%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO032^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 08:48:45 AM UTC 2026
% Result : Theorem 0.26s 0.34s
% Output : Refutation 0.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO032^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 % Computer : n008.cluster.edu
% 0.07/0.22 % Model : x86_64 x86_64
% 0.07/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.22 % Memory : 8046.5625MB
% 0.07/0.22 % OS : Linux 6.8.0-71-generic
% 0.07/0.22 % CPULimit : 300
% 0.07/0.22 % WCLimit : 300
% 0.07/0.22 % DateTime : Tue Sep 29 16:24:02 UTC 2026
% 0.07/0.22 % CPUTime :
% 0.07/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.27 Running first-order model finding
% 0.07/0.27 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
% 0.26/0.34 % (3366031)Will run a generic schedule for satisfiability detection.
% 0.26/0.34 % (3366039)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2969438776:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.26/0.34 % (3366038)% WARNING: option uhcvi not known.
% 0.26/0.34 % (3366037)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2868268789_3000 on theBenchmark for (3000ds/0Mi)
% 0.26/0.34 % (3366041)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2260651225:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.26/0.34 % (3366038)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2833325027:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.26/0.34 % (3366041)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.26/0.34 % (3366040)dis+10_1_sil=32000:sp=arity:random_seed=3051794109:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.26/0.34 % (3366038)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.26/0.34 % Exception at run slice level
% 0.26/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.26/0.34 % (3366038)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.26/0.34 % (3366042)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2331602190:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.26/0.34 % (3366043)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3729731975:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.26/0.34 % (3366043) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3366031-3366043"...
% 0.26/0.34 % (3366043)...printing done.
% 0.26/0.34 % (3366039) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3366031-3366039"...
% 0.26/0.34 % (3366043)Refutation found. Thanks to Tanya!
% 0.26/0.34 % SZS status Theorem for theBenchmark
% 0.26/0.34 % SZS output start Proof for theBenchmark
% 0.26/0.34 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.26/0.34 thf(func_def_3, type, sK0: (($o > $o > $o) > $o)).
% 0.26/0.34 thf(func_def_4, type, sK1: (($o > $o > $o) > $o)).
% 0.26/0.34 thf(func_def_5, type, vNOT: ($o > $o)).
% 0.26/0.34 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.26/0.34 thf(func_def_7, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.26/0.34 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.26/0.34 thf(func_def_9, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.26/0.34 thf(func_def_10, type, vOR: ($o > $o > $o)).
% 0.26/0.34 thf(func_def_11, type, vAND: ($o > $o > $o)).
% 0.26/0.34 thf(func_def_12, type, db2: !>[X0: $tType]:(X0)).
% 0.26/0.34 thf(func_def_14, type, db3: !>[X0: $tType]:(X0)).
% 0.26/0.34 thf(func_def_15, type, db4: !>[X0: $tType]:(X0)).
% 0.26/0.34 thf(f1,conjecture,(
% 0.26/0.34 ? [X0 : ($o > $o > $o)] : ! [X1 : $o,X2 : $o] : ((X0 @ X1 @ X2) <=> (X2 | X1))),
% 0.26/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.26/0.34 thf(f2,negated_conjecture,(
% 0.26/0.34 ~ ? [X0 : ($o > $o > $o)] : ! [X1 : $o,X2 : $o] : ((X0 @ X1 @ X2) <=> (X2 | X1))),
% 0.26/0.34 inference(negated_conjecture,[status(cth)],[f1])).
% 0.26/0.34 thf(f3,plain,(
% 0.26/0.34 ~ ? [X0 : ($o > $o > $o)] : ! [X1 : $o,X2 : $o] : ((X0 @ X1 @ X2) <=> (X2 | X1))),
% 0.26/0.34 inference(rectify,[],[f2])).
% 0.26/0.34 thf(f4,plain,(
% 0.26/0.34 ~ ? [X0 : ($o > $o > $o)] : ! [X1 : $o,X2 : $o] : ((((X0 @ X1 @ X2)) = $true) <=> (($true = X2) | ($true = X1)))),
% 0.26/0.34 inference(fool_elimination,[],[f3])).
% 0.26/0.34 thf(f5,plain,(
% 0.26/0.34 ! [X0 : ($o > $o > $o)] : ? [X1 : $o,X2 : $o] : ((((X0 @ X1 @ X2)) = $true) <~> (($true = X2) | ($true = X1)))),
% 0.26/0.34 inference(ennf_transformation,[],[f4])).
% 0.26/0.34 thf(f6,plain,(
% 0.26/0.34 ! [X0 : ($o > $o > $o)] : ? [X1 : $o,X2 : $o] : (((($true != X2) & ($true != X1)) | (((X0 @ X1 @ X2)) != $true)) & ((($true = X2) | ($true = X1)) | (((X0 @ X1 @ X2)) = $true)))),
% 0.26/0.34 inference(nnf_transformation,[],[f5])).
% 0.26/0.34 thf(f7,plain,(
% 0.26/0.34 ! [X0 : ($o > $o > $o)] : ? [X1 : $o,X2 : $o] : (((($true != X2) & ($true != X1)) | (((X0 @ X1 @ X2)) != $true)) & (($true = X2) | ($true = X1) | (((X0 @ X1 @ X2)) = $true)))),
% 0.26/0.34 inference(flattening,[],[f6])).
% 0.26/0.34 thf(f8,plain,(
% 0.26/0.34 ! [X0 : ($o > $o > $o)] : (((($true != ((sK1 @ X0))) & ($true != ((sK0 @ X0)))) | ($true != ((X0 @ (sK0 @ X0) @ (sK1 @ X0))))) & (($true = ((sK1 @ X0))) | ($true = ((sK0 @ X0))) | ($true = ((X0 @ (sK0 @ X0) @ (sK1 @ X0))))))),
% 0.26/0.34 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X2,sK1 @ X0),skolemize(X2,sK1 @ X0)],[f7])).
% 0.26/0.34 thf(f9,plain,(
% 0.26/0.34 ( ! [X0 : ($o > $o > $o)] : (($true = ((X0 @ (sK0 @ X0) @ (sK1 @ X0)))) | ($true = ((sK0 @ X0))) | ($true = ((sK1 @ X0)))) )),
% 0.26/0.34 inference(cnf_transformation,[],[f8])).
% 0.26/0.34 thf(f10,plain,(
% 0.26/0.34 ( ! [X0 : ($o > $o > $o)] : (($true != ((sK0 @ X0))) | ($true != ((X0 @ (sK0 @ X0) @ (sK1 @ X0))))) )),
% 0.26/0.34 inference(cnf_transformation,[],[f8])).
% 0.26/0.34 thf(f11,plain,(
% 0.26/0.34 ( ! [X0 : ($o > $o > $o)] : (($true != ((sK1 @ X0))) | ($true != ((X0 @ (sK0 @ X0) @ (sK1 @ X0))))) )),
% 0.26/0.34 inference(cnf_transformation,[],[f8])).
% 0.26/0.34 thf(f18,plain,(
% 0.26/0.34 ($true = (((^[Y0 : $o]: ((^[Y1 : $o]: (Y0 | Y1)))) @ (sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y0 | Y1))))) @ (sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y0 | Y1)))))))) | ($true = ((sK0 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y0 | Y1))))))) | ($true = ((sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y0 | Y1)))))))),
% 0.26/0.34 inference(primitive_instantiation,[],[f9])).
% 0.26/0.34 thf(f59,plain,(
% 0.26/0.34 ($true = (((sK0 @ |) | (sK1 @ |)))) | ($true = ((sK0 @ |))) | ($true = ((sK1 @ |)))),
% 0.26/0.34 inference(beta-eta_normalization,[],[f18])).
% 0.26/0.34 thf(f60,plain,(
% 0.26/0.34 ($true = ((sK1 @ |))) | ($true = ((sK0 @ |))) | ($true = ((sK1 @ |))) | ($true = ((sK0 @ |)))),
% 0.26/0.34 inference(or_proxy_clausification,[],[f59])).
% 0.26/0.34 thf(f61,plain,(
% 0.26/0.34 ($true = ((sK1 @ |))) | ($true = ((sK0 @ |)))),
% 0.26/0.34 inference(duplicate_literal_removal,[],[f60])).
% 0.26/0.34 thf(f116,definition,(
% 0.26/0.34 spl2_9 <=> ($true = ((sK0 @ |)))),
% 0.26/0.34 introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition])).
% 0.26/0.34 thf(f118,plain,(
% 0.26/0.34 ($true = ((sK0 @ |))) | ~spl2_9),
% 0.26/0.34 inference(avatar_component_clause,[],[f116])).
% 0.26/0.34 thf(f120,definition,(
% 0.26/0.34 spl2_10 <=> ($true = ((sK1 @ |)))),
% 0.26/0.34 introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition])).
% 0.26/0.34 thf(f122,plain,(
% 0.26/0.34 ($true = ((sK1 @ |))) | ~spl2_10),
% 0.26/0.34 inference(avatar_component_clause,[],[f120])).
% 0.26/0.34 thf(f123,plain,(
% 0.26/0.34 spl2_9 | spl2_10),
% 0.26/0.34 inference(avatar_split_clause,[],[f61,f120,f116])).
% 0.26/0.34 thf(f135,plain,(
% 0.26/0.34 ($true != $true) | ($true != (($true | (sK1 @ |)))) | ~spl2_9),
% 0.26/0.34 inference(constrained_superposition,[],[f10,f118])).
% 0.26/0.34 thf(f137,plain,(
% 0.26/0.34 ($true != $true) | ($true = $false) | ~spl2_9),
% 0.26/0.34 inference(or_proxy_clausification,[],[f135])).
% 0.26/0.34 thf(f138,plain,(
% 0.26/0.34 $false | ~spl2_9),
% 0.26/0.34 inference(trivial_inequality_removal,[],[f137])).
% 0.26/0.34 thf(f139,plain,(
% 0.26/0.34 ~spl2_9),
% 0.26/0.34 inference(avatar_contradiction_clause,[],[f138])).
% 0.26/0.34 thf(f144,plain,(
% 0.26/0.34 ($true != $true) | ($true != (((sK0 @ |) | $true))) | ~spl2_10),
% 0.26/0.34 inference(constrained_superposition,[],[f11,f122])).
% 0.26/0.34 thf(f145,plain,(
% 0.26/0.34 ($true != $true) | ($true = $false) | ~spl2_10),
% 0.26/0.34 inference(or_proxy_clausification,[],[f144])).
% 0.26/0.34 thf(f148,plain,(
% 0.26/0.34 $false | ~spl2_10),
% 0.26/0.34 inference(trivial_inequality_removal,[],[f145])).
% 0.26/0.34 thf(f149,plain,(
% 0.26/0.34 ~spl2_10),
% 0.26/0.34 inference(avatar_contradiction_clause,[],[f148])).
% 0.26/0.34 cnf(s6, plain, spl2_9 | spl2_10, inference(sat_conversion,[],[f123])).
% 0.26/0.34 cnf(s10, plain, ~spl2_9, inference(sat_conversion,[],[f139])).
% 0.26/0.34 cnf(s11, plain, ~spl2_10, inference(sat_conversion,[],[f149])).
% 0.26/0.34 cnf(s12, plain, $false, inference(rat,[],[s6,s11,s10])).
% 0.26/0.34 thf(f150,plain,(
% 0.26/0.34 $false),
% 0.26/0.34 inference(avatar_sat_refutation,[],[s12])).
% 0.26/0.34 % SZS output end Proof for theBenchmark
% 0.26/0.34 % (3366043)------------------------------
% 0.26/0.34 % (3366043)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.34 % (3366043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.34 % (3366043)CaDiCaL version: 2.1.3
% 0.26/0.34 % (3366043)Termination reason: Refutation
% 0.26/0.34 % (3366043)Time elapsed: 0.012 s
% 0.26/0.34 % (3366043)Peak memory usage: 13 MB
% 0.26/0.34 % (3366043)Instructions burned: 11 (million)
% 0.26/0.34 % (3366031)Success in time 0.051 s
% 0.26/0.34 % Vampire exiting
%------------------------------------------------------------------------------