%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU970^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 08:34:29 AM UTC 2026
% Result : Theorem 0.05s 0.18s
% Output : Refutation 0.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU970^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.05/0.12 % Computer : n012.cluster.edu
% 0.05/0.12 % Model : x86_64 x86_64
% 0.05/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.12 % Memory : 8046.5625MB
% 0.05/0.12 % OS : Linux 6.8.0-71-generic
% 0.05/0.12 % CPULimit : 300
% 0.05/0.12 % WCLimit : 300
% 0.05/0.12 % DateTime : Tue Sep 29 14:53:13 UTC 2026
% 0.05/0.12 % CPUTime :
% 0.05/0.12 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.05/0.14 Running first-order model finding
% 0.05/0.14 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
% 0.05/0.18 % (211904)Will run a generic schedule for satisfiability detection.
% 0.05/0.18 % (211910)% WARNING: option uhcvi not known.
% 0.05/0.18 % (211911)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1591479022:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.05/0.18 % (211909)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3948662632_2999 on theBenchmark for (2999ds/0Mi)
% 0.05/0.18 % (211910)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=399132846:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.05/0.18 % (211912)dis+10_1_sil=32000:sp=arity:random_seed=428658511:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.05/0.18 % (211913)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3162815797:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.05/0.18 % (211914)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1605829417:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.05/0.18 % (211910)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.05/0.18 % (211915)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3053327682:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.05/0.18 % (211913)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.05/0.18 % Exception at run slice level
% 0.05/0.18 User error: % (211910)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.05/0.18 Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.05/0.18 % (211923)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4245959024:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.05/0.18 % Exception at run slice level
% 0.05/0.18 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.05/0.18 % (211910) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-211904-211910"...
% 0.05/0.18 % (211912) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-211904-211912"...
% 0.05/0.18 % (211910)...printing done.
% 0.05/0.18 % (211910)Refutation found. Thanks to Tanya!
% 0.05/0.18 % SZS status Theorem for theBenchmark
% 0.05/0.18 % SZS output start Proof for theBenchmark
% 0.05/0.18 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.05/0.18 thf(func_def_0, type, s: ($i > $i)).
% 0.05/0.18 thf(func_def_1, type, cCKB_E2: ($i > $i > $o)).
% 0.05/0.18 thf(func_def_3, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.05/0.18 thf(func_def_4, type, vIMP: ($o > $o > $o)).
% 0.05/0.18 thf(func_def_5, type, vAND: ($o > $o > $o)).
% 0.05/0.18 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.05/0.18 thf(func_def_7, type, db2: !>[X0: $tType]:(X0)).
% 0.05/0.18 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.05/0.18 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.05/0.18 thf(func_def_15, type, vNOT: ($o > $o)).
% 0.05/0.18 thf(func_def_16, type, sK3: (($i > $o) > $i)).
% 0.05/0.18 thf(func_def_17, type, sK4: (($i > $o) > $i)).
% 0.05/0.18 thf(func_def_18, type, sK5: ($i > $o)).
% 0.05/0.18 thf(func_def_19, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.05/0.18 thf(f1,axiom,(
% 0.05/0.18 (cCKB_E2 = (^[X0 : $i, X1 : $i] : (! [X2 : ($i > $o)] : ((! [X3 : $i] : ((X2 @ X3) => (X2 @ (s @ (s @ X3)))) & (X2 @ X0)) => (X2 @ X1)))))),
% 0.05/0.18 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB_E2_def)).
% 0.05/0.18 thf(f2,conjecture,(
% 0.05/0.18 ! [X0 : $i,X1 : $i,X2 : $i] : (((cCKB_E2 @ X1 @ X2) & (cCKB_E2 @ X0 @ X1)) => (cCKB_E2 @ X0 @ X2))),
% 0.05/0.18 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB_L34000_pme)).
% 0.05/0.18 thf(f3,negated_conjecture,(
% 0.05/0.18 ~ ! [X0 : $i,X1 : $i,X2 : $i] : (((cCKB_E2 @ X1 @ X2) & (cCKB_E2 @ X0 @ X1)) => (cCKB_E2 @ X0 @ X2))),
% 0.05/0.18 inference(negated_conjecture,[status(cth)],[f2])).
% 0.05/0.18 thf(f4,plain,(
% 0.05/0.18 (cCKB_E2 = (^[X0 : $i, X1 : $i] : (! [X2 : ($i > $o)] : ((! [X3 : $i] : ((X2 @ X3) => (X2 @ (s @ (s @ X3)))) & (X2 @ X0)) => (X2 @ X1)))))),
% 0.05/0.18 inference(rectify,[],[f1])).
% 0.05/0.18 thf(f5,plain,(
% 0.05/0.18 (cCKB_E2 = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((Y2 @ Y0) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ (s @ Y3))))))) => (Y2 @ Y1))))))))),
% 0.05/0.18 inference(fool_elimination,[],[f4])).
% 0.05/0.18 thf(f6,plain,(
% 0.05/0.18 ~ ! [X0 : $i,X1 : $i,X2 : $i] : (((cCKB_E2 @ X1 @ X2) & (cCKB_E2 @ X0 @ X1)) => (cCKB_E2 @ X0 @ X2))),
% 0.05/0.18 inference(rectify,[],[f3])).
% 0.05/0.18 thf(f7,plain,(
% 0.05/0.18 ~ ! [X0 : $i,X1 : $i,X2 : $i] : (((((cCKB_E2 @ X1 @ X2)) = $true) & (((cCKB_E2 @ X0 @ X1)) = $true)) => (((cCKB_E2 @ X0 @ X2)) = $true))),
% 0.05/0.18 inference(fool_elimination,[],[f6])).
% 0.05/0.18 thf(f8,plain,(
% 0.05/0.18 ? [X0 : $i,X1 : $i,X2 : $i] : ((((cCKB_E2 @ X0 @ X2)) != $true) & ((((cCKB_E2 @ X1 @ X2)) = $true) & (((cCKB_E2 @ X0 @ X1)) = $true)))),
% 0.05/0.18 inference(ennf_transformation,[],[f7])).
% 0.05/0.18 thf(f9,plain,(
% 0.05/0.18 ? [X0 : $i,X1 : $i,X2 : $i] : ((((cCKB_E2 @ X0 @ X2)) != $true) & (((cCKB_E2 @ X1 @ X2)) = $true) & (((cCKB_E2 @ X0 @ X1)) = $true))),
% 0.05/0.18 inference(flattening,[],[f8])).
% 0.05/0.18 thf(f10,plain,(
% 0.05/0.18 ($true != ((cCKB_E2 @ sK0 @ sK2))) & ($true = ((cCKB_E2 @ sK1 @ sK2))) & ($true = ((cCKB_E2 @ sK0 @ sK1)))),
% 0.05/0.18 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f9])).
% 0.05/0.18 thf(f11,plain,(
% 0.05/0.18 (cCKB_E2 = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((Y2 @ Y0) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ (s @ Y3))))))) => (Y2 @ Y1))))))))),
% 0.05/0.18 inference(cnf_transformation,[],[f5])).
% 0.05/0.18 thf(f12,plain,(
% 0.05/0.18 ($true = ((cCKB_E2 @ sK0 @ sK1)))),
% 0.05/0.18 inference(cnf_transformation,[],[f10])).
% 0.05/0.18 thf(f13,plain,(
% 0.05/0.18 ($true = ((cCKB_E2 @ sK1 @ sK2)))),
% 0.05/0.18 inference(cnf_transformation,[],[f10])).
% 0.05/0.18 thf(f14,plain,(
% 0.05/0.18 ($true != ((cCKB_E2 @ sK0 @ sK2)))),
% 0.05/0.18 inference(cnf_transformation,[],[f10])).
% 0.05/0.18 thf(f16,definition,(
% 0.05/0.18 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.05/0.18 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.05/0.18 thf(f17,plain,(
% 0.05/0.18 ($true != (((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((Y2 @ Y0) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ (s @ Y3))))))) => (Y2 @ Y1))))))) @ sK0 @ sK2)))),
% 0.05/0.18 inference(definition_unfolding,[],[f14,f11])).
% 0.05/0.18 thf(f18,plain,(
% 0.05/0.18 ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((Y2 @ Y0) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ (s @ Y3))))))) => (Y2 @ Y1))))))) @ sK1 @ sK2)))),
% 0.05/0.18 inference(definition_unfolding,[],[f13,f11])).
% 0.05/0.18 thf(f19,plain,(
% 0.05/0.18 ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (((Y2 @ Y0) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y2 @ (s @ (s @ Y3))))))) => (Y2 @ Y1))))))) @ sK0 @ sK1)))),
% 0.05/0.18 inference(definition_unfolding,[],[f12,f11])).
% 0.05/0.18 thf(f20,plain,(
% 0.05/0.18 ($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ sK0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ (s @ Y1))))))) => (Y0 @ sK1))))))),
% 0.05/0.18 inference(beta-eta_normalization,[],[f19])).
% 0.05/0.18 thf(f21,plain,(
% 0.05/0.18 ( ! [X1 : ($i > $o)] : (($true = (((^[Y0 : $i > $o]: (((Y0 @ sK0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ (s @ Y1))))))) => (Y0 @ sK1))) @ X1)))) )),
% 0.05/0.18 inference(pi_proxy_clausification,[],[f20])).
% 0.05/0.18 thf(f22,plain,(
% 0.05/0.18 ( ! [X1 : ($i > $o)] : (($true = ((((X1 @ sK0) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ (s @ Y0))))))) => (X1 @ sK1))))) )),
% 0.05/0.18 inference(beta-eta_normalization,[],[f21])).
% 0.05/0.18 thf(f23,plain,(
% 0.05/0.18 ( ! [X1 : ($i > $o)] : (($false = (((X1 @ sK0) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ (s @ Y0))))))))) | ($true = ((X1 @ sK1)))) )),
% 0.05/0.18 inference(imp_proxy_clausification,[],[f22])).
% 0.05/0.18 thf(f24,plain,(
% 0.05/0.18 ( ! [X1 : ($i > $o)] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ (s @ Y0)))))))) | ($true = ((X1 @ sK1))) | ($false = ((X1 @ sK0)))) )),
% 0.05/0.18 inference(and_proxy_clausification,[],[f23])).
% 0.05/0.18 thf(f25,plain,(
% 0.05/0.18 ( ! [X1 : ($i > $o)] : (($false = (((^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ (s @ Y0))))) @ (sK3 @ X1)))) | ($true = ((X1 @ sK1))) | ($false = ((X1 @ sK0)))) )),
% 0.05/0.18 inference(sigma_proxy_clausification,[],[f24])).
% 0.05/0.18 thf(f26,plain,(
% 0.05/0.18 ( ! [X1 : ($i > $o)] : (($false = (((X1 @ (sK3 @ X1)) => (X1 @ (s @ (s @ (sK3 @ X1))))))) | ($true = ((X1 @ sK1))) | ($false = ((X1 @ sK0)))) )),
% 0.05/0.18 inference(beta-eta_normalization,[],[f25])).
% 0.05/0.18 thf(f27,plain,(
% 0.05/0.18 ( ! [X1 : ($i > $o)] : (($false = ((X1 @ (s @ (s @ (sK3 @ X1)))))) | ($true = ((X1 @ sK1))) | ($false = ((X1 @ sK0)))) )),
% 0.05/0.18 inference(imp_proxy_clausification,[],[f26])).
% 0.05/0.18 thf(f28,plain,(
% 0.05/0.18 ( ! [X1 : ($i > $o)] : (($true = ((X1 @ (sK3 @ X1)))) | ($true = ((X1 @ sK1))) | ($false = ((X1 @ sK0)))) )),
% 0.05/0.18 inference(imp_proxy_clausification,[],[f26])).
% 0.05/0.18 thf(f29,plain,(
% 0.05/0.18 ($true = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ sK1) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ (s @ Y1))))))) => (Y0 @ sK2))))))),
% 0.05/0.18 inference(beta-eta_normalization,[],[f18])).
% 0.05/0.18 thf(f30,plain,(
% 0.05/0.18 ( ! [X1 : ($i > $o)] : (($true = (((^[Y0 : $i > $o]: (((Y0 @ sK1) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ (s @ Y1))))))) => (Y0 @ sK2))) @ X1)))) )),
% 0.05/0.18 inference(pi_proxy_clausification,[],[f29])).
% 0.05/0.18 thf(f31,plain,(
% 0.05/0.18 ( ! [X1 : ($i > $o)] : (($true = ((((X1 @ sK1) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ (s @ Y0))))))) => (X1 @ sK2))))) )),
% 0.05/0.18 inference(beta-eta_normalization,[],[f30])).
% 0.05/0.18 thf(f32,plain,(
% 0.05/0.18 ( ! [X1 : ($i > $o)] : (($false = (((X1 @ sK1) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ (s @ Y0))))))))) | ($true = ((X1 @ sK2)))) )),
% 0.05/0.18 inference(imp_proxy_clausification,[],[f31])).
% 0.05/0.18 thf(f33,plain,(
% 0.05/0.18 ( ! [X1 : ($i > $o)] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ (s @ Y0)))))))) | ($true = ((X1 @ sK2))) | ($false = ((X1 @ sK1)))) )),
% 0.05/0.18 inference(and_proxy_clausification,[],[f32])).
% 0.05/0.18 thf(f34,plain,(
% 0.05/0.18 ( ! [X1 : ($i > $o)] : (($false = (((^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (s @ (s @ Y0))))) @ (sK4 @ X1)))) | ($true = ((X1 @ sK2))) | ($false = ((X1 @ sK1)))) )),
% 0.05/0.18 inference(sigma_proxy_clausification,[],[f33])).
% 0.05/0.18 thf(f35,plain,(
% 0.05/0.18 ( ! [X1 : ($i > $o)] : (($false = (((X1 @ (sK4 @ X1)) => (X1 @ (s @ (s @ (sK4 @ X1))))))) | ($true = ((X1 @ sK2))) | ($false = ((X1 @ sK1)))) )),
% 0.05/0.18 inference(beta-eta_normalization,[],[f34])).
% 0.05/0.18 thf(f36,plain,(
% 0.05/0.18 ( ! [X1 : ($i > $o)] : (($false = ((X1 @ (s @ (s @ (sK4 @ X1)))))) | ($true = ((X1 @ sK2))) | ($false = ((X1 @ sK1)))) )),
% 0.05/0.18 inference(imp_proxy_clausification,[],[f35])).
% 0.05/0.18 thf(f37,plain,(
% 0.05/0.18 ( ! [X1 : ($i > $o)] : (($true = ((X1 @ (sK4 @ X1)))) | ($true = ((X1 @ sK2))) | ($false = ((X1 @ sK1)))) )),
% 0.05/0.18 inference(imp_proxy_clausification,[],[f35])).
% 0.05/0.18 thf(f38,plain,(
% 0.05/0.18 ($true != ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ sK0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ (s @ Y1))))))) => (Y0 @ sK2))))))),
% 0.05/0.18 inference(beta-eta_normalization,[],[f17])).
% 0.05/0.18 thf(f39,plain,(
% 0.05/0.18 ($false = (((^[Y0 : $i > $o]: (((Y0 @ sK0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (s @ (s @ Y1))))))) => (Y0 @ sK2))) @ sK5)))),
% 0.05/0.18 inference(sigma_proxy_clausification,[],[f38])).
% 0.05/0.18 thf(f40,plain,(
% 0.05/0.18 ($false = ((((sK5 @ sK0) & (!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) => (sK5 @ (s @ (s @ Y0))))))) => (sK5 @ sK2))))),
% 0.05/0.18 inference(beta-eta_normalization,[],[f39])).
% 0.05/0.18 thf(f41,plain,(
% 0.05/0.18 ($false = ((sK5 @ sK2)))),
% 0.05/0.18 inference(imp_proxy_clausification,[],[f40])).
% 0.05/0.18 thf(f42,plain,(
% 0.05/0.18 ($true = (((sK5 @ sK0) & (!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) => (sK5 @ (s @ (s @ Y0)))))))))),
% 0.05/0.18 inference(imp_proxy_clausification,[],[f40])).
% 0.05/0.18 thf(f43,plain,(
% 0.05/0.18 ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0) => (sK5 @ (s @ (s @ Y0))))))))),
% 0.05/0.18 inference(and_proxy_clausification,[],[f42])).
% 0.05/0.18 thf(f44,plain,(
% 0.05/0.18 ($true = ((sK5 @ sK0)))),
% 0.05/0.18 inference(and_proxy_clausification,[],[f42])).
% 0.05/0.18 thf(f45,plain,(
% 0.05/0.18 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((sK5 @ Y0) => (sK5 @ (s @ (s @ Y0))))) @ X1)))) )),
% 0.05/0.18 inference(pi_proxy_clausification,[],[f43])).
% 0.05/0.18 thf(f46,plain,(
% 0.05/0.18 ( ! [X1 : $i] : (($true = (((sK5 @ X1) => (sK5 @ (s @ (s @ X1))))))) )),
% 0.05/0.18 inference(beta-eta_normalization,[],[f45])).
% 0.05/0.18 thf(f47,plain,(
% 0.05/0.18 ( ! [X1 : $i] : (($true = ((sK5 @ (s @ (s @ X1))))) | ($false = ((sK5 @ X1)))) )),
% 0.05/0.18 inference(imp_proxy_clausification,[],[f46])).
% 0.05/0.18 thf(f66,plain,(
% 0.05/0.18 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ sK0))) | ($true = ((X0 @ sK1))) | ($false = ((X0 @ sK0))) | ($false != ((X0 @ (sK3 @ X0))))) )),
% 0.05/0.18 inference(equality_factoring,[],[f28])).
% 0.05/0.18 thf(f90,plain,(
% 0.05/0.18 ( ! [X0 : ($i > $o)] : (($false != ((X0 @ (sK3 @ X0)))) | ($false = ((X0 @ sK0))) | ($true = ((X0 @ sK1)))) )),
% 0.05/0.18 inference(forward_subsumption_resolution,[],[f66,f16])).
% 0.05/0.18 thf(f302,plain,(
% 0.05/0.18 ( ! [X0 : $i] : (($true = $false) | ($true = (((^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK1))) | ($false = (((^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK0))) | ($false = ((sK5 @ X0))) | (((sK3 @ sK5)) != X0)) )),
% 0.05/0.18 inference(constrained_superposition,[],[f27,f47])).
% 0.05/0.18 thf(f304,plain,(
% 0.05/0.18 ( ! [X0 : $i] : (($true = $false) | ($true = (((^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK2))) | ($false = (((^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK1))) | ($false = ((sK5 @ X0))) | (((sK4 @ sK5)) != X0)) )),
% 0.05/0.18 inference(constrained_superposition,[],[f36,f47])).
% 0.05/0.18 thf(f308,plain,(
% 0.05/0.18 ( ! [X0 : $i] : (($true = (((^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK2))) | ($false = (((^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK1))) | ($false = ((sK5 @ X0))) | (((sK4 @ sK5)) != X0)) )),
% 0.05/0.18 inference(trivial_inequality_removal,[],[f304])).
% 0.05/0.18 thf(f309,plain,(
% 0.05/0.18 ( ! [X0 : $i] : (($true = ((sK5 @ sK2))) | ($false = ((sK5 @ sK1))) | ($false = ((sK5 @ X0))) | (((sK4 @ sK5)) != X0)) )),
% 0.05/0.18 inference(beta-eta_normalization,[],[f308])).
% 0.05/0.18 thf(f312,plain,(
% 0.05/0.18 ( ! [X0 : $i] : (($true = (((^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK1))) | ($false = (((^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK0))) | ($false = ((sK5 @ X0))) | (((sK3 @ sK5)) != X0)) )),
% 0.05/0.18 inference(trivial_inequality_removal,[],[f302])).
% 0.05/0.18 thf(f313,plain,(
% 0.05/0.18 ( ! [X0 : $i] : (($true = ((sK5 @ sK1))) | ($false = ((sK5 @ sK0))) | ($false = ((sK5 @ X0))) | (((sK3 @ sK5)) != X0)) )),
% 0.05/0.18 inference(beta-eta_normalization,[],[f312])).
% 0.05/0.18 thf(f323,plain,(
% 0.05/0.18 ( ! [X0 : $i] : (($true = $false) | ($false = ((sK5 @ sK1))) | ($false = ((sK5 @ X0))) | (((sK4 @ sK5)) != X0)) )),
% 0.05/0.18 inference(forward_demodulation,[],[f309,f41])).
% 0.05/0.18 thf(f324,plain,(
% 0.05/0.18 ( ! [X0 : $i] : (($false = ((sK5 @ sK1))) | ($false = ((sK5 @ X0))) | (((sK4 @ sK5)) != X0)) )),
% 0.05/0.18 inference(trivial_inequality_removal,[],[f323])).
% 0.05/0.18 thf(f325,plain,(
% 0.05/0.18 ( ! [X0 : $i] : (($true = $false) | ($true = ((sK5 @ sK1))) | ($false = ((sK5 @ X0))) | (((sK3 @ sK5)) != X0)) )),
% 0.05/0.18 inference(forward_demodulation,[],[f313,f44])).
% 0.05/0.18 thf(f326,plain,(
% 0.05/0.18 ( ! [X0 : $i] : (($true = ((sK5 @ sK1))) | ($false = ((sK5 @ X0))) | (((sK3 @ sK5)) != X0)) )),
% 0.05/0.18 inference(trivial_inequality_removal,[],[f325])).
% 0.05/0.18 thf(f333,definition,(
% 0.05/0.18 spl6_8 <=> ! [X0 : $i] : (($false = ((sK5 @ X0))) | (((sK4 @ sK5)) != X0))),
% 0.05/0.18 introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition])).
% 0.05/0.18 thf(f334,plain,(
% 0.05/0.18 ( ! [X0 : $i] : ((((sK4 @ sK5)) != X0) | ($false = ((sK5 @ X0)))) ) | ~spl6_8),
% 0.05/0.18 inference(avatar_component_clause,[],[f333])).
% 0.05/0.18 thf(f336,definition,(
% 0.05/0.18 spl6_9 <=> ($false = ((sK5 @ sK1)))),
% 0.05/0.18 introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition])).
% 0.05/0.18 thf(f338,plain,(
% 0.05/0.18 ($false = ((sK5 @ sK1))) | ~spl6_9),
% 0.05/0.18 inference(avatar_component_clause,[],[f336])).
% 0.05/0.18 thf(f339,plain,(
% 0.05/0.18 spl6_8 | spl6_9),
% 0.05/0.18 inference(avatar_split_clause,[],[f324,f336,f333])).
% 0.05/0.18 thf(f341,definition,(
% 0.05/0.18 spl6_10 <=> ! [X0 : $i] : (($false = ((sK5 @ X0))) | (((sK3 @ sK5)) != X0))),
% 0.05/0.18 introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition])).
% 0.05/0.18 thf(f342,plain,(
% 0.05/0.18 ( ! [X0 : $i] : ((((sK3 @ sK5)) != X0) | ($false = ((sK5 @ X0)))) ) | ~spl6_10),
% 0.05/0.18 inference(avatar_component_clause,[],[f341])).
% 0.05/0.18 thf(f344,definition,(
% 0.05/0.18 spl6_11 <=> ($true = ((sK5 @ sK1)))),
% 0.05/0.18 introduced(definition,[new_symbols(definition,[spl6_11])],[avatar_definition])).
% 0.05/0.18 thf(f346,plain,(
% 0.05/0.18 ($true = ((sK5 @ sK1))) | ~spl6_11),
% 0.05/0.18 inference(avatar_component_clause,[],[f344])).
% 0.05/0.18 thf(f347,plain,(
% 0.05/0.18 spl6_10 | spl6_11),
% 0.05/0.18 inference(avatar_split_clause,[],[f326,f344,f341])).
% 0.05/0.18 thf(f707,plain,(
% 0.05/0.18 ($true = $false) | (~spl6_9 | ~spl6_11)),
% 0.05/0.18 inference(forward_demodulation,[],[f346,f338])).
% 0.05/0.18 thf(f708,plain,(
% 0.05/0.18 $false | (~spl6_9 | ~spl6_11)),
% 0.05/0.18 inference(trivial_inequality_removal,[],[f707])).
% 0.05/0.18 thf(f709,plain,(
% 0.05/0.18 ~spl6_9 | ~spl6_11),
% 0.05/0.18 inference(avatar_contradiction_clause,[],[f708])).
% 0.05/0.18 thf(f711,plain,(
% 0.05/0.18 ($false = ((sK5 @ (sK4 @ sK5)))) | ~spl6_8),
% 0.05/0.18 inference(equality_resolution,[],[f334])).
% 0.05/0.18 thf(f719,plain,(
% 0.05/0.18 ($true = $false) | ($true = (((^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK2))) | ($false = (((^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK1))) | ~spl6_8),
% 0.05/0.18 inference(constrained_superposition,[],[f37,f711])).
% 0.05/0.18 thf(f728,plain,(
% 0.05/0.18 ($true = (((^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK2))) | ($false = (((^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK1))) | ~spl6_8),
% 0.05/0.18 inference(trivial_inequality_removal,[],[f719])).
% 0.05/0.18 thf(f729,plain,(
% 0.05/0.18 ($true = ((sK5 @ sK2))) | ($false = ((sK5 @ sK1))) | ~spl6_8),
% 0.05/0.18 inference(beta-eta_normalization,[],[f728])).
% 0.05/0.18 thf(f745,plain,(
% 0.05/0.18 ($false = ((sK5 @ (sK3 @ sK5)))) | ~spl6_10),
% 0.05/0.18 inference(equality_resolution,[],[f342])).
% 0.05/0.18 thf(f751,plain,(
% 0.05/0.18 ($false != $false) | ($false = (((^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK0))) | ($true = (((^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK1))) | ~spl6_10),
% 0.05/0.18 inference(constrained_superposition,[],[f90,f745])).
% 0.05/0.18 thf(f769,plain,(
% 0.05/0.18 ($false = (((^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK0))) | ($true = (((^[Y0 : $i]: (sK5 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ sK1))) | ~spl6_10),
% 0.05/0.18 inference(trivial_inequality_removal,[],[f751])).
% 0.05/0.18 thf(f770,plain,(
% 0.05/0.18 ($false = ((sK5 @ sK0))) | ($true = ((sK5 @ sK1))) | ~spl6_10),
% 0.05/0.18 inference(beta-eta_normalization,[],[f769])).
% 0.05/0.18 thf(f783,plain,(
% 0.05/0.18 ($true = $false) | ($true = ((sK5 @ sK1))) | ~spl6_10),
% 0.05/0.18 inference(forward_demodulation,[],[f770,f44])).
% 0.05/0.18 thf(f784,plain,(
% 0.05/0.18 ($true = ((sK5 @ sK1))) | ~spl6_10),
% 0.05/0.18 inference(trivial_inequality_removal,[],[f783])).
% 0.05/0.18 thf(f788,plain,(
% 0.05/0.18 ($true = $false) | (~spl6_9 | ~spl6_10)),
% 0.05/0.18 inference(forward_demodulation,[],[f784,f338])).
% 0.05/0.18 thf(f789,plain,(
% 0.05/0.18 $false | (~spl6_9 | ~spl6_10)),
% 0.05/0.18 inference(trivial_inequality_removal,[],[f788])).
% 0.05/0.18 thf(f790,plain,(
% 0.05/0.18 ~spl6_9 | ~spl6_10),
% 0.05/0.18 inference(avatar_contradiction_clause,[],[f789])).
% 0.05/0.18 thf(f791,plain,(
% 0.05/0.18 ($true = $false) | ($false = ((sK5 @ sK1))) | ~spl6_8),
% 0.05/0.18 inference(forward_demodulation,[],[f729,f41])).
% 0.05/0.18 thf(f792,plain,(
% 0.05/0.18 ($false = ((sK5 @ sK1))) | ~spl6_8),
% 0.05/0.18 inference(trivial_inequality_removal,[],[f791])).
% 0.05/0.18 thf(f800,plain,(
% 0.05/0.18 spl6_9 | ~spl6_8),
% 0.05/0.18 inference(avatar_split_clause,[],[f792,f333,f336])).
% 0.05/0.18 cnf(s6, plain, spl6_8 | spl6_9, inference(sat_conversion,[],[f339])).
% 0.05/0.18 cnf(s7, plain, spl6_10 | spl6_11, inference(sat_conversion,[],[f347])).
% 0.05/0.18 cnf(s19, plain, ~spl6_9 | ~spl6_11, inference(sat_conversion,[],[f709])).
% 0.05/0.18 cnf(s20, plain, ~spl6_9 | ~spl6_10, inference(sat_conversion,[],[f790])).
% 0.05/0.18 cnf(s22, plain, ~spl6_8 | spl6_9, inference(sat_conversion,[],[f800])).
% 0.05/0.18 cnf(s26, plain, ~spl6_9, inference(rat,[],[s7,s19,s20])).
% 0.05/0.18 cnf(s27, plain, ~spl6_8, inference(rat,[],[s22,s26])).
% 0.05/0.18 cnf(s29, plain, $false, inference(rat,[],[s6,s26,s27])).
% 0.05/0.18 thf(f801,plain,(
% 0.05/0.18 $false),
% 0.05/0.18 inference(avatar_sat_refutation,[],[s29])).
% 0.05/0.18 % SZS output end Proof for theBenchmark
% 0.05/0.18 % (211910)------------------------------
% 0.05/0.18 % (211910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.05/0.18 % (211910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.05/0.18 % (211910)CaDiCaL version: 2.1.3
% 0.05/0.18 % (211910)Termination reason: Refutation
% 0.05/0.18 % (211910)Time elapsed: 0.014 s
% 0.05/0.18 % (211910)Peak memory usage: 13 MB
% 0.05/0.18 % (211910)Instructions burned: 49 (million)
% 0.05/0.18 % (211904)Success in time 0.04 s
% 0.05/0.18 % Vampire exiting
%------------------------------------------------------------------------------