%------------------------------------------------------------------------------
% File : Vampire-SAT---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 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 08:49:47 AM UTC 2026
% Result : Theorem 0.09s 0.24s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO361^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n026.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 16:51:42 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 Running first-order model finding
% 0.09/0.20 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
% 0.09/0.24 % (852275)Will run a generic schedule for satisfiability detection.
% 0.09/0.24 % (852282)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=845298990:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.24 % (852282) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-852275-852282"...
% 0.09/0.24 % (852282)...printing done.
% 0.09/0.24 % (852281)% WARNING: option uhcvi not known.
% 0.09/0.24 % (852282)Refutation found. Thanks to Tanya!
% 0.09/0.24 % SZS status Theorem for theBenchmark
% 0.09/0.24 % SZS output start Proof for theBenchmark
% 0.09/0.24 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.24 thf(func_def_5, type, sK2: ($i > $i > $o)).
% 0.09/0.24 thf(func_def_6, type, sK3: (($i > $i > $o) > $i)).
% 0.09/0.24 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.09/0.24 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.09/0.24 thf(func_def_10, type, db1: !>[X0: $tType]:(X0)).
% 0.09/0.24 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.09/0.24 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.09/0.24 thf(f1,conjecture,(
% 0.09/0.24 ! [X0 : $i,X1 : $i] : ((X0 = X1) <=> ! [X2 : ($i > $i > $o)] : (! [X3 : $i] : (X2 @ X3 @ X3) => (X2 @ X0 @ X1)))),
% 0.09/0.24 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM47)).
% 0.09/0.24 thf(f2,negated_conjecture,(
% 0.09/0.24 ~ ! [X0 : $i,X1 : $i] : ((X0 = X1) <=> ! [X2 : ($i > $i > $o)] : (! [X3 : $i] : (X2 @ X3 @ X3) => (X2 @ X0 @ X1)))),
% 0.09/0.24 inference(negated_conjecture,[status(cth)],[f1])).
% 0.09/0.24 thf(f3,plain,(
% 0.09/0.24 ~ ! [X0 : $i,X1 : $i] : ((X0 = X1) <=> ! [X2 : ($i > $i > $o)] : (! [X3 : $i] : (X2 @ X3 @ X3) => (X2 @ X0 @ X1)))),
% 0.09/0.24 inference(rectify,[],[f2])).
% 0.09/0.24 thf(f4,plain,(
% 0.09/0.24 ~ ! [X0 : $i,X1 : $i] : ((X0 = X1) <=> ! [X2 : ($i > $i > $o)] : (! [X3 : $i] : (((X2 @ X3 @ X3)) = $true) => (((X2 @ X0 @ X1)) = $true)))),
% 0.09/0.24 inference(fool_elimination,[],[f3])).
% 0.09/0.24 thf(f5,plain,(
% 0.09/0.24 ? [X0 : $i,X1 : $i] : ((X0 = X1) <~> ! [X2 : ($i > $i > $o)] : ((((X2 @ X0 @ X1)) = $true) | ? [X3 : $i] : (((X2 @ X3 @ X3)) != $true)))),
% 0.09/0.24 inference(ennf_transformation,[],[f4])).
% 0.09/0.24 thf(f6,plain,(
% 0.09/0.24 ? [X0 : $i,X1 : $i] : ((? [X2 : ($i > $i > $o)] : ((((X2 @ X0 @ X1)) != $true) & ! [X3 : $i] : (((X2 @ X3 @ X3)) = $true)) | (X0 != X1)) & (! [X2 : ($i > $i > $o)] : ((((X2 @ X0 @ X1)) = $true) | ? [X3 : $i] : (((X2 @ X3 @ X3)) != $true)) | (X0 = X1)))),
% 0.09/0.24 inference(nnf_transformation,[],[f5])).
% 0.09/0.24 thf(f7,plain,(
% 0.09/0.24 ? [X0 : $i,X1 : $i] : ((? [X2 : ($i > $i > $o)] : ((((X2 @ X0 @ X1)) != $true) & ! [X3 : $i] : (((X2 @ X3 @ X3)) = $true)) | (X0 != X1)) & (! [X4 : ($i > $i > $o)] : (($true = ((X4 @ X0 @ X1))) | ? [X5 : $i] : ($true != ((X4 @ X5 @ X5)))) | (X0 = X1)))),
% 0.09/0.24 inference(rectify,[],[f6])).
% 0.09/0.24 thf(f8,plain,(
% 0.09/0.24 ((($true != ((sK2 @ sK0 @ sK1))) & ! [X3 : $i] : ($true = ((sK2 @ X3 @ X3)))) | (sK0 != sK1)) & (! [X4 : ($i > $i > $o)] : (($true = ((X4 @ sK0 @ sK1))) | ($true != ((X4 @ (sK3 @ X4) @ (sK3 @ X4))))) | (sK0 = sK1))),
% 0.09/0.24 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X5,sK3 @ X4)],[f7])).
% 0.09/0.24 thf(f9,plain,(
% 0.09/0.24 ( ! [X4 : ($i > $i > $o)] : (($true = ((X4 @ sK0 @ sK1))) | ($true != ((X4 @ (sK3 @ X4) @ (sK3 @ X4)))) | (sK0 = sK1)) )),
% 0.09/0.24 inference(cnf_transformation,[],[f8])).
% 0.09/0.24 thf(f10,plain,(
% 0.09/0.24 ( ! [X3 : $i] : (($true = ((sK2 @ X3 @ X3))) | (sK0 != sK1)) )),
% 0.09/0.24 inference(cnf_transformation,[],[f8])).
% 0.09/0.24 thf(f11,plain,(
% 0.09/0.24 ($true != ((sK2 @ sK0 @ sK1))) | (sK0 != sK1)),
% 0.09/0.24 inference(cnf_transformation,[],[f8])).
% 0.09/0.24 thf(f15,definition,(
% 0.09/0.24 spl4_1 <=> (sK0 = sK1)),
% 0.09/0.24 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.09/0.24 thf(f16,plain,(
% 0.09/0.24 (sK0 = sK1) | ~spl4_1),
% 0.09/0.24 inference(avatar_component_clause,[],[f15])).
% 0.09/0.24 thf(f17,plain,(
% 0.09/0.24 (sK0 != sK1) | spl4_1),
% 0.09/0.24 inference(avatar_component_clause,[],[f15])).
% 0.09/0.24 thf(f19,definition,(
% 0.09/0.24 spl4_2 <=> ($true = ((sK2 @ sK0 @ sK1)))),
% 0.09/0.24 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.09/0.24 thf(f21,plain,(
% 0.09/0.24 ($true != ((sK2 @ sK0 @ sK1))) | spl4_2),
% 0.09/0.24 inference(avatar_component_clause,[],[f19])).
% 0.09/0.24 thf(f22,plain,(
% 0.09/0.24 ~spl4_1 | ~spl4_2),
% 0.09/0.24 inference(avatar_split_clause,[],[f11,f19,f15])).
% 0.09/0.24 thf(f23,plain,(
% 0.09/0.24 ( ! [X4 : ($i > $i > $o)] : (($true != ((X4 @ (sK3 @ X4) @ (sK3 @ X4)))) | ($true = ((X4 @ sK0 @ sK1)))) ) | spl4_1),
% 0.09/0.24 inference(forward_subsumption_resolution,[],[f9,f17])).
% 0.09/0.24 thf(f30,plain,(
% 0.09/0.24 ($true != (((^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1)))) @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1))))) @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1)))))))) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1)))) @ sK0 @ sK1))) | spl4_1),
% 0.09/0.24 inference(primitive_instantiation,[],[f23])).
% 0.09/0.24 thf(f47,plain,(
% 0.09/0.24 ($true != (((sK3 @ =) = (sK3 @ =)))) | ($true = ((sK0 = sK1))) | spl4_1),
% 0.09/0.24 inference(beta-eta_normalization,[],[f30])).
% 0.09/0.24 thf(f48,plain,(
% 0.09/0.24 (((sK3 @ =)) != ((sK3 @ =))) | ($true = ((sK0 = sK1))) | spl4_1),
% 0.09/0.24 inference(equality_proxy_clausification,[],[f47])).
% 0.09/0.24 thf(f49,plain,(
% 0.09/0.24 (((sK3 @ =)) != ((sK3 @ =))) | (sK0 = sK1) | spl4_1),
% 0.09/0.24 inference(equality_proxy_clausification,[],[f48])).
% 0.09/0.24 thf(f50,plain,(
% 0.09/0.24 (sK0 = sK1) | spl4_1),
% 0.09/0.24 inference(trivial_inequality_removal,[],[f49])).
% 0.09/0.24 thf(f51,plain,(
% 0.09/0.24 $false | spl4_1),
% 0.09/0.24 inference(forward_subsumption_resolution,[],[f50,f17])).
% 0.09/0.24 thf(f52,plain,(
% 0.09/0.24 spl4_1),
% 0.09/0.24 inference(avatar_contradiction_clause,[],[f51])).
% 0.09/0.24 thf(f73,plain,(
% 0.09/0.24 ($true != ((sK2 @ sK0 @ sK0))) | (~spl4_1 | spl4_2)),
% 0.09/0.24 inference(constrained_superposition,[],[f21,f16])).
% 0.09/0.24 thf(f101,plain,(
% 0.09/0.24 ( ! [X3 : $i] : (($true = ((sK2 @ X3 @ X3)))) ) | ~spl4_1),
% 0.09/0.24 inference(forward_subsumption_resolution,[],[f10,f16])).
% 0.09/0.24 thf(f102,plain,(
% 0.09/0.24 ($true != $true) | (~spl4_1 | spl4_2)),
% 0.09/0.24 inference(constrained_superposition,[],[f73,f101])).
% 0.09/0.24 thf(f103,plain,(
% 0.09/0.24 $false | (~spl4_1 | spl4_2)),
% 0.09/0.24 inference(trivial_inequality_removal,[],[f102])).
% 0.09/0.24 thf(f104,plain,(
% 0.09/0.24 ~spl4_1 | spl4_2),
% 0.09/0.24 inference(avatar_contradiction_clause,[],[f103])).
% 0.09/0.24 cnf(s7, plain, ~spl4_1 | ~spl4_2, inference(sat_conversion,[],[f22])).
% 0.09/0.24 cnf(s14, plain, spl4_1, inference(sat_conversion,[],[f52])).
% 0.09/0.24 cnf(s41, plain, ~spl4_1 | spl4_2, inference(sat_conversion,[],[f104])).
% 0.09/0.24 cnf(s42, plain, spl4_2, inference(rat,[],[s41,s14])).
% 0.09/0.24 cnf(s44, plain, $false, inference(rat,[],[s7,s42,s14])).
% 0.09/0.24 thf(f105,plain,(
% 0.09/0.24 $false),
% 0.09/0.24 inference(avatar_sat_refutation,[],[s44])).
% 0.09/0.24 % SZS output end Proof for theBenchmark
% 0.09/0.24 % (852282)------------------------------
% 0.09/0.24 % (852282)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.24 % (852282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.24 % (852282)CaDiCaL version: 2.1.3
% 0.09/0.24 % (852282)Termination reason: Refutation
% 0.09/0.24 % (852282)Time elapsed: 0.002 s
% 0.09/0.24 % (852282)Peak memory usage: 12 MB
% 0.09/0.24 % (852282)Instructions burned: 5 (million)
% 0.09/0.24 % (852275)Success in time 0.031 s
% 0.09/0.24 % Vampire exiting
%------------------------------------------------------------------------------