 inference(constrained_superposition,[],[f170,f35])).
% 0.09/0.28 thf(f301,plain,(
% 0.09/0.28 ( ! [X0 : $i] : (($false = (((^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ c1))) | ($true = (((^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK0))) | ($false = ((sK2 @ X0))) | (((sK1 @ sK2)) != X0)) )),
% 0.09/0.28 inference(trivial_inequality_removal,[],[f278])).
% 0.09/0.28 thf(f302,plain,(
% 0.09/0.28 ( ! [X0 : $i] : (($false = ((sK2 @ c1))) | ($true = ((sK2 @ sK0))) | ($false = ((sK2 @ X0))) | (((sK1 @ sK2)) != X0)) )),
% 0.09/0.28 inference(beta-eta_normalization,[],[f301])).
% 0.09/0.28 thf(f343,plain,(
% 0.09/0.28 ( ! [X0 : $i] : (($true = $false) | ($true = ((sK2 @ sK0))) | ($false = ((sK2 @ X0))) | (((sK1 @ sK2)) != X0)) )),
% 0.09/0.28 inference(forward_demodulation,[],[f302,f32])).
% 0.09/0.28 thf(f344,plain,(
% 0.09/0.28 ( ! [X0 : $i] : (($true = ((sK2 @ sK0))) | ($false = ((sK2 @ X0))) | (((sK1 @ sK2)) != X0)) )),
% 0.09/0.28 inference(trivial_inequality_removal,[],[f343])).
% 0.09/0.28 thf(f345,plain,(
% 0.09/0.28 ( ! [X0 : $i] : (($true = $false) | ($false = ((sK2 @ X0))) | (((sK1 @ sK2)) != X0)) )),
% 0.09/0.28 inference(forward_demodulation,[],[f344,f99])).
% 0.09/0.28 thf(f346,plain,(
% 0.09/0.28 ( ! [X0 : $i] : (($false = ((sK2 @ X0))) | (((sK1 @ sK2)) != X0)) )),
% 0.09/0.28 inference(trivial_inequality_removal,[],[f345])).
% 0.09/0.28 thf(f347,plain,(
% 0.09/0.28 spl3_5),
% 0.09/0.28 inference(avatar_split_clause,[],[f346,f185])).
% 0.09/0.28 thf(f519,plain,(
% 0.09/0.28 ($false = ((sK2 @ (sK1 @ sK2)))) | ~spl3_5),
% 0.09/0.28 inference(equality_resolution,[],[f186])).
% 0.09/0.28 thf(f566,plain,(
% 0.09/0.28 ($false != $false) | ($false = (((^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ c1))) | ($true = (((^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK0))) | ~spl3_5),
% 0.09/0.28 inference(constrained_superposition,[],[f82,f519])).
% 0.09/0.28 thf(f581,plain,(
% 0.09/0.28 ($false = (((^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ c1))) | ($true = (((^[Y0 : $i]: (sK2 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK0))) | ~spl3_5),
% 0.09/0.28 inference(trivial_inequality_removal,[],[f566])).
% 0.09/0.28 thf(f582,plain,(
% 0.09/0.28 ($false = ((sK2 @ c1))) | ($true = ((sK2 @ sK0))) | ~spl3_5),
% 0.09/0.28 inference(beta-eta_normalization,[],[f581])).
% 0.09/0.28 thf(f592,plain,(
% 0.09/0.28 ($true = $false) | ($true = ((sK2 @ sK0))) | ~spl3_5),
% 0.09/0.28 inference(forward_demodulation,[],[f582,f32])).
% 0.09/0.28 thf(f593,plain,(
% 0.09/0.28 ($true = ((sK2 @ sK0))) | ~spl3_5),
% 0.09/0.28 inference(trivial_inequality_removal,[],[f592])).
% 0.09/0.28 thf(f596,plain,(
% 0.09/0.28 ($true = $false) | ~spl3_5),
% 0.09/0.28 inference(forward_demodulation,[],[f593,f99])).
% 0.09/0.28 thf(f597,plain,(
% 0.09/0.28 $false | ~spl3_5),
% 0.09/0.28 inference(trivial_inequality_removal,[],[f596])).
% 0.09/0.28 thf(f598,plain,(
% 0.09/0.28 ~spl3_5),
% 0.09/0.28 inference(avatar_contradiction_clause,[],[f597])).
% 0.09/0.28 cnf(s11, plain, spl3_5, inference(sat_conversion,[],[f347])).
% 0.09/0.28 cnf(s14, plain, ~spl3_5, inference(sat_conversion,[],[f598])).
% 0.09/0.28 cnf(s15, plain, $false, inference(rat,[],[s11,s14])).
% 0.09/0.28 thf(f599,plain,(
% 0.09/0.28 $false),
% 0.09/0.28 inference(avatar_sat_refutation,[],[s15])).
% 0.09/0.28 % SZS output end Proof for theBenchmark
% 0.09/0.28 % (3971851)------------------------------
% 0.09/0.28 % (3971851)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.28 % (3971851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.28 % (3971851)CaDiCaL version: 2.1.3
% 0.09/0.28 % (3971851)Termination reason: Refutation
% 0.09/0.28 % (3971851)Time elapsed: 0.012 s
% 0.09/0.28 % (3971851)Peak memory usage: 13 MB
% 0.09/0.28 % (3971851)Instructions burned: 37 (million)
% 0.09/0.28 % (3971843)Success in time 0.041 s
% 0.09/0.28 % Vampire exiting
%------------------------------------------------------------------------------