%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO356^5 : 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 : n019.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 08:47:30 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO356^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n019.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 16:48:33 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 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
% 0.23/0.29 % (1045429)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.29 % (1045450)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=345092918:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.23/0.29 % (1045450) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1045429-1045450"...
% 0.23/0.29 % (1045450)...printing done.
% 0.23/0.29 % (1045450)Refutation found. Thanks to Tanya!
% 0.23/0.29 % SZS status Theorem for theBenchmark
% 0.23/0.29 % SZS output start Proof for theBenchmark
% 0.23/0.29 thf(type_def_5, type, a: $tType).
% 0.23/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.29 thf(func_def_0, type, v: a).
% 0.23/0.29 thf(func_def_1, type, u: a).
% 0.23/0.29 thf(func_def_5, type, sK0: ((a > a > $o) > a)).
% 0.23/0.29 thf(func_def_6, type, sK1: (a > $o)).
% 0.23/0.29 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.23/0.29 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.23/0.29 thf(func_def_10, type, db1: !>[X0: $tType]:(X0)).
% 0.23/0.29 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.23/0.29 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.23/0.29 thf(f1,conjecture,(
% 0.23/0.29 ! [X0 : (a > a > $o)] : (! [X1 : a] : (X0 @ X1 @ X1) => (X0 @ u @ v)) => ! [X2 : (a > $o)] : ((X2 @ u) => (X2 @ v))),
% 0.23/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cE1LEIBEQ2_pme)).
% 0.23/0.29 thf(f2,negated_conjecture,(
% 0.23/0.29 ~(! [X0 : (a > a > $o)] : (! [X1 : a] : (X0 @ X1 @ X1) => (X0 @ u @ v)) => ! [X2 : (a > $o)] : ((X2 @ u) => (X2 @ v)))),
% 0.23/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.23/0.29 thf(f3,plain,(
% 0.23/0.29 ~(! [X0 : (a > a > $o)] : (! [X1 : a] : (X0 @ X1 @ X1) => (X0 @ u @ v)) => ! [X2 : (a > $o)] : ((X2 @ u) => (X2 @ v)))),
% 0.23/0.29 inference(rectify,[],[f2])).
% 0.23/0.29 thf(f4,plain,(
% 0.23/0.29 ~(! [X0 : (a > a > $o)] : (! [X1 : a] : (((X0 @ X1 @ X1)) = $true) => (((X0 @ u @ v)) = $true)) => ! [X2 : (a > $o)] : ((((X2 @ u)) = $true) => (((X2 @ v)) = $true)))),
% 0.23/0.29 inference(fool_elimination,[],[f3])).
% 0.23/0.29 thf(f5,plain,(
% 0.23/0.29 ! [X0 : (a > a > $o)] : ((((X0 @ u @ v)) = $true) | ? [X1 : a] : (((X0 @ X1 @ X1)) != $true)) & ? [X2 : (a > $o)] : ((((X2 @ v)) != $true) & (((X2 @ u)) = $true))),
% 0.23/0.29 inference(ennf_transformation,[],[f4])).
% 0.23/0.29 thf(f6,plain,(
% 0.23/0.29 ! [X0 : (a > a > $o)] : ((((X0 @ u @ v)) = $true) | ($true != ((X0 @ (sK0 @ X0) @ (sK0 @ X0))))) & (($true != ((sK1 @ v))) & ($true = ((sK1 @ u))))),
% 0.23/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1]),skolemize(X1,sK0 @ X0),skolemize(X2,sK1)],[f5])).
% 0.23/0.29 thf(f7,plain,(
% 0.23/0.29 ($true = ((sK1 @ u)))),
% 0.23/0.29 inference(cnf_transformation,[],[f6])).
% 0.23/0.29 thf(f8,plain,(
% 0.23/0.29 ($true != ((sK1 @ v)))),
% 0.23/0.29 inference(cnf_transformation,[],[f6])).
% 0.23/0.29 thf(f9,plain,(
% 0.23/0.29 ( ! [X0 : (a > a > $o)] : (($true != ((X0 @ (sK0 @ X0) @ (sK0 @ X0)))) | (((X0 @ u @ v)) = $true)) )),
% 0.23/0.29 inference(cnf_transformation,[],[f6])).
% 0.23/0.29 thf(f12,definition,(
% 0.23/0.29 spl2_1 <=> ($true = ((sK1 @ v)))),
% 0.23/0.29 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.23/0.29 thf(f15,plain,(
% 0.23/0.29 ~spl2_1),
% 0.23/0.29 inference(avatar_split_clause,[],[f8,f12])).
% 0.23/0.29 thf(f17,definition,(
% 0.23/0.29 spl2_2 <=> ($true = ((sK1 @ u)))),
% 0.23/0.29 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.23/0.29 thf(f20,plain,(
% 0.23/0.29 spl2_2),
% 0.23/0.29 inference(avatar_split_clause,[],[f7,f17])).
% 0.23/0.29 thf(f21,plain,(
% 0.23/0.29 ($true = (((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ u @ v))) | ($true != (((^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))) @ (sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1))))) @ (sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1))))))))),
% 0.23/0.29 inference(primitive_instantiation,[],[f9])).
% 0.23/0.29 thf(f28,plain,(
% 0.23/0.29 ($true = ((u = v))) | ($true != (((sK0 @ =) = (sK0 @ =))))),
% 0.23/0.29 inference(beta-eta_normalization,[],[f21])).
% 0.23/0.29 thf(f29,plain,(
% 0.23/0.29 (u = v) | ($true != (((sK0 @ =) = (sK0 @ =))))),
% 0.23/0.29 inference(equality_proxy_clausification,[],[f28])).
% 0.23/0.29 thf(f30,plain,(
% 0.23/0.29 (((sK0 @ =)) != ((sK0 @ =))) | (u = v)),
% 0.23/0.29 inference(equality_proxy_clausification,[],[f29])).
% 0.23/0.29 thf(f31,plain,(
% 0.23/0.29 (u = v)),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f30])).
% 0.23/0.29 thf(f43,definition,(
% 0.23/0.29 spl2_3 <=> (u = v)),
% 0.23/0.29 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.23/0.29 thf(f46,plain,(
% 0.23/0.29 spl2_3),
% 0.23/0.29 inference(avatar_split_clause,[],[f31,f43])).
% 0.23/0.29 thf(f47,definition,(
% 0.23/0.29 (u != v) | ($true != ((sK1 @ u))) | ($true = ((sK1 @ v)))),
% 0.23/0.29 introduced(theory,[theory_tautology_sat_conflict])).
% 0.23/0.29 cnf(s1, plain, ~spl2_1, inference(sat_conversion,[],[f15])).
% 0.23/0.29 cnf(s2, plain, spl2_2, inference(sat_conversion,[],[f20])).
% 0.23/0.29 cnf(s3, plain, spl2_3, inference(sat_conversion,[],[f46])).
% 0.23/0.29 cnf(s4, plain, spl2_1 | ~spl2_2 | ~spl2_3, inference(sat_conversion,[],[f47])).
% 0.23/0.29 cnf(s5, plain, spl2_1, inference(rat,[],[s4,s3,s2])).
% 0.23/0.29 cnf(s6, plain, $false, inference(rat,[],[s1,s5])).
% 0.23/0.29 thf(f48,plain,(
% 0.23/0.29 $false),
% 0.23/0.29 inference(avatar_sat_refutation,[],[s6])).
% 0.23/0.29 % SZS output end Proof for theBenchmark
% 0.23/0.29 % (1045450)------------------------------
% 0.23/0.29 % (1045450)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (1045450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (1045450)CaDiCaL version: 2.1.3
% 0.23/0.29 % (1045450)Termination reason: Refutation
% 0.23/0.29 % (1045450)Time elapsed: 0.002 s
% 0.23/0.29 % (1045450)Peak memory usage: 13 MB
% 0.23/0.29 % (1045450)Instructions burned: 2 (million)
% 0.23/0.29 % (1045429)Success in time 0.038 s
% 0.23/0.29 % Vampire exiting
%------------------------------------------------------------------------------