0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : vampire --mode casc -t %d %s 0.03/0.26 % Computer : n003.star.cs.uiowa.edu 0.03/0.26 % Model : x86_64 x86_64 0.03/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.26 % Memory : 32218.625MB 0.03/0.26 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.26 % CPULimit : 300 0.03/0.26 % DateTime : Sat Jul 14 04:29:10 CDT 2018 0.03/0.26 % CPUTime : 0.07/0.30 % dis+11_6_add=large:afr=on:afp=100000:afq=1.2:amm=off:anc=none:cond=fast:gs=on:gsaa=from_current:gsem=off:irw=on:lma=on:lwlo=on:nm=64:nwc=1:sas=z3:sos=on:sp=occurrence:tha=off:thi=strong:updr=off_2 on theBenchmark 0.07/0.34 % Refutation found. Thanks to Tanya! 0.07/0.34 % SZS status Theorem for theBenchmark 0.07/0.34 % SZS output start Proof for theBenchmark 0.07/0.34 tff(type_def_5, type, uni: $tType). 0.07/0.34 tff(type_def_6, type, ty: $tType). 0.07/0.34 tff(type_def_7, type, bool: $tType). 0.07/0.34 tff(type_def_8, type, tuple0: $tType). 0.07/0.34 tff(func_def_0, type, witness: ty > uni). 0.07/0.34 tff(func_def_1, type, int: ty). 0.07/0.34 tff(func_def_2, type, real: ty). 0.07/0.34 tff(func_def_3, type, bool1: ty). 0.07/0.34 tff(func_def_4, type, true: bool). 0.07/0.34 tff(func_def_5, type, false: bool). 0.07/0.34 tff(func_def_6, type, match_bool: (ty * bool * uni * uni) > uni). 0.07/0.34 tff(func_def_7, type, tuple01: ty). 0.07/0.34 tff(func_def_8, type, tuple02: tuple0). 0.07/0.34 tff(func_def_9, type, qtmark: ty). 0.07/0.34 tff(func_def_10, type, power: ($int * $int) > $int). 0.07/0.34 tff(func_def_11, type, abs: $int > $int). 0.07/0.34 tff(func_def_12, type, div: ($int * $int) > $int). 0.07/0.34 tff(func_def_13, type, mod: ($int * $int) > $int). 0.07/0.34 tff(func_def_14, type, ref: ty > ty). 0.07/0.34 tff(func_def_15, type, mk_ref: (ty * uni) > uni). 0.07/0.34 tff(func_def_16, type, contents: (ty * uni) > uni). 0.07/0.34 tff(func_def_23, type, sK0: $int). 0.07/0.34 tff(func_def_24, type, sK1: $int). 0.07/0.34 tff(func_def_25, type, sK2: $int). 0.07/0.34 tff(func_def_26, type, sK3: $int). 0.07/0.34 tff(func_def_27, type, sK4: $int). 0.07/0.34 tff(pred_def_1, type, sort: (ty * uni) > $o). 0.07/0.34 tff(f16,conjecture,( 0.07/0.34 ! [X1 : $int,X6 : $int] : ($lesseq(0,X6) => ! [X8 : $int,X9 : $int,X10 : $int] : (($lesseq(0,X8) & power(X1,X6) = $product(X10,power(X9,X8))) => (~$less(0,X8) => power(X1,X6) = X10)))), 0.07/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wP_parameter_fast_exp_imperative)). 0.07/0.34 tff(f17,negated_conjecture,( 0.07/0.34 ~! [X1 : $int,X6 : $int] : ($lesseq(0,X6) => ! [X8 : $int,X9 : $int,X10 : $int] : (($lesseq(0,X8) & power(X1,X6) = $product(X10,power(X9,X8))) => (~$less(0,X8) => power(X1,X6) = X10)))), 0.07/0.34 inference(negated_conjecture,[],[f16])). 0.07/0.34 tff(f19,axiom,( 0.07/0.34 ! [X1 : $int,X2 : $int] : (0 != X2 => ($less(mod(X1,X2),abs(X2)) & $less($uminus(abs(X2)),mod(X1,X2))))), 0.07/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mod_bound)). 0.07/0.34 tff(f20,axiom,( 0.07/0.34 ! [X1 : $int] : ((~$lesseq(0,X1) => abs(X1) = $uminus(X1)) & ($lesseq(0,X1) => abs(X1) = X1))), 0.07/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abs_def)). 0.07/0.34 tff(f28,axiom,( 0.07/0.34 ! [X1 : $int] : power(X1,0) = 1), 0.07/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_0)). 0.07/0.34 tff(f39,plain,( 0.07/0.34 ~! [X1 : $int,X6 : $int] : (~$less(X6,0) => ! [X8 : $int,X9 : $int,X10 : $int] : ((~$less(X8,0) & power(X1,X6) = $product(X10,power(X9,X8))) => (~$less(0,X8) => power(X1,X6) = X10)))), 0.07/0.34 inference(evaluation,[],[f17])). 0.07/0.34 tff(f41,plain,( 0.07/0.34 ! [X1 : $int] : (($less(X1,0) => abs(X1) = $uminus(X1)) & (~$less(X1,0) => abs(X1) = X1))), 0.07/0.34 inference(evaluation,[],[f20])). 0.07/0.34 tff(f59,plain,( 0.07/0.34 ~! [X0 : $int,X1 : $int] : (~$less(X1,0) => ! [X2 : $int,X3 : $int,X4 : $int] : ((~$less(X2,0) & power(X0,X1) = $product(X4,power(X3,X2))) => (~$less(0,X2) => power(X0,X1) = X4)))), 0.07/0.34 inference(rectify,[],[f39])). 0.07/0.34 tff(f65,plain,( 0.07/0.34 ! [X0 : $int] : power(X0,0) = 1), 0.07/0.34 inference(rectify,[],[f28])). 0.07/0.34 tff(f66,plain,( 0.07/0.34 ! [X0 : $int] : (($less(X0,0) => abs(X0) = $uminus(X0)) & (~$less(X0,0) => abs(X0) = X0))), 0.07/0.34 inference(rectify,[],[f41])). 0.07/0.34 tff(f71,plain,( 0.07/0.34 ! [X0 : $int,X1 : $int] : (0 != X1 => ($less(mod(X0,X1),abs(X1)) & $less($uminus(abs(X1)),mod(X0,X1))))), 0.07/0.34 inference(rectify,[],[f19])). 0.07/0.34 tff(f93,plain,( 0.07/0.34 ? [X0 : $int,X1 : $int] : (? [X2 : $int,X3 : $int,X4 : $int] : ((power(X0,X1) != X4 & ~$less(0,X2)) & (~$less(X2,0) & power(X0,X1) = $product(X4,power(X3,X2)))) & ~$less(X1,0))), 0.07/0.34 inference(ennf_transformation,[],[f59])). 0.07/0.34 tff(f94,plain,( 0.07/0.34 ? [X0 : $int,X1 : $int] : (? [X2 : $int,X3 : $int,X4 : $int] : (power(X0,X1) != X4 & ~$less(0,X2) & ~$less(X2,0) & power(X0,X1) = $product(X4,power(X3,X2))) & ~$less(X1,0))), 0.07/0.34 inference(flattening,[],[f93])). 0.07/0.34 tff(f95,plain,( 0.07/0.34 ! [X0 : $int] : ((abs(X0) = $uminus(X0) | ~$less(X0,0)) & (abs(X0) = X0 | $less(X0,0)))), 0.07/0.34 inference(ennf_transformation,[],[f66])). 0.07/0.34 tff(f98,plain,( 0.07/0.34 ! [X0 : $int,X1 : $int] : (($less(mod(X0,X1),abs(X1)) & $less($uminus(abs(X1)),mod(X0,X1))) | 0 = X1)), 0.07/0.34 inference(ennf_transformation,[],[f71])). 0.07/0.34 tff(f130,plain,( 0.07/0.34 ? [X0 : $int,X1 : $int] : (? [X2 : $int,X3 : $int,X4 : $int] : (power(X0,X1) != X4 & ~$less(0,X2) & ~$less(X2,0) & power(X0,X1) = $product(X4,power(X3,X2))) & ~$less(X1,0)) => (? [X4 : $int,X3 : $int,X2 : $int] : (power(sK0,sK1) != X4 & ~$less(0,X2) & ~$less(X2,0) & power(sK0,sK1) = $product(X4,power(X3,X2))) & ~$less(sK1,0))), 0.07/0.34 introduced(choice_axiom,[])). 0.07/0.34 tff(f131,plain,( 0.07/0.34 ( ! [X0:$int,X1:$int] : (? [X2 : $int,X3 : $int,X4 : $int] : (power(X0,X1) != X4 & ~$less(0,X2) & ~$less(X2,0) & power(X0,X1) = $product(X4,power(X3,X2))) => (power(X0,X1) != sK4 & ~$less(0,sK2) & ~$less(sK2,0) & power(X0,X1) = $product(sK4,power(sK3,sK2)))) )), 0.07/0.34 introduced(choice_axiom,[])). 0.07/0.34 tff(f132,plain,( 0.07/0.34 (power(sK0,sK1) != sK4 & ~$less(0,sK2) & ~$less(sK2,0) & power(sK0,sK1) = $product(sK4,power(sK3,sK2))) & ~$less(sK1,0)), 0.07/0.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f94,f131,f130])). 0.07/0.34 tff(f135,plain,( 0.07/0.34 ~$less(sK1,0)), 0.07/0.34 inference(cnf_transformation,[],[f132])). 0.07/0.34 tff(f136,plain,( 0.07/0.34 power(sK0,sK1) = $product(sK4,power(sK3,sK2))), 0.07/0.34 inference(cnf_transformation,[],[f132])). 0.07/0.34 tff(f137,plain,( 0.07/0.34 ~$less(sK2,0)), 0.07/0.34 inference(cnf_transformation,[],[f132])). 0.07/0.34 tff(f138,plain,( 0.07/0.34 ~$less(0,sK2)), 0.07/0.34 inference(cnf_transformation,[],[f132])). 0.07/0.34 tff(f139,plain,( 0.07/0.34 power(sK0,sK1) != sK4), 0.07/0.34 inference(cnf_transformation,[],[f132])). 0.07/0.34 tff(f147,plain,( 0.07/0.34 ( ! [X0:$int] : (power(X0,0) = 1) )), 0.07/0.34 inference(cnf_transformation,[],[f65])). 0.07/0.34 tff(f148,plain,( 0.07/0.34 ( ! [X0:$int] : ($less(X0,0) | abs(X0) = X0) )), 0.07/0.34 inference(cnf_transformation,[],[f95])). 0.07/0.34 tff(f155,plain,( 0.07/0.34 ( ! [X0:$int,X1:$int] : ($less($uminus(abs(X1)),mod(X0,X1)) | 0 = X1) )), 0.07/0.34 inference(cnf_transformation,[],[f98])). 0.07/0.34 tff(f156,plain,( 0.07/0.34 ( ! [X0:$int,X1:$int] : ($less(mod(X0,X1),abs(X1)) | 0 = X1) )), 0.07/0.34 inference(cnf_transformation,[],[f98])). 0.07/0.34 tff(f186,plain,( 0.07/0.34 spl5_1 <=> power(sK0,sK1) != sK4), 0.07/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_1])])). 0.07/0.34 tff(f187,plain,( 0.07/0.34 power(sK0,sK1) != sK4 | ~spl5_1), 0.07/0.34 inference(avatar_component_clause,[],[f186])). 0.07/0.34 tff(f188,plain,( 0.07/0.34 ~spl5_1), 0.07/0.34 inference(avatar_split_clause,[],[f139,f186])). 0.07/0.34 tff(f193,plain,( 0.07/0.34 spl5_3 <=> ~$less(0,sK2)), 0.07/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_3])])). 0.07/0.34 tff(f195,plain,( 0.07/0.34 ~spl5_3), 0.07/0.34 inference(avatar_split_clause,[],[f138,f193])). 0.07/0.34 tff(f200,plain,( 0.07/0.34 spl5_5 <=> ~$less(sK2,0)), 0.07/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_5])])). 0.07/0.34 tff(f201,plain,( 0.07/0.34 ~$less(sK2,0) | ~spl5_5), 0.07/0.34 inference(avatar_component_clause,[],[f200])). 0.07/0.34 tff(f202,plain,( 0.07/0.34 ~spl5_5), 0.07/0.34 inference(avatar_split_clause,[],[f137,f200])). 0.07/0.34 tff(f207,plain,( 0.07/0.34 spl5_6 <=> power(sK0,sK1) = $product(sK4,power(sK3,sK2))), 0.07/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_6])])). 0.07/0.34 tff(f208,plain,( 0.07/0.34 power(sK0,sK1) = $product(sK4,power(sK3,sK2)) | ~spl5_6), 0.07/0.34 inference(avatar_component_clause,[],[f207])). 0.07/0.34 tff(f209,plain,( 0.07/0.34 spl5_6), 0.07/0.34 inference(avatar_split_clause,[],[f136,f207])). 0.07/0.34 tff(f214,plain,( 0.07/0.34 spl5_9 <=> ~$less(sK1,0)), 0.07/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_9])])). 0.07/0.34 tff(f215,plain,( 0.07/0.34 ~$less(sK1,0) | ~spl5_9), 0.07/0.34 inference(avatar_component_clause,[],[f214])). 0.07/0.34 tff(f216,plain,( 0.07/0.34 ~spl5_9), 0.07/0.34 inference(avatar_split_clause,[],[f135,f214])). 0.07/0.34 tff(f217,plain,( 0.07/0.34 abs(sK2) = sK2 | ~spl5_5), 0.07/0.34 inference(resolution,[],[f201,f148])). 0.07/0.34 tff(f228,plain,( 0.07/0.34 spl5_10 <=> abs(sK2) = sK2), 0.07/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_10])])). 0.07/0.34 tff(f229,plain,( 0.07/0.34 abs(sK2) = sK2 | ~spl5_10), 0.07/0.34 inference(avatar_component_clause,[],[f228])). 0.07/0.34 tff(f230,plain,( 0.07/0.34 spl5_10 | spl5_5), 0.07/0.34 inference(avatar_split_clause,[],[f217,f200,f228])). 0.07/0.34 tff(f231,plain,( 0.07/0.34 abs(sK1) = sK1 | ~spl5_9), 0.07/0.34 inference(resolution,[],[f215,f148])). 0.07/0.34 tff(f242,plain,( 0.07/0.34 spl5_12 <=> abs(sK1) = sK1), 0.07/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_12])])). 0.07/0.34 tff(f243,plain,( 0.07/0.34 abs(sK1) = sK1 | ~spl5_12), 0.07/0.34 inference(avatar_component_clause,[],[f242])). 0.07/0.34 tff(f244,plain,( 0.07/0.34 spl5_12 | spl5_9), 0.07/0.34 inference(avatar_split_clause,[],[f231,f214,f242])). 0.07/0.34 tff(f246,plain,( 0.07/0.34 ( ! [X1:$int] : ($less($uminus(sK2),mod(X1,sK2)) | 0 = sK2) ) | ~spl5_10), 0.07/0.34 inference(superposition,[],[f155,f229])). 0.07/0.34 tff(f247,plain,( 0.07/0.34 ( ! [X2:$int] : ($less(mod(X2,sK2),sK2) | 0 = sK2) ) | ~spl5_10), 0.07/0.34 inference(superposition,[],[f156,f229])). 0.07/0.34 tff(f254,plain,( 0.07/0.34 spl5_14 <=> 0 = sK2), 0.07/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_14])])). 0.07/0.34 tff(f255,plain,( 0.07/0.34 0 = sK2 | ~spl5_14), 0.07/0.34 inference(avatar_component_clause,[],[f254])). 0.07/0.34 tff(f257,plain,( 0.07/0.34 spl5_16 <=> ! [X1 : $int] : $less($uminus(sK2),mod(X1,sK2))), 0.07/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_16])])). 0.07/0.34 tff(f259,plain,( 0.07/0.34 spl5_14 | spl5_16 | ~spl5_10), 0.07/0.34 inference(avatar_split_clause,[],[f246,f228,f257,f254])). 0.07/0.34 tff(f261,plain,( 0.07/0.34 spl5_18 <=> ! [X2 : $int] : $less(mod(X2,sK2),sK2)), 0.07/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_18])])). 0.07/0.34 tff(f263,plain,( 0.07/0.34 spl5_14 | spl5_18 | ~spl5_10), 0.07/0.34 inference(avatar_split_clause,[],[f247,f228,f261,f254])). 0.07/0.34 tff(f264,plain,( 0.07/0.34 abs(0) = 0 | (~spl5_10 | ~spl5_14)), 0.07/0.34 inference(backward_demodulation,[],[f255,f229])). 0.07/0.34 tff(f271,plain,( 0.07/0.34 spl5_20 <=> abs(0) = 0), 0.07/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_20])])). 0.07/0.34 tff(f273,plain,( 0.07/0.34 spl5_20 | ~spl5_10 | ~spl5_14), 0.07/0.34 inference(avatar_split_clause,[],[f264,f254,f228,f271])). 0.07/0.34 tff(f275,plain,( 0.07/0.34 ( ! [X1:$int] : ($less($uminus(sK1),mod(X1,sK1)) | 0 = sK1) ) | ~spl5_12), 0.07/0.34 inference(superposition,[],[f155,f243])). 0.07/0.34 tff(f276,plain,( 0.07/0.34 ( ! [X2:$int] : ($less(mod(X2,sK1),sK1) | 0 = sK1) ) | ~spl5_12), 0.07/0.34 inference(superposition,[],[f156,f243])). 0.07/0.34 tff(f283,plain,( 0.07/0.34 spl5_22 <=> 0 = sK1), 0.07/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_22])])). 0.07/0.34 tff(f284,plain,( 0.07/0.34 0 = sK1 | ~spl5_22), 0.07/0.34 inference(avatar_component_clause,[],[f283])). 0.07/0.34 tff(f286,plain,( 0.07/0.34 spl5_24 <=> ! [X1 : $int] : $less($uminus(sK1),mod(X1,sK1))), 0.07/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_24])])). 0.07/0.34 tff(f288,plain,( 0.07/0.34 spl5_22 | spl5_24 | ~spl5_12), 0.07/0.34 inference(avatar_split_clause,[],[f275,f242,f286,f283])). 0.07/0.34 tff(f290,plain,( 0.07/0.34 spl5_26 <=> ! [X2 : $int] : $less(mod(X2,sK1),sK1)), 0.07/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_26])])). 0.07/0.34 tff(f292,plain,( 0.07/0.34 spl5_22 | spl5_26 | ~spl5_12), 0.07/0.34 inference(avatar_split_clause,[],[f276,f242,f290,f283])). 0.07/0.34 tff(f293,plain,( 0.07/0.34 abs(0) = 0 | (~spl5_12 | ~spl5_22)), 0.07/0.34 inference(backward_demodulation,[],[f284,f243])). 0.07/0.34 tff(f295,plain,( 0.07/0.34 spl5_20 | ~spl5_12 | ~spl5_22), 0.07/0.34 inference(avatar_split_clause,[],[f293,f283,f242,f271])). 0.07/0.34 tff(f301,plain,( 0.07/0.34 power(sK0,0) != sK4 | (~spl5_1 | ~spl5_22)), 0.07/0.34 inference(forward_demodulation,[],[f187,f284])). 0.07/0.34 tff(f302,plain,( 0.07/0.34 1 != sK4 | (~spl5_1 | ~spl5_22)), 0.07/0.34 inference(forward_demodulation,[],[f301,f147])). 0.07/0.34 tff(f307,plain,( 0.07/0.34 spl5_29 <=> 1 != sK4), 0.07/0.34 introduced(avatar_definition,[new_symbols(naming,[spl5_29])])). 0.07/0.34 tff(f308,plain,( 0.07/0.34 1 != sK4 | ~spl5_29), 0.07/0.34 inference(avatar_component_clause,[],[f307])). 0.07/0.34 tff(f309,plain,( 0.07/0.34 ~spl5_29 | spl5_1 | ~spl5_22), 0.07/0.34 inference(avatar_split_clause,[],[f302,f283,f186,f307])). 0.07/0.34 tff(f310,plain,( 0.07/0.34 power(sK0,sK1) = $product(sK4,power(sK3,0)) | (~spl5_6 | ~spl5_14)), 0.07/0.34 inference(forward_demodulation,[],[f208,f255])). 0.07/0.34 tff(f311,plain,( 0.07/0.34 power(sK0,sK1) = $product(sK4,1) | (~spl5_6 | ~spl5_14)), 0.07/0.34 inference(forward_demodulation,[],[f310,f147])). 0.07/0.34 tff(f312,plain,( 0.07/0.34 power(sK0,sK1) = sK4 | (~spl5_6 | ~spl5_14)), 0.07/0.34 inference(evaluation,[],[f311])). 0.07/0.34 tff(f313,plain,( 0.07/0.34 power(sK0,0) = sK4 | (~spl5_6 | ~spl5_14 | ~spl5_22)), 0.07/0.34 inference(forward_demodulation,[],[f312,f284])). 0.07/0.34 tff(f314,plain,( 0.07/0.34 1 = sK4 | (~spl5_6 | ~spl5_14 | ~spl5_22)), 0.07/0.34 inference(forward_demodulation,[],[f313,f147])). 0.07/0.34 tff(f315,plain,( 0.07/0.34 $false | (~spl5_6 | ~spl5_14 | ~spl5_22 | ~spl5_29)), 0.07/0.34 inference(subsumption_resolution,[],[f314,f308])). 0.07/0.34 tff(f316,plain,( 0.07/0.34 ~spl5_6 | ~spl5_14 | ~spl5_22 | spl5_29), 0.07/0.34 inference(avatar_contradiction_clause,[],[f315])). 0.07/0.34 tff(f317,plain,( 0.07/0.34 $false | (~spl5_6 | ~spl5_14)), 0.07/0.34 inference(global_subsumption,[],[f139,f312])). 0.07/0.34 tff(f318,plain,( 0.07/0.34 ~spl5_6 | ~spl5_14), 0.07/0.34 inference(avatar_contradiction_clause,[],[f317])). 0.07/0.34 tff(f319,plain,( 0.07/0.34 $false), 0.07/0.34 inference(avatar_sat_refutation,[],[f188,f195,f202,f209,f216,f230,f244,f259,f263,f273,f288,f292,f295,f309,f316,f318])). 0.07/0.34 % SZS output end Proof for theBenchmark 0.07/0.34 % ------------------------------ 0.07/0.34 % Version: Vampire 4.2.2 (commit 552c234 on 2018-07-02 14:53:33 +0100) 0.07/0.34 % Termination reason: Refutation 0.07/0.34 0.07/0.34 % Memory used [KB]: 5245 0.07/0.34 % Time elapsed: 0.040 s 0.07/0.34 % ------------------------------ 0.07/0.34 % ------------------------------ 0.07/0.34 % Success in time 0.076 s 0.07/0.35 EOF