%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO301^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:47:23 AM UTC 2026
% Result : Theorem 0.24s 0.30s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO301^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n003.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 16:46:14 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.30 % (2732073)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.30 % (2732079)lrs+10_16_si=on:nwc=1.5:random_seed=2545878342:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.30 % (2732080)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3937837464:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.30 % (2732079) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2732073-2732079"...
% 0.24/0.30 % (2732080) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2732073-2732080"...
% 0.24/0.30 % (2732079)...printing done.
% 0.24/0.30 % (2732080)...printing done.
% 0.24/0.30 % (2732079)Refutation found. Thanks to Tanya!
% 0.24/0.30 % SZS status Theorem for theBenchmark
% 0.24/0.30 % SZS output start Proof for theBenchmark
% 0.24/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.24/0.30 thf(func_def_0, type, f: ($i > $i)).
% 0.24/0.30 thf(func_def_1, type, cP: ($i > $o)).
% 0.24/0.30 thf(func_def_6, type, sK0: (($i > $o) > $i)).
% 0.24/0.30 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.24/0.30 thf(func_def_8, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.24/0.30 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.24/0.30 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.24/0.30 thf(f1,conjecture,(
% 0.24/0.30 (cP @ (f @ b)) => ? [X0 : $i,X1 : ($i > $o)] : ((X1 @ (f @ X0)) & ! [X2 : $i] : ((X1 @ X2) => (cP @ X2)))),
% 0.24/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBLEDSOE5)).
% 0.24/0.30 thf(f2,negated_conjecture,(
% 0.24/0.30 ~((cP @ (f @ b)) => ? [X0 : $i,X1 : ($i > $o)] : ((X1 @ (f @ X0)) & ! [X2 : $i] : ((X1 @ X2) => (cP @ X2))))),
% 0.24/0.30 inference(negated_conjecture,[status(cth)],[f1])).
% 0.24/0.30 thf(f3,plain,(
% 0.24/0.30 ~((cP @ (f @ b)) => ? [X0 : $i,X1 : ($i > $o)] : ((X1 @ (f @ X0)) & ! [X2 : $i] : ((X1 @ X2) => (cP @ X2))))),
% 0.24/0.30 inference(rectify,[],[f2])).
% 0.24/0.30 thf(f4,plain,(
% 0.24/0.30 ~((((cP @ (f @ b))) = $true) => ? [X1 : ($i > $o),X0 : $i] : (! [X2 : $i] : ((((X1 @ X2)) = $true) => (((cP @ X2)) = $true)) & (((X1 @ (f @ X0))) = $true)))),
% 0.24/0.30 inference(fool_elimination,[],[f3])).
% 0.24/0.30 thf(f5,plain,(
% 0.24/0.30 ! [X1 : ($i > $o),X0 : $i] : ((((X1 @ (f @ X0))) != $true) | ? [X2 : $i] : ((((cP @ X2)) != $true) & (((X1 @ X2)) = $true))) & (((cP @ (f @ b))) = $true)),
% 0.24/0.30 inference(ennf_transformation,[],[f4])).
% 0.24/0.30 thf(f6,plain,(
% 0.24/0.30 ! [X0 : ($i > $o),X1 : $i] : (($true != ((X0 @ (f @ X1)))) | ? [X2 : $i] : ((((cP @ X2)) != $true) & (((X0 @ X2)) = $true))) & (((cP @ (f @ b))) = $true)),
% 0.24/0.30 inference(rectify,[],[f5])).
% 0.24/0.30 thf(f7,plain,(
% 0.24/0.30 ! [X0 : ($i > $o),X1 : $i] : (($true != ((X0 @ (f @ X1)))) | (($true != ((cP @ (sK0 @ X0)))) & ($true = ((X0 @ (sK0 @ X0)))))) & (((cP @ (f @ b))) = $true)),
% 0.24/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X0)],[f6])).
% 0.24/0.30 thf(f8,plain,(
% 0.24/0.30 (((cP @ (f @ b))) = $true)),
% 0.24/0.30 inference(cnf_transformation,[],[f7])).
% 0.24/0.30 thf(f9,plain,(
% 0.24/0.30 ( ! [X0 : ($i > $o),X1 : $i] : (($true != ((X0 @ (f @ X1)))) | ($true = ((X0 @ (sK0 @ X0))))) )),
% 0.24/0.30 inference(cnf_transformation,[],[f7])).
% 0.24/0.30 thf(f10,plain,(
% 0.24/0.30 ( ! [X0 : ($i > $o),X1 : $i] : (($true != ((cP @ (sK0 @ X0)))) | ($true != ((X0 @ (f @ X1))))) )),
% 0.24/0.30 inference(cnf_transformation,[],[f7])).
% 0.24/0.30 thf(f17,plain,(
% 0.24/0.30 ( ! [X0 : $i] : (($true = (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK0 @ (^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | ($true != $true) | (b != X0)) )),
% 0.24/0.30 inference(constrained_superposition,[],[f9,f8])).
% 0.24/0.30 thf(f27,plain,(
% 0.24/0.30 ( ! [X0 : $i] : (($true = (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK0 @ (^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | (b != X0)) )),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f17])).
% 0.24/0.30 thf(f28,plain,(
% 0.24/0.30 ( ! [X0 : $i] : ((((cP @ (sK0 @ cP))) = $true) | (b != X0)) )),
% 0.24/0.30 inference(beta-eta_normalization,[],[f27])).
% 0.24/0.30 thf(f31,definition,(
% 0.24/0.30 spl1_1 <=> (((cP @ (sK0 @ cP))) = $true)),
% 0.24/0.30 introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition])).
% 0.24/0.30 thf(f33,plain,(
% 0.24/0.30 (((cP @ (sK0 @ cP))) = $true) | ~spl1_1),
% 0.24/0.30 inference(avatar_component_clause,[],[f31])).
% 0.24/0.30 thf(f35,definition,(
% 0.24/0.30 spl1_2 <=> ! [X0 : $i] : (b != X0)),
% 0.24/0.30 introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition])).
% 0.24/0.30 thf(f36,plain,(
% 0.24/0.30 ( ! [X0 : $i] : ((b != X0)) ) | ~spl1_2),
% 0.24/0.30 inference(avatar_component_clause,[],[f35])).
% 0.24/0.30 thf(f37,plain,(
% 0.24/0.30 spl1_1 | spl1_2),
% 0.24/0.30 inference(avatar_split_clause,[],[f28,f35,f31])).
% 0.24/0.30 thf(f38,plain,(
% 0.24/0.30 $false | ~spl1_2),
% 0.24/0.30 inference(equality_resolution,[],[f36])).
% 0.24/0.30 thf(f39,plain,(
% 0.24/0.30 ~spl1_2),
% 0.24/0.30 inference(avatar_contradiction_clause,[],[f38])).
% 0.24/0.30 thf(f43,plain,(
% 0.24/0.30 ( ! [X0 : $i] : (($true != $true) | ($true != ((cP @ (f @ X0))))) ) | ~spl1_1),
% 0.24/0.30 inference(constrained_superposition,[],[f10,f33])).
% 0.24/0.30 thf(f44,plain,(
% 0.24/0.30 ( ! [X0 : $i] : (($true != ((cP @ (f @ X0))))) ) | ~spl1_1),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f43])).
% 0.24/0.30 thf(f45,plain,(
% 0.24/0.30 ($true != $true) | ~spl1_1),
% 0.24/0.30 inference(constrained_superposition,[],[f44,f8])).
% 0.24/0.30 thf(f46,plain,(
% 0.24/0.30 $false | ~spl1_1),
% 0.24/0.30 inference(trivial_inequality_removal,[],[f45])).
% 0.24/0.30 thf(f47,plain,(
% 0.24/0.30 ~spl1_1),
% 0.24/0.30 inference(avatar_contradiction_clause,[],[f46])).
% 0.24/0.30 cnf(s1, plain, spl1_1 | spl1_2, inference(sat_conversion,[],[f37])).
% 0.24/0.30 cnf(s2, plain, ~spl1_2, inference(sat_conversion,[],[f39])).
% 0.24/0.30 cnf(s3, plain, ~spl1_1, inference(sat_conversion,[],[f47])).
% 0.24/0.30 cnf(s4, plain, $false, inference(rat,[],[s1,s2,s3])).
% 0.24/0.30 thf(f48,plain,(
% 0.24/0.30 $false),
% 0.24/0.30 inference(avatar_sat_refutation,[],[s4])).
% 0.24/0.30 % SZS output end Proof for theBenchmark
% 0.24/0.30 % (2732079)------------------------------
% 0.24/0.30 % (2732079)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.30 % (2732079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.30 % (2732079)CaDiCaL version: 2.1.3
% 0.24/0.30 % (2732079)Termination reason: Refutation
% 0.24/0.30 % (2732079)Time elapsed: 0.003 s
% 0.24/0.30 % (2732079)Peak memory usage: 13 MB
% 0.24/0.30 % (2732079)Instructions burned: 3 (million)
% 0.24/0.30 % (2732073)Success in time 0.037 s
% 0.24/0.30 % Vampire exiting
%------------------------------------------------------------------------------