%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO381^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : Wed Sep 30 08:49:49 AM UTC 2026
% Result : Theorem 0.08s 0.27s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO381^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n005.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 : Tue Sep 29 16:49:31 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
% 0.08/0.27 % (1909754)Will run a generic schedule for satisfiability detection.
% 0.08/0.27 % (1909771)dis+10_1_sil=32000:sp=arity:random_seed=3413902842:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.27 % (1909771) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1909754-1909771"...
% 0.08/0.27 % (1909771)...printing done.
% 0.08/0.27 % (1909771)Refutation found. Thanks to Tanya!
% 0.08/0.27 % SZS status Theorem for theBenchmark
% 0.08/0.27 % SZS output start Proof for theBenchmark
% 0.08/0.27 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.27 thf(func_def_0, type, cR: ($i > $i > $o)).
% 0.08/0.27 thf(func_def_4, type, sK0: ($i > $i)).
% 0.08/0.27 thf(func_def_5, type, sK1: ($i > $i)).
% 0.08/0.27 thf(f1,conjecture,(
% 0.08/0.27 ? [X0 : $i] : (? [X1 : $i] : ! [X2 : $i] : (cR @ X1 @ X2) <=> ! [X3 : $i] : (cR @ X0 @ X3))),
% 0.08/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX_2002_12_17)).
% 0.08/0.27 thf(f2,negated_conjecture,(
% 0.08/0.27 ~ ? [X0 : $i] : (? [X1 : $i] : ! [X2 : $i] : (cR @ X1 @ X2) <=> ! [X3 : $i] : (cR @ X0 @ X3))),
% 0.08/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.08/0.27 thf(f3,plain,(
% 0.08/0.27 ~ ? [X0 : $i] : (? [X1 : $i] : ! [X2 : $i] : (cR @ X1 @ X2) <=> ! [X3 : $i] : (cR @ X0 @ X3))),
% 0.08/0.27 inference(rectify,[],[f2])).
% 0.08/0.27 thf(f4,plain,(
% 0.08/0.27 ~ ? [X0 : $i] : (? [X1 : $i] : ! [X2 : $i] : (((cR @ X1 @ X2)) = $true) <=> ! [X3 : $i] : (((cR @ X0 @ X3)) = $true))),
% 0.08/0.27 inference(fool_elimination,[],[f3])).
% 0.08/0.27 thf(f5,plain,(
% 0.08/0.27 ! [X0 : $i] : (? [X1 : $i] : ! [X2 : $i] : (((cR @ X1 @ X2)) = $true) <~> ! [X3 : $i] : (((cR @ X0 @ X3)) = $true))),
% 0.08/0.27 inference(ennf_transformation,[],[f4])).
% 0.08/0.27 thf(f6,plain,(
% 0.08/0.27 ! [X0 : $i] : ((? [X3 : $i] : (((cR @ X0 @ X3)) != $true) | ! [X1 : $i] : ? [X2 : $i] : (((cR @ X1 @ X2)) != $true)) & (! [X3 : $i] : (((cR @ X0 @ X3)) = $true) | ? [X1 : $i] : ! [X2 : $i] : (((cR @ X1 @ X2)) = $true)))),
% 0.08/0.27 inference(nnf_transformation,[],[f5])).
% 0.08/0.27 thf(f7,plain,(
% 0.08/0.27 ! [X0 : $i] : ((? [X1 : $i] : ($true != ((cR @ X0 @ X1))) | ! [X2 : $i] : ? [X3 : $i] : ($true != ((cR @ X2 @ X3)))) & (! [X4 : $i] : ($true = ((cR @ X0 @ X4))) | ? [X5 : $i] : ! [X6 : $i] : ($true = ((cR @ X5 @ X6)))))),
% 0.08/0.27 inference(rectify,[],[f6])).
% 0.08/0.27 thf(f8,plain,(
% 0.08/0.27 ! [X0 : $i] : ((($true != ((cR @ X0 @ (sK0 @ X0)))) | ! [X2 : $i] : ($true != ((cR @ X2 @ (sK1 @ X2))))) & (! [X4 : $i] : ($true = ((cR @ X0 @ X4))) | ! [X6 : $i] : ($true = ((cR @ sK2 @ X6)))))),
% 0.08/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,sK2]),skolemize(X3,sK1 @ X2),skolemize(X3,sK1 @ X2),skolemize(X5,sK2)],[f7])).
% 0.08/0.27 thf(f9,plain,(
% 0.08/0.27 ( ! [X0 : $i,X6 : $i,X4 : $i] : (($true = ((cR @ X0 @ X4))) | ($true = ((cR @ sK2 @ X6)))) )),
% 0.08/0.27 inference(cnf_transformation,[],[f8])).
% 0.08/0.27 thf(f10,plain,(
% 0.08/0.27 ( ! [X2 : $i,X0 : $i] : (($true != ((cR @ X0 @ (sK0 @ X0)))) | ($true != ((cR @ X2 @ (sK1 @ X2))))) )),
% 0.08/0.27 inference(cnf_transformation,[],[f8])).
% 0.08/0.27 thf(f14,definition,(
% 0.08/0.27 spl3_1 <=> ! [X6 : $i] : ($true = ((cR @ sK2 @ X6)))),
% 0.08/0.27 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.08/0.27 thf(f15,plain,(
% 0.08/0.27 ( ! [X6 : $i] : (($true = ((cR @ sK2 @ X6)))) ) | ~spl3_1),
% 0.08/0.27 inference(avatar_component_clause,[],[f14])).
% 0.08/0.27 thf(f17,definition,(
% 0.08/0.27 spl3_2 <=> ! [X4 : $i,X0 : $i] : ($true = ((cR @ X0 @ X4)))),
% 0.08/0.27 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 0.08/0.27 thf(f18,plain,(
% 0.08/0.27 ( ! [X0 : $i,X4 : $i] : (($true = ((cR @ X0 @ X4)))) ) | ~spl3_2),
% 0.08/0.27 inference(avatar_component_clause,[],[f17])).
% 0.08/0.27 thf(f19,plain,(
% 0.08/0.27 spl3_1 | spl3_2),
% 0.08/0.27 inference(avatar_split_clause,[],[f9,f17,f14])).
% 0.08/0.27 thf(f21,definition,(
% 0.08/0.27 spl3_3 <=> ! [X2 : $i] : ($true != ((cR @ X2 @ (sK1 @ X2))))),
% 0.08/0.27 introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition])).
% 0.08/0.27 thf(f22,plain,(
% 0.08/0.27 ( ! [X2 : $i] : (($true != ((cR @ X2 @ (sK1 @ X2))))) ) | ~spl3_3),
% 0.08/0.27 inference(avatar_component_clause,[],[f21])).
% 0.08/0.27 thf(f24,definition,(
% 0.08/0.27 spl3_4 <=> ! [X0 : $i] : ($true != ((cR @ X0 @ (sK0 @ X0))))),
% 0.08/0.27 introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition])).
% 0.08/0.27 thf(f25,plain,(
% 0.08/0.27 ( ! [X0 : $i] : (($true != ((cR @ X0 @ (sK0 @ X0))))) ) | ~spl3_4),
% 0.08/0.27 inference(avatar_component_clause,[],[f24])).
% 0.08/0.27 thf(f26,plain,(
% 0.08/0.27 spl3_3 | spl3_4),
% 0.08/0.27 inference(avatar_split_clause,[],[f10,f24,f21])).
% 0.08/0.27 thf(f27,plain,(
% 0.08/0.27 $false | (~spl3_2 | ~spl3_3)),
% 0.08/0.27 inference(forward_subsumption_resolution,[],[f22,f18])).
% 0.08/0.27 thf(f28,plain,(
% 0.08/0.27 ~spl3_2 | ~spl3_3),
% 0.08/0.27 inference(avatar_contradiction_clause,[],[f27])).
% 0.08/0.27 thf(f29,plain,(
% 0.08/0.27 ($true != $true) | (~spl3_1 | ~spl3_3)),
% 0.08/0.27 inference(constrained_superposition,[],[f22,f15])).
% 0.08/0.27 thf(f30,plain,(
% 0.08/0.27 $false | (~spl3_1 | ~spl3_3)),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f29])).
% 0.08/0.27 thf(f31,plain,(
% 0.08/0.27 ~spl3_1 | ~spl3_3),
% 0.08/0.27 inference(avatar_contradiction_clause,[],[f30])).
% 0.08/0.27 thf(f32,plain,(
% 0.08/0.27 $false | (~spl3_2 | ~spl3_4)),
% 0.08/0.27 inference(forward_subsumption_resolution,[],[f25,f18])).
% 0.08/0.27 thf(f33,plain,(
% 0.08/0.27 ~spl3_2 | ~spl3_4),
% 0.08/0.27 inference(avatar_contradiction_clause,[],[f32])).
% 0.08/0.27 thf(f34,plain,(
% 0.08/0.27 ($true != $true) | (~spl3_1 | ~spl3_4)),
% 0.08/0.27 inference(constrained_superposition,[],[f25,f15])).
% 0.08/0.27 thf(f35,plain,(
% 0.08/0.27 $false | (~spl3_1 | ~spl3_4)),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f34])).
% 0.08/0.27 thf(f36,plain,(
% 0.08/0.27 ~spl3_1 | ~spl3_4),
% 0.08/0.27 inference(avatar_contradiction_clause,[],[f35])).
% 0.08/0.27 cnf(s1, plain, spl3_1 | spl3_2, inference(sat_conversion,[],[f19])).
% 0.08/0.27 cnf(s2, plain, spl3_3 | spl3_4, inference(sat_conversion,[],[f26])).
% 0.08/0.27 cnf(s3, plain, ~spl3_2 | ~spl3_3, inference(sat_conversion,[],[f28])).
% 0.08/0.27 cnf(s4, plain, ~spl3_1 | ~spl3_3, inference(sat_conversion,[],[f31])).
% 0.08/0.27 cnf(s5, plain, ~spl3_2 | ~spl3_4, inference(sat_conversion,[],[f33])).
% 0.08/0.27 cnf(s6, plain, ~spl3_1 | ~spl3_4, inference(sat_conversion,[],[f36])).
% 0.08/0.27 cnf(s7, plain, ~spl3_2, inference(rat,[],[s2,s3,s5])).
% 0.08/0.27 cnf(s8, plain, spl3_1, inference(rat,[],[s1,s7])).
% 0.08/0.27 cnf(s9, plain, ~spl3_4, inference(rat,[],[s6,s8])).
% 0.08/0.27 cnf(s10, plain, ~spl3_3, inference(rat,[],[s4,s8])).
% 0.08/0.27 cnf(s11, plain, $false, inference(rat,[],[s2,s9,s10])).
% 0.08/0.27 thf(f37,plain,(
% 0.08/0.27 $false),
% 0.08/0.27 inference(avatar_sat_refutation,[],[s11])).
% 0.08/0.27 % SZS output end Proof for theBenchmark
% 0.08/0.27 % (1909771)------------------------------
% 0.08/0.27 % (1909771)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.27 % (1909771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.27 % (1909771)CaDiCaL version: 2.1.3
% 0.08/0.27 % (1909771)Termination reason: Refutation
% 0.08/0.27 % (1909771)Time elapsed: 0.002 s
% 0.08/0.27 % (1909771)Peak memory usage: 12 MB
% 0.08/0.27 % (1909771)Instructions burned: 2 (million)
% 0.08/0.27 % (1909754)Success in time 0.035 s
% 0.08/0.27 % Vampire exiting
%------------------------------------------------------------------------------