%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET680^3 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 08:23:48 AM UTC 2026
% Result : Theorem 0.17s 0.28s
% Output : Refutation 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET680^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n016.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 13:45:35 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.17/0.28 % (366079)Will run a generic schedule for satisfiability detection.
% 0.17/0.28 % (366095)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2717889414_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.28 % Exception at run slice level
% 0.17/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.28 % (366096)% WARNING: option uhcvi not known.
% 0.17/0.28 % (366099)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=201586430:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.28 % (366096)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=480532027:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.28 % (366097)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1243784116:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.28 % (366098)dis+10_1_sil=32000:sp=arity:random_seed=1265238294:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.28 % (366101)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1128913346:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.28 % (366099)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.17/0.28 % (366096)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.17/0.28 % (366096)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.17/0.28 % (366099) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-366079-366099"...
% 0.17/0.28 % (366100)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2248850417:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.28 % (366096) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-366079-366096"...
% 0.17/0.28 % (366098) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-366079-366098"...
% 0.17/0.28 % (366101) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-366079-366101"...
% 0.17/0.28 % (366097) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-366079-366097"...
% 0.17/0.28 % (366099)...printing done.
% 0.17/0.28 % (366096)...printing done.
% 0.17/0.28 % (366098)...printing done.
% 0.17/0.28 % (366101)...printing done.
% 0.17/0.28 % (366099)Refutation found. Thanks to Tanya!
% 0.17/0.28 % SZS status Theorem for theBenchmark
% 0.17/0.28 % SZS output start Proof for theBenchmark
% 0.17/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.17/0.28 thf(func_def_0, type, in: ($i > ($i > $o) > $o)).
% 0.17/0.28 thf(func_def_2, type, is_a: ($i > ($i > $o) > $o)).
% 0.17/0.28 thf(func_def_3, type, emptyset: ($i > $o)).
% 0.17/0.28 thf(func_def_4, type, unord_pair: ($i > $i > $i > $o)).
% 0.17/0.28 thf(func_def_5, type, singleton: ($i > $i > $o)).
% 0.17/0.28 thf(func_def_6, type, union: (($i > $o) > ($i > $o) > $i > $o)).
% 0.17/0.28 thf(func_def_7, type, excl_union: (($i > $o) > ($i > $o) > $i > $o)).
% 0.17/0.28 thf(func_def_8, type, intersection: (($i > $o) > ($i > $o) > $i > $o)).
% 0.17/0.28 thf(func_def_9, type, setminus: (($i > $o) > ($i > $o) > $i > $o)).
% 0.17/0.28 thf(func_def_10, type, complement: (($i > $o) > $i > $o)).
% 0.17/0.28 thf(func_def_11, type, disjoint: (($i > $o) > ($i > $o) > $o)).
% 0.17/0.28 thf(func_def_12, type, subset: (($i > $o) > ($i > $o) > $o)).
% 0.17/0.28 thf(func_def_13, type, meets: (($i > $o) > ($i > $o) > $o)).
% 0.17/0.28 thf(func_def_14, type, misses: (($i > $o) > ($i > $o) > $o)).
% 0.17/0.28 thf(func_def_15, type, cartesian_product: (($i > $o) > ($i > $o) > $i > $i > $o)).
% 0.17/0.28 thf(func_def_16, type, pair_rel: ($i > $i > $i > $i > $o)).
% 0.17/0.28 thf(func_def_17, type, id_rel: (($i > $o) > $i > $i > $o)).
% 0.17/0.28 thf(func_def_18, type, sub_rel: (($i > $i > $o) > ($i > $i > $o) > $o)).
% 0.17/0.28 thf(func_def_19, type, is_rel_on: (($i > $i > $o) > ($i > $o) > ($i > $o) > $o)).
% 0.17/0.28 thf(func_def_20, type, restrict_rel_domain: (($i > $i > $o) > ($i > $o) > $i > $i > $o)).
% 0.17/0.28 thf(func_def_21, type, rel_diagonal: ($i > $i > $o)).
% 0.17/0.28 thf(func_def_22, type, rel_composition: (($i > $i > $o) > ($i > $i > $o) > $i > $i > $o)).
% 0.17/0.28 thf(func_def_23, type, reflexive: (($i > $i > $o) > $o)).
% 0.17/0.28 thf(func_def_24, type, irreflexive: (($i > $i > $o) > $o)).
% 0.17/0.28 thf(func_def_25, type, symmetric: (($i > $i > $o) > $o)).
% 0.17/0.28 thf(func_def_26, type, transitive: (($i > $i > $o) > $o)).
% 0.17/0.28 thf(func_def_27, type, equiv_rel: (($i > $i > $o) > $o)).
% 0.17/0.28 thf(func_def_28, type, rel_codomain: (($i > $i > $o) > $i > $o)).
% 0.17/0.28 thf(func_def_29, type, rel_domain: (($i > $i > $o) > $i > $o)).
% 0.17/0.28 thf(func_def_30, type, rel_inverse: (($i > $i > $o) > $i > $i > $o)).
% 0.17/0.28 thf(func_def_31, type, equiv_classes: (($i > $i > $o) > ($i > $o) > $o)).
% 0.17/0.28 thf(func_def_32, type, restrict_rel_codomain: (($i > $i > $o) > ($i > $o) > $i > $i > $o)).
% 0.17/0.28 thf(func_def_33, type, rel_field: (($i > $i > $o) > $i > $o)).
% 0.17/0.28 thf(func_def_34, type, well_founded: (($i > $i > $o) > $o)).
% 0.17/0.28 thf(func_def_35, type, upwards_well_founded: (($i > $i > $o) > $o)).
% 0.17/0.28 thf(func_def_36, type, db0: !>[X0: $tType]:(X0)).
% 0.17/0.28 thf(func_def_37, type, db1: !>[X0: $tType]:(X0)).
% 0.17/0.28 thf(func_def_38, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.17/0.28 thf(func_def_41, type, vOR: ($o > $o > $o)).
% 0.17/0.28 thf(func_def_42, type, db2: !>[X0: $tType]:(X0)).
% 0.17/0.28 thf(func_def_43, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.17/0.28 thf(func_def_44, type, vAND: ($o > $o > $o)).
% 0.17/0.28 thf(func_def_45, type, vNOT: ($o > $o)).
% 0.17/0.28 thf(func_def_46, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.17/0.28 thf(func_def_47, type, vIMP: ($o > $o > $o)).
% 0.17/0.28 thf(func_def_48, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.17/0.28 thf(func_def_49, type, db3: !>[X0: $tType]:(X0)).
% 0.17/0.28 thf(func_def_50, type, db4: !>[X0: $tType]:(X0)).
% 0.17/0.28 thf(func_def_51, type, vIFF: ($o > $o > $o)).
% 0.17/0.28 thf(func_def_52, type, sK0: ($i > $i > $o)).
% 0.17/0.28 thf(func_def_53, type, sK1: ($i > $o)).
% 0.17/0.28 thf(func_def_54, type, sK2: ($i > $o)).
% 0.17/0.28 thf(f19,axiom,(
% 0.17/0.28 (is_rel_on = (^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : ($i > $o)] : (! [X3 : $i,X4 : $i] : ((X0 @ X3 @ X4) => ((X2 @ X4) & (X1 @ X3))))))),
% 0.17/0.28 file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',is_rel_on)).
% 0.17/0.28 thf(f29,axiom,(
% 0.17/0.28 (rel_domain = (^[X0 : ($i > $i > $o), X1 : $i] : (? [X2 : $i] : (X0 @ X1 @ X2))))),
% 0.17/0.28 file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',rel_domain)).
% 0.17/0.28 thf(f36,conjecture,(
% 0.17/0.28 ! [X0 : ($i > $i > $o),X1 : ($i > $o),X2 : ($i > $o)] : ((is_rel_on @ X0 @ X1 @ X2) => ! [X3 : $i] : ((X1 @ X3) => ((rel_domain @ X0 @ X3) <=> ? [X4 : $i] : ((X0 @ X3 @ X4) & (X2 @ X4)))))),
% 0.17/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm)).
% 0.17/0.28 thf(f37,negated_conjecture,(
% 0.17/0.28 ~ ! [X0 : ($i > $i > $o),X1 : ($i > $o),X2 : ($i > $o)] : ((is_rel_on @ X0 @ X1 @ X2) => ! [X3 : $i] : ((X1 @ X3) => ((rel_domain @ X0 @ X3) <=> ? [X4 : $i] : ((X0 @ X3 @ X4) & (X2 @ X4)))))),
% 0.17/0.28 inference(negated_conjecture,[status(cth)],[f36])).
% 0.17/0.28 thf(f67,plain,(
% 0.17/0.28 (is_rel_on = (^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : ($i > $o)] : (! [X3 : $i,X4 : $i] : ((X0 @ X3 @ X4) => ((X2 @ X4) & (X1 @ X3))))))),
% 0.17/0.28 inference(rectify,[],[f19])).
% 0.17/0.28 thf(f68,plain,(
% 0.17/0.28 (is_rel_on = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) => ((Y1 @ Y4) & (Y2 @ Y3)))))))))))))),
% 0.17/0.28 inference(fool_elimination,[],[f67])).
% 0.17/0.28 thf(f86,plain,(
% 0.17/0.28 (rel_domain = (^[X0 : ($i > $i > $o), X1 : $i] : (? [X2 : $i] : (X0 @ X1 @ X2))))),
% 0.17/0.28 inference(rectify,[],[f29])).
% 0.17/0.28 thf(f87,plain,(
% 0.17/0.28 (rel_domain = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.17/0.28 inference(fool_elimination,[],[f86])).
% 0.17/0.28 thf(f99,plain,(
% 0.17/0.28 ~ ! [X0 : ($i > $i > $o),X1 : ($i > $o),X2 : ($i > $o)] : ((is_rel_on @ X0 @ X1 @ X2) => ! [X3 : $i] : ((X1 @ X3) => ((rel_domain @ X0 @ X3) <=> ? [X4 : $i] : ((X0 @ X3 @ X4) & (X2 @ X4)))))),
% 0.17/0.28 inference(rectify,[],[f37])).
% 0.17/0.28 thf(f100,plain,(
% 0.17/0.28 ~ ! [X0 : ($i > $i > $o),X1 : ($i > $o),X2 : ($i > $o)] : ((((is_rel_on @ X0 @ X1 @ X2)) = $true) => ! [X3 : $i] : ((((X1 @ X3)) = $true) => ((((rel_domain @ X0 @ X3)) = $true) <=> ? [X4 : $i] : ((((X0 @ X3 @ X4)) = $true) & (((X2 @ X4)) = $true)))))),
% 0.17/0.28 inference(fool_elimination,[],[f99])).
% 0.17/0.28 thf(f101,plain,(
% 0.17/0.28 ? [X0 : ($i > $i > $o),X1 : ($i > $o),X2 : ($i > $o)] : (? [X3 : $i] : (((((rel_domain @ X0 @ X3)) = $true) <~> ? [X4 : $i] : ((((X0 @ X3 @ X4)) = $true) & (((X2 @ X4)) = $true))) & (((X1 @ X3)) = $true)) & (((is_rel_on @ X0 @ X1 @ X2)) = $true))),
% 0.17/0.28 inference(ennf_transformation,[],[f100])).
% 0.17/0.28 thf(f102,plain,(
% 0.17/0.28 ? [X0 : ($i > $i > $o),X1 : ($i > $o),X2 : ($i > $o)] : (? [X3 : $i] : (((! [X4 : $i] : ((((X0 @ X3 @ X4)) != $true) | (((X2 @ X4)) != $true)) | (((rel_domain @ X0 @ X3)) != $true)) & (? [X4 : $i] : ((((X0 @ X3 @ X4)) = $true) & (((X2 @ X4)) = $true)) | (((rel_domain @ X0 @ X3)) = $true))) & (((X1 @ X3)) = $true)) & (((is_rel_on @ X0 @ X1 @ X2)) = $true))),
% 0.17/0.28 inference(nnf_transformation,[],[f101])).
% 0.17/0.28 thf(f103,plain,(
% 0.17/0.28 ? [X0 : ($i > $i > $o),X1 : ($i > $o),X2 : ($i > $o)] : (? [X3 : $i] : ((! [X4 : $i] : ((((X0 @ X3 @ X4)) != $true) | (((X2 @ X4)) != $true)) | (((rel_domain @ X0 @ X3)) != $true)) & (? [X4 : $i] : ((((X0 @ X3 @ X4)) = $true) & (((X2 @ X4)) = $true)) | (((rel_domain @ X0 @ X3)) = $true)) & (((X1 @ X3)) = $true)) & (((is_rel_on @ X0 @ X1 @ X2)) = $true))),
% 0.17/0.28 inference(flattening,[],[f102])).
% 0.17/0.28 thf(f104,plain,(
% 0.17/0.28 ? [X0 : ($i > $i > $o),X1 : ($i > $o),X2 : ($i > $o)] : (? [X3 : $i] : ((! [X4 : $i] : ((((X0 @ X3 @ X4)) != $true) | (((X2 @ X4)) != $true)) | (((rel_domain @ X0 @ X3)) != $true)) & (? [X5 : $i] : (($true = ((X0 @ X3 @ X5))) & ($true = ((X2 @ X5)))) | (((rel_domain @ X0 @ X3)) = $true)) & (((X1 @ X3)) = $true)) & (((is_rel_on @ X0 @ X1 @ X2)) = $true))),
% 0.17/0.28 inference(rectify,[],[f103])).
% 0.17/0.28 thf(f105,plain,(
% 0.17/0.28 ((! [X4 : $i] : (($true != ((sK0 @ sK3 @ X4))) | ($true != ((sK2 @ X4)))) | ($true != ((rel_domain @ sK0 @ sK3)))) & ((($true = ((sK0 @ sK3 @ sK4))) & ($true = ((sK2 @ sK4)))) | ($true = ((rel_domain @ sK0 @ sK3)))) & ($true = ((sK1 @ sK3)))) & ($true = ((is_rel_on @ sK0 @ sK1 @ sK2)))),
% 0.17/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X5,sK4)],[f104])).
% 0.17/0.28 thf(f124,plain,(
% 0.17/0.28 (is_rel_on = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) => ((Y1 @ Y4) & (Y2 @ Y3)))))))))))))),
% 0.17/0.28 inference(cnf_transformation,[],[f68])).
% 0.17/0.28 thf(f134,plain,(
% 0.17/0.28 (rel_domain = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.17/0.28 inference(cnf_transformation,[],[f87])).
% 0.17/0.28 thf(f141,plain,(
% 0.17/0.28 ($true = ((is_rel_on @ sK0 @ sK1 @ sK2)))),
% 0.17/0.28 inference(cnf_transformation,[],[f105])).
% 0.17/0.28 thf(f144,plain,(
% 0.17/0.28 ($true = ((sK0 @ sK3 @ sK4))) | ($true = ((rel_domain @ sK0 @ sK3)))),
% 0.17/0.28 inference(cnf_transformation,[],[f105])).
% 0.17/0.28 thf(f145,plain,(
% 0.17/0.28 ( ! [X4 : $i] : (($true != ((sK0 @ sK3 @ X4))) | ($true != ((sK2 @ X4))) | ($true != ((rel_domain @ sK0 @ sK3)))) )),
% 0.17/0.28 inference(cnf_transformation,[],[f105])).
% 0.17/0.28 thf(f147,definition,(
% 0.17/0.28 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.17/0.28 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.17/0.28 thf(f151,plain,(
% 0.17/0.28 ( ! [X4 : $i] : (($true != ((sK0 @ sK3 @ X4))) | ($true != ((sK2 @ X4))) | ($true != (((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))) @ sK0 @ sK3)))) )),
% 0.17/0.28 inference(definition_unfolding,[],[f145,f134])).
% 0.17/0.28 thf(f152,plain,(
% 0.17/0.28 ($true = ((sK0 @ sK3 @ sK4))) | ($true = (((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))) @ sK0 @ sK3)))),
% 0.17/0.28 inference(definition_unfolding,[],[f144,f134])).
% 0.17/0.28 thf(f154,plain,(
% 0.17/0.28 ($true = (((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) => ((Y1 @ Y4) & (Y2 @ Y3)))))))))))) @ sK0 @ sK1 @ sK2)))),
% 0.17/0.28 inference(definition_unfolding,[],[f141,f124])).
% 0.17/0.28 thf(f155,plain,(
% 0.17/0.28 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1 @ Y0) => ((sK1 @ Y1) & (sK2 @ Y0)))))))))),
% 0.17/0.28 inference(beta-eta_normalization,[],[f154])).
% 0.17/0.28 thf(f156,plain,(
% 0.17/0.28 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1 @ Y0) => ((sK1 @ Y1) & (sK2 @ Y0)))))) @ X1)))) )),
% 0.17/0.28 inference(pi_proxy_clausification,[],[f155])).
% 0.17/0.28 thf(f157,plain,(
% 0.17/0.28 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0 @ X1) => ((sK1 @ Y0) & (sK2 @ X1)))))))) )),
% 0.17/0.28 inference(beta-eta_normalization,[],[f156])).
% 0.17/0.28 thf(f158,plain,(
% 0.17/0.28 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((sK0 @ Y0 @ X1) => ((sK1 @ Y0) & (sK2 @ X1)))) @ X2)))) )),
% 0.17/0.28 inference(pi_proxy_clausification,[],[f157])).
% 0.17/0.28 thf(f159,plain,(
% 0.17/0.28 ( ! [X2 : $i,X1 : $i] : (($true = (((sK0 @ X2 @ X1) => ((sK1 @ X2) & (sK2 @ X1)))))) )),
% 0.17/0.28 inference(beta-eta_normalization,[],[f158])).
% 0.17/0.28 thf(f160,plain,(
% 0.17/0.28 ( ! [X2 : $i,X1 : $i] : (($false = ((sK0 @ X2 @ X1))) | ($true = (((sK1 @ X2) & (sK2 @ X1))))) )),
% 0.17/0.28 inference(imp_proxy_clausification,[],[f159])).
% 0.17/0.28 thf(f161,plain,(
% 0.17/0.28 ( ! [X2 : $i,X1 : $i] : (($false = ((sK0 @ X2 @ X1))) | ($true = ((sK2 @ X1)))) )),
% 0.17/0.28 inference(and_proxy_clausification,[],[f160])).
% 0.17/0.28 thf(f165,plain,(
% 0.17/0.28 ($true = ((sK0 @ sK3 @ sK4))) | ($true = ((?? @ $i @ (sK0 @ sK3))))),
% 0.17/0.28 inference(beta-eta_normalization,[],[f152])).
% 0.17/0.28 thf(f166,plain,(
% 0.17/0.28 ($true = ((sK0 @ sK3 @ sK4))) | ($true = ((sK0 @ sK3 @ sK6)))),
% 0.17/0.28 inference(sigma_proxy_clausification,[],[f165])).
% 0.17/0.28 thf(f167,plain,(
% 0.17/0.28 ( ! [X4 : $i] : (($true != ((sK0 @ sK3 @ X4))) | ($true != ((sK2 @ X4))) | ($true != ((?? @ $i @ (sK0 @ sK3))))) )),
% 0.17/0.28 inference(beta-eta_normalization,[],[f151])).
% 0.17/0.28 thf(f168,plain,(
% 0.17/0.28 ( ! [X4 : $i,X5 : $i] : (($true != ((sK0 @ sK3 @ X4))) | ($true != ((sK2 @ X4))) | ($false = ((sK0 @ sK3 @ X5)))) )),
% 0.17/0.28 inference(pi_proxy_clausification,[],[f167])).
% 0.17/0.28 thf(f179,definition,(
% 0.17/0.28 spl7_3 <=> ($true = ((sK0 @ sK3 @ sK6)))),
% 0.17/0.28 introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition])).
% 0.17/0.28 thf(f181,plain,(
% 0.17/0.28 ($true = ((sK0 @ sK3 @ sK6))) | ~spl7_3),
% 0.17/0.28 inference(avatar_component_clause,[],[f179])).
% 0.17/0.28 thf(f183,definition,(
% 0.17/0.28 spl7_4 <=> ($true = ((sK0 @ sK3 @ sK4)))),
% 0.17/0.28 introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition])).
% 0.17/0.28 thf(f185,plain,(
% 0.17/0.28 ($true = ((sK0 @ sK3 @ sK4))) | ~spl7_4),
% 0.17/0.28 inference(avatar_component_clause,[],[f183])).
% 0.17/0.28 thf(f186,plain,(
% 0.17/0.28 spl7_3 | spl7_4),
% 0.17/0.28 inference(avatar_split_clause,[],[f166,f183,f179])).
% 0.17/0.28 thf(f188,definition,(
% 0.17/0.28 spl7_5 <=> ! [X5 : $i] : ($false = ((sK0 @ sK3 @ X5)))),
% 0.17/0.28 introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition])).
% 0.17/0.28 thf(f189,plain,(
% 0.17/0.28 ( ! [X5 : $i] : (($false = ((sK0 @ sK3 @ X5)))) ) | ~spl7_5),
% 0.17/0.28 inference(avatar_component_clause,[],[f188])).
% 0.17/0.28 thf(f191,definition,(
% 0.17/0.28 spl7_6 <=> ! [X4 : $i] : (($true != ((sK0 @ sK3 @ X4))) | ($true != ((sK2 @ X4))))),
% 0.17/0.28 introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition])).
% 0.17/0.28 thf(f192,plain,(
% 0.17/0.28 ( ! [X4 : $i] : (($true != ((sK0 @ sK3 @ X4))) | ($true != ((sK2 @ X4)))) ) | ~spl7_6),
% 0.17/0.28 inference(avatar_component_clause,[],[f191])).
% 0.17/0.28 thf(f193,plain,(
% 0.17/0.28 spl7_5 | spl7_6),
% 0.17/0.28 inference(avatar_split_clause,[],[f168,f191,f188])).
% 0.17/0.28 thf(f194,plain,(
% 0.17/0.28 ($false = $true) | (~spl7_3 | ~spl7_5)),
% 0.17/0.28 inference(constrained_superposition,[],[f189,f181])).
% 0.17/0.28 thf(f198,plain,(
% 0.17/0.28 $false | (~spl7_3 | ~spl7_5)),
% 0.17/0.28 inference(trivial_inequality_removal,[],[f194])).
% 0.17/0.28 thf(f199,plain,(
% 0.17/0.28 ~spl7_3 | ~spl7_5),
% 0.17/0.28 inference(avatar_contradiction_clause,[],[f198])).
% 0.17/0.28 thf(f205,plain,(
% 0.17/0.28 ( ! [X0 : $i] : (($true != $true) | ($true != ((sK2 @ X0))) | ($false = ((sK0 @ sK3 @ X0)))) ) | ~spl7_6),
% 0.17/0.28 inference(constrained_superposition,[],[f192,f147])).
% 0.17/0.28 thf(f207,plain,(
% 0.17/0.28 ( ! [X0 : $i] : (($true != ((sK2 @ X0))) | ($false = ((sK0 @ sK3 @ X0)))) ) | ~spl7_6),
% 0.17/0.28 inference(trivial_inequality_removal,[],[f205])).
% 0.17/0.28 thf(f213,plain,(
% 0.17/0.28 ( ! [X0 : $i] : (($false = ((sK0 @ sK3 @ X0)))) ) | ~spl7_6),
% 0.17/0.28 inference(forward_subsumption_resolution,[],[f207,f161])).
% 0.17/0.28 thf(f214,plain,(
% 0.17/0.28 spl7_5 | ~spl7_6),
% 0.17/0.28 inference(avatar_split_clause,[],[f213,f191,f188])).
% 0.17/0.28 thf(f225,plain,(
% 0.17/0.28 ($false = $true) | (~spl7_4 | ~spl7_5)),
% 0.17/0.28 inference(constrained_superposition,[],[f189,f185])).
% 0.17/0.28 thf(f232,plain,(
% 0.17/0.28 $false | (~spl7_4 | ~spl7_5)),
% 0.17/0.28 inference(trivial_inequality_removal,[],[f225])).
% 0.17/0.28 thf(f233,plain,(
% 0.17/0.28 ~spl7_4 | ~spl7_5),
% 0.17/0.28 inference(avatar_contradiction_clause,[],[f232])).
% 0.17/0.28 cnf(s2, plain, spl7_3 | spl7_4, inference(sat_conversion,[],[f186])).
% 0.17/0.28 cnf(s3, plain, spl7_5 | spl7_6, inference(sat_conversion,[],[f193])).
% 0.17/0.28 cnf(s5, plain, ~spl7_3 | ~spl7_5, inference(sat_conversion,[],[f199])).
% 0.17/0.28 cnf(s6, plain, spl7_5 | ~spl7_6, inference(sat_conversion,[],[f214])).
% 0.17/0.28 cnf(s10, plain, ~spl7_4 | ~spl7_5, inference(sat_conversion,[],[f233])).
% 0.17/0.28 cnf(s12, plain, spl7_5, inference(rat,[],[s3,s6])).
% 0.17/0.28 cnf(s13, plain, ~spl7_4, inference(rat,[],[s10,s12])).
% 0.17/0.28 cnf(s15, plain, ~spl7_3, inference(rat,[],[s5,s12])).
% 0.17/0.28 cnf(s16, plain, $false, inference(rat,[],[s2,s13,s15])).
% 0.17/0.28 thf(f234,plain,(
% 0.17/0.28 $false),
% 0.17/0.28 inference(avatar_sat_refutation,[],[s16])).
% 0.17/0.28 % SZS output end Proof for theBenchmark
% 0.17/0.28 % (366099)------------------------------
% 0.17/0.28 % (366099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.28 % (366099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.28 % (366099)CaDiCaL version: 2.1.3
% 0.17/0.28 % (366099)Termination reason: Refutation
% 0.17/0.28 % (366099)Time elapsed: 0.008 s
% 0.17/0.28 % (366099)Peak memory usage: 13 MB
% 0.17/0.28 % (366099)Instructions burned: 13 (million)
% 0.17/0.28 % (366079)Success in time 0.055 s
% 0.17/0.28 % Vampire exiting
%------------------------------------------------------------------------------