%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO365_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 : n002.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 02:30:44 PM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO365_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n002.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 17:39:07 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.20/0.27 % (562799)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (562810)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3681516052:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.27 % (562810) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-562799-562810"...
% 0.20/0.27 % (562810)...printing done.
% 0.20/0.27 % (562805)% WARNING: option uhcvi not known.
% 0.20/0.27 % (562810)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% 0.20/0.27 tff(func_def_0, type, bG0: $o).
% 0.20/0.27 tff(func_def_3, type, bG1: $o).
% 0.20/0.27 tff(pred_def_2, type, cC: $o > $o).
% 0.20/0.27 tff(f1,axiom,(
% 0.20/0.27 (cEXT2 = cC(cA) => cC(cA))),
% 0.20/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEXT2_def)).
% 0.20/0.27 tff(f3,conjecture,(
% 0.20/0.27 cEXT_eq_0 => cEXT2),
% 0.20/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEXT2A)).
% 0.20/0.27 tff(f4,negated_conjecture,(
% 0.20/0.27 ~(cEXT_eq_0 => cEXT2)),
% 0.20/0.27 inference(negated_conjecture,[status(cth)],[f3])).
% 0.20/0.27 tff(f5,definition,(
% 0.20/0.27 cA <=> (bG0 = $true)),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[bG0])],[fool_formula_definition])).
% 0.20/0.27 tff(f6,definition,(
% 0.20/0.27 cA <=> ($true = bG1)),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[bG1])],[fool_formula_definition])).
% 0.20/0.27 tff(f7,plain,(
% 0.20/0.27 cEXT2 <=> (cC(bG0) => cC(bG1))),
% 0.20/0.27 inference(fool_elimination,[],[f1,f6,f5])).
% 0.20/0.27 tff(f11,plain,(
% 0.20/0.27 (cC(bG0) => cC(bG1)) => cEXT2),
% 0.20/0.27 inference(unused_predicate_definition_removal,[],[f7])).
% 0.20/0.27 tff(f12,plain,(
% 0.20/0.27 cEXT2 | (~cC(bG1) & cC(bG0))),
% 0.20/0.27 inference(ennf_transformation,[],[f11])).
% 0.20/0.27 tff(f14,plain,(
% 0.20/0.27 ~cEXT2 & cEXT_eq_0),
% 0.20/0.27 inference(ennf_transformation,[],[f4])).
% 0.20/0.27 tff(f15,plain,(
% 0.20/0.27 (cA | ($true != bG1)) & (($true = bG1) | ~cA)),
% 0.20/0.27 inference(nnf_transformation,[],[f6])).
% 0.20/0.27 tff(f16,plain,(
% 0.20/0.27 (cA | (bG0 != $true)) & ((bG0 = $true) | ~cA)),
% 0.20/0.27 inference(nnf_transformation,[],[f5])).
% 0.20/0.27 tff(f18,plain,(
% 0.20/0.27 ($true = bG1) | ~cA),
% 0.20/0.27 inference(cnf_transformation,[],[f15])).
% 0.20/0.27 tff(f19,plain,(
% 0.20/0.27 cA | ($true != bG1)),
% 0.20/0.27 inference(cnf_transformation,[],[f15])).
% 0.20/0.27 tff(f20,plain,(
% 0.20/0.27 (bG0 = $true) | ~cA),
% 0.20/0.27 inference(cnf_transformation,[],[f16])).
% 0.20/0.27 tff(f21,plain,(
% 0.20/0.27 cA | (bG0 != $true)),
% 0.20/0.27 inference(cnf_transformation,[],[f16])).
% 0.20/0.27 tff(f22,plain,(
% 0.20/0.27 cEXT2 | cC(bG0)),
% 0.20/0.27 inference(cnf_transformation,[],[f12])).
% 0.20/0.27 tff(f23,plain,(
% 0.20/0.27 cEXT2 | ~cC(bG1)),
% 0.20/0.27 inference(cnf_transformation,[],[f12])).
% 0.20/0.27 tff(f27,plain,(
% 0.20/0.27 ~cEXT2),
% 0.20/0.27 inference(cnf_transformation,[],[f14])).
% 0.20/0.27 tff(f29,definition,(
% 0.20/0.27 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.27 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.27 tff(f35,definition,(
% 0.20/0.27 spl2_1 <=> cC(bG0)),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.20/0.27 tff(f37,plain,(
% 0.20/0.27 cC(bG0) | ~spl2_1),
% 0.20/0.27 inference(avatar_component_clause,[],[f35])).
% 0.20/0.27 tff(f39,definition,(
% 0.20/0.27 spl2_2 <=> cEXT2),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.20/0.27 tff(f41,plain,(
% 0.20/0.27 cEXT2 | ~spl2_2),
% 0.20/0.27 inference(avatar_component_clause,[],[f39])).
% 0.20/0.27 tff(f42,plain,(
% 0.20/0.27 spl2_1 | spl2_2),
% 0.20/0.27 inference(avatar_split_clause,[],[f22,f39,f35])).
% 0.20/0.27 tff(f44,definition,(
% 0.20/0.27 spl2_3 <=> cC(bG1)),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.20/0.27 tff(f46,plain,(
% 0.20/0.27 ~cC(bG1) | spl2_3),
% 0.20/0.27 inference(avatar_component_clause,[],[f44])).
% 0.20/0.27 tff(f47,plain,(
% 0.20/0.27 ~spl2_3 | spl2_2),
% 0.20/0.27 inference(avatar_split_clause,[],[f23,f39,f44])).
% 0.20/0.27 tff(f49,definition,(
% 0.20/0.27 spl2_4 <=> cA),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition])).
% 0.20/0.27 tff(f53,definition,(
% 0.20/0.27 spl2_5 <=> (bG0 = $true)),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition])).
% 0.20/0.27 tff(f54,plain,(
% 0.20/0.27 (bG0 != $true) | spl2_5),
% 0.20/0.27 inference(avatar_component_clause,[],[f53])).
% 0.20/0.27 tff(f55,plain,(
% 0.20/0.27 (bG0 = $true) | ~spl2_5),
% 0.20/0.27 inference(avatar_component_clause,[],[f53])).
% 0.20/0.27 tff(f56,plain,(
% 0.20/0.27 ~spl2_4 | spl2_5),
% 0.20/0.27 inference(avatar_split_clause,[],[f20,f53,f49])).
% 0.20/0.27 tff(f57,plain,(
% 0.20/0.27 ~spl2_5 | spl2_4),
% 0.20/0.27 inference(avatar_split_clause,[],[f21,f49,f53])).
% 0.20/0.27 tff(f59,definition,(
% 0.20/0.27 spl2_6 <=> ($true = bG1)),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition])).
% 0.20/0.27 tff(f60,plain,(
% 0.20/0.27 ($true != bG1) | spl2_6),
% 0.20/0.27 inference(avatar_component_clause,[],[f59])).
% 0.20/0.27 tff(f61,plain,(
% 0.20/0.27 ($true = bG1) | ~spl2_6),
% 0.20/0.27 inference(avatar_component_clause,[],[f59])).
% 0.20/0.27 tff(f62,plain,(
% 0.20/0.27 ~spl2_4 | spl2_6),
% 0.20/0.27 inference(avatar_split_clause,[],[f18,f59,f49])).
% 0.20/0.27 tff(f63,plain,(
% 0.20/0.27 ~spl2_6 | spl2_4),
% 0.20/0.27 inference(avatar_split_clause,[],[f19,f49,f59])).
% 0.20/0.27 tff(f64,plain,(
% 0.20/0.27 $false | ~spl2_2),
% 0.20/0.27 inference(resolution,[],[f41,f27])).
% 0.20/0.27 tff(f65,plain,(
% 0.20/0.27 ~spl2_2),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f64])).
% 0.20/0.27 tff(f68,plain,(
% 0.20/0.27 ($true != $true) | (bG0 = $false) | spl2_5),
% 0.20/0.27 inference(superposition,[],[f54,f29])).
% 0.20/0.27 tff(f70,plain,(
% 0.20/0.27 ($true != $true) | (bG1 = $false) | spl2_6),
% 0.20/0.27 inference(superposition,[],[f60,f29])).
% 0.20/0.27 tff(f73,plain,(
% 0.20/0.27 (bG1 = $false) | spl2_6),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f70])).
% 0.20/0.27 tff(f74,plain,(
% 0.20/0.27 (bG0 = $false) | spl2_5),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f68])).
% 0.20/0.27 tff(f76,definition,(
% 0.20/0.27 spl2_7 <=> (bG1 = $false)),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition])).
% 0.20/0.27 tff(f78,plain,(
% 0.20/0.27 (bG1 = $false) | ~spl2_7),
% 0.20/0.27 inference(avatar_component_clause,[],[f76])).
% 0.20/0.27 tff(f80,definition,(
% 0.20/0.27 spl2_8 <=> cC($true)),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition])).
% 0.20/0.27 tff(f84,plain,(
% 0.20/0.27 spl2_7 | spl2_6),
% 0.20/0.27 inference(avatar_split_clause,[],[f73,f59,f76])).
% 0.20/0.27 tff(f86,definition,(
% 0.20/0.27 spl2_9 <=> (bG0 = $false)),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition])).
% 0.20/0.27 tff(f88,plain,(
% 0.20/0.27 (bG0 = $false) | ~spl2_9),
% 0.20/0.27 inference(avatar_component_clause,[],[f86])).
% 0.20/0.27 tff(f90,plain,(
% 0.20/0.27 spl2_9 | spl2_5),
% 0.20/0.27 inference(avatar_split_clause,[],[f74,f53,f86])).
% 0.20/0.27 tff(f94,plain,(
% 0.20/0.27 ~cC($false) | (spl2_3 | ~spl2_7)),
% 0.20/0.27 inference(superposition,[],[f46,f78])).
% 0.20/0.27 tff(f98,plain,(
% 0.20/0.27 cC($false) | (~spl2_1 | ~spl2_9)),
% 0.20/0.27 inference(superposition,[],[f37,f88])).
% 0.20/0.27 tff(f100,plain,(
% 0.20/0.27 $false | (~spl2_1 | spl2_3 | ~spl2_7 | ~spl2_9)),
% 0.20/0.27 inference(resolution,[],[f98,f94])).
% 0.20/0.27 tff(f101,plain,(
% 0.20/0.27 ~spl2_1 | spl2_3 | ~spl2_7 | ~spl2_9),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f100])).
% 0.20/0.27 tff(f104,plain,(
% 0.20/0.27 cC($true) | (~spl2_1 | ~spl2_5)),
% 0.20/0.27 inference(superposition,[],[f37,f55])).
% 0.20/0.27 tff(f109,plain,(
% 0.20/0.27 spl2_8 | ~spl2_1 | ~spl2_5),
% 0.20/0.27 inference(avatar_split_clause,[],[f104,f53,f35,f80])).
% 0.20/0.27 tff(f111,plain,(
% 0.20/0.27 ~cC($true) | (spl2_3 | ~spl2_6)),
% 0.20/0.27 inference(superposition,[],[f46,f61])).
% 0.20/0.27 tff(f112,plain,(
% 0.20/0.27 ~spl2_8 | spl2_3 | ~spl2_6),
% 0.20/0.27 inference(avatar_split_clause,[],[f111,f59,f44,f80])).
% 0.20/0.27 cnf(s1, plain, spl2_1 | spl2_2, inference(sat_conversion,[],[f42])).
% 0.20/0.27 cnf(s2, plain, spl2_2 | ~spl2_3, inference(sat_conversion,[],[f47])).
% 0.20/0.27 cnf(s3, plain, ~spl2_4 | spl2_5, inference(sat_conversion,[],[f56])).
% 0.20/0.27 cnf(s4, plain, spl2_4 | ~spl2_5, inference(sat_conversion,[],[f57])).
% 0.20/0.27 cnf(s5, plain, ~spl2_4 | spl2_6, inference(sat_conversion,[],[f62])).
% 0.20/0.27 cnf(s6, plain, spl2_4 | ~spl2_6, inference(sat_conversion,[],[f63])).
% 0.20/0.27 cnf(s7, plain, ~spl2_2, inference(sat_conversion,[],[f65])).
% 0.20/0.27 cnf(s9, plain, spl2_6 | spl2_7, inference(sat_conversion,[],[f84])).
% 0.20/0.27 cnf(s11, plain, spl2_5 | spl2_9, inference(sat_conversion,[],[f90])).
% 0.20/0.27 cnf(s12, plain, ~spl2_1 | spl2_3 | ~spl2_7 | ~spl2_9, inference(sat_conversion,[],[f101])).
% 0.20/0.27 cnf(s15, plain, ~spl2_1 | ~spl2_5 | spl2_8, inference(sat_conversion,[],[f109])).
% 0.20/0.27 cnf(s16, plain, spl2_3 | ~spl2_6 | ~spl2_8, inference(sat_conversion,[],[f112])).
% 0.20/0.27 cnf(s17, plain, ~spl2_3, inference(rat,[],[s2,s7])).
% 0.20/0.27 cnf(s18, plain, spl2_1, inference(rat,[],[s1,s7])).
% 0.20/0.27 cnf(s19, plain, spl2_4, inference(rat,[],[s12,s11,s9,s4,s6,s17,s18])).
% 0.20/0.27 cnf(s20, plain, spl2_6, inference(rat,[],[s5,s19])).
% 0.20/0.27 cnf(s21, plain, spl2_5, inference(rat,[],[s3,s19])).
% 0.20/0.27 cnf(s22, plain, ~spl2_8, inference(rat,[],[s16,s17,s20])).
% 0.20/0.27 cnf(s23, plain, $false, inference(rat,[],[s15,s18,s22,s21])).
% 0.20/0.27 tff(f113,plain,(
% 0.20/0.27 $false),
% 0.20/0.27 inference(avatar_sat_refutation,[],[s23])).
% 0.20/0.27 % SZS output end Proof for theBenchmark
% 0.20/0.27 % (562810)------------------------------
% 0.20/0.27 % (562810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (562810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (562810)CaDiCaL version: 2.1.3
% 0.20/0.27 % (562810)Termination reason: Refutation
% 0.20/0.27 % (562810)Time elapsed: 0.002 s
% 0.20/0.27 % (562810)Peak memory usage: 13 MB
% 0.20/0.27 % (562810)Instructions burned: 2 (million)
% 0.20/0.27 % (562799)Success in time 0.032 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------