%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN023^2 : 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 : 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 08:20:01 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN023^2 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n014.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 13:06:00 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
% 0.09/0.24 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
% 0.20/0.29 % (2619734)Will run a generic schedule for satisfiability detection.
% 0.20/0.29 % (2619745)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1003691791:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.29 % (2619740)% WARNING: option uhcvi not known.
% 0.20/0.29 % (2619741)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4057110862:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.29 % (2619739)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1113318870_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.29 % (2619740)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2588369247:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.29 % (2619742)dis+10_1_sil=32000:sp=arity:random_seed=4052898694:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.29 % (2619743)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=158314073:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.29 % (2619744)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1049099649:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.29 % (2619740)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % Exception at run slice level
% 0.20/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.29 % (2619743)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % (2619740)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.29 % (2619745) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2619734-2619745"...
% 0.20/0.29 % (2619745)...printing done.
% 0.20/0.29 % (2619745)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% 0.20/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.29 thf(func_def_1, type, s: ($i > $i)).
% 0.20/0.29 thf(func_def_2, type, ite: ($o > $i > $i > $i)).
% 0.20/0.29 thf(func_def_3, type, h: ($i > $i)).
% 0.20/0.29 thf(func_def_7, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.29 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.20/0.29 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.29 thf(f1,conjecture,(
% 0.20/0.29 (! [X3 : $i] : (((h @ X3)) = ((ite @ (X3 = zero) @ (s @ zero) @ 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 @ zero))) = zero) & (((X4 @ zero)) = ((s @ zero))))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',n10)).
% 0.20/0.29 thf(f2,negated_conjecture,(
% 0.20/0.29 ~((! [X3 : $i] : (((h @ X3)) = ((ite @ (X3 = zero) @ (s @ zero) @ 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 @ zero))) = zero) & (((X4 @ zero)) = ((s @ zero)))))),
% 0.20/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.29 thf(f3,plain,(
% 0.20/0.29 ~((! [X0 : $i] : (((h @ X0)) = ((ite @ (zero = X0) @ (s @ zero) @ zero))) & ! [X1 : $o,X2 : $i,X3 : $i] : (~X1 => (((ite @ X1 @ X2 @ X3)) = X3)) & ! [X4 : $o,X5 : $i,X6 : $i] : (X4 => (((ite @ X4 @ X5 @ X6)) = X5))) => ? [X7 : ($i > $i)] : ((zero = ((X7 @ (s @ zero)))) & (((s @ zero)) = ((X7 @ zero)))))),
% 0.20/0.29 inference(rectify,[],[f2])).
% 0.20/0.29 thf(f4,plain,(
% 0.20/0.29 ~((! [X0 : $i] : (((h @ X0)) = ((ite @ (zero = X0) @ (s @ zero) @ zero))) & ! [X1 : $o,X2 : $i,X3 : $i] : (~ ($true = X1) => (((ite @ X1 @ X2 @ X3)) = X3)) & ! [X4 : $o,X5 : $i,X6 : $i] : (($true = X4) => (((ite @ X4 @ X5 @ X6)) = X5))) => ? [X7 : ($i > $i)] : ((zero = ((X7 @ (s @ zero)))) & (((s @ zero)) = ((X7 @ zero)))))),
% 0.20/0.29 inference(fool_elimination,[],[f3])).
% 0.20/0.29 thf(f5,plain,(
% 0.20/0.29 ~((! [X0 : $i] : (((h @ X0)) = ((ite @ (zero = X0) @ (s @ zero) @ zero))) & ! [X1 : $o,X2 : $i,X3 : $i] : (($true != X1) => (((ite @ X1 @ X2 @ X3)) = X3)) & ! [X4 : $o,X5 : $i,X6 : $i] : (($true = X4) => (((ite @ X4 @ X5 @ X6)) = X5))) => ? [X7 : ($i > $i)] : ((zero = ((X7 @ (s @ zero)))) & (((s @ zero)) = ((X7 @ zero)))))),
% 0.20/0.29 inference(flattening,[],[f4])).
% 0.20/0.29 thf(f6,plain,(
% 0.20/0.29 ! [X7 : ($i > $i)] : ((zero != ((X7 @ (s @ zero)))) | (((s @ zero)) != ((X7 @ zero)))) & (! [X0 : $i] : (((h @ X0)) = ((ite @ (zero = X0) @ (s @ zero) @ zero))) & ! [X1 : $o,X2 : $i,X3 : $i] : ((((ite @ X1 @ X2 @ X3)) = X3) | ($true = X1)) & ! [X4 : $o,X5 : $i,X6 : $i] : ((((ite @ X4 @ X5 @ X6)) = X5) | ($true != X4)))),
% 0.20/0.29 inference(ennf_transformation,[],[f5])).
% 0.20/0.29 thf(f7,plain,(
% 0.20/0.29 ! [X7 : ($i > $i)] : ((zero != ((X7 @ (s @ zero)))) | (((s @ zero)) != ((X7 @ zero)))) & ! [X0 : $i] : (((h @ X0)) = ((ite @ (zero = X0) @ (s @ zero) @ zero))) & ! [X1 : $o,X2 : $i,X3 : $i] : ((((ite @ X1 @ X2 @ X3)) = X3) | ($true = X1)) & ! [X4 : $o,X5 : $i,X6 : $i] : ((((ite @ X4 @ X5 @ X6)) = X5) | ($true != X4))),
% 0.20/0.29 inference(flattening,[],[f6])).
% 0.20/0.29 thf(f8,plain,(
% 0.20/0.29 ! [X0 : ($i > $i)] : ((zero != ((X0 @ (s @ zero)))) | (((s @ zero)) != ((X0 @ zero)))) & ! [X1 : $i] : (((h @ X1)) = ((ite @ (zero = X1) @ (s @ zero) @ zero))) & ! [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))),
% 0.20/0.29 inference(rectify,[],[f7])).
% 0.20/0.29 thf(f9,plain,(
% 0.20/0.29 ( ! [X6 : $i,X7 : $i,X5 : $o] : ((((ite @ X5 @ X6 @ X7)) = X6) | ($true != X5)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f8])).
% 0.20/0.29 thf(f10,plain,(
% 0.20/0.29 ( ! [X2 : $o,X3 : $i,X4 : $i] : ((((ite @ X2 @ X3 @ X4)) = X4) | ($true = X2)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f8])).
% 0.20/0.29 thf(f11,plain,(
% 0.20/0.29 ( ! [X1 : $i] : ((((h @ X1)) = ((ite @ (zero = X1) @ (s @ zero) @ zero)))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f8])).
% 0.20/0.29 thf(f12,plain,(
% 0.20/0.29 ( ! [X0 : ($i > $i)] : ((((s @ zero)) != ((X0 @ zero))) | (zero != ((X0 @ (s @ zero))))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f8])).
% 0.20/0.29 thf(f14,definition,(
% 0.20/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.29 thf(f15,plain,(
% 0.20/0.29 ( ! [X6 : $i,X7 : $i] : ((((ite @ $true @ X6 @ X7)) = X6)) )),
% 0.20/0.29 inference(equality_resolution,[],[f9])).
% 0.20/0.29 thf(f16,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $i),X3 : $i,X0 : $i,X1 : ($i > $i)] : ((((s @ zero)) != X0) | (zero != (((^[Y0 : $i]: (ite @ ((^[Y1 : $i]: ($true)) @ Y0) @ (X1 @ Y0) @ (X2 @ Y0))) @ (s @ zero)))) | (((X1 @ zero)) != X0) | (((X2 @ zero)) != X3)) )),
% 0.20/0.29 inference(constrained_superposition,[],[f12,f15])).
% 0.20/0.29 thf(f18,plain,(
% 0.20/0.29 (zero != (((^[Y0 : $i]: (s @ ((^[Y1 : $i]: (zero)) @ Y0))) @ (s @ zero))))),
% 0.20/0.29 inference(equality_resolution,[],[f12])).
% 0.20/0.29 thf(f19,plain,(
% 0.20/0.29 (zero != ((s @ zero)))),
% 0.20/0.29 inference(beta-eta_normalization,[],[f18])).
% 0.20/0.29 thf(f21,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $i),X3 : $i,X0 : $i,X1 : ($i > $i)] : ((zero != ((ite @ $true @ (X1 @ (s @ zero)) @ (X2 @ (s @ zero))))) | (((s @ zero)) != X0) | (((X1 @ zero)) != X0) | (((X2 @ zero)) != X3)) )),
% 0.20/0.29 inference(beta-eta_normalization,[],[f16])).
% 0.20/0.29 thf(f36,plain,(
% 0.20/0.29 ( ! [X0 : $i] : ((zero = ((h @ X0))) | ($true = ((zero = X0)))) )),
% 0.20/0.29 inference(constrained_superposition,[],[f10,f11])).
% 0.20/0.29 thf(f51,plain,(
% 0.20/0.29 ( ! [X0 : $i] : ((zero = ((h @ X0))) | (zero = X0)) )),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f36])).
% 0.20/0.29 thf(f82,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X3 : ($i > $i),X0 : $i,X1 : ($i > $i),X4 : $i,X5 : $i] : ((zero != ((ite @ $true @ (X1 @ (s @ zero)) @ (h @ X0)))) | (((s @ zero)) != X4) | (((X1 @ zero)) != X4) | ((((^[Y0 : $i]: (ite @ (X2 @ Y0) @ (X3 @ Y0) @ ((^[Y1 : $i]: (zero)) @ Y0))) @ zero)) != X5) | (((s @ zero)) != ((X3 @ (s @ zero)))) | (((zero = X0)) != ((X2 @ (s @ zero))))) )),
% 0.20/0.29 inference(constrained_superposition,[],[f21,f11])).
% 0.20/0.29 thf(f104,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X3 : ($i > $i),X0 : $i,X1 : ($i > $i),X4 : $i,X5 : $i] : ((zero != ((ite @ $true @ (X1 @ (s @ zero)) @ (h @ X0)))) | (((s @ zero)) != X4) | (((X1 @ zero)) != X4) | ((((^[Y0 : $i]: (ite @ (X2 @ Y0) @ (X3 @ Y0) @ ((^[Y1 : $i]: (zero)) @ Y0))) @ zero)) != X5) | (((s @ zero)) != ((X3 @ (s @ zero)))) | (((zero = X0)) = $false) | ($false = ((X2 @ (s @ zero))))) )),
% 0.20/0.29 inference(xor_proxy_clausification,[],[f82])).
% 0.20/0.29 thf(f105,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X3 : ($i > $i),X0 : $i,X1 : ($i > $i),X4 : $i,X5 : $i] : ((zero != ((ite @ $true @ (X1 @ (s @ zero)) @ (h @ X0)))) | (((s @ zero)) != X4) | (((X1 @ zero)) != X4) | ((((^[Y0 : $i]: (ite @ (X2 @ Y0) @ (X3 @ Y0) @ ((^[Y1 : $i]: (zero)) @ Y0))) @ zero)) != X5) | (((s @ zero)) != ((X3 @ (s @ zero)))) | (zero != X0) | ($false = ((X2 @ (s @ zero))))) )),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f104])).
% 0.20/0.29 thf(f106,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X3 : ($i > $i),X0 : $i,X1 : ($i > $i),X4 : $i,X5 : $i] : ((zero != ((ite @ $true @ (X1 @ (s @ zero)) @ (h @ X0)))) | (((s @ zero)) != X4) | (((X1 @ zero)) != X4) | (((ite @ (X2 @ zero) @ (X3 @ zero) @ zero)) != X5) | (((s @ zero)) != ((X3 @ (s @ zero)))) | (zero != X0) | ($false = ((X2 @ (s @ zero))))) )),
% 0.20/0.29 inference(beta-eta_normalization,[],[f105])).
% 0.20/0.29 thf(f119,definition,(
% 0.20/0.29 spl0_10 <=> ! [X2 : $i,X0 : ($i > $i)] : ((zero != ((X0 @ (s @ zero)))) | (((X0 @ zero)) != X2) | (((s @ zero)) != X2))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition])).
% 0.20/0.29 thf(f120,plain,(
% 0.20/0.29 ( ! [X2 : $i,X0 : ($i > $i)] : ((zero != ((X0 @ (s @ zero)))) | (((s @ zero)) != X2) | (((X0 @ zero)) != X2)) ) | ~spl0_10),
% 0.20/0.29 inference(avatar_component_clause,[],[f119])).
% 0.20/0.29 thf(f123,definition,(
% 0.20/0.29 spl0_11 <=> ! [X2 : $i,X0 : ($i > $i),X3 : $i] : ((((s @ zero)) != X3) | (((X0 @ (s @ zero))) != X2) | (zero = X2) | (((h @ (X0 @ zero))) != X3))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition])).
% 0.20/0.29 thf(f124,plain,(
% 0.20/0.29 ( ! [X2 : $i,X3 : $i,X0 : ($i > $i)] : ((((s @ zero)) != X3) | (zero = X2) | (((h @ (X0 @ zero))) != X3) | (((X0 @ (s @ zero))) != X2)) ) | ~spl0_11),
% 0.20/0.29 inference(avatar_component_clause,[],[f123])).
% 0.20/0.29 thf(f155,definition,(
% 0.20/0.29 spl0_20 <=> ! [X2 : ($i > $o),X5 : $i,X3 : ($i > $i)] : ((((ite @ (X2 @ zero) @ (X3 @ zero) @ zero)) != X5) | ($false = ((X2 @ (s @ zero)))) | (((s @ zero)) != ((X3 @ (s @ zero)))))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition])).
% 0.20/0.29 thf(f156,plain,(
% 0.20/0.29 ( ! [X2 : ($i > $o),X3 : ($i > $i),X5 : $i] : ((((s @ zero)) != ((X3 @ (s @ zero)))) | ($false = ((X2 @ (s @ zero)))) | (((ite @ (X2 @ zero) @ (X3 @ zero) @ zero)) != X5)) ) | ~spl0_20),
% 0.20/0.29 inference(avatar_component_clause,[],[f155])).
% 0.20/0.29 thf(f158,definition,(
% 0.20/0.29 spl0_21 <=> ! [X4 : $i,X0 : $i,X1 : ($i > $i)] : ((zero != ((ite @ $true @ (X1 @ (s @ zero)) @ (h @ X0)))) | (zero != X0) | (((X1 @ zero)) != X4) | (((s @ zero)) != X4))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition])).
% 0.20/0.29 thf(f159,plain,(
% 0.20/0.29 ( ! [X0 : $i,X1 : ($i > $i),X4 : $i] : ((zero != ((ite @ $true @ (X1 @ (s @ zero)) @ (h @ X0)))) | (zero != X0) | (((s @ zero)) != X4) | (((X1 @ zero)) != X4)) ) | ~spl0_21),
% 0.20/0.29 inference(avatar_component_clause,[],[f158])).
% 0.20/0.29 thf(f160,plain,(
% 0.20/0.29 spl0_20 | spl0_21),
% 0.20/0.29 inference(avatar_split_clause,[],[f106,f158,f155])).
% 0.20/0.29 thf(f177,plain,(
% 0.20/0.29 ( ! [X2 : $i,X0 : ($i > $i),X1 : $i] : ((zero != zero) | (((s @ zero)) != X2) | ((((^[Y0 : $i]: (h @ (X0 @ Y0))) @ zero)) != X2) | (zero = X1) | (((X0 @ (s @ zero))) != X1)) ) | ~spl0_10),
% 0.20/0.29 inference(constrained_superposition,[],[f120,f51])).
% 0.20/0.29 thf(f180,plain,(
% 0.20/0.29 ( ! [X2 : $i,X0 : ($i > $i),X1 : $i] : ((((s @ zero)) != X2) | ((((^[Y0 : $i]: (h @ (X0 @ Y0))) @ zero)) != X2) | (zero = X1) | (((X0 @ (s @ zero))) != X1)) ) | ~spl0_10),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f177])).
% 0.20/0.29 thf(f181,plain,(
% 0.20/0.29 ( ! [X2 : $i,X0 : ($i > $i),X1 : $i] : ((((s @ zero)) != X2) | (((h @ (X0 @ zero))) != X2) | (zero = X1) | (((X0 @ (s @ zero))) != X1)) ) | ~spl0_10),
% 0.20/0.29 inference(beta-eta_normalization,[],[f180])).
% 0.20/0.29 thf(f296,plain,(
% 0.20/0.29 ( ! [X0 : $i,X1 : ($i > $i)] : ((((s @ zero)) != ((h @ (X1 @ zero)))) | (zero = X0) | (((X1 @ (s @ zero))) != X0)) ) | ~spl0_11),
% 0.20/0.29 inference(equality_resolution,[],[f124])).
% 0.20/0.29 thf(f323,definition,(
% 0.20/0.29 spl0_33 <=> (((s @ zero)) = ((h @ zero)))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition])).
% 0.20/0.29 thf(f324,plain,(
% 0.20/0.29 (((s @ zero)) = ((h @ zero))) | ~spl0_33),
% 0.20/0.29 inference(avatar_component_clause,[],[f323])).
% 0.20/0.29 thf(f347,plain,(
% 0.20/0.29 spl0_11 | ~spl0_10),
% 0.20/0.29 inference(avatar_split_clause,[],[f181,f119,f123])).
% 0.20/0.29 thf(f496,definition,(
% 0.20/0.29 spl0_43 <=> ! [X0 : $i] : (zero != X0)),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl0_43])],[avatar_definition])).
% 0.20/0.29 thf(f497,plain,(
% 0.20/0.29 ( ! [X0 : $i] : ((zero != X0)) ) | ~spl0_43),
% 0.20/0.29 inference(avatar_component_clause,[],[f496])).
% 0.20/0.29 thf(f534,definition,(
% 0.20/0.29 spl0_52 <=> ! [X1 : $i] : ((zero = X1) | (((s @ zero)) != X1))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl0_52])],[avatar_definition])).
% 0.20/0.29 thf(f535,plain,(
% 0.20/0.29 ( ! [X1 : $i] : ((((s @ zero)) != X1) | (zero = X1)) ) | ~spl0_52),
% 0.20/0.29 inference(avatar_component_clause,[],[f534])).
% 0.20/0.29 thf(f592,plain,(
% 0.20/0.29 ( ! [X0 : ($i > $o),X1 : $i] : (($false = ((X0 @ (s @ zero)))) | (((ite @ (X0 @ zero) @ ((^[Y0 : $i]: (Y0)) @ zero) @ zero)) != X1)) ) | ~spl0_20),
% 0.20/0.29 inference(equality_resolution,[],[f156])).
% 0.20/0.29 thf(f618,plain,(
% 0.20/0.29 ( ! [X2 : $i,X0 : ($i > $i),X1 : $i] : ((zero != ((X0 @ (s @ zero)))) | (zero != X1) | (((s @ zero)) != X2) | (((X0 @ zero)) != X2)) ) | ~spl0_21),
% 0.20/0.29 inference(constrained_superposition,[],[f159,f15])).
% 0.20/0.29 thf(f636,plain,(
% 0.20/0.29 ( ! [X0 : ($i > $o),X1 : $i] : ((((ite @ (X0 @ zero) @ zero @ zero)) != X1) | ($false = ((X0 @ (s @ zero))))) ) | ~spl0_20),
% 0.20/0.29 inference(beta-eta_normalization,[],[f592])).
% 0.20/0.29 thf(f638,plain,(
% 0.20/0.29 ( ! [X0 : $i] : ((zero != X0) | ($false = (((^[Y0 : $i]: ($true)) @ (s @ zero))))) ) | ~spl0_20),
% 0.20/0.29 inference(constrained_superposition,[],[f636,f15])).
% 0.20/0.29 thf(f641,plain,(
% 0.20/0.29 ( ! [X0 : $i] : ((zero != X0) | ($true = $false)) ) | ~spl0_20),
% 0.20/0.29 inference(beta-eta_normalization,[],[f638])).
% 0.20/0.29 thf(f642,plain,(
% 0.20/0.29 ( ! [X0 : $i] : ((zero != X0)) ) | ~spl0_20),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f641])).
% 0.20/0.29 thf(f643,plain,(
% 0.20/0.29 spl0_43 | ~spl0_20),
% 0.20/0.29 inference(avatar_split_clause,[],[f642,f155,f496])).
% 0.20/0.29 thf(f646,plain,(
% 0.20/0.29 ( ! [X2 : $i,X0 : $o,X1 : $i] : ((((ite @ X0 @ X1 @ X2)) = X1) | ($false = X0)) )),
% 0.20/0.29 inference(constrained_superposition,[],[f15,f14])).
% 0.20/0.29 thf(f654,plain,(
% 0.20/0.29 $false | ~spl0_43),
% 0.20/0.29 inference(equality_resolution,[],[f497])).
% 0.20/0.29 thf(f655,plain,(
% 0.20/0.29 ~spl0_43),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f654])).
% 0.20/0.29 thf(f656,plain,(
% 0.20/0.29 spl0_43 | spl0_10 | ~spl0_21),
% 0.20/0.29 inference(avatar_split_clause,[],[f618,f158,f119,f496])).
% 0.20/0.29 thf(f694,plain,(
% 0.20/0.29 ( ! [X0 : $i] : ((((s @ zero)) = ((h @ X0))) | (((zero = X0)) = $false)) )),
% 0.20/0.29 inference(constrained_superposition,[],[f11,f646])).
% 0.20/0.29 thf(f695,plain,(
% 0.20/0.29 ( ! [X0 : $i] : ((zero != X0) | (((s @ zero)) = ((h @ X0)))) )),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f694])).
% 0.20/0.29 thf(f726,plain,(
% 0.20/0.29 (((s @ zero)) = ((h @ zero)))),
% 0.20/0.29 inference(equality_resolution,[],[f695])).
% 0.20/0.29 thf(f727,plain,(
% 0.20/0.29 spl0_33),
% 0.20/0.29 inference(avatar_split_clause,[],[f726,f323])).
% 0.20/0.29 thf(f738,plain,(
% 0.20/0.29 ( ! [X0 : $i] : ((((s @ zero)) != ((s @ zero))) | (zero = X0) | ((((^[Y0 : $i]: (Y0)) @ (s @ zero))) != X0)) ) | (~spl0_11 | ~spl0_33)),
% 0.20/0.29 inference(constrained_superposition,[],[f296,f324])).
% 0.20/0.29 thf(f742,plain,(
% 0.20/0.29 ( ! [X0 : $i] : ((zero = X0) | ((((^[Y0 : $i]: (Y0)) @ (s @ zero))) != X0)) ) | (~spl0_11 | ~spl0_33)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f738])).
% 0.20/0.29 thf(f743,plain,(
% 0.20/0.29 ( ! [X0 : $i] : ((zero = X0) | (((s @ zero)) != X0)) ) | (~spl0_11 | ~spl0_33)),
% 0.20/0.29 inference(beta-eta_normalization,[],[f742])).
% 0.20/0.29 thf(f753,plain,(
% 0.20/0.29 spl0_52 | ~spl0_11 | ~spl0_33),
% 0.20/0.29 inference(avatar_split_clause,[],[f743,f323,f123,f534])).
% 0.20/0.29 thf(f755,plain,(
% 0.20/0.29 (zero = ((s @ zero))) | ~spl0_52),
% 0.20/0.29 inference(equality_resolution,[],[f535])).
% 0.20/0.29 thf(f762,plain,(
% 0.20/0.29 (zero != zero) | ~spl0_52),
% 0.20/0.29 inference(constrained_superposition,[],[f19,f755])).
% 0.20/0.29 thf(f768,plain,(
% 0.20/0.29 $false | ~spl0_52),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f762])).
% 0.20/0.29 thf(f769,plain,(
% 0.20/0.29 ~spl0_52),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f768])).
% 0.20/0.29 cnf(s12, plain, spl0_20 | spl0_21, inference(sat_conversion,[],[f160])).
% 0.20/0.29 cnf(s28, plain, ~spl0_10 | spl0_11, inference(sat_conversion,[],[f347])).
% 0.20/0.29 cnf(s50, plain, ~spl0_20 | spl0_43, inference(sat_conversion,[],[f643])).
% 0.20/0.29 cnf(s51, plain, ~spl0_43, inference(sat_conversion,[],[f655])).
% 0.20/0.29 cnf(s52, plain, spl0_10 | ~spl0_21 | spl0_43, inference(sat_conversion,[],[f656])).
% 0.20/0.29 cnf(s56, plain, spl0_33, inference(sat_conversion,[],[f727])).
% 0.20/0.29 cnf(s59, plain, ~spl0_11 | ~spl0_33 | spl0_52, inference(sat_conversion,[],[f753])).
% 0.20/0.29 cnf(s60, plain, ~spl0_52, inference(sat_conversion,[],[f769])).
% 0.20/0.29 cnf(s66, plain, ~spl0_11 | ~spl0_33, inference(rat,[],[s59,s60])).
% 0.20/0.29 cnf(s67, plain, ~spl0_11, inference(rat,[],[s66,s56])).
% 0.20/0.29 cnf(s70, plain, ~spl0_20, inference(rat,[],[s50,s51])).
% 0.20/0.29 cnf(s74, plain, ~spl0_10, inference(rat,[],[s28,s67])).
% 0.20/0.29 cnf(s75, plain, ~spl0_21, inference(rat,[],[s52,s51,s74])).
% 0.20/0.29 cnf(s77, plain, $false, inference(rat,[],[s12,s75,s70])).
% 0.20/0.29 thf(f784,plain,(
% 0.20/0.29 $false),
% 0.20/0.29 inference(avatar_sat_refutation,[],[s77])).
% 0.20/0.29 % SZS output end Proof for theBenchmark
% 0.20/0.29 % (2619745)------------------------------
% 0.20/0.29 % (2619745)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2619745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2619745)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2619745)Termination reason: Refutation
% 0.20/0.29 % (2619745)Time elapsed: 0.018 s
% 0.20/0.29 % (2619745)Peak memory usage: 13 MB
% 0.20/0.29 % (2619745)Instructions burned: 57 (million)
% 0.20/0.29 % (2619734)Success in time 0.052 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------