%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PUZ081^2 : TPTP v9.3.1. Bugfixed v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 0.24s
% Output : Refutation 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ081^2 : TPTP v9.3.1. Bugfixed v7.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n010.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 13:21:48 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 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
% 0.07/0.24 % (2833034)Will run a generic schedule for satisfiability detection.
% 0.07/0.24 % (2833041)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4128598734:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.24 % (2833041) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2833034-2833041"...
% 0.07/0.24 % (2833041)...printing done.
% 0.07/0.24 % (2833041)Refutation found. Thanks to Tanya!
% 0.07/0.24 % SZS status Theorem for theBenchmark
% 0.07/0.24 % SZS output start Proof for theBenchmark
% 0.07/0.24 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.07/0.24 thf(func_def_2, type, knight: ($i > $o)).
% 0.07/0.24 thf(func_def_3, type, knave: ($i > $o)).
% 0.07/0.24 thf(func_def_4, type, says: ($i > $o > $o)).
% 0.07/0.24 thf(func_def_8, type, vAND: ($o > $o > $o)).
% 0.07/0.24 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.07/0.24 thf(f1,axiom,(
% 0.07/0.24 ! [X0 : $i] : ((knight @ X0) <~> (knave @ X0))),
% 0.07/0.24 file('/export/starexec/sandbox/benchmark/theBenchmark.p',knights_xor_knaves)).
% 0.07/0.24 thf(f6,conjecture,(
% 0.07/0.24 ? [X0 : ($i > $o),X1 : ($i > $o)] : ((X1 @ mel) & (X0 @ zoey) & ((X1 = knave) | (X1 = knight)) & ((X0 = knave) | (X0 = knight)))),
% 0.07/0.24 file('/export/starexec/sandbox/benchmark/theBenchmark.p',what_are_zoey_and_mel)).
% 0.07/0.24 thf(f7,negated_conjecture,(
% 0.07/0.24 ~ ? [X0 : ($i > $o),X1 : ($i > $o)] : ((X1 @ mel) & (X0 @ zoey) & ((X1 = knave) | (X1 = knight)) & ((X0 = knave) | (X0 = knight)))),
% 0.07/0.24 inference(negated_conjecture,[status(cth)],[f6])).
% 0.07/0.24 thf(f8,plain,(
% 0.07/0.24 ! [X0 : $i] : ((knight @ X0) <~> (knave @ X0))),
% 0.07/0.24 inference(rectify,[],[f1])).
% 0.07/0.24 thf(f9,plain,(
% 0.07/0.24 ! [X0 : $i] : (((knight @ X0)) != ((knave @ X0)))),
% 0.07/0.24 inference(fool_elimination,[],[f8])).
% 0.07/0.24 thf(f18,plain,(
% 0.07/0.24 ~ ? [X0 : ($i > $o),X1 : ($i > $o)] : ((X1 @ mel) & (X0 @ zoey) & ((X1 = knave) | (X1 = knight)) & ((X0 = knave) | (X0 = knight)))),
% 0.07/0.24 inference(rectify,[],[f7])).
% 0.07/0.24 thf(f19,plain,(
% 0.07/0.24 ~ ? [X0 : ($i > $o),X1 : ($i > $o)] : ((((X1 @ mel)) = $true) & (((X0 @ zoey)) = $true) & ((knave = X1) | (knight = X1)) & ((knave = X0) | (knight = X0)))),
% 0.07/0.24 inference(fool_elimination,[],[f18])).
% 0.07/0.24 thf(f25,plain,(
% 0.07/0.24 ! [X0 : ($i > $o),X1 : ($i > $o)] : ((((X1 @ mel)) != $true) | (((X0 @ zoey)) != $true) | ((knave != X1) & (knight != X1)) | ((knave != X0) & (knight != X0)))),
% 0.07/0.24 inference(ennf_transformation,[],[f19])).
% 0.07/0.24 thf(f26,plain,(
% 0.07/0.24 ( ! [X0 : $i] : ((((knight @ X0)) != ((knave @ X0)))) )),
% 0.07/0.24 inference(cnf_transformation,[],[f9])).
% 0.07/0.24 thf(f31,plain,(
% 0.07/0.24 ( ! [X0 : ($i > $o),X1 : ($i > $o)] : ((((X1 @ mel)) != $true) | (((X0 @ zoey)) != $true) | (knight != X1) | (knight != X0)) )),
% 0.07/0.24 inference(cnf_transformation,[],[f25])).
% 0.07/0.24 thf(f32,plain,(
% 0.07/0.24 ( ! [X0 : ($i > $o),X1 : ($i > $o)] : ((((X1 @ mel)) != $true) | (((X0 @ zoey)) != $true) | (knight != X1) | (knave != X0)) )),
% 0.07/0.24 inference(cnf_transformation,[],[f25])).
% 0.07/0.24 thf(f33,plain,(
% 0.07/0.24 ( ! [X0 : ($i > $o),X1 : ($i > $o)] : ((((X1 @ mel)) != $true) | (((X0 @ zoey)) != $true) | (knave != X1) | (knight != X0)) )),
% 0.07/0.24 inference(cnf_transformation,[],[f25])).
% 0.07/0.24 thf(f34,plain,(
% 0.07/0.24 ( ! [X0 : ($i > $o),X1 : ($i > $o)] : ((((X1 @ mel)) != $true) | (((X0 @ zoey)) != $true) | (knave != X1) | (knave != X0)) )),
% 0.07/0.24 inference(cnf_transformation,[],[f25])).
% 0.07/0.24 thf(f36,definition,(
% 0.07/0.24 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.07/0.24 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.07/0.24 thf(f38,plain,(
% 0.07/0.24 ( ! [X0 : ($i > $o)] : ((((knave @ mel)) != $true) | (((X0 @ zoey)) != $true) | (knave != X0)) )),
% 0.07/0.24 inference(equality_resolution,[],[f34])).
% 0.07/0.24 thf(f39,plain,(
% 0.07/0.24 (((knave @ mel)) != $true) | (((knave @ zoey)) != $true)),
% 0.07/0.24 inference(equality_resolution,[],[f38])).
% 0.07/0.24 thf(f40,plain,(
% 0.07/0.24 ( ! [X0 : ($i > $o)] : ((((knave @ mel)) != $true) | (((X0 @ zoey)) != $true) | (knight != X0)) )),
% 0.07/0.24 inference(equality_resolution,[],[f33])).
% 0.07/0.24 thf(f41,plain,(
% 0.07/0.24 (((knave @ mel)) != $true) | ($true != ((knight @ zoey)))),
% 0.07/0.24 inference(equality_resolution,[],[f40])).
% 0.07/0.24 thf(f42,plain,(
% 0.07/0.24 ( ! [X0 : ($i > $o)] : (($true != ((knight @ mel))) | (((X0 @ zoey)) != $true) | (knave != X0)) )),
% 0.07/0.24 inference(equality_resolution,[],[f32])).
% 0.07/0.24 thf(f43,plain,(
% 0.07/0.24 ($true != ((knight @ mel))) | (((knave @ zoey)) != $true)),
% 0.07/0.24 inference(equality_resolution,[],[f42])).
% 0.07/0.24 thf(f44,plain,(
% 0.07/0.24 ( ! [X0 : ($i > $o)] : (($true != ((knight @ mel))) | (((X0 @ zoey)) != $true) | (knight != X0)) )),
% 0.07/0.24 inference(equality_resolution,[],[f31])).
% 0.07/0.24 thf(f45,plain,(
% 0.07/0.24 ($true != ((knight @ mel))) | ($true != ((knight @ zoey)))),
% 0.07/0.24 inference(equality_resolution,[],[f44])).
% 0.07/0.24 thf(f46,plain,(
% 0.07/0.24 ( ! [X0 : $i] : ((((knight @ X0)) = $true) | (((knave @ X0)) = $true)) )),
% 0.07/0.24 inference(xor_proxy_clausification,[],[f26])).
% 0.07/0.24 thf(f49,definition,(
% 0.07/0.24 spl0_1 <=> (((knave @ zoey)) = $true)),
% 0.07/0.24 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.07/0.24 thf(f51,plain,(
% 0.07/0.24 (((knave @ zoey)) != $true) | spl0_1),
% 0.07/0.24 inference(avatar_component_clause,[],[f49])).
% 0.07/0.24 thf(f53,definition,(
% 0.07/0.24 spl0_2 <=> (((knave @ mel)) = $true)),
% 0.07/0.24 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.07/0.24 thf(f55,plain,(
% 0.07/0.24 (((knave @ mel)) != $true) | spl0_2),
% 0.07/0.24 inference(avatar_component_clause,[],[f53])).
% 0.07/0.24 thf(f56,plain,(
% 0.07/0.24 ~spl0_1 | ~spl0_2),
% 0.07/0.24 inference(avatar_split_clause,[],[f39,f53,f49])).
% 0.07/0.24 thf(f58,definition,(
% 0.07/0.24 spl0_3 <=> ($true = ((knight @ zoey)))),
% 0.07/0.24 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 0.07/0.24 thf(f60,plain,(
% 0.07/0.24 ($true != ((knight @ zoey))) | spl0_3),
% 0.07/0.24 inference(avatar_component_clause,[],[f58])).
% 0.07/0.24 thf(f61,plain,(
% 0.07/0.24 ~spl0_3 | ~spl0_2),
% 0.07/0.24 inference(avatar_split_clause,[],[f41,f53,f58])).
% 0.07/0.24 thf(f63,definition,(
% 0.07/0.24 spl0_4 <=> ($true = ((knight @ mel)))),
% 0.07/0.24 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
% 0.07/0.24 thf(f65,plain,(
% 0.07/0.24 ($true != ((knight @ mel))) | spl0_4),
% 0.07/0.24 inference(avatar_component_clause,[],[f63])).
% 0.07/0.24 thf(f66,plain,(
% 0.07/0.24 ~spl0_3 | ~spl0_4),
% 0.07/0.24 inference(avatar_split_clause,[],[f45,f63,f58])).
% 0.07/0.24 thf(f227,plain,(
% 0.07/0.24 ($true != $true) | ($false = ((knight @ zoey))) | spl0_3),
% 0.07/0.24 inference(constrained_superposition,[],[f60,f36])).
% 0.07/0.24 thf(f228,plain,(
% 0.07/0.24 ($false = ((knight @ zoey))) | spl0_3),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f227])).
% 0.07/0.24 thf(f238,plain,(
% 0.07/0.24 ($true = $false) | (((knave @ zoey)) = $true) | spl0_3),
% 0.07/0.24 inference(constrained_superposition,[],[f46,f228])).
% 0.07/0.24 thf(f243,plain,(
% 0.07/0.24 (((knave @ zoey)) = $true) | spl0_3),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f238])).
% 0.07/0.24 thf(f248,plain,(
% 0.07/0.24 $false | (spl0_1 | spl0_3)),
% 0.07/0.24 inference(forward_subsumption_resolution,[],[f243,f51])).
% 0.07/0.24 thf(f249,plain,(
% 0.07/0.24 spl0_1 | spl0_3),
% 0.07/0.24 inference(avatar_contradiction_clause,[],[f248])).
% 0.07/0.24 thf(f250,plain,(
% 0.07/0.24 ~spl0_1 | ~spl0_4),
% 0.07/0.24 inference(avatar_split_clause,[],[f43,f63,f49])).
% 0.07/0.24 thf(f252,plain,(
% 0.07/0.24 ($true != $true) | (((knave @ mel)) = $true) | spl0_4),
% 0.07/0.24 inference(constrained_superposition,[],[f65,f46])).
% 0.07/0.24 thf(f253,plain,(
% 0.07/0.24 (((knave @ mel)) = $true) | spl0_4),
% 0.07/0.24 inference(trivial_inequality_removal,[],[f252])).
% 0.07/0.24 thf(f255,plain,(
% 0.07/0.24 $false | (spl0_2 | spl0_4)),
% 0.07/0.24 inference(forward_subsumption_resolution,[],[f253,f55])).
% 0.07/0.24 thf(f256,plain,(
% 0.07/0.24 spl0_2 | spl0_4),
% 0.07/0.24 inference(avatar_contradiction_clause,[],[f255])).
% 0.07/0.24 cnf(s14, plain, ~spl0_1 | ~spl0_2, inference(sat_conversion,[],[f56])).
% 0.07/0.24 cnf(s18, plain, ~spl0_2 | ~spl0_3, inference(sat_conversion,[],[f61])).
% 0.07/0.24 cnf(s22, plain, ~spl0_3 | ~spl0_4, inference(sat_conversion,[],[f66])).
% 0.07/0.24 cnf(s79, plain, spl0_1 | spl0_3, inference(sat_conversion,[],[f249])).
% 0.07/0.24 cnf(s88, plain, ~spl0_1 | ~spl0_4, inference(sat_conversion,[],[f250])).
% 0.07/0.24 cnf(s91, plain, spl0_2 | spl0_4, inference(sat_conversion,[],[f256])).
% 0.07/0.24 cnf(s93, plain, ~spl0_3, inference(rat,[],[s91,s18,s22])).
% 0.07/0.24 cnf(s94, plain, spl0_1, inference(rat,[],[s79,s93])).
% 0.07/0.24 cnf(s96, plain, ~spl0_4, inference(rat,[],[s88,s94])).
% 0.07/0.24 cnf(s97, plain, ~spl0_2, inference(rat,[],[s14,s94])).
% 0.07/0.24 cnf(s98, plain, $false, inference(rat,[],[s91,s96,s97])).
% 0.07/0.24 thf(f257,plain,(
% 0.07/0.24 $false),
% 0.07/0.24 inference(avatar_sat_refutation,[],[s98])).
% 0.07/0.24 % SZS output end Proof for theBenchmark
% 0.07/0.24 % (2833041)------------------------------
% 0.07/0.24 % (2833041)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.24 % (2833041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.24 % (2833041)CaDiCaL version: 2.1.3
% 0.07/0.24 % (2833041)Termination reason: Refutation
% 0.07/0.24 % (2833041)Time elapsed: 0.003 s
% 0.07/0.24 % (2833041)Peak memory usage: 13 MB
% 0.07/0.24 % (2833041)Instructions burned: 8 (million)
% 0.07/0.24 % (2833034)Success in time 0.024 s
% 0.07/0.24 % Vampire exiting
%------------------------------------------------------------------------------