%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO017_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 : n004.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 02:29:34 PM UTC 2026
% Result : Theorem 0.20s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO017_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n004.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 17:21:22 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.20/0.26 % (529910)Will run a generic schedule for satisfiability detection.
% 0.20/0.26 % (529921)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1353110290:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.26 % (529921) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-529910-529921"...
% 0.20/0.26 % (529921)...printing done.
% 0.20/0.26 % (529921)Refutation found. Thanks to Tanya!
% 0.20/0.26 % SZS status Theorem for theBenchmark
% 0.20/0.26 % SZS output start Proof for theBenchmark
% 0.20/0.26 tff(func_def_2, type, bG0: $o).
% 0.20/0.26 tff(pred_def_1, type, h: $o > $o).
% 0.20/0.26 tff(f1,conjecture,(
% 0.20/0.26 (h((h($true) = h($false))) = h($false))),
% 0.20/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.20/0.26 tff(f2,negated_conjecture,(
% 0.20/0.26 ~ (h((h($true) = h($false))) = h($false))),
% 0.20/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.26 tff(f3,definition,(
% 0.20/0.26 (h($true) <=> h($false)) <=> ($true = bG0)),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[bG0])],[fool_formula_definition])).
% 0.20/0.26 tff(f4,plain,(
% 0.20/0.26 ~(h(bG0) <=> h($false))),
% 0.20/0.26 inference(fool_elimination,[],[f2,f3])).
% 0.20/0.26 tff(f5,plain,(
% 0.20/0.26 h(bG0) <~> h($false)),
% 0.20/0.26 inference(ennf_transformation,[],[f4])).
% 0.20/0.26 tff(f6,plain,(
% 0.20/0.26 (((h($true) | ~h($false)) & (h($false) | ~h($true))) | ($true != bG0)) & (($true = bG0) | ((~h($false) | ~h($true)) & (h($false) | h($true))))),
% 0.20/0.26 inference(nnf_transformation,[],[f3])).
% 0.20/0.26 tff(f7,plain,(
% 0.20/0.26 (~h($false) | ~h(bG0)) & (h($false) | h(bG0))),
% 0.20/0.26 inference(nnf_transformation,[],[f5])).
% 0.20/0.26 tff(f10,plain,(
% 0.20/0.26 h($false) | ~h($true) | ($true != bG0)),
% 0.20/0.26 inference(cnf_transformation,[],[f6])).
% 0.20/0.26 tff(f11,plain,(
% 0.20/0.26 h($true) | ~h($false) | ($true != bG0)),
% 0.20/0.26 inference(cnf_transformation,[],[f6])).
% 0.20/0.26 tff(f12,plain,(
% 0.20/0.26 h($false) | h(bG0)),
% 0.20/0.26 inference(cnf_transformation,[],[f7])).
% 0.20/0.26 tff(f13,plain,(
% 0.20/0.26 ~h($false) | ~h(bG0)),
% 0.20/0.26 inference(cnf_transformation,[],[f7])).
% 0.20/0.26 tff(f15,definition,(
% 0.20/0.26 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.26 tff(f17,definition,(
% 0.20/0.26 spl1_1 <=> h(bG0)),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition])).
% 0.20/0.26 tff(f18,plain,(
% 0.20/0.26 ~h(bG0) | spl1_1),
% 0.20/0.26 inference(avatar_component_clause,[],[f17])).
% 0.20/0.26 tff(f19,plain,(
% 0.20/0.26 h(bG0) | ~spl1_1),
% 0.20/0.26 inference(avatar_component_clause,[],[f17])).
% 0.20/0.26 tff(f21,definition,(
% 0.20/0.26 spl1_2 <=> h($false)),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition])).
% 0.20/0.26 tff(f24,plain,(
% 0.20/0.26 spl1_1 | spl1_2),
% 0.20/0.26 inference(avatar_split_clause,[],[f12,f21,f17])).
% 0.20/0.26 tff(f25,plain,(
% 0.20/0.26 ~spl1_1 | ~spl1_2),
% 0.20/0.26 inference(avatar_split_clause,[],[f13,f21,f17])).
% 0.20/0.26 tff(f27,definition,(
% 0.20/0.26 spl1_3 <=> h($true)),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition])).
% 0.20/0.26 tff(f31,definition,(
% 0.20/0.26 spl1_4 <=> ($true = bG0)),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition])).
% 0.20/0.26 tff(f32,plain,(
% 0.20/0.26 ($true != bG0) | spl1_4),
% 0.20/0.26 inference(avatar_component_clause,[],[f31])).
% 0.20/0.26 tff(f36,plain,(
% 0.20/0.26 ~spl1_4 | ~spl1_3 | spl1_2),
% 0.20/0.26 inference(avatar_split_clause,[],[f10,f21,f27,f31])).
% 0.20/0.26 tff(f37,plain,(
% 0.20/0.26 ~spl1_4 | ~spl1_2 | spl1_3),
% 0.20/0.26 inference(avatar_split_clause,[],[f11,f27,f21,f31])).
% 0.20/0.26 tff(f41,plain,(
% 0.20/0.26 ($true != $true) | ($false = bG0) | spl1_4),
% 0.20/0.26 inference(superposition,[],[f32,f15])).
% 0.20/0.26 tff(f44,plain,(
% 0.20/0.26 ($false = bG0) | spl1_4),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f41])).
% 0.20/0.26 tff(f47,plain,(
% 0.20/0.26 ~h($false) | (spl1_1 | spl1_4)),
% 0.20/0.26 inference(superposition,[],[f18,f44])).
% 0.20/0.26 tff(f49,plain,(
% 0.20/0.26 ~spl1_2 | spl1_1 | spl1_4),
% 0.20/0.26 inference(avatar_split_clause,[],[f47,f31,f17,f21])).
% 0.20/0.26 tff(f50,plain,(
% 0.20/0.26 h($true) | ($false = bG0) | ~spl1_1),
% 0.20/0.26 inference(superposition,[],[f19,f15])).
% 0.20/0.26 tff(f52,definition,(
% 0.20/0.26 spl1_5 <=> ($false = bG0)),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition])).
% 0.20/0.26 tff(f54,plain,(
% 0.20/0.26 ($false = bG0) | ~spl1_5),
% 0.20/0.26 inference(avatar_component_clause,[],[f52])).
% 0.20/0.26 tff(f55,plain,(
% 0.20/0.26 spl1_5 | spl1_3 | ~spl1_1),
% 0.20/0.26 inference(avatar_split_clause,[],[f50,f17,f27,f52])).
% 0.20/0.26 tff(f57,plain,(
% 0.20/0.26 h($false) | (~spl1_1 | ~spl1_5)),
% 0.20/0.26 inference(superposition,[],[f19,f54])).
% 0.20/0.26 tff(f59,plain,(
% 0.20/0.26 spl1_2 | ~spl1_1 | ~spl1_5),
% 0.20/0.26 inference(avatar_split_clause,[],[f57,f52,f17,f21])).
% 0.20/0.26 tff(f60,plain,(
% 0.20/0.26 spl1_5 | spl1_4),
% 0.20/0.26 inference(avatar_split_clause,[],[f44,f31,f52])).
% 0.20/0.26 tff(f61,plain,(
% 0.20/0.26 ~h($true) | ($false = bG0) | spl1_1),
% 0.20/0.26 inference(superposition,[],[f18,f15])).
% 0.20/0.26 tff(f62,plain,(
% 0.20/0.26 spl1_5 | ~spl1_3 | spl1_1),
% 0.20/0.26 inference(avatar_split_clause,[],[f61,f17,f27,f52])).
% 0.20/0.26 tff(f64,plain,(
% 0.20/0.26 ~h($false) | (spl1_1 | ~spl1_5)),
% 0.20/0.26 inference(superposition,[],[f18,f54])).
% 0.20/0.26 tff(f66,plain,(
% 0.20/0.26 ~spl1_2 | spl1_1 | ~spl1_5),
% 0.20/0.26 inference(avatar_split_clause,[],[f64,f52,f17,f21])).
% 0.20/0.26 cnf(s1, plain, spl1_1 | spl1_2, inference(sat_conversion,[],[f24])).
% 0.20/0.26 cnf(s2, plain, ~spl1_1 | ~spl1_2, inference(sat_conversion,[],[f25])).
% 0.20/0.26 cnf(s5, plain, spl1_2 | ~spl1_3 | ~spl1_4, inference(sat_conversion,[],[f36])).
% 0.20/0.26 cnf(s6, plain, ~spl1_2 | spl1_3 | ~spl1_4, inference(sat_conversion,[],[f37])).
% 0.20/0.26 cnf(s7, plain, spl1_1 | ~spl1_2 | spl1_4, inference(sat_conversion,[],[f49])).
% 0.20/0.26 cnf(s8, plain, ~spl1_1 | spl1_3 | spl1_5, inference(sat_conversion,[],[f55])).
% 0.20/0.26 cnf(s9, plain, ~spl1_1 | spl1_2 | ~spl1_5, inference(sat_conversion,[],[f59])).
% 0.20/0.26 cnf(s10, plain, spl1_4 | spl1_5, inference(sat_conversion,[],[f60])).
% 0.20/0.26 cnf(s11, plain, spl1_1 | ~spl1_3 | spl1_5, inference(sat_conversion,[],[f62])).
% 0.20/0.26 cnf(s12, plain, spl1_1 | ~spl1_2 | ~spl1_5, inference(sat_conversion,[],[f66])).
% 0.20/0.26 cnf(s13, plain, ~spl1_2 | spl1_1, inference(rat,[],[s11,s6,s7,s12])).
% 0.20/0.26 cnf(s14, plain, spl1_1, inference(rat,[],[s13,s1])).
% 0.20/0.26 cnf(s15, plain, ~spl1_2, inference(rat,[],[s2,s14])).
% 0.20/0.26 cnf(s16, plain, ~spl1_5, inference(rat,[],[s9,s15,s14])).
% 0.20/0.26 cnf(s17, plain, spl1_4, inference(rat,[],[s10,s16])).
% 0.20/0.26 cnf(s18, plain, spl1_3, inference(rat,[],[s8,s14,s16])).
% 0.20/0.26 cnf(s19, plain, $false, inference(rat,[],[s5,s15,s17,s18])).
% 0.20/0.26 tff(f67,plain,(
% 0.20/0.26 $false),
% 0.20/0.26 inference(avatar_sat_refutation,[],[s19])).
% 0.20/0.26 % SZS output end Proof for theBenchmark
% 0.20/0.26 % (529921)------------------------------
% 0.20/0.26 % (529921)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.26 % (529921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.26 % (529921)CaDiCaL version: 2.1.3
% 0.20/0.26 % (529921)Termination reason: Refutation
% 0.20/0.26 % (529921)Time elapsed: 0.002 s
% 0.20/0.26 % (529921)Peak memory usage: 13 MB
% 0.20/0.26 % (529921)Instructions burned: 2 (million)
% 0.20/0.26 % (529910)Success in time 0.033 s
% 0.20/0.26 % Vampire exiting
%------------------------------------------------------------------------------