%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV405^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 08:39:28 AM UTC 2026
% Result : Theorem 0.26s 0.38s
% Output : Refutation 0.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEV405^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.27 % Computer : n026.cluster.edu
% 0.11/0.27 % Model : x86_64 x86_64
% 0.11/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.27 % Memory : 8046.5625MB
% 0.11/0.27 % OS : Linux 6.8.0-71-generic
% 0.11/0.27 % CPULimit : 300
% 0.11/0.27 % WCLimit : 300
% 0.11/0.27 % DateTime : Tue Sep 29 15:47:12 UTC 2026
% 0.11/0.27 % CPUTime :
% 0.11/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.26/0.32 Running first-order model finding
% 0.26/0.32 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.26/0.38 % (767016)Will run a generic schedule for satisfiability detection.
% 0.26/0.38 % (767024)dis+10_1_sil=32000:sp=arity:random_seed=1002461965:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.26/0.38 % (767024) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-767016-767024"...
% 0.26/0.38 % (767024)...printing done.
% 0.26/0.38 % (767024)Refutation found. Thanks to Tanya!
% 0.26/0.38 % SZS status Theorem for theBenchmark
% 0.26/0.38 % SZS output start Proof for theBenchmark
% 0.26/0.38 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.26/0.38 thf(func_def_0, type, cA: $o).
% 0.26/0.38 thf(func_def_2, type, sK0: (($i > $o) > $i)).
% 0.26/0.38 thf(func_def_5, type, vNOT: ($o > $o)).
% 0.26/0.38 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 0.26/0.38 thf(func_def_8, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.26/0.38 thf(f1,conjecture,(
% 0.26/0.38 ? [X0 : ($i > $o)] : ! [X1 : $i] : ((X0 @ X1) <=> cA)),
% 0.26/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCOMP1)).
% 0.26/0.38 thf(f2,negated_conjecture,(
% 0.26/0.38 ~ ? [X0 : ($i > $o)] : ! [X1 : $i] : ((X0 @ X1) <=> cA)),
% 0.26/0.38 inference(negated_conjecture,[status(cth)],[f1])).
% 0.26/0.38 thf(f3,plain,(
% 0.26/0.38 ~ ? [X0 : ($i > $o)] : ! [X1 : $i] : ((X0 @ X1) <=> cA)),
% 0.26/0.38 inference(rectify,[],[f2])).
% 0.26/0.38 thf(f4,plain,(
% 0.26/0.38 ~ ? [X0 : ($i > $o)] : ! [X1 : $i] : (((X0 @ X1)) = cA)),
% 0.26/0.38 inference(fool_elimination,[],[f3])).
% 0.26/0.38 thf(f5,plain,(
% 0.26/0.38 ! [X0 : ($i > $o)] : ? [X1 : $i] : (((X0 @ X1)) != cA)),
% 0.26/0.38 inference(ennf_transformation,[],[f4])).
% 0.26/0.38 thf(f6,plain,(
% 0.26/0.38 ! [X0 : ($i > $o)] : (cA != ((X0 @ (sK0 @ X0))))),
% 0.26/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f5])).
% 0.26/0.38 thf(f7,plain,(
% 0.26/0.38 ( ! [X0 : ($i > $o)] : ((cA != ((X0 @ (sK0 @ X0))))) )),
% 0.26/0.38 inference(cnf_transformation,[],[f6])).
% 0.26/0.38 thf(f10,plain,(
% 0.26/0.38 ( ! [X0 : ($i > $o)] : ((cA = $true) | (((X0 @ (sK0 @ X0))) = $true)) )),
% 0.26/0.38 inference(xor_proxy_clausification,[],[f7])).
% 0.26/0.38 thf(f11,plain,(
% 0.26/0.38 ( ! [X0 : ($i > $o)] : ((cA = $false) | (((X0 @ (sK0 @ X0))) = $false)) )),
% 0.26/0.38 inference(xor_proxy_clausification,[],[f7])).
% 0.26/0.38 thf(f13,definition,(
% 0.26/0.38 spl1_1 <=> ! [X0 : ($i > $o)] : (((X0 @ (sK0 @ X0))) = $false)),
% 0.26/0.38 introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition])).
% 0.26/0.38 thf(f14,plain,(
% 0.26/0.38 ( ! [X0 : ($i > $o)] : ((((X0 @ (sK0 @ X0))) = $false)) ) | ~spl1_1),
% 0.26/0.38 inference(avatar_component_clause,[],[f13])).
% 0.26/0.38 thf(f16,definition,(
% 0.26/0.38 spl1_2 <=> (cA = $false)),
% 0.26/0.38 introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition])).
% 0.26/0.38 thf(f18,plain,(
% 0.26/0.38 (cA = $false) | ~spl1_2),
% 0.26/0.38 inference(avatar_component_clause,[],[f16])).
% 0.26/0.38 thf(f19,plain,(
% 0.26/0.38 spl1_1 | spl1_2),
% 0.26/0.38 inference(avatar_split_clause,[],[f11,f16,f13])).
% 0.26/0.38 thf(f21,definition,(
% 0.26/0.38 spl1_3 <=> ! [X0 : ($i > $o)] : (((X0 @ (sK0 @ X0))) = $true)),
% 0.26/0.38 introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition])).
% 0.26/0.38 thf(f22,plain,(
% 0.26/0.38 ( ! [X0 : ($i > $o)] : ((((X0 @ (sK0 @ X0))) = $true)) ) | ~spl1_3),
% 0.26/0.38 inference(avatar_component_clause,[],[f21])).
% 0.26/0.38 thf(f24,definition,(
% 0.26/0.38 spl1_4 <=> (cA = $true)),
% 0.26/0.38 introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition])).
% 0.26/0.38 thf(f26,plain,(
% 0.26/0.38 (cA = $true) | ~spl1_4),
% 0.26/0.38 inference(avatar_component_clause,[],[f24])).
% 0.26/0.38 thf(f27,plain,(
% 0.26/0.38 spl1_3 | spl1_4),
% 0.26/0.38 inference(avatar_split_clause,[],[f10,f24,f21])).
% 0.26/0.38 thf(f29,plain,(
% 0.26/0.38 ($true = (((^[Y0 : $i]: ($false)) @ (sK0 @ (^[Y0 : $i]: ($false)))))) | ~spl1_3),
% 0.26/0.38 inference(primitive_instantiation,[],[f22])).
% 0.26/0.38 thf(f39,plain,(
% 0.26/0.38 ($true = $false) | ~spl1_3),
% 0.26/0.38 inference(beta-eta_normalization,[],[f29])).
% 0.26/0.38 thf(f40,plain,(
% 0.26/0.38 $false | ~spl1_3),
% 0.26/0.38 inference(trivial_inequality_removal,[],[f39])).
% 0.26/0.38 thf(f41,plain,(
% 0.26/0.38 ~spl1_3),
% 0.26/0.38 inference(avatar_contradiction_clause,[],[f40])).
% 0.26/0.38 thf(f43,plain,(
% 0.26/0.38 ($true = $false) | (~spl1_2 | ~spl1_4)),
% 0.26/0.38 inference(forward_demodulation,[],[f26,f18])).
% 0.26/0.38 thf(f44,plain,(
% 0.26/0.38 $false | (~spl1_2 | ~spl1_4)),
% 0.26/0.38 inference(trivial_inequality_removal,[],[f43])).
% 0.26/0.38 thf(f45,plain,(
% 0.26/0.38 ~spl1_2 | ~spl1_4),
% 0.26/0.38 inference(avatar_contradiction_clause,[],[f44])).
% 0.26/0.38 thf(f55,plain,(
% 0.26/0.38 ($false = (((^[Y0 : $i]: ($true)) @ (sK0 @ (^[Y0 : $i]: ($true)))))) | ~spl1_1),
% 0.26/0.38 inference(primitive_instantiation,[],[f14])).
% 0.26/0.38 thf(f79,plain,(
% 0.26/0.38 ($true = $false) | ~spl1_1),
% 0.26/0.38 inference(beta-eta_normalization,[],[f55])).
% 0.26/0.38 thf(f80,plain,(
% 0.26/0.38 $false | ~spl1_1),
% 0.26/0.38 inference(trivial_inequality_removal,[],[f79])).
% 0.26/0.38 thf(f81,plain,(
% 0.26/0.38 ~spl1_1),
% 0.26/0.38 inference(avatar_contradiction_clause,[],[f80])).
% 0.26/0.38 cnf(s1, plain, spl1_1 | spl1_2, inference(sat_conversion,[],[f19])).
% 0.26/0.38 cnf(s2, plain, spl1_3 | spl1_4, inference(sat_conversion,[],[f27])).
% 0.26/0.38 cnf(s5, plain, ~spl1_3, inference(sat_conversion,[],[f41])).
% 0.26/0.38 cnf(s6, plain, ~spl1_2 | ~spl1_4, inference(sat_conversion,[],[f45])).
% 0.26/0.38 cnf(s11, plain, ~spl1_1, inference(sat_conversion,[],[f81])).
% 0.26/0.38 cnf(s12, plain, spl1_4, inference(rat,[],[s2,s5])).
% 0.26/0.38 cnf(s13, plain, ~spl1_2, inference(rat,[],[s6,s12])).
% 0.26/0.38 cnf(s14, plain, $false, inference(rat,[],[s1,s13,s11])).
% 0.26/0.38 thf(f82,plain,(
% 0.26/0.38 $false),
% 0.26/0.38 inference(avatar_sat_refutation,[],[s14])).
% 0.26/0.38 % SZS output end Proof for theBenchmark
% 0.26/0.38 % (767024)------------------------------
% 0.26/0.38 % (767024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.38 % (767024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.38 % (767024)CaDiCaL version: 2.1.3
% 0.26/0.38 % (767024)Termination reason: Refutation
% 0.26/0.38 % (767024)Time elapsed: 0.002 s
% 0.26/0.38 % (767024)Peak memory usage: 12 MB
% 0.26/0.38 % (767024)Instructions burned: 2 (million)
% 0.26/0.38 % (767016)Success in time 0.046 s
% 0.26/0.38 % Vampire exiting
%------------------------------------------------------------------------------