%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO113^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 08:48:59 AM UTC 2026
% Result : Theorem 0.20s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO113^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n015.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 : Tue Sep 29 16:37:33 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.20/0.26 % (3754732)Will run a generic schedule for satisfiability detection.
% 0.20/0.26 % (3754743)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2718233668:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.20/0.26 % (3754743)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.26 % (3754740)% WARNING: option uhcvi not known.
% 0.20/0.26 % (3754743) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3754732-3754743"...
% 0.20/0.26 % (3754743)...printing done.
% 0.20/0.26 % (3754739)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4071839736_3000 on theBenchmark for (3000ds/0Mi)
% 0.20/0.26 % (3754741)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=514491803:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.20/0.26 % (3754740)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1832834010:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.20/0.26 % (3754742)dis+10_1_sil=32000:sp=arity:random_seed=3576801063:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.20/0.26 % (3754740)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.26 % (3754744)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1283383545:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.20/0.26 % Exception at run slice level
% 0.20/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.26 % (3754745)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3356799007:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.20/0.26 % (3754740)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.26 % (3754743)Refutation found. Thanks to Tanya!
% 0.20/0.26 % SZS status Theorem for theBenchmark
% 0.20/0.26 % SZS output start Proof for theBenchmark
% 0.20/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.26 thf(func_def_0, type, cNUMBER: ($i > $o)).
% 0.20/0.26 thf(func_def_1, type, cODD: ($i > $o)).
% 0.20/0.26 thf(func_def_2, type, cEVEN: ($i > $o)).
% 0.20/0.26 thf(func_def_3, type, cS: ($i > $i)).
% 0.20/0.26 thf(f1,conjecture,(
% 0.20/0.26 (! [X0 : $i] : ((cNUMBER @ X0) <=> ((cODD @ X0) | (cEVEN @ X0))) & ((! [X1 : $i] : (((cNUMBER @ (cS @ X1)) & (cNUMBER @ X1)) => ((cNUMBER @ (cS @ (cS @ X1))) & (cNUMBER @ (cS @ X1)))) & (cNUMBER @ (cS @ c0)) & (cNUMBER @ c0)) => ! [X1 : $i] : ((cNUMBER @ (cS @ X1)) & (cNUMBER @ X1))) & ! [X0 : $i] : ((cODD @ X0) => (cODD @ (cS @ (cS @ X0)))) & (cODD @ (cS @ c0)) & ! [X0 : $i] : ((cEVEN @ X0) => (cEVEN @ (cS @ (cS @ X0)))) & (cEVEN @ c0)) => ! [X0 : $i] : (cNUMBER @ X0)),
% 0.20/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM350)).
% 0.20/0.26 thf(f2,negated_conjecture,(
% 0.20/0.26 ~((! [X0 : $i] : ((cNUMBER @ X0) <=> ((cODD @ X0) | (cEVEN @ X0))) & ((! [X1 : $i] : (((cNUMBER @ (cS @ X1)) & (cNUMBER @ X1)) => ((cNUMBER @ (cS @ (cS @ X1))) & (cNUMBER @ (cS @ X1)))) & (cNUMBER @ (cS @ c0)) & (cNUMBER @ c0)) => ! [X1 : $i] : ((cNUMBER @ (cS @ X1)) & (cNUMBER @ X1))) & ! [X0 : $i] : ((cODD @ X0) => (cODD @ (cS @ (cS @ X0)))) & (cODD @ (cS @ c0)) & ! [X0 : $i] : ((cEVEN @ X0) => (cEVEN @ (cS @ (cS @ X0)))) & (cEVEN @ c0)) => ! [X0 : $i] : (cNUMBER @ X0))),
% 0.20/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.26 thf(f3,plain,(
% 0.20/0.26 ~((! [X0 : $i] : ((cNUMBER @ X0) <=> ((cODD @ X0) | (cEVEN @ X0))) & ((! [X1 : $i] : (((cNUMBER @ (cS @ X1)) & (cNUMBER @ X1)) => ((cNUMBER @ (cS @ (cS @ X1))) & (cNUMBER @ (cS @ X1)))) & (cNUMBER @ (cS @ c0)) & (cNUMBER @ c0)) => ! [X2 : $i] : ((cNUMBER @ (cS @ X2)) & (cNUMBER @ X2))) & ! [X3 : $i] : ((cODD @ X3) => (cODD @ (cS @ (cS @ X3)))) & (cODD @ (cS @ c0)) & ! [X4 : $i] : ((cEVEN @ X4) => (cEVEN @ (cS @ (cS @ X4)))) & (cEVEN @ c0)) => ! [X5 : $i] : (cNUMBER @ X5))),
% 0.20/0.26 inference(rectify,[],[f2])).
% 0.20/0.26 thf(f4,plain,(
% 0.20/0.26 ~((! [X0 : $i] : ((((cNUMBER @ X0)) = $true) <=> ((((cODD @ X0)) = $true) | (((cEVEN @ X0)) = $true))) & ((! [X1 : $i] : (((((cNUMBER @ (cS @ X1))) = $true) & (((cNUMBER @ X1)) = $true)) => ((((cNUMBER @ (cS @ (cS @ X1)))) = $true) & (((cNUMBER @ (cS @ X1))) = $true))) & (((cNUMBER @ (cS @ c0))) = $true) & (((cNUMBER @ c0)) = $true)) => ! [X2 : $i] : ((((cNUMBER @ (cS @ X2))) = $true) & (((cNUMBER @ X2)) = $true))) & ! [X3 : $i] : ((((cODD @ X3)) = $true) => (((cODD @ (cS @ (cS @ X3)))) = $true)) & (((cODD @ (cS @ c0))) = $true) & ! [X4 : $i] : ((((cEVEN @ X4)) = $true) => (((cEVEN @ (cS @ (cS @ X4)))) = $true)) & (((cEVEN @ c0)) = $true)) => ! [X5 : $i] : (((cNUMBER @ X5)) = $true))),
% 0.20/0.26 inference(fool_elimination,[],[f3])).
% 0.20/0.26 thf(f5,plain,(
% 0.20/0.26 ? [X5 : $i] : (((cNUMBER @ X5)) != $true) & (! [X0 : $i] : ((((cNUMBER @ X0)) = $true) <=> ((((cODD @ X0)) = $true) | (((cEVEN @ X0)) = $true))) & (! [X2 : $i] : ((((cNUMBER @ (cS @ X2))) = $true) & (((cNUMBER @ X2)) = $true)) | (? [X1 : $i] : (((((cNUMBER @ (cS @ (cS @ X1)))) != $true) | (((cNUMBER @ (cS @ X1))) != $true)) & ((((cNUMBER @ (cS @ X1))) = $true) & (((cNUMBER @ X1)) = $true))) | (((cNUMBER @ (cS @ c0))) != $true) | (((cNUMBER @ c0)) != $true))) & ! [X3 : $i] : ((((cODD @ (cS @ (cS @ X3)))) = $true) | (((cODD @ X3)) != $true)) & (((cODD @ (cS @ c0))) = $true) & ! [X4 : $i] : ((((cEVEN @ (cS @ (cS @ X4)))) = $true) | (((cEVEN @ X4)) != $true)) & (((cEVEN @ c0)) = $true))),
% 0.20/0.26 inference(ennf_transformation,[],[f4])).
% 0.20/0.26 thf(f6,plain,(
% 0.20/0.26 ? [X5 : $i] : (((cNUMBER @ X5)) != $true) & ! [X0 : $i] : ((((cNUMBER @ X0)) = $true) <=> ((((cODD @ X0)) = $true) | (((cEVEN @ X0)) = $true))) & (! [X2 : $i] : ((((cNUMBER @ (cS @ X2))) = $true) & (((cNUMBER @ X2)) = $true)) | ? [X1 : $i] : (((((cNUMBER @ (cS @ (cS @ X1)))) != $true) | (((cNUMBER @ (cS @ X1))) != $true)) & (((cNUMBER @ (cS @ X1))) = $true) & (((cNUMBER @ X1)) = $true)) | (((cNUMBER @ (cS @ c0))) != $true) | (((cNUMBER @ c0)) != $true)) & ! [X3 : $i] : ((((cODD @ (cS @ (cS @ X3)))) = $true) | (((cODD @ X3)) != $true)) & (((cODD @ (cS @ c0))) = $true) & ! [X4 : $i] : ((((cEVEN @ (cS @ (cS @ X4)))) = $true) | (((cEVEN @ X4)) != $true)) & (((cEVEN @ c0)) = $true)),
% 0.20/0.26 inference(flattening,[],[f5])).
% 0.20/0.26 thf(f7,plain,(
% 0.20/0.26 ? [X5 : $i] : (((cNUMBER @ X5)) != $true) & ! [X0 : $i] : (((((cNUMBER @ X0)) = $true) | ((((cODD @ X0)) != $true) & (((cEVEN @ X0)) != $true))) & (((((cODD @ X0)) = $true) | (((cEVEN @ X0)) = $true)) | (((cNUMBER @ X0)) != $true))) & (! [X2 : $i] : ((((cNUMBER @ (cS @ X2))) = $true) & (((cNUMBER @ X2)) = $true)) | ? [X1 : $i] : (((((cNUMBER @ (cS @ (cS @ X1)))) != $true) | (((cNUMBER @ (cS @ X1))) != $true)) & (((cNUMBER @ (cS @ X1))) = $true) & (((cNUMBER @ X1)) = $true)) | (((cNUMBER @ (cS @ c0))) != $true) | (((cNUMBER @ c0)) != $true)) & ! [X3 : $i] : ((((cODD @ (cS @ (cS @ X3)))) = $true) | (((cODD @ X3)) != $true)) & (((cODD @ (cS @ c0))) = $true) & ! [X4 : $i] : ((((cEVEN @ (cS @ (cS @ X4)))) = $true) | (((cEVEN @ X4)) != $true)) & (((cEVEN @ c0)) = $true)),
% 0.20/0.26 inference(nnf_transformation,[],[f6])).
% 0.20/0.26 thf(f8,plain,(
% 0.20/0.26 ? [X5 : $i] : (((cNUMBER @ X5)) != $true) & ! [X0 : $i] : (((((cNUMBER @ X0)) = $true) | ((((cODD @ X0)) != $true) & (((cEVEN @ X0)) != $true))) & ((((cODD @ X0)) = $true) | (((cEVEN @ X0)) = $true) | (((cNUMBER @ X0)) != $true))) & (! [X2 : $i] : ((((cNUMBER @ (cS @ X2))) = $true) & (((cNUMBER @ X2)) = $true)) | ? [X1 : $i] : (((((cNUMBER @ (cS @ (cS @ X1)))) != $true) | (((cNUMBER @ (cS @ X1))) != $true)) & (((cNUMBER @ (cS @ X1))) = $true) & (((cNUMBER @ X1)) = $true)) | (((cNUMBER @ (cS @ c0))) != $true) | (((cNUMBER @ c0)) != $true)) & ! [X3 : $i] : ((((cODD @ (cS @ (cS @ X3)))) = $true) | (((cODD @ X3)) != $true)) & (((cODD @ (cS @ c0))) = $true) & ! [X4 : $i] : ((((cEVEN @ (cS @ (cS @ X4)))) = $true) | (((cEVEN @ X4)) != $true)) & (((cEVEN @ c0)) = $true)),
% 0.20/0.26 inference(flattening,[],[f7])).
% 0.20/0.26 thf(f9,plain,(
% 0.20/0.26 ? [X0 : $i] : (((cNUMBER @ X0)) != $true) & ! [X1 : $i] : (((((cNUMBER @ X1)) = $true) | (($true != ((cODD @ X1))) & ($true != ((cEVEN @ X1))))) & (($true = ((cODD @ X1))) | ($true = ((cEVEN @ X1))) | (((cNUMBER @ X1)) != $true))) & (! [X2 : $i] : ((((cNUMBER @ (cS @ X2))) = $true) & (((cNUMBER @ X2)) = $true)) | ? [X3 : $i] : ((($true != ((cNUMBER @ (cS @ (cS @ X3))))) | ($true != ((cNUMBER @ (cS @ X3))))) & ($true = ((cNUMBER @ (cS @ X3)))) & ($true = ((cNUMBER @ X3)))) | (((cNUMBER @ (cS @ c0))) != $true) | (((cNUMBER @ c0)) != $true)) & ! [X4 : $i] : (($true = ((cODD @ (cS @ (cS @ X4))))) | ($true != ((cODD @ X4)))) & (((cODD @ (cS @ c0))) = $true) & ! [X5 : $i] : (($true = ((cEVEN @ (cS @ (cS @ X5))))) | ($true != ((cEVEN @ X5)))) & (((cEVEN @ c0)) = $true)),
% 0.20/0.26 inference(rectify,[],[f8])).
% 0.20/0.26 thf(f10,plain,(
% 0.20/0.26 ($true != ((cNUMBER @ sK0))) & ! [X1 : $i] : (((((cNUMBER @ X1)) = $true) | (($true != ((cODD @ X1))) & ($true != ((cEVEN @ X1))))) & (($true = ((cODD @ X1))) | ($true = ((cEVEN @ X1))) | (((cNUMBER @ X1)) != $true))) & (! [X2 : $i] : ((((cNUMBER @ (cS @ X2))) = $true) & (((cNUMBER @ X2)) = $true)) | ((($true != ((cNUMBER @ (cS @ (cS @ sK1))))) | ($true != ((cNUMBER @ (cS @ sK1))))) & ($true = ((cNUMBER @ (cS @ sK1)))) & ($true = ((cNUMBER @ sK1)))) | (((cNUMBER @ (cS @ c0))) != $true) | (((cNUMBER @ c0)) != $true)) & ! [X4 : $i] : (($true = ((cODD @ (cS @ (cS @ X4))))) | ($true != ((cODD @ X4)))) & (((cODD @ (cS @ c0))) = $true) & ! [X5 : $i] : (($true = ((cEVEN @ (cS @ (cS @ X5))))) | ($true != ((cEVEN @ X5)))) & (((cEVEN @ c0)) = $true)),
% 0.20/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X3,sK1)],[f9])).
% 0.20/0.26 thf(f11,plain,(
% 0.20/0.26 (((cEVEN @ c0)) = $true)),
% 0.20/0.26 inference(cnf_transformation,[],[f10])).
% 0.20/0.26 thf(f12,plain,(
% 0.20/0.26 ( ! [X5 : $i] : (($true = ((cEVEN @ (cS @ (cS @ X5))))) | ($true != ((cEVEN @ X5)))) )),
% 0.20/0.26 inference(cnf_transformation,[],[f10])).
% 0.20/0.26 thf(f13,plain,(
% 0.20/0.26 (((cODD @ (cS @ c0))) = $true)),
% 0.20/0.26 inference(cnf_transformation,[],[f10])).
% 0.20/0.26 thf(f14,plain,(
% 0.20/0.26 ( ! [X4 : $i] : (($true = ((cODD @ (cS @ (cS @ X4))))) | ($true != ((cODD @ X4)))) )),
% 0.20/0.26 inference(cnf_transformation,[],[f10])).
% 0.20/0.26 thf(f16,plain,(
% 0.20/0.26 ( ! [X2 : $i] : ((((cNUMBER @ X2)) = $true) | ($true = ((cNUMBER @ (cS @ sK1)))) | (((cNUMBER @ (cS @ c0))) != $true) | (((cNUMBER @ c0)) != $true)) )),
% 0.20/0.26 inference(cnf_transformation,[],[f10])).
% 0.20/0.26 thf(f17,plain,(
% 0.20/0.26 ( ! [X2 : $i] : ((((cNUMBER @ X2)) = $true) | ($true != ((cNUMBER @ (cS @ (cS @ sK1))))) | ($true != ((cNUMBER @ (cS @ sK1)))) | (((cNUMBER @ (cS @ c0))) != $true) | (((cNUMBER @ c0)) != $true)) )),
% 0.20/0.26 inference(cnf_transformation,[],[f10])).
% 0.20/0.26 thf(f18,plain,(
% 0.20/0.26 ( ! [X2 : $i] : ((((cNUMBER @ (cS @ X2))) = $true) | ($true = ((cNUMBER @ sK1))) | (((cNUMBER @ (cS @ c0))) != $true) | (((cNUMBER @ c0)) != $true)) )),
% 0.20/0.26 inference(cnf_transformation,[],[f10])).
% 0.20/0.26 thf(f21,plain,(
% 0.20/0.26 ( ! [X1 : $i] : (($true = ((cEVEN @ X1))) | ($true = ((cODD @ X1))) | (((cNUMBER @ X1)) != $true)) )),
% 0.20/0.26 inference(cnf_transformation,[],[f10])).
% 0.20/0.26 thf(f22,plain,(
% 0.20/0.26 ( ! [X1 : $i] : (($true != ((cEVEN @ X1))) | (((cNUMBER @ X1)) = $true)) )),
% 0.20/0.26 inference(cnf_transformation,[],[f10])).
% 0.20/0.26 thf(f23,plain,(
% 0.20/0.26 ( ! [X1 : $i] : (($true != ((cODD @ X1))) | (((cNUMBER @ X1)) = $true)) )),
% 0.20/0.26 inference(cnf_transformation,[],[f10])).
% 0.20/0.26 thf(f24,plain,(
% 0.20/0.26 ($true != ((cNUMBER @ sK0)))),
% 0.20/0.26 inference(cnf_transformation,[],[f10])).
% 0.20/0.26 thf(f26,definition,(
% 0.20/0.26 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.26 thf(f28,definition,(
% 0.20/0.26 spl2_1 <=> (((cNUMBER @ c0)) = $true)),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.20/0.26 thf(f30,plain,(
% 0.20/0.26 (((cNUMBER @ c0)) != $true) | spl2_1),
% 0.20/0.26 inference(avatar_component_clause,[],[f28])).
% 0.20/0.26 thf(f32,definition,(
% 0.20/0.26 spl2_2 <=> (((cNUMBER @ (cS @ c0))) = $true)),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.20/0.26 thf(f34,plain,(
% 0.20/0.26 (((cNUMBER @ (cS @ c0))) != $true) | spl2_2),
% 0.20/0.26 inference(avatar_component_clause,[],[f32])).
% 0.20/0.26 thf(f36,definition,(
% 0.20/0.26 spl2_3 <=> ($true = ((cNUMBER @ sK1)))),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.20/0.26 thf(f38,plain,(
% 0.20/0.26 ($true = ((cNUMBER @ sK1))) | ~spl2_3),
% 0.20/0.26 inference(avatar_component_clause,[],[f36])).
% 0.20/0.26 thf(f40,definition,(
% 0.20/0.26 spl2_4 <=> ! [X2 : $i] : (((cNUMBER @ X2)) = $true)),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition])).
% 0.20/0.26 thf(f41,plain,(
% 0.20/0.26 ( ! [X2 : $i] : ((((cNUMBER @ X2)) = $true)) ) | ~spl2_4),
% 0.20/0.26 inference(avatar_component_clause,[],[f40])).
% 0.20/0.26 thf(f44,definition,(
% 0.20/0.26 spl2_5 <=> ($true = ((cNUMBER @ (cS @ sK1))))),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition])).
% 0.20/0.26 thf(f47,plain,(
% 0.20/0.26 ~spl2_1 | ~spl2_2 | spl2_5 | spl2_4),
% 0.20/0.26 inference(avatar_split_clause,[],[f16,f40,f44,f32,f28])).
% 0.20/0.26 thf(f49,definition,(
% 0.20/0.26 spl2_6 <=> ($true = ((cNUMBER @ (cS @ (cS @ sK1)))))),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition])).
% 0.20/0.26 thf(f51,plain,(
% 0.20/0.26 ($true != ((cNUMBER @ (cS @ (cS @ sK1))))) | spl2_6),
% 0.20/0.26 inference(avatar_component_clause,[],[f49])).
% 0.20/0.26 thf(f52,plain,(
% 0.20/0.26 ~spl2_1 | ~spl2_2 | ~spl2_5 | ~spl2_6 | spl2_4),
% 0.20/0.26 inference(avatar_split_clause,[],[f17,f40,f49,f44,f32,f28])).
% 0.20/0.26 thf(f54,definition,(
% 0.20/0.26 spl2_7 <=> ! [X2 : $i] : (((cNUMBER @ (cS @ X2))) = $true)),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition])).
% 0.20/0.26 thf(f55,plain,(
% 0.20/0.26 ( ! [X2 : $i] : ((((cNUMBER @ (cS @ X2))) = $true)) ) | ~spl2_7),
% 0.20/0.26 inference(avatar_component_clause,[],[f54])).
% 0.20/0.26 thf(f56,plain,(
% 0.20/0.26 ~spl2_1 | ~spl2_2 | spl2_3 | spl2_7),
% 0.20/0.26 inference(avatar_split_clause,[],[f18,f54,f36,f32,f28])).
% 0.20/0.26 thf(f59,plain,(
% 0.20/0.26 ($true != $true) | (((cNUMBER @ c0)) = $true)),
% 0.20/0.26 inference(constrained_superposition,[],[f22,f11])).
% 0.20/0.26 thf(f60,plain,(
% 0.20/0.26 (((cNUMBER @ c0)) = $true)),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f59])).
% 0.20/0.26 thf(f61,plain,(
% 0.20/0.26 $false | spl2_1),
% 0.20/0.26 inference(forward_subsumption_resolution,[],[f60,f30])).
% 0.20/0.26 thf(f62,plain,(
% 0.20/0.26 spl2_1),
% 0.20/0.26 inference(avatar_contradiction_clause,[],[f61])).
% 0.20/0.26 thf(f63,plain,(
% 0.20/0.26 ($true != $true) | (((cNUMBER @ (cS @ c0))) = $true)),
% 0.20/0.26 inference(constrained_superposition,[],[f23,f13])).
% 0.20/0.26 thf(f64,plain,(
% 0.20/0.26 (((cNUMBER @ (cS @ c0))) = $true)),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f63])).
% 0.20/0.26 thf(f65,plain,(
% 0.20/0.26 $false | spl2_2),
% 0.20/0.26 inference(forward_subsumption_resolution,[],[f64,f34])).
% 0.20/0.26 thf(f66,plain,(
% 0.20/0.26 spl2_2),
% 0.20/0.26 inference(avatar_contradiction_clause,[],[f65])).
% 0.20/0.26 thf(f67,plain,(
% 0.20/0.26 ($true != $true) | ~spl2_4),
% 0.20/0.26 inference(constrained_superposition,[],[f24,f41])).
% 0.20/0.26 thf(f68,plain,(
% 0.20/0.26 $false | ~spl2_4),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f67])).
% 0.20/0.26 thf(f69,plain,(
% 0.20/0.26 ~spl2_4),
% 0.20/0.26 inference(avatar_contradiction_clause,[],[f68])).
% 0.20/0.26 thf(f70,plain,(
% 0.20/0.26 ($true != $true) | (spl2_6 | ~spl2_7)),
% 0.20/0.26 inference(constrained_superposition,[],[f51,f55])).
% 0.20/0.26 thf(f71,plain,(
% 0.20/0.26 $false | (spl2_6 | ~spl2_7)),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f70])).
% 0.20/0.26 thf(f72,plain,(
% 0.20/0.26 spl2_6 | ~spl2_7),
% 0.20/0.26 inference(avatar_contradiction_clause,[],[f71])).
% 0.20/0.26 thf(f74,plain,(
% 0.20/0.26 ( ! [X0 : $i] : (($true != $true) | ($true = ((cNUMBER @ (cS @ (cS @ X0))))) | (((cEVEN @ X0)) != $true)) )),
% 0.20/0.26 inference(constrained_superposition,[],[f22,f12])).
% 0.20/0.26 thf(f75,plain,(
% 0.20/0.26 ( ! [X0 : $i] : (($true = ((cNUMBER @ (cS @ (cS @ X0))))) | (((cEVEN @ X0)) != $true)) )),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f74])).
% 0.20/0.26 thf(f76,plain,(
% 0.20/0.26 ( ! [X0 : $i] : (($true != $true) | ($true = ((cNUMBER @ (cS @ (cS @ X0))))) | (((cODD @ X0)) != $true)) )),
% 0.20/0.26 inference(constrained_superposition,[],[f23,f14])).
% 0.20/0.26 thf(f77,plain,(
% 0.20/0.26 ( ! [X0 : $i] : (($true = ((cNUMBER @ (cS @ (cS @ X0))))) | (((cODD @ X0)) != $true)) )),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f76])).
% 0.20/0.26 thf(f78,plain,(
% 0.20/0.26 ($true != $true) | ($true != ((cEVEN @ sK1))) | spl2_6),
% 0.20/0.26 inference(constrained_superposition,[],[f51,f75])).
% 0.20/0.26 thf(f79,plain,(
% 0.20/0.26 ($true != ((cEVEN @ sK1))) | spl2_6),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f78])).
% 0.20/0.26 thf(f83,plain,(
% 0.20/0.26 ($true != $true) | (((cNUMBER @ (cS @ (cS @ sK1)))) = $false) | spl2_6),
% 0.20/0.26 inference(constrained_superposition,[],[f51,f26])).
% 0.20/0.26 thf(f89,plain,(
% 0.20/0.26 (((cNUMBER @ (cS @ (cS @ sK1)))) = $false) | spl2_6),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f83])).
% 0.20/0.26 thf(f110,plain,(
% 0.20/0.26 ($true != $true) | ($true = ((cODD @ sK1))) | ($true != ((cNUMBER @ sK1))) | spl2_6),
% 0.20/0.26 inference(constrained_superposition,[],[f79,f21])).
% 0.20/0.26 thf(f113,plain,(
% 0.20/0.26 ($true = ((cODD @ sK1))) | ($true != ((cNUMBER @ sK1))) | spl2_6),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f110])).
% 0.20/0.26 thf(f114,plain,(
% 0.20/0.26 ($true = ((cODD @ sK1))) | (~spl2_3 | spl2_6)),
% 0.20/0.26 inference(forward_subsumption_resolution,[],[f113,f38])).
% 0.20/0.26 thf(f151,plain,(
% 0.20/0.26 ($true = $false) | ($true != ((cODD @ sK1))) | spl2_6),
% 0.20/0.26 inference(constrained_superposition,[],[f77,f89])).
% 0.20/0.26 thf(f156,plain,(
% 0.20/0.26 ($true != ((cODD @ sK1))) | spl2_6),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f151])).
% 0.20/0.26 thf(f161,plain,(
% 0.20/0.26 $false | (~spl2_3 | spl2_6)),
% 0.20/0.26 inference(forward_subsumption_resolution,[],[f156,f114])).
% 0.20/0.26 thf(f162,plain,(
% 0.20/0.26 ~spl2_3 | spl2_6),
% 0.20/0.26 inference(avatar_contradiction_clause,[],[f161])).
% 0.20/0.26 cnf(s2, plain, ~spl2_1 | ~spl2_2 | spl2_4 | spl2_5, inference(sat_conversion,[],[f47])).
% 0.20/0.26 cnf(s3, plain, ~spl2_1 | ~spl2_2 | spl2_4 | ~spl2_5 | ~spl2_6, inference(sat_conversion,[],[f52])).
% 0.20/0.26 cnf(s4, plain, ~spl2_1 | ~spl2_2 | spl2_3 | spl2_7, inference(sat_conversion,[],[f56])).
% 0.20/0.26 cnf(s7, plain, spl2_1, inference(sat_conversion,[],[f62])).
% 0.20/0.26 cnf(s8, plain, spl2_2, inference(sat_conversion,[],[f66])).
% 0.20/0.26 cnf(s9, plain, ~spl2_4, inference(sat_conversion,[],[f69])).
% 0.20/0.26 cnf(s10, plain, spl2_6 | ~spl2_7, inference(sat_conversion,[],[f72])).
% 0.20/0.26 cnf(s13, plain, ~spl2_3 | spl2_6, inference(sat_conversion,[],[f162])).
% 0.20/0.26 cnf(s16, plain, spl2_3 | spl2_7, inference(rat,[],[s4,s8,s7])).
% 0.20/0.26 cnf(s17, plain, ~spl2_5 | ~spl2_6, inference(rat,[],[s3,s9,s8,s7])).
% 0.20/0.26 cnf(s18, plain, spl2_5, inference(rat,[],[s2,s9,s8,s7])).
% 0.20/0.26 cnf(s19, plain, ~spl2_6, inference(rat,[],[s17,s18])).
% 0.20/0.26 cnf(s20, plain, ~spl2_3, inference(rat,[],[s13,s19])).
% 0.20/0.26 cnf(s21, plain, ~spl2_7, inference(rat,[],[s10,s19])).
% 0.20/0.26 cnf(s22, plain, $false, inference(rat,[],[s16,s21,s20])).
% 0.20/0.26 thf(f163,plain,(
% 0.20/0.26 $false),
% 0.20/0.26 inference(avatar_sat_refutation,[],[s22])).
% 0.20/0.26 % SZS output end Proof for theBenchmark
% 0.20/0.26 % (3754743)------------------------------
% 0.20/0.26 % (3754743)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.26 % (3754743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.26 % (3754743)CaDiCaL version: 2.1.3
% 0.20/0.26 % (3754743)Termination reason: Refutation
% 0.20/0.26 % (3754743)Time elapsed: 0.004 s
% 0.20/0.26 % (3754743)Peak memory usage: 12 MB
% 0.20/0.26 % (3754743)Instructions burned: 12 (million)
% 0.20/0.26 % (3754732)Success in time 0.024 s
% 0.20/0.26 % Vampire exiting
%------------------------------------------------------------------------------