%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n010.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 08:19:53 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : Refutation 0.23s
% 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.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n010.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 13:06:33 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.29 % (2818702)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.29 % (2818710)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=755890655:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.23/0.29 % (2818713)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.29 % (2818713)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.23/0.29 % (2818710) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2818702-2818710"...
% 0.23/0.29 % (2818710)...printing done.
% 0.23/0.29 % (2818710)Refutation found. Thanks to Tanya!
% 0.23/0.29 % SZS status Theorem for theBenchmark
% 0.23/0.29 % SZS output start Proof for theBenchmark
% 0.23/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.29 thf(func_def_1, type, s: ($i > $i)).
% 0.23/0.29 thf(func_def_2, type, ite: ($o > $i > $i > $i)).
% 0.23/0.29 thf(func_def_3, type, h: ($i > $i)).
% 0.23/0.29 thf(func_def_7, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.23/0.29 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.23/0.29 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.23/0.29 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.23/0.29 thf(f1,conjecture,(
% 0.23/0.29 (! [X3 : $i] : (((ite @ (X3 = zero) @ (s @ zero) @ zero)) = ((h @ X3))) & ! [X0 : $o,X1 : $i,X2 : $i] : (X0 => (((ite @ X0 @ X1 @ X2)) = X1)) & ! [X0 : $o,X2 : $i,X1 : $i] : (~X0 => (((ite @ X0 @ X1 @ X2)) = X2))) => ? [X4 : ($i > $i)] : ((((X4 @ zero)) = ((s @ zero))) & (((X4 @ (s @ zero))) = zero))),
% 0.23/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',n10)).
% 0.23/0.29 thf(f2,negated_conjecture,(
% 0.23/0.29 ~((! [X3 : $i] : (((ite @ (X3 = zero) @ (s @ zero) @ zero)) = ((h @ X3))) & ! [X0 : $o,X1 : $i,X2 : $i] : (X0 => (((ite @ X0 @ X1 @ X2)) = X1)) & ! [X0 : $o,X2 : $i,X1 : $i] : (~X0 => (((ite @ X0 @ X1 @ X2)) = X2))) => ? [X4 : ($i > $i)] : ((((X4 @ zero)) = ((s @ zero))) & (((X4 @ (s @ zero))) = zero)))),
% 0.23/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.23/0.29 thf(f3,plain,(
% 0.23/0.29 ~((! [X0 : $i] : (((ite @ (zero = X0) @ (s @ zero) @ zero)) = ((h @ X0))) & ! [X1 : $o,X2 : $i,X3 : $i] : (X1 => (((ite @ X1 @ X2 @ X3)) = X2)) & ! [X4 : $o,X5 : $i,X6 : $i] : (~X4 => (((ite @ X4 @ X6 @ X5)) = X5))) => ? [X7 : ($i > $i)] : ((((s @ zero)) = ((X7 @ zero))) & (zero = ((X7 @ (s @ zero))))))),
% 0.23/0.29 inference(rectify,[],[f2])).
% 0.23/0.29 thf(f4,plain,(
% 0.23/0.29 ~((! [X0 : $i] : (((ite @ (zero = X0) @ (s @ zero) @ zero)) = ((h @ X0))) & ! [X1 : $o,X2 : $i,X3 : $i] : (($true = X1) => (((ite @ X1 @ X2 @ X3)) = X2)) & ! [X4 : $o,X5 : $i,X6 : $i] : (~ ($true = X4) => (((ite @ X4 @ X6 @ X5)) = X5))) => ? [X7 : ($i > $i)] : ((zero = ((X7 @ (s @ zero)))) & (((s @ zero)) = ((X7 @ zero)))))),
% 0.23/0.29 inference(fool_elimination,[],[f3])).
% 0.23/0.29 thf(f5,plain,(
% 0.23/0.29 ~((! [X4 : $o,X6 : $i,X5 : $i] : (($true != X4) => (((ite @ X4 @ X6 @ X5)) = X5)) & ! [X0 : $i] : (((ite @ (zero = X0) @ (s @ zero) @ zero)) = ((h @ X0))) & ! [X1 : $o,X2 : $i,X3 : $i] : (($true = X1) => (((ite @ X1 @ X2 @ X3)) = X2))) => ? [X7 : ($i > $i)] : ((zero = ((X7 @ (s @ zero)))) & (((s @ zero)) = ((X7 @ zero)))))),
% 0.23/0.29 inference(flattening,[],[f4])).
% 0.23/0.29 thf(f6,plain,(
% 0.23/0.29 ! [X7 : ($i > $i)] : ((zero != ((X7 @ (s @ zero)))) | (((s @ zero)) != ((X7 @ zero)))) & (! [X6 : $i,X5 : $i,X4 : $o] : (($true = X4) | (((ite @ X4 @ X6 @ X5)) = X5)) & ! [X0 : $i] : (((ite @ (zero = X0) @ (s @ zero) @ zero)) = ((h @ X0))) & ! [X3 : $i,X1 : $o,X2 : $i] : ((((ite @ X1 @ X2 @ X3)) = X2) | ($true != X1)))),
% 0.23/0.29 inference(ennf_transformation,[],[f5])).
% 0.23/0.29 thf(f7,plain,(
% 0.23/0.29 ! [X7 : ($i > $i)] : ((zero != ((X7 @ (s @ zero)))) | (((s @ zero)) != ((X7 @ zero)))) & ! [X0 : $i] : (((ite @ (zero = X0) @ (s @ zero) @ zero)) = ((h @ X0))) & ! [X6 : $i,X5 : $i,X4 : $o] : (($true = X4) | (((ite @ X4 @ X6 @ X5)) = X5)) & ! [X3 : $i,X1 : $o,X2 : $i] : ((((ite @ X1 @ X2 @ X3)) = X2) | ($true != X1))),
% 0.23/0.29 inference(flattening,[],[f6])).
% 0.23/0.29 thf(f8,plain,(
% 0.23/0.29 ! [X0 : ($i > $i)] : ((zero != ((X0 @ (s @ zero)))) | (((s @ zero)) != ((X0 @ zero)))) & ! [X1 : $i] : (((h @ X1)) = ((ite @ (zero = X1) @ (s @ zero) @ zero))) & ! [X2 : $i,X3 : $i,X4 : $o] : (($true = X4) | (((ite @ X4 @ X2 @ X3)) = X3)) & ! [X5 : $i,X6 : $o,X7 : $i] : ((((ite @ X6 @ X7 @ X5)) = X7) | ($true != X6))),
% 0.23/0.29 inference(rectify,[],[f7])).
% 0.23/0.29 thf(f9,plain,(
% 0.23/0.29 ( ! [X6 : $o,X7 : $i,X5 : $i] : ((((ite @ X6 @ X7 @ X5)) = X7) | ($true != X6)) )),
% 0.23/0.29 inference(cnf_transformation,[],[f8])).
% 0.23/0.29 thf(f10,plain,(
% 0.23/0.29 ( ! [X2 : $i,X3 : $i,X4 : $o] : ((((ite @ X4 @ X2 @ X3)) = X3) | ($true = X4)) )),
% 0.23/0.29 inference(cnf_transformation,[],[f8])).
% 0.23/0.29 thf(f11,plain,(
% 0.23/0.29 ( ! [X1 : $i] : ((((h @ X1)) = ((ite @ (zero = X1) @ (s @ zero) @ zero)))) )),
% 0.23/0.29 inference(cnf_transformation,[],[f8])).
% 0.23/0.29 thf(f12,plain,(
% 0.23/0.29 ( ! [X0 : ($i > $i)] : ((((s @ zero)) != ((X0 @ zero))) | (zero != ((X0 @ (s @ zero))))) )),
% 0.23/0.29 inference(cnf_transformation,[],[f8])).
% 0.23/0.29 thf(f14,plain,(
% 0.23/0.29 ( ! [X7 : $i,X5 : $i] : ((((ite @ $true @ X7 @ X5)) = X7)) )),
% 0.23/0.29 inference(equality_resolution,[],[f9])).
% 0.23/0.29 thf(f17,plain,(
% 0.23/0.29 ( ! [X0 : $i] : ((zero = ((h @ X0))) | ($true = ((zero = X0)))) )),
% 0.23/0.29 inference(superposition,[],[f10,f11])).
% 0.23/0.29 thf(f18,plain,(
% 0.23/0.29 ( ! [X0 : $i] : ((zero = ((h @ X0))) | (zero = X0)) )),
% 0.23/0.29 inference(equality_proxy_clausification,[],[f17])).
% 0.23/0.29 thf(f28,plain,(
% 0.23/0.29 (((s @ zero)) != ((ite @ (zero = zero) @ (s @ zero) @ zero))) | (zero != ((h @ (s @ zero))))),
% 0.23/0.29 inference(superposition,[],[f12,f11])).
% 0.23/0.29 thf(f29,plain,(
% 0.23/0.29 (zero != ((s @ (s @ zero))))),
% 0.23/0.29 inference(equality_resolution,[],[f12])).
% 0.23/0.29 thf(f30,plain,(
% 0.23/0.29 (zero != ((h @ (s @ zero)))) | (((s @ zero)) != ((ite @ $true @ (s @ zero) @ zero)))),
% 0.23/0.29 inference(boolean_simplification,[],[f28])).
% 0.23/0.29 thf(f33,plain,(
% 0.23/0.29 (zero != ((h @ (s @ zero))))),
% 0.23/0.29 inference(forward_subsumption_resolution,[],[f30,f14])).
% 0.23/0.29 thf(f35,definition,(
% 0.23/0.29 spl0_1 <=> (zero = ((s @ (s @ zero))))),
% 0.23/0.29 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.23/0.29 thf(f38,plain,(
% 0.23/0.29 ~spl0_1),
% 0.23/0.29 inference(avatar_split_clause,[],[f29,f35])).
% 0.23/0.29 thf(f43,definition,(
% 0.23/0.29 spl0_3 <=> (zero = ((s @ zero)))),
% 0.23/0.29 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 0.23/0.29 thf(f45,plain,(
% 0.23/0.29 (zero != ((s @ zero))) | spl0_3),
% 0.23/0.29 inference(avatar_component_clause,[],[f43])).
% 0.23/0.29 thf(f48,definition,(
% 0.23/0.29 spl0_4 <=> (zero = ((h @ (s @ zero))))),
% 0.23/0.29 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
% 0.23/0.29 thf(f50,plain,(
% 0.23/0.29 (zero != ((h @ (s @ zero)))) | spl0_4),
% 0.23/0.29 inference(avatar_component_clause,[],[f48])).
% 0.23/0.29 thf(f51,plain,(
% 0.23/0.29 ~spl0_4),
% 0.23/0.29 inference(avatar_split_clause,[],[f33,f48])).
% 0.23/0.29 thf(f83,plain,(
% 0.23/0.29 (zero != zero) | (zero = ((s @ zero))) | spl0_4),
% 0.23/0.29 inference(superposition,[],[f50,f18])).
% 0.23/0.29 thf(f86,plain,(
% 0.23/0.29 (zero = ((s @ zero))) | spl0_4),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f83])).
% 0.23/0.29 thf(f87,plain,(
% 0.23/0.29 $false | (spl0_3 | spl0_4)),
% 0.23/0.29 inference(forward_subsumption_resolution,[],[f86,f45])).
% 0.23/0.29 thf(f88,plain,(
% 0.23/0.29 spl0_3 | spl0_4),
% 0.23/0.29 inference(avatar_contradiction_clause,[],[f87])).
% 0.23/0.29 thf(f94,definition,(
% 0.23/0.29 (zero != ((s @ zero))) | (zero = ((s @ (s @ zero))))),
% 0.23/0.29 introduced(theory,[theory_tautology_sat_conflict])).
% 0.23/0.29 cnf(s1, plain, ~spl0_1, inference(sat_conversion,[],[f38])).
% 0.23/0.29 cnf(s3, plain, ~spl0_4, inference(sat_conversion,[],[f51])).
% 0.23/0.29 cnf(s6, plain, spl0_3 | spl0_4, inference(sat_conversion,[],[f88])).
% 0.23/0.29 cnf(s8, plain, spl0_1 | ~spl0_3, inference(sat_conversion,[],[f94])).
% 0.23/0.29 cnf(s10, plain, spl0_3, inference(rat,[],[s6,s3])).
% 0.23/0.29 cnf(s11, plain, spl0_1, inference(rat,[],[s8,s10])).
% 0.23/0.29 cnf(s14, plain, $false, inference(rat,[],[s1,s11])).
% 0.23/0.29 thf(f95,plain,(
% 0.23/0.29 $false),
% 0.23/0.29 inference(avatar_sat_refutation,[],[s14])).
% 0.23/0.29 % SZS output end Proof for theBenchmark
% 0.23/0.29 % (2818710)------------------------------
% 0.23/0.29 % (2818710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (2818710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (2818710)CaDiCaL version: 2.1.3
% 0.23/0.29 % (2818710)Termination reason: Refutation
% 0.23/0.29 % (2818710)Time elapsed: 0.004 s
% 0.23/0.29 % (2818710)Peak memory usage: 13 MB
% 0.23/0.29 % (2818710)Instructions burned: 7 (million)
% 0.23/0.29 % (2818702)Success in time 0.034 s
% 0.23/0.29 % Vampire exiting
%------------------------------------------------------------------------------