%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO361^5 : 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 : n016.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 08:47:31 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO361^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n016.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:53:49 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 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
% 0.20/0.27 % (607544)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (607554)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=107611610:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.27 % (607554) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-607544-607554"...
% 0.20/0.27 % (607554)...printing done.
% 0.20/0.27 % (607554)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% 0.20/0.27 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.27 thf(func_def_5, type, sK2: ($i > $i > $o)).
% 0.20/0.27 thf(func_def_6, type, sK3: (($i > $i > $o) > $i)).
% 0.20/0.27 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.20/0.27 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.27 thf(func_def_10, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.27 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.27 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.27 thf(f1,conjecture,(
% 0.20/0.27 ! [X1 : $i,X0 : $i] : (! [X2 : ($i > $i > $o)] : (! [X3 : $i] : (X2 @ X3 @ X3) => (X2 @ X0 @ X1)) <=> (X0 = X1))),
% 0.20/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM47)).
% 0.20/0.27 thf(f2,negated_conjecture,(
% 0.20/0.27 ~ ! [X1 : $i,X0 : $i] : (! [X2 : ($i > $i > $o)] : (! [X3 : $i] : (X2 @ X3 @ X3) => (X2 @ X0 @ X1)) <=> (X0 = X1))),
% 0.20/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.27 thf(f3,plain,(
% 0.20/0.27 ~ ! [X0 : $i,X1 : $i] : (! [X2 : ($i > $i > $o)] : (! [X3 : $i] : (X2 @ X3 @ X3) => (X2 @ X1 @ X0)) <=> (X0 = X1))),
% 0.20/0.27 inference(rectify,[],[f2])).
% 0.20/0.27 thf(f4,plain,(
% 0.20/0.27 ~ ! [X1 : $i,X0 : $i] : ((X0 = X1) <=> ! [X2 : ($i > $i > $o)] : (! [X3 : $i] : (((X2 @ X3 @ X3)) = $true) => (((X2 @ X1 @ X0)) = $true)))),
% 0.20/0.27 inference(fool_elimination,[],[f3])).
% 0.20/0.27 thf(f5,plain,(
% 0.20/0.27 ? [X0 : $i,X1 : $i] : ((X0 = X1) <~> ! [X2 : ($i > $i > $o)] : (? [X3 : $i] : (((X2 @ X3 @ X3)) != $true) | (((X2 @ X1 @ X0)) = $true)))),
% 0.20/0.27 inference(ennf_transformation,[],[f4])).
% 0.20/0.27 thf(f6,plain,(
% 0.20/0.27 ? [X0 : $i,X1 : $i] : ((? [X2 : ($i > $i > $o)] : (! [X3 : $i] : (((X2 @ X3 @ X3)) = $true) & (((X2 @ X1 @ X0)) != $true)) | (X0 != X1)) & (! [X2 : ($i > $i > $o)] : (? [X3 : $i] : (((X2 @ X3 @ X3)) != $true) | (((X2 @ X1 @ X0)) = $true)) | (X0 = X1)))),
% 0.20/0.27 inference(nnf_transformation,[],[f5])).
% 0.20/0.27 thf(f7,plain,(
% 0.20/0.27 ? [X0 : $i,X1 : $i] : ((? [X2 : ($i > $i > $o)] : (! [X3 : $i] : (((X2 @ X3 @ X3)) = $true) & (((X2 @ X1 @ X0)) != $true)) | (X0 != X1)) & (! [X4 : ($i > $i > $o)] : (? [X5 : $i] : ($true != ((X4 @ X5 @ X5))) | (((X4 @ X1 @ X0)) = $true)) | (X0 = X1)))),
% 0.20/0.27 inference(rectify,[],[f6])).
% 0.20/0.27 thf(f8,plain,(
% 0.20/0.27 ((! [X3 : $i] : (((sK2 @ X3 @ X3)) = $true) & ($true != ((sK2 @ sK1 @ sK0)))) | (sK1 != sK0)) & (! [X4 : ($i > $i > $o)] : (($true != ((X4 @ (sK3 @ X4) @ (sK3 @ X4)))) | (((X4 @ sK1 @ sK0)) = $true)) | (sK1 = sK0))),
% 0.20/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X5,sK3 @ X4)],[f7])).
% 0.20/0.27 thf(f9,plain,(
% 0.20/0.27 ( ! [X4 : ($i > $i > $o)] : ((((X4 @ sK1 @ sK0)) = $true) | (sK1 = sK0) | ($true != ((X4 @ (sK3 @ X4) @ (sK3 @ X4))))) )),
% 0.20/0.27 inference(cnf_transformation,[],[f8])).
% 0.20/0.27 thf(f10,plain,(
% 0.20/0.27 (sK1 != sK0) | ($true != ((sK2 @ sK1 @ sK0)))),
% 0.20/0.27 inference(cnf_transformation,[],[f8])).
% 0.20/0.27 thf(f11,plain,(
% 0.20/0.27 ( ! [X3 : $i] : ((sK1 != sK0) | (((sK2 @ X3 @ X3)) = $true)) )),
% 0.20/0.27 inference(cnf_transformation,[],[f8])).
% 0.20/0.27 thf(f15,definition,(
% 0.20/0.27 spl4_1 <=> ! [X4 : ($i > $i > $o)] : ((((X4 @ sK1 @ sK0)) = $true) | ($true != ((X4 @ (sK3 @ X4) @ (sK3 @ X4)))))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.20/0.27 thf(f16,plain,(
% 0.20/0.27 ( ! [X4 : ($i > $i > $o)] : (($true != ((X4 @ (sK3 @ X4) @ (sK3 @ X4)))) | (((X4 @ sK1 @ sK0)) = $true)) ) | ~spl4_1),
% 0.20/0.27 inference(avatar_component_clause,[],[f15])).
% 0.20/0.27 thf(f18,definition,(
% 0.20/0.27 spl4_2 <=> (sK1 = sK0)),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.20/0.27 thf(f19,plain,(
% 0.20/0.27 (sK1 = sK0) | ~spl4_2),
% 0.20/0.27 inference(avatar_component_clause,[],[f18])).
% 0.20/0.27 thf(f20,plain,(
% 0.20/0.27 spl4_1 | spl4_2),
% 0.20/0.27 inference(avatar_split_clause,[],[f9,f18,f15])).
% 0.20/0.27 thf(f22,definition,(
% 0.20/0.27 spl4_3 <=> ! [X3 : $i] : (((sK2 @ X3 @ X3)) = $true)),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
% 0.20/0.27 thf(f23,plain,(
% 0.20/0.27 ( ! [X3 : $i] : ((((sK2 @ X3 @ X3)) = $true)) ) | ~spl4_3),
% 0.20/0.27 inference(avatar_component_clause,[],[f22])).
% 0.20/0.27 thf(f24,plain,(
% 0.20/0.27 (sK1 != sK0) | spl4_2),
% 0.20/0.27 inference(avatar_component_clause,[],[f18])).
% 0.20/0.27 thf(f25,plain,(
% 0.20/0.27 spl4_3 | ~spl4_2),
% 0.20/0.27 inference(avatar_split_clause,[],[f11,f18,f22])).
% 0.20/0.27 thf(f27,definition,(
% 0.20/0.27 spl4_4 <=> ($true = ((sK2 @ sK1 @ sK0)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
% 0.20/0.27 thf(f28,plain,(
% 0.20/0.27 ($true != ((sK2 @ sK1 @ sK0))) | spl4_4),
% 0.20/0.27 inference(avatar_component_clause,[],[f27])).
% 0.20/0.27 thf(f29,plain,(
% 0.20/0.27 ~spl4_4 | ~spl4_2),
% 0.20/0.27 inference(avatar_split_clause,[],[f10,f18,f27])).
% 0.20/0.27 thf(f30,plain,(
% 0.20/0.27 ($true != ((sK2 @ sK1 @ sK1))) | (~spl4_2 | spl4_4)),
% 0.20/0.27 inference(forward_demodulation,[],[f28,f19])).
% 0.20/0.27 thf(f31,plain,(
% 0.20/0.27 $false | (~spl4_2 | ~spl4_3 | spl4_4)),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f30,f23])).
% 0.20/0.27 thf(f32,plain,(
% 0.20/0.27 ~spl4_2 | ~spl4_3 | spl4_4),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f31])).
% 0.20/0.27 thf(f33,plain,(
% 0.20/0.27 ((((^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1)))) @ sK1 @ sK0)) = $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1))))))) != $true) | ~spl4_1),
% 0.20/0.27 inference(primitive_instantiation,[],[f16])).
% 0.20/0.27 thf(f53,plain,(
% 0.20/0.27 (((sK1 = sK0)) = $true) | ((((sK3 @ =) = (sK3 @ =))) != $true) | ~spl4_1),
% 0.20/0.27 inference(beta-eta_normalization,[],[f33])).
% 0.20/0.27 thf(f54,plain,(
% 0.20/0.27 (sK1 = sK0) | ((((sK3 @ =) = (sK3 @ =))) != $true) | ~spl4_1),
% 0.20/0.27 inference(equality_proxy_clausification,[],[f53])).
% 0.20/0.27 thf(f55,plain,(
% 0.20/0.27 (((sK3 @ =)) != ((sK3 @ =))) | (sK1 = sK0) | ~spl4_1),
% 0.20/0.27 inference(equality_proxy_clausification,[],[f54])).
% 0.20/0.27 thf(f56,plain,(
% 0.20/0.27 (sK1 = sK0) | ~spl4_1),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f55])).
% 0.20/0.27 thf(f57,plain,(
% 0.20/0.27 $false | (~spl4_1 | spl4_2)),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f56,f24])).
% 0.20/0.27 thf(f58,plain,(
% 0.20/0.27 ~spl4_1 | spl4_2),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f57])).
% 0.20/0.27 cnf(s1, plain, spl4_1 | spl4_2, inference(sat_conversion,[],[f20])).
% 0.20/0.27 cnf(s2, plain, ~spl4_2 | spl4_3, inference(sat_conversion,[],[f25])).
% 0.20/0.27 cnf(s3, plain, ~spl4_2 | ~spl4_4, inference(sat_conversion,[],[f29])).
% 0.20/0.27 cnf(s4, plain, ~spl4_2 | ~spl4_3 | spl4_4, inference(sat_conversion,[],[f32])).
% 0.20/0.27 cnf(s5, plain, ~spl4_1 | spl4_2, inference(sat_conversion,[],[f58])).
% 0.20/0.27 cnf(s6, plain, ~spl4_2, inference(rat,[],[s4,s2,s3])).
% 0.20/0.27 cnf(s7, plain, ~spl4_1, inference(rat,[],[s5,s6])).
% 0.20/0.27 cnf(s8, plain, $false, inference(rat,[],[s1,s6,s7])).
% 0.20/0.27 thf(f59,plain,(
% 0.20/0.27 $false),
% 0.20/0.27 inference(avatar_sat_refutation,[],[s8])).
% 0.20/0.27 % SZS output end Proof for theBenchmark
% 0.20/0.27 % (607554)------------------------------
% 0.20/0.27 % (607554)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (607554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (607554)CaDiCaL version: 2.1.3
% 0.20/0.27 % (607554)Termination reason: Refutation
% 0.20/0.27 % (607554)Time elapsed: 0.002 s
% 0.20/0.27 % (607554)Peak memory usage: 13 MB
% 0.20/0.27 % (607554)Instructions burned: 4 (million)
% 0.20/0.27 % (607544)Success in time 0.039 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------