%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV256^5 : 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 : n001.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 08:38:08 AM UTC 2026
% Result : Theorem 0.22s 0.31s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV256^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n001.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 15:33:51 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running higher-order theorem proving
% 0.22/0.27 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
% 0.22/0.31 % (1385395)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.31 % (1385401)lrs+10_16_si=on:nwc=1.5:random_seed=1982784765:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.31 % (1385401) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1385395-1385401"...
% 0.22/0.31 % (1385406)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.31 % (1385406)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.31 % (1385401)...printing done.
% 0.22/0.31 % (1385401)Refutation found. Thanks to Tanya!
% 0.22/0.31 % SZS status Theorem for theBenchmark
% 0.22/0.31 % SZS output start Proof for theBenchmark
% 0.22/0.31 thf(type_def_5, type, a: $tType).
% 0.22/0.31 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.31 thf(func_def_0, type, cOPEN: ((a > $o) > $o)).
% 0.22/0.31 thf(func_def_4, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.31 thf(func_def_5, type, vAND: ($o > $o > $o)).
% 0.22/0.31 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.31 thf(func_def_7, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.31 thf(func_def_8, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.31 thf(func_def_9, type, sK0: (((a > $o) > $o) > a > $o)).
% 0.22/0.31 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.22/0.31 thf(func_def_11, type, sK1: a).
% 0.22/0.31 thf(func_def_12, type, sK2: (a > $o)).
% 0.22/0.31 thf(f1,conjecture,(
% 0.22/0.31 ! [X0 : ((a > $o) > $o)] : (! [X1 : (a > $o)] : ((X0 @ X1) => (cOPEN @ X1)) => (cOPEN @ (^[X1 : a] : (? [X2 : (a > $o)] : ((X0 @ X2) & (X2 @ X1)))))) => (cOPEN @ (^[X1 : a] : ($false)))),
% 0.22/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM625A_pme)).
% 0.22/0.31 thf(f2,negated_conjecture,(
% 0.22/0.31 ~(! [X0 : ((a > $o) > $o)] : (! [X1 : (a > $o)] : ((X0 @ X1) => (cOPEN @ X1)) => (cOPEN @ (^[X1 : a] : (? [X2 : (a > $o)] : ((X0 @ X2) & (X2 @ X1)))))) => (cOPEN @ (^[X1 : a] : ($false))))),
% 0.22/0.31 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.31 thf(f3,plain,(
% 0.22/0.31 ~(! [X0 : ((a > $o) > $o)] : (! [X1 : (a > $o)] : ((X0 @ X1) => (cOPEN @ X1)) => (cOPEN @ (^[X2 : a] : (? [X3 : (a > $o)] : ((X0 @ X3) & (X3 @ X2)))))) => (cOPEN @ (^[X4 : a] : ($false))))),
% 0.22/0.31 inference(rectify,[],[f2])).
% 0.22/0.31 thf(f4,plain,(
% 0.22/0.31 ~(! [X0 : ((a > $o) > $o)] : (! [X1 : (a > $o)] : ((((X0 @ X1)) = $true) => (((cOPEN @ X1)) = $true)) => (((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1))))))) = $true)) => (((cOPEN @ (^[Y0 : a]: ($false)))) = $true))),
% 0.22/0.31 inference(fool_elimination,[],[f3])).
% 0.22/0.31 thf(f5,plain,(
% 0.22/0.31 ! [X0 : ((a > $o) > $o)] : (? [X1 : (a > $o)] : ((((cOPEN @ X1)) != $true) & (((X0 @ X1)) = $true)) | (((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1))))))) = $true)) & (((cOPEN @ (^[Y0 : a]: ($false)))) != $true)),
% 0.22/0.31 inference(ennf_transformation,[],[f4])).
% 0.22/0.31 thf(f6,plain,(
% 0.22/0.31 ! [X0 : ((a > $o) > $o)] : (((((cOPEN @ (sK0 @ X0))) != $true) & (((X0 @ (sK0 @ X0))) = $true)) | (((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1))))))) = $true)) & (((cOPEN @ (^[Y0 : a]: ($false)))) != $true)),
% 0.22/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f5])).
% 0.22/0.31 thf(f7,plain,(
% 0.22/0.31 (((cOPEN @ (^[Y0 : a]: ($false)))) != $true)),
% 0.22/0.31 inference(cnf_transformation,[],[f6])).
% 0.22/0.31 thf(f8,plain,(
% 0.22/0.31 ( ! [X0 : ((a > $o) > $o)] : ((((X0 @ (sK0 @ X0))) = $true) | (((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & (X0 @ Y1))))))) = $true)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f6])).
% 0.22/0.31 thf(f13,plain,(
% 0.22/0.31 (((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & ((^[Y2 : a > $o]: ($false)) @ Y1))))))) = $true) | ($true = (((^[Y0 : a > $o]: ($false)) @ (sK0 @ (^[Y0 : a > $o]: ($false))))))),
% 0.22/0.31 inference(primitive_instantiation,[],[f8])).
% 0.22/0.31 thf(f24,plain,(
% 0.22/0.31 ($false = $true) | (((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & $false)))))) = $true)),
% 0.22/0.31 inference(beta-eta_normalization,[],[f13])).
% 0.22/0.31 thf(f25,plain,(
% 0.22/0.31 (((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ Y0) & $false)))))) = $true)),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f24])).
% 0.22/0.31 thf(f26,plain,(
% 0.22/0.31 (((cOPEN @ (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ($false)))))) = $true)),
% 0.22/0.31 inference(boolean_simplification,[],[f25])).
% 0.22/0.31 thf(f34,plain,(
% 0.22/0.31 ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ($false)))) != (^[Y0 : a]: ($false))) | ($true != $true)),
% 0.22/0.31 inference(constrained_superposition,[],[f7,f26])).
% 0.22/0.31 thf(f35,plain,(
% 0.22/0.31 ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ($false)))) != (^[Y0 : a]: ($false)))),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f34])).
% 0.22/0.31 thf(f36,plain,(
% 0.22/0.31 ((((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ($false)))) @ sK1)) != (((^[Y0 : a]: ($false)) @ sK1)))),
% 0.22/0.31 inference(negative_extensionality,[],[f35])).
% 0.22/0.31 thf(f37,plain,(
% 0.22/0.31 ((((^[Y0 : a]: ($false)) @ sK1)) = $true) | ((((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ($false)))) @ sK1)) = $true)),
% 0.22/0.31 inference(xor_proxy_clausification,[],[f36])).
% 0.22/0.31 thf(f41,plain,(
% 0.22/0.31 ($false = $true) | (((?? @ (a > $o) @ (^[Y0 : a > $o]: ($false)))) = $true)),
% 0.22/0.31 inference(beta-eta_normalization,[],[f37])).
% 0.22/0.31 thf(f42,plain,(
% 0.22/0.31 ($false = $true) | ((((^[Y0 : a > $o]: ($false)) @ sK2)) = $true)),
% 0.22/0.31 inference(sigma_proxy_clausification,[],[f41])).
% 0.22/0.31 thf(f43,plain,(
% 0.22/0.31 ((((^[Y0 : a > $o]: ($false)) @ sK2)) = $true)),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f42])).
% 0.22/0.31 thf(f44,plain,(
% 0.22/0.31 ($false = $true)),
% 0.22/0.31 inference(beta-eta_normalization,[],[f43])).
% 0.22/0.31 thf(f45,plain,(
% 0.22/0.31 $false),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f44])).
% 0.22/0.31 % SZS output end Proof for theBenchmark
% 0.22/0.31 % (1385401)------------------------------
% 0.22/0.31 % (1385401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (1385401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (1385401)CaDiCaL version: 2.1.3
% 0.22/0.31 % (1385401)Termination reason: Refutation
% 0.22/0.31 % (1385401)Time elapsed: 0.004 s
% 0.22/0.31 % (1385401)Peak memory usage: 12 MB
% 0.22/0.31 % (1385401)Instructions burned: 5 (million)
% 0.22/0.31 % (1385395)Success in time 0.035 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------