%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PUZ082_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 : Tue Sep 29 12:32:15 PM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : Refutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ082_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n005.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 22:40:16 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.12/0.45 % (243727)Will run a generic schedule for satisfiability detection.
% 0.12/0.45 % (243740)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3832764521:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.45 % (243740) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-243727-243740"...
% 0.12/0.45 % (243735)% WARNING: option uhcvi not known.
% 0.12/0.45 % (243740)...printing done.
% 0.12/0.45 % (243740)Refutation found. Thanks to Tanya!
% 0.12/0.45 % SZS status Theorem for theBenchmark
% 0.12/0.45 % SZS output start Proof for theBenchmark
% 0.12/0.45 tff(func_def_3, type, bG0: $o > $o).
% 0.12/0.45 tff(func_def_4, type, bG1: $o).
% 0.12/0.45 tff(func_def_5, type, bG2: $o > $o).
% 0.12/0.45 tff(func_def_6, type, sK3: $o).
% 0.12/0.45 tff(pred_def_1, type, says: ($i * $o) > $o).
% 0.12/0.45 tff(f1,axiom,(
% 0.12/0.45 says(peter,! [X0 : $o] : (says(peter,X0) => ~X0))),
% 0.12/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1)).
% 0.12/0.45 tff(f2,conjecture,(
% 0.12/0.45 ~ ! [X0 : $o] : (says(peter,X0) => ~X0)),
% 0.12/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm)).
% 0.12/0.45 tff(f3,negated_conjecture,(
% 0.12/0.45 ~ ~ ! [X0 : $o] : (says(peter,X0) => ~X0)),
% 0.12/0.45 inference(negated_conjecture,[status(cth)],[f2])).
% 0.12/0.45 tff(f4,plain,(
% 0.12/0.45 says(peter,! [X0 : $o] : (says(peter,X0) => ~X0))),
% 0.12/0.45 inference(rectify,[],[f1])).
% 0.12/0.45 tff(f5,definition,(
% 0.12/0.45 ! [X0 : $o] : (($true = X0) <=> ($true = bG0(X0)))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[bG0])],[fool_formula_definition])).
% 0.12/0.45 tff(f6,definition,(
% 0.12/0.45 ! [X0 : $o] : (says(peter,bG0(X0)) => ~ ($true = X0)) <=> ($true = bG1)),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[bG1])],[fool_formula_definition])).
% 0.12/0.45 tff(f7,plain,(
% 0.12/0.45 says(peter,bG1)),
% 0.12/0.45 inference(fool_elimination,[],[f4,f6,f5])).
% 0.12/0.45 tff(f8,plain,(
% 0.12/0.45 ~ ~ ! [X0 : $o] : (says(peter,X0) => ~X0)),
% 0.12/0.45 inference(rectify,[],[f3])).
% 0.12/0.45 tff(f9,definition,(
% 0.12/0.45 ! [X0 : $o] : (($true = X0) <=> ($true = bG2(X0)))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[bG2])],[fool_formula_definition])).
% 0.12/0.45 tff(f10,plain,(
% 0.12/0.45 ~ ~ ! [X0 : $o] : (says(peter,bG2(X0)) => ~ ($true = X0))),
% 0.12/0.45 inference(fool_elimination,[],[f8,f9])).
% 0.12/0.45 tff(f11,plain,(
% 0.12/0.45 ! [X0 : $o] : (says(peter,bG0(X0)) => ($true != X0)) <=> ($true = bG1)),
% 0.12/0.45 inference(flattening,[],[f6])).
% 0.12/0.45 tff(f12,plain,(
% 0.12/0.45 ! [X0 : $o] : (says(peter,bG2(X0)) => ($true != X0))),
% 0.12/0.45 inference(flattening,[],[f10])).
% 0.12/0.45 tff(f13,plain,(
% 0.12/0.45 ! [X0 : $o] : (($true != X0) | ~says(peter,bG0(X0))) <=> ($true = bG1)),
% 0.12/0.45 inference(ennf_transformation,[],[f11])).
% 0.12/0.45 tff(f14,plain,(
% 0.12/0.45 ! [X0 : $o] : (($true != X0) | ~says(peter,bG2(X0)))),
% 0.12/0.45 inference(ennf_transformation,[],[f12])).
% 0.12/0.45 tff(f15,plain,(
% 0.12/0.45 ! [X0 : $o] : ((($true = X0) | ($true != bG2(X0))) & (($true = bG2(X0)) | ($true != X0)))),
% 0.12/0.45 inference(nnf_transformation,[],[f9])).
% 0.12/0.45 tff(f16,plain,(
% 0.12/0.45 (! [X0 : $o] : (($true != X0) | ~says(peter,bG0(X0))) | ($true != bG1)) & (($true = bG1) | ? [X0 : $o] : (($true = X0) & says(peter,bG0(X0))))),
% 0.12/0.45 inference(nnf_transformation,[],[f13])).
% 0.12/0.45 tff(f17,plain,(
% 0.12/0.45 (! [X0 : $o] : (($true != X0) | ~says(peter,bG0(X0))) | ($true != bG1)) & (($true = bG1) | ? [X1 : $o] : (($true = X1) & says(peter,bG0(X1))))),
% 0.12/0.45 inference(rectify,[],[f16])).
% 0.12/0.45 tff(f18,plain,(
% 0.12/0.45 (! [X0 : $o] : (($true != X0) | ~says(peter,bG0(X0))) | ($true != bG1)) & (($true = bG1) | (($true = sK3) & says(peter,bG0(sK3))))),
% 0.12/0.45 inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3)],[f17])).
% 0.12/0.45 tff(f19,plain,(
% 0.12/0.45 ! [X0 : $o] : ((($true = X0) | ($true != bG0(X0))) & (($true = bG0(X0)) | ($true != X0)))),
% 0.12/0.45 inference(nnf_transformation,[],[f5])).
% 0.12/0.45 tff(f20,plain,(
% 0.12/0.45 ( ! [X0 : $o] : (($true != X0) | ($true = bG2(X0))) )),
% 0.12/0.45 inference(cnf_transformation,[],[f15])).
% 0.12/0.45 tff(f22,plain,(
% 0.12/0.45 ($true = bG1) | says(peter,bG0(sK3))),
% 0.12/0.45 inference(cnf_transformation,[],[f18])).
% 0.12/0.45 tff(f23,plain,(
% 0.12/0.45 ($true = bG1) | ($true = sK3)),
% 0.12/0.45 inference(cnf_transformation,[],[f18])).
% 0.12/0.45 tff(f25,plain,(
% 0.12/0.45 ( ! [X0 : $o] : (($true != X0) | ($true = bG0(X0))) )),
% 0.12/0.45 inference(cnf_transformation,[],[f19])).
% 0.12/0.45 tff(f27,plain,(
% 0.12/0.45 says(peter,bG1)),
% 0.12/0.45 inference(cnf_transformation,[],[f7])).
% 0.12/0.45 tff(f28,plain,(
% 0.12/0.45 ( ! [X0 : $o] : (~says(peter,bG2(X0)) | ($true != X0)) )),
% 0.12/0.45 inference(cnf_transformation,[],[f14])).
% 0.12/0.45 tff(f30,definition,(
% 0.12/0.45 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.12/0.45 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.12/0.45 tff(f32,definition,(
% 0.12/0.45 spl4_1 <=> says(peter,bG0(sK3))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.12/0.45 tff(f34,plain,(
% 0.12/0.45 says(peter,bG0(sK3)) | ~spl4_1),
% 0.12/0.45 inference(avatar_component_clause,[],[f32])).
% 0.12/0.45 tff(f36,definition,(
% 0.12/0.45 spl4_2 <=> ($true = bG1)),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.12/0.45 tff(f37,plain,(
% 0.12/0.45 ($true != bG1) | spl4_2),
% 0.12/0.45 inference(avatar_component_clause,[],[f36])).
% 0.12/0.45 tff(f38,plain,(
% 0.12/0.45 ($true = bG1) | ~spl4_2),
% 0.12/0.45 inference(avatar_component_clause,[],[f36])).
% 0.12/0.45 tff(f39,plain,(
% 0.12/0.45 spl4_1 | spl4_2),
% 0.12/0.45 inference(avatar_split_clause,[],[f22,f36,f32])).
% 0.12/0.45 tff(f41,definition,(
% 0.12/0.45 spl4_3 <=> ($true = sK3)),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
% 0.12/0.45 tff(f43,plain,(
% 0.12/0.45 ($true = sK3) | ~spl4_3),
% 0.12/0.45 inference(avatar_component_clause,[],[f41])).
% 0.12/0.45 tff(f44,plain,(
% 0.12/0.45 spl4_3 | spl4_2),
% 0.12/0.45 inference(avatar_split_clause,[],[f23,f36,f41])).
% 0.12/0.45 tff(f49,plain,(
% 0.12/0.45 says(peter,$true) | ~spl4_2),
% 0.12/0.45 inference(superposition,[],[f27,f38])).
% 0.12/0.45 tff(f54,plain,(
% 0.12/0.45 ( ! [X0 : $o] : (~says(peter,$true) | ($true != X0) | (bG2(X0) = $false)) )),
% 0.12/0.45 inference(superposition,[],[f28,f30])).
% 0.12/0.45 tff(f56,plain,(
% 0.12/0.45 ( ! [X0 : $o] : (($true != X0) | (bG2(X0) = $false)) ) | ~spl4_2),
% 0.12/0.45 inference(forward_subsumption_resolution,[],[f54,f49])).
% 0.12/0.45 tff(f58,plain,(
% 0.12/0.45 ($false = bG2($true)) | ~spl4_2),
% 0.12/0.45 inference(equality_resolution,[],[f56])).
% 0.12/0.45 tff(f60,plain,(
% 0.12/0.45 ($true = bG2($true))),
% 0.12/0.45 inference(equality_resolution,[],[f20])).
% 0.12/0.45 tff(f61,plain,(
% 0.12/0.45 ($true = $false) | ~spl4_2),
% 0.12/0.45 inference(forward_demodulation,[],[f60,f58])).
% 0.12/0.45 tff(f62,plain,(
% 0.12/0.45 $false | ~spl4_2),
% 0.12/0.45 inference(trivial_inequality_removal,[],[f61])).
% 0.12/0.45 tff(f63,plain,(
% 0.12/0.45 ~spl4_2),
% 0.12/0.45 inference(avatar_contradiction_clause,[],[f62])).
% 0.12/0.45 tff(f65,definition,(
% 0.12/0.45 spl4_5 <=> ! [X0 : $o] : (($true != X0) | (bG2(X0) = $false))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition])).
% 0.12/0.45 tff(f66,plain,(
% 0.12/0.45 ( ! [X0 : $o] : (($true != X0) | (bG2(X0) = $false)) ) | ~spl4_5),
% 0.12/0.45 inference(avatar_component_clause,[],[f65])).
% 0.12/0.45 tff(f68,definition,(
% 0.12/0.45 spl4_6 <=> says(peter,$true)),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition])).
% 0.12/0.45 tff(f70,plain,(
% 0.12/0.45 ~says(peter,$true) | spl4_6),
% 0.12/0.45 inference(avatar_component_clause,[],[f68])).
% 0.12/0.45 tff(f71,plain,(
% 0.12/0.45 spl4_5 | ~spl4_6),
% 0.12/0.45 inference(avatar_split_clause,[],[f54,f68,f65])).
% 0.12/0.45 tff(f73,definition,(
% 0.12/0.45 spl4_7 <=> (bG1 = $false)),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition])).
% 0.12/0.45 tff(f75,plain,(
% 0.12/0.45 (bG1 = $false) | ~spl4_7),
% 0.12/0.45 inference(avatar_component_clause,[],[f73])).
% 0.12/0.45 tff(f78,plain,(
% 0.12/0.45 ($true != $true) | (bG1 = $false) | spl4_2),
% 0.12/0.45 inference(superposition,[],[f37,f30])).
% 0.12/0.45 tff(f79,plain,(
% 0.12/0.45 (bG1 = $false) | spl4_2),
% 0.12/0.45 inference(trivial_inequality_removal,[],[f78])).
% 0.12/0.45 tff(f80,plain,(
% 0.12/0.45 spl4_7 | spl4_2),
% 0.12/0.45 inference(avatar_split_clause,[],[f79,f36,f73])).
% 0.12/0.45 tff(f83,plain,(
% 0.12/0.45 ($false = bG2($true)) | ~spl4_5),
% 0.12/0.45 inference(equality_resolution,[],[f66])).
% 0.12/0.45 tff(f84,plain,(
% 0.12/0.45 says(peter,bG0($true)) | (~spl4_1 | ~spl4_3)),
% 0.12/0.45 inference(superposition,[],[f34,f43])).
% 0.12/0.45 tff(f91,plain,(
% 0.12/0.45 ~says(peter,$false) | ($true != $true) | ~spl4_5),
% 0.12/0.45 inference(superposition,[],[f28,f83])).
% 0.12/0.45 tff(f92,plain,(
% 0.12/0.45 ~says(peter,$false) | ~spl4_5),
% 0.12/0.45 inference(trivial_inequality_removal,[],[f91])).
% 0.12/0.45 tff(f99,plain,(
% 0.12/0.45 ($true = bG0($true))),
% 0.12/0.45 inference(equality_resolution,[],[f25])).
% 0.12/0.45 tff(f121,plain,(
% 0.12/0.45 says(peter,$false) | ~spl4_7),
% 0.12/0.45 inference(superposition,[],[f27,f75])).
% 0.12/0.45 tff(f123,plain,(
% 0.12/0.45 $false | (~spl4_5 | ~spl4_7)),
% 0.12/0.45 inference(forward_subsumption_resolution,[],[f121,f92])).
% 0.12/0.45 tff(f124,plain,(
% 0.12/0.45 ~spl4_5 | ~spl4_7),
% 0.12/0.45 inference(avatar_contradiction_clause,[],[f123])).
% 0.12/0.45 tff(f151,plain,(
% 0.12/0.45 says(peter,$true) | (~spl4_1 | ~spl4_3)),
% 0.12/0.45 inference(superposition,[],[f84,f99])).
% 0.12/0.45 tff(f164,plain,(
% 0.12/0.45 $false | (~spl4_1 | ~spl4_3 | spl4_6)),
% 0.12/0.45 inference(forward_subsumption_resolution,[],[f151,f70])).
% 0.12/0.45 tff(f165,plain,(
% 0.12/0.45 ~spl4_1 | ~spl4_3 | spl4_6),
% 0.12/0.45 inference(avatar_contradiction_clause,[],[f164])).
% 0.12/0.45 cnf(s1, plain, spl4_1 | spl4_2, inference(sat_conversion,[],[f39])).
% 0.12/0.45 cnf(s2, plain, spl4_2 | spl4_3, inference(sat_conversion,[],[f44])).
% 0.12/0.45 cnf(s4, plain, ~spl4_2, inference(sat_conversion,[],[f63])).
% 0.12/0.45 cnf(s5, plain, spl4_5 | ~spl4_6, inference(sat_conversion,[],[f71])).
% 0.12/0.45 cnf(s7, plain, spl4_2 | spl4_7, inference(sat_conversion,[],[f80])).
% 0.12/0.45 cnf(s9, plain, ~spl4_5 | ~spl4_7, inference(sat_conversion,[],[f124])).
% 0.12/0.45 cnf(s14, plain, ~spl4_1 | ~spl4_3 | spl4_6, inference(sat_conversion,[],[f165])).
% 0.12/0.45 cnf(s15, plain, spl4_7, inference(rat,[],[s7,s4])).
% 0.12/0.45 cnf(s16, plain, ~spl4_5, inference(rat,[],[s9,s15])).
% 0.12/0.45 cnf(s17, plain, ~spl4_6, inference(rat,[],[s5,s16])).
% 0.12/0.45 cnf(s18, plain, spl4_3, inference(rat,[],[s2,s4])).
% 0.12/0.45 cnf(s19, plain, ~spl4_1, inference(rat,[],[s14,s17,s18])).
% 0.12/0.45 cnf(s20, plain, $false, inference(rat,[],[s1,s4,s19])).
% 0.12/0.45 tff(f166,plain,(
% 0.12/0.45 $false),
% 0.12/0.45 inference(avatar_sat_refutation,[],[s20])).
% 0.12/0.45 % SZS output end Proof for theBenchmark
% 0.12/0.45 % (243740)------------------------------
% 0.12/0.45 % (243740)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.45 % (243740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.45 % (243740)CaDiCaL version: 2.1.3
% 0.12/0.45 % (243740)Termination reason: Refutation
% 0.12/0.45 % (243740)Time elapsed: 0.003 s
% 0.12/0.45 % (243740)Peak memory usage: 12 MB
% 0.12/0.45 % (243740)Instructions burned: 5 (million)
% 0.12/0.45 % (243727)Success in time 0.035 s
% 0.12/0.45 % Vampire exiting
%------------------------------------------------------------------------------