%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO020^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 08:48:44 AM UTC 2026
% Result : Theorem 0.08s 0.24s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO020^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n014.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 16:23:08 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 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
% 0.08/0.24 % (2872608)Will run a generic schedule for satisfiability detection.
% 0.08/0.24 % (2872615)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=68956311:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.24 % (2872615) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2872608-2872615"...
% 0.08/0.24 % (2872615)...printing done.
% 0.08/0.24 % (2872615)Refutation found. Thanks to Tanya!
% 0.08/0.24 % SZS status Theorem for theBenchmark
% 0.08/0.24 % SZS output start Proof for theBenchmark
% 0.08/0.24 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.24 thf(func_def_0, type, leibeq: ($o > $o > $o)).
% 0.08/0.24 thf(func_def_2, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.08/0.24 thf(func_def_3, type, vIMP: ($o > $o > $o)).
% 0.08/0.24 thf(func_def_4, type, db0: !>[X0: $tType]:(X0)).
% 0.08/0.24 thf(func_def_5, type, db2: !>[X0: $tType]:(X0)).
% 0.08/0.24 thf(func_def_6, type, db1: !>[X0: $tType]:(X0)).
% 0.08/0.24 thf(func_def_7, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.08/0.24 thf(func_def_8, type, vAND: ($o > $o > $o)).
% 0.08/0.24 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.08/0.24 thf(func_def_10, type, vOR: ($o > $o > $o)).
% 0.08/0.24 thf(func_def_13, type, sK0: $o).
% 0.08/0.24 thf(func_def_14, type, sK1: $o).
% 0.08/0.24 thf(func_def_15, type, sK2: ($o > $o)).
% 0.08/0.24 thf(f1,axiom,(
% 0.08/0.24 (leibeq = (^[X0 : $o, X1 : $o] : (! [X2 : ($o > $o)] : ((X2 @ X0) => (X2 @ X1)))))),
% 0.08/0.24 file('/export/starexec/sandbox/benchmark/theBenchmark.p',leibeq)).
% 0.08/0.24 thf(f2,conjecture,(
% 0.08/0.24 ! [X0 : $o,X1 : $o] : (leibeq @ X1 & X0 @ ~(~X1 | ~X0))),
% 0.08/0.24 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.08/0.24 thf(f3,negated_conjecture,(
% 0.08/0.24 ~ ! [X0 : $o,X1 : $o] : (leibeq @ X1 & X0 @ ~(~X1 | ~X0))),
% 0.08/0.24 inference(negated_conjecture,[status(cth)],[f2])).
% 0.08/0.24 thf(f4,plain,(
% 0.08/0.24 (leibeq = (^[X0 : $o, X1 : $o] : (! [X2 : ($o > $o)] : ((X2 @ X0) => (X2 @ X1)))))),
% 0.08/0.24 inference(rectify,[],[f1])).
% 0.08/0.24 thf(f5,plain,(
% 0.08/0.24 (leibeq = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 0.08/0.24 inference(fool_elimination,[],[f4])).
% 0.08/0.24 thf(f6,plain,(
% 0.08/0.24 ~ ! [X0 : $o,X1 : $o] : (leibeq @ X1 & X0 @ ~(~X1 | ~X0))),
% 0.08/0.24 inference(rectify,[],[f3])).
% 0.08/0.24 thf(f7,plain,(
% 0.08/0.24 ~ ! [X0 : $o,X1 : $o] : (((leibeq @ (X0 & X1) @ (~ ((~ X0) | (~ X1))))) = $true)),
% 0.08/0.24 inference(fool_elimination,[],[f6])).
% 0.08/0.24 thf(f8,plain,(
% 0.08/0.24 ? [X0 : $o,X1 : $o] : (((leibeq @ (X0 & X1) @ (~ ((~ X0) | (~ X1))))) != $true)),
% 0.08/0.24 inference(ennf_transformation,[],[f7])).
% 0.08/0.24 thf(f9,plain,(
% 0.08/0.24 ($true != ((leibeq @ (sK0 & sK1) @ (~ ((~ sK0) | (~ sK1))))))),
% 0.08/0.24 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f8])).
% 0.08/0.24 thf(f10,plain,(
% 0.08/0.24 (leibeq = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 0.08/0.24 inference(cnf_transformation,[],[f5])).
% 0.08/0.24 thf(f11,plain,(
% 0.08/0.24 ($true != ((leibeq @ (sK0 & sK1) @ (~ ((~ sK0) | (~ sK1))))))),
% 0.08/0.24 inference(cnf_transformation,[],[f9])).
% 0.08/0.24 thf(f13,definition,(
% 0.08/0.24 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.08/0.24 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.08/0.24 thf(f14,plain,(
% 0.08/0.24 ($true != (((^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ (sK0 & sK1) @ (~ ((~ sK0) | (~ sK1))))))),
% 0.08/0.24 inference(definition_unfolding,[],[f11,f10])).
% 0.08/0.24 thf(f15,plain,(
% 0.08/0.24 ($true != ((!! @ ($o > $o) @ (^[Y0 : $o > $o]: ((Y0 @ (sK0 & sK1)) => (Y0 @ (~ ((~ sK0) | (~ sK1)))))))))),
% 0.08/0.24 inference(beta-eta_normalization,[],[f14])).
% 0.08/0.24 thf(f16,plain,(
% 0.08/0.24 ($false = (((^[Y0 : $o > $o]: ((Y0 @ (sK0 & sK1)) => (Y0 @ (~ ((~ sK0) | (~ sK1)))))) @ sK2)))),
% 0.08/0.24 inference(sigma_proxy_clausification,[],[f15])).
% 0.08/0.24 thf(f17,plain,(
% 0.08/0.24 ($false = (((sK2 @ (sK0 & sK1)) => (sK2 @ (~ ((~ sK0) | (~ sK1)))))))),
% 0.08/0.24 inference(beta-eta_normalization,[],[f16])).
% 0.08/0.24 thf(f18,plain,(
% 0.08/0.24 ($false = ((sK2 @ (~ ((~ sK0) | (~ sK1))))))),
% 0.08/0.24 inference(imp_proxy_clausification,[],[f17])).
% 0.08/0.24 thf(f19,plain,(
% 0.08/0.24 ($true = ((sK2 @ (sK0 & sK1))))),
% 0.08/0.24 inference(imp_proxy_clausification,[],[f17])).
% 0.08/0.24 thf(f36,plain,(
% 0.08/0.24 ($false = ((sK2 @ (~ ((~ sK0) | (~ $true)))))) | (sK1 = $false)),
% 0.08/0.24 inference(constrained_superposition,[],[f18,f13])).
% 0.08/0.24 thf(f37,plain,(
% 0.08/0.24 ($true = ((sK2 @ (sK0 & $true)))) | (sK1 = $false)),
% 0.08/0.24 inference(constrained_superposition,[],[f19,f13])).
% 0.08/0.24 thf(f39,plain,(
% 0.08/0.24 ($true = ((sK2 @ sK0))) | (sK1 = $false)),
% 0.08/0.24 inference(boolean_simplification,[],[f37])).
% 0.08/0.24 thf(f40,plain,(
% 0.08/0.24 ($false = ((sK2 @ (~ ((~ sK0) | $false))))) | (sK1 = $false)),
% 0.08/0.24 inference(boolean_simplification,[],[f36])).
% 0.08/0.24 thf(f41,plain,(
% 0.08/0.24 ($false = ((sK2 @ (~ (~ sK0))))) | (sK1 = $false)),
% 0.08/0.24 inference(boolean_simplification,[],[f40])).
% 0.08/0.24 thf(f42,plain,(
% 0.08/0.24 ($false = ((sK2 @ sK0))) | (sK1 = $false)),
% 0.08/0.24 inference(boolean_simplification,[],[f41])).
% 0.08/0.24 thf(f70,definition,(
% 0.08/0.24 spl3_3 <=> (sK1 = $false)),
% 0.08/0.24 introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition])).
% 0.08/0.24 thf(f71,plain,(
% 0.08/0.24 (sK1 != $false) | spl3_3),
% 0.08/0.24 inference(avatar_component_clause,[],[f70])).
% 0.08/0.24 thf(f72,plain,(
% 0.08/0.24 (sK1 = $false) | ~spl3_3),
% 0.08/0.24 inference(avatar_component_clause,[],[f70])).
% 0.08/0.24 thf(f74,definition,(
% 0.08/0.24 spl3_4 <=> ($true = ((sK2 @ sK0)))),
% 0.08/0.24 introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition])).
% 0.08/0.24 thf(f76,plain,(
% 0.08/0.24 ($true = ((sK2 @ sK0))) | ~spl3_4),
% 0.08/0.24 inference(avatar_component_clause,[],[f74])).
% 0.08/0.24 thf(f77,plain,(
% 0.08/0.24 spl3_3 | spl3_4),
% 0.08/0.24 inference(avatar_split_clause,[],[f39,f74,f70])).
% 0.08/0.24 thf(f79,plain,(
% 0.08/0.24 ($false = ((sK2 @ (~ ((~ sK0) | (~ $false)))))) | ~spl3_3),
% 0.08/0.24 inference(constrained_superposition,[],[f18,f72])).
% 0.08/0.24 thf(f80,plain,(
% 0.08/0.24 ($true = ((sK2 @ (sK0 & $false)))) | ~spl3_3),
% 0.08/0.24 inference(constrained_superposition,[],[f19,f72])).
% 0.08/0.24 thf(f81,plain,(
% 0.08/0.24 ($true = ((sK2 @ $false))) | ~spl3_3),
% 0.08/0.24 inference(boolean_simplification,[],[f80])).
% 0.08/0.24 thf(f82,plain,(
% 0.08/0.24 ($false = ((sK2 @ (~ ((~ sK0) | $true))))) | ~spl3_3),
% 0.08/0.24 inference(boolean_simplification,[],[f79])).
% 0.08/0.24 thf(f83,plain,(
% 0.08/0.24 ($false = ((sK2 @ (~ $true)))) | ~spl3_3),
% 0.08/0.24 inference(boolean_simplification,[],[f82])).
% 0.08/0.24 thf(f84,plain,(
% 0.08/0.24 ($false = ((sK2 @ $false))) | ~spl3_3),
% 0.08/0.24 inference(boolean_simplification,[],[f83])).
% 0.08/0.24 thf(f87,plain,(
% 0.08/0.24 ($true = $false) | ~spl3_3),
% 0.08/0.24 inference(constrained_superposition,[],[f84,f81])).
% 0.08/0.24 thf(f91,plain,(
% 0.08/0.24 $false | ~spl3_3),
% 0.08/0.24 inference(trivial_inequality_removal,[],[f87])).
% 0.08/0.24 thf(f92,plain,(
% 0.08/0.24 ~spl3_3),
% 0.08/0.24 inference(avatar_contradiction_clause,[],[f91])).
% 0.08/0.24 thf(f96,plain,(
% 0.08/0.24 ($false = ((sK2 @ sK0))) | spl3_3),
% 0.08/0.24 inference(forward_subsumption_resolution,[],[f42,f71])).
% 0.08/0.24 thf(f99,plain,(
% 0.08/0.24 ($true = $false) | (spl3_3 | ~spl3_4)),
% 0.08/0.24 inference(constrained_superposition,[],[f96,f76])).
% 0.08/0.24 thf(f103,plain,(
% 0.08/0.24 $false | (spl3_3 | ~spl3_4)),
% 0.08/0.24 inference(trivial_inequality_removal,[],[f99])).
% 0.08/0.24 thf(f104,plain,(
% 0.08/0.24 spl3_3 | ~spl3_4),
% 0.08/0.24 inference(avatar_contradiction_clause,[],[f103])).
% 0.08/0.24 cnf(s22, plain, spl3_3 | spl3_4, inference(sat_conversion,[],[f77])).
% 0.08/0.24 cnf(s30, plain, ~spl3_3, inference(sat_conversion,[],[f92])).
% 0.08/0.24 cnf(s40, plain, spl3_3 | ~spl3_4, inference(sat_conversion,[],[f104])).
% 0.08/0.24 cnf(s42, plain, ~spl3_4, inference(rat,[],[s40,s30])).
% 0.08/0.24 cnf(s43, plain, $false, inference(rat,[],[s22,s42,s30])).
% 0.08/0.24 thf(f106,plain,(
% 0.08/0.24 $false),
% 0.08/0.24 inference(avatar_sat_refutation,[],[s43])).
% 0.08/0.24 % SZS output end Proof for theBenchmark
% 0.08/0.24 % (2872615)------------------------------
% 0.08/0.24 % (2872615)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.24 % (2872615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.24 % (2872615)CaDiCaL version: 2.1.3
% 0.08/0.24 % (2872615)Termination reason: Refutation
% 0.08/0.24 % (2872615)Time elapsed: 0.003 s
% 0.08/0.24 % (2872615)Peak memory usage: 13 MB
% 0.08/0.24 % (2872615)Instructions burned: 5 (million)
% 0.08/0.24 % (2872608)Success in time 0.033 s
% 0.08/0.24 % Vampire exiting
%------------------------------------------------------------------------------