%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO255^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 08:49:36 AM UTC 2026
% Result : Theorem 0.18s 0.26s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO255^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n011.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:41:46 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.18/0.26 % (323079)Will run a generic schedule for satisfiability detection.
% 0.18/0.26 % (323099)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3156969793:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.26 % (323099)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.26 % (323099) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-323079-323099"...
% 0.18/0.26 % (323099)...printing done.
% 0.18/0.26 % (323096)% WARNING: option uhcvi not known.
% 0.18/0.26 % (323099)Refutation found. Thanks to Tanya!
% 0.18/0.26 % SZS status Theorem for theBenchmark
% 0.18/0.26 % SZS output start Proof for theBenchmark
% 0.18/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.18/0.26 thf(func_def_0, type, cP: ($i > $o)).
% 0.18/0.26 thf(func_def_5, type, sK0: (($i > $o) > $i)).
% 0.18/0.26 thf(func_def_6, type, vNOT: ($o > $o)).
% 0.18/0.26 thf(func_def_7, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.18/0.26 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.18/0.26 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.18/0.26 thf(f1,conjecture,(
% 0.18/0.26 (cP @ a) => ? [X0 : ($i > $o)] : (? [X2 : $i] : (X0 @ X2) & ! [X1 : $i] : ((X0 @ X1) => (cP @ X1)))),
% 0.18/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBLEDSOE3)).
% 0.18/0.26 thf(f2,negated_conjecture,(
% 0.18/0.26 ~((cP @ a) => ? [X0 : ($i > $o)] : (? [X2 : $i] : (X0 @ X2) & ! [X1 : $i] : ((X0 @ X1) => (cP @ X1))))),
% 0.18/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.18/0.26 thf(f3,plain,(
% 0.18/0.26 ~((cP @ a) => ? [X0 : ($i > $o)] : (? [X1 : $i] : (X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (cP @ X2))))),
% 0.18/0.26 inference(rectify,[],[f2])).
% 0.18/0.26 thf(f4,plain,(
% 0.18/0.26 ~((((cP @ a)) = $true) => ? [X0 : ($i > $o)] : (? [X1 : $i] : (((X0 @ X1)) = $true) & ! [X2 : $i] : ((((X0 @ X2)) = $true) => (((cP @ X2)) = $true))))),
% 0.18/0.26 inference(fool_elimination,[],[f3])).
% 0.18/0.26 thf(f5,plain,(
% 0.18/0.26 ! [X0 : ($i > $o)] : (! [X1 : $i] : (((X0 @ X1)) != $true) | ? [X2 : $i] : ((((cP @ X2)) != $true) & (((X0 @ X2)) = $true))) & (((cP @ a)) = $true)),
% 0.18/0.26 inference(ennf_transformation,[],[f4])).
% 0.18/0.26 thf(f6,plain,(
% 0.18/0.26 ! [X0 : ($i > $o)] : (! [X1 : $i] : (((X0 @ X1)) != $true) | (($true != ((cP @ (sK0 @ X0)))) & ($true = ((X0 @ (sK0 @ X0)))))) & (((cP @ a)) = $true)),
% 0.18/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X0)],[f5])).
% 0.18/0.26 thf(f7,plain,(
% 0.18/0.26 (((cP @ a)) = $true)),
% 0.18/0.26 inference(cnf_transformation,[],[f6])).
% 0.18/0.26 thf(f8,plain,(
% 0.18/0.26 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ X1)) != $true) | ($true = ((X0 @ (sK0 @ X0))))) )),
% 0.18/0.26 inference(cnf_transformation,[],[f6])).
% 0.18/0.26 thf(f9,plain,(
% 0.18/0.26 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ X1)) != $true) | ($true != ((cP @ (sK0 @ X0))))) )),
% 0.18/0.26 inference(cnf_transformation,[],[f6])).
% 0.18/0.26 thf(f19,plain,(
% 0.18/0.26 ( ! [X0 : $i] : (($true != $true) | ($true = (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK0 @ (^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | (a != X0)) )),
% 0.18/0.26 inference(constrained_superposition,[],[f8,f7])).
% 0.18/0.26 thf(f30,plain,(
% 0.18/0.26 ( ! [X0 : $i] : (($true = (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK0 @ (^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | (a != X0)) )),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f19])).
% 0.18/0.26 thf(f31,plain,(
% 0.18/0.26 ( ! [X0 : $i] : (($true = ((cP @ (sK0 @ cP)))) | (a != X0)) )),
% 0.18/0.26 inference(beta-eta_normalization,[],[f30])).
% 0.18/0.26 thf(f51,definition,(
% 0.18/0.26 spl1_3 <=> ! [X0 : $i] : (a != X0)),
% 0.18/0.26 introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition])).
% 0.18/0.26 thf(f52,plain,(
% 0.18/0.26 ( ! [X0 : $i] : ((a != X0)) ) | ~spl1_3),
% 0.18/0.26 inference(avatar_component_clause,[],[f51])).
% 0.18/0.26 thf(f54,definition,(
% 0.18/0.26 spl1_4 <=> ($true = ((cP @ (sK0 @ cP))))),
% 0.18/0.26 introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition])).
% 0.18/0.26 thf(f56,plain,(
% 0.18/0.26 ($true = ((cP @ (sK0 @ cP)))) | ~spl1_4),
% 0.18/0.26 inference(avatar_component_clause,[],[f54])).
% 0.18/0.26 thf(f57,plain,(
% 0.18/0.26 spl1_3 | spl1_4),
% 0.18/0.26 inference(avatar_split_clause,[],[f31,f54,f51])).
% 0.18/0.26 thf(f58,plain,(
% 0.18/0.26 $false | ~spl1_3),
% 0.18/0.26 inference(equality_resolution,[],[f52])).
% 0.18/0.26 thf(f59,plain,(
% 0.18/0.26 ~spl1_3),
% 0.18/0.26 inference(avatar_contradiction_clause,[],[f58])).
% 0.18/0.26 thf(f63,plain,(
% 0.18/0.26 ( ! [X0 : $i] : (($true != $true) | ($true != ((cP @ (sK0 @ (^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | (a != X0)) )),
% 0.18/0.26 inference(constrained_superposition,[],[f9,f7])).
% 0.18/0.26 thf(f79,plain,(
% 0.18/0.26 ( ! [X0 : $i] : (($true != ((cP @ (sK0 @ (^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | (a != X0)) )),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f63])).
% 0.18/0.26 thf(f80,plain,(
% 0.18/0.26 ( ! [X0 : $i] : (($true != ((cP @ (sK0 @ cP)))) | (a != X0)) )),
% 0.18/0.26 inference(beta-eta_normalization,[],[f79])).
% 0.18/0.26 thf(f98,plain,(
% 0.18/0.26 ( ! [X0 : $i] : ((a != X0)) ) | ~spl1_4),
% 0.18/0.26 inference(forward_subsumption_resolution,[],[f80,f56])).
% 0.18/0.26 thf(f99,plain,(
% 0.18/0.26 spl1_3 | ~spl1_4),
% 0.18/0.26 inference(avatar_split_clause,[],[f98,f54,f51])).
% 0.18/0.26 cnf(s2, plain, spl1_3 | spl1_4, inference(sat_conversion,[],[f57])).
% 0.18/0.26 cnf(s3, plain, ~spl1_3, inference(sat_conversion,[],[f59])).
% 0.18/0.26 cnf(s6, plain, spl1_3 | ~spl1_4, inference(sat_conversion,[],[f99])).
% 0.18/0.26 cnf(s7, plain, ~spl1_4, inference(rat,[],[s6,s3])).
% 0.18/0.26 cnf(s8, plain, $false, inference(rat,[],[s2,s7,s3])).
% 0.18/0.26 thf(f100,plain,(
% 0.18/0.26 $false),
% 0.18/0.26 inference(avatar_sat_refutation,[],[s8])).
% 0.18/0.26 % SZS output end Proof for theBenchmark
% 0.18/0.26 % (323099)------------------------------
% 0.18/0.26 % (323099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.26 % (323099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.26 % (323099)CaDiCaL version: 2.1.3
% 0.18/0.26 % (323099)Termination reason: Refutation
% 0.18/0.26 % (323099)Time elapsed: 0.002 s
% 0.18/0.26 % (323099)Peak memory usage: 12 MB
% 0.18/0.26 % (323099)Instructions burned: 4 (million)
% 0.18/0.26 % (323079)Success in time 0.03 s
% 0.18/0.26 % Vampire exiting
%------------------------------------------------------------------------------