%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV162^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 08:39:04 AM UTC 2026
% Result : Theorem 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV162^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n026.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 15:20:42 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.26 % (723680)Will run a generic schedule for satisfiability detection.
% 0.19/0.26 % (723686)% WARNING: option uhcvi not known.
% 0.19/0.26 % (723686)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3502506269:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.26 % (723686)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.26 % (723686)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.26 % (723686) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-723680-723686"...
% 0.19/0.26 % (723686)...printing done.
% 0.19/0.26 % (723686)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Theorem for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% 0.19/0.26 thf(type_def_5, type, a: $tType).
% 0.19/0.26 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.26 thf(func_def_3, type, db1: !>[X0: $tType]:(X0)).
% 0.19/0.26 thf(func_def_4, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.26 thf(func_def_5, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.26 thf(func_def_6, type, sK0: (a > a > $o)).
% 0.19/0.26 thf(func_def_7, type, sK1: ((a > a > a) > a)).
% 0.19/0.26 thf(func_def_8, type, sK2: a).
% 0.19/0.26 thf(func_def_9, type, sK3: a).
% 0.19/0.26 thf(f1,conjecture,(
% 0.19/0.26 ! [X0 : (a > a > $o)] : (! [X1 : a,X2 : a] : (X0 @ X1 @ X2) <=> ! [X3 : ((a > a > a) > a)] : (X0 @ (X3 @ (^[X1 : a, X2 : a] : (X1))) @ (X3 @ (^[X1 : a, X2 : a] : (X2)))))),
% 0.19/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM184_pme)).
% 0.19/0.26 thf(f2,negated_conjecture,(
% 0.19/0.26 ~ ! [X0 : (a > a > $o)] : (! [X1 : a,X2 : a] : (X0 @ X1 @ X2) <=> ! [X3 : ((a > a > a) > a)] : (X0 @ (X3 @ (^[X1 : a, X2 : a] : (X1))) @ (X3 @ (^[X1 : a, X2 : a] : (X2)))))),
% 0.19/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.19/0.26 thf(f3,plain,(
% 0.19/0.26 ~ ! [X0 : (a > a > $o)] : (! [X1 : a,X2 : a] : (X0 @ X1 @ X2) <=> ! [X3 : ((a > a > a) > a)] : (X0 @ (X3 @ (^[X4 : a, X5 : a] : (X4))) @ (X3 @ (^[X6 : a, X7 : a] : (X7)))))),
% 0.19/0.26 inference(rectify,[],[f2])).
% 0.19/0.26 thf(f4,plain,(
% 0.19/0.26 ~ ! [X0 : (a > a > $o)] : (! [X1 : a,X2 : a] : (((X0 @ X1 @ X2)) = $true) <=> ! [X3 : ((a > a > a) > a)] : ($true = ((X0 @ (X3 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X3 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))))))),
% 0.19/0.26 inference(fool_elimination,[],[f3])).
% 0.19/0.26 thf(f5,plain,(
% 0.19/0.26 ? [X0 : (a > a > $o)] : (! [X1 : a,X2 : a] : (((X0 @ X1 @ X2)) = $true) <~> ! [X3 : ((a > a > a) > a)] : ($true = ((X0 @ (X3 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X3 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))))))),
% 0.19/0.26 inference(ennf_transformation,[],[f4])).
% 0.19/0.26 thf(f6,plain,(
% 0.19/0.26 ? [X0 : (a > a > $o)] : ((? [X3 : ((a > a > a) > a)] : ($true != ((X0 @ (X3 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X3 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))))) | ? [X1 : a,X2 : a] : (((X0 @ X1 @ X2)) != $true)) & (! [X3 : ((a > a > a) > a)] : ($true = ((X0 @ (X3 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X3 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))))) | ! [X1 : a,X2 : a] : (((X0 @ X1 @ X2)) = $true)))),
% 0.19/0.26 inference(nnf_transformation,[],[f5])).
% 0.19/0.26 thf(f7,plain,(
% 0.19/0.26 ? [X0 : (a > a > $o)] : ((? [X1 : ((a > a > a) > a)] : ($true != ((X0 @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))))) | ? [X2 : a,X3 : a] : ($true != ((X0 @ X2 @ X3)))) & (! [X4 : ((a > a > a) > a)] : ($true = ((X0 @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))))) | ! [X5 : a,X6 : a] : ($true = ((X0 @ X5 @ X6)))))),
% 0.19/0.26 inference(rectify,[],[f6])).
% 0.19/0.26 thf(f8,plain,(
% 0.19/0.26 (($true != ((sK0 @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))))) | ($true != ((sK0 @ sK2 @ sK3)))) & (! [X4 : ((a > a > a) > a)] : ($true = ((sK0 @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))))) | ! [X5 : a,X6 : a] : ($true = ((sK0 @ X5 @ X6))))),
% 0.19/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f7])).
% 0.19/0.26 thf(f9,plain,(
% 0.19/0.26 ( ! [X6 : a,X4 : ((a > a > a) > a),X5 : a] : (($true = ((sK0 @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))))) | ($true = ((sK0 @ X5 @ X6)))) )),
% 0.19/0.26 inference(cnf_transformation,[],[f8])).
% 0.19/0.26 thf(f10,plain,(
% 0.19/0.26 ($true != ((sK0 @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))))) | ($true != ((sK0 @ sK2 @ sK3)))),
% 0.19/0.26 inference(cnf_transformation,[],[f8])).
% 0.19/0.26 thf(f12,definition,(
% 0.19/0.26 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.19/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.19/0.26 thf(f14,definition,(
% 0.19/0.26 spl4_1 <=> ! [X6 : a,X5 : a] : ($true = ((sK0 @ X5 @ X6)))),
% 0.19/0.26 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.19/0.26 thf(f15,plain,(
% 0.19/0.26 ( ! [X6 : a,X5 : a] : (($true = ((sK0 @ X5 @ X6)))) ) | ~spl4_1),
% 0.19/0.26 inference(avatar_component_clause,[],[f14])).
% 0.19/0.26 thf(f17,definition,(
% 0.19/0.26 spl4_2 <=> ! [X4 : ((a > a > a) > a)] : ($true = ((sK0 @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))))),
% 0.19/0.26 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.19/0.26 thf(f18,plain,(
% 0.19/0.26 ( ! [X4 : ((a > a > a) > a)] : (($true = ((sK0 @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (X4 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))))) ) | ~spl4_2),
% 0.19/0.26 inference(avatar_component_clause,[],[f17])).
% 0.19/0.26 thf(f19,plain,(
% 0.19/0.26 spl4_1 | spl4_2),
% 0.19/0.26 inference(avatar_split_clause,[],[f9,f17,f14])).
% 0.19/0.26 thf(f21,definition,(
% 0.19/0.26 spl4_3 <=> ($true = ((sK0 @ sK2 @ sK3)))),
% 0.19/0.26 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
% 0.19/0.26 thf(f23,plain,(
% 0.19/0.26 ($true != ((sK0 @ sK2 @ sK3))) | spl4_3),
% 0.19/0.26 inference(avatar_component_clause,[],[f21])).
% 0.19/0.26 thf(f25,definition,(
% 0.19/0.26 spl4_4 <=> ($true = ((sK0 @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1))))))))),
% 0.19/0.26 introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
% 0.19/0.26 thf(f27,plain,(
% 0.19/0.26 ($true != ((sK0 @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0))))) @ (sK1 @ (^[Y0 : a]: ((^[Y1 : a]: (Y1)))))))) | spl4_4),
% 0.19/0.26 inference(avatar_component_clause,[],[f25])).
% 0.19/0.26 thf(f28,plain,(
% 0.19/0.26 ~spl4_3 | ~spl4_4),
% 0.19/0.26 inference(avatar_split_clause,[],[f10,f25,f21])).
% 0.19/0.26 thf(f29,plain,(
% 0.19/0.26 $false | (~spl4_2 | spl4_4)),
% 0.19/0.26 inference(forward_subsumption_resolution,[],[f27,f18])).
% 0.19/0.26 thf(f30,plain,(
% 0.19/0.26 ~spl4_2 | spl4_4),
% 0.19/0.26 inference(avatar_contradiction_clause,[],[f29])).
% 0.19/0.26 thf(f36,definition,(
% 0.19/0.26 spl4_5 <=> ! [X0 : ((a > a > a) > a)] : (sK2 != ((X0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0)))))))),
% 0.19/0.26 introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition])).
% 0.19/0.26 thf(f37,plain,(
% 0.19/0.26 ( ! [X0 : ((a > a > a) > a)] : ((sK2 != ((X0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0)))))))) ) | ~spl4_5),
% 0.19/0.26 inference(avatar_component_clause,[],[f36])).
% 0.19/0.26 thf(f42,plain,(
% 0.19/0.26 $false | (~spl4_1 | spl4_3)),
% 0.19/0.26 inference(backward_subsumption_resolution,[],[f23,f15])).
% 0.19/0.26 thf(f43,plain,(
% 0.19/0.26 ~spl4_1 | spl4_3),
% 0.19/0.26 inference(avatar_contradiction_clause,[],[f42])).
% 0.19/0.26 thf(f44,plain,(
% 0.19/0.26 $false | (~spl4_1 | spl4_4)),
% 0.19/0.26 inference(forward_subsumption_resolution,[],[f27,f15])).
% 0.19/0.26 thf(f45,plain,(
% 0.19/0.26 ~spl4_1 | spl4_4),
% 0.19/0.26 inference(avatar_contradiction_clause,[],[f44])).
% 0.19/0.26 thf(f58,plain,(
% 0.19/0.26 ($true != $true) | (((sK0 @ sK2 @ sK3)) = $false) | spl4_3),
% 0.19/0.26 inference(constrained_superposition,[],[f23,f12])).
% 0.19/0.26 thf(f60,plain,(
% 0.19/0.26 (((sK0 @ sK2 @ sK3)) = $false) | spl4_3),
% 0.19/0.26 inference(trivial_inequality_removal,[],[f58])).
% 0.19/0.26 thf(f66,plain,(
% 0.19/0.26 ( ! [X0 : ((a > a > a) > a)] : (($true = $false) | (sK2 != ((X0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0)))))))) ) | (~spl4_2 | spl4_3)),
% 0.19/0.26 inference(constrained_superposition,[],[f60,f18])).
% 0.19/0.26 thf(f74,plain,(
% 0.19/0.26 ( ! [X0 : ((a > a > a) > a)] : ((sK2 != ((X0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0)))))))) ) | (~spl4_2 | spl4_3)),
% 0.19/0.26 inference(trivial_inequality_removal,[],[f66])).
% 0.19/0.26 thf(f77,plain,(
% 0.19/0.26 spl4_5 | ~spl4_2 | spl4_3),
% 0.19/0.26 inference(avatar_split_clause,[],[f74,f21,f17,f36])).
% 0.19/0.26 thf(f80,plain,(
% 0.19/0.26 $false | ~spl4_5),
% 0.19/0.26 inference(equality_resolution,[],[f37])).
% 0.19/0.26 thf(f83,plain,(
% 0.19/0.26 ~spl4_5),
% 0.19/0.26 inference(avatar_contradiction_clause,[],[f80])).
% 0.19/0.26 cnf(s1, plain, spl4_1 | spl4_2, inference(sat_conversion,[],[f19])).
% 0.19/0.26 cnf(s2, plain, ~spl4_3 | ~spl4_4, inference(sat_conversion,[],[f28])).
% 0.19/0.26 cnf(s3, plain, ~spl4_2 | spl4_4, inference(sat_conversion,[],[f30])).
% 0.19/0.26 cnf(s5, plain, ~spl4_1 | spl4_3, inference(sat_conversion,[],[f43])).
% 0.19/0.26 cnf(s6, plain, ~spl4_1 | spl4_4, inference(sat_conversion,[],[f45])).
% 0.19/0.26 cnf(s15, plain, ~spl4_2 | spl4_3 | spl4_5, inference(sat_conversion,[],[f77])).
% 0.19/0.26 cnf(s18, plain, ~spl4_5, inference(sat_conversion,[],[f83])).
% 0.19/0.26 cnf(s20, plain, ~spl4_2 | spl4_3, inference(rat,[],[s15,s18])).
% 0.19/0.26 cnf(s26, plain, ~spl4_2, inference(rat,[],[s2,s3,s20])).
% 0.19/0.26 cnf(s27, plain, spl4_1, inference(rat,[],[s1,s26])).
% 0.19/0.26 cnf(s28, plain, spl4_4, inference(rat,[],[s6,s27])).
% 0.19/0.26 cnf(s29, plain, spl4_3, inference(rat,[],[s5,s27])).
% 0.19/0.26 cnf(s30, plain, $false, inference(rat,[],[s2,s28,s29])).
% 0.19/0.26 thf(f84,plain,(
% 0.19/0.26 $false),
% 0.19/0.26 inference(avatar_sat_refutation,[],[s30])).
% 0.19/0.26 % SZS output end Proof for theBenchmark
% 0.19/0.26 % (723686)------------------------------
% 0.19/0.26 % (723686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.26 % (723686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.26 % (723686)CaDiCaL version: 2.1.3
% 0.19/0.26 % (723686)Termination reason: Refutation
% 0.19/0.26 % (723686)Time elapsed: 0.003 s
% 0.19/0.26 % (723686)Peak memory usage: 13 MB
% 0.19/0.26 % (723686)Instructions burned: 6 (million)
% 0.19/0.26 % (723680)Success in time 0.027 s
% 0.19/0.26 % Vampire exiting
%------------------------------------------------------------------------------