%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO040^2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 08:48:46 AM 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 : SYO040^2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n003.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 16:25:53 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 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
% 0.08/0.24 % (2699356)Will run a generic schedule for satisfiability detection.
% 0.08/0.24 % (2699367)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2354724877:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.24 % (2699362)% WARNING: option uhcvi not known.
% 0.08/0.24 % (2699367) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2699356-2699367"...
% 0.08/0.24 % (2699367)...printing done.
% 0.08/0.24 % (2699367)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 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.24 thf(func_def_0, type, f: ($o > $o)).
% 0.08/0.24 thf(func_def_1, type, h: ($o > $i)).
% 0.08/0.24 thf(func_def_2, type, x: $o).
% 0.08/0.24 thf(f1,conjecture,(
% 0.08/0.24 (((h @ (f @ (f @ (f @ x))))) = ((h @ (f @ x))))),
% 0.08/0.24 file('/export/starexec/sandbox/benchmark/theBenchmark.p',2)).
% 0.08/0.24 thf(f2,negated_conjecture,(
% 0.08/0.24 ~ (((h @ (f @ (f @ (f @ x))))) = ((h @ (f @ x))))),
% 0.08/0.24 inference(negated_conjecture,[status(cth)],[f1])).
% 0.08/0.24 thf(f3,plain,(
% 0.08/0.24 (((h @ (f @ (f @ (f @ x))))) != ((h @ (f @ x))))),
% 0.08/0.24 inference(flattening,[],[f2])).
% 0.08/0.24 thf(f4,plain,(
% 0.08/0.24 (((h @ (f @ (f @ (f @ x))))) != ((h @ (f @ x))))),
% 0.08/0.24 inference(cnf_transformation,[],[f3])).
% 0.08/0.24 thf(f6,definition,(
% 0.08/0.24 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.08/0.24 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.08/0.24 thf(f12,plain,(
% 0.08/0.24 (((h @ (f @ x))) != ((h @ $true))) | (((f @ (f @ (f @ x)))) = $false)),
% 0.08/0.24 inference(constrained_superposition,[],[f4,f6])).
% 0.08/0.24 thf(f19,definition,(
% 0.08/0.24 spl0_1 <=> (((f @ (f @ (f @ x)))) = $false)),
% 0.08/0.24 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.08/0.24 thf(f20,plain,(
% 0.08/0.24 (((f @ (f @ (f @ x)))) != $false) | spl0_1),
% 0.08/0.24 inference(avatar_component_clause,[],[f19])).
% 0.08/0.24 thf(f21,plain,(
% 0.08/0.24 (((f @ (f @ (f @ x)))) = $false) | ~spl0_1),
% 0.08/0.24 inference(avatar_component_clause,[],[f19])).
% 0.08/0.24 thf(f23,definition,(
% 0.08/0.24 spl0_2 <=> (((h @ (f @ x))) = ((h @ $true)))),
% 0.08/0.24 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.08/0.24 thf(f25,plain,(
% 0.08/0.24 (((h @ (f @ x))) != ((h @ $true))) | spl0_2),
% 0.08/0.24 inference(avatar_component_clause,[],[f23])).
% 0.08/0.24 thf(f26,plain,(
% 0.08/0.24 spl0_1 | ~spl0_2),
% 0.08/0.24 inference(avatar_split_clause,[],[f12,f23,f19])).
% 0.08/0.24 thf(f28,definition,(
% 0.08/0.24 spl0_3 <=> (((f @ (f @ x))) = $false)),
% 0.08/0.24 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 0.08/0.24 thf(f29,plain,(
% 0.08/0.24 (((f @ (f @ x))) != $false) | spl0_3),
% 0.08/0.24 inference(avatar_component_clause,[],[f28])).
% 0.08/0.24 thf(f30,plain,(
% 0.08/0.24 (((f @ (f @ x))) = $false) | ~spl0_3),
% 0.08/0.24 inference(avatar_component_clause,[],[f28])).
% 0.08/0.24 thf(f37,definition,(
% 0.08/0.24 spl0_5 <=> (((f @ x)) = $false)),
% 0.08/0.24 introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition])).
% 0.08/0.24 thf(f38,plain,(
% 0.08/0.24 (((f @ x)) != $false) | spl0_5),
% 0.08/0.24 inference(avatar_component_clause,[],[f37])).
% 0.08/0.24 thf(f39,plain,(
% 0.08/0.24 (((f @ x)) = $false) | ~spl0_5),
% 0.08/0.24 inference(avatar_component_clause,[],[f37])).
% 0.08/0.24 thf(f46,definition,(
% 0.08/0.24 spl0_7 <=> (x = $false)),
% 0.08/0.24 introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition])).
% 0.08/0.24 thf(f48,plain,(
% 0.08/0.24 (x = $false) | ~spl0_7),
% 0.08/0.24 inference(avatar_component_clause,[],[f46])).
% 0.08/0.24 thf(f55,plain,(
% 0.08/0.24 ($false != ((f @ $true))) | (x = $false) | spl0_5),
% 0.08/0.24 inference(constrained_superposition,[],[f38,f6])).
% 0.08/0.24 thf(f58,definition,(
% 0.08/0.24 spl0_9 <=> ($false = ((f @ $true)))),
% 0.08/0.24 introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition])).
% 0.08/0.24 thf(f59,plain,(
% 0.08/0.24 ($false = ((f @ $true))) | ~spl0_9),
% 0.08/0.24 inference(avatar_component_clause,[],[f58])).
% 0.08/0.24 thf(f61,plain,(
% 0.08/0.24 spl0_7 | ~spl0_9 | spl0_5),
% 0.08/0.24 inference(avatar_split_clause,[],[f55,f37,f58,f46])).
% 0.08/0.24 thf(f69,definition,(
% 0.08/0.24 spl0_10 <=> ($false = ((f @ (f @ $true))))),
% 0.08/0.24 introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition])).
% 0.08/0.24 thf(f70,plain,(
% 0.08/0.24 ($false = ((f @ (f @ $true)))) | ~spl0_10),
% 0.08/0.24 inference(avatar_component_clause,[],[f69])).
% 0.08/0.24 thf(f80,plain,(
% 0.08/0.24 ($false != ((f @ $true))) | (((f @ (f @ x))) = $false) | spl0_1),
% 0.08/0.24 inference(constrained_superposition,[],[f20,f6])).
% 0.08/0.24 thf(f88,plain,(
% 0.08/0.24 (((h @ $true)) != ((h @ $true))) | (((f @ x)) = $false) | spl0_2),
% 0.08/0.24 inference(constrained_superposition,[],[f25,f6])).
% 0.08/0.24 thf(f89,plain,(
% 0.08/0.24 (((f @ x)) = $false) | spl0_2),
% 0.08/0.24 inference(trivial_inequality_removal,[],[f88])).
% 0.08/0.24 thf(f90,plain,(
% 0.08/0.24 spl0_5 | spl0_2),
% 0.08/0.24 inference(avatar_split_clause,[],[f89,f23,f37])).
% 0.08/0.24 thf(f96,plain,(
% 0.08/0.24 ($false = ((f @ $true))) | (x = $false) | ~spl0_5),
% 0.08/0.24 inference(constrained_superposition,[],[f39,f6])).
% 0.08/0.24 thf(f102,plain,(
% 0.08/0.24 ($false != ((f @ $false))) | (spl0_3 | ~spl0_5)),
% 0.08/0.24 inference(constrained_superposition,[],[f29,f39])).
% 0.08/0.24 thf(f107,plain,(
% 0.08/0.24 spl0_7 | spl0_9 | ~spl0_5),
% 0.08/0.24 inference(avatar_split_clause,[],[f96,f37,f58,f46])).
% 0.08/0.24 thf(f109,definition,(
% 0.08/0.24 spl0_13 <=> ! [X0 : $o] : (($false = X0) | ($false = ((f @ X0))))),
% 0.08/0.24 introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition])).
% 0.08/0.24 thf(f110,plain,(
% 0.08/0.24 ( ! [X0 : $o] : (($false = ((f @ X0))) | ($false = X0)) ) | ~spl0_13),
% 0.08/0.24 inference(avatar_component_clause,[],[f109])).
% 0.08/0.24 thf(f112,plain,(
% 0.08/0.24 spl0_3 | ~spl0_9 | spl0_1),
% 0.08/0.24 inference(avatar_split_clause,[],[f80,f19,f58,f28])).
% 0.08/0.24 thf(f113,plain,(
% 0.08/0.24 ( ! [X0 : $o] : (($false = ((f @ X0))) | ($false = X0)) ) | ~spl0_9),
% 0.08/0.24 inference(constrained_superposition,[],[f59,f6])).
% 0.08/0.24 thf(f116,plain,(
% 0.08/0.24 spl0_13 | ~spl0_9),
% 0.08/0.24 inference(avatar_split_clause,[],[f113,f58,f109])).
% 0.08/0.24 thf(f119,plain,(
% 0.08/0.24 ($false = ((f @ $false))) | (~spl0_5 | ~spl0_7)),
% 0.08/0.24 inference(constrained_superposition,[],[f39,f48])).
% 0.08/0.24 thf(f134,plain,(
% 0.08/0.24 ($false = ((f @ $false))) | (~spl0_3 | ~spl0_5)),
% 0.08/0.24 inference(constrained_superposition,[],[f30,f39])).
% 0.08/0.24 thf(f137,plain,(
% 0.08/0.24 ($false != ((f @ $false))) | (spl0_1 | ~spl0_3)),
% 0.08/0.24 inference(constrained_superposition,[],[f20,f30])).
% 0.08/0.24 thf(f146,plain,(
% 0.08/0.24 ($false = ((f @ $true))) | ($false = ((f @ $true))) | ~spl0_10),
% 0.08/0.24 inference(constrained_superposition,[],[f70,f6])).
% 0.08/0.24 thf(f151,plain,(
% 0.08/0.24 ($false = ((f @ $true))) | ~spl0_10),
% 0.08/0.24 inference(duplicate_literal_removal,[],[f146])).
% 0.08/0.24 thf(f153,plain,(
% 0.08/0.24 spl0_9 | ~spl0_10),
% 0.08/0.24 inference(avatar_split_clause,[],[f151,f69,f58])).
% 0.08/0.24 thf(f173,plain,(
% 0.08/0.24 ($false = ((f @ (f @ $true)))) | (((f @ x)) = $false) | ~spl0_1),
% 0.08/0.24 inference(constrained_superposition,[],[f21,f6])).
% 0.08/0.24 thf(f181,plain,(
% 0.08/0.24 (((h @ (f @ x))) != ((h @ $false))) | ~spl0_1),
% 0.08/0.24 inference(constrained_superposition,[],[f4,f21])).
% 0.08/0.24 thf(f197,plain,(
% 0.08/0.24 (((h @ $false)) != ((h @ $false))) | (~spl0_1 | ~spl0_5)),
% 0.08/0.24 inference(constrained_superposition,[],[f181,f39])).
% 0.08/0.24 thf(f198,plain,(
% 0.08/0.24 $false | (~spl0_1 | ~spl0_5)),
% 0.08/0.24 inference(trivial_inequality_removal,[],[f197])).
% 0.08/0.24 thf(f199,plain,(
% 0.08/0.24 ~spl0_1 | ~spl0_5),
% 0.08/0.24 inference(avatar_contradiction_clause,[],[f198])).
% 0.08/0.24 thf(f203,definition,(
% 0.08/0.24 spl0_14 <=> ($false = ((f @ $false)))),
% 0.08/0.24 introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition])).
% 0.08/0.24 thf(f208,plain,(
% 0.08/0.24 spl0_5 | spl0_10 | ~spl0_1),
% 0.08/0.24 inference(avatar_split_clause,[],[f173,f19,f69,f37])).
% 0.08/0.24 thf(f216,plain,(
% 0.08/0.24 ($false != ((f @ $false))) | (spl0_5 | ~spl0_7)),
% 0.08/0.24 inference(constrained_superposition,[],[f38,f48])).
% 0.08/0.24 thf(f218,plain,(
% 0.08/0.24 ~spl0_14 | spl0_5 | ~spl0_7),
% 0.08/0.24 inference(avatar_split_clause,[],[f216,f46,f37,f203])).
% 0.08/0.24 thf(f231,plain,(
% 0.08/0.24 ($false = ((f @ $false))) | (((f @ x)) = $false) | (~spl0_1 | ~spl0_13)),
% 0.08/0.24 inference(constrained_superposition,[],[f21,f110])).
% 0.08/0.24 thf(f247,plain,(
% 0.08/0.24 spl0_5 | spl0_14 | ~spl0_1 | ~spl0_13),
% 0.08/0.24 inference(avatar_split_clause,[],[f231,f109,f19,f203,f37])).
% 0.08/0.24 thf(f250,plain,(
% 0.08/0.24 spl0_14 | ~spl0_5 | ~spl0_7),
% 0.08/0.24 inference(avatar_split_clause,[],[f119,f46,f37,f203])).
% 0.08/0.24 thf(f251,plain,(
% 0.08/0.24 ~spl0_14 | spl0_3 | ~spl0_5),
% 0.08/0.24 inference(avatar_split_clause,[],[f102,f37,f28,f203])).
% 0.08/0.24 thf(f256,plain,(
% 0.08/0.24 ~spl0_14 | spl0_1 | ~spl0_3),
% 0.08/0.24 inference(avatar_split_clause,[],[f137,f28,f19,f203])).
% 0.08/0.24 thf(f261,plain,(
% 0.08/0.24 spl0_14 | ~spl0_3 | ~spl0_5),
% 0.08/0.24 inference(avatar_split_clause,[],[f134,f37,f28,f203])).
% 0.08/0.24 cnf(s1, plain, spl0_1 | ~spl0_2, inference(sat_conversion,[],[f26])).
% 0.08/0.24 cnf(s5, plain, spl0_5 | spl0_7 | ~spl0_9, inference(sat_conversion,[],[f61])).
% 0.08/0.24 cnf(s8, plain, spl0_2 | spl0_5, inference(sat_conversion,[],[f90])).
% 0.08/0.24 cnf(s11, plain, ~spl0_5 | spl0_7 | spl0_9, inference(sat_conversion,[],[f107])).
% 0.08/0.24 cnf(s13, plain, spl0_1 | spl0_3 | ~spl0_9, inference(sat_conversion,[],[f112])).
% 0.08/0.24 cnf(s14, plain, ~spl0_9 | spl0_13, inference(sat_conversion,[],[f116])).
% 0.08/0.24 cnf(s18, plain, spl0_9 | ~spl0_10, inference(sat_conversion,[],[f153])).
% 0.08/0.24 cnf(s20, plain, ~spl0_1 | ~spl0_5, inference(sat_conversion,[],[f199])).
% 0.08/0.24 cnf(s25, plain, ~spl0_1 | spl0_5 | spl0_10, inference(sat_conversion,[],[f208])).
% 0.08/0.24 cnf(s28, plain, spl0_5 | ~spl0_7 | ~spl0_14, inference(sat_conversion,[],[f218])).
% 0.08/0.24 cnf(s31, plain, ~spl0_1 | spl0_5 | ~spl0_13 | spl0_14, inference(sat_conversion,[],[f247])).
% 0.08/0.24 cnf(s33, plain, ~spl0_5 | ~spl0_7 | spl0_14, inference(sat_conversion,[],[f250])).
% 0.08/0.24 cnf(s34, plain, spl0_3 | ~spl0_5 | ~spl0_14, inference(sat_conversion,[],[f251])).
% 0.08/0.24 cnf(s37, plain, spl0_1 | ~spl0_3 | ~spl0_14, inference(sat_conversion,[],[f256])).
% 0.08/0.24 cnf(s43, plain, ~spl0_3 | ~spl0_5 | spl0_14, inference(sat_conversion,[],[f261])).
% 0.08/0.24 cnf(s44, plain, spl0_3 | spl0_1, inference(rat,[],[s33,s11,s34,s13,s8,s1])).
% 0.08/0.24 cnf(s45, plain, spl0_1, inference(rat,[],[s37,s43,s44,s8,s1])).
% 0.08/0.24 cnf(s46, plain, ~spl0_5, inference(rat,[],[s20,s45])).
% 0.08/0.24 cnf(s47, plain, spl0_10, inference(rat,[],[s25,s46,s45])).
% 0.08/0.24 cnf(s51, plain, spl0_9, inference(rat,[],[s18,s47])).
% 0.08/0.24 cnf(s53, plain, spl0_13, inference(rat,[],[s14,s51])).
% 0.08/0.24 cnf(s54, plain, spl0_7, inference(rat,[],[s5,s46,s51])).
% 0.08/0.24 cnf(s56, plain, spl0_14, inference(rat,[],[s31,s46,s45,s53])).
% 0.08/0.24 cnf(s57, plain, $false, inference(rat,[],[s28,s46,s56,s54])).
% 0.08/0.24 thf(f262,plain,(
% 0.08/0.24 $false),
% 0.08/0.24 inference(avatar_sat_refutation,[],[s57])).
% 0.08/0.24 % SZS output end Proof for theBenchmark
% 0.08/0.24 % (2699367)------------------------------
% 0.08/0.24 % (2699367)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.24 % (2699367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.24 % (2699367)CaDiCaL version: 2.1.3
% 0.08/0.24 % (2699367)Termination reason: Refutation
% 0.08/0.24 % (2699367)Time elapsed: 0.005 s
% 0.08/0.24 % (2699367)Peak memory usage: 12 MB
% 0.08/0.24 % (2699367)Instructions burned: 11 (million)
% 0.08/0.24 % (2699356)Success in time 0.027 s
% 0.08/0.24 % Vampire exiting
%------------------------------------------------------------------------------