%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO222^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:47:13 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO222^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n020.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 16:40:49 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 Running higher-order theorem proving
% 0.09/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.25 % (1280345)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.25 % (1280364)lrs+10_16_si=on:nwc=1.5:random_seed=432953830:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.09/0.25 % (1280364) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1280345-1280364"...
% 0.09/0.25 % (1280364)...printing done.
% 0.09/0.25 % (1280369)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.09/0.25 % (1280369)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
% 0.09/0.25 % (1280364)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% 0.09/0.25 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.25 thf(func_def_0, type, f: ($i > $i)).
% 0.09/0.25 thf(func_def_2, type, cP: ($i > $o)).
% 0.09/0.25 thf(func_def_6, type, sK0: (($i > $o) > $i)).
% 0.09/0.25 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.09/0.25 thf(func_def_9, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.09/0.25 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.09/0.25 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.09/0.25 thf(func_def_12, type, sK2: ($i > $i)).
% 0.09/0.25 thf(func_def_13, type, sK3: ($i > $i > $i)).
% 0.09/0.25 thf(f1,conjecture,(
% 0.09/0.25 ? [X0 : ($i > $o)] : (! [X1 : $i] : ((X0 @ (f @ X1)) => (cP @ X1)) & (((cP @ a) & ! [X2 : $i,X1 : $i] : ((((f @ X1)) = ((f @ X2))) => (X1 = X2))) => ? [X3 : $i] : (X0 @ X3)))),
% 0.09/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM115A)).
% 0.09/0.25 thf(f2,negated_conjecture,(
% 0.09/0.25 ~ ? [X0 : ($i > $o)] : (! [X1 : $i] : ((X0 @ (f @ X1)) => (cP @ X1)) & (((cP @ a) & ! [X2 : $i,X1 : $i] : ((((f @ X1)) = ((f @ X2))) => (X1 = X2))) => ? [X3 : $i] : (X0 @ X3)))),
% 0.09/0.25 inference(negated_conjecture,[status(cth)],[f1])).
% 0.09/0.25 thf(f3,plain,(
% 0.09/0.25 ~ ? [X0 : ($i > $o)] : (! [X1 : $i] : ((X0 @ (f @ X1)) => (cP @ X1)) & (((cP @ a) & ! [X2 : $i,X3 : $i] : ((((f @ X2)) = ((f @ X3))) => (X2 = X3))) => ? [X4 : $i] : (X0 @ X4)))),
% 0.09/0.25 inference(rectify,[],[f2])).
% 0.09/0.25 thf(f4,plain,(
% 0.09/0.25 ~ ? [X0 : ($i > $o)] : (((! [X3 : $i,X2 : $i] : ((((f @ X2)) = ((f @ X3))) => (X2 = X3)) & (((cP @ a)) = $true)) => ? [X4 : $i] : (((X0 @ X4)) = $true)) & ! [X1 : $i] : ((((X0 @ (f @ X1))) = $true) => (((cP @ X1)) = $true)))),
% 0.09/0.25 inference(fool_elimination,[],[f3])).
% 0.09/0.25 thf(f5,plain,(
% 0.09/0.25 ! [X0 : ($i > $o)] : ((! [X4 : $i] : (((X0 @ X4)) != $true) & (! [X2 : $i,X3 : $i] : ((((f @ X2)) != ((f @ X3))) | (X2 = X3)) & (((cP @ a)) = $true))) | ? [X1 : $i] : ((((X0 @ (f @ X1))) = $true) & (((cP @ X1)) != $true)))),
% 0.09/0.25 inference(ennf_transformation,[],[f4])).
% 0.09/0.25 thf(f6,plain,(
% 0.09/0.25 ! [X0 : ($i > $o)] : (? [X1 : $i] : ((((X0 @ (f @ X1))) = $true) & (((cP @ X1)) != $true)) | ((((cP @ a)) = $true) & ! [X4 : $i] : (((X0 @ X4)) != $true) & ! [X2 : $i,X3 : $i] : ((((f @ X2)) != ((f @ X3))) | (X2 = X3))))),
% 0.09/0.25 inference(flattening,[],[f5])).
% 0.09/0.25 thf(f7,plain,(
% 0.09/0.25 ! [X0 : ($i > $o)] : (? [X1 : $i] : ((((X0 @ (f @ X1))) = $true) & (((cP @ X1)) != $true)) | ((((cP @ a)) = $true) & ! [X2 : $i] : (((X0 @ X2)) != $true) & ! [X3 : $i,X4 : $i] : ((((f @ X4)) != ((f @ X3))) | (X3 = X4))))),
% 0.09/0.25 inference(rectify,[],[f6])).
% 0.09/0.25 thf(f8,plain,(
% 0.09/0.25 ! [X0 : ($i > $o)] : (((((X0 @ (f @ (sK0 @ X0)))) = $true) & (((cP @ (sK0 @ X0))) != $true)) | ((((cP @ a)) = $true) & ! [X2 : $i] : (((X0 @ X2)) != $true) & ! [X3 : $i,X4 : $i] : ((((f @ X4)) != ((f @ X3))) | (X3 = X4))))),
% 0.09/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f7])).
% 0.09/0.25 thf(f10,plain,(
% 0.09/0.25 ( ! [X2 : $i,X0 : ($i > $o)] : ((((cP @ (sK0 @ X0))) != $true) | (((X0 @ X2)) != $true)) )),
% 0.09/0.25 inference(cnf_transformation,[],[f8])).
% 0.09/0.25 thf(f12,plain,(
% 0.09/0.25 ( ! [X3 : $i,X0 : ($i > $o),X4 : $i] : ((((f @ X4)) != ((f @ X3))) | (((X0 @ (f @ (sK0 @ X0)))) = $true) | (X3 = X4)) )),
% 0.09/0.25 inference(cnf_transformation,[],[f8])).
% 0.09/0.25 thf(f13,plain,(
% 0.09/0.25 ( ! [X2 : $i,X0 : ($i > $o)] : ((((X0 @ X2)) != $true) | (((X0 @ (f @ (sK0 @ X0)))) = $true)) )),
% 0.09/0.25 inference(cnf_transformation,[],[f8])).
% 0.09/0.25 thf(f14,plain,(
% 0.09/0.25 ( ! [X0 : ($i > $o)] : ((((cP @ a)) = $true) | (((X0 @ (f @ (sK0 @ X0)))) = $true)) )),
% 0.09/0.25 inference(cnf_transformation,[],[f8])).
% 0.09/0.25 thf(f21,definition,(
% 0.09/0.25 spl1_2 <=> (((cP @ a)) = $true)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition])).
% 0.09/0.25 thf(f23,plain,(
% 0.09/0.25 (((cP @ a)) = $true) | ~spl1_2),
% 0.09/0.25 inference(avatar_component_clause,[],[f21])).
% 0.09/0.25 thf(f26,definition,(
% 0.09/0.25 spl1_3 <=> ! [X0 : ($i > $o)] : (((X0 @ (f @ (sK0 @ X0)))) = $true)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition])).
% 0.09/0.25 thf(f27,plain,(
% 0.09/0.25 ( ! [X0 : ($i > $o)] : ((((X0 @ (f @ (sK0 @ X0)))) = $true)) ) | ~spl1_3),
% 0.09/0.25 inference(avatar_component_clause,[],[f26])).
% 0.09/0.25 thf(f28,plain,(
% 0.09/0.25 spl1_3 | spl1_2),
% 0.09/0.25 inference(avatar_split_clause,[],[f14,f21,f26])).
% 0.09/0.25 thf(f30,definition,(
% 0.09/0.25 spl1_4 <=> ! [X4 : $i,X3 : $i] : ((((f @ X4)) != ((f @ X3))) | (X3 = X4))),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition])).
% 0.09/0.25 thf(f31,plain,(
% 0.09/0.25 ( ! [X3 : $i,X4 : $i] : ((((f @ X4)) != ((f @ X3))) | (X3 = X4)) ) | ~spl1_4),
% 0.09/0.25 inference(avatar_component_clause,[],[f30])).
% 0.09/0.25 thf(f32,plain,(
% 0.09/0.25 spl1_3 | spl1_4),
% 0.09/0.25 inference(avatar_split_clause,[],[f12,f30,f26])).
% 0.09/0.25 thf(f35,plain,(
% 0.09/0.25 ( ! [X0 : $i] : ((((f @ (sK0 @ (= @ X0)))) = X0)) )),
% 0.09/0.25 inference(leibniz_equality_elimination,[],[f13])).
% 0.09/0.25 thf(f69,plain,(
% 0.09/0.25 ( ! [X0 : $i,X1 : $i] : ((((f @ X1)) != X0) | (((sK0 @ (= @ X0))) = X1)) ) | ~spl1_4),
% 0.09/0.25 inference(constrained_superposition,[],[f31,f35])).
% 0.09/0.25 thf(f85,plain,(
% 0.09/0.25 ( ! [X0 : $i] : ((((sK0 @ (= @ (f @ X0)))) = X0)) ) | ~spl1_4),
% 0.09/0.25 inference(equality_resolution,[],[f69])).
% 0.09/0.25 thf(f87,plain,(
% 0.09/0.25 ( ! [X0 : $i,X1 : $i] : (((((f @ X0) = X1)) != $true) | ($true != ((cP @ X0)))) ) | ~spl1_4),
% 0.09/0.25 inference(constrained_superposition,[],[f10,f85])).
% 0.09/0.25 thf(f90,plain,(
% 0.09/0.25 ( ! [X0 : $i,X1 : $i] : (($true != ((cP @ X0))) | (((f @ X0)) != X1)) ) | ~spl1_4),
% 0.09/0.25 inference(equality_proxy_clausification,[],[f87])).
% 0.09/0.25 thf(f91,plain,(
% 0.09/0.25 ( ! [X0 : $i] : (($true != $true) | (((f @ a)) != X0)) ) | (~spl1_2 | ~spl1_4)),
% 0.09/0.25 inference(constrained_superposition,[],[f90,f23])).
% 0.09/0.25 thf(f93,plain,(
% 0.09/0.25 ( ! [X0 : $i] : ((((f @ a)) != X0)) ) | (~spl1_2 | ~spl1_4)),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f91])).
% 0.09/0.25 thf(f95,plain,(
% 0.09/0.25 $false | (~spl1_2 | ~spl1_4)),
% 0.09/0.25 inference(equality_resolution,[],[f93])).
% 0.09/0.25 thf(f96,plain,(
% 0.09/0.25 ~spl1_2 | ~spl1_4),
% 0.09/0.25 inference(avatar_contradiction_clause,[],[f95])).
% 0.09/0.25 thf(f102,plain,(
% 0.09/0.25 ($true = (((^[Y0 : $i]: ($false)) @ (f @ (sK0 @ (^[Y0 : $i]: ($false))))))) | ~spl1_3),
% 0.09/0.25 inference(primitive_instantiation,[],[f27])).
% 0.09/0.25 thf(f121,plain,(
% 0.09/0.25 ($false = $true) | ~spl1_3),
% 0.09/0.25 inference(beta-eta_normalization,[],[f102])).
% 0.09/0.25 thf(f122,plain,(
% 0.09/0.25 $false | ~spl1_3),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f121])).
% 0.09/0.25 thf(f123,plain,(
% 0.09/0.25 ~spl1_3),
% 0.09/0.25 inference(avatar_contradiction_clause,[],[f122])).
% 0.09/0.25 cnf(s2, plain, spl1_2 | spl1_3, inference(sat_conversion,[],[f28])).
% 0.09/0.25 cnf(s3, plain, spl1_3 | spl1_4, inference(sat_conversion,[],[f32])).
% 0.09/0.25 cnf(s7, plain, ~spl1_2 | ~spl1_4, inference(sat_conversion,[],[f96])).
% 0.09/0.25 cnf(s10, plain, ~spl1_3, inference(sat_conversion,[],[f123])).
% 0.09/0.25 cnf(s14, plain, spl1_4, inference(rat,[],[s3,s10])).
% 0.09/0.25 cnf(s15, plain, ~spl1_2, inference(rat,[],[s7,s14])).
% 0.09/0.25 cnf(s16, plain, $false, inference(rat,[],[s2,s10,s15])).
% 0.09/0.25 thf(f134,plain,(
% 0.09/0.25 $false),
% 0.09/0.25 inference(avatar_sat_refutation,[],[s16])).
% 0.09/0.25 % SZS output end Proof for theBenchmark
% 0.09/0.25 % (1280364)------------------------------
% 0.09/0.25 % (1280364)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (1280364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (1280364)CaDiCaL version: 2.1.3
% 0.09/0.25 % (1280364)Termination reason: Refutation
% 0.09/0.25 % (1280364)Time elapsed: 0.004 s
% 0.09/0.25 % (1280364)Peak memory usage: 13 MB
% 0.09/0.25 % (1280364)Instructions burned: 8 (million)
% 0.09/0.25 % (1280345)Success in time 0.038 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------