%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO039_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 02:29:38 PM UTC 2026
% Result : Theorem 0.08s 0.24s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO039_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n005.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 17:22:02 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 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
% 0.08/0.24 % (938972)Will run a generic schedule for satisfiability detection.
% 0.08/0.24 % (938978)% WARNING: option uhcvi not known.
% 0.08/0.24 % (938983)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=671191511:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.24 % (938983) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-938972-938983"...
% 0.08/0.24 % (938983)...printing done.
% 0.08/0.24 % (938977)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2423194935_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.24 % (938980)dis+10_1_sil=32000:sp=arity:random_seed=4003220676:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.24 % (938981)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2772263562:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.24 % (938978)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4007258261:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.24 % (938979)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1828054770:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.24 % (938983)Refutation found. Thanks to Tanya!
% 0.08/0.24 % SZS status Theorem for theBenchmark
% 0.08/0.24 % SZS output start Proof for theBenchmark
% 0.08/0.24 tff(func_def_0, type, h: $o > $i).
% 0.08/0.24 tff(func_def_3, type, bG0: $o).
% 0.08/0.24 tff(func_def_4, type, bG1: $o).
% 0.08/0.24 tff(f1,conjecture,(
% 0.08/0.24 h(h($false) = h(~$false)) = h($false)),
% 0.08/0.24 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',1)).
% 0.08/0.24 tff(f2,negated_conjecture,(
% 0.08/0.24 ~ h(h($false) = h(~$false)) = h($false)),
% 0.08/0.24 inference(negated_conjecture,[status(cth)],[f1])).
% 0.08/0.24 tff(f3,plain,(
% 0.08/0.24 ~ h(h($false) = h(~$false)) = h($false)),
% 0.08/0.24 inference(rectify,[],[f2])).
% 0.08/0.24 tff(f4,definition,(
% 0.08/0.24 ~$false <=> (bG0 = $true)),
% 0.08/0.24 introduced(definition,[new_symbols(definition,[bG0])],[fool_formula_definition])).
% 0.08/0.24 tff(f5,definition,(
% 0.08/0.24 h($false) = h(bG0) <=> ($true = bG1)),
% 0.08/0.24 introduced(definition,[new_symbols(definition,[bG1])],[fool_formula_definition])).
% 0.08/0.24 tff(f6,plain,(
% 0.08/0.24 ~ h($false) = h(bG1)),
% 0.08/0.24 inference(fool_elimination,[],[f3,f5,f4])).
% 0.08/0.24 tff(f7,plain,(
% 0.08/0.24 (bG0 = $true)),
% 0.08/0.24 inference(true_and_false_elimination,[],[f4])).
% 0.08/0.24 tff(f8,plain,(
% 0.08/0.24 h($false) != h(bG1)),
% 0.08/0.24 inference(flattening,[],[f6])).
% 0.08/0.24 tff(f9,plain,(
% 0.08/0.24 (h($false) = h(bG0) | ($true != bG1)) & (($true = bG1) | h($false) != h(bG0))),
% 0.08/0.24 inference(nnf_transformation,[],[f5])).
% 0.08/0.24 tff(f11,plain,(
% 0.08/0.24 h($false) = h(bG0) | ($true != bG1)),
% 0.08/0.24 inference(cnf_transformation,[],[f9])).
% 0.08/0.24 tff(f12,plain,(
% 0.08/0.24 (bG0 = $true)),
% 0.08/0.24 inference(cnf_transformation,[],[f7])).
% 0.08/0.24 tff(f13,plain,(
% 0.08/0.24 h($false) != h(bG1)),
% 0.08/0.24 inference(cnf_transformation,[],[f8])).
% 0.08/0.24 tff(f15,definition,(
% 0.08/0.24 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.08/0.24 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.08/0.24 tff(f16,plain,(
% 0.08/0.24 h($false) = h($true) | ($true != bG1)),
% 0.08/0.24 inference(definition_unfolding,[],[f11,f12])).
% 0.08/0.24 tff(f19,definition,(
% 0.08/0.24 spl2_1 <=> h($false) = h($true)),
% 0.08/0.24 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.08/0.24 tff(f23,definition,(
% 0.08/0.24 spl2_2 <=> ($true = bG1)),
% 0.08/0.24 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.08/0.24 tff(f24,plain,(
% 0.08/0.24 ($true != bG1) | spl2_2),
% 0.08/0.24 inference(avatar_component_clause,[],[f23])).
% 0.08/0.24 tff(f27,plain,(
% 0.08/0.24 ~spl2_2 | spl2_1),
% 0.08/0.24 inference(avatar_split_clause,[],[f16,f19,f23])).
% 0.08/0.24 tff(f30,plain,(
% 0.08/0.24 ($true != $true) | ($false = bG1) | spl2_2),
% 0.08/0.24 inference(superposition,[],[f24,f15])).
% 0.08/0.24 tff(f31,plain,(
% 0.08/0.24 h($false) != h($true) | ($false = bG1)),
% 0.08/0.24 inference(superposition,[],[f13,f15])).
% 0.08/0.24 tff(f33,plain,(
% 0.08/0.24 ($false = bG1) | spl2_2),
% 0.08/0.24 inference(trivial_inequality_removal,[],[f30])).
% 0.08/0.24 tff(f36,plain,(
% 0.08/0.24 h($false) != h($false) | spl2_2),
% 0.08/0.24 inference(superposition,[],[f13,f33])).
% 0.08/0.24 tff(f37,plain,(
% 0.08/0.24 $false | spl2_2),
% 0.08/0.24 inference(trivial_inequality_removal,[],[f36])).
% 0.08/0.24 tff(f38,plain,(
% 0.08/0.24 spl2_2),
% 0.08/0.24 inference(avatar_contradiction_clause,[],[f37])).
% 0.08/0.24 tff(f41,definition,(
% 0.08/0.24 spl2_3 <=> ($false = bG1)),
% 0.08/0.24 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.08/0.24 tff(f43,plain,(
% 0.08/0.24 ($false = bG1) | ~spl2_3),
% 0.08/0.24 inference(avatar_component_clause,[],[f41])).
% 0.08/0.24 tff(f44,plain,(
% 0.08/0.24 spl2_3 | ~spl2_1),
% 0.08/0.24 inference(avatar_split_clause,[],[f31,f19,f41])).
% 0.08/0.24 tff(f46,plain,(
% 0.08/0.24 h($false) != h($false) | ~spl2_3),
% 0.08/0.24 inference(superposition,[],[f13,f43])).
% 0.08/0.24 tff(f47,plain,(
% 0.08/0.24 $false | ~spl2_3),
% 0.08/0.24 inference(trivial_inequality_removal,[],[f46])).
% 0.08/0.24 tff(f48,plain,(
% 0.08/0.24 ~spl2_3),
% 0.08/0.24 inference(avatar_contradiction_clause,[],[f47])).
% 0.08/0.24 cnf(s2, plain, spl2_1 | ~spl2_2, inference(sat_conversion,[],[f27])).
% 0.08/0.24 cnf(s3, plain, spl2_2, inference(sat_conversion,[],[f38])).
% 0.08/0.24 cnf(s4, plain, ~spl2_1 | spl2_3, inference(sat_conversion,[],[f44])).
% 0.08/0.24 cnf(s5, plain, ~spl2_3, inference(sat_conversion,[],[f48])).
% 0.08/0.24 cnf(s6, plain, ~spl2_1, inference(rat,[],[s4,s5])).
% 0.08/0.24 cnf(s7, plain, $false, inference(rat,[],[s2,s3,s6])).
% 0.08/0.24 tff(f50,plain,(
% 0.08/0.24 $false),
% 0.08/0.24 inference(avatar_sat_refutation,[],[s7])).
% 0.08/0.24 % SZS output end Proof for theBenchmark
% 0.08/0.24 % (938983)------------------------------
% 0.08/0.24 % (938983)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.24 % (938983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.24 % (938983)CaDiCaL version: 2.1.3
% 0.08/0.24 % (938983)Termination reason: Refutation
% 0.08/0.24 % (938983)Time elapsed: 0.001 s
% 0.08/0.24 % (938983)Peak memory usage: 12 MB
% 0.08/0.24 % (938983)Instructions burned: 1 (million)
% 0.08/0.24 % (938972)Success in time 0.028 s
% 0.08/0.24 % Vampire exiting
%------------------------------------------------------------------------------