%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN024^2 : 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 : n016.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 0.34s 0.42s
% Output : Refutation 0.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN024^2 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.28 % Computer : n016.cluster.edu
% 0.11/0.28 % Model : x86_64 x86_64
% 0.11/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.28 % Memory : 8046.5625MB
% 0.11/0.28 % OS : Linux 6.8.0-71-generic
% 0.11/0.28 % CPULimit : 300
% 0.11/0.28 % WCLimit : 300
% 0.11/0.28 % DateTime : Tue Sep 29 13:11:04 UTC 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.30/0.34 Running first-order model finding
% 0.30/0.34 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
% 0.34/0.42 % (316027)Will run a generic schedule for satisfiability detection.
% 0.34/0.42 % (316035)dis+10_1_sil=32000:sp=arity:random_seed=4223451447:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.34/0.42 % (316033)% WARNING: option uhcvi not known.
% 0.34/0.42 % (316034)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3975772952:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.34/0.42 % (316033)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3101499127:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.34/0.42 % (316032)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1947364751_2999 on theBenchmark for (2999ds/0Mi)
% 0.34/0.42 % (316036)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=955974353:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.34/0.42 % (316033)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.34/0.42 % (316038)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1924426466:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.34/0.42 % (316037)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1544365153:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.34/0.42 % (316036)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.34/0.42 % (316033)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.34/0.42 % Exception at run slice level
% 0.34/0.42 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.34/0.42 % (316038) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-316027-316038"...
% 0.34/0.42 % (316038)...printing done.
% 0.34/0.42 % (316038)Refutation found. Thanks to Tanya!
% 0.34/0.42 % SZS status Theorem for theBenchmark
% 0.34/0.42 % SZS output start Proof for theBenchmark
% 0.34/0.42 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.34/0.42 thf(func_def_1, type, s: ($i > $i)).
% 0.34/0.42 thf(func_def_2, type, ite: ($o > $i > $i > $i)).
% 0.34/0.42 thf(func_def_3, type, h: ($i > $i)).
% 0.34/0.42 thf(func_def_7, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.34/0.42 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.34/0.42 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.34/0.42 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.34/0.42 thf(f1,conjecture,(
% 0.34/0.42 (! [X3 : $i] : (((h @ X3)) = ((ite @ (X3 = zero) @ (s @ zero) @ 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)))) = zero) & (((X4 @ (s @ zero))) = zero) & (((X4 @ zero)) = ((s @ zero))))),
% 0.34/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',n10)).
% 0.34/0.42 thf(f2,negated_conjecture,(
% 0.34/0.42 ~((! [X3 : $i] : (((h @ X3)) = ((ite @ (X3 = zero) @ (s @ zero) @ 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)))) = zero) & (((X4 @ (s @ zero))) = zero) & (((X4 @ zero)) = ((s @ zero)))))),
% 0.34/0.42 inference(negated_conjecture,[status(cth)],[f1])).
% 0.34/0.42 thf(f3,plain,(
% 0.34/0.42 ~((! [X0 : $i] : (((h @ X0)) = ((ite @ (zero = X0) @ (s @ zero) @ 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)] : ((zero = ((X9 @ (s @ (s @ zero))))) & (zero = ((X9 @ (s @ zero)))) & (((s @ zero)) = ((X9 @ zero)))))),
% 0.34/0.42 inference(rectify,[],[f2])).
% 0.34/0.42 thf(f4,plain,(
% 0.34/0.42 ~((! [X0 : $i] : (((h @ X0)) = ((ite @ (zero = X0) @ (s @ zero) @ 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)] : ((zero = ((X9 @ (s @ (s @ zero))))) & (zero = ((X9 @ (s @ zero)))) & (((s @ zero)) = ((X9 @ zero)))))),
% 0.34/0.42 inference(fool_elimination,[],[f3])).
% 0.34/0.42 thf(f5,plain,(
% 0.34/0.42 ~((! [X0 : $i] : (((h @ X0)) = ((ite @ (zero = X0) @ (s @ zero) @ 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 > $i)] : ((zero = ((X9 @ (s @ (s @ zero))))) & (zero = ((X9 @ (s @ zero)))) & (((s @ zero)) = ((X9 @ zero)))))),
% 0.34/0.42 inference(flattening,[],[f4])).
% 0.34/0.42 thf(f6,plain,(
% 0.34/0.42 ! [X9 : ($i > $i)] : ((zero != ((X9 @ (s @ (s @ zero))))) | (zero != ((X9 @ (s @ zero)))) | (((s @ zero)) != ((X9 @ zero)))) & (! [X0 : $i] : (((h @ X0)) = ((ite @ (zero = X0) @ (s @ zero) @ 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)))),
% 0.34/0.42 inference(ennf_transformation,[],[f5])).
% 0.34/0.42 thf(f7,plain,(
% 0.34/0.42 ! [X9 : ($i > $i)] : ((zero != ((X9 @ (s @ (s @ zero))))) | (zero != ((X9 @ (s @ zero)))) | (((s @ zero)) != ((X9 @ zero)))) & ! [X0 : $i] : (((h @ X0)) = ((ite @ (zero = X0) @ (s @ zero) @ 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))),
% 0.34/0.42 inference(flattening,[],[f6])).
% 0.34/0.42 thf(f8,plain,(
% 0.34/0.42 ! [X0 : ($i > $i)] : ((zero != ((X0 @ (s @ (s @ zero))))) | (zero != ((X0 @ (s @ zero)))) | (((s @ zero)) != ((X0 @ zero)))) & ! [X1 : $i] : (((h @ X1)) = ((ite @ (zero = X1) @ (s @ zero) @ 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))),
% 0.34/0.42 inference(rectify,[],[f7])).
% 0.34/0.42 thf(f9,plain,(
% 0.34/0.42 ( ! [X8 : $i,X9 : $i,X7 : $o] : ((((ite @ X7 @ X8 @ X9)) = X8) | ($true != X7)) )),
% 0.34/0.42 inference(cnf_transformation,[],[f8])).
% 0.34/0.42 thf(f10,plain,(
% 0.34/0.42 ( ! [X6 : $i,X4 : $o,X5 : $i] : ((((ite @ X4 @ X5 @ X6)) = X6) | ($true = X4)) )),
% 0.34/0.42 inference(cnf_transformation,[],[f8])).
% 0.34/0.42 thf(f11,plain,(
% 0.34/0.42 ( ! [X3 : $i] : ((((s @ X3)) != zero)) )),
% 0.34/0.42 inference(cnf_transformation,[],[f8])).
% 0.34/0.42 thf(f12,plain,(
% 0.34/0.42 ( ! [X2 : $i] : ((((s @ X2)) != X2)) )),
% 0.34/0.42 inference(cnf_transformation,[],[f8])).
% 0.34/0.42 thf(f13,plain,(
% 0.34/0.42 ( ! [X1 : $i] : ((((h @ X1)) = ((ite @ (zero = X1) @ (s @ zero) @ zero)))) )),
% 0.34/0.42 inference(cnf_transformation,[],[f8])).
% 0.34/0.42 thf(f14,plain,(
% 0.34/0.42 ( ! [X0 : ($i > $i)] : ((((s @ zero)) != ((X0 @ zero))) | (zero != ((X0 @ (s @ zero)))) | (zero != ((X0 @ (s @ (s @ zero)))))) )),
% 0.34/0.42 inference(cnf_transformation,[],[f8])).
% 0.34/0.42 thf(f16,definition,(
% 0.34/0.42 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.34/0.42 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.34/0.42 thf(f17,plain,(
% 0.34/0.42 ( ! [X8 : $i,X9 : $i] : ((((ite @ $true @ X8 @ X9)) = X8)) )),
% 0.34/0.42 inference(equality_resolution,[],[f9])).
% 0.34/0.42 thf(f39,plain,(
% 0.34/0.42 ( ! [X0 : $i] : ((zero = ((h @ X0))) | ($true = ((zero = X0)))) )),
% 0.34/0.42 inference(constrained_superposition,[],[f10,f13])).
% 0.34/0.42 thf(f54,plain,(
% 0.34/0.42 ( ! [X0 : $i] : ((zero = ((h @ X0))) | (zero = X0)) )),
% 0.34/0.42 inference(equality_proxy_clausification,[],[f39])).
% 0.34/0.42 thf(f85,plain,(
% 0.34/0.42 ( ! [X2 : $i,X0 : $o,X1 : $i] : ((((ite @ X0 @ X1 @ X2)) = X1) | ($false = X0)) )),
% 0.34/0.42 inference(constrained_superposition,[],[f17,f16])).
% 0.34/0.42 thf(f97,plain,(
% 0.34/0.42 ( ! [X0 : $i] : ((((s @ zero)) = ((h @ X0))) | (((zero = X0)) = $false)) )),
% 0.34/0.42 inference(constrained_superposition,[],[f13,f85])).
% 0.34/0.42 thf(f98,plain,(
% 0.34/0.42 ( ! [X0 : $i] : ((zero != X0) | (((s @ zero)) = ((h @ X0)))) )),
% 0.34/0.42 inference(equality_proxy_clausification,[],[f97])).
% 0.34/0.42 thf(f120,plain,(
% 0.34/0.42 (((s @ zero)) = ((h @ zero)))),
% 0.34/0.42 inference(equality_resolution,[],[f98])).
% 0.34/0.42 thf(f121,plain,(
% 0.34/0.42 (((s @ zero)) != ((s @ zero))) | (zero != (((^[Y0 : $i]: (h @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (s @ zero)))) | (zero != (((^[Y0 : $i]: (h @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (s @ (s @ zero)))))),
% 0.34/0.42 inference(constrained_superposition,[],[f14,f120])).
% 0.34/0.42 thf(f129,plain,(
% 0.34/0.42 (zero != (((^[Y0 : $i]: (h @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (s @ zero)))) | (zero != (((^[Y0 : $i]: (h @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (s @ (s @ zero)))))),
% 0.34/0.42 inference(trivial_inequality_removal,[],[f121])).
% 0.34/0.42 thf(f130,plain,(
% 0.34/0.42 (zero != ((h @ (s @ zero)))) | (zero != ((h @ (s @ (s @ zero)))))),
% 0.34/0.42 inference(beta-eta_normalization,[],[f129])).
% 0.34/0.42 thf(f132,definition,(
% 0.34/0.42 spl0_11 <=> (zero = ((h @ (s @ (s @ zero)))))),
% 0.34/0.42 introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition])).
% 0.34/0.42 thf(f134,plain,(
% 0.34/0.42 (zero != ((h @ (s @ (s @ zero))))) | spl0_11),
% 0.34/0.42 inference(avatar_component_clause,[],[f132])).
% 0.34/0.42 thf(f136,definition,(
% 0.34/0.42 spl0_12 <=> (zero = ((h @ (s @ zero))))),
% 0.34/0.42 introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition])).
% 0.34/0.42 thf(f138,plain,(
% 0.34/0.42 (zero != ((h @ (s @ zero)))) | spl0_12),
% 0.34/0.42 inference(avatar_component_clause,[],[f136])).
% 0.34/0.42 thf(f139,plain,(
% 0.34/0.42 ~spl0_11 | ~spl0_12),
% 0.34/0.42 inference(avatar_split_clause,[],[f130,f136,f132])).
% 0.34/0.42 thf(f141,plain,(
% 0.34/0.42 (zero != zero) | (zero = ((s @ zero))) | spl0_12),
% 0.34/0.42 inference(constrained_superposition,[],[f138,f54])).
% 0.34/0.42 thf(f142,plain,(
% 0.34/0.42 (zero = ((s @ zero))) | spl0_12),
% 0.34/0.42 inference(trivial_inequality_removal,[],[f141])).
% 0.34/0.42 thf(f145,plain,(
% 0.34/0.42 (zero != zero) | spl0_12),
% 0.34/0.42 inference(constrained_superposition,[],[f12,f142])).
% 0.34/0.42 thf(f153,plain,(
% 0.34/0.42 $false | spl0_12),
% 0.34/0.42 inference(trivial_inequality_removal,[],[f145])).
% 0.34/0.42 thf(f154,plain,(
% 0.34/0.42 spl0_12),
% 0.34/0.42 inference(avatar_contradiction_clause,[],[f153])).
% 0.34/0.42 thf(f171,plain,(
% 0.34/0.42 (zero != zero) | (zero = ((s @ (s @ zero)))) | spl0_11),
% 0.34/0.42 inference(constrained_superposition,[],[f134,f54])).
% 0.34/0.42 thf(f172,plain,(
% 0.34/0.42 (zero = ((s @ (s @ zero)))) | spl0_11),
% 0.34/0.42 inference(trivial_inequality_removal,[],[f171])).
% 0.34/0.42 thf(f175,plain,(
% 0.34/0.42 (zero != zero) | spl0_11),
% 0.34/0.42 inference(constrained_superposition,[],[f11,f172])).
% 0.34/0.42 thf(f177,plain,(
% 0.34/0.42 $false | spl0_11),
% 0.34/0.42 inference(trivial_inequality_removal,[],[f175])).
% 0.34/0.42 thf(f178,plain,(
% 0.34/0.42 spl0_11),
% 0.34/0.42 inference(avatar_contradiction_clause,[],[f177])).
% 0.34/0.42 cnf(s9, plain, ~spl0_11 | ~spl0_12, inference(sat_conversion,[],[f139])).
% 0.34/0.42 cnf(s11, plain, spl0_12, inference(sat_conversion,[],[f154])).
% 0.34/0.42 cnf(s12, plain, spl0_11, inference(sat_conversion,[],[f178])).
% 0.34/0.42 cnf(s13, plain, $false, inference(rat,[],[s9,s11,s12])).
% 0.34/0.42 thf(f180,plain,(
% 0.34/0.42 $false),
% 0.34/0.42 inference(avatar_sat_refutation,[],[s13])).
% 0.34/0.42 % SZS output end Proof for theBenchmark
% 0.34/0.42 % (316038)------------------------------
% 0.34/0.42 % (316038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.42 % (316038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.42 % (316038)CaDiCaL version: 2.1.3
% 0.34/0.42 % (316038)Termination reason: Refutation
% 0.34/0.42 % (316038)Time elapsed: 0.015 s
% 0.34/0.42 % (316038)Peak memory usage: 13 MB
% 0.34/0.42 % (316038)Instructions burned: 13 (million)
% 0.34/0.42 % (316027)Success in time 0.066 s
% 0.34/0.42 % Vampire exiting
%------------------------------------------------------------------------------