%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN025^3 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 08:20:02 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
% 0.00/0.03 % Problem : NUN025^3 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n014.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:06:16 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 0.22/0.29 % (2620670)Will run a generic schedule for satisfiability detection.
% 0.22/0.29 % (2620675)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=48709368_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.29 % Exception at run slice level
% 0.22/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.29 % (2620676)% WARNING: option uhcvi not known.
% 0.22/0.29 % (2620676)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=593246121:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.29 % (2620677)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=719592131:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.29 % (2620678)dis+10_1_sil=32000:sp=arity:random_seed=4280794909:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.29 % (2620679)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2122720279:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.29 % (2620676)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.29 % (2620680)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3286820690:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.29 % (2620681)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=618996500:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.29 % (2620679)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.29 % (2620676)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.29 % (2620683)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4058039540:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.22/0.29 % Exception at run slice level
% 0.22/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.29 % (2620691)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1702883456:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.29 % (2620681) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2620670-2620681"...
% 0.22/0.29 % (2620681)...printing done.
% 0.22/0.29 % (2620691) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2620670-2620691"...
% 0.22/0.29 % (2620681)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, sTfun: ($tType * $tType) > $tType).
% 0.22/0.29 thf(func_def_1, type, s: ($i > $i)).
% 0.22/0.29 thf(func_def_2, type, ite: ($o > $i > $i > $i)).
% 0.22/0.29 thf(func_def_3, type, h: ($i > $i)).
% 0.22/0.29 thf(func_def_7, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.29 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.22/0.29 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.29 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.29 thf(f1,conjecture,(
% 0.22/0.29 (! [X3 : $i] : (((h @ X3)) = ((ite @ (X3 = zero) @ (s @ zero) @ (ite @ (X3 = ((s @ zero))) @ zero @ (s @ zero))))) & ! [X3 : $i] : (((s @ X3)) != X3) & ! [X3 : $i] : (((s @ X3)) != zero) & ! [X0 : $o,X1 : $i,X2 : $i] : (~X0 => (((ite @ X0 @ X1 @ X2)) = X2)) & ! [X0 : $o,X1 : $i,X2 : $i] : (X0 => (((ite @ X0 @ X1 @ X2)) = X1))) => ? [X4 : ($i > $i)] : ((((X4 @ (s @ (s @ zero)))) = ((s @ zero))) & (((X4 @ (s @ zero))) = zero) & (((X4 @ zero)) = ((s @ zero))))),
% 0.22/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n10)).
% 0.22/0.29 thf(f2,negated_conjecture,(
% 0.22/0.29 ~((! [X3 : $i] : (((h @ X3)) = ((ite @ (X3 = zero) @ (s @ zero) @ (ite @ (X3 = ((s @ zero))) @ zero @ (s @ zero))))) & ! [X3 : $i] : (((s @ X3)) != X3) & ! [X3 : $i] : (((s @ X3)) != zero) & ! [X0 : $o,X1 : $i,X2 : $i] : (~X0 => (((ite @ X0 @ X1 @ X2)) = X2)) & ! [X0 : $o,X1 : $i,X2 : $i] : (X0 => (((ite @ X0 @ X1 @ X2)) = X1))) => ? [X4 : ($i > $i)] : ((((X4 @ (s @ (s @ zero)))) = ((s @ zero))) & (((X4 @ (s @ zero))) = zero) & (((X4 @ zero)) = ((s @ zero)))))),
% 0.22/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.29 thf(f3,plain,(
% 0.22/0.29 ~((! [X0 : $i] : (((h @ X0)) = ((ite @ (zero = X0) @ (s @ zero) @ (ite @ (((s @ zero)) = X0) @ zero @ (s @ zero))))) & ! [X1 : $i] : (((s @ X1)) != X1) & ! [X2 : $i] : (zero != ((s @ X2))) & ! [X3 : $o,X4 : $i,X5 : $i] : (~X3 => (((ite @ X3 @ X4 @ X5)) = X5)) & ! [X6 : $o,X7 : $i,X8 : $i] : (X6 => (((ite @ X6 @ X7 @ X8)) = X7))) => ? [X9 : ($i > $i)] : ((((s @ zero)) = ((X9 @ (s @ (s @ zero))))) & (zero = ((X9 @ (s @ zero)))) & (((s @ zero)) = ((X9 @ zero)))))),
% 0.22/0.29 inference(rectify,[],[f2])).
% 0.22/0.29 thf(f4,plain,(
% 0.22/0.29 ~((! [X0 : $i] : (((h @ X0)) = ((ite @ (zero = X0) @ (s @ zero) @ (ite @ ((s @ zero) = X0) @ zero @ (s @ zero))))) & ! [X1 : $i] : (((s @ X1)) != X1) & ! [X2 : $i] : (zero != ((s @ X2))) & ! [X3 : $o,X4 : $i,X5 : $i] : (~ ($true = X3) => (((ite @ X3 @ X4 @ X5)) = X5)) & ! [X6 : $o,X7 : $i,X8 : $i] : (($true = X6) => (((ite @ X6 @ X7 @ X8)) = X7))) => ? [X9 : ($i > $i)] : ((((s @ zero)) = ((X9 @ (s @ (s @ zero))))) & (zero = ((X9 @ (s @ zero)))) & (((s @ zero)) = ((X9 @ zero)))))),
% 0.22/0.29 inference(fool_elimination,[],[f3])).
% 0.22/0.29 thf(f5,plain,(
% 0.22/0.29 ~((! [X0 : $i] : (((h @ X0)) = ((ite @ (zero = X0) @ (s @ zero) @ (ite @ ((s @ zero) = X0) @ zero @ (s @ zero))))) & ! [X1 : $i] : (((s @ X1)) != X1) & ! [X2 : $i] : (zero != ((s @ X2))) & ! [X3 : $o,X4 : $i,X5 : $i] : (($true != X3) => (((ite @ X3 @ X4 @ X5)) = X5)) & ! [X6 : $o,X7 : $i,X8 : $i] : (($true = X6) => (((ite @ X6 @ X7 @ X8)) = X7))) => ? [X9 : ($i > $i)] : ((((s @ zero)) = ((X9 @ (s @ (s @ zero))))) & (zero = ((X9 @ (s @ zero)))) & (((s @ zero)) = ((X9 @ zero)))))),
% 0.22/0.29 inference(flattening,[],[f4])).
% 0.22/0.29 thf(f6,plain,(
% 0.22/0.29 ! [X9 : ($i > $i)] : ((((s @ zero)) != ((X9 @ (s @ (s @ zero))))) | (zero != ((X9 @ (s @ zero)))) | (((s @ zero)) != ((X9 @ zero)))) & (! [X0 : $i] : (((h @ X0)) = ((ite @ (zero = X0) @ (s @ zero) @ (ite @ ((s @ zero) = X0) @ zero @ (s @ zero))))) & ! [X1 : $i] : (((s @ X1)) != X1) & ! [X2 : $i] : (zero != ((s @ X2))) & ! [X3 : $o,X4 : $i,X5 : $i] : ((((ite @ X3 @ X4 @ X5)) = X5) | ($true = X3)) & ! [X6 : $o,X7 : $i,X8 : $i] : ((((ite @ X6 @ X7 @ X8)) = X7) | ($true != X6)))),
% 0.22/0.29 inference(ennf_transformation,[],[f5])).
% 0.22/0.29 thf(f7,plain,(
% 0.22/0.29 ! [X9 : ($i > $i)] : ((((s @ zero)) != ((X9 @ (s @ (s @ zero))))) | (zero != ((X9 @ (s @ zero)))) | (((s @ zero)) != ((X9 @ zero)))) & ! [X0 : $i] : (((h @ X0)) = ((ite @ (zero = X0) @ (s @ zero) @ (ite @ ((s @ zero) = X0) @ zero @ (s @ zero))))) & ! [X1 : $i] : (((s @ X1)) != X1) & ! [X2 : $i] : (zero != ((s @ X2))) & ! [X3 : $o,X4 : $i,X5 : $i] : ((((ite @ X3 @ X4 @ X5)) = X5) | ($true = X3)) & ! [X6 : $o,X7 : $i,X8 : $i] : ((((ite @ X6 @ X7 @ X8)) = X7) | ($true != X6))),
% 0.22/0.29 inference(flattening,[],[f6])).
% 0.22/0.29 thf(f8,plain,(
% 0.22/0.29 ! [X0 : ($i > $i)] : ((((s @ zero)) != ((X0 @ (s @ (s @ zero))))) | (zero != ((X0 @ (s @ zero)))) | (((s @ zero)) != ((X0 @ zero)))) & ! [X1 : $i] : (((h @ X1)) = ((ite @ (zero = X1) @ (s @ zero) @ (ite @ ((s @ zero) = X1) @ zero @ (s @ zero))))) & ! [X2 : $i] : (((s @ X2)) != X2) & ! [X3 : $i] : (((s @ X3)) != zero) & ! [X4 : $o,X5 : $i,X6 : $i] : ((((ite @ X4 @ X5 @ X6)) = X6) | ($true = X4)) & ! [X7 : $o,X8 : $i,X9 : $i] : ((((ite @ X7 @ X8 @ X9)) = X8) | ($true != X7))),
% 0.22/0.29 inference(rectify,[],[f7])).
% 0.22/0.29 thf(f9,plain,(
% 0.22/0.29 ( ! [X8 : $i,X9 : $i,X7 : $o] : ((((ite @ X7 @ X8 @ X9)) = X8) | ($true != X7)) )),
% 0.22/0.29 inference(cnf_transformation,[],[f8])).
% 0.22/0.29 thf(f10,plain,(
% 0.22/0.29 ( ! [X6 : $i,X4 : $o,X5 : $i] : ((((ite @ X4 @ X5 @ X6)) = X6) | ($true = X4)) )),
% 0.22/0.29 inference(cnf_transformation,[],[f8])).
% 0.22/0.29 thf(f11,plain,(
% 0.22/0.29 ( ! [X3 : $i] : ((((s @ X3)) != zero)) )),
% 0.22/0.29 inference(cnf_transformation,[],[f8])).
% 0.22/0.29 thf(f12,plain,(
% 0.22/0.29 ( ! [X2 : $i] : ((((s @ X2)) != X2)) )),
% 0.22/0.29 inference(cnf_transformation,[],[f8])).
% 0.22/0.29 thf(f13,plain,(
% 0.22/0.29 ( ! [X1 : $i] : ((((h @ X1)) = ((ite @ (zero = X1) @ (s @ zero) @ (ite @ ((s @ zero) = X1) @ zero @ (s @ zero)))))) )),
% 0.22/0.29 inference(cnf_transformation,[],[f8])).
% 0.22/0.29 thf(f14,plain,(
% 0.22/0.29 ( ! [X0 : ($i > $i)] : ((((s @ zero)) != ((X0 @ (s @ (s @ zero))))) | (zero != ((X0 @ (s @ zero)))) | (((s @ zero)) != ((X0 @ zero)))) )),
% 0.22/0.29 inference(cnf_transformation,[],[f8])).
% 0.22/0.29 thf(f16,definition,(
% 0.22/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.22/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.22/0.29 thf(f17,plain,(
% 0.22/0.29 ( ! [X8 : $i,X9 : $i] : ((((ite @ $true @ X8 @ X9)) = X8)) )),
% 0.22/0.29 inference(equality_resolution,[],[f9])).
% 0.22/0.29 thf(f38,plain,(
% 0.22/0.29 ( ! [X2 : $i,X0 : $o,X1 : $i] : ((((ite @ X0 @ X1 @ X2)) = X1) | ($false = X0)) )),
% 0.22/0.29 inference(constrained_superposition,[],[f17,f16])).
% 0.22/0.29 thf(f88,plain,(
% 0.22/0.29 ( ! [X0 : $i] : ((((s @ zero)) = ((h @ X0))) | (((zero = X0)) = $false)) )),
% 0.22/0.29 inference(constrained_superposition,[],[f38,f13])).
% 0.22/0.29 thf(f89,plain,(
% 0.22/0.29 ( ! [X0 : $i] : ((((h @ X0)) = ((ite @ ((s @ zero) = X0) @ zero @ (s @ zero)))) | ($true = ((zero = X0)))) )),
% 0.22/0.29 inference(constrained_superposition,[],[f10,f13])).
% 0.22/0.29 thf(f107,plain,(
% 0.22/0.29 ( ! [X0 : $i] : ((((h @ X0)) = ((ite @ ((s @ zero) = X0) @ zero @ (s @ zero)))) | (zero = X0)) )),
% 0.22/0.29 inference(equality_proxy_clausification,[],[f89])).
% 0.22/0.29 thf(f108,plain,(
% 0.22/0.29 ( ! [X0 : $i] : ((zero != X0) | (((s @ zero)) = ((h @ X0)))) )),
% 0.22/0.29 inference(equality_proxy_clausification,[],[f88])).
% 0.22/0.29 thf(f143,plain,(
% 0.22/0.29 (((s @ zero)) = ((h @ zero)))),
% 0.22/0.29 inference(equality_resolution,[],[f108])).
% 0.22/0.29 thf(f164,plain,(
% 0.22/0.29 ( ! [X0 : $i] : ((zero = ((h @ X0))) | ((((s @ zero) = X0)) = $false) | (zero = X0)) )),
% 0.22/0.29 inference(constrained_superposition,[],[f38,f107])).
% 0.22/0.29 thf(f165,plain,(
% 0.22/0.29 ( ! [X0 : $i] : ((((s @ zero)) = ((h @ X0))) | ($true = (((s @ zero) = X0))) | (zero = X0)) )),
% 0.22/0.29 inference(constrained_superposition,[],[f10,f107])).
% 0.22/0.29 thf(f167,plain,(
% 0.22/0.29 ( ! [X0 : $i] : ((((s @ zero)) = ((h @ X0))) | (((s @ zero)) = X0) | (zero = X0)) )),
% 0.22/0.29 inference(equality_proxy_clausification,[],[f165])).
% 0.22/0.29 thf(f168,plain,(
% 0.22/0.29 ( ! [X0 : $i] : ((((s @ zero)) != X0) | (zero = ((h @ X0))) | (zero = X0)) )),
% 0.22/0.29 inference(equality_proxy_clausification,[],[f164])).
% 0.22/0.29 thf(f186,plain,(
% 0.22/0.29 (zero = ((h @ (s @ zero)))) | (zero = ((s @ zero)))),
% 0.22/0.29 inference(equality_resolution,[],[f168])).
% 0.22/0.29 thf(f188,definition,(
% 0.22/0.29 spl0_17 <=> (zero = ((s @ zero)))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition])).
% 0.22/0.29 thf(f190,plain,(
% 0.22/0.29 (zero = ((s @ zero))) | ~spl0_17),
% 0.22/0.29 inference(avatar_component_clause,[],[f188])).
% 0.22/0.29 thf(f192,definition,(
% 0.22/0.29 spl0_18 <=> (zero = ((h @ (s @ zero))))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition])).
% 0.22/0.29 thf(f195,plain,(
% 0.22/0.29 spl0_17 | spl0_18),
% 0.22/0.29 inference(avatar_split_clause,[],[f186,f192,f188])).
% 0.22/0.29 thf(f218,plain,(
% 0.22/0.29 (zero != zero) | ~spl0_17),
% 0.22/0.29 inference(constrained_superposition,[],[f12,f190])).
% 0.22/0.29 thf(f228,plain,(
% 0.22/0.29 $false | ~spl0_17),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f218])).
% 0.22/0.29 thf(f229,plain,(
% 0.22/0.29 ~spl0_17),
% 0.22/0.29 inference(avatar_contradiction_clause,[],[f228])).
% 0.22/0.29 thf(f235,plain,(
% 0.22/0.29 ( ! [X0 : ($i > $i),X1 : $i] : ((((s @ zero)) != ((s @ zero))) | (zero != (((^[Y0 : $i]: (h @ (X0 @ Y0))) @ (s @ zero)))) | (((s @ zero)) != (((^[Y0 : $i]: (h @ (X0 @ Y0))) @ zero))) | (((s @ zero)) = X1) | (zero = X1) | (((X0 @ (s @ (s @ zero)))) != X1)) )),
% 0.22/0.29 inference(constrained_superposition,[],[f14,f167])).
% 0.22/0.29 thf(f236,plain,(
% 0.22/0.29 ( ! [X0 : ($i > $i),X1 : $i] : ((zero != (((^[Y0 : $i]: (h @ (X0 @ Y0))) @ (s @ zero)))) | (((s @ zero)) != (((^[Y0 : $i]: (h @ (X0 @ Y0))) @ zero))) | (((s @ zero)) = X1) | (zero = X1) | (((X0 @ (s @ (s @ zero)))) != X1)) )),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f235])).
% 0.22/0.29 thf(f237,plain,(
% 0.22/0.29 ( ! [X0 : ($i > $i),X1 : $i] : ((((s @ zero)) != ((h @ (X0 @ zero)))) | (zero != ((h @ (X0 @ (s @ zero))))) | (((s @ zero)) = X1) | (zero = X1) | (((X0 @ (s @ (s @ zero)))) != X1)) )),
% 0.22/0.29 inference(beta-eta_normalization,[],[f236])).
% 0.22/0.29 thf(f281,definition,(
% 0.22/0.29 spl0_20 <=> (zero = ((s @ (s @ zero))))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition])).
% 0.22/0.29 thf(f283,plain,(
% 0.22/0.29 (zero = ((s @ (s @ zero)))) | ~spl0_20),
% 0.22/0.29 inference(avatar_component_clause,[],[f281])).
% 0.22/0.29 thf(f473,plain,(
% 0.22/0.29 (zero != zero) | ~spl0_20),
% 0.22/0.29 inference(constrained_superposition,[],[f11,f283])).
% 0.22/0.29 thf(f476,plain,(
% 0.22/0.29 $false | ~spl0_20),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f473])).
% 0.22/0.29 thf(f477,plain,(
% 0.22/0.29 ~spl0_20),
% 0.22/0.29 inference(avatar_contradiction_clause,[],[f476])).
% 0.22/0.29 thf(f662,plain,(
% 0.22/0.29 ( ! [X0 : $i] : ((((s @ zero)) != ((s @ zero))) | (zero != ((h @ ((^[Y0 : $i]: (Y0)) @ (s @ zero))))) | (((s @ zero)) = X0) | (zero = X0) | ((((^[Y0 : $i]: (Y0)) @ (s @ (s @ zero)))) != X0)) )),
% 0.22/0.29 inference(constrained_superposition,[],[f237,f143])).
% 0.22/0.29 thf(f672,plain,(
% 0.22/0.29 ( ! [X0 : $i] : ((zero != ((h @ ((^[Y0 : $i]: (Y0)) @ (s @ zero))))) | (((s @ zero)) = X0) | (zero = X0) | ((((^[Y0 : $i]: (Y0)) @ (s @ (s @ zero)))) != X0)) )),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f662])).
% 0.22/0.29 thf(f673,plain,(
% 0.22/0.29 ( ! [X0 : $i] : ((zero != ((h @ (s @ zero)))) | (((s @ zero)) = X0) | (zero = X0) | (((s @ (s @ zero))) != X0)) )),
% 0.22/0.29 inference(beta-eta_normalization,[],[f672])).
% 0.22/0.29 thf(f766,definition,(
% 0.22/0.29 spl0_38 <=> ! [X0 : $i] : ((((s @ zero)) = X0) | (((s @ (s @ zero))) != X0) | (zero = X0))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl0_38])],[avatar_definition])).
% 0.22/0.29 thf(f767,plain,(
% 0.22/0.29 ( ! [X0 : $i] : ((((s @ (s @ zero))) != X0) | (((s @ zero)) = X0) | (zero = X0)) ) | ~spl0_38),
% 0.22/0.29 inference(avatar_component_clause,[],[f766])).
% 0.22/0.29 thf(f768,plain,(
% 0.22/0.29 spl0_38 | ~spl0_18),
% 0.22/0.29 inference(avatar_split_clause,[],[f673,f192,f766])).
% 0.22/0.29 thf(f872,plain,(
% 0.22/0.29 (((s @ zero)) = ((s @ (s @ zero)))) | (zero = ((s @ (s @ zero)))) | ~spl0_38),
% 0.22/0.29 inference(equality_resolution,[],[f767])).
% 0.22/0.29 thf(f874,definition,(
% 0.22/0.29 spl0_60 <=> (((s @ zero)) = ((s @ (s @ zero))))),
% 0.22/0.29 introduced(definition,[new_symbols(definition,[spl0_60])],[avatar_definition])).
% 0.22/0.29 thf(f876,plain,(
% 0.22/0.29 (((s @ zero)) = ((s @ (s @ zero)))) | ~spl0_60),
% 0.22/0.29 inference(avatar_component_clause,[],[f874])).
% 0.22/0.29 thf(f877,plain,(
% 0.22/0.29 spl0_20 | spl0_60 | ~spl0_38),
% 0.22/0.29 inference(avatar_split_clause,[],[f872,f766,f874,f281])).
% 0.22/0.29 thf(f881,plain,(
% 0.22/0.29 (((s @ zero)) != ((s @ zero))) | ~spl0_60),
% 0.22/0.29 inference(constrained_superposition,[],[f12,f876])).
% 0.22/0.29 thf(f885,plain,(
% 0.22/0.29 $false | ~spl0_60),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f881])).
% 0.22/0.29 thf(f886,plain,(
% 0.22/0.29 ~spl0_60),
% 0.22/0.29 inference(avatar_contradiction_clause,[],[f885])).
% 0.22/0.29 cnf(s12, plain, spl0_17 | spl0_18, inference(sat_conversion,[],[f195])).
% 0.22/0.29 cnf(s15, plain, ~spl0_17, inference(sat_conversion,[],[f229])).
% 0.22/0.29 cnf(s34, plain, ~spl0_20, inference(sat_conversion,[],[f477])).
% 0.22/0.29 cnf(s41, plain, ~spl0_18 | spl0_38, inference(sat_conversion,[],[f768])).
% 0.22/0.29 cnf(s62, plain, spl0_20 | ~spl0_38 | spl0_60, inference(sat_conversion,[],[f877])).
% 0.22/0.29 cnf(s63, plain, ~spl0_60, inference(sat_conversion,[],[f886])).
% 0.22/0.29 cnf(s65, plain, spl0_20 | ~spl0_38, inference(rat,[],[s62,s63])).
% 0.22/0.29 cnf(s66, plain, ~spl0_38, inference(rat,[],[s65,s34])).
% 0.22/0.29 cnf(s67, plain, ~spl0_18, inference(rat,[],[s41,s66])).
% 0.22/0.29 cnf(s73, plain, $false, inference(rat,[],[s12,s67,s15])).
% 0.22/0.29 thf(f894,plain,(
% 0.22/0.29 $false),
% 0.22/0.29 inference(avatar_sat_refutation,[],[s73])).
% 0.22/0.29 % SZS output end Proof for theBenchmark
% 0.22/0.29 % (2620681)------------------------------
% 0.22/0.29 % (2620681)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (2620681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (2620681)CaDiCaL version: 2.1.3
% 0.22/0.29 % (2620681)Termination reason: Refutation
% 0.22/0.29 % (2620681)Time elapsed: 0.037 s
% 0.22/0.29 % (2620681)Peak memory usage: 13 MB
% 0.22/0.29 % (2620681)Instructions burned: 67 (million)
% 0.22/0.29 % (2620670)Success in time 0.075 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------