%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO513^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 08:50:21 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO513^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n009.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 17:12:00 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.28 % (92726)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (92735)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3751785196:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (92735)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (92732)% WARNING: option uhcvi not known.
% 0.20/0.28 % (92732)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=272302558:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (92731)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3110807464_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (92732)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (92733)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3861693932:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (92732)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.28 % (92734)dis+10_1_sil=32000:sp=arity:random_seed=951361576:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % Exception at run slice level
% 0.20/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.28 % (92736)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3485867624:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (92735) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-92726-92735"...
% 0.20/0.28 % (92735)...printing done.
% 0.20/0.28 % (92735)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% 0.20/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.28 thf(func_def_3, type, sK0: ((($o > $o) > $o) > $o > $o)).
% 0.20/0.28 thf(func_def_4, type, sK1: ((($o > $o) > $o) > $o)).
% 0.20/0.28 thf(func_def_5, type, vNOT: ($o > $o)).
% 0.20/0.28 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.28 thf(func_def_7, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.28 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.28 thf(func_def_10, type, sK3: ((($o > $o) > ($o > $o) > ($o > $o) > $o) > $o > $o)).
% 0.20/0.28 thf(func_def_11, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.28 thf(func_def_12, type, db3: !>[X0: $tType]:(X0)).
% 0.20/0.28 thf(func_def_13, type, db4: !>[X0: $tType]:(X0)).
% 0.20/0.28 thf(func_def_14, type, db5: !>[X0: $tType]:(X0)).
% 0.20/0.28 thf(func_def_15, type, sK4: ((($o > $o) > $o) > (($o > $o) > ($o > $o) > $o) > $o > $o)).
% 0.20/0.28 thf(f1,conjecture,(
% 0.20/0.28 ? [X0 : (($o > $o) > $o)] : ! [X1 : ($o > $o)] : (? [X2 : $o] : (X1 @ X2) => (X1 @ (X0 @ X1)))),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choiceo)).
% 0.20/0.28 thf(f2,negated_conjecture,(
% 0.20/0.28 ~ ? [X0 : (($o > $o) > $o)] : ! [X1 : ($o > $o)] : (? [X2 : $o] : (X1 @ X2) => (X1 @ (X0 @ X1)))),
% 0.20/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.28 thf(f3,plain,(
% 0.20/0.28 ~ ? [X0 : (($o > $o) > $o)] : ! [X1 : ($o > $o)] : (? [X2 : $o] : (X1 @ X2) => (X1 @ (X0 @ X1)))),
% 0.20/0.28 inference(rectify,[],[f2])).
% 0.20/0.28 thf(f4,plain,(
% 0.20/0.28 ~ ? [X0 : (($o > $o) > $o)] : ! [X1 : ($o > $o)] : (? [X2 : $o] : (((X1 @ X2)) = $true) => (((X1 @ (X0 @ X1))) = $true))),
% 0.20/0.28 inference(fool_elimination,[],[f3])).
% 0.20/0.28 thf(f5,plain,(
% 0.20/0.28 ! [X0 : (($o > $o) > $o)] : ? [X1 : ($o > $o)] : ((((X1 @ (X0 @ X1))) != $true) & ? [X2 : $o] : (((X1 @ X2)) = $true))),
% 0.20/0.28 inference(ennf_transformation,[],[f4])).
% 0.20/0.28 thf(f6,plain,(
% 0.20/0.28 ! [X0 : (($o > $o) > $o)] : (($true != ((sK0 @ X0 @ (X0 @ (sK0 @ X0))))) & ($true = ((sK0 @ X0 @ (sK1 @ X0)))))),
% 0.20/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X2,sK1 @ X0),skolemize(X2,sK1 @ X0)],[f5])).
% 0.20/0.28 thf(f7,plain,(
% 0.20/0.28 ( ! [X0 : (($o > $o) > $o)] : (($true = ((sK0 @ X0 @ (sK1 @ X0))))) )),
% 0.20/0.28 inference(cnf_transformation,[],[f6])).
% 0.20/0.28 thf(f8,plain,(
% 0.20/0.28 ( ! [X0 : (($o > $o) > $o)] : (($true != ((sK0 @ X0 @ (X0 @ (sK0 @ X0)))))) )),
% 0.20/0.28 inference(cnf_transformation,[],[f6])).
% 0.20/0.28 thf(f10,definition,(
% 0.20/0.28 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.28 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.28 thf(f20,plain,(
% 0.20/0.28 ( ! [X0 : (($o > $o) > $o)] : (($true = ((sK0 @ X0 @ $true))) | (((sK1 @ X0)) = $false)) )),
% 0.20/0.28 inference(constrained_superposition,[],[f7,f10])).
% 0.20/0.28 thf(f21,plain,(
% 0.20/0.28 ( ! [X0 : (($o > $o) > $o)] : ((((X0 @ (sK0 @ X0))) = $false) | ($true != ((sK0 @ X0 @ $true)))) )),
% 0.20/0.28 inference(constrained_superposition,[],[f8,f10])).
% 0.20/0.28 thf(f49,definition,(
% 0.20/0.28 spl2_2 <=> ($true = ((sK0 @ (^[Y0 : $o > $o]: (Y0 @ $true)) @ $true)))),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.20/0.28 thf(f50,plain,(
% 0.20/0.28 ($true = ((sK0 @ (^[Y0 : $o > $o]: (Y0 @ $true)) @ $true))) | ~spl2_2),
% 0.20/0.28 inference(avatar_component_clause,[],[f49])).
% 0.20/0.28 thf(f51,plain,(
% 0.20/0.28 ($true != ((sK0 @ (^[Y0 : $o > $o]: (Y0 @ $true)) @ $true))) | spl2_2),
% 0.20/0.28 inference(avatar_component_clause,[],[f49])).
% 0.20/0.28 thf(f96,definition,(
% 0.20/0.28 spl2_3 <=> ($false = ((sK0 @ (^[Y0 : $o > $o]: (Y0 @ $true)) @ $true)))),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.20/0.28 thf(f98,plain,(
% 0.20/0.28 ($false = ((sK0 @ (^[Y0 : $o > $o]: (Y0 @ $true)) @ $true))) | ~spl2_3),
% 0.20/0.28 inference(avatar_component_clause,[],[f96])).
% 0.20/0.28 thf(f327,plain,(
% 0.20/0.28 ($true != $true) | ($false = ((sK0 @ (^[Y0 : $o > $o]: (Y0 @ $true)) @ $true))) | spl2_2),
% 0.20/0.28 inference(constrained_superposition,[],[f51,f10])).
% 0.20/0.28 thf(f328,plain,(
% 0.20/0.28 ($true != $true) | ($false = ((sK1 @ (^[Y0 : $o > $o]: (Y0 @ $true))))) | spl2_2),
% 0.20/0.28 inference(constrained_superposition,[],[f51,f20])).
% 0.20/0.28 thf(f333,plain,(
% 0.20/0.28 ($false = ((sK1 @ (^[Y0 : $o > $o]: (Y0 @ $true))))) | spl2_2),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f328])).
% 0.20/0.28 thf(f334,plain,(
% 0.20/0.28 ($false = ((sK0 @ (^[Y0 : $o > $o]: (Y0 @ $true)) @ $true))) | spl2_2),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f327])).
% 0.20/0.28 thf(f338,plain,(
% 0.20/0.28 spl2_3 | spl2_2),
% 0.20/0.28 inference(avatar_split_clause,[],[f334,f49,f96])).
% 0.20/0.28 thf(f340,plain,(
% 0.20/0.28 ($true = ((sK0 @ (^[Y0 : $o > $o]: (Y0 @ $true)) @ $false))) | spl2_2),
% 0.20/0.28 inference(constrained_superposition,[],[f7,f333])).
% 0.20/0.28 thf(f352,plain,(
% 0.20/0.28 ($true != ((sK0 @ (^[Y0 : $o > $o]: (Y0 @ ((^[Y1 : $o > $o]: ($true)) @ Y0))) @ $false))) | ~spl2_3),
% 0.20/0.28 inference(constrained_superposition,[],[f8,f98])).
% 0.20/0.28 thf(f358,plain,(
% 0.20/0.28 ($true != ((sK0 @ (^[Y0 : $o > $o]: (Y0 @ $true)) @ $false))) | ~spl2_3),
% 0.20/0.28 inference(beta-eta_normalization,[],[f352])).
% 0.20/0.28 thf(f363,plain,(
% 0.20/0.28 $false | (spl2_2 | ~spl2_3)),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f358,f340])).
% 0.20/0.28 thf(f364,plain,(
% 0.20/0.28 spl2_2 | ~spl2_3),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f363])).
% 0.20/0.28 thf(f390,plain,(
% 0.20/0.28 ($true = $false) | ($true != ((sK0 @ (^[Y0 : $o > $o]: (Y0 @ ((^[Y1 : $o > $o]: ($true)) @ Y0))) @ $true))) | ~spl2_2),
% 0.20/0.28 inference(constrained_superposition,[],[f50,f21])).
% 0.20/0.28 thf(f408,plain,(
% 0.20/0.28 ($true != ((sK0 @ (^[Y0 : $o > $o]: (Y0 @ ((^[Y1 : $o > $o]: ($true)) @ Y0))) @ $true))) | ~spl2_2),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f390])).
% 0.20/0.28 thf(f409,plain,(
% 0.20/0.28 ($true != ((sK0 @ (^[Y0 : $o > $o]: (Y0 @ $true)) @ $true))) | ~spl2_2),
% 0.20/0.28 inference(beta-eta_normalization,[],[f408])).
% 0.20/0.28 thf(f419,plain,(
% 0.20/0.28 $false | ~spl2_2),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f409,f50])).
% 0.20/0.28 thf(f420,plain,(
% 0.20/0.28 ~spl2_2),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f419])).
% 0.20/0.28 cnf(s14, plain, spl2_2 | spl2_3, inference(sat_conversion,[],[f338])).
% 0.20/0.28 cnf(s15, plain, spl2_2 | ~spl2_3, inference(sat_conversion,[],[f364])).
% 0.20/0.28 cnf(s20, plain, ~spl2_2, inference(sat_conversion,[],[f420])).
% 0.20/0.28 cnf(s21, plain, ~spl2_3, inference(rat,[],[s15,s20])).
% 0.20/0.28 cnf(s22, plain, $false, inference(rat,[],[s14,s21,s20])).
% 0.20/0.28 thf(f421,plain,(
% 0.20/0.28 $false),
% 0.20/0.28 inference(avatar_sat_refutation,[],[s22])).
% 0.20/0.28 % SZS output end Proof for theBenchmark
% 0.20/0.28 % (92735)------------------------------
% 0.20/0.28 % (92735)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (92735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (92735)CaDiCaL version: 2.1.3
% 0.20/0.28 % (92735)Termination reason: Refutation
% 0.20/0.28 % (92735)Time elapsed: 0.013 s
% 0.20/0.28 % (92735)Peak memory usage: 13 MB
% 0.20/0.28 % (92735)Instructions burned: 41 (million)
% 0.20/0.28 % (92726)Success in time 0.042 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------