%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PUZ081^3 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 08:21:00 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : Refutation 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ081^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n013.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:21:06 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 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
% 0.07/0.26 % (2089762)Will run a generic schedule for satisfiability detection.
% 0.07/0.26 % (2089778)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3718172740:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.26 % (2089777)% WARNING: option uhcvi not known.
% 0.07/0.26 % (2089778) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2089762-2089778"...
% 0.07/0.26 % (2089778)...printing done.
% 0.07/0.26 % (2089778)Refutation found. Thanks to Tanya!
% 0.07/0.26 % SZS status Theorem for theBenchmark
% 0.07/0.26 % SZS output start Proof for theBenchmark
% 0.07/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.07/0.26 thf(func_def_2, type, knight: ($i > $o)).
% 0.07/0.26 thf(func_def_3, type, knave: ($i > $o)).
% 0.07/0.26 thf(func_def_4, type, says: ($i > $o > $o)).
% 0.07/0.26 thf(func_def_8, type, vAND: ($o > $o > $o)).
% 0.07/0.26 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.07/0.26 thf(f1,axiom,(
% 0.07/0.26 ! [X0 : $i] : ((knight @ X0) <~> (knave @ X0))),
% 0.07/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knights_xor_knaves)).
% 0.07/0.26 thf(f2,axiom,(
% 0.07/0.26 ! [X0 : $i,X1 : $o] : (((says @ X0 @ X1) & (knight @ X0)) => X1)),
% 0.07/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knights_tell_truth)).
% 0.07/0.26 thf(f3,axiom,(
% 0.07/0.26 ! [X0 : $i,X1 : $o] : (((says @ X0 @ X1) & (knave @ X0)) => ~X1)),
% 0.07/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knaves_lie)).
% 0.07/0.26 thf(f4,axiom,(
% 0.07/0.26 (says @ zoey @ (knave @ mel))),
% 0.07/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zoey_speaks)).
% 0.07/0.26 thf(f6,conjecture,(
% 0.07/0.26 ? [X0 : $i,X1 : $i] : ((knave @ X1) & (knight @ X0))),
% 0.07/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',who_is_knight_and_knave)).
% 0.07/0.26 thf(f7,negated_conjecture,(
% 0.07/0.26 ~ ? [X0 : $i,X1 : $i] : ((knave @ X1) & (knight @ X0))),
% 0.07/0.26 inference(negated_conjecture,[status(cth)],[f6])).
% 0.07/0.26 thf(f8,plain,(
% 0.07/0.26 ! [X0 : $i] : ((knight @ X0) <~> (knave @ X0))),
% 0.07/0.26 inference(rectify,[],[f1])).
% 0.07/0.26 thf(f9,plain,(
% 0.07/0.26 ! [X0 : $i] : (((knight @ X0)) != ((knave @ X0)))),
% 0.07/0.26 inference(fool_elimination,[],[f8])).
% 0.07/0.26 thf(f10,plain,(
% 0.07/0.26 ! [X0 : $i,X1 : $o] : (((says @ X0 @ X1) & (knight @ X0)) => X1)),
% 0.07/0.26 inference(rectify,[],[f2])).
% 0.07/0.26 thf(f11,plain,(
% 0.07/0.26 ! [X0 : $i,X1 : $o] : (((((says @ X0 @ X1)) = $true) & (((knight @ X0)) = $true)) => ($true = X1))),
% 0.07/0.26 inference(fool_elimination,[],[f10])).
% 0.07/0.26 thf(f12,plain,(
% 0.07/0.26 ! [X0 : $i,X1 : $o] : (((says @ X0 @ X1) & (knave @ X0)) => ~X1)),
% 0.07/0.26 inference(rectify,[],[f3])).
% 0.07/0.26 thf(f13,plain,(
% 0.07/0.26 ! [X0 : $i,X1 : $o] : (((((says @ X0 @ X1)) = $true) & (((knave @ X0)) = $true)) => ~ ($true = X1))),
% 0.07/0.26 inference(fool_elimination,[],[f12])).
% 0.07/0.26 thf(f14,plain,(
% 0.07/0.26 (says @ zoey @ (knave @ mel))),
% 0.07/0.26 inference(rectify,[],[f4])).
% 0.07/0.26 thf(f15,plain,(
% 0.07/0.26 (((says @ zoey @ (knave @ mel))) = $true)),
% 0.07/0.26 inference(fool_elimination,[],[f14])).
% 0.07/0.26 thf(f18,plain,(
% 0.07/0.26 ~ ? [X0 : $i,X1 : $i] : ((knave @ X1) & (knight @ X0))),
% 0.07/0.26 inference(rectify,[],[f7])).
% 0.07/0.26 thf(f19,plain,(
% 0.07/0.26 ~ ? [X0 : $i,X1 : $i] : ((((knave @ X1)) = $true) & (((knight @ X0)) = $true))),
% 0.07/0.26 inference(fool_elimination,[],[f18])).
% 0.07/0.26 thf(f20,plain,(
% 0.07/0.26 ! [X0 : $i,X1 : $o] : (((((says @ X0 @ X1)) = $true) & (((knave @ X0)) = $true)) => ($true != X1))),
% 0.07/0.26 inference(flattening,[],[f13])).
% 0.07/0.26 thf(f21,plain,(
% 0.07/0.26 ! [X0 : $i,X1 : $o] : (($true = X1) | ((((says @ X0 @ X1)) != $true) | (((knight @ X0)) != $true)))),
% 0.07/0.26 inference(ennf_transformation,[],[f11])).
% 0.07/0.26 thf(f22,plain,(
% 0.07/0.26 ! [X0 : $i,X1 : $o] : (($true = X1) | (((says @ X0 @ X1)) != $true) | (((knight @ X0)) != $true))),
% 0.07/0.26 inference(flattening,[],[f21])).
% 0.07/0.26 thf(f23,plain,(
% 0.07/0.26 ! [X0 : $i,X1 : $o] : (($true != X1) | ((((says @ X0 @ X1)) != $true) | (((knave @ X0)) != $true)))),
% 0.07/0.26 inference(ennf_transformation,[],[f20])).
% 0.07/0.26 thf(f24,plain,(
% 0.07/0.26 ! [X0 : $i,X1 : $o] : (($true != X1) | (((says @ X0 @ X1)) != $true) | (((knave @ X0)) != $true))),
% 0.07/0.26 inference(flattening,[],[f23])).
% 0.07/0.26 thf(f25,plain,(
% 0.07/0.26 ! [X0 : $i,X1 : $i] : ((((knave @ X1)) != $true) | (((knight @ X0)) != $true))),
% 0.07/0.26 inference(ennf_transformation,[],[f19])).
% 0.07/0.26 thf(f26,plain,(
% 0.07/0.26 ( ! [X0 : $i] : ((((knight @ X0)) != ((knave @ X0)))) )),
% 0.07/0.26 inference(cnf_transformation,[],[f9])).
% 0.07/0.26 thf(f27,plain,(
% 0.07/0.26 ( ! [X0 : $i,X1 : $o] : (($true = X1) | (((says @ X0 @ X1)) != $true) | (((knight @ X0)) != $true)) )),
% 0.07/0.26 inference(cnf_transformation,[],[f22])).
% 0.07/0.26 thf(f28,plain,(
% 0.07/0.26 ( ! [X0 : $i,X1 : $o] : (($true != X1) | (((says @ X0 @ X1)) != $true) | (((knave @ X0)) != $true)) )),
% 0.07/0.26 inference(cnf_transformation,[],[f24])).
% 0.07/0.26 thf(f29,plain,(
% 0.07/0.26 (((says @ zoey @ (knave @ mel))) = $true)),
% 0.07/0.26 inference(cnf_transformation,[],[f15])).
% 0.07/0.26 thf(f31,plain,(
% 0.07/0.26 ( ! [X0 : $i,X1 : $i] : ((((knave @ X1)) != $true) | (((knight @ X0)) != $true)) )),
% 0.07/0.26 inference(cnf_transformation,[],[f25])).
% 0.07/0.26 thf(f33,definition,(
% 0.07/0.26 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.07/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.07/0.26 thf(f34,plain,(
% 0.07/0.26 ( ! [X0 : $i] : (($true != ((says @ X0 @ $true))) | (((knave @ X0)) != $true)) )),
% 0.07/0.26 inference(equality_resolution,[],[f28])).
% 0.07/0.26 thf(f35,plain,(
% 0.07/0.26 ( ! [X0 : $i] : ((((knight @ X0)) = $true) | (((knave @ X0)) = $true)) )),
% 0.07/0.26 inference(xor_proxy_clausification,[],[f26])).
% 0.07/0.26 thf(f38,definition,(
% 0.07/0.26 spl0_1 <=> ! [X0 : $i] : (((knight @ X0)) != $true)),
% 0.07/0.26 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.07/0.26 thf(f39,plain,(
% 0.07/0.26 ( ! [X0 : $i] : ((((knight @ X0)) != $true)) ) | ~spl0_1),
% 0.07/0.26 inference(avatar_component_clause,[],[f38])).
% 0.07/0.26 thf(f41,definition,(
% 0.07/0.26 spl0_2 <=> ! [X1 : $i] : (((knave @ X1)) != $true)),
% 0.07/0.26 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.07/0.26 thf(f42,plain,(
% 0.07/0.26 ( ! [X1 : $i] : ((((knave @ X1)) != $true)) ) | ~spl0_2),
% 0.07/0.26 inference(avatar_component_clause,[],[f41])).
% 0.07/0.26 thf(f43,plain,(
% 0.07/0.26 spl0_1 | spl0_2),
% 0.07/0.26 inference(avatar_split_clause,[],[f31,f41,f38])).
% 0.07/0.26 thf(f58,plain,(
% 0.07/0.26 ( ! [X0 : $i] : (($true != $true) | (((knave @ X0)) = $false)) ) | ~spl0_2),
% 0.07/0.26 inference(constrained_superposition,[],[f42,f33])).
% 0.07/0.26 thf(f64,plain,(
% 0.07/0.26 ( ! [X0 : $i] : ((((knave @ X0)) = $false)) ) | ~spl0_2),
% 0.07/0.26 inference(trivial_inequality_removal,[],[f58])).
% 0.07/0.26 thf(f161,plain,(
% 0.07/0.26 ( ! [X0 : $i] : ((((knight @ X0)) = $true)) ) | ~spl0_2),
% 0.07/0.26 inference(forward_subsumption_resolution,[],[f35,f42])).
% 0.07/0.26 thf(f176,plain,(
% 0.07/0.26 ($true = ((says @ zoey @ $false))) | ~spl0_2),
% 0.07/0.26 inference(forward_demodulation,[],[f29,f64])).
% 0.07/0.26 thf(f177,plain,(
% 0.07/0.26 ( ! [X0 : $i,X1 : $o] : ((((says @ X0 @ X1)) != $true) | ($true = X1)) ) | ~spl0_2),
% 0.07/0.26 inference(forward_subsumption_resolution,[],[f27,f161])).
% 0.07/0.26 thf(f183,plain,(
% 0.07/0.26 ($true != $true) | ($true = $false) | ~spl0_2),
% 0.07/0.26 inference(constrained_superposition,[],[f177,f176])).
% 0.07/0.26 thf(f184,plain,(
% 0.07/0.26 $false | ~spl0_2),
% 0.07/0.26 inference(trivial_inequality_removal,[],[f183])).
% 0.07/0.26 thf(f185,plain,(
% 0.07/0.26 ~spl0_2),
% 0.07/0.26 inference(avatar_contradiction_clause,[],[f184])).
% 0.07/0.26 thf(f197,plain,(
% 0.07/0.26 ( ! [X0 : $i] : ((((knave @ X0)) = $true)) ) | ~spl0_1),
% 0.07/0.26 inference(forward_subsumption_resolution,[],[f35,f39])).
% 0.07/0.26 thf(f198,plain,(
% 0.07/0.26 ($true = ((says @ zoey @ $true))) | ~spl0_1),
% 0.07/0.26 inference(forward_demodulation,[],[f29,f197])).
% 0.07/0.26 thf(f203,plain,(
% 0.07/0.26 ($true != $true) | (((knave @ zoey)) != $true) | ~spl0_1),
% 0.07/0.26 inference(constrained_superposition,[],[f34,f198])).
% 0.07/0.26 thf(f204,plain,(
% 0.07/0.26 (((knave @ zoey)) != $true) | ~spl0_1),
% 0.07/0.26 inference(trivial_inequality_removal,[],[f203])).
% 0.07/0.26 thf(f208,plain,(
% 0.07/0.26 $false | ~spl0_1),
% 0.07/0.26 inference(forward_subsumption_resolution,[],[f204,f197])).
% 0.07/0.26 thf(f209,plain,(
% 0.07/0.26 ~spl0_1),
% 0.07/0.26 inference(avatar_contradiction_clause,[],[f208])).
% 0.07/0.26 cnf(s11, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f43])).
% 0.07/0.26 cnf(s56, plain, ~spl0_2, inference(sat_conversion,[],[f185])).
% 0.07/0.26 cnf(s77, plain, ~spl0_1, inference(sat_conversion,[],[f209])).
% 0.07/0.26 cnf(s80, plain, $false, inference(rat,[],[s11,s56,s77])).
% 0.07/0.26 thf(f210,plain,(
% 0.07/0.26 $false),
% 0.07/0.26 inference(avatar_sat_refutation,[],[s80])).
% 0.07/0.26 % SZS output end Proof for theBenchmark
% 0.07/0.26 % (2089778)------------------------------
% 0.07/0.26 % (2089778)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (2089778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (2089778)CaDiCaL version: 2.1.3
% 0.07/0.26 % (2089778)Termination reason: Refutation
% 0.07/0.26 % (2089778)Time elapsed: 0.004 s
% 0.07/0.26 % (2089778)Peak memory usage: 13 MB
% 0.07/0.26 % (2089778)Instructions burned: 8 (million)
% 0.07/0.26 % (2089762)Success in time 0.035 s
% 0.07/0.26 % Vampire exiting
%------------------------------------------------------------------------------