%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO030^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 08:48:45 AM UTC 2026
% Result : Theorem 0.40s 0.28s
% Output : Refutation 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO030^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n005.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 16:23:16 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 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
% 0.40/0.28 % (1872574)Will run a generic schedule for satisfiability detection.
% 0.40/0.28 % (1872581)% WARNING: option uhcvi not known.
% 0.40/0.28 % (1872581)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2898706790:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.40/0.28 % (1872581)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.40/0.28 % (1872581)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.40/0.28 % (1872580)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=197695659_2999 on theBenchmark for (2999ds/0Mi)
% 0.40/0.28 % (1872582)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1829230991:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.40/0.28 % Exception at run slice level% (1872584)dis+10_1_sil=32000:sp=arity:random_seed=416876427:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.40/0.28
% 0.40/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.40/0.28 % (1872590)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1375226117:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.40/0.28 % (1872586)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=174825086:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.40/0.28 % (1872586)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.40/0.28 % (1872588)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3869625285:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.40/0.28 % (1872600)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=595045223:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.40/0.28 % Exception at run slice level
% 0.40/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.40/0.28 % (1872584) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1872574-1872584"...
% 0.40/0.28 % (1872584)...printing done.
% 0.40/0.28 % (1872584)Refutation found. Thanks to Tanya!
% 0.40/0.28 % SZS status Theorem for theBenchmark
% 0.40/0.28 % SZS output start Proof for theBenchmark
% 0.40/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.40/0.28 thf(func_def_0, type, leibeq: ($o > $o > $o)).
% 0.40/0.28 thf(func_def_2, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.40/0.28 thf(func_def_3, type, vIMP: ($o > $o > $o)).
% 0.40/0.28 thf(func_def_4, type, db0: !>[X0: $tType]:(X0)).
% 0.40/0.28 thf(func_def_5, type, db2: !>[X0: $tType]:(X0)).
% 0.40/0.28 thf(func_def_6, type, db1: !>[X0: $tType]:(X0)).
% 0.40/0.28 thf(func_def_7, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.40/0.28 thf(func_def_10, type, sK0: (($o > $o) > $o)).
% 0.40/0.28 thf(func_def_11, type, vNOT: ($o > $o)).
% 0.40/0.28 thf(func_def_12, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.40/0.28 thf(f1,axiom,(
% 0.40/0.28 (leibeq = (^[X0 : $o, X1 : $o] : (! [X2 : ($o > $o)] : ((X2 @ X0) => (X2 @ X1)))))),
% 0.40/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leibeq)).
% 0.40/0.28 thf(f2,conjecture,(
% 0.40/0.28 ~ ! [X0 : ($o > $o)] : ? [X1 : $o] : (leibeq @ (X0 @ X1) @ X1)),
% 0.40/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 0.40/0.28 thf(f3,negated_conjecture,(
% 0.40/0.28 ~ ~ ! [X0 : ($o > $o)] : ? [X1 : $o] : (leibeq @ (X0 @ X1) @ X1)),
% 0.40/0.28 inference(negated_conjecture,[status(cth)],[f2])).
% 0.40/0.28 thf(f4,plain,(
% 0.40/0.28 (leibeq = (^[X0 : $o, X1 : $o] : (! [X2 : ($o > $o)] : ((X2 @ X0) => (X2 @ X1)))))),
% 0.40/0.28 inference(rectify,[],[f1])).
% 0.40/0.28 thf(f5,plain,(
% 0.40/0.28 (leibeq = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 0.40/0.28 inference(fool_elimination,[],[f4])).
% 0.40/0.28 thf(f6,plain,(
% 0.40/0.28 ~ ~ ! [X0 : ($o > $o)] : ? [X1 : $o] : (leibeq @ (X0 @ X1) @ X1)),
% 0.40/0.28 inference(rectify,[],[f3])).
% 0.40/0.28 thf(f7,plain,(
% 0.40/0.28 ~ ~ ! [X0 : ($o > $o)] : ? [X1 : $o] : (((leibeq @ (X0 @ X1) @ X1)) = $true)),
% 0.40/0.28 inference(fool_elimination,[],[f6])).
% 0.40/0.28 thf(f8,plain,(
% 0.40/0.28 ! [X0 : ($o > $o)] : ? [X1 : $o] : (((leibeq @ (X0 @ X1) @ X1)) = $true)),
% 0.40/0.28 inference(flattening,[],[f7])).
% 0.40/0.28 thf(f9,plain,(
% 0.40/0.28 ! [X0 : ($o > $o)] : ($true = ((leibeq @ (X0 @ (sK0 @ X0)) @ (sK0 @ X0))))),
% 0.40/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f8])).
% 0.40/0.28 thf(f10,plain,(
% 0.40/0.28 (leibeq = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 0.40/0.28 inference(cnf_transformation,[],[f5])).
% 0.40/0.28 thf(f11,plain,(
% 0.40/0.28 ( ! [X0 : ($o > $o)] : (($true = ((leibeq @ (X0 @ (sK0 @ X0)) @ (sK0 @ X0))))) )),
% 0.40/0.28 inference(cnf_transformation,[],[f9])).
% 0.40/0.28 thf(f13,definition,(
% 0.40/0.28 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.40/0.28 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.40/0.28 thf(f14,plain,(
% 0.40/0.28 ( ! [X0 : ($o > $o)] : (($true = (((^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ (X0 @ (sK0 @ X0)) @ (sK0 @ X0))))) )),
% 0.40/0.28 inference(definition_unfolding,[],[f11,f10])).
% 0.40/0.28 thf(f15,plain,(
% 0.40/0.28 ( ! [X0 : ($o > $o)] : (($true = ((!! @ ($o > $o) @ (^[Y0 : $o > $o]: ((Y0 @ (X0 @ (sK0 @ X0))) => (Y0 @ (sK0 @ X0)))))))) )),
% 0.40/0.28 inference(beta-eta_normalization,[],[f14])).
% 0.40/0.28 thf(f16,plain,(
% 0.40/0.28 ( ! [X0 : ($o > $o),X1 : ($o > $o)] : (($true = (((^[Y0 : $o > $o]: ((Y0 @ (X0 @ (sK0 @ X0))) => (Y0 @ (sK0 @ X0)))) @ X1)))) )),
% 0.40/0.28 inference(pi_proxy_clausification,[],[f15])).
% 0.40/0.28 thf(f17,plain,(
% 0.40/0.28 ( ! [X0 : ($o > $o),X1 : ($o > $o)] : (($true = (((X1 @ (X0 @ (sK0 @ X0))) => (X1 @ (sK0 @ X0)))))) )),
% 0.40/0.28 inference(beta-eta_normalization,[],[f16])).
% 0.40/0.28 thf(f18,plain,(
% 0.40/0.28 ( ! [X0 : ($o > $o),X1 : ($o > $o)] : (($false = ((X1 @ (X0 @ (sK0 @ X0))))) | ($true = ((X1 @ (sK0 @ X0))))) )),
% 0.40/0.28 inference(imp_proxy_clausification,[],[f17])).
% 0.40/0.28 thf(f21,plain,(
% 0.40/0.28 ( ! [X0 : ($o > $o)] : (($false = (((^[Y0 : $o]: (Y0)) @ (X0 @ (sK0 @ X0))))) | ($true = (((^[Y0 : $o]: (Y0)) @ (sK0 @ X0))))) )),
% 0.40/0.28 inference(primitive_instantiation,[],[f18])).
% 0.40/0.28 thf(f44,plain,(
% 0.40/0.28 ( ! [X0 : ($o > $o)] : ((((X0 @ (sK0 @ X0))) = $false) | ($true = ((sK0 @ X0)))) )),
% 0.40/0.28 inference(beta-eta_normalization,[],[f21])).
% 0.40/0.28 thf(f83,plain,(
% 0.40/0.28 ( ! [X0 : ($o > $o),X1 : ($o > $o)] : (($false = ((X0 @ (X1 @ $true)))) | ($true = ((X0 @ $true))) | ($false = ((sK0 @ X1)))) )),
% 0.40/0.28 inference(constrained_superposition,[],[f18,f13])).
% 0.40/0.28 thf(f610,plain,(
% 0.40/0.28 ( ! [X0 : ($o > $o)] : (($true = ((X0 @ $true))) | (((sK0 @ X0)) = $false)) )),
% 0.40/0.28 inference(leibniz_equality_elimination,[],[f83])).
% 0.40/0.28 thf(f774,definition,(
% 0.40/0.28 spl1_13 <=> ! [X1 : ($o > $o)] : (($false = ((sK0 @ X1))) | ($true = ((X1 @ $true))))),
% 0.40/0.28 introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition])).
% 0.40/0.28 thf(f775,plain,(
% 0.40/0.28 ( ! [X1 : ($o > $o)] : (($false = ((sK0 @ X1))) | ($true = ((X1 @ $true)))) ) | ~spl1_13),
% 0.40/0.28 inference(avatar_component_clause,[],[f774])).
% 0.40/0.28 thf(f777,definition,(
% 0.40/0.28 spl1_14 <=> ! [X0 : ($o > $o)] : (($false = ((X0 @ $false))) | ($true = ((X0 @ $true))))),
% 0.40/0.28 introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition])).
% 0.40/0.28 thf(f778,plain,(
% 0.40/0.28 ( ! [X0 : ($o > $o)] : (($true = ((X0 @ $true))) | ($false = ((X0 @ $false)))) ) | ~spl1_14),
% 0.40/0.28 inference(avatar_component_clause,[],[f777])).
% 0.40/0.28 thf(f783,plain,(
% 0.40/0.28 spl1_13),
% 0.40/0.28 inference(avatar_split_clause,[],[f610,f774])).
% 0.40/0.28 thf(f788,plain,(
% 0.40/0.28 ( ! [X0 : ($o > $o)] : (($false = ((X0 @ $false))) | ($true = $false) | ($true = ((X0 @ $true)))) ) | ~spl1_13),
% 0.40/0.28 inference(constrained_superposition,[],[f44,f775])).
% 0.40/0.28 thf(f807,plain,(
% 0.40/0.28 ( ! [X0 : ($o > $o)] : (($false = ((X0 @ $false))) | ($true = ((X0 @ $true)))) ) | ~spl1_13),
% 0.40/0.28 inference(trivial_inequality_removal,[],[f788])).
% 0.40/0.28 thf(f819,plain,(
% 0.40/0.28 spl1_14 | ~spl1_13),
% 0.40/0.28 inference(avatar_split_clause,[],[f807,f774,f777])).
% 0.40/0.28 thf(f1003,plain,(
% 0.40/0.28 ($true = $false) | ~spl1_14),
% 0.40/0.28 inference(leibniz_equality_elimination,[],[f778])).
% 0.40/0.28 thf(f1110,plain,(
% 0.40/0.28 $false | ~spl1_14),
% 0.40/0.28 inference(trivial_inequality_removal,[],[f1003])).
% 0.40/0.28 thf(f1111,plain,(
% 0.40/0.28 ~spl1_14),
% 0.40/0.28 inference(avatar_contradiction_clause,[],[f1110])).
% 0.40/0.28 cnf(s24, plain, spl1_13, inference(sat_conversion,[],[f783])).
% 0.40/0.28 cnf(s27, plain, ~spl1_13 | spl1_14, inference(sat_conversion,[],[f819])).
% 0.40/0.28 cnf(s37, plain, ~spl1_14, inference(sat_conversion,[],[f1111])).
% 0.40/0.28 cnf(s40, plain, ~spl1_13, inference(rat,[],[s27,s37])).
% 0.40/0.28 cnf(s41, plain, $false, inference(rat,[],[s24,s40])).
% 0.40/0.28 thf(f1118,plain,(
% 0.40/0.28 $false),
% 0.40/0.28 inference(avatar_sat_refutation,[],[s41])).
% 0.40/0.28 % SZS output end Proof for theBenchmark
% 0.40/0.28 % (1872584)------------------------------
% 0.40/0.28 % (1872584)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.28 % (1872584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.28 % (1872584)CaDiCaL version: 2.1.3
% 0.40/0.28 % (1872584)Termination reason: Refutation
% 0.40/0.28 % (1872584)Time elapsed: 0.029 s
% 0.40/0.28 % (1872584)Peak memory usage: 13 MB
% 0.40/0.28 % (1872584)Instructions burned: 53 (million)
% 0.40/0.28 % (1872574)Success in time 0.067 s
% 0.40/0.28 % Vampire exiting
%------------------------------------------------------------------------------