%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV405^5 : 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 : n009.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 08:38:35 AM UTC 2026
% Result : Theorem 0.21s 0.35s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV405^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 % Computer : n009.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Tue Sep 29 15:44:30 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.30 Running higher-order theorem proving
% 0.21/0.31 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
% 0.21/0.35 % (4165550)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.35 % (4165558)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=2212263282: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)
% 0.21/0.35 % (4165558) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4165550-4165558"...
% 0.21/0.35 % (4165558)...printing done.
% 0.21/0.35 % (4165558)Refutation found. Thanks to Tanya!
% 0.21/0.35 % SZS status Theorem for theBenchmark
% 0.21/0.35 % SZS output start Proof for theBenchmark
% 0.21/0.35 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.35 thf(func_def_0, type, cA: $o).
% 0.21/0.35 thf(func_def_2, type, sK0: (($i > $o) > $i)).
% 0.21/0.35 thf(func_def_5, type, vNOT: ($o > $o)).
% 0.21/0.35 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.35 thf(func_def_8, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.35 thf(f1,conjecture,(
% 0.21/0.35 ? [X0 : ($i > $o)] : ! [X1 : $i] : ((X0 @ X1) <=> cA)),
% 0.21/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCOMP1)).
% 0.21/0.35 thf(f2,negated_conjecture,(
% 0.21/0.35 ~ ? [X0 : ($i > $o)] : ! [X1 : $i] : ((X0 @ X1) <=> cA)),
% 0.21/0.35 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.35 thf(f3,plain,(
% 0.21/0.35 ~ ? [X0 : ($i > $o)] : ! [X1 : $i] : ((X0 @ X1) <=> cA)),
% 0.21/0.35 inference(rectify,[],[f2])).
% 0.21/0.35 thf(f4,plain,(
% 0.21/0.35 ~ ? [X0 : ($i > $o)] : ! [X1 : $i] : (((X0 @ X1)) = cA)),
% 0.21/0.35 inference(fool_elimination,[],[f3])).
% 0.21/0.35 thf(f5,plain,(
% 0.21/0.35 ! [X0 : ($i > $o)] : ? [X1 : $i] : (((X0 @ X1)) != cA)),
% 0.21/0.35 inference(ennf_transformation,[],[f4])).
% 0.21/0.35 thf(f6,plain,(
% 0.21/0.35 ! [X0 : ($i > $o)] : (cA != ((X0 @ (sK0 @ X0))))),
% 0.21/0.35 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f5])).
% 0.21/0.35 thf(f7,plain,(
% 0.21/0.35 ( ! [X0 : ($i > $o)] : ((cA != ((X0 @ (sK0 @ X0))))) )),
% 0.21/0.35 inference(cnf_transformation,[],[f6])).
% 0.21/0.35 thf(f9,plain,(
% 0.21/0.35 ( ! [X0 : ($i > $o)] : ((cA = $true) | (((X0 @ (sK0 @ X0))) = $true)) )),
% 0.21/0.35 inference(xor_proxy_clausification,[],[f7])).
% 0.21/0.35 thf(f10,plain,(
% 0.21/0.35 ( ! [X0 : ($i > $o)] : (($false = ((X0 @ (sK0 @ X0)))) | (cA = $false)) )),
% 0.21/0.35 inference(xor_proxy_clausification,[],[f7])).
% 0.21/0.35 thf(f12,definition,(
% 0.21/0.35 spl1_1 <=> ! [X0 : ($i > $o)] : ($false = ((X0 @ (sK0 @ X0))))),
% 0.21/0.35 introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition])).
% 0.21/0.35 thf(f13,plain,(
% 0.21/0.35 ( ! [X0 : ($i > $o)] : (($false = ((X0 @ (sK0 @ X0))))) ) | ~spl1_1),
% 0.21/0.35 inference(avatar_component_clause,[],[f12])).
% 0.21/0.35 thf(f15,definition,(
% 0.21/0.35 spl1_2 <=> (cA = $false)),
% 0.21/0.35 introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition])).
% 0.21/0.35 thf(f17,plain,(
% 0.21/0.35 (cA = $false) | ~spl1_2),
% 0.21/0.35 inference(avatar_component_clause,[],[f15])).
% 0.21/0.35 thf(f18,plain,(
% 0.21/0.35 spl1_1 | spl1_2),
% 0.21/0.35 inference(avatar_split_clause,[],[f10,f15,f12])).
% 0.21/0.35 thf(f20,definition,(
% 0.21/0.35 spl1_3 <=> ! [X0 : ($i > $o)] : (((X0 @ (sK0 @ X0))) = $true)),
% 0.21/0.35 introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition])).
% 0.21/0.35 thf(f21,plain,(
% 0.21/0.35 ( ! [X0 : ($i > $o)] : ((((X0 @ (sK0 @ X0))) = $true)) ) | ~spl1_3),
% 0.21/0.35 inference(avatar_component_clause,[],[f20])).
% 0.21/0.35 thf(f23,definition,(
% 0.21/0.35 spl1_4 <=> (cA = $true)),
% 0.21/0.35 introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition])).
% 0.21/0.35 thf(f25,plain,(
% 0.21/0.35 (cA = $true) | ~spl1_4),
% 0.21/0.35 inference(avatar_component_clause,[],[f23])).
% 0.21/0.35 thf(f26,plain,(
% 0.21/0.35 spl1_3 | spl1_4),
% 0.21/0.35 inference(avatar_split_clause,[],[f9,f23,f20])).
% 0.21/0.35 thf(f28,plain,(
% 0.21/0.35 ((((^[Y0 : $i]: ($false)) @ (sK0 @ (^[Y0 : $i]: ($false))))) = $true) | ~spl1_3),
% 0.21/0.35 inference(primitive_instantiation,[],[f21])).
% 0.21/0.35 thf(f31,plain,(
% 0.21/0.35 ($false = $true) | ~spl1_3),
% 0.21/0.35 inference(beta-eta_normalization,[],[f28])).
% 0.21/0.35 thf(f32,plain,(
% 0.21/0.35 $false | ~spl1_3),
% 0.21/0.35 inference(trivial_inequality_removal,[],[f31])).
% 0.21/0.35 thf(f33,plain,(
% 0.21/0.35 ~spl1_3),
% 0.21/0.35 inference(avatar_contradiction_clause,[],[f32])).
% 0.21/0.35 thf(f36,plain,(
% 0.21/0.35 ($false = $true) | (~spl1_2 | ~spl1_4)),
% 0.21/0.35 inference(forward_demodulation,[],[f25,f17])).
% 0.21/0.35 thf(f37,plain,(
% 0.21/0.35 $false | (~spl1_2 | ~spl1_4)),
% 0.21/0.35 inference(trivial_inequality_removal,[],[f36])).
% 0.21/0.35 thf(f38,plain,(
% 0.21/0.35 ~spl1_2 | ~spl1_4),
% 0.21/0.35 inference(avatar_contradiction_clause,[],[f37])).
% 0.21/0.35 thf(f42,plain,(
% 0.21/0.35 ((((^[Y0 : $i]: ($true)) @ (sK0 @ (^[Y0 : $i]: ($true))))) = $false) | ~spl1_1),
% 0.21/0.35 inference(primitive_instantiation,[],[f13])).
% 0.21/0.35 thf(f48,plain,(
% 0.21/0.35 ($false = $true) | ~spl1_1),
% 0.21/0.35 inference(beta-eta_normalization,[],[f42])).
% 0.21/0.35 thf(f49,plain,(
% 0.21/0.35 $false | ~spl1_1),
% 0.21/0.35 inference(trivial_inequality_removal,[],[f48])).
% 0.21/0.35 thf(f50,plain,(
% 0.21/0.35 ~spl1_1),
% 0.21/0.35 inference(avatar_contradiction_clause,[],[f49])).
% 0.21/0.35 cnf(s1, plain, spl1_1 | spl1_2, inference(sat_conversion,[],[f18])).
% 0.21/0.35 cnf(s2, plain, spl1_3 | spl1_4, inference(sat_conversion,[],[f26])).
% 0.21/0.35 cnf(s3, plain, ~spl1_3, inference(sat_conversion,[],[f33])).
% 0.21/0.35 cnf(s4, plain, ~spl1_2 | ~spl1_4, inference(sat_conversion,[],[f38])).
% 0.21/0.35 cnf(s5, plain, ~spl1_1, inference(sat_conversion,[],[f50])).
% 0.21/0.35 cnf(s6, plain, spl1_4, inference(rat,[],[s2,s3])).
% 0.21/0.35 cnf(s7, plain, ~spl1_2, inference(rat,[],[s4,s6])).
% 0.21/0.35 cnf(s8, plain, $false, inference(rat,[],[s1,s7,s5])).
% 0.21/0.35 thf(f51,plain,(
% 0.21/0.35 $false),
% 0.21/0.35 inference(avatar_sat_refutation,[],[s8])).
% 0.21/0.35 % SZS output end Proof for theBenchmark
% 0.21/0.35 % (4165558)------------------------------
% 0.21/0.35 % (4165558)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (4165558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (4165558)CaDiCaL version: 2.1.3
% 0.21/0.35 % (4165558)Termination reason: Refutation
% 0.21/0.35 % (4165558)Time elapsed: 0.002 s
% 0.21/0.35 % (4165558)Peak memory usage: 13 MB
% 0.21/0.35 % (4165558)Instructions burned: 2 (million)
% 0.21/0.35 % (4165550)Success in time 0.026 s
% 0.21/0.35 % Vampire exiting
%------------------------------------------------------------------------------