%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN057^5 : 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 : n018.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 08:41:50 AM UTC 2026
% Result : Theorem 0.10s 0.24s
% Output : Refutation 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN057^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n018.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 16:16:57 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 Running first-order model finding
% 0.10/0.21 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
% 0.10/0.24 % (281533)Will run a generic schedule for satisfiability detection.
% 0.10/0.24 % (281545)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1914734696:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.10/0.24 % (281545)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.24 % (281545) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-281533-281545"...
% 0.10/0.24 % (281545)...printing done.
% 0.10/0.24 % (281545)Refutation found. Thanks to Tanya!
% 0.10/0.24 % SZS status Theorem for theBenchmark
% 0.10/0.24 % SZS output start Proof for theBenchmark
% 0.10/0.24 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.10/0.24 thf(func_def_0, type, cI: ($i > $o)).
% 0.10/0.24 thf(func_def_1, type, cJ: ($i > $o)).
% 0.10/0.24 thf(func_def_2, type, cH: ($i > $o)).
% 0.10/0.24 thf(func_def_3, type, cG: ($i > $o)).
% 0.10/0.24 thf(func_def_4, type, cF: ($i > $o)).
% 0.10/0.24 thf(f1,conjecture,(
% 0.10/0.24 ((? [X0 : $i] : (~(cG @ X0) & (cH @ X0)) => ! [X0 : $i] : ((cI @ X0) => ~(cH @ X0))) & ! [X0 : $i] : (((cI @ X0) & (cJ @ X0)) => (cF @ X0)) & ! [X0 : $i] : ((cF @ X0) => (cH @ X0)) & ? [X0 : $i] : (~(cG @ X0) & (cF @ X0))) => ! [X0 : $i] : ((cJ @ X0) => ~(cI @ X0))),
% 0.10/0.24 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPELL27)).
% 0.10/0.24 thf(f2,negated_conjecture,(
% 0.10/0.24 ~(((? [X0 : $i] : (~(cG @ X0) & (cH @ X0)) => ! [X0 : $i] : ((cI @ X0) => ~(cH @ X0))) & ! [X0 : $i] : (((cI @ X0) & (cJ @ X0)) => (cF @ X0)) & ! [X0 : $i] : ((cF @ X0) => (cH @ X0)) & ? [X0 : $i] : (~(cG @ X0) & (cF @ X0))) => ! [X0 : $i] : ((cJ @ X0) => ~(cI @ X0)))),
% 0.10/0.24 inference(negated_conjecture,[status(cth)],[f1])).
% 0.10/0.24 thf(f3,plain,(
% 0.10/0.24 ~(((? [X0 : $i] : (~(cG @ X0) & (cH @ X0)) => ! [X1 : $i] : ((cI @ X1) => ~(cH @ X1))) & ! [X2 : $i] : (((cI @ X2) & (cJ @ X2)) => (cF @ X2)) & ! [X3 : $i] : ((cF @ X3) => (cH @ X3)) & ? [X4 : $i] : (~(cG @ X4) & (cF @ X4))) => ! [X5 : $i] : ((cJ @ X5) => ~(cI @ X5)))),
% 0.10/0.24 inference(rectify,[],[f2])).
% 0.10/0.24 thf(f4,plain,(
% 0.10/0.24 ~(((? [X0 : $i] : (~ (((cG @ X0)) = $true) & (((cH @ X0)) = $true)) => ! [X1 : $i] : ((((cI @ X1)) = $true) => ~ (((cH @ X1)) = $true))) & ! [X2 : $i] : (((((cI @ X2)) = $true) & (((cJ @ X2)) = $true)) => (((cF @ X2)) = $true)) & ! [X3 : $i] : ((((cF @ X3)) = $true) => (((cH @ X3)) = $true)) & ? [X4 : $i] : (~ (((cG @ X4)) = $true) & (((cF @ X4)) = $true))) => ! [X5 : $i] : ((((cJ @ X5)) = $true) => ~ (((cI @ X5)) = $true)))),
% 0.10/0.24 inference(fool_elimination,[],[f3])).
% 0.10/0.24 thf(f5,plain,(
% 0.10/0.24 ~(((? [X0 : $i] : ((((cG @ X0)) != $true) & (((cH @ X0)) = $true)) => ! [X1 : $i] : ((((cI @ X1)) = $true) => (((cH @ X1)) != $true))) & ! [X2 : $i] : (((((cI @ X2)) = $true) & (((cJ @ X2)) = $true)) => (((cF @ X2)) = $true)) & ! [X3 : $i] : ((((cF @ X3)) = $true) => (((cH @ X3)) = $true)) & ? [X4 : $i] : ((((cG @ X4)) != $true) & (((cF @ X4)) = $true))) => ! [X5 : $i] : ((((cJ @ X5)) = $true) => (((cI @ X5)) != $true)))),
% 0.10/0.24 inference(flattening,[],[f4])).
% 0.10/0.24 thf(f6,plain,(
% 0.10/0.24 ? [X5 : $i] : ((((cI @ X5)) = $true) & (((cJ @ X5)) = $true)) & ((! [X1 : $i] : ((((cH @ X1)) != $true) | (((cI @ X1)) != $true)) | ! [X0 : $i] : ((((cG @ X0)) = $true) | (((cH @ X0)) != $true))) & ! [X2 : $i] : ((((cF @ X2)) = $true) | ((((cI @ X2)) != $true) | (((cJ @ X2)) != $true))) & ! [X3 : $i] : ((((cH @ X3)) = $true) | (((cF @ X3)) != $true)) & ? [X4 : $i] : ((((cG @ X4)) != $true) & (((cF @ X4)) = $true)))),
% 0.10/0.24 inference(ennf_transformation,[],[f5])).
% 0.10/0.24 thf(f7,plain,(
% 0.10/0.24 ? [X5 : $i] : ((((cI @ X5)) = $true) & (((cJ @ X5)) = $true)) & (! [X1 : $i] : ((((cH @ X1)) != $true) | (((cI @ X1)) != $true)) | ! [X0 : $i] : ((((cG @ X0)) = $true) | (((cH @ X0)) != $true))) & ! [X2 : $i] : ((((cF @ X2)) = $true) | (((cI @ X2)) != $true) | (((cJ @ X2)) != $true)) & ! [X3 : $i] : ((((cH @ X3)) = $true) | (((cF @ X3)) != $true)) & ? [X4 : $i] : ((((cG @ X4)) != $true) & (((cF @ X4)) = $true))),
% 0.10/0.24 inference(flattening,[],[f6])).
% 0.10/0.24 thf(f8,plain,(
% 0.10/0.24 ? [X0 : $i] : ((((cI @ X0)) = $true) & (((cJ @ X0)) = $true)) & (! [X1 : $i] : ((((cH @ X1)) != $true) | (((cI @ X1)) != $true)) | ! [X2 : $i] : (($true = ((cG @ X2))) | ($true != ((cH @ X2))))) & ! [X3 : $i] : ((((cF @ X3)) = $true) | ($true != ((cI @ X3))) | ($true != ((cJ @ X3)))) & ! [X4 : $i] : (($true = ((cH @ X4))) | (((cF @ X4)) != $true)) & ? [X5 : $i] : (($true != ((cG @ X5))) & ($true = ((cF @ X5))))),
% 0.10/0.24 inference(rectify,[],[f7])).
% 0.10/0.24 thf(f9,plain,(
% 0.10/0.24 (($true = ((cI @ sK0))) & ($true = ((cJ @ sK0)))) & (! [X1 : $i] : ((((cH @ X1)) != $true) | (((cI @ X1)) != $true)) | ! [X2 : $i] : (($true = ((cG @ X2))) | ($true != ((cH @ X2))))) & ! [X3 : $i] : ((((cF @ X3)) = $true) | ($true != ((cI @ X3))) | ($true != ((cJ @ X3)))) & ! [X4 : $i] : (($true = ((cH @ X4))) | (((cF @ X4)) != $true)) & (($true != ((cG @ sK1))) & ($true = ((cF @ sK1))))),
% 0.10/0.24 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X5,sK1)],[f8])).
% 0.10/0.24 thf(f10,plain,(
% 0.10/0.24 ($true = ((cF @ sK1)))),
% 0.10/0.24 inference(cnf_transformation,[],[f9])).
% 0.10/0.24 thf(f11,plain,(
% 0.10/0.24 ($true != ((cG @ sK1)))),
% 0.10/0.24 inference(cnf_transformation,[],[f9])).
% 0.10/0.24 thf(f12,plain,(
% 0.10/0.24 ( ! [X4 : $i] : ((((cF @ X4)) != $true) | ($true = ((cH @ X4)))) )),
% 0.10/0.24 inference(cnf_transformation,[],[f9])).
% 0.10/0.24 thf(f13,plain,(
% 0.10/0.24 ( ! [X3 : $i] : (($true != ((cJ @ X3))) | ($true != ((cI @ X3))) | (((cF @ X3)) = $true)) )),
% 0.10/0.24 inference(cnf_transformation,[],[f9])).
% 0.10/0.24 thf(f14,plain,(
% 0.10/0.24 ( ! [X2 : $i,X1 : $i] : ((((cH @ X1)) != $true) | (((cI @ X1)) != $true) | ($true = ((cG @ X2))) | ($true != ((cH @ X2)))) )),
% 0.10/0.24 inference(cnf_transformation,[],[f9])).
% 0.10/0.24 thf(f15,plain,(
% 0.10/0.24 ($true = ((cJ @ sK0)))),
% 0.10/0.24 inference(cnf_transformation,[],[f9])).
% 0.10/0.24 thf(f16,plain,(
% 0.10/0.24 ($true = ((cI @ sK0)))),
% 0.10/0.24 inference(cnf_transformation,[],[f9])).
% 0.10/0.24 thf(f18,definition,(
% 0.10/0.24 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.10/0.24 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.10/0.24 thf(f20,definition,(
% 0.10/0.24 spl2_1 <=> ! [X2 : $i] : (($true = ((cG @ X2))) | ($true != ((cH @ X2))))),
% 0.10/0.24 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.10/0.24 thf(f21,plain,(
% 0.10/0.24 ( ! [X2 : $i] : (($true = ((cG @ X2))) | ($true != ((cH @ X2)))) ) | ~spl2_1),
% 0.10/0.24 inference(avatar_component_clause,[],[f20])).
% 0.10/0.24 thf(f23,definition,(
% 0.10/0.24 spl2_2 <=> ! [X1 : $i] : ((((cH @ X1)) != $true) | (((cI @ X1)) != $true))),
% 0.10/0.24 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.10/0.24 thf(f24,plain,(
% 0.10/0.24 ( ! [X1 : $i] : ((((cH @ X1)) != $true) | (((cI @ X1)) != $true)) ) | ~spl2_2),
% 0.10/0.24 inference(avatar_component_clause,[],[f23])).
% 0.10/0.24 thf(f25,plain,(
% 0.10/0.24 spl2_1 | spl2_2),
% 0.10/0.24 inference(avatar_split_clause,[],[f14,f23,f20])).
% 0.10/0.24 thf(f26,plain,(
% 0.10/0.24 ($true != $true) | ($true = ((cH @ sK1)))),
% 0.10/0.24 inference(constrained_superposition,[],[f12,f10])).
% 0.10/0.24 thf(f27,plain,(
% 0.10/0.24 ($true = ((cH @ sK1)))),
% 0.10/0.24 inference(trivial_inequality_removal,[],[f26])).
% 0.10/0.24 thf(f30,plain,(
% 0.10/0.24 ($true != $true) | ($true != ((cI @ sK0))) | ($true = ((cF @ sK0)))),
% 0.10/0.24 inference(constrained_superposition,[],[f13,f15])).
% 0.10/0.24 thf(f31,plain,(
% 0.10/0.24 ($true != ((cI @ sK0))) | ($true = ((cF @ sK0)))),
% 0.10/0.24 inference(trivial_inequality_removal,[],[f30])).
% 0.10/0.24 thf(f32,plain,(
% 0.10/0.24 ($true = ((cF @ sK0)))),
% 0.10/0.24 inference(forward_subsumption_resolution,[],[f31,f16])).
% 0.10/0.24 thf(f33,plain,(
% 0.10/0.24 ($true != $true) | ($true = ((cH @ sK0)))),
% 0.10/0.24 inference(constrained_superposition,[],[f12,f32])).
% 0.10/0.24 thf(f34,plain,(
% 0.10/0.24 ($true = ((cH @ sK0)))),
% 0.10/0.24 inference(trivial_inequality_removal,[],[f33])).
% 0.10/0.24 thf(f38,plain,(
% 0.10/0.24 ($true != $true) | (((cG @ sK1)) = $false)),
% 0.10/0.24 inference(constrained_superposition,[],[f11,f18])).
% 0.10/0.24 thf(f40,plain,(
% 0.10/0.24 ( ! [X0 : $i] : (($true != $true) | (((cI @ X0)) != $true) | (((cH @ X0)) = $false)) ) | ~spl2_2),
% 0.10/0.24 inference(constrained_superposition,[],[f24,f18])).
% 0.10/0.24 thf(f44,plain,(
% 0.10/0.24 ( ! [X0 : $i] : ((((cH @ X0)) = $false) | (((cI @ X0)) != $true)) ) | ~spl2_2),
% 0.10/0.24 inference(trivial_inequality_removal,[],[f40])).
% 0.10/0.24 thf(f46,plain,(
% 0.10/0.24 (((cG @ sK1)) = $false)),
% 0.10/0.24 inference(trivial_inequality_removal,[],[f38])).
% 0.10/0.24 thf(f63,plain,(
% 0.10/0.24 ($true = $false) | ($true != ((cI @ sK0))) | ~spl2_2),
% 0.10/0.24 inference(constrained_superposition,[],[f34,f44])).
% 0.10/0.24 thf(f68,plain,(
% 0.10/0.24 ($true != ((cI @ sK0))) | ~spl2_2),
% 0.10/0.24 inference(trivial_inequality_removal,[],[f63])).
% 0.10/0.24 thf(f73,plain,(
% 0.10/0.24 $false | ~spl2_2),
% 0.10/0.24 inference(forward_subsumption_resolution,[],[f68,f16])).
% 0.10/0.24 thf(f74,plain,(
% 0.10/0.24 ~spl2_2),
% 0.10/0.24 inference(avatar_contradiction_clause,[],[f73])).
% 0.10/0.24 thf(f75,plain,(
% 0.10/0.24 ($true = $false) | ($true != ((cH @ sK1))) | ~spl2_1),
% 0.10/0.24 inference(constrained_superposition,[],[f21,f46])).
% 0.10/0.24 thf(f80,plain,(
% 0.10/0.24 ($true != ((cH @ sK1))) | ~spl2_1),
% 0.10/0.24 inference(trivial_inequality_removal,[],[f75])).
% 0.10/0.24 thf(f85,plain,(
% 0.10/0.24 $false | ~spl2_1),
% 0.10/0.24 inference(forward_subsumption_resolution,[],[f80,f27])).
% 0.10/0.24 thf(f86,plain,(
% 0.10/0.24 ~spl2_1),
% 0.10/0.24 inference(avatar_contradiction_clause,[],[f85])).
% 0.10/0.24 cnf(s1, plain, spl2_1 | spl2_2, inference(sat_conversion,[],[f25])).
% 0.10/0.24 cnf(s4, plain, ~spl2_2, inference(sat_conversion,[],[f74])).
% 0.10/0.24 cnf(s7, plain, ~spl2_1, inference(sat_conversion,[],[f86])).
% 0.10/0.24 cnf(s8, plain, $false, inference(rat,[],[s1,s4,s7])).
% 0.10/0.24 thf(f87,plain,(
% 0.10/0.24 $false),
% 0.10/0.24 inference(avatar_sat_refutation,[],[s8])).
% 0.10/0.24 % SZS output end Proof for theBenchmark
% 0.10/0.24 % (281545)------------------------------
% 0.10/0.24 % (281545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.24 % (281545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.24 % (281545)CaDiCaL version: 2.1.3
% 0.10/0.24 % (281545)Termination reason: Refutation
% 0.10/0.24 % (281545)Time elapsed: 0.002 s
% 0.10/0.24 % (281545)Peak memory usage: 12 MB
% 0.10/0.24 % (281545)Instructions burned: 5 (million)
% 0.10/0.24 % (281533)Success in time 0.017 s
% 0.10/0.24 % Vampire exiting
%------------------------------------------------------------------------------