%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN025^1 : 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 : n001.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 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN025^1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n001.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:11:50 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 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
% 0.20/0.30 % (1212186)Will run a generic schedule for satisfiability detection.
% 0.20/0.30 % (1212196)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1965314639:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.30 % (1212192)% WARNING: option uhcvi not known.
% 0.20/0.30 % (1212191)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3299208499_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.30 % (1212195)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3724988598:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.30 % (1212192)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2968396810:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.30 % (1212193)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=174922485:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.30 % (1212195)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.30 % (1212192)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.30 % Exception at run slice level
% 0.20/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.30 % (1212192)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.30 % (1212197)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2377690939:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.30 % (1212194)dis+10_1_sil=32000:sp=arity:random_seed=3258831727:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.30 % (1212203)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1844846437:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.30 % Exception at run slice level
% 0.20/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.30 % (1212196) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1212186-1212196"...
% 0.20/0.30 % (1212196)...printing done.
% 0.20/0.30 % (1212196)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% 0.20/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.30 thf(func_def_1, type, s: ($i > $i)).
% 0.20/0.30 thf(func_def_2, type, ite: ($o > $i > $i > $i)).
% 0.20/0.30 thf(func_def_6, type, vNOT: ($o > $o)).
% 0.20/0.30 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_8, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.30 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.30 thf(f1,conjecture,(
% 0.20/0.30 (! [X3 : $i] : (((s @ X3)) != X3) & ! [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))))),
% 0.20/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',n9)).
% 0.20/0.30 thf(f2,negated_conjecture,(
% 0.20/0.30 ~((! [X3 : $i] : (((s @ X3)) != X3) & ! [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)))))),
% 0.20/0.30 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.30 thf(f3,plain,(
% 0.20/0.30 ~((! [X0 : $i] : (((s @ X0)) != X0) & ! [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)] : ((((s @ zero)) = ((X7 @ (s @ (s @ zero))))) & (zero = ((X7 @ (s @ zero)))) & (((s @ zero)) = ((X7 @ zero)))))),
% 0.20/0.30 inference(rectify,[],[f2])).
% 0.20/0.30 thf(f4,plain,(
% 0.20/0.30 ~((! [X0 : $i] : (((s @ X0)) != X0) & ! [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)] : ((((s @ zero)) = ((X7 @ (s @ (s @ zero))))) & (zero = ((X7 @ (s @ zero)))) & (((s @ zero)) = ((X7 @ zero)))))),
% 0.20/0.30 inference(fool_elimination,[],[f3])).
% 0.20/0.30 thf(f5,plain,(
% 0.20/0.30 ~((! [X0 : $i] : (((s @ X0)) != X0) & ! [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 > $i)] : ((((s @ zero)) = ((X7 @ (s @ (s @ zero))))) & (zero = ((X7 @ (s @ zero)))) & (((s @ zero)) = ((X7 @ zero)))))),
% 0.20/0.30 inference(flattening,[],[f4])).
% 0.20/0.30 thf(f6,plain,(
% 0.20/0.30 ! [X7 : ($i > $i)] : ((((s @ zero)) != ((X7 @ (s @ (s @ zero))))) | (zero != ((X7 @ (s @ zero)))) | (((s @ zero)) != ((X7 @ zero)))) & (! [X0 : $i] : (((s @ X0)) != X0) & ! [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)))),
% 0.20/0.30 inference(ennf_transformation,[],[f5])).
% 0.20/0.30 thf(f7,plain,(
% 0.20/0.30 ! [X7 : ($i > $i)] : ((((s @ zero)) != ((X7 @ (s @ (s @ zero))))) | (zero != ((X7 @ (s @ zero)))) | (((s @ zero)) != ((X7 @ zero)))) & ! [X0 : $i] : (((s @ X0)) != X0) & ! [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))),
% 0.20/0.30 inference(flattening,[],[f6])).
% 0.20/0.30 thf(f8,plain,(
% 0.20/0.30 ! [X0 : ($i > $i)] : ((((s @ zero)) != ((X0 @ (s @ (s @ zero))))) | (zero != ((X0 @ (s @ zero)))) | (((s @ zero)) != ((X0 @ zero)))) & ! [X1 : $i] : (((s @ X1)) != 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))),
% 0.20/0.30 inference(rectify,[],[f7])).
% 0.20/0.30 thf(f9,plain,(
% 0.20/0.30 ( ! [X6 : $i,X7 : $i,X5 : $o] : (($true != X5) | (((ite @ X5 @ X6 @ X7)) = X6)) )),
% 0.20/0.30 inference(cnf_transformation,[],[f8])).
% 0.20/0.30 thf(f10,plain,(
% 0.20/0.30 ( ! [X2 : $o,X3 : $i,X4 : $i] : ((((ite @ X2 @ X3 @ X4)) = X4) | ($true = X2)) )),
% 0.20/0.30 inference(cnf_transformation,[],[f8])).
% 0.20/0.30 thf(f11,plain,(
% 0.20/0.30 ( ! [X1 : $i] : ((((s @ X1)) != X1)) )),
% 0.20/0.30 inference(cnf_transformation,[],[f8])).
% 0.20/0.30 thf(f12,plain,(
% 0.20/0.30 ( ! [X0 : ($i > $i)] : ((((s @ zero)) != ((X0 @ (s @ (s @ zero))))) | (zero != ((X0 @ (s @ zero)))) | (((s @ zero)) != ((X0 @ zero)))) )),
% 0.20/0.30 inference(cnf_transformation,[],[f8])).
% 0.20/0.30 thf(f13,definition,(
% 0.20/0.30 ($true != $false)),
% 0.20/0.30 introduced(theory,[fool_distinctness_axiom])).
% 0.20/0.30 thf(f14,definition,(
% 0.20/0.30 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.30 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.30 thf(f15,plain,(
% 0.20/0.30 ( ! [X0 : $i,X1 : $i] : ((((ite @ $true @ X0 @ X1)) = X0)) )),
% 0.20/0.30 inference(equality_resolution,[],[f9])).
% 0.20/0.30 thf(f17,plain,(
% 0.20/0.30 ( ! [X2 : ($i > $i),X3 : ($i > $i),X0 : $i,X1 : ($i > $o),X4 : $o,X5 : $i] : ((((s @ 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)) )),
% 0.20/0.30 inference(constrained_superposition,[],[f12,f10])).
% 0.20/0.30 thf(f21,plain,(
% 0.20/0.30 ( ! [X2 : ($i > $i),X3 : ($i > $i),X0 : $i,X1 : ($i > $o),X4 : $o,X5 : $i] : ((((s @ 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)) )),
% 0.20/0.30 inference(xor_proxy_clausification,[],[f17])).
% 0.20/0.30 thf(f24,plain,(
% 0.20/0.30 ( ! [X2 : ($i > $i),X3 : ($i > $i),X0 : $i,X1 : ($i > $o),X4 : $o,X5 : $i] : ((((s @ 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) | ($true = ((X1 @ (s @ (s @ zero))))) | (((X2 @ (s @ (s @ zero)))) != X5) | (((X3 @ (s @ (s @ zero)))) != X0)) )),
% 0.20/0.30 inference(duplicate_literal_removal,[],[f21])).
% 0.20/0.30 thf(f25,plain,(
% 0.20/0.30 ( ! [X2 : ($i > $i),X3 : ($i > $i),X0 : $i,X1 : ($i > $o),X4 : $o,X5 : $i] : ((((s @ zero)) != X0) | (zero != ((ite @ (X1 @ (s @ zero)) @ (X2 @ (s @ zero)) @ (X3 @ (s @ zero))))) | (((s @ zero)) != ((ite @ (X1 @ zero) @ (X2 @ zero) @ (X3 @ zero)))) | ($true = X4) | ($true = ((X1 @ (s @ (s @ zero))))) | (((X2 @ (s @ (s @ zero)))) != X5) | (((X3 @ (s @ (s @ zero)))) != X0)) )),
% 0.20/0.30 inference(beta-eta_normalization,[],[f24])).
% 0.20/0.30 thf(f28,definition,(
% 0.20/0.30 spl0_1 <=> ! [X4 : $o] : ($true = X4)),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.20/0.30 thf(f29,plain,(
% 0.20/0.30 ( ! [X4 : $o] : (($true = X4)) ) | ~spl0_1),
% 0.20/0.30 inference(avatar_component_clause,[],[f28])).
% 0.20/0.30 thf(f31,definition,(
% 0.20/0.30 spl0_2 <=> ! [X5 : $i,X0 : $i,X3 : ($i > $i),X2 : ($i > $i),X1 : ($i > $o)] : ((((s @ zero)) != X0) | (zero != ((ite @ (X1 @ (s @ zero)) @ (X2 @ (s @ zero)) @ (X3 @ (s @ zero))))) | (((X3 @ (s @ (s @ zero)))) != X0) | (((X2 @ (s @ (s @ zero)))) != X5) | ($true = ((X1 @ (s @ (s @ zero))))) | (((s @ zero)) != ((ite @ (X1 @ zero) @ (X2 @ zero) @ (X3 @ zero)))))),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.20/0.30 thf(f32,plain,(
% 0.20/0.30 ( ! [X2 : ($i > $i),X3 : ($i > $i),X0 : $i,X1 : ($i > $o),X5 : $i] : ((((s @ zero)) != X0) | (zero != ((ite @ (X1 @ (s @ zero)) @ (X2 @ (s @ zero)) @ (X3 @ (s @ zero))))) | ($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),
% 0.20/0.30 inference(avatar_component_clause,[],[f31])).
% 0.20/0.30 thf(f33,plain,(
% 0.20/0.30 spl0_1 | spl0_2),
% 0.20/0.30 inference(avatar_split_clause,[],[f25,f31,f28])).
% 0.20/0.30 thf(f78,plain,(
% 0.20/0.30 ( ! [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)))) | (((s @ zero)) != ((X2 @ (s @ (s @ zero))))) | (((X1 @ (s @ (s @ zero)))) != X3)) ) | ~spl0_2),
% 0.20/0.30 inference(equality_resolution,[],[f32])).
% 0.20/0.30 thf(f86,plain,(
% 0.20/0.30 ( ! [X2 : ($i > $i),X3 : $i,X0 : ($i > $o),X1 : ($i > $i)] : ((zero != ((ite @ $true @ (X1 @ (s @ zero)) @ (X2 @ (s @ zero))))) | ($true = ((X0 @ (s @ (s @ zero))))) | (((s @ zero)) != ((ite @ (X0 @ zero) @ (X1 @ zero) @ (X2 @ zero)))) | (((s @ zero)) != ((X2 @ (s @ (s @ zero))))) | (((X1 @ (s @ (s @ zero)))) != X3) | ($false = ((X0 @ (s @ zero))))) ) | ~spl0_2),
% 0.20/0.30 inference(constrained_superposition,[],[f78,f14])).
% 0.20/0.30 thf(f114,plain,(
% 0.20/0.30 ( ! [X2 : ($i > $i),X3 : $i,X0 : ($i > $o),X1 : ($i > $i)] : ((((s @ zero)) != ((ite @ (X0 @ zero) @ (X1 @ zero) @ (X2 @ zero)))) | ($true = ((X0 @ (s @ (s @ zero))))) | (zero != ((X1 @ (s @ zero)))) | (((s @ zero)) != ((X2 @ (s @ (s @ zero))))) | ($false = ((X0 @ (s @ zero)))) | (((X1 @ (s @ (s @ zero)))) != X3)) ) | ~spl0_2),
% 0.20/0.30 inference(forward_demodulation,[],[f86,f15])).
% 0.20/0.30 thf(f151,plain,(
% 0.20/0.30 ( ! [X0 : $o] : (($false != X0)) ) | ~spl0_1),
% 0.20/0.30 inference(constrained_superposition,[],[f13,f29])).
% 0.20/0.30 thf(f314,plain,(
% 0.20/0.30 $false | ~spl0_1),
% 0.20/0.30 inference(equality_resolution,[],[f151])).
% 0.20/0.30 thf(f315,plain,(
% 0.20/0.30 ~spl0_1),
% 0.20/0.30 inference(avatar_contradiction_clause,[],[f314])).
% 0.20/0.30 thf(f527,plain,(
% 0.20/0.30 ( ! [X2 : ($i > $i),X3 : $i,X0 : ($i > $i),X1 : ($i > $o)] : ((((s @ zero)) != ((X0 @ zero))) | ($true = ((X1 @ (s @ (s @ zero))))) | (zero != ((X2 @ (s @ zero)))) | (((s @ zero)) != ((X0 @ (s @ (s @ zero))))) | ($false = ((X1 @ (s @ zero)))) | (((X2 @ (s @ (s @ zero)))) != X3) | ($true = ((X1 @ zero)))) ) | ~spl0_2),
% 0.20/0.30 inference(constrained_superposition,[],[f114,f10])).
% 0.20/0.30 thf(f892,definition,(
% 0.20/0.30 spl0_63 <=> ! [X2 : ($i > $i),X3 : $i] : ((zero != ((X2 @ (s @ zero)))) | (((X2 @ (s @ (s @ zero)))) != X3))),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl0_63])],[avatar_definition])).
% 0.20/0.30 thf(f893,plain,(
% 0.20/0.30 ( ! [X2 : ($i > $i),X3 : $i] : ((zero != ((X2 @ (s @ zero)))) | (((X2 @ (s @ (s @ zero)))) != X3)) ) | ~spl0_63),
% 0.20/0.30 inference(avatar_component_clause,[],[f892])).
% 0.20/0.30 thf(f895,definition,(
% 0.20/0.30 spl0_64 <=> ! [X1 : ($i > $o)] : (($true = ((X1 @ (s @ (s @ zero))))) | ($true = ((X1 @ zero))) | ($false = ((X1 @ (s @ zero)))))),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl0_64])],[avatar_definition])).
% 0.20/0.30 thf(f896,plain,(
% 0.20/0.30 ( ! [X1 : ($i > $o)] : (($true = ((X1 @ (s @ (s @ zero))))) | ($true = ((X1 @ zero))) | ($false = ((X1 @ (s @ zero))))) ) | ~spl0_64),
% 0.20/0.30 inference(avatar_component_clause,[],[f895])).
% 0.20/0.30 thf(f898,definition,(
% 0.20/0.30 spl0_65 <=> ! [X0 : ($i > $i)] : ((((s @ zero)) != ((X0 @ zero))) | (((s @ zero)) != ((X0 @ (s @ (s @ zero))))))),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl0_65])],[avatar_definition])).
% 0.20/0.30 thf(f899,plain,(
% 0.20/0.30 ( ! [X0 : ($i > $i)] : ((((s @ zero)) != ((X0 @ (s @ (s @ zero))))) | (((s @ zero)) != ((X0 @ zero)))) ) | ~spl0_65),
% 0.20/0.30 inference(avatar_component_clause,[],[f898])).
% 0.20/0.30 thf(f900,plain,(
% 0.20/0.30 spl0_63 | spl0_64 | spl0_65 | ~spl0_2),
% 0.20/0.30 inference(avatar_split_clause,[],[f527,f31,f898,f895,f892])).
% 0.20/0.30 thf(f934,plain,(
% 0.20/0.30 ( ! [X0 : $i] : (((((^[Y0 : $i]: (zero)) @ (s @ (s @ zero)))) != X0)) ) | ~spl0_63),
% 0.20/0.30 inference(equality_resolution,[],[f893])).
% 0.20/0.30 thf(f935,plain,(
% 0.20/0.30 ( ! [X0 : $i] : ((zero != X0)) ) | ~spl0_63),
% 0.20/0.30 inference(beta-eta_normalization,[],[f934])).
% 0.20/0.30 thf(f963,plain,(
% 0.20/0.30 $false | ~spl0_63),
% 0.20/0.30 inference(equality_resolution,[],[f935])).
% 0.20/0.30 thf(f964,plain,(
% 0.20/0.30 ~spl0_63),
% 0.20/0.30 inference(avatar_contradiction_clause,[],[f963])).
% 0.20/0.30 thf(f1044,plain,(
% 0.20/0.30 (((s @ zero)) = ((s @ (s @ zero)))) | ($true = (((s @ zero) = zero))) | ~spl0_64),
% 0.20/0.30 inference(leibniz_equality_elimination,[],[f896])).
% 0.20/0.30 thf(f1086,plain,(
% 0.20/0.30 (((s @ zero)) = ((s @ (s @ zero)))) | (zero = ((s @ zero))) | ~spl0_64),
% 0.20/0.30 inference(equality_proxy_clausification,[],[f1044])).
% 0.20/0.30 thf(f1093,plain,(
% 0.20/0.30 (zero = ((s @ zero))) | ~spl0_64),
% 0.20/0.30 inference(forward_subsumption_resolution,[],[f1086,f11])).
% 0.20/0.30 thf(f1097,plain,(
% 0.20/0.30 $false | ~spl0_64),
% 0.20/0.30 inference(forward_subsumption_resolution,[],[f1093,f11])).
% 0.20/0.30 thf(f1098,plain,(
% 0.20/0.30 ~spl0_64),
% 0.20/0.30 inference(avatar_contradiction_clause,[],[f1097])).
% 0.20/0.30 thf(f1107,plain,(
% 0.20/0.30 (((s @ zero)) != (((^[Y0 : $i]: (s @ ((^[Y1 : $i]: (zero)) @ Y0))) @ zero))) | ~spl0_65),
% 0.20/0.30 inference(equality_resolution,[],[f899])).
% 0.20/0.30 thf(f1108,plain,(
% 0.20/0.30 (((s @ zero)) != ((s @ zero))) | ~spl0_65),
% 0.20/0.30 inference(beta-eta_normalization,[],[f1107])).
% 0.20/0.30 thf(f1109,plain,(
% 0.20/0.30 $false | ~spl0_65),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f1108])).
% 0.20/0.30 thf(f1110,plain,(
% 0.20/0.30 ~spl0_65),
% 0.20/0.30 inference(avatar_contradiction_clause,[],[f1109])).
% 0.20/0.30 cnf(s1, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f33])).
% 0.20/0.30 cnf(s24, plain, ~spl0_1, inference(sat_conversion,[],[f315])).
% 0.20/0.30 cnf(s68, plain, ~spl0_2 | spl0_63 | spl0_64 | spl0_65, inference(sat_conversion,[],[f900])).
% 0.20/0.30 cnf(s72, plain, ~spl0_63, inference(sat_conversion,[],[f964])).
% 0.20/0.30 cnf(s77, plain, ~spl0_64, inference(sat_conversion,[],[f1098])).
% 0.20/0.30 cnf(s80, plain, ~spl0_65, inference(sat_conversion,[],[f1110])).
% 0.20/0.30 cnf(s84, plain, ~spl0_2, inference(rat,[],[s68,s80,s77,s72])).
% 0.20/0.30 cnf(s88, plain, $false, inference(rat,[],[s1,s84,s24])).
% 0.20/0.30 thf(f1135,plain,(
% 0.20/0.30 $false),
% 0.20/0.30 inference(avatar_sat_refutation,[],[s88])).
% 0.20/0.30 % SZS output end Proof for theBenchmark
% 0.20/0.30 % (1212196)------------------------------
% 0.20/0.30 % (1212196)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (1212196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (1212196)CaDiCaL version: 2.1.3
% 0.20/0.30 % (1212196)Termination reason: Refutation
% 0.20/0.30 % (1212196)Time elapsed: 0.032 s
% 0.20/0.30 % (1212196)Peak memory usage: 13 MB
% 0.20/0.30 % (1212196)Instructions burned: 120 (million)
% 0.20/0.30 % (1212186)Success in time 0.068 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------