%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN024^1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 08:20:01 AM UTC 2026
% Result : Theorem 0.21s 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN024^1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n011.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 13:06:16 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
% 0.21/0.31 % (60666)Will run a generic schedule for satisfiability detection.
% 0.21/0.31 % (60672)% WARNING: option uhcvi not known.
% 0.21/0.31 % (60672)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2017136556:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.31 % (60672)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.31 % (60672)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.31 % (60674)dis+10_1_sil=32000:sp=arity:random_seed=2412956699:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.31 % (60671)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3571949071_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.31 % (60673)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2333755014:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.31 % (60675)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4095848655:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.31 % Exception at run slice level
% 0.21/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.31 % (60676)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1648206945:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.31 % (60675)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.31 % (60677)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3570681217:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.31 % (60685)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3676908850:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.21/0.31 % Exception at run slice level
% 0.21/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.31 % (60676) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-60666-60676"...
% 0.21/0.31 % (60674) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-60666-60674"...
% 0.21/0.31 % (60676)...printing done.
% 0.21/0.31 % (60676)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% 0.21/0.31 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.31 thf(func_def_1, type, s: ($i > $i)).
% 0.21/0.31 thf(func_def_2, type, ite: ($o > $i > $i > $i)).
% 0.21/0.31 thf(func_def_6, type, vNOT: ($o > $o)).
% 0.21/0.31 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.31 thf(func_def_8, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.31 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.31 thf(f1,conjecture,(
% 0.21/0.31 (! [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)))) = zero) & (((X4 @ (s @ zero))) = zero) & (((X4 @ zero)) = ((s @ zero))))),
% 0.21/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',n9)).
% 0.21/0.31 thf(f2,negated_conjecture,(
% 0.21/0.31 ~((! [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)))) = zero) & (((X4 @ (s @ zero))) = zero) & (((X4 @ zero)) = ((s @ zero)))))),
% 0.21/0.31 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.31 thf(f3,plain,(
% 0.21/0.31 ~((! [X0 : $i] : (((s @ X0)) != X0) & ! [X1 : $i] : (zero != ((s @ X1))) & ! [X2 : $o,X3 : $i,X4 : $i] : (~X2 => (((ite @ X2 @ X3 @ X4)) = X4)) & ! [X5 : $o,X6 : $i,X7 : $i] : (X5 => (((ite @ X5 @ X6 @ X7)) = X6))) => ? [X8 : ($i > $i)] : ((zero = ((X8 @ (s @ (s @ zero))))) & (zero = ((X8 @ (s @ zero)))) & (((s @ zero)) = ((X8 @ zero)))))),
% 0.21/0.31 inference(rectify,[],[f2])).
% 0.21/0.31 thf(f4,plain,(
% 0.21/0.31 ~((! [X0 : $i] : (((s @ X0)) != X0) & ! [X1 : $i] : (zero != ((s @ X1))) & ! [X2 : $o,X3 : $i,X4 : $i] : (~ ($true = X2) => (((ite @ X2 @ X3 @ X4)) = X4)) & ! [X5 : $o,X6 : $i,X7 : $i] : (($true = X5) => (((ite @ X5 @ X6 @ X7)) = X6))) => ? [X8 : ($i > $i)] : ((zero = ((X8 @ (s @ (s @ zero))))) & (zero = ((X8 @ (s @ zero)))) & (((s @ zero)) = ((X8 @ zero)))))),
% 0.21/0.31 inference(fool_elimination,[],[f3])).
% 0.21/0.31 thf(f5,plain,(
% 0.21/0.31 ~((! [X0 : $i] : (((s @ X0)) != X0) & ! [X1 : $i] : (zero != ((s @ X1))) & ! [X2 : $o,X3 : $i,X4 : $i] : (($true != X2) => (((ite @ X2 @ X3 @ X4)) = X4)) & ! [X5 : $o,X6 : $i,X7 : $i] : (($true = X5) => (((ite @ X5 @ X6 @ X7)) = X6))) => ? [X8 : ($i > $i)] : ((zero = ((X8 @ (s @ (s @ zero))))) & (zero = ((X8 @ (s @ zero)))) & (((s @ zero)) = ((X8 @ zero)))))),
% 0.21/0.31 inference(flattening,[],[f4])).
% 0.21/0.31 thf(f6,plain,(
% 0.21/0.31 ! [X8 : ($i > $i)] : ((zero != ((X8 @ (s @ (s @ zero))))) | (zero != ((X8 @ (s @ zero)))) | (((s @ zero)) != ((X8 @ zero)))) & (! [X0 : $i] : (((s @ X0)) != X0) & ! [X1 : $i] : (zero != ((s @ X1))) & ! [X2 : $o,X3 : $i,X4 : $i] : ((((ite @ X2 @ X3 @ X4)) = X4) | ($true = X2)) & ! [X5 : $o,X6 : $i,X7 : $i] : ((((ite @ X5 @ X6 @ X7)) = X6) | ($true != X5)))),
% 0.21/0.31 inference(ennf_transformation,[],[f5])).
% 0.21/0.31 thf(f7,plain,(
% 0.21/0.31 ! [X8 : ($i > $i)] : ((zero != ((X8 @ (s @ (s @ zero))))) | (zero != ((X8 @ (s @ zero)))) | (((s @ zero)) != ((X8 @ zero)))) & ! [X0 : $i] : (((s @ X0)) != X0) & ! [X1 : $i] : (zero != ((s @ X1))) & ! [X2 : $o,X3 : $i,X4 : $i] : ((((ite @ X2 @ X3 @ X4)) = X4) | ($true = X2)) & ! [X5 : $o,X6 : $i,X7 : $i] : ((((ite @ X5 @ X6 @ X7)) = X6) | ($true != X5))),
% 0.21/0.31 inference(flattening,[],[f6])).
% 0.21/0.31 thf(f8,plain,(
% 0.21/0.31 ! [X0 : ($i > $i)] : ((zero != ((X0 @ (s @ (s @ zero))))) | (zero != ((X0 @ (s @ zero)))) | (((s @ zero)) != ((X0 @ 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))),
% 0.21/0.31 inference(rectify,[],[f7])).
% 0.21/0.31 thf(f9,plain,(
% 0.21/0.31 ( ! [X8 : $i,X6 : $o,X7 : $i] : (($true != X6) | (((ite @ X6 @ X7 @ X8)) = X7)) )),
% 0.21/0.31 inference(cnf_transformation,[],[f8])).
% 0.21/0.31 thf(f10,plain,(
% 0.21/0.31 ( ! [X3 : $o,X4 : $i,X5 : $i] : ((((ite @ X3 @ X4 @ X5)) = X5) | ($true = X3)) )),
% 0.21/0.31 inference(cnf_transformation,[],[f8])).
% 0.21/0.31 thf(f11,plain,(
% 0.21/0.31 ( ! [X2 : $i] : ((zero != ((s @ X2)))) )),
% 0.21/0.31 inference(cnf_transformation,[],[f8])).
% 0.21/0.31 thf(f13,plain,(
% 0.21/0.31 ( ! [X0 : ($i > $i)] : ((zero != ((X0 @ (s @ (s @ zero))))) | (zero != ((X0 @ (s @ zero)))) | (((s @ zero)) != ((X0 @ zero)))) )),
% 0.21/0.31 inference(cnf_transformation,[],[f8])).
% 0.21/0.31 thf(f14,definition,(
% 0.21/0.31 ($true != $false)),
% 0.21/0.31 introduced(theory,[fool_distinctness_axiom])).
% 0.21/0.31 thf(f15,definition,(
% 0.21/0.31 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.21/0.31 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.21/0.31 thf(f16,plain,(
% 0.21/0.31 ( ! [X0 : $i,X1 : $i] : ((((ite @ $true @ X0 @ X1)) = X0)) )),
% 0.21/0.31 inference(equality_resolution,[],[f9])).
% 0.21/0.31 thf(f17,plain,(
% 0.21/0.31 ( ! [X2 : ($i > $i),X3 : ($i > $i),X0 : $i,X1 : ($i > $o),X4 : $o,X5 : $i] : ((zero != X0) | (zero != (((^[Y0 : $i]: (ite @ (X1 @ Y0) @ (X2 @ Y0) @ (X3 @ Y0))) @ (s @ zero)))) | (((s @ zero)) != (((^[Y0 : $i]: (ite @ (X1 @ Y0) @ (X2 @ Y0) @ (X3 @ Y0))) @ zero))) | ($true = X4) | (((X1 @ (s @ (s @ zero)))) != X4) | (((X2 @ (s @ (s @ zero)))) != X5) | (((X3 @ (s @ (s @ zero)))) != X0)) )),
% 0.21/0.31 inference(constrained_superposition,[],[f13,f10])).
% 0.21/0.31 thf(f23,plain,(
% 0.21/0.31 ( ! [X2 : ($i > $i),X3 : ($i > $i),X0 : $i,X1 : ($i > $o),X4 : $o,X5 : $i] : ((zero != X0) | (zero != (((^[Y0 : $i]: (ite @ (X1 @ Y0) @ (X2 @ Y0) @ (X3 @ Y0))) @ (s @ zero)))) | (((s @ zero)) != (((^[Y0 : $i]: (ite @ (X1 @ Y0) @ (X2 @ Y0) @ (X3 @ Y0))) @ zero))) | ($true = X4) | ($true = ((X1 @ (s @ (s @ zero))))) | (((X2 @ (s @ (s @ zero)))) != X5) | (((X3 @ (s @ (s @ zero)))) != X0) | ($true = X4)) )),
% 0.21/0.31 inference(xor_proxy_clausification,[],[f17])).
% 0.21/0.31 thf(f26,plain,(
% 0.21/0.31 ( ! [X2 : ($i > $i),X3 : ($i > $i),X0 : $i,X1 : ($i > $o),X4 : $o,X5 : $i] : ((zero != X0) | (zero != (((^[Y0 : $i]: (ite @ (X1 @ Y0) @ (X2 @ Y0) @ (X3 @ Y0))) @ (s @ zero)))) | (((s @ zero)) != (((^[Y0 : $i]: (ite @ (X1 @ Y0) @ (X2 @ Y0) @ (X3 @ Y0))) @ zero))) | ($true = X4) | ($true = ((X1 @ (s @ (s @ zero))))) | (((X2 @ (s @ (s @ zero)))) != X5) | (((X3 @ (s @ (s @ zero)))) != X0)) )),
% 0.21/0.31 inference(duplicate_literal_removal,[],[f23])).
% 0.21/0.31 thf(f27,plain,(
% 0.21/0.31 ( ! [X2 : ($i > $i),X3 : ($i > $i),X0 : $i,X1 : ($i > $o),X4 : $o,X5 : $i] : ((zero != X0) | (zero != ((ite @ (X1 @ (s @ zero)) @ (X2 @ (s @ zero)) @ (X3 @ (s @ zero))))) | (((s @ zero)) != ((ite @ (X1 @ zero) @ (X2 @ zero) @ (X3 @ zero)))) | ($true = X4) | ($true = ((X1 @ (s @ (s @ zero))))) | (((X2 @ (s @ (s @ zero)))) != X5) | (((X3 @ (s @ (s @ zero)))) != X0)) )),
% 0.21/0.31 inference(beta-eta_normalization,[],[f26])).
% 0.21/0.31 thf(f30,definition,(
% 0.21/0.31 spl0_1 <=> ! [X4 : $o] : ($true = X4)),
% 0.21/0.31 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.21/0.31 thf(f31,plain,(
% 0.21/0.31 ( ! [X4 : $o] : (($true = X4)) ) | ~spl0_1),
% 0.21/0.31 inference(avatar_component_clause,[],[f30])).
% 0.21/0.31 thf(f33,definition,(
% 0.21/0.31 spl0_2 <=> ! [X5 : $i,X0 : $i,X3 : ($i > $i),X2 : ($i > $i),X1 : ($i > $o)] : ((zero != X0) | (zero != ((ite @ (X1 @ (s @ zero)) @ (X2 @ (s @ zero)) @ (X3 @ (s @ zero))))) | (((X3 @ (s @ (s @ zero)))) != X0) | (((X2 @ (s @ (s @ zero)))) != X5) | ($true = ((X1 @ (s @ (s @ zero))))) | (((s @ zero)) != ((ite @ (X1 @ zero) @ (X2 @ zero) @ (X3 @ zero)))))),
% 0.21/0.31 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.21/0.31 thf(f34,plain,(
% 0.21/0.31 ( ! [X2 : ($i > $i),X3 : ($i > $i),X0 : $i,X1 : ($i > $o),X5 : $i] : ((zero != X0) | (zero != ((ite @ (X1 @ (s @ zero)) @ (X2 @ (s @ zero)) @ (X3 @ (s @ zero))))) | ($true = ((X1 @ (s @ (s @ zero))))) | (((s @ zero)) != ((ite @ (X1 @ zero) @ (X2 @ zero) @ (X3 @ zero)))) | (((X3 @ (s @ (s @ zero)))) != X0) | (((X2 @ (s @ (s @ zero)))) != X5)) ) | ~spl0_2),
% 0.21/0.31 inference(avatar_component_clause,[],[f33])).
% 0.21/0.31 thf(f35,plain,(
% 0.21/0.31 spl0_1 | spl0_2),
% 0.21/0.31 inference(avatar_split_clause,[],[f27,f33,f30])).
% 0.21/0.31 thf(f79,plain,(
% 0.21/0.31 ( ! [X2 : ($i > $i),X3 : $i,X0 : ($i > $o),X1 : ($i > $i)] : ((zero != ((ite @ (X0 @ (s @ zero)) @ (X1 @ (s @ zero)) @ (X2 @ (s @ zero))))) | ($true = ((X0 @ (s @ (s @ zero))))) | (((s @ zero)) != ((ite @ (X0 @ zero) @ (X1 @ zero) @ (X2 @ zero)))) | (zero != ((X2 @ (s @ (s @ zero))))) | (((X1 @ (s @ (s @ zero)))) != X3)) ) | ~spl0_2),
% 0.21/0.31 inference(equality_resolution,[],[f34])).
% 0.21/0.31 thf(f89,plain,(
% 0.21/0.31 ( ! [X2 : ($i > $i),X3 : $i,X0 : ($i > $i),X1 : ($i > $o)] : ((((s @ zero)) != ((ite @ (X1 @ zero) @ (X2 @ zero) @ (X0 @ zero)))) | ($true = ((X1 @ (s @ (s @ zero))))) | (zero != ((X0 @ (s @ zero)))) | (zero != ((X0 @ (s @ (s @ zero))))) | ($true = ((X1 @ (s @ zero)))) | (((X2 @ (s @ (s @ zero)))) != X3)) ) | ~spl0_2),
% 0.21/0.31 inference(constrained_superposition,[],[f79,f10])).
% 0.21/0.31 thf(f152,plain,(
% 0.21/0.31 ( ! [X0 : $o] : (($false != X0)) ) | ~spl0_1),
% 0.21/0.31 inference(constrained_superposition,[],[f14,f31])).
% 0.21/0.31 thf(f223,plain,(
% 0.21/0.31 ( ! [X2 : ($i > $i),X3 : $i,X0 : ($i > $o),X1 : ($i > $i)] : ((((s @ zero)) != ((ite @ $true @ (X1 @ zero) @ (X2 @ zero)))) | ($true = ((X0 @ (s @ (s @ zero))))) | (zero != ((X2 @ (s @ zero)))) | (zero != ((X2 @ (s @ (s @ zero))))) | ($true = ((X0 @ (s @ zero)))) | (((X1 @ (s @ (s @ zero)))) != X3) | ($false = ((X0 @ zero)))) ) | ~spl0_2),
% 0.21/0.31 inference(constrained_superposition,[],[f89,f15])).
% 0.21/0.31 thf(f255,definition,(
% 0.21/0.31 spl0_15 <=> ! [X2 : ($i > $i)] : ((zero != ((X2 @ (s @ zero)))) | (zero != ((X2 @ (s @ (s @ zero))))))),
% 0.21/0.31 introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition])).
% 0.21/0.31 thf(f256,plain,(
% 0.21/0.31 ( ! [X2 : ($i > $i)] : ((zero != ((X2 @ (s @ (s @ zero))))) | (zero != ((X2 @ (s @ zero))))) ) | ~spl0_15),
% 0.21/0.31 inference(avatar_component_clause,[],[f255])).
% 0.21/0.31 thf(f258,definition,(
% 0.21/0.31 spl0_16 <=> ! [X1 : ($i > $o)] : (($true = ((X1 @ (s @ (s @ zero))))) | ($false = ((X1 @ zero))) | ($true = ((X1 @ (s @ zero)))))),
% 0.21/0.31 introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition])).
% 0.21/0.31 thf(f259,plain,(
% 0.21/0.31 ( ! [X1 : ($i > $o)] : (($true = ((X1 @ (s @ (s @ zero))))) | ($false = ((X1 @ zero))) | ($true = ((X1 @ (s @ zero))))) ) | ~spl0_16),
% 0.21/0.31 inference(avatar_component_clause,[],[f258])).
% 0.21/0.31 thf(f261,definition,(
% 0.21/0.31 spl0_17 <=> ! [X0 : ($i > $i),X3 : $i] : ((((s @ zero)) != ((X0 @ zero))) | (((X0 @ (s @ (s @ zero)))) != X3))),
% 0.21/0.31 introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition])).
% 0.21/0.31 thf(f262,plain,(
% 0.21/0.31 ( ! [X3 : $i,X0 : ($i > $i)] : ((((s @ zero)) != ((X0 @ zero))) | (((X0 @ (s @ (s @ zero)))) != X3)) ) | ~spl0_17),
% 0.21/0.31 inference(avatar_component_clause,[],[f261])).
% 0.21/0.31 thf(f264,plain,(
% 0.21/0.31 ( ! [X2 : ($i > $i),X3 : $i,X0 : ($i > $o),X1 : ($i > $i)] : ((((s @ zero)) != ((X1 @ zero))) | ($true = ((X0 @ (s @ (s @ zero))))) | (zero != ((X2 @ (s @ zero)))) | (zero != ((X2 @ (s @ (s @ zero))))) | ($true = ((X0 @ (s @ zero)))) | (((X1 @ (s @ (s @ zero)))) != X3) | ($false = ((X0 @ zero)))) ) | ~spl0_2),
% 0.21/0.31 inference(forward_demodulation,[],[f223,f16])).
% 0.21/0.31 thf(f314,plain,(
% 0.21/0.31 $false | ~spl0_1),
% 0.21/0.31 inference(equality_resolution,[],[f152])).
% 0.21/0.31 thf(f315,plain,(
% 0.21/0.31 ~spl0_1),
% 0.21/0.31 inference(avatar_contradiction_clause,[],[f314])).
% 0.21/0.31 thf(f327,plain,(
% 0.21/0.31 spl0_15 | spl0_16 | spl0_17 | ~spl0_2),
% 0.21/0.31 inference(avatar_split_clause,[],[f264,f33,f261,f258,f255])).
% 0.21/0.31 thf(f331,plain,(
% 0.21/0.31 (zero = ((s @ (s @ zero)))) | ($true = ((zero = (s @ zero)))) | ~spl0_16),
% 0.21/0.31 inference(leibniz_equality_elimination,[],[f259])).
% 0.21/0.31 thf(f361,plain,(
% 0.21/0.31 (zero = ((s @ (s @ zero)))) | (zero = ((s @ zero))) | ~spl0_16),
% 0.21/0.31 inference(equality_proxy_clausification,[],[f331])).
% 0.21/0.31 thf(f363,plain,(
% 0.21/0.31 (zero = ((s @ zero))) | ~spl0_16),
% 0.21/0.31 inference(forward_subsumption_resolution,[],[f361,f11])).
% 0.21/0.31 thf(f364,plain,(
% 0.21/0.31 $false | ~spl0_16),
% 0.21/0.31 inference(forward_subsumption_resolution,[],[f363,f11])).
% 0.21/0.31 thf(f365,plain,(
% 0.21/0.31 ~spl0_16),
% 0.21/0.31 inference(avatar_contradiction_clause,[],[f364])).
% 0.21/0.31 thf(f409,plain,(
% 0.21/0.31 (zero != (((^[Y0 : $i]: (zero)) @ (s @ zero)))) | ~spl0_15),
% 0.21/0.31 inference(equality_resolution,[],[f256])).
% 0.21/0.31 thf(f410,plain,(
% 0.21/0.31 (zero != zero) | ~spl0_15),
% 0.21/0.31 inference(beta-eta_normalization,[],[f409])).
% 0.21/0.31 thf(f411,plain,(
% 0.21/0.31 $false | ~spl0_15),
% 0.21/0.31 inference(trivial_inequality_removal,[],[f410])).
% 0.21/0.31 thf(f412,plain,(
% 0.21/0.31 ~spl0_15),
% 0.21/0.31 inference(avatar_contradiction_clause,[],[f411])).
% 0.21/0.31 thf(f482,plain,(
% 0.21/0.31 ( ! [X0 : $i] : (((((^[Y0 : $i]: (s @ ((^[Y1 : $i]: (zero)) @ Y0))) @ (s @ (s @ zero)))) != X0)) ) | ~spl0_17),
% 0.21/0.31 inference(equality_resolution,[],[f262])).
% 0.21/0.31 thf(f483,plain,(
% 0.21/0.31 ( ! [X0 : $i] : ((((s @ zero)) != X0)) ) | ~spl0_17),
% 0.21/0.31 inference(beta-eta_normalization,[],[f482])).
% 0.21/0.31 thf(f534,plain,(
% 0.21/0.31 $false | ~spl0_17),
% 0.21/0.31 inference(equality_resolution,[],[f483])).
% 0.21/0.31 thf(f535,plain,(
% 0.21/0.31 ~spl0_17),
% 0.21/0.31 inference(avatar_contradiction_clause,[],[f534])).
% 0.21/0.31 cnf(s1, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f35])).
% 0.21/0.31 cnf(s24, plain, ~spl0_1, inference(sat_conversion,[],[f315])).
% 0.21/0.31 cnf(s27, plain, ~spl0_2 | spl0_15 | spl0_16 | spl0_17, inference(sat_conversion,[],[f327])).
% 0.21/0.31 cnf(s30, plain, ~spl0_16, inference(sat_conversion,[],[f365])).
% 0.21/0.31 cnf(s31, plain, ~spl0_15, inference(sat_conversion,[],[f412])).
% 0.21/0.31 cnf(s35, plain, ~spl0_17, inference(sat_conversion,[],[f535])).
% 0.21/0.31 cnf(s37, plain, ~spl0_2, inference(rat,[],[s27,s35,s30,s31])).
% 0.21/0.31 cnf(s41, plain, $false, inference(rat,[],[s1,s37,s24])).
% 0.21/0.31 thf(f536,plain,(
% 0.21/0.31 $false),
% 0.21/0.31 inference(avatar_sat_refutation,[],[s41])).
% 0.21/0.31 % SZS output end Proof for theBenchmark
% 0.21/0.31 % (60676)------------------------------
% 0.21/0.31 % (60676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (60676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (60676)CaDiCaL version: 2.1.3
% 0.21/0.31 % (60676)Termination reason: Refutation
% 0.21/0.31 % (60676)Time elapsed: 0.027 s
% 0.21/0.31 % (60676)Peak memory usage: 13 MB
% 0.21/0.31 % (60676)Instructions burned: 53 (million)
% 0.21/0.31 % (60666)Success in time 0.069 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------