0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s 0.14/0.34 % Computer : n024.cluster.edu 0.14/0.34 % Model : x86_64 x86_64 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.34 % Memory : 8042.1875MB 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.34 % CPULimit : 960 0.14/0.34 % WCLimit : 120 0.14/0.34 % DateTime : Tue Aug 9 04:52:52 EDT 2022 0.14/0.34 % CPUTime : 0.14/0.36 This is a FOF_ problem 0.14/0.36 Running vampire --ignore_missing on --mode casc -t 960 /export/starexec/sandbox2/benchmark/theBenchmark.p 0.14/0.36 % (26337)Running in auto input_syntax mode. Trying TPTP 0.61/0.80 % (26339)dis+10_16_awrs=decay:awrsf=256:afr=on:afp=40000:afq=2.0:amm=off:bsr=on:cond=on:er=known:gsp=on:irw=on:lma=on:nm=6:newcnf=on:nwc=3:sas=z3:sd=4:ss=axioms:s2a=on:sp=frequency:updr=off_8 on theBenchmark 0.61/0.83 % (26340)dis+11_3_av=off:fsr=off:lcm=predicate:lma=on:nm=4:nwc=1:sd=3:ss=axioms:st=1.2:sos=on:updr=off_4 on theBenchmark 0.61/0.83 % (26342)dis+11_2:1_add=large:afp=1000:afq=1.2:amm=sco:anc=none:cond=on:gs=on:gsem=off:nm=16:newcnf=on:nwc=1:sas=z3:sd=1:ss=axioms:st=1.2:sos=on:sp=reverse_arity:updr=off_5 on theBenchmark 0.61/0.83 % (26343)dis+1002_8:1_av=off:br=off:cond=on:irw=on:lma=on:nm=32:nwc=1:sp=occurrence:urr=on_89 on theBenchmark 0.61/0.83 % (26344)dis-1_2:3_av=off:cond=on:fsr=off:irw=on:lma=on:nwc=3:sd=3:ss=axioms:st=3.0:sp=occurrence:updr=off_9 on theBenchmark 0.61/0.83 % (26341)dis+1_5:1_aac=none:afr=on:afp=100000:afq=1.4:amm=sco:anc=none:br=off:gsp=on:gs=on:gsem=on:lcm=reverse:nm=6:nwc=1:nicw=on:sas=z3:sos=on:urr=on_1 on theBenchmark 0.61/0.84 % (26345)dis+10_3_add=off:afp=40000:afq=1.0:amm=sco:anc=none:er=filter:gs=on:gsem=off:irw=on:lma=on:nm=4:nwc=1.3:sp=reverse_arity:updr=off_2 on theBenchmark 0.61/0.85 % (26346)lrs+1_8:1_av=off:cond=fast:fde=unused:lcm=predicate:nm=16:nwc=10:stl=60:sp=occurrence:urr=ec_only_3 on theBenchmark 0.62/0.91 % (26339)First to succeed. 0.62/0.92 % (26339)Refutation found. Thanks to Tanya! 0.62/0.92 % SZS status Theorem for theBenchmark 0.62/0.92 % SZS output start Proof for theBenchmark 0.62/0.92 fof(f7272,plain,( 0.62/0.92 $false), 0.62/0.92 inference(avatar_smt_refutation,[],[f6641,f6646,f6651,f6656,f6661,f6666,f6671,f6676,f6681,f6686,f6691,f6696,f6701,f6706,f6711,f6716,f6721,f6726,f6731,f6736,f6737,f6746,f6751,f6752,f6757,f6762,f6767,f6772,f6777,f6782,f6783,f6788,f6793,f6798,f6803,f6808,f6809,f6814,f6819,f6824,f6829,f6834,f6839,f6845,f6857,f6868,f6873,f6881,f6886,f6897,f6902,f6909,f6917,f6922,f6931,f6932,f6933,f6941,f6946,f6959,f6960,f6972,f6977,f6994,f6995,f7007,f7012,f7042,f7047,f7067,f7125,f7130,f7134,f7153,f7158,f7162,f7175,f7180,f7184,f7210,f7215,f7222,f7232,f7237,f7244,f7258,f7263,f7271])). 0.62/0.92 fof(f7271,plain,( 0.62/0.92 spl36_1 | ~spl36_83 | ~spl36_84), 0.62/0.92 inference(avatar_contradiction_clause,[],[f7270])). 0.62/0.92 fof(f7270,plain,( 0.62/0.92 $false | (spl36_1 | ~spl36_83 | ~spl36_84)), 0.62/0.92 inference(subsumption_resolution,[],[f7268,f6640])). 0.62/0.92 fof(f6640,plain,( 0.62/0.92 ~c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts) | spl36_1), 0.62/0.92 inference(avatar_component_clause,[],[f6638])). 0.62/0.92 fof(f6638,plain,( 0.62/0.92 spl36_1 <=> c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_1])])). 0.62/0.92 fof(f7268,plain,( 0.62/0.92 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts) | (~spl36_83 | ~spl36_84)), 0.62/0.92 inference(resolution,[],[f7265,f7262])). 0.62/0.92 fof(f7262,plain,( 0.62/0.92 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_G) | ~spl36_84), 0.62/0.92 inference(avatar_component_clause,[],[f7260])). 0.62/0.92 fof(f7260,plain,( 0.62/0.92 spl36_84 <=> c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_G)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_84])])). 0.62/0.92 fof(f7265,plain,( 0.62/0.92 ( ! [X0] : (~c_Hoare__Mirabelle_Ohoare__derivs(t_a,X0,v_G) | c_Hoare__Mirabelle_Ohoare__derivs(t_a,X0,v_ts)) ) | ~spl36_83), 0.62/0.92 inference(resolution,[],[f7257,f5890])). 0.62/0.92 fof(f5890,plain,( 0.62/0.92 ( ! [X2,X3,X0,X1] : (~c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X1) | ~c_Hoare__Mirabelle_Ohoare__derivs(X3,X0,X2) | c_Hoare__Mirabelle_Ohoare__derivs(X3,X0,X1)) )), 0.62/0.92 inference(cnf_transformation,[],[f5605])). 0.62/0.92 fof(f5605,plain,( 0.62/0.92 ! [X0,X1,X2,X3] : (c_Hoare__Mirabelle_Ohoare__derivs(X3,X0,X1) | ~c_Hoare__Mirabelle_Ohoare__derivs(X3,X0,X2) | ~c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X1))), 0.62/0.92 inference(flattening,[],[f5604])). 0.62/0.92 fof(f5604,plain,( 0.62/0.92 ! [X0,X1,X2,X3] : ((c_Hoare__Mirabelle_Ohoare__derivs(X3,X0,X1) | ~c_Hoare__Mirabelle_Ohoare__derivs(X3,X0,X2)) | ~c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X1))), 0.62/0.92 inference(ennf_transformation,[],[f5233])). 0.62/0.92 fof(f5233,plain,( 0.62/0.92 ! [X0,X1,X2,X3] : (c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X1) => (c_Hoare__Mirabelle_Ohoare__derivs(X3,X0,X2) => c_Hoare__Mirabelle_Ohoare__derivs(X3,X0,X1)))), 0.62/0.92 inference(rectify,[],[f4766])). 0.62/0.92 fof(f4766,axiom,( 0.62/0.92 ! [X110,X108,X270,X9] : (c_Hoare__Mirabelle_Ohoare__derivs(X9,X270,X108) => (c_Hoare__Mirabelle_Ohoare__derivs(X9,X110,X270) => c_Hoare__Mirabelle_Ohoare__derivs(X9,X110,X108)))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cut)). 0.62/0.92 fof(f7257,plain,( 0.62/0.92 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,v_ts) | ~spl36_83), 0.62/0.92 inference(avatar_component_clause,[],[f7255])). 0.62/0.92 fof(f7255,plain,( 0.62/0.92 spl36_83 <=> c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,v_ts)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_83])])). 0.62/0.92 fof(f7263,plain,( 0.62/0.92 spl36_84 | ~spl36_3), 0.62/0.92 inference(avatar_split_clause,[],[f7251,f6648,f7260])). 0.62/0.92 fof(f6648,plain,( 0.62/0.92 spl36_3 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),v_Ga))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_3])])). 0.62/0.92 fof(f7251,plain,( 0.62/0.92 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_G) | ~spl36_3), 0.62/0.92 inference(resolution,[],[f5891,f6650])). 0.62/0.92 fof(f6650,plain,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),v_Ga)) | ~spl36_3), 0.62/0.92 inference(avatar_component_clause,[],[f6648])). 0.62/0.92 fof(f5891,plain,( 0.62/0.92 ( ! [X2,X0,X1] : (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_HOL_Obool)),X1),X0)) | c_Hoare__Mirabelle_Ohoare__derivs(X2,X0,X1)) )), 0.62/0.92 inference(cnf_transformation,[],[f5606])). 0.62/0.92 fof(f5606,plain,( 0.62/0.92 ! [X0,X1,X2] : (c_Hoare__Mirabelle_Ohoare__derivs(X2,X0,X1) | ~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_HOL_Obool)),X1),X0)))), 0.62/0.92 inference(ennf_transformation,[],[f5234])). 0.62/0.92 fof(f5234,plain,( 0.62/0.92 ! [X0,X1,X2] : (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_HOL_Obool)),X1),X0)) => c_Hoare__Mirabelle_Ohoare__derivs(X2,X0,X1))), 0.62/0.92 inference(rectify,[],[f3233])). 0.62/0.92 fof(f3233,axiom,( 0.62/0.92 ! [X110,X108,X9] : (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X9),tc_HOL_Obool)),X108),X110)) => c_Hoare__Mirabelle_Ohoare__derivs(X9,X110,X108))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_asm)). 0.62/0.92 fof(f7258,plain,( 0.62/0.92 spl36_83 | ~spl36_2), 0.62/0.92 inference(avatar_split_clause,[],[f7250,f6643,f7255])). 0.62/0.92 fof(f6643,plain,( 0.62/0.92 spl36_2 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_G))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_2])])). 0.62/0.92 fof(f7250,plain,( 0.62/0.92 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,v_ts) | ~spl36_2), 0.62/0.92 inference(resolution,[],[f5891,f6645])). 0.62/0.92 fof(f6645,plain,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_G)) | ~spl36_2), 0.62/0.92 inference(avatar_component_clause,[],[f6643])). 0.62/0.92 fof(f7244,plain,( 0.62/0.92 spl36_82 | ~spl36_23 | ~spl36_38), 0.62/0.92 inference(avatar_split_clause,[],[f7239,f6826,f6748,f7241])). 0.62/0.92 fof(f7241,plain,( 0.62/0.92 spl36_82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_82])])). 0.62/0.92 fof(f6748,plain,( 0.62/0.92 spl36_23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_23])])). 0.62/0.92 fof(f6826,plain,( 0.62/0.92 spl36_38 <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_38])])). 0.62/0.92 fof(f7239,plain,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))) | (~spl36_23 | ~spl36_38)), 0.62/0.92 inference(forward_demodulation,[],[f6750,f6828])). 0.62/0.92 fof(f6828,plain,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls | ~spl36_38), 0.62/0.92 inference(avatar_component_clause,[],[f6826])). 0.62/0.92 fof(f6750,plain,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) | ~spl36_23), 0.62/0.92 inference(avatar_component_clause,[],[f6748])). 0.62/0.92 fof(f7237,plain,( 0.62/0.92 spl36_81 | ~spl36_79), 0.62/0.92 inference(avatar_split_clause,[],[f7225,f7219,f7234])). 0.62/0.92 fof(f7234,plain,( 0.62/0.92 spl36_81 <=> sP33(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_81])])). 0.62/0.92 fof(f7219,plain,( 0.62/0.92 spl36_79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_79])])). 0.62/0.92 fof(f7225,plain,( 0.62/0.92 sP33(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls)) | ~spl36_79), 0.62/0.92 inference(resolution,[],[f7221,f6628])). 0.62/0.92 fof(f6628,plain,( 0.62/0.92 ( ! [X3,X0] : (~hBOOL(hAPP(X0,X3)) | sP33(X0)) )), 0.62/0.92 inference(cnf_transformation,[],[f6628_D])). 0.62/0.92 fof(f6628_D,plain,( 0.62/0.92 ( ! [X0] : (( ! [X3] : ~hBOOL(hAPP(X0,X3)) ) <=> ~sP33(X0)) )), 0.62/0.92 introduced(general_splitting_component_introduction,[new_symbols(naming,[sP33])])). 0.62/0.92 fof(f7221,plain,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))) | ~spl36_79), 0.62/0.92 inference(avatar_component_clause,[],[f7219])). 0.62/0.92 fof(f7232,plain,( 0.62/0.92 spl36_80 | ~spl36_79), 0.62/0.92 inference(avatar_split_clause,[],[f7224,f7219,f7229])). 0.62/0.92 fof(f7229,plain,( 0.62/0.92 spl36_80 <=> sP34(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_80])])). 0.62/0.92 fof(f7224,plain,( 0.62/0.92 sP34(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls)) | ~spl36_79), 0.62/0.92 inference(resolution,[],[f7221,f6630])). 0.62/0.92 fof(f6630,plain,( 0.62/0.92 ( ! [X3,X0] : (~hBOOL(hAPP(X0,X3)) | sP34(X0)) )), 0.62/0.92 inference(cnf_transformation,[],[f6630_D])). 0.62/0.92 fof(f6630_D,plain,( 0.62/0.92 ( ! [X0] : (( ! [X3] : ~hBOOL(hAPP(X0,X3)) ) <=> ~sP34(X0)) )), 0.62/0.92 introduced(general_splitting_component_introduction,[new_symbols(naming,[sP34])])). 0.62/0.92 fof(f7222,plain,( 0.62/0.92 spl36_79 | ~spl36_22 | ~spl36_38), 0.62/0.92 inference(avatar_split_clause,[],[f7217,f6826,f6743,f7219])). 0.62/0.92 fof(f6743,plain,( 0.62/0.92 spl36_22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_22])])). 0.62/0.92 fof(f7217,plain,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))) | (~spl36_22 | ~spl36_38)), 0.62/0.92 inference(forward_demodulation,[],[f6744,f6828])). 0.62/0.92 fof(f6744,plain,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) | ~spl36_22), 0.62/0.92 inference(avatar_component_clause,[],[f6743])). 0.62/0.92 fof(f7215,plain,( 0.62/0.92 ~spl36_78 | ~spl36_3), 0.62/0.92 inference(avatar_split_clause,[],[f7203,f6648,f7212])). 0.62/0.92 fof(f7212,plain,( 0.62/0.92 spl36_78 <=> sP30(v_Ga,v_G)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_78])])). 0.62/0.92 fof(f7203,plain,( 0.62/0.92 ~sP30(v_Ga,v_G) | ~spl36_3), 0.62/0.92 inference(resolution,[],[f6623,f6650])). 0.62/0.92 fof(f6623,plain,( 0.62/0.92 ( ! [X3,X0,X1] : (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X0)) | ~sP30(X0,X3)) )), 0.62/0.92 inference(general_splitting,[],[f5898,f6622_D])). 0.62/0.92 fof(f6622,plain,( 0.62/0.92 ( ! [X2,X3,X0] : (~hBOOL(hAPP(X3,X2)) | hBOOL(hAPP(X0,X2)) | sP30(X0,X3)) )), 0.62/0.92 inference(cnf_transformation,[],[f6622_D])). 0.62/0.92 fof(f6622_D,plain,( 0.62/0.92 ( ! [X3,X0] : (( ! [X2] : (~hBOOL(hAPP(X3,X2)) | hBOOL(hAPP(X0,X2))) ) <=> ~sP30(X0,X3)) )), 0.62/0.92 introduced(general_splitting_component_introduction,[new_symbols(naming,[sP30])])). 0.62/0.92 fof(f5898,plain,( 0.62/0.92 ( ! [X2,X3,X0,X1] : (~hBOOL(hAPP(X3,X2)) | ~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X0)) | hBOOL(hAPP(X0,X2))) )), 0.62/0.92 inference(cnf_transformation,[],[f5616])). 0.62/0.92 fof(f5616,plain,( 0.62/0.92 ! [X0,X1,X2,X3] : (hBOOL(hAPP(X0,X2)) | ~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X0)) | ~hBOOL(hAPP(X3,X2)))), 0.62/0.92 inference(flattening,[],[f5615])). 0.62/0.92 fof(f5615,plain,( 0.62/0.92 ! [X0,X1,X2,X3] : ((hBOOL(hAPP(X0,X2)) | ~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X0))) | ~hBOOL(hAPP(X3,X2)))), 0.62/0.92 inference(ennf_transformation,[],[f5241])). 0.62/0.92 fof(f5241,plain,( 0.62/0.92 ! [X0,X1,X2,X3] : (hBOOL(hAPP(X3,X2)) => (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X0)) => hBOOL(hAPP(X0,X2))))), 0.62/0.92 inference(rectify,[],[f62])). 0.62/0.92 fof(f62,axiom,( 0.62/0.92 ! [X54,X9,X15,X17] : (hBOOL(hAPP(X17,X15)) => (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool)),X17),X54)) => hBOOL(hAPP(X54,X15))))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate1D)). 0.62/0.92 fof(f7210,plain,( 0.62/0.92 ~spl36_77 | ~spl36_2), 0.62/0.92 inference(avatar_split_clause,[],[f7202,f6643,f7207])). 0.62/0.92 fof(f7207,plain,( 0.62/0.92 spl36_77 <=> sP30(v_G,v_ts)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_77])])). 0.62/0.92 fof(f7202,plain,( 0.62/0.92 ~sP30(v_G,v_ts) | ~spl36_2), 0.62/0.92 inference(resolution,[],[f6623,f6645])). 0.62/0.92 fof(f7184,plain,( 0.62/0.92 ~spl36_75 | spl36_76), 0.62/0.92 inference(avatar_split_clause,[],[f7170,f7182,f7177])). 0.62/0.92 fof(f7177,plain,( 0.62/0.92 spl36_75 <=> sP33(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_75])])). 0.62/0.92 fof(f7182,plain,( 0.62/0.92 spl36_76 <=> ! [X5] : hBOOL(sK21(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X5))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_76])])). 0.62/0.92 fof(f7170,plain,( 0.62/0.92 ( ! [X5] : (hBOOL(sK21(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X5)) | ~sP33(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )), 0.62/0.92 inference(superposition,[],[f6629,f6386])). 0.62/0.92 fof(f6386,plain,( 0.62/0.92 ( ! [X0] : (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0) )), 0.62/0.92 inference(cnf_transformation,[],[f5547])). 0.62/0.92 fof(f5547,plain,( 0.62/0.92 ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0), 0.62/0.92 inference(rectify,[],[f4454])). 0.62/0.92 fof(f4454,axiom,( 0.62/0.92 ! [X28] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X28) = X28), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1)). 0.62/0.92 fof(f6629,plain,( 0.62/0.92 ( ! [X0,X1] : (hBOOL(hAPP(X0,sK21(X0,X1))) | ~sP33(X0)) )), 0.62/0.92 inference(general_splitting,[],[f6326,f6628_D])). 0.62/0.92 fof(f6326,plain,( 0.62/0.92 ( ! [X3,X0,X1] : (~hBOOL(hAPP(X0,X3)) | hBOOL(hAPP(X0,sK21(X0,X1)))) )), 0.62/0.92 inference(cnf_transformation,[],[f5507])). 0.62/0.92 fof(f5507,plain,( 0.62/0.92 ! [X0,X1] : (? [X2] : (hBOOL(hAPP(X0,X2)) & hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))) <=> ? [X3] : hBOOL(hAPP(X0,X3)))), 0.62/0.92 inference(rectify,[],[f5121])). 0.62/0.92 fof(f5121,axiom,( 0.62/0.92 ! [X17,X9] : (? [X25] : (hBOOL(hAPP(X17,X25)) & hBOOL(hAPP(hAPP(c_member(X9),X25),c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))))) <=> ? [X63] : hBOOL(hAPP(X17,X63)))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bex__UNIV)). 0.62/0.92 fof(f7180,plain,( 0.62/0.92 spl36_75 | spl36_53), 0.62/0.92 inference(avatar_split_clause,[],[f7168,f6915,f7177])). 0.62/0.92 fof(f6915,plain,( 0.62/0.92 spl36_53 <=> ! [X0] : ~hBOOL(X0)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_53])])). 0.62/0.92 fof(f7168,plain,( 0.62/0.92 ( ! [X3] : (~hBOOL(X3) | sP33(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )), 0.62/0.92 inference(superposition,[],[f6628,f6386])). 0.62/0.92 fof(f7175,plain,( 0.62/0.92 spl36_74 | spl36_53), 0.62/0.92 inference(avatar_split_clause,[],[f7167,f6915,f7172])). 0.62/0.92 fof(f7172,plain,( 0.62/0.92 spl36_74 <=> sP34(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_74])])). 0.62/0.92 fof(f7167,plain,( 0.62/0.92 ( ! [X2] : (~hBOOL(X2) | sP34(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )), 0.62/0.92 inference(superposition,[],[f6630,f6386])). 0.62/0.92 fof(f7162,plain,( 0.62/0.92 ~spl36_72 | spl36_73), 0.62/0.92 inference(avatar_split_clause,[],[f7148,f7160,f7155])). 0.62/0.92 fof(f7155,plain,( 0.62/0.92 spl36_72 <=> sP33(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_72])])). 0.62/0.92 fof(f7160,plain,( 0.62/0.92 spl36_73 <=> ! [X5] : hBOOL(sK21(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X5))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_73])])). 0.62/0.92 fof(f7148,plain,( 0.62/0.92 ( ! [X5] : (hBOOL(sK21(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X5)) | ~sP33(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )), 0.62/0.92 inference(superposition,[],[f6629,f6385])). 0.62/0.92 fof(f6385,plain,( 0.62/0.92 ( ! [X0] : (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0) )), 0.62/0.92 inference(cnf_transformation,[],[f5546])). 0.62/0.92 fof(f5546,plain,( 0.62/0.92 ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0), 0.62/0.92 inference(rectify,[],[f553])). 0.62/0.92 fof(f553,axiom,( 0.62/0.92 ! [X37] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X37) = X37), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1)). 0.62/0.92 fof(f7158,plain,( 0.62/0.92 spl36_72 | spl36_53), 0.62/0.92 inference(avatar_split_clause,[],[f7146,f6915,f7155])). 0.62/0.92 fof(f7146,plain,( 0.62/0.92 ( ! [X3] : (~hBOOL(X3) | sP33(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )), 0.62/0.92 inference(superposition,[],[f6628,f6385])). 0.62/0.92 fof(f7153,plain,( 0.62/0.92 spl36_71 | spl36_53), 0.62/0.92 inference(avatar_split_clause,[],[f7145,f6915,f7150])). 0.62/0.92 fof(f7150,plain,( 0.62/0.92 spl36_71 <=> sP34(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_71])])). 0.62/0.92 fof(f7145,plain,( 0.62/0.92 ( ! [X2] : (~hBOOL(X2) | sP34(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )), 0.62/0.92 inference(superposition,[],[f6630,f6385])). 0.62/0.92 fof(f7134,plain,( 0.62/0.92 ~spl36_69 | spl36_70), 0.62/0.92 inference(avatar_split_clause,[],[f7120,f7132,f7127])). 0.62/0.92 fof(f7127,plain,( 0.62/0.92 spl36_69 <=> sP33(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_69])])). 0.62/0.92 fof(f7132,plain,( 0.62/0.92 spl36_70 <=> ! [X5] : hBOOL(sK21(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_70])])). 0.62/0.92 fof(f7120,plain,( 0.62/0.92 ( ! [X5] : (hBOOL(sK21(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5)) | ~sP33(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) )), 0.62/0.92 inference(superposition,[],[f6629,f6314])). 0.62/0.92 fof(f6314,plain,( 0.62/0.92 ( ! [X0] : (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0) )), 0.62/0.92 inference(cnf_transformation,[],[f5497])). 0.62/0.92 fof(f5497,plain,( 0.62/0.92 ! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0), 0.62/0.92 inference(rectify,[],[f3652])). 0.62/0.92 fof(f3652,axiom,( 0.62/0.92 ! [X37] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X37) = X37), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0)). 0.62/0.92 fof(f7130,plain,( 0.62/0.92 spl36_69 | spl36_53), 0.62/0.92 inference(avatar_split_clause,[],[f7118,f6915,f7127])). 0.62/0.92 fof(f7118,plain,( 0.62/0.92 ( ! [X3] : (~hBOOL(X3) | sP33(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) )), 0.62/0.92 inference(superposition,[],[f6628,f6314])). 0.62/0.92 fof(f7125,plain,( 0.62/0.92 spl36_68 | spl36_53), 0.62/0.92 inference(avatar_split_clause,[],[f7117,f6915,f7122])). 0.62/0.92 fof(f7122,plain,( 0.62/0.92 spl36_68 <=> sP34(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_68])])). 0.62/0.92 fof(f7117,plain,( 0.62/0.92 ( ! [X2] : (~hBOOL(X2) | sP34(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) )), 0.62/0.92 inference(superposition,[],[f6630,f6314])). 0.62/0.92 fof(f7067,plain,( 0.62/0.92 ~spl36_67 | spl36_43), 0.62/0.92 inference(avatar_split_clause,[],[f7062,f6854,f7064])). 0.62/0.92 fof(f7064,plain,( 0.62/0.92 spl36_67 <=> sP33(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_67])])). 0.62/0.92 fof(f6854,plain,( 0.62/0.92 spl36_43 <=> hBOOL(c_Int_OPls)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_43])])). 0.62/0.92 fof(f7062,plain,( 0.62/0.92 ~sP33(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls)) | spl36_43), 0.62/0.92 inference(subsumption_resolution,[],[f7058,f6855])). 0.62/0.92 fof(f6855,plain,( 0.62/0.92 ~hBOOL(c_Int_OPls) | spl36_43), 0.62/0.92 inference(avatar_component_clause,[],[f6854])). 0.62/0.92 fof(f7058,plain,( 0.62/0.92 hBOOL(c_Int_OPls) | ~sP33(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls))), 0.62/0.92 inference(superposition,[],[f6629,f6456])). 0.62/0.92 fof(f6456,plain,( 0.62/0.92 ( ! [X0] : (c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X0)) )), 0.62/0.92 inference(cnf_transformation,[],[f5579])). 0.62/0.92 fof(f5579,plain,( 0.62/0.92 ! [X0] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X0)), 0.62/0.92 inference(rectify,[],[f4033])). 0.62/0.92 fof(f4033,axiom,( 0.62/0.92 ! [X107] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X107)), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Pls)). 0.62/0.92 fof(f7047,plain,( 0.62/0.92 spl36_66 | spl36_53), 0.62/0.92 inference(avatar_split_clause,[],[f7036,f6915,f7044])). 0.62/0.92 fof(f7044,plain,( 0.62/0.92 spl36_66 <=> sP33(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_66])])). 0.62/0.92 fof(f7036,plain,( 0.62/0.92 ( ! [X1] : (~hBOOL(X1) | sP33(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls))) )), 0.62/0.92 inference(superposition,[],[f6628,f6455])). 0.62/0.92 fof(f6455,plain,( 0.62/0.92 ( ! [X0] : (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X0) = X0) )), 0.62/0.92 inference(cnf_transformation,[],[f2193])). 0.62/0.92 fof(f2193,axiom,( 0.62/0.92 ! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X0) = X0), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls)). 0.62/0.92 fof(f7042,plain,( 0.62/0.92 spl36_65 | spl36_53), 0.62/0.92 inference(avatar_split_clause,[],[f7035,f6915,f7039])). 0.62/0.92 fof(f7039,plain,( 0.62/0.92 spl36_65 <=> sP34(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_65])])). 0.62/0.92 fof(f7035,plain,( 0.62/0.92 ( ! [X0] : (~hBOOL(X0) | sP34(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls))) )), 0.62/0.92 inference(superposition,[],[f6630,f6455])). 0.62/0.92 fof(f7012,plain,( 0.62/0.92 spl36_64 | ~spl36_63 | ~spl36_34), 0.62/0.92 inference(avatar_split_clause,[],[f6997,f6805,f7004,f7009])). 0.62/0.92 fof(f7009,plain,( 0.62/0.92 spl36_64 <=> sP33(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_64])])). 0.62/0.92 fof(f7004,plain,( 0.62/0.92 spl36_63 <=> hBOOL(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_63])])). 0.62/0.92 fof(f6805,plain,( 0.62/0.92 spl36_34 <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_34])])). 0.62/0.92 fof(f6997,plain,( 0.62/0.92 ~hBOOL(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | sP33(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat)) | ~spl36_34), 0.62/0.92 inference(superposition,[],[f6628,f6807])). 0.62/0.92 fof(f6807,plain,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) | ~spl36_34), 0.62/0.92 inference(avatar_component_clause,[],[f6805])). 0.62/0.92 fof(f7007,plain,( 0.62/0.92 spl36_62 | ~spl36_63 | ~spl36_34), 0.62/0.92 inference(avatar_split_clause,[],[f6996,f6805,f7004,f7000])). 0.62/0.92 fof(f7000,plain,( 0.62/0.92 spl36_62 <=> sP34(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_62])])). 0.62/0.92 fof(f6996,plain,( 0.62/0.92 ~hBOOL(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | sP34(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat)) | ~spl36_34), 0.62/0.92 inference(superposition,[],[f6630,f6807])). 0.62/0.92 fof(f6995,plain,( 0.62/0.92 spl36_49 | ~spl36_3), 0.62/0.92 inference(avatar_split_clause,[],[f6987,f6648,f6899])). 0.62/0.92 fof(f6899,plain,( 0.62/0.92 spl36_49 <=> sP33(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_49])])). 0.62/0.92 fof(f6987,plain,( 0.62/0.92 sP33(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G)) | ~spl36_3), 0.62/0.92 inference(resolution,[],[f6650,f6628])). 0.62/0.92 fof(f6994,plain,( 0.62/0.92 spl36_61 | ~spl36_3), 0.62/0.92 inference(avatar_split_clause,[],[f6986,f6648,f6991])). 0.62/0.92 fof(f6991,plain,( 0.62/0.92 spl36_61 <=> sP34(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_61])])). 0.62/0.92 fof(f6986,plain,( 0.62/0.92 sP34(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G)) | ~spl36_3), 0.62/0.92 inference(resolution,[],[f6650,f6630])). 0.62/0.92 fof(f6977,plain,( 0.62/0.92 spl36_60 | ~spl36_59 | ~spl36_13), 0.62/0.92 inference(avatar_split_clause,[],[f6962,f6698,f6969,f6974])). 0.62/0.92 fof(f6974,plain,( 0.62/0.92 spl36_60 <=> sP33(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_60])])). 0.62/0.92 fof(f6969,plain,( 0.62/0.92 spl36_59 <=> hBOOL(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_59])])). 0.62/0.92 fof(f6698,plain,( 0.62/0.92 spl36_13 <=> c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_13])])). 0.62/0.92 fof(f6962,plain,( 0.62/0.92 ~hBOOL(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | sP33(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral)) | ~spl36_13), 0.62/0.92 inference(superposition,[],[f6628,f6700])). 0.62/0.92 fof(f6700,plain,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls) | ~spl36_13), 0.62/0.92 inference(avatar_component_clause,[],[f6698])). 0.62/0.92 fof(f6972,plain,( 0.62/0.92 spl36_58 | ~spl36_59 | ~spl36_13), 0.62/0.92 inference(avatar_split_clause,[],[f6961,f6698,f6969,f6965])). 0.62/0.92 fof(f6965,plain,( 0.62/0.92 spl36_58 <=> sP34(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_58])])). 0.62/0.92 fof(f6961,plain,( 0.62/0.92 ~hBOOL(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) | sP34(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral)) | ~spl36_13), 0.62/0.92 inference(superposition,[],[f6630,f6700])). 0.62/0.92 fof(f6960,plain,( 0.62/0.92 spl36_48 | ~spl36_2), 0.62/0.92 inference(avatar_split_clause,[],[f6952,f6643,f6894])). 0.62/0.92 fof(f6894,plain,( 0.62/0.92 spl36_48 <=> sP33(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_48])])). 0.62/0.92 fof(f6952,plain,( 0.62/0.92 sP33(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts)) | ~spl36_2), 0.62/0.92 inference(resolution,[],[f6645,f6628])). 0.62/0.92 fof(f6959,plain,( 0.62/0.92 spl36_57 | ~spl36_2), 0.62/0.92 inference(avatar_split_clause,[],[f6951,f6643,f6956])). 0.62/0.92 fof(f6956,plain,( 0.62/0.92 spl36_57 <=> sP34(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_57])])). 0.62/0.92 fof(f6951,plain,( 0.62/0.92 sP34(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts)) | ~spl36_2), 0.62/0.92 inference(resolution,[],[f6645,f6630])). 0.62/0.92 fof(f6946,plain,( 0.62/0.92 spl36_56 | spl36_53), 0.62/0.92 inference(avatar_split_clause,[],[f6935,f6915,f6943])). 0.62/0.92 fof(f6943,plain,( 0.62/0.92 spl36_56 <=> sP34(c_Int_Onumber__class_Onumber__of(tc_Int_Oint))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_56])])). 0.62/0.92 fof(f6935,plain,( 0.62/0.92 ( ! [X1] : (~hBOOL(X1) | sP34(c_Int_Onumber__class_Onumber__of(tc_Int_Oint))) )), 0.62/0.92 inference(superposition,[],[f6630,f6472])). 0.62/0.92 fof(f6472,plain,( 0.62/0.92 ( ! [X0] : (hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0) )), 0.62/0.92 inference(cnf_transformation,[],[f583])). 0.62/0.92 fof(f583,axiom,( 0.62/0.92 ! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__is__id)). 0.62/0.92 fof(f6941,plain,( 0.62/0.92 spl36_55 | spl36_53), 0.62/0.92 inference(avatar_split_clause,[],[f6934,f6915,f6938])). 0.62/0.92 fof(f6938,plain,( 0.62/0.92 spl36_55 <=> sP34(c_Nat_Osize__class_Osize(tc_Nat_Onat))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_55])])). 0.62/0.92 fof(f6934,plain,( 0.62/0.92 ( ! [X0] : (~hBOOL(X0) | sP34(c_Nat_Osize__class_Osize(tc_Nat_Onat))) )), 0.62/0.92 inference(superposition,[],[f6630,f6401])). 0.62/0.92 fof(f6401,plain,( 0.62/0.92 ( ! [X0] : (hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X0) = X0) )), 0.62/0.92 inference(cnf_transformation,[],[f5557])). 0.62/0.92 fof(f5557,plain,( 0.62/0.92 ! [X0] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X0) = X0), 0.62/0.92 inference(rectify,[],[f3987])). 0.62/0.92 fof(f3987,axiom,( 0.62/0.92 ! [X37] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X37) = X37), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__size)). 0.62/0.92 fof(f6933,plain,( 0.62/0.92 ~spl36_53), 0.62/0.92 inference(avatar_contradiction_clause,[],[f6928])). 0.62/0.92 fof(f6928,plain,( 0.62/0.92 $false | ~spl36_53), 0.62/0.92 inference(subsumption_resolution,[],[f5912,f6916])). 0.62/0.92 fof(f6916,plain,( 0.62/0.92 ( ! [X0] : (~hBOOL(X0)) ) | ~spl36_53), 0.62/0.92 inference(avatar_component_clause,[],[f6915])). 0.62/0.92 fof(f5912,plain,( 0.62/0.92 ( ! [X0] : (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X0))) )), 0.62/0.92 inference(cnf_transformation,[],[f5251])). 0.62/0.92 fof(f5251,plain,( 0.62/0.92 ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X0))), 0.62/0.92 inference(rectify,[],[f4979])). 0.62/0.92 fof(f4979,axiom,( 0.62/0.92 ! [X37] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X37),X37))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl)). 0.62/0.92 fof(f6932,plain,( 0.62/0.92 ~spl36_3 | ~spl36_53), 0.62/0.92 inference(avatar_contradiction_clause,[],[f6927])). 0.62/0.92 fof(f6927,plain,( 0.62/0.92 $false | (~spl36_3 | ~spl36_53)), 0.62/0.92 inference(subsumption_resolution,[],[f6650,f6916])). 0.62/0.92 fof(f6931,plain,( 0.62/0.92 ~spl36_2 | ~spl36_53), 0.62/0.92 inference(avatar_contradiction_clause,[],[f6926])). 0.62/0.92 fof(f6926,plain,( 0.62/0.92 $false | (~spl36_2 | ~spl36_53)), 0.62/0.92 inference(subsumption_resolution,[],[f6645,f6916])). 0.62/0.92 fof(f6922,plain,( 0.62/0.92 spl36_54 | spl36_53), 0.62/0.92 inference(avatar_split_clause,[],[f6891,f6915,f6919])). 0.62/0.92 fof(f6919,plain,( 0.62/0.92 spl36_54 <=> sP33(c_Int_Onumber__class_Onumber__of(tc_Int_Oint))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_54])])). 0.62/0.92 fof(f6891,plain,( 0.62/0.92 ( ! [X1] : (~hBOOL(X1) | sP33(c_Int_Onumber__class_Onumber__of(tc_Int_Oint))) )), 0.62/0.92 inference(superposition,[],[f6628,f6472])). 0.62/0.92 fof(f6917,plain,( 0.62/0.92 spl36_52 | spl36_53), 0.62/0.92 inference(avatar_split_clause,[],[f6890,f6915,f6911])). 0.62/0.92 fof(f6911,plain,( 0.62/0.92 spl36_52 <=> sP33(c_Nat_Osize__class_Osize(tc_Nat_Onat))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_52])])). 0.62/0.92 fof(f6890,plain,( 0.62/0.92 ( ! [X0] : (~hBOOL(X0) | sP33(c_Nat_Osize__class_Osize(tc_Nat_Onat))) )), 0.62/0.92 inference(superposition,[],[f6628,f6401])). 0.62/0.92 fof(f6909,plain,( 0.62/0.92 spl36_50 | spl36_51), 0.62/0.92 inference(avatar_split_clause,[],[f6889,f6907,f6904])). 0.62/0.92 fof(f6904,plain,( 0.62/0.92 spl36_50 <=> ! [X1] : sP31(X1)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_50])])). 0.62/0.92 fof(f6907,plain,( 0.62/0.92 spl36_51 <=> ! [X0] : sP33(X0)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_51])])). 0.62/0.92 fof(f6889,plain,( 0.62/0.92 ( ! [X0,X1] : (sP33(X0) | sP31(X1)) )), 0.62/0.92 inference(resolution,[],[f6628,f6624])). 0.62/0.92 fof(f6624,plain,( 0.62/0.92 ( ! [X2,X0] : (hBOOL(hAPP(X0,X2)) | sP31(X2)) )), 0.62/0.92 inference(cnf_transformation,[],[f6624_D])). 0.62/0.92 fof(f6624_D,plain,( 0.62/0.92 ( ! [X2] : (( ! [X0] : hBOOL(hAPP(X0,X2)) ) <=> ~sP31(X2)) )), 0.62/0.92 introduced(general_splitting_component_introduction,[new_symbols(naming,[sP31])])). 0.62/0.92 fof(f6902,plain,( 0.62/0.92 spl36_49 | ~spl36_3), 0.62/0.92 inference(avatar_split_clause,[],[f6888,f6648,f6899])). 0.62/0.92 fof(f6888,plain,( 0.62/0.92 sP33(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G)) | ~spl36_3), 0.62/0.92 inference(resolution,[],[f6628,f6650])). 0.62/0.92 fof(f6897,plain,( 0.62/0.92 spl36_48 | ~spl36_2), 0.62/0.92 inference(avatar_split_clause,[],[f6887,f6643,f6894])). 0.62/0.92 fof(f6887,plain,( 0.62/0.92 sP33(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts)) | ~spl36_2), 0.62/0.92 inference(resolution,[],[f6628,f6645])). 0.62/0.92 fof(f6886,plain,( 0.62/0.92 spl36_47 | ~spl36_3), 0.62/0.92 inference(avatar_split_clause,[],[f6875,f6648,f6883])). 0.62/0.92 fof(f6883,plain,( 0.62/0.92 spl36_47 <=> sP32(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),v_Ga))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_47])])). 0.62/0.92 fof(f6875,plain,( 0.62/0.92 sP32(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),v_Ga)) | ~spl36_3), 0.62/0.92 inference(resolution,[],[f6861,f6650])). 0.62/0.92 fof(f6861,plain,( 0.62/0.92 ( ! [X0] : (~hBOOL(X0) | sP32(X0)) )), 0.62/0.92 inference(superposition,[],[f6626,f6401])). 0.62/0.92 fof(f6626,plain,( 0.62/0.92 ( ! [X2,X0] : (~hBOOL(hAPP(X0,X2)) | sP32(X2)) )), 0.62/0.92 inference(cnf_transformation,[],[f6626_D])). 0.62/0.92 fof(f6626_D,plain,( 0.62/0.92 ( ! [X2] : (( ! [X0] : ~hBOOL(hAPP(X0,X2)) ) <=> ~sP32(X2)) )), 0.62/0.92 introduced(general_splitting_component_introduction,[new_symbols(naming,[sP32])])). 0.62/0.92 fof(f6881,plain,( 0.62/0.92 spl36_46 | ~spl36_2), 0.62/0.92 inference(avatar_split_clause,[],[f6874,f6643,f6878])). 0.62/0.92 fof(f6878,plain,( 0.62/0.92 spl36_46 <=> sP32(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_G))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_46])])). 0.62/0.92 fof(f6874,plain,( 0.62/0.92 sP32(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_G)) | ~spl36_2), 0.62/0.92 inference(resolution,[],[f6861,f6645])). 0.62/0.92 fof(f6873,plain,( 0.62/0.92 spl36_45 | ~spl36_3), 0.62/0.92 inference(avatar_split_clause,[],[f6859,f6648,f6870])). 0.62/0.92 fof(f6870,plain,( 0.62/0.92 spl36_45 <=> sP32(v_Ga)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_45])])). 0.62/0.92 fof(f6859,plain,( 0.62/0.92 sP32(v_Ga) | ~spl36_3), 0.62/0.92 inference(resolution,[],[f6626,f6650])). 0.62/0.92 fof(f6868,plain,( 0.62/0.92 spl36_44 | ~spl36_2), 0.62/0.92 inference(avatar_split_clause,[],[f6858,f6643,f6865])). 0.62/0.92 fof(f6865,plain,( 0.62/0.92 spl36_44 <=> sP32(v_G)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_44])])). 0.62/0.92 fof(f6858,plain,( 0.62/0.92 sP32(v_G) | ~spl36_2), 0.62/0.92 inference(resolution,[],[f6626,f6645])). 0.62/0.92 fof(f6857,plain,( 0.62/0.92 spl36_42 | spl36_43 | ~spl36_37), 0.62/0.92 inference(avatar_split_clause,[],[f6848,f6821,f6854,f6850])). 0.62/0.92 fof(f6850,plain,( 0.62/0.92 spl36_42 <=> sP31(c_Int_OPls)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_42])])). 0.62/0.92 fof(f6821,plain,( 0.62/0.92 spl36_37 <=> c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_37])])). 0.62/0.92 fof(f6848,plain,( 0.62/0.92 hBOOL(c_Int_OPls) | sP31(c_Int_OPls) | ~spl36_37), 0.62/0.92 inference(superposition,[],[f6624,f6823])). 0.62/0.92 fof(f6823,plain,( 0.62/0.92 c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) | ~spl36_37), 0.62/0.92 inference(avatar_component_clause,[],[f6821])). 0.62/0.92 fof(f6845,plain,( 0.62/0.92 ~spl36_41 | spl36_24 | ~spl36_38), 0.62/0.92 inference(avatar_split_clause,[],[f6840,f6826,f6754,f6842])). 0.62/0.92 fof(f6842,plain,( 0.62/0.92 spl36_41 <=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_OPls), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_41])])). 0.62/0.92 fof(f6754,plain,( 0.62/0.92 spl36_24 <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_24])])). 0.62/0.92 fof(f6840,plain,( 0.62/0.92 c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Int_OPls | (spl36_24 | ~spl36_38)), 0.62/0.92 inference(forward_demodulation,[],[f6756,f6828])). 0.62/0.92 fof(f6756,plain,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) | spl36_24), 0.62/0.92 inference(avatar_component_clause,[],[f6754])). 0.62/0.92 fof(f6839,plain,( 0.62/0.92 spl36_40), 0.62/0.92 inference(avatar_split_clause,[],[f6499,f6836])). 0.62/0.92 fof(f6836,plain,( 0.62/0.92 spl36_40 <=> class_Orderings_Olinorder(tc_Int_Oint)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_40])])). 0.62/0.92 fof(f6499,plain,( 0.62/0.92 class_Orderings_Olinorder(tc_Int_Oint)), 0.62/0.92 inference(cnf_transformation,[],[f5011])). 0.62/0.92 fof(f5011,axiom,( 0.62/0.92 class_Orderings_Olinorder(tc_Int_Oint)), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder)). 0.62/0.92 fof(f6834,plain,( 0.62/0.92 spl36_39), 0.62/0.92 inference(avatar_split_clause,[],[f6498,f6831])). 0.62/0.92 fof(f6831,plain,( 0.62/0.92 spl36_39 <=> class_Orderings_Olinorder(tc_Nat_Onat)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_39])])). 0.62/0.92 fof(f6498,plain,( 0.62/0.92 class_Orderings_Olinorder(tc_Nat_Onat)), 0.62/0.92 inference(cnf_transformation,[],[f5215])). 0.62/0.92 fof(f5215,axiom,( 0.62/0.92 class_Orderings_Olinorder(tc_Nat_Onat)), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder)). 0.62/0.92 fof(f6829,plain,( 0.62/0.92 spl36_38), 0.62/0.92 inference(avatar_split_clause,[],[f6465,f6826])). 0.62/0.92 fof(f6465,plain,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls), 0.62/0.92 inference(cnf_transformation,[],[f4090])). 0.62/0.92 fof(f4090,axiom,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pls__def)). 0.62/0.92 fof(f6824,plain,( 0.62/0.92 spl36_37), 0.62/0.92 inference(avatar_split_clause,[],[f6464,f6821])). 0.62/0.92 fof(f6464,plain,( 0.62/0.92 c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)), 0.62/0.92 inference(cnf_transformation,[],[f3860])). 0.62/0.92 fof(f3860,axiom,( 0.62/0.92 c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Pls)). 0.62/0.92 fof(f6819,plain,( 0.62/0.92 ~spl36_36), 0.62/0.92 inference(avatar_split_clause,[],[f6463,f6816])). 0.62/0.92 fof(f6816,plain,( 0.62/0.92 spl36_36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_36])])). 0.62/0.92 fof(f6463,plain,( 0.62/0.92 ~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls))), 0.62/0.92 inference(cnf_transformation,[],[f902])). 0.62/0.92 fof(f902,axiom,( 0.62/0.92 ~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I2_J)). 0.62/0.92 fof(f6814,plain,( 0.62/0.92 spl36_35), 0.62/0.92 inference(avatar_split_clause,[],[f6462,f6811])). 0.62/0.92 fof(f6811,plain,( 0.62/0.92 spl36_35 <=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_35])])). 0.62/0.92 fof(f6462,plain,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls)), 0.62/0.92 inference(cnf_transformation,[],[f814])). 0.62/0.92 fof(f814,axiom,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls)), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__is__num__zero)). 0.62/0.92 fof(f6809,plain,( 0.62/0.92 spl36_34), 0.62/0.92 inference(avatar_split_clause,[],[f6461,f6805])). 0.62/0.92 fof(f6461,plain,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)), 0.62/0.92 inference(cnf_transformation,[],[f3737])). 0.62/0.92 fof(f3737,axiom,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__Pls)). 0.62/0.92 fof(f6808,plain,( 0.62/0.92 spl36_34), 0.62/0.92 inference(avatar_split_clause,[],[f6460,f6805])). 0.62/0.92 fof(f6460,plain,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)), 0.62/0.92 inference(cnf_transformation,[],[f906])). 0.62/0.92 fof(f906,axiom,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I113_J)). 0.62/0.92 fof(f6803,plain,( 0.62/0.92 spl36_33), 0.62/0.92 inference(avatar_split_clause,[],[f6459,f6800])). 0.62/0.92 fof(f6800,plain,( 0.62/0.92 spl36_33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_33])])). 0.62/0.92 fof(f6459,plain,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls))), 0.62/0.92 inference(cnf_transformation,[],[f3494])). 0.62/0.92 fof(f3494,axiom,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I19_J)). 0.62/0.92 fof(f6798,plain,( 0.62/0.92 ~spl36_32), 0.62/0.92 inference(avatar_split_clause,[],[f6458,f6795])). 0.62/0.92 fof(f6795,plain,( 0.62/0.92 spl36_32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_32])])). 0.62/0.92 fof(f6458,plain,( 0.62/0.92 ~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 0.62/0.92 inference(cnf_transformation,[],[f4500])). 0.62/0.92 fof(f4500,axiom,( 0.62/0.92 ~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I1_J)). 0.62/0.92 fof(f6793,plain,( 0.62/0.92 spl36_31), 0.62/0.92 inference(avatar_split_clause,[],[f6457,f6790])). 0.62/0.92 fof(f6790,plain,( 0.62/0.92 spl36_31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls)))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_31])])). 0.62/0.92 fof(f6457,plain,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls)))), 0.62/0.92 inference(cnf_transformation,[],[f3981])). 0.62/0.92 fof(f3981,axiom,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls)))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of2)). 0.62/0.92 fof(f6788,plain,( 0.62/0.92 spl36_30), 0.62/0.92 inference(avatar_split_clause,[],[f6530,f6785])). 0.62/0.92 fof(f6785,plain,( 0.62/0.92 spl36_30 <=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_30])])). 0.62/0.92 fof(f6530,plain,( 0.62/0.92 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))), 0.62/0.92 inference(definition_unfolding,[],[f6433,f6425])). 0.62/0.92 fof(f6425,plain,( 0.62/0.92 ( ! [X0] : (c_Int_OBit1(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)),X0)) )), 0.62/0.92 inference(cnf_transformation,[],[f2276])). 0.62/0.92 fof(f2276,axiom,( 0.62/0.92 ! [X0] : c_Int_OBit1(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)),X0)), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__def)). 0.62/0.92 fof(f6433,plain,( 0.62/0.92 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))), 0.62/0.92 inference(cnf_transformation,[],[f2321])). 0.62/0.92 fof(f2321,axiom,( 0.62/0.92 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__num__one)). 0.62/0.92 fof(f6783,plain,( 0.62/0.92 spl36_29), 0.62/0.92 inference(avatar_split_clause,[],[f6529,f6779])). 0.62/0.92 fof(f6779,plain,( 0.62/0.92 spl36_29 <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_29])])). 0.62/0.92 fof(f6529,plain,( 0.62/0.92 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))), 0.62/0.92 inference(definition_unfolding,[],[f6432,f6425])). 0.62/0.92 fof(f6432,plain,( 0.62/0.92 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))), 0.62/0.92 inference(cnf_transformation,[],[f2485])). 0.62/0.92 fof(f2485,axiom,( 0.62/0.92 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Numeral1__eq1__nat)). 0.62/0.92 fof(f6782,plain,( 0.62/0.92 spl36_29), 0.62/0.92 inference(avatar_split_clause,[],[f6528,f6779])). 0.62/0.92 fof(f6528,plain,( 0.62/0.92 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))), 0.62/0.92 inference(definition_unfolding,[],[f6431,f6425])). 0.62/0.92 fof(f6431,plain,( 0.62/0.92 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))), 0.62/0.92 inference(cnf_transformation,[],[f2234])). 0.62/0.92 fof(f2234,axiom,( 0.62/0.92 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__numeral__1__eq__1)). 0.62/0.92 fof(f6777,plain,( 0.62/0.92 spl36_28), 0.62/0.92 inference(avatar_split_clause,[],[f6527,f6774])). 0.62/0.92 fof(f6774,plain,( 0.62/0.92 spl36_28 <=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_28])])). 0.62/0.92 fof(f6527,plain,( 0.62/0.92 hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))), 0.62/0.92 inference(definition_unfolding,[],[f6430,f6425])). 0.62/0.92 fof(f6430,plain,( 0.62/0.92 hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))), 0.62/0.92 inference(cnf_transformation,[],[f4738])). 0.62/0.92 fof(f4738,axiom,( 0.62/0.92 hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__1__eq__Suc__0)). 0.62/0.92 fof(f6772,plain,( 0.62/0.92 spl36_27), 0.62/0.92 inference(avatar_split_clause,[],[f6526,f6769])). 0.62/0.92 fof(f6769,plain,( 0.62/0.92 spl36_27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_27])])). 0.62/0.92 fof(f6526,plain,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))), 0.62/0.92 inference(definition_unfolding,[],[f6429,f6425,f6425])). 0.62/0.92 fof(f6429,plain,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))), 0.62/0.92 inference(cnf_transformation,[],[f1923])). 0.62/0.92 fof(f1923,axiom,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J)). 0.62/0.92 fof(f6767,plain,( 0.62/0.92 spl36_26), 0.62/0.92 inference(avatar_split_clause,[],[f6525,f6764])). 0.62/0.92 fof(f6764,plain,( 0.62/0.92 spl36_26 <=> hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_26])])). 0.62/0.92 fof(f6525,plain,( 0.62/0.92 hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))), 0.62/0.92 inference(definition_unfolding,[],[f6428,f6425,f6425])). 0.62/0.92 fof(f6428,plain,( 0.62/0.92 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), 0.62/0.92 inference(cnf_transformation,[],[f529])). 0.62/0.92 fof(f529,axiom,( 0.62/0.92 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__3__eq__3)). 0.62/0.92 fof(f6762,plain,( 0.62/0.92 spl36_25), 0.62/0.92 inference(avatar_split_clause,[],[f6402,f6759])). 0.62/0.92 fof(f6759,plain,( 0.62/0.92 spl36_25 <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_25])])). 0.62/0.92 fof(f6402,plain,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 0.62/0.92 inference(cnf_transformation,[],[f404])). 0.62/0.92 fof(f404,axiom,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I3_J)). 0.62/0.92 fof(f6757,plain,( 0.62/0.92 ~spl36_24), 0.62/0.92 inference(avatar_split_clause,[],[f6391,f6754])). 0.62/0.92 fof(f6391,plain,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint)), 0.62/0.92 inference(cnf_transformation,[],[f3042])). 0.62/0.92 fof(f3042,axiom,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint)), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__neq__1)). 0.62/0.92 fof(f6752,plain,( 0.62/0.92 spl36_22), 0.62/0.92 inference(avatar_split_clause,[],[f6390,f6743])). 0.62/0.92 fof(f6390,plain,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))), 0.62/0.92 inference(cnf_transformation,[],[f4958])). 0.62/0.92 fof(f4958,axiom,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__less__1)). 0.62/0.92 fof(f6751,plain,( 0.62/0.92 spl36_23), 0.62/0.92 inference(avatar_split_clause,[],[f6389,f6748])). 0.62/0.92 fof(f6389,plain,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))), 0.62/0.92 inference(cnf_transformation,[],[f2984])). 0.62/0.92 fof(f2984,axiom,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J)). 0.62/0.92 fof(f6746,plain,( 0.62/0.92 spl36_21 | ~spl36_22), 0.62/0.92 inference(avatar_split_clause,[],[f6600,f6743,f6739])). 0.62/0.92 fof(f6739,plain,( 0.62/0.92 spl36_21 <=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_21])])). 0.62/0.92 fof(f6600,plain,( 0.62/0.92 ~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) | c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))), 0.62/0.92 inference(equality_resolution,[],[f6599])). 0.62/0.92 fof(f6599,plain,( 0.62/0.92 ( ! [X0] : (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) | c_Groups_Oone__class_Oone(tc_Int_Oint) != X0 | c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)) )), 0.62/0.92 inference(equality_resolution,[],[f6371])). 0.62/0.92 fof(f6371,plain,( 0.62/0.92 ( ! [X0,X1] : (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) | c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 | c_Groups_Oone__class_Oone(tc_Int_Oint) != X0 | c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)) )), 0.62/0.92 inference(cnf_transformation,[],[f5840])). 0.62/0.92 fof(f5840,plain,( 0.62/0.92 ! [X0,X1] : ((c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) <=> (c_Groups_Oone__class_Oone(tc_Int_Oint) = X0 & c_Groups_Oone__class_Oone(tc_Int_Oint) = X1)) | ~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)))), 0.62/0.92 inference(ennf_transformation,[],[f5537])). 0.62/0.92 fof(f5537,plain,( 0.62/0.92 ! [X0,X1] : (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) => (c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) <=> (c_Groups_Oone__class_Oone(tc_Int_Oint) = X0 & c_Groups_Oone__class_Oone(tc_Int_Oint) = X1)))), 0.62/0.92 inference(rectify,[],[f275])). 0.62/0.92 fof(f275,axiom,( 0.62/0.92 ! [X30,X35] : (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X35)) => (c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X35),X30) <=> (c_Groups_Oone__class_Oone(tc_Int_Oint) = X30 & c_Groups_Oone__class_Oone(tc_Int_Oint) = X35)))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff)). 0.62/0.92 fof(f6737,plain,( 0.62/0.92 spl36_20), 0.62/0.92 inference(avatar_split_clause,[],[f6598,f6733])). 0.62/0.92 fof(f6733,plain,( 0.62/0.92 spl36_20 <=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_20])])). 0.62/0.92 fof(f6598,plain,( 0.62/0.92 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))), 0.62/0.92 inference(equality_resolution,[],[f6597])). 0.62/0.92 fof(f6597,plain,( 0.62/0.92 ( ! [X1] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))) )), 0.62/0.92 inference(equality_resolution,[],[f6366])). 0.62/0.92 fof(f6366,plain,( 0.62/0.92 ( ! [X0,X1] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0 | c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) )), 0.62/0.92 inference(cnf_transformation,[],[f5535])). 0.62/0.92 fof(f5535,plain,( 0.62/0.92 ! [X0,X1] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) <=> (c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0))), 0.62/0.92 inference(rectify,[],[f2729])). 0.62/0.92 fof(f2729,axiom,( 0.62/0.92 ! [X30,X35] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X35),X30) <=> (c_Groups_Oone__class_Oone(tc_Nat_Onat) = X35 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = X30))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff)). 0.62/0.92 fof(f6736,plain,( 0.62/0.92 spl36_20), 0.62/0.92 inference(avatar_split_clause,[],[f6596,f6733])). 0.62/0.92 fof(f6596,plain,( 0.62/0.92 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))), 0.62/0.92 inference(equality_resolution,[],[f6595])). 0.62/0.92 fof(f6595,plain,( 0.62/0.92 ( ! [X1] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))) )), 0.62/0.92 inference(equality_resolution,[],[f6363])). 0.62/0.92 fof(f6363,plain,( 0.62/0.92 ( ! [X0,X1] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0 | c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)) )), 0.62/0.92 inference(cnf_transformation,[],[f5534])). 0.62/0.92 fof(f5534,plain,( 0.62/0.92 ! [X0,X1] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) <=> (c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0))), 0.62/0.92 inference(rectify,[],[f1967])). 0.62/0.92 fof(f1967,axiom,( 0.62/0.92 ! [X30,X35] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X35),X30) <=> (c_Groups_Oone__class_Oone(tc_Nat_Onat) = X35 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = X30))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff)). 0.62/0.92 fof(f6731,plain,( 0.62/0.92 spl36_19), 0.62/0.92 inference(avatar_split_clause,[],[f6351,f6728])). 0.62/0.92 fof(f6728,plain,( 0.62/0.92 spl36_19 <=> class_Enum_Oenum(tc_HOL_Obool)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_19])])). 0.62/0.92 fof(f6351,plain,( 0.62/0.92 class_Enum_Oenum(tc_HOL_Obool)), 0.62/0.92 inference(cnf_transformation,[],[f3183])). 0.62/0.92 fof(f3183,axiom,( 0.62/0.92 class_Enum_Oenum(tc_HOL_Obool)), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Enum_Oenum)). 0.62/0.92 fof(f6726,plain,( 0.62/0.92 ~spl36_18), 0.62/0.92 inference(avatar_split_clause,[],[f6348,f6723])). 0.62/0.92 fof(f6723,plain,( 0.62/0.92 spl36_18 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool))))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_18])])). 0.62/0.92 fof(f6348,plain,( 0.62/0.92 ~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool))))), 0.62/0.92 inference(cnf_transformation,[],[f3348])). 0.62/0.92 fof(f3348,axiom,( 0.62/0.92 ~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool))))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_infinite__UNIV__int)). 0.62/0.92 fof(f6721,plain,( 0.62/0.92 ~spl36_17), 0.62/0.92 inference(avatar_split_clause,[],[f6347,f6718])). 0.62/0.92 fof(f6718,plain,( 0.62/0.92 spl36_17 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_17])])). 0.62/0.92 fof(f6347,plain,( 0.62/0.92 ~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))), 0.62/0.92 inference(cnf_transformation,[],[f1123])). 0.62/0.92 fof(f1123,axiom,( 0.62/0.92 ~hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_infinite__UNIV__nat)). 0.62/0.92 fof(f6716,plain,( 0.62/0.92 spl36_16), 0.62/0.92 inference(avatar_split_clause,[],[f6592,f6713])). 0.62/0.92 fof(f6713,plain,( 0.62/0.92 spl36_16 <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_16])])). 0.62/0.92 fof(f6592,plain,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 0.62/0.92 inference(equality_resolution,[],[f6591])). 0.62/0.92 fof(f6591,plain,( 0.62/0.92 ( ! [X0] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0) )), 0.62/0.92 inference(equality_resolution,[],[f6300])). 0.62/0.92 fof(f6300,plain,( 0.62/0.92 ( ! [X0,X1] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0) )), 0.62/0.92 inference(cnf_transformation,[],[f5487])). 0.62/0.92 fof(f5487,plain,( 0.62/0.92 ! [X0,X1] : ((c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1) <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0))), 0.62/0.92 inference(rectify,[],[f147])). 0.62/0.92 fof(f147,axiom,( 0.62/0.92 ! [X30,X35] : ((c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X30 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X35) <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X35),X30))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0)). 0.62/0.92 fof(f6711,plain,( 0.62/0.92 spl36_15), 0.62/0.92 inference(avatar_split_clause,[],[f6203,f6708])). 0.62/0.92 fof(f6708,plain,( 0.62/0.92 spl36_15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_15])])). 0.62/0.92 fof(f6203,plain,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 0.62/0.92 inference(cnf_transformation,[],[f1395])). 0.62/0.92 fof(f1395,axiom,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J)). 0.62/0.92 fof(f6706,plain,( 0.62/0.92 spl36_14), 0.62/0.92 inference(avatar_split_clause,[],[f6198,f6703])). 0.62/0.92 fof(f6703,plain,( 0.62/0.92 spl36_14 <=> class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_14])])). 0.62/0.92 fof(f6198,plain,( 0.62/0.92 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral)), 0.62/0.92 inference(cnf_transformation,[],[f1142])). 0.62/0.92 fof(f1142,axiom,( 0.62/0.92 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral)), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder)). 0.62/0.92 fof(f6701,plain,( 0.62/0.92 spl36_13), 0.62/0.92 inference(avatar_split_clause,[],[f6197,f6698])). 0.62/0.92 fof(f6197,plain,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls)), 0.62/0.92 inference(cnf_transformation,[],[f4666])). 0.62/0.92 fof(f4666,axiom,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls)), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__code__numeral__code)). 0.62/0.92 fof(f6696,plain,( 0.62/0.92 spl36_12), 0.62/0.92 inference(avatar_split_clause,[],[f6500,f6693])). 0.62/0.92 fof(f6693,plain,( 0.62/0.92 spl36_12 <=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_12])])). 0.62/0.92 fof(f6500,plain,( 0.62/0.92 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))), 0.62/0.92 inference(definition_unfolding,[],[f6196,f6425])). 0.62/0.92 fof(f6196,plain,( 0.62/0.92 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls))), 0.62/0.92 inference(cnf_transformation,[],[f4347])). 0.62/0.92 fof(f4347,axiom,( 0.62/0.92 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__code__numeral__code)). 0.62/0.92 fof(f6691,plain,( 0.62/0.92 spl36_11), 0.62/0.92 inference(avatar_split_clause,[],[f6195,f6688])). 0.62/0.92 fof(f6688,plain,( 0.62/0.92 spl36_11 <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_11])])). 0.62/0.92 fof(f6195,plain,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), 0.62/0.92 inference(cnf_transformation,[],[f5037])). 0.62/0.92 fof(f5037,axiom,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Osize_I3_J)). 0.62/0.92 fof(f6686,plain,( 0.62/0.92 spl36_10), 0.62/0.92 inference(avatar_split_clause,[],[f6194,f6683])). 0.62/0.92 fof(f6683,plain,( 0.62/0.92 spl36_10 <=> c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_10])])). 0.62/0.92 fof(f6194,plain,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), 0.62/0.92 inference(cnf_transformation,[],[f4103])). 0.62/0.92 fof(f4103,axiom,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral__zero__minus__one)). 0.62/0.92 fof(f6681,plain,( 0.62/0.92 spl36_9), 0.62/0.92 inference(avatar_split_clause,[],[f6571,f6678])). 0.62/0.92 fof(f6678,plain,( 0.62/0.92 spl36_9 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_9])])). 0.62/0.92 fof(f6571,plain,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), 0.62/0.92 inference(equality_resolution,[],[f6077])). 0.62/0.92 fof(f6077,plain,( 0.62/0.92 ( ! [X0] : (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0) )), 0.62/0.92 inference(cnf_transformation,[],[f5347])). 0.62/0.92 fof(f5347,plain,( 0.62/0.92 ! [X0] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), 0.62/0.92 inference(rectify,[],[f1734])). 0.62/0.92 fof(f1734,axiom,( 0.62/0.92 ! [X30] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq)). 0.62/0.92 fof(f6676,plain,( 0.62/0.92 ~spl36_8), 0.62/0.92 inference(avatar_split_clause,[],[f6570,f6673])). 0.62/0.92 fof(f6673,plain,( 0.62/0.92 spl36_8 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_8])])). 0.62/0.92 fof(f6570,plain,( 0.62/0.92 ~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), 0.62/0.92 inference(equality_resolution,[],[f6068])). 0.62/0.92 fof(f6068,plain,( 0.62/0.92 ( ! [X0] : (~hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0) )), 0.62/0.92 inference(cnf_transformation,[],[f5340])). 0.62/0.92 fof(f5340,plain,( 0.62/0.92 ! [X0] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)))), 0.62/0.92 inference(rectify,[],[f4905])). 0.62/0.92 fof(f4905,axiom,( 0.62/0.92 ! [X30] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30)))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv)). 0.62/0.92 fof(f6671,plain,( 0.62/0.92 spl36_7), 0.62/0.92 inference(avatar_split_clause,[],[f6018,f6668])). 0.62/0.92 fof(f6668,plain,( 0.62/0.92 spl36_7 <=> class_Nat_Osize(tc_Code__Numeral_Ocode__numeral)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_7])])). 0.62/0.92 fof(f6018,plain,( 0.62/0.92 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral)), 0.62/0.92 inference(cnf_transformation,[],[f2014])). 0.62/0.92 fof(f2014,axiom,( 0.62/0.92 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral)), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Nat_Osize)). 0.62/0.92 fof(f6666,plain,( 0.62/0.92 spl36_6), 0.62/0.92 inference(avatar_split_clause,[],[f6017,f6663])). 0.62/0.92 fof(f6663,plain,( 0.62/0.92 spl36_6 <=> class_Nat_Osize(tc_Nat_Onat)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_6])])). 0.62/0.92 fof(f6017,plain,( 0.62/0.92 class_Nat_Osize(tc_Nat_Onat)), 0.62/0.92 inference(cnf_transformation,[],[f4134])). 0.62/0.92 fof(f4134,axiom,( 0.62/0.92 class_Nat_Osize(tc_Nat_Onat)), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Nat_Osize)). 0.62/0.92 fof(f6661,plain,( 0.62/0.92 spl36_5), 0.62/0.92 inference(avatar_split_clause,[],[f6016,f6658])). 0.62/0.92 fof(f6658,plain,( 0.62/0.92 spl36_5 <=> class_Nat_Osize(tc_HOL_Obool)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_5])])). 0.62/0.92 fof(f6016,plain,( 0.62/0.92 class_Nat_Osize(tc_HOL_Obool)), 0.62/0.92 inference(cnf_transformation,[],[f5067])). 0.62/0.92 fof(f5067,axiom,( 0.62/0.92 class_Nat_Osize(tc_HOL_Obool)), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Nat_Osize)). 0.62/0.92 fof(f6656,plain,( 0.62/0.92 spl36_4), 0.62/0.92 inference(avatar_split_clause,[],[f5931,f6653])). 0.62/0.92 fof(f6653,plain,( 0.62/0.92 spl36_4 <=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat)), 0.62/0.92 introduced(avatar_definition,[new_symbols(naming,[spl36_4])])). 0.62/0.92 fof(f5931,plain,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat)), 0.62/0.92 inference(cnf_transformation,[],[f2058])). 0.62/0.92 fof(f2058,axiom,( 0.62/0.92 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat)), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__nat__def)). 0.62/0.92 fof(f6651,plain,( 0.62/0.92 spl36_3), 0.62/0.92 inference(avatar_split_clause,[],[f5887,f6648])). 0.62/0.92 fof(f5887,plain,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),v_Ga))), 0.62/0.92 inference(cnf_transformation,[],[f1418])). 0.62/0.92 fof(f1418,axiom,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),v_Ga))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)). 0.62/0.92 fof(f6646,plain,( 0.62/0.92 spl36_2), 0.62/0.92 inference(avatar_split_clause,[],[f5886,f6643])). 0.62/0.92 fof(f5886,plain,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_G))), 0.62/0.92 inference(cnf_transformation,[],[f2379])). 0.62/0.92 fof(f2379,axiom,( 0.62/0.92 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_G))), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 0.62/0.92 fof(f6641,plain,( 0.62/0.92 ~spl36_1), 0.62/0.92 inference(avatar_split_clause,[],[f5885,f6638])). 0.62/0.92 fof(f5885,plain,( 0.62/0.92 ~c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts)), 0.62/0.92 inference(cnf_transformation,[],[f5230])). 0.62/0.92 fof(f5230,plain,( 0.62/0.92 ~c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts)), 0.62/0.92 inference(flattening,[],[f3145])). 0.62/0.92 fof(f3145,negated_conjecture,( 0.62/0.92 ~c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts)), 0.62/0.92 inference(negated_conjecture,[],[f3144])). 0.62/0.92 fof(f3144,conjecture,( 0.62/0.92 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts)), 0.62/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2)). 0.62/0.92 % SZS output end Proof for theBenchmark 0.62/0.92 % (26339)------------------------------ 0.62/0.92 % (26339)Version: Vampire 4.7 (commit 2d02e4655 on 2022-07-11 21:15:24 +0200) 0.62/0.92 % (26339)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0 0.62/0.92 % (26339)Termination reason: Refutation 0.62/0.92 0.62/0.92 % (26339)Memory used [KB]: 8443 0.62/0.92 % (26339)Time elapsed: 0.116 s 0.62/0.92 % (26339)------------------------------ 0.62/0.92 % (26339)------------------------------ 0.62/0.92 % (26337)Success in time 0.556 s 0.62/0.92 EOF