0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : vampire --mode casc -t %d %s 0.02/0.23 % Computer : n182.star.cs.uiowa.edu 0.02/0.23 % Model : x86_64 x86_64 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.23 % Memory : 32218.625MB 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.23 % CPULimit : 300 0.02/0.23 % DateTime : Sat Jul 14 05:02:39 CDT 2018 0.02/0.23 % CPUTime : 0.06/0.27 % 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 0.06/0.41 % Refutation found. Thanks to Tanya! 0.06/0.41 % SZS status Theorem for theBenchmark 0.06/0.41 % SZS output start Proof for theBenchmark 0.06/0.41 tff(type_def_5, type, uni: $tType). 0.06/0.41 tff(type_def_6, type, ty: $tType). 0.06/0.41 tff(type_def_7, type, bool1: $tType). 0.06/0.41 tff(type_def_8, type, tuple02: $tType). 0.06/0.41 tff(type_def_9, type, elt4: $tType). 0.06/0.41 tff(type_def_10, type, array_elt2: $tType). 0.06/0.41 tff(type_def_11, type, map_int_elt2: $tType). 0.06/0.41 tff(func_def_0, type, witness1: ty > uni). 0.06/0.41 tff(func_def_1, type, int: ty). 0.06/0.41 tff(func_def_2, type, real: ty). 0.06/0.41 tff(func_def_3, type, bool: ty). 0.06/0.41 tff(func_def_4, type, true1: bool1). 0.06/0.41 tff(func_def_5, type, false1: bool1). 0.06/0.41 tff(func_def_6, type, match_bool1: (ty * bool1 * uni * uni) > uni). 0.06/0.41 tff(func_def_7, type, tuple0: ty). 0.06/0.41 tff(func_def_8, type, tuple03: tuple02). 0.06/0.41 tff(func_def_9, type, qtmark: ty). 0.06/0.41 tff(func_def_10, type, map: (ty * ty) > ty). 0.06/0.41 tff(func_def_11, type, get: (ty * ty * uni * uni) > uni). 0.06/0.41 tff(func_def_12, type, set: (ty * ty * uni * uni * uni) > uni). 0.06/0.41 tff(func_def_13, type, const: (ty * ty * uni) > uni). 0.06/0.41 tff(func_def_14, type, array: ty > ty). 0.06/0.41 tff(func_def_15, type, mk_array1: (ty * $int * uni) > uni). 0.06/0.41 tff(func_def_16, type, length1: (ty * uni) > $int). 0.06/0.41 tff(func_def_17, type, elts: (ty * uni) > uni). 0.06/0.41 tff(func_def_18, type, get2: (ty * uni * $int) > uni). 0.06/0.41 tff(func_def_19, type, t2tb: $int > uni). 0.06/0.41 tff(func_def_20, type, tb2t: uni > $int). 0.06/0.41 tff(func_def_21, type, set2: (ty * uni * $int * uni) > uni). 0.06/0.41 tff(func_def_22, type, make1: (ty * $int * uni) > uni). 0.06/0.41 tff(func_def_23, type, elt5: ty). 0.06/0.41 tff(func_def_24, type, t2tb7: elt4 > uni). 0.06/0.41 tff(func_def_25, type, tb2t7: uni > elt4). 0.06/0.41 tff(func_def_26, type, t2tb8: array_elt2 > uni). 0.06/0.41 tff(func_def_27, type, tb2t8: uni > array_elt2). 0.06/0.41 tff(func_def_28, type, ref: ty > ty). 0.06/0.41 tff(func_def_29, type, mk_ref: (ty * uni) > uni). 0.06/0.41 tff(func_def_30, type, contents: (ty * uni) > uni). 0.06/0.41 tff(func_def_31, type, occ1: (ty * uni * uni * $int * $int) > $int). 0.06/0.41 tff(func_def_32, type, abs: $int > $int). 0.06/0.41 tff(func_def_33, type, div: ($int * $int) > $int). 0.06/0.41 tff(func_def_34, type, mod: ($int * $int) > $int). 0.06/0.41 tff(func_def_35, type, min: ($int * $int) > $int). 0.06/0.41 tff(func_def_36, type, max: ($int * $int) > $int). 0.06/0.41 tff(func_def_37, type, t2tb9: map_int_elt2 > uni). 0.06/0.41 tff(func_def_38, type, tb2t9: uni > map_int_elt2). 0.06/0.41 tff(func_def_45, type, sK0: $int). 0.06/0.41 tff(func_def_46, type, sK1: map_int_elt2). 0.06/0.41 tff(func_def_47, type, sK2: $int). 0.06/0.41 tff(func_def_48, type, sK3: map_int_elt2). 0.06/0.41 tff(func_def_49, type, sK4: $int). 0.06/0.41 tff(func_def_50, type, sK5: map_int_elt2). 0.06/0.41 tff(func_def_51, type, sK6: $int). 0.06/0.41 tff(func_def_52, type, sK7: array_elt2 > $int). 0.06/0.41 tff(func_def_53, type, sK8: array_elt2 > $int). 0.06/0.41 tff(func_def_54, type, sK9: (array_elt2 * $int * $int) > $int). 0.06/0.41 tff(func_def_55, type, sK10: (array_elt2 * $int * $int) > $int). 0.06/0.41 tff(func_def_56, type, sK11: (ty * uni * uni * $int * $int) > uni). 0.06/0.41 tff(func_def_57, type, sK12: (ty * uni * uni * $int * $int) > $int). 0.06/0.41 tff(func_def_58, type, sK13: (ty * uni * uni * $int * $int) > $int). 0.06/0.41 tff(func_def_59, type, sK14: (ty * uni * uni * $int * $int) > $int). 0.06/0.41 tff(func_def_60, type, sK15: (ty * uni * uni * $int * $int * $int) > $int). 0.06/0.41 tff(func_def_61, type, sK16: (ty * uni * uni * $int * $int) > $int). 0.06/0.41 tff(func_def_62, type, sK17: (ty * uni * uni * $int * $int * $int * $int) > $int). 0.06/0.41 tff(func_def_65, type, '$inst19': $int). 0.06/0.41 tff(func_def_66, type, '$inst20': $int). 0.06/0.41 tff(func_def_67, type, '$inst21': $int). 0.06/0.41 tff(pred_def_1, type, sort1: (ty * uni) > $o). 0.06/0.41 tff(pred_def_2, type, le3: (elt4 * elt4) > $o). 0.06/0.41 tff(pred_def_3, type, sorted_sub3: (array_elt2 * $int * $int) > $o). 0.06/0.41 tff(pred_def_4, type, sorted3: array_elt2 > $o). 0.06/0.41 tff(pred_def_5, type, permut2: (ty * uni * uni * $int * $int) > $o). 0.06/0.41 tff(pred_def_6, type, map_eq_sub1: (ty * uni * uni * $int * $int) > $o). 0.06/0.41 tff(pred_def_7, type, array_eq_sub1: (ty * uni * uni * $int * $int) > $o). 0.06/0.41 tff(pred_def_8, type, array_eq: (ty * uni * uni) > $o). 0.06/0.41 tff(pred_def_9, type, exchange2: (ty * uni * uni * $int * $int * $int * $int) > $o). 0.06/0.41 tff(pred_def_10, type, exchange3: (ty * uni * uni * $int * $int) > $o). 0.06/0.41 tff(pred_def_11, type, permut3: (ty * uni * uni * $int * $int) > $o). 0.06/0.41 tff(pred_def_12, type, permut_sub1: (ty * uni * uni * $int * $int) > $o). 0.06/0.41 tff(pred_def_13, type, permut_all: (ty * uni * uni) > $o). 0.06/0.41 tff(f5,axiom,( 0.06/0.41 ! [X4 : $int,X9 : $int] : ($lesseq(X4,X9) => min(X4,X9) = X4)), 0.06/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',min_x)). 0.06/0.41 tff(f18,axiom,( 0.06/0.41 ! [X0 : ty,X6 : uni,X13 : uni] : ((permut2(X0,elts(X0,X6),elts(X0,X13),0,length1(X0,X6)) & length1(X0,X6) = length1(X0,X13)) <=> permut_all(X0,X6,X13))), 0.06/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',permut_all_def)). 0.06/0.41 tff(f20,axiom,( 0.06/0.41 ! [X0 : array_elt2,X12 : $int,X1 : $int] : (sorted_sub3(X0,X12,X1) <=> ! [X18 : $int,X19 : $int] : (($less(X19,X1) & $lesseq(X18,X19) & $lesseq(X12,X18)) => le3(tb2t7(get2(elt5,t2tb8(X0),X18)),tb2t7(get2(elt5,t2tb8(X0),X19)))))), 0.06/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',sorted_sub_def2)). 0.06/0.41 tff(f25,axiom,( 0.06/0.41 ! [X4 : $int,X9 : $int] : (($less(X4,X9) & $lesseq(0,X4)) => div(X4,X9) = 0)), 0.06/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',div_inf)). 0.06/0.41 tff(f30,axiom,( 0.06/0.41 ! [X4 : $int,X9 : $int] : (min(X4,X9) = X9 | min(X4,X9) = X4)), 0.06/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',min_is_some)). 0.06/0.41 tff(f31,conjecture,( 0.06/0.41 ! [X0 : $int,X6 : map_int_elt2] : ($lesseq(0,X0) => ! [X20 : $int,X21 : map_int_elt2] : (($lesseq(0,X20) & ! [X7 : $int] : (($lesseq(0,X7) & $less(X7,X20)) => tb2t7(get(elt5,int,t2tb9(X6),t2tb(X7))) = tb2t7(get(elt5,int,t2tb9(X21),t2tb(X7)))) & X0 = X20) => ! [X22 : $int,X13 : map_int_elt2] : (($lesseq(1,X22) & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X6)),mk_array1(elt5,X0,t2tb9(X13))) & ! [X23 : $int] : (($less($product(X23,X22),X0) & $lesseq(0,$product(X23,X22))) => sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X13))),$product(X23,X22),min(X0,$sum($product(X23,X22),X22))))) => ($less(X22,X0) => ! [X23 : $int] : (($lesseq(0,$product(X23,X22)) & $less($product(X23,X22),X0)) => sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X13))),$product(X23,X22),min(X0,$sum($product(X23,X22),X22))))))))), 0.06/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',wP_parameter_bottom_up_mergesort)). 0.06/0.41 tff(f32,negated_conjecture,( 0.06/0.41 ~! [X0 : $int,X6 : map_int_elt2] : ($lesseq(0,X0) => ! [X20 : $int,X21 : map_int_elt2] : (($lesseq(0,X20) & ! [X7 : $int] : (($lesseq(0,X7) & $less(X7,X20)) => tb2t7(get(elt5,int,t2tb9(X6),t2tb(X7))) = tb2t7(get(elt5,int,t2tb9(X21),t2tb(X7)))) & X0 = X20) => ! [X22 : $int,X13 : map_int_elt2] : (($lesseq(1,X22) & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X6)),mk_array1(elt5,X0,t2tb9(X13))) & ! [X23 : $int] : (($less($product(X23,X22),X0) & $lesseq(0,$product(X23,X22))) => sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X13))),$product(X23,X22),min(X0,$sum($product(X23,X22),X22))))) => ($less(X22,X0) => ! [X23 : $int] : (($lesseq(0,$product(X23,X22)) & $less($product(X23,X22),X0)) => sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X13))),$product(X23,X22),min(X0,$sum($product(X23,X22),X22))))))))), 0.06/0.41 inference(negated_conjecture,[],[f31])). 0.06/0.41 tff(f41,axiom,( 0.06/0.41 ! [X4 : $int,X9 : $int] : (0 != X9 => ($less($uminus(abs(X9)),mod(X4,X9)) & $less(mod(X4,X9),abs(X9))))), 0.06/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mod_bound)). 0.06/0.41 tff(f43,axiom,( 0.06/0.41 ! [X0 : ty,X1 : $int,X2 : uni] : length1(X0,mk_array1(X0,X1,X2)) = X1), 0.06/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',length_def1)). 0.06/0.41 tff(f48,axiom,( 0.06/0.41 ! [X4 : $int,X9 : $int] : ($lesseq(X9,X4) => min(X4,X9) = min(X9,X4))), 0.06/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',min_sym)). 0.06/0.41 tff(f50,axiom,( 0.06/0.41 ! [X4 : $int,X9 : $int] : (($lesseq($uminus(X9),X4) & $lesseq(X4,X9)) <=> $lesseq(abs(X4),X9))), 0.06/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',abs_le)). 0.06/0.41 tff(f53,axiom,( 0.06/0.41 ! [X4 : $int,X9 : $int] : ($lesseq(X9,X4) => max(X4,X9) = X4)), 0.06/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_x)). 0.06/0.41 tff(f56,axiom,( 0.06/0.41 ! [X4 : $int,X9 : $int] : ($lesseq(X9,max(X4,X9)) & $lesseq(X4,max(X4,X9)))), 0.06/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_is_ge)). 0.06/0.41 tff(f61,axiom,( 0.06/0.41 ! [X4 : $int] : ((~$lesseq(0,X4) => abs(X4) = $uminus(X4)) & ($lesseq(0,X4) => abs(X4) = X4))), 0.06/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',abs_def)). 0.06/0.41 tff(f77,axiom,( 0.06/0.41 ! [X4 : $int,X9 : $int] : (0 != X9 => $lesseq(abs($product(div(X4,X9),X9)),abs(X4)))), 0.06/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',rounds_toward_zero)). 0.06/0.41 tff(f80,axiom,( 0.06/0.41 ! [X4 : $int,X9 : $int] : (0 != X9 => $sum($product(X9,div(X4,X9)),mod(X4,X9)) = X4)), 0.06/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',div_mod)). 0.06/0.41 tff(f85,axiom,( 0.06/0.41 ! [X4 : $int,X9 : $int] : ($lesseq(X9,X4) => max(X4,X9) = max(X9,X4))), 0.06/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_sym)). 0.06/0.41 tff(f94,axiom,( 0.06/0.41 ! [X4 : $int,X9 : $int] : (($less(X4,X9) & $lesseq(0,X4)) => mod(X4,X9) = X4)), 0.06/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mod_inf)). 0.06/0.41 tff(f98,axiom,( 0.06/0.41 ! [X4 : $int,X9 : $int] : ($lesseq(X9,X4) => min(X4,X9) = X9)), 0.06/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',min_y)). 0.06/0.41 tff(f99,axiom,( 0.06/0.41 ! [X4 : $int,X9 : $int] : ($lesseq(X4,X9) => max(X4,X9) = X9)), 0.06/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_y)). 0.06/0.41 tff(f100,plain,( 0.06/0.41 ~! [X0 : $int,X6 : map_int_elt2] : (~$less(X0,0) => ! [X20 : $int,X21 : map_int_elt2] : ((~$less(X20,0) & ! [X7 : $int] : ((~$less(X7,0) & $less(X7,X20)) => tb2t7(get(elt5,int,t2tb9(X6),t2tb(X7))) = tb2t7(get(elt5,int,t2tb9(X21),t2tb(X7)))) & X0 = X20) => ! [X22 : $int,X13 : map_int_elt2] : ((~$less(X22,1) & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X6)),mk_array1(elt5,X0,t2tb9(X13))) & ! [X23 : $int] : (($less($product(X23,X22),X0) & ~$less($product(X23,X22),0)) => sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X13))),$product(X23,X22),min(X0,$sum($product(X23,X22),X22))))) => ($less(X22,X0) => ! [X23 : $int] : ((~$less($product(X23,X22),0) & $less($product(X23,X22),X0)) => sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X13))),$product(X23,X22),min(X0,$sum($product(X23,X22),X22))))))))), 0.06/0.41 inference(evaluation,[],[f32])). 0.06/0.41 tff(f102,plain,( 0.06/0.41 ! [X4 : $int] : (($less(X4,0) => abs(X4) = $uminus(X4)) & (~$less(X4,0) => abs(X4) = X4))), 0.06/0.41 inference(evaluation,[],[f61])). 0.06/0.41 tff(f104,plain,( 0.06/0.41 ! [X4 : $int,X9 : $int] : (~$less(max(X4,X9),X9) & ~$less(max(X4,X9),X4))), 0.06/0.41 inference(evaluation,[],[f56])). 0.06/0.41 tff(f106,plain,( 0.06/0.41 ! [X4 : $int,X9 : $int] : (0 != X9 => ~$less(abs(X4),abs($product(div(X4,X9),X9))))), 0.06/0.41 inference(evaluation,[],[f77])). 0.06/0.41 tff(f107,plain,( 0.06/0.41 ! [X4 : $int,X9 : $int] : (~$less(X9,X4) => min(X4,X9) = X4)), 0.06/0.41 inference(evaluation,[],[f5])). 0.06/0.41 tff(f108,plain,( 0.06/0.41 ! [X4 : $int,X9 : $int] : (~$less(X9,X4) => max(X4,X9) = X9)), 0.06/0.41 inference(evaluation,[],[f99])). 0.06/0.41 tff(f109,plain,( 0.06/0.41 ! [X4 : $int,X9 : $int] : (~$less(X4,X9) => max(X4,X9) = X4)), 0.06/0.41 inference(evaluation,[],[f53])). 0.06/0.41 tff(f110,plain,( 0.06/0.41 ! [X4 : $int,X9 : $int] : (~$less(X4,X9) => min(X4,X9) = X9)), 0.06/0.41 inference(evaluation,[],[f98])). 0.06/0.41 tff(f111,plain,( 0.06/0.41 ! [X4 : $int,X9 : $int] : (~$less(X4,X9) => min(X4,X9) = min(X9,X4))), 0.06/0.41 inference(evaluation,[],[f48])). 0.06/0.41 tff(f112,plain,( 0.06/0.41 ! [X4 : $int,X9 : $int] : (~$less(X4,X9) => max(X4,X9) = max(X9,X4))), 0.06/0.41 inference(evaluation,[],[f85])). 0.06/0.41 tff(f117,plain,( 0.06/0.41 ! [X4 : $int,X9 : $int] : (($less(X4,X9) & ~$less(X4,0)) => mod(X4,X9) = X4)), 0.06/0.41 inference(evaluation,[],[f94])). 0.06/0.41 tff(f118,plain,( 0.06/0.41 ! [X4 : $int,X9 : $int] : (($less(X4,X9) & ~$less(X4,0)) => div(X4,X9) = 0)), 0.06/0.41 inference(evaluation,[],[f25])). 0.06/0.41 tff(f120,plain,( 0.06/0.41 ! [X4 : $int,X9 : $int] : ((~$less(X4,$uminus(X9)) & ~$less(X9,X4)) <=> ~$less(X9,abs(X4)))), 0.06/0.41 inference(evaluation,[],[f50])). 0.06/0.41 tff(f124,plain,( 0.06/0.41 ! [X0 : array_elt2,X12 : $int,X1 : $int] : (sorted_sub3(X0,X12,X1) <=> ! [X18 : $int,X19 : $int] : (($less(X19,X1) & ~$less(X19,X18) & ~$less(X18,X12)) => le3(tb2t7(get2(elt5,t2tb8(X0),X18)),tb2t7(get2(elt5,t2tb8(X0),X19)))))), 0.06/0.41 inference(evaluation,[],[f20])). 0.06/0.41 tff(f142,plain,( 0.06/0.41 ~! [X0 : $int,X1 : map_int_elt2] : (~$less(X0,0) => ! [X2 : $int,X3 : map_int_elt2] : ((~$less(X2,0) & ! [X4 : $int] : ((~$less(X4,0) & $less(X4,X2)) => tb2t7(get(elt5,int,t2tb9(X1),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X3),t2tb(X4)))) & X0 = X2) => ! [X5 : $int,X6 : map_int_elt2] : ((~$less(X5,1) & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X6))) & ! [X7 : $int] : (($less($product(X7,X5),X0) & ~$less($product(X7,X5),0)) => sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X7,X5),min(X0,$sum($product(X7,X5),X5))))) => ($less(X5,X0) => ! [X8 : $int] : ((~$less($product(X8,X5),0) & $less($product(X8,X5),X0)) => sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X8,X5),min(X0,$sum($product(X8,X5),X5))))))))), 0.06/0.41 inference(rectify,[],[f100])). 0.06/0.41 tff(f158,plain,( 0.06/0.41 ! [X0 : $int] : (($less(X0,0) => abs(X0) = $uminus(X0)) & (~$less(X0,0) => abs(X0) = X0))), 0.06/0.41 inference(rectify,[],[f102])). 0.06/0.41 tff(f166,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (~$less(max(X0,X1),X1) & ~$less(max(X0,X1),X0))), 0.06/0.41 inference(rectify,[],[f104])). 0.06/0.41 tff(f170,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (min(X0,X1) = X1 | min(X0,X1) = X0)), 0.06/0.41 inference(rectify,[],[f30])). 0.06/0.41 tff(f171,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (0 != X1 => ~$less(abs(X0),abs($product(div(X0,X1),X1))))), 0.06/0.41 inference(rectify,[],[f106])). 0.06/0.41 tff(f172,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (0 != X1 => $sum($product(X1,div(X0,X1)),mod(X0,X1)) = X0)), 0.06/0.41 inference(rectify,[],[f80])). 0.06/0.41 tff(f173,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (0 != X1 => ($less($uminus(abs(X1)),mod(X0,X1)) & $less(mod(X0,X1),abs(X1))))), 0.06/0.41 inference(rectify,[],[f41])). 0.06/0.41 tff(f174,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (~$less(X1,X0) => min(X0,X1) = X0)), 0.06/0.41 inference(rectify,[],[f107])). 0.06/0.41 tff(f175,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (~$less(X1,X0) => max(X0,X1) = X1)), 0.06/0.41 inference(rectify,[],[f108])). 0.06/0.41 tff(f176,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (~$less(X0,X1) => max(X0,X1) = X0)), 0.06/0.41 inference(rectify,[],[f109])). 0.06/0.41 tff(f177,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (~$less(X0,X1) => min(X0,X1) = X1)), 0.06/0.41 inference(rectify,[],[f110])). 0.06/0.41 tff(f178,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (~$less(X0,X1) => min(X0,X1) = min(X1,X0))), 0.06/0.41 inference(rectify,[],[f111])). 0.06/0.41 tff(f179,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (~$less(X0,X1) => max(X0,X1) = max(X1,X0))), 0.06/0.41 inference(rectify,[],[f112])). 0.06/0.41 tff(f184,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (($less(X0,X1) & ~$less(X0,0)) => mod(X0,X1) = X0)), 0.06/0.41 inference(rectify,[],[f117])). 0.06/0.41 tff(f185,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (($less(X0,X1) & ~$less(X0,0)) => div(X0,X1) = 0)), 0.06/0.41 inference(rectify,[],[f118])). 0.06/0.41 tff(f187,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : ((~$less(X0,$uminus(X1)) & ~$less(X1,X0)) <=> ~$less(X1,abs(X0)))), 0.06/0.41 inference(rectify,[],[f120])). 0.06/0.41 tff(f201,plain,( 0.06/0.41 ! [X0 : array_elt2,X1 : $int,X2 : $int] : (sorted_sub3(X0,X1,X2) <=> ! [X3 : $int,X4 : $int] : (($less(X4,X2) & ~$less(X4,X3) & ~$less(X3,X1)) => le3(tb2t7(get2(elt5,t2tb8(X0),X3)),tb2t7(get2(elt5,t2tb8(X0),X4)))))), 0.06/0.41 inference(rectify,[],[f124])). 0.06/0.41 tff(f202,plain,( 0.06/0.41 ! [X0 : ty,X1 : uni,X2 : uni] : ((permut2(X0,elts(X0,X1),elts(X0,X2),0,length1(X0,X1)) & length1(X0,X1) = length1(X0,X2)) <=> permut_all(X0,X1,X2))), 0.06/0.41 inference(rectify,[],[f18])). 0.06/0.41 tff(f233,plain,( 0.06/0.41 ? [X0 : $int,X1 : map_int_elt2] : (? [X2 : $int,X3 : map_int_elt2] : (? [X5 : $int,X6 : map_int_elt2] : ((? [X8 : $int] : (~sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X8,X5),min(X0,$sum($product(X8,X5),X5))) & (~$less($product(X8,X5),0) & $less($product(X8,X5),X0))) & $less(X5,X0)) & (~$less(X5,1) & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X6))) & ! [X7 : $int] : (sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X7,X5),min(X0,$sum($product(X7,X5),X5))) | (~$less($product(X7,X5),X0) | $less($product(X7,X5),0))))) & (~$less(X2,0) & ! [X4 : $int] : (tb2t7(get(elt5,int,t2tb9(X1),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X3),t2tb(X4))) | ($less(X4,0) | ~$less(X4,X2))) & X0 = X2)) & ~$less(X0,0))), 0.06/0.41 inference(ennf_transformation,[],[f142])). 0.06/0.41 tff(f234,plain,( 0.06/0.41 ? [X0 : $int,X1 : map_int_elt2] : (? [X2 : $int,X3 : map_int_elt2] : (? [X5 : $int,X6 : map_int_elt2] : (? [X8 : $int] : (~sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X8,X5),min(X0,$sum($product(X8,X5),X5))) & ~$less($product(X8,X5),0) & $less($product(X8,X5),X0)) & $less(X5,X0) & ~$less(X5,1) & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X6))) & ! [X7 : $int] : (sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X6))),$product(X7,X5),min(X0,$sum($product(X7,X5),X5))) | ~$less($product(X7,X5),X0) | $less($product(X7,X5),0))) & ~$less(X2,0) & ! [X4 : $int] : (tb2t7(get(elt5,int,t2tb9(X1),t2tb(X4))) = tb2t7(get(elt5,int,t2tb9(X3),t2tb(X4))) | $less(X4,0) | ~$less(X4,X2)) & X0 = X2) & ~$less(X0,0))), 0.06/0.41 inference(flattening,[],[f233])). 0.06/0.41 tff(f235,plain,( 0.06/0.41 ! [X0 : $int] : ((abs(X0) = $uminus(X0) | ~$less(X0,0)) & (abs(X0) = X0 | $less(X0,0)))), 0.06/0.41 inference(ennf_transformation,[],[f158])). 0.06/0.41 tff(f240,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (~$less(abs(X0),abs($product(div(X0,X1),X1))) | 0 = X1)), 0.06/0.41 inference(ennf_transformation,[],[f171])). 0.06/0.41 tff(f241,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : ($sum($product(X1,div(X0,X1)),mod(X0,X1)) = X0 | 0 = X1)), 0.06/0.41 inference(ennf_transformation,[],[f172])). 0.06/0.41 tff(f242,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (($less($uminus(abs(X1)),mod(X0,X1)) & $less(mod(X0,X1),abs(X1))) | 0 = X1)), 0.06/0.41 inference(ennf_transformation,[],[f173])). 0.06/0.41 tff(f244,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (min(X0,X1) = X0 | $less(X1,X0))), 0.06/0.41 inference(ennf_transformation,[],[f174])). 0.06/0.41 tff(f245,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (max(X0,X1) = X1 | $less(X1,X0))), 0.06/0.41 inference(ennf_transformation,[],[f175])). 0.06/0.41 tff(f246,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (max(X0,X1) = X0 | $less(X0,X1))), 0.06/0.41 inference(ennf_transformation,[],[f176])). 0.06/0.41 tff(f247,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (min(X0,X1) = X1 | $less(X0,X1))), 0.06/0.41 inference(ennf_transformation,[],[f177])). 0.06/0.41 tff(f248,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (min(X0,X1) = min(X1,X0) | $less(X0,X1))), 0.06/0.41 inference(ennf_transformation,[],[f178])). 0.06/0.41 tff(f249,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (max(X0,X1) = max(X1,X0) | $less(X0,X1))), 0.06/0.41 inference(ennf_transformation,[],[f179])). 0.06/0.41 tff(f259,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (mod(X0,X1) = X0 | (~$less(X0,X1) | $less(X0,0)))), 0.06/0.41 inference(ennf_transformation,[],[f184])). 0.06/0.41 tff(f260,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (mod(X0,X1) = X0 | ~$less(X0,X1) | $less(X0,0))), 0.06/0.41 inference(flattening,[],[f259])). 0.06/0.41 tff(f261,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (div(X0,X1) = 0 | (~$less(X0,X1) | $less(X0,0)))), 0.06/0.41 inference(ennf_transformation,[],[f185])). 0.06/0.41 tff(f262,plain,( 0.06/0.41 ! [X0 : $int,X1 : $int] : (div(X0,X1) = 0 | ~$less(X0,X1) | $less(X0,0))), 0.06/0.41 inference(flattening,[],[f261])). 0.06/0.41 tff(f276,plain,( 0.06/0.41 ! [X0 : array_elt2,X1 : $int,X2 : $int] : (sorted_sub3(X0,X1,X2) <=> ! [X3 : $int,X4 : $int] : (le3(tb2t7(get2(elt5,t2tb8(X0),X3)),tb2t7(get2(elt5,t2tb8(X0),X4))) | (~$less(X4,X2) | $less(X4,X3) | $less(X3,X1))))), 0.06/0.41 inference(ennf_transformation,[],[f201])). 0.06/0.41 tff(f277,plain,( 0.06/0.41 ! [X0 : array_elt2,X1 : $int,X2 : $int] : (sorted_sub3(X0,X1,X2) <=> ! [X3 : $int,X4 : $int] : (le3(tb2t7(get2(elt5,t2tb8(X0),X3)),tb2t7(get2(elt5,t2tb8(X0),X4))) | ~$less(X4,X2) | $less(X4,X3) | $less(X3,X1)))), 0.06/0.41 inference(flattening,[],[f276])). 0.06/0.41 tff(f315,plain,( 0.06/0.41 ? [X0 : $int,X1 : map_int_elt2] : (? [X2 : $int,X3 : map_int_elt2] : (? [X4 : $int,X5 : map_int_elt2] : (? [X6 : $int] : (~sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X6,X4),min(X0,$sum($product(X6,X4),X4))) & ~$less($product(X6,X4),0) & $less($product(X6,X4),X0)) & $less(X4,X0) & ~$less(X4,1) & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X5))) & ! [X7 : $int] : (sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X7,X4),min(X0,$sum($product(X7,X4),X4))) | ~$less($product(X7,X4),X0) | $less($product(X7,X4),0))) & ~$less(X2,0) & ! [X8 : $int] : (tb2t7(get(elt5,int,t2tb9(X1),t2tb(X8))) = tb2t7(get(elt5,int,t2tb9(X3),t2tb(X8))) | $less(X8,0) | ~$less(X8,X2)) & X0 = X2) & ~$less(X0,0))), 0.06/0.41 inference(rectify,[],[f234])). 0.06/0.41 tff(f316,plain,( 0.06/0.41 ? [X0 : $int,X1 : map_int_elt2] : (? [X2 : $int,X3 : map_int_elt2] : (? [X4 : $int,X5 : map_int_elt2] : (? [X6 : $int] : (~sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X6,X4),min(X0,$sum($product(X6,X4),X4))) & ~$less($product(X6,X4),0) & $less($product(X6,X4),X0)) & $less(X4,X0) & ~$less(X4,1) & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X5))) & ! [X7 : $int] : (sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X7,X4),min(X0,$sum($product(X7,X4),X4))) | ~$less($product(X7,X4),X0) | $less($product(X7,X4),0))) & ~$less(X2,0) & ! [X8 : $int] : (tb2t7(get(elt5,int,t2tb9(X1),t2tb(X8))) = tb2t7(get(elt5,int,t2tb9(X3),t2tb(X8))) | $less(X8,0) | ~$less(X8,X2)) & X0 = X2) & ~$less(X0,0)) => (? [X3 : map_int_elt2,X2 : $int] : (? [X5 : map_int_elt2,X4 : $int] : (? [X6 : $int] : (~sorted_sub3(tb2t8(mk_array1(elt5,sK0,t2tb9(X5))),$product(X6,X4),min(sK0,$sum($product(X6,X4),X4))) & ~$less($product(X6,X4),0) & $less($product(X6,X4),sK0)) & $less(X4,sK0) & ~$less(X4,1) & permut_all(elt5,mk_array1(elt5,sK0,t2tb9(sK1)),mk_array1(elt5,sK0,t2tb9(X5))) & ! [X7 : $int] : (sorted_sub3(tb2t8(mk_array1(elt5,sK0,t2tb9(X5))),$product(X7,X4),min(sK0,$sum($product(X7,X4),X4))) | ~$less($product(X7,X4),sK0) | $less($product(X7,X4),0))) & ~$less(X2,0) & ! [X8 : $int] : (tb2t7(get(elt5,int,t2tb9(sK1),t2tb(X8))) = tb2t7(get(elt5,int,t2tb9(X3),t2tb(X8))) | $less(X8,0) | ~$less(X8,X2)) & sK0 = X2) & ~$less(sK0,0))), 0.06/0.41 introduced(choice_axiom,[])). 0.06/0.41 tff(f317,plain,( 0.06/0.41 ( ! [X0:$int,X1:map_int_elt2] : (? [X2 : $int,X3 : map_int_elt2] : (? [X4 : $int,X5 : map_int_elt2] : (? [X6 : $int] : (~sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X6,X4),min(X0,$sum($product(X6,X4),X4))) & ~$less($product(X6,X4),0) & $less($product(X6,X4),X0)) & $less(X4,X0) & ~$less(X4,1) & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X5))) & ! [X7 : $int] : (sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X7,X4),min(X0,$sum($product(X7,X4),X4))) | ~$less($product(X7,X4),X0) | $less($product(X7,X4),0))) & ~$less(X2,0) & ! [X8 : $int] : (tb2t7(get(elt5,int,t2tb9(X1),t2tb(X8))) = tb2t7(get(elt5,int,t2tb9(X3),t2tb(X8))) | $less(X8,0) | ~$less(X8,X2)) & X0 = X2) => (? [X4 : $int,X5 : map_int_elt2] : (? [X6 : $int] : (~sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X6,X4),min(X0,$sum($product(X6,X4),X4))) & ~$less($product(X6,X4),0) & $less($product(X6,X4),X0)) & $less(X4,X0) & ~$less(X4,1) & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X5))) & ! [X7 : $int] : (sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X7,X4),min(X0,$sum($product(X7,X4),X4))) | ~$less($product(X7,X4),X0) | $less($product(X7,X4),0))) & ~$less(sK2,0) & ! [X8 : $int] : (tb2t7(get(elt5,int,t2tb9(sK3),t2tb(X8))) = tb2t7(get(elt5,int,t2tb9(X1),t2tb(X8))) | $less(X8,0) | ~$less(X8,sK2)) & sK2 = X0)) )), 0.06/0.41 introduced(choice_axiom,[])). 0.06/0.42 tff(f318,plain,( 0.06/0.42 ( ! [X0:$int,X1:map_int_elt2] : (? [X4 : $int,X5 : map_int_elt2] : (? [X6 : $int] : (~sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X6,X4),min(X0,$sum($product(X6,X4),X4))) & ~$less($product(X6,X4),0) & $less($product(X6,X4),X0)) & $less(X4,X0) & ~$less(X4,1) & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(X5))) & ! [X7 : $int] : (sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X7,X4),min(X0,$sum($product(X7,X4),X4))) | ~$less($product(X7,X4),X0) | $less($product(X7,X4),0))) => (? [X6 : $int] : (~sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(sK5))),$product(X6,sK4),min(X0,$sum($product(X6,sK4),sK4))) & ~$less($product(X6,sK4),0) & $less($product(X6,sK4),X0)) & $less(sK4,X0) & ~$less(sK4,1) & permut_all(elt5,mk_array1(elt5,X0,t2tb9(X1)),mk_array1(elt5,X0,t2tb9(sK5))) & ! [X7 : $int] : (sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(sK5))),$product(X7,sK4),min(X0,$sum($product(X7,sK4),sK4))) | ~$less($product(X7,sK4),X0) | $less($product(X7,sK4),0)))) )), 0.06/0.42 introduced(choice_axiom,[])). 0.06/0.42 tff(f319,plain,( 0.06/0.42 ( ! [X4:$int,X0:$int,X5:map_int_elt2] : (? [X6 : $int] : (~sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(X6,X4),min(X0,$sum($product(X6,X4),X4))) & ~$less($product(X6,X4),0) & $less($product(X6,X4),X0)) => (~sorted_sub3(tb2t8(mk_array1(elt5,X0,t2tb9(X5))),$product(sK6,X4),min(X0,$sum($product(sK6,X4),X4))) & ~$less($product(sK6,X4),0) & $less($product(sK6,X4),X0))) )), 0.06/0.42 introduced(choice_axiom,[])). 0.06/0.42 tff(f320,plain,( 0.06/0.42 (((~sorted_sub3(tb2t8(mk_array1(elt5,sK0,t2tb9(sK5))),$product(sK6,sK4),min(sK0,$sum($product(sK6,sK4),sK4))) & ~$less($product(sK6,sK4),0) & $less($product(sK6,sK4),sK0)) & $less(sK4,sK0) & ~$less(sK4,1) & permut_all(elt5,mk_array1(elt5,sK0,t2tb9(sK1)),mk_array1(elt5,sK0,t2tb9(sK5))) & ! [X7 : $int] : (sorted_sub3(tb2t8(mk_array1(elt5,sK0,t2tb9(sK5))),$product(X7,sK4),min(sK0,$sum($product(X7,sK4),sK4))) | ~$less($product(X7,sK4),sK0) | $less($product(X7,sK4),0))) & ~$less(sK2,0) & ! [X8 : $int] : (tb2t7(get(elt5,int,t2tb9(sK1),t2tb(X8))) = tb2t7(get(elt5,int,t2tb9(sK3),t2tb(X8))) | $less(X8,0) | ~$less(X8,sK2)) & sK0 = sK2) & ~$less(sK0,0)), 0.06/0.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f315,f319,f318,f317,f316])). 0.06/0.42 tff(f325,plain,( 0.06/0.42 ! [X0 : $int,X1 : $int] : (((~$less(X0,$uminus(X1)) & ~$less(X1,X0)) | $less(X1,abs(X0))) & (~$less(X1,abs(X0)) | ($less(X0,$uminus(X1)) | $less(X1,X0))))), 0.06/0.42 inference(nnf_transformation,[],[f187])). 0.06/0.42 tff(f326,plain,( 0.06/0.42 ! [X0 : $int,X1 : $int] : (((~$less(X0,$uminus(X1)) & ~$less(X1,X0)) | $less(X1,abs(X0))) & (~$less(X1,abs(X0)) | $less(X0,$uminus(X1)) | $less(X1,X0)))), 0.06/0.42 inference(flattening,[],[f325])). 0.06/0.42 tff(f329,plain,( 0.06/0.42 ! [X0 : array_elt2,X1 : $int,X2 : $int] : ((sorted_sub3(X0,X1,X2) | ? [X3 : $int,X4 : $int] : (~le3(tb2t7(get2(elt5,t2tb8(X0),X3)),tb2t7(get2(elt5,t2tb8(X0),X4))) & $less(X4,X2) & ~$less(X4,X3) & ~$less(X3,X1))) & (! [X3 : $int,X4 : $int] : (le3(tb2t7(get2(elt5,t2tb8(X0),X3)),tb2t7(get2(elt5,t2tb8(X0),X4))) | ~$less(X4,X2) | $less(X4,X3) | $less(X3,X1)) | ~sorted_sub3(X0,X1,X2)))), 0.06/0.42 inference(nnf_transformation,[],[f277])). 0.06/0.42 tff(f330,plain,( 0.06/0.42 ! [X0 : array_elt2,X1 : $int,X2 : $int] : ((sorted_sub3(X0,X1,X2) | ? [X3 : $int,X4 : $int] : (~le3(tb2t7(get2(elt5,t2tb8(X0),X3)),tb2t7(get2(elt5,t2tb8(X0),X4))) & $less(X4,X2) & ~$less(X4,X3) & ~$less(X3,X1))) & (! [X5 : $int,X6 : $int] : (le3(tb2t7(get2(elt5,t2tb8(X0),X5)),tb2t7(get2(elt5,t2tb8(X0),X6))) | ~$less(X6,X2) | $less(X6,X5) | $less(X5,X1)) | ~sorted_sub3(X0,X1,X2)))), 0.06/0.42 inference(rectify,[],[f329])). 0.06/0.42 tff(f331,plain,( 0.06/0.42 ! [X2 : $int,X1 : $int,X0 : array_elt2] : (? [X3 : $int,X4 : $int] : (~le3(tb2t7(get2(elt5,t2tb8(X0),X3)),tb2t7(get2(elt5,t2tb8(X0),X4))) & $less(X4,X2) & ~$less(X4,X3) & ~$less(X3,X1)) => (~le3(tb2t7(get2(elt5,t2tb8(X0),sK9(X0,X1,X2))),tb2t7(get2(elt5,t2tb8(X0),sK10(X0,X1,X2)))) & $less(sK10(X0,X1,X2),X2) & ~$less(sK10(X0,X1,X2),sK9(X0,X1,X2)) & ~$less(sK9(X0,X1,X2),X1)))), 0.06/0.42 introduced(choice_axiom,[])). 0.06/0.42 tff(f332,plain,( 0.06/0.42 ! [X0 : array_elt2,X1 : $int,X2 : $int] : ((sorted_sub3(X0,X1,X2) | (~le3(tb2t7(get2(elt5,t2tb8(X0),sK9(X0,X1,X2))),tb2t7(get2(elt5,t2tb8(X0),sK10(X0,X1,X2)))) & $less(sK10(X0,X1,X2),X2) & ~$less(sK10(X0,X1,X2),sK9(X0,X1,X2)) & ~$less(sK9(X0,X1,X2),X1))) & (! [X5 : $int,X6 : $int] : (le3(tb2t7(get2(elt5,t2tb8(X0),X5)),tb2t7(get2(elt5,t2tb8(X0),X6))) | ~$less(X6,X2) | $less(X6,X5) | $less(X5,X1)) | ~sorted_sub3(X0,X1,X2)))), 0.06/0.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f330,f331])). 0.06/0.42 tff(f333,plain,( 0.06/0.42 ! [X0 : ty,X1 : uni,X2 : uni] : (((permut2(X0,elts(X0,X1),elts(X0,X2),0,length1(X0,X1)) & length1(X0,X1) = length1(X0,X2)) | ~permut_all(X0,X1,X2)) & (permut_all(X0,X1,X2) | (~permut2(X0,elts(X0,X1),elts(X0,X2),0,length1(X0,X1)) | length1(X0,X1) != length1(X0,X2))))), 0.06/0.42 inference(nnf_transformation,[],[f202])). 0.06/0.42 tff(f334,plain,( 0.06/0.42 ! [X0 : ty,X1 : uni,X2 : uni] : (((permut2(X0,elts(X0,X1),elts(X0,X2),0,length1(X0,X1)) & length1(X0,X1) = length1(X0,X2)) | ~permut_all(X0,X1,X2)) & (permut_all(X0,X1,X2) | ~permut2(X0,elts(X0,X1),elts(X0,X2),0,length1(X0,X1)) | length1(X0,X1) != length1(X0,X2)))), 0.06/0.42 inference(flattening,[],[f333])). 0.06/0.42 tff(f362,plain,( 0.06/0.42 ~$less(sK0,0)), 0.06/0.42 inference(cnf_transformation,[],[f320])). 0.06/0.42 tff(f363,plain,( 0.06/0.42 sK0 = sK2), 0.06/0.42 inference(cnf_transformation,[],[f320])). 0.06/0.42 tff(f364,plain,( 0.06/0.42 ( ! [X8:$int] : (~$less(X8,sK2) | $less(X8,0) | tb2t7(get(elt5,int,t2tb9(sK1),t2tb(X8))) = tb2t7(get(elt5,int,t2tb9(sK3),t2tb(X8)))) )), 0.06/0.42 inference(cnf_transformation,[],[f320])). 0.06/0.42 tff(f365,plain,( 0.06/0.42 ~$less(sK2,0)), 0.06/0.42 inference(cnf_transformation,[],[f320])). 0.06/0.42 tff(f366,plain,( 0.06/0.42 ( ! [X7:$int] : (sorted_sub3(tb2t8(mk_array1(elt5,sK0,t2tb9(sK5))),$product(X7,sK4),min(sK0,$sum($product(X7,sK4),sK4))) | ~$less($product(X7,sK4),sK0) | $less($product(X7,sK4),0)) )), 0.06/0.42 inference(cnf_transformation,[],[f320])). 0.06/0.42 tff(f367,plain,( 0.06/0.42 permut_all(elt5,mk_array1(elt5,sK0,t2tb9(sK1)),mk_array1(elt5,sK0,t2tb9(sK5)))), 0.06/0.42 inference(cnf_transformation,[],[f320])). 0.06/0.42 tff(f368,plain,( 0.06/0.42 ~$less(sK4,1)), 0.06/0.42 inference(cnf_transformation,[],[f320])). 0.06/0.42 tff(f369,plain,( 0.06/0.42 $less(sK4,sK0)), 0.06/0.42 inference(cnf_transformation,[],[f320])). 0.06/0.42 tff(f370,plain,( 0.06/0.42 $less($product(sK6,sK4),sK0)), 0.06/0.42 inference(cnf_transformation,[],[f320])). 0.06/0.42 tff(f371,plain,( 0.06/0.42 ~$less($product(sK6,sK4),0)), 0.06/0.42 inference(cnf_transformation,[],[f320])). 0.06/0.42 tff(f372,plain,( 0.06/0.42 ~sorted_sub3(tb2t8(mk_array1(elt5,sK0,t2tb9(sK5))),$product(sK6,sK4),min(sK0,$sum($product(sK6,sK4),sK4)))), 0.06/0.42 inference(cnf_transformation,[],[f320])). 0.06/0.42 tff(f390,plain,( 0.06/0.42 ( ! [X0:$int] : ($less(X0,0) | abs(X0) = X0) )), 0.06/0.42 inference(cnf_transformation,[],[f235])). 0.06/0.42 tff(f391,plain,( 0.06/0.42 ( ! [X0:$int] : (~$less(X0,0) | abs(X0) = $uminus(X0)) )), 0.06/0.42 inference(cnf_transformation,[],[f235])). 0.06/0.42 tff(f405,plain,( 0.06/0.42 ( ! [X0:$int,X1:$int] : (~$less(max(X0,X1),X1)) )), 0.06/0.42 inference(cnf_transformation,[],[f166])). 0.06/0.42 tff(f410,plain,( 0.06/0.42 ( ! [X0:$int,X1:$int] : (min(X0,X1) = X1 | min(X0,X1) = X0) )), 0.06/0.42 inference(cnf_transformation,[],[f170])). 0.06/0.42 tff(f411,plain,( 0.06/0.42 ( ! [X0:$int,X1:$int] : (~$less(abs(X0),abs($product(div(X0,X1),X1))) | 0 = X1) )), 0.06/0.42 inference(cnf_transformation,[],[f240])). 0.06/0.42 tff(f412,plain,( 0.06/0.42 ( ! [X0:$int,X1:$int] : ($sum($product(X1,div(X0,X1)),mod(X0,X1)) = X0 | 0 = X1) )), 0.06/0.42 inference(cnf_transformation,[],[f241])). 0.06/0.42 tff(f413,plain,( 0.06/0.42 ( ! [X0:$int,X1:$int] : ($less(mod(X0,X1),abs(X1)) | 0 = X1) )), 0.06/0.42 inference(cnf_transformation,[],[f242])). 0.06/0.42 tff(f414,plain,( 0.06/0.42 ( ! [X0:$int,X1:$int] : ($less($uminus(abs(X1)),mod(X0,X1)) | 0 = X1) )), 0.06/0.42 inference(cnf_transformation,[],[f242])). 0.06/0.42 tff(f416,plain,( 0.06/0.42 ( ! [X0:$int,X1:$int] : ($less(X1,X0) | min(X0,X1) = X0) )), 0.06/0.42 inference(cnf_transformation,[],[f244])). 0.06/0.42 tff(f417,plain,( 0.06/0.42 ( ! [X0:$int,X1:$int] : ($less(X1,X0) | max(X0,X1) = X1) )), 0.06/0.42 inference(cnf_transformation,[],[f245])). 0.06/0.42 tff(f418,plain,( 0.06/0.42 ( ! [X0:$int,X1:$int] : ($less(X0,X1) | max(X0,X1) = X0) )), 0.06/0.42 inference(cnf_transformation,[],[f246])). 0.06/0.42 tff(f419,plain,( 0.06/0.42 ( ! [X0:$int,X1:$int] : ($less(X0,X1) | min(X0,X1) = X1) )), 0.06/0.42 inference(cnf_transformation,[],[f247])). 0.06/0.42 tff(f420,plain,( 0.06/0.42 ( ! [X0:$int,X1:$int] : ($less(X0,X1) | min(X0,X1) = min(X1,X0)) )), 0.06/0.42 inference(cnf_transformation,[],[f248])). 0.06/0.42 tff(f421,plain,( 0.06/0.42 ( ! [X0:$int,X1:$int] : ($less(X0,X1) | max(X0,X1) = max(X1,X0)) )), 0.06/0.42 inference(cnf_transformation,[],[f249])). 0.06/0.42 tff(f428,plain,( 0.06/0.42 ( ! [X0:$int,X1:$int] : (~$less(X0,X1) | mod(X0,X1) = X0 | $less(X0,0)) )), 0.06/0.42 inference(cnf_transformation,[],[f260])). 0.06/0.42 tff(f429,plain,( 0.06/0.42 ( ! [X0:$int,X1:$int] : (~$less(X0,X1) | div(X0,X1) = 0 | $less(X0,0)) )), 0.06/0.42 inference(cnf_transformation,[],[f262])). 0.06/0.42 tff(f432,plain,( 0.06/0.42 ( ! [X0:$int,X1:$int] : (~$less(X1,X0) | $less(X1,abs(X0))) )), 0.06/0.42 inference(cnf_transformation,[],[f326])). 0.06/0.42 tff(f437,plain,( 0.06/0.42 ( ! [X2:uni,X0:ty,X1:$int] : (length1(X0,mk_array1(X0,X1,X2)) = X1) )), 0.06/0.42 inference(cnf_transformation,[],[f43])). 0.06/0.42 tff(f452,plain,( 0.06/0.42 ( ! [X2:$int,X0:array_elt2,X1:$int] : (sorted_sub3(X0,X1,X2) | ~$less(sK9(X0,X1,X2),X1)) )), 0.06/0.42 inference(cnf_transformation,[],[f332])). 0.06/0.42 tff(f453,plain,( 0.06/0.42 ( ! [X2:$int,X0:array_elt2,X1:$int] : (sorted_sub3(X0,X1,X2) | ~$less(sK10(X0,X1,X2),sK9(X0,X1,X2))) )), 0.06/0.42 inference(cnf_transformation,[],[f332])). 0.06/0.42 tff(f454,plain,( 0.06/0.42 ( ! [X2:$int,X0:array_elt2,X1:$int] : (sorted_sub3(X0,X1,X2) | $less(sK10(X0,X1,X2),X2)) )), 0.06/0.42 inference(cnf_transformation,[],[f332])). 0.06/0.42 tff(f458,plain,( 0.06/0.42 ( ! [X2:uni,X0:ty,X1:uni] : (~permut_all(X0,X1,X2) | permut2(X0,elts(X0,X1),elts(X0,X2),0,length1(X0,X1))) )), 0.06/0.42 inference(cnf_transformation,[],[f334])). 0.06/0.42 tff(f531,plain,( 0.06/0.42 ~sorted_sub3(tb2t8(mk_array1(elt5,sK2,t2tb9(sK5))),$product(sK6,sK4),min(sK2,$sum($product(sK6,sK4),sK4)))), 0.06/0.42 inference(definition_unfolding,[],[f372,f363,f363])). 0.06/0.42 tff(f532,plain,( 0.06/0.42 $less($product(sK6,sK4),sK2)), 0.06/0.42 inference(definition_unfolding,[],[f370,f363])). 0.06/0.42 tff(f533,plain,( 0.06/0.42 $less(sK4,sK2)), 0.06/0.42 inference(definition_unfolding,[],[f369,f363])). 0.06/0.42 tff(f534,plain,( 0.06/0.42 permut_all(elt5,mk_array1(elt5,sK2,t2tb9(sK1)),mk_array1(elt5,sK2,t2tb9(sK5)))), 0.06/0.42 inference(definition_unfolding,[],[f367,f363,f363])). 0.06/0.42 tff(f535,plain,( 0.06/0.42 ( ! [X7:$int] : (~$less($product(X7,sK4),sK2) | sorted_sub3(tb2t8(mk_array1(elt5,sK2,t2tb9(sK5))),$product(X7,sK4),min(sK2,$sum($product(X7,sK4),sK4))) | $less($product(X7,sK4),0)) )), 0.06/0.42 inference(definition_unfolding,[],[f366,f363,f363,f363])). 0.06/0.42 tff(f536,plain,( 0.06/0.42 ~$less(sK2,0)), 0.06/0.42 inference(definition_unfolding,[],[f362,f363])). 0.06/0.42 tff(f552,plain,( 0.06/0.42 spl18_1 <=> ~sorted_sub3(tb2t8(mk_array1(elt5,sK2,t2tb9(sK5))),$product(sK6,sK4),min(sK2,$sum($product(sK6,sK4),sK4)))), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_1])])). 0.06/0.42 tff(f553,plain,( 0.06/0.42 ~sorted_sub3(tb2t8(mk_array1(elt5,sK2,t2tb9(sK5))),$product(sK6,sK4),min(sK2,$sum($product(sK6,sK4),sK4))) | ~spl18_1), 0.06/0.42 inference(avatar_component_clause,[],[f552])). 0.06/0.42 tff(f554,plain,( 0.06/0.42 ~spl18_1), 0.06/0.42 inference(avatar_split_clause,[],[f531,f552])). 0.06/0.42 tff(f559,plain,( 0.06/0.42 spl18_3 <=> ~$less($product(sK6,sK4),0)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_3])])). 0.06/0.42 tff(f560,plain,( 0.06/0.42 ~$less($product(sK6,sK4),0) | ~spl18_3), 0.06/0.42 inference(avatar_component_clause,[],[f559])). 0.06/0.42 tff(f561,plain,( 0.06/0.42 ~spl18_3), 0.06/0.42 inference(avatar_split_clause,[],[f371,f559])). 0.06/0.42 tff(f566,plain,( 0.06/0.42 spl18_4 <=> $less($product(sK6,sK4),sK2)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_4])])). 0.06/0.42 tff(f567,plain,( 0.06/0.42 $less($product(sK6,sK4),sK2) | ~spl18_4), 0.06/0.42 inference(avatar_component_clause,[],[f566])). 0.06/0.42 tff(f568,plain,( 0.06/0.42 spl18_4), 0.06/0.42 inference(avatar_split_clause,[],[f532,f566])). 0.06/0.42 tff(f573,plain,( 0.06/0.42 spl18_6 <=> $less(sK4,sK2)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_6])])). 0.06/0.42 tff(f574,plain,( 0.06/0.42 $less(sK4,sK2) | ~spl18_6), 0.06/0.42 inference(avatar_component_clause,[],[f573])). 0.06/0.42 tff(f575,plain,( 0.06/0.42 spl18_6), 0.06/0.42 inference(avatar_split_clause,[],[f533,f573])). 0.06/0.42 tff(f580,plain,( 0.06/0.42 spl18_9 <=> ~$less(sK4,1)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_9])])). 0.06/0.42 tff(f581,plain,( 0.06/0.42 ~$less(sK4,1) | ~spl18_9), 0.06/0.42 inference(avatar_component_clause,[],[f580])). 0.06/0.42 tff(f582,plain,( 0.06/0.42 ~spl18_9), 0.06/0.42 inference(avatar_split_clause,[],[f368,f580])). 0.06/0.42 tff(f587,plain,( 0.06/0.42 spl18_10 <=> permut_all(elt5,mk_array1(elt5,sK2,t2tb9(sK1)),mk_array1(elt5,sK2,t2tb9(sK5)))), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_10])])). 0.06/0.42 tff(f588,plain,( 0.06/0.42 permut_all(elt5,mk_array1(elt5,sK2,t2tb9(sK1)),mk_array1(elt5,sK2,t2tb9(sK5))) | ~spl18_10), 0.06/0.42 inference(avatar_component_clause,[],[f587])). 0.06/0.42 tff(f589,plain,( 0.06/0.42 spl18_10), 0.06/0.42 inference(avatar_split_clause,[],[f534,f587])). 0.06/0.42 tff(f594,plain,( 0.06/0.42 spl18_13 <=> ~$less(sK2,0)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_13])])). 0.06/0.42 tff(f595,plain,( 0.06/0.42 ~$less(sK2,0) | ~spl18_13), 0.06/0.42 inference(avatar_component_clause,[],[f594])). 0.06/0.42 tff(f596,plain,( 0.06/0.42 ~spl18_13), 0.06/0.42 inference(avatar_split_clause,[],[f365,f594])). 0.06/0.42 tff(f597,plain,( 0.06/0.42 ~spl18_13), 0.06/0.42 inference(avatar_split_clause,[],[f536,f594])). 0.06/0.42 tff(f598,plain,( 0.06/0.42 mod(sK4,sK2) = sK4 | $less(sK4,0) | ~spl18_6), 0.06/0.42 inference(resolution,[],[f574,f428])). 0.06/0.42 tff(f599,plain,( 0.06/0.42 div(sK4,sK2) = 0 | $less(sK4,0) | ~spl18_6), 0.06/0.42 inference(resolution,[],[f574,f429])). 0.06/0.42 tff(f600,plain,( 0.06/0.42 $less(sK4,abs(sK2)) | ~spl18_6), 0.06/0.42 inference(resolution,[],[f574,f432])). 0.06/0.42 tff(f606,plain,( 0.06/0.42 spl18_15 <=> ~$less(sK4,0)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_15])])). 0.06/0.42 tff(f607,plain,( 0.06/0.42 ~$less(sK4,0) | ~spl18_15), 0.06/0.42 inference(avatar_component_clause,[],[f606])). 0.06/0.42 tff(f609,plain,( 0.06/0.42 spl18_14 <=> $less(sK4,0)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_14])])). 0.06/0.42 tff(f615,plain,( 0.06/0.42 spl18_16 <=> mod(sK4,sK2) = sK4), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_16])])). 0.06/0.42 tff(f616,plain,( 0.06/0.42 mod(sK4,sK2) = sK4 | ~spl18_16), 0.06/0.42 inference(avatar_component_clause,[],[f615])). 0.06/0.42 tff(f617,plain,( 0.06/0.42 spl18_14 | spl18_16 | ~spl18_6), 0.06/0.42 inference(avatar_split_clause,[],[f598,f573,f615,f609])). 0.06/0.42 tff(f622,plain,( 0.06/0.42 spl18_18 <=> div(sK4,sK2) = 0), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_18])])). 0.06/0.42 tff(f623,plain,( 0.06/0.42 div(sK4,sK2) = 0 | ~spl18_18), 0.06/0.42 inference(avatar_component_clause,[],[f622])). 0.06/0.42 tff(f624,plain,( 0.06/0.42 spl18_14 | spl18_18 | ~spl18_6), 0.06/0.42 inference(avatar_split_clause,[],[f599,f573,f622,f609])). 0.06/0.42 tff(f629,plain,( 0.06/0.42 spl18_20 <=> $less(sK4,abs(sK2))), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_20])])). 0.06/0.42 tff(f630,plain,( 0.06/0.42 $less(sK4,abs(sK2)) | ~spl18_20), 0.06/0.42 inference(avatar_component_clause,[],[f629])). 0.06/0.42 tff(f631,plain,( 0.06/0.42 spl18_20 | ~spl18_6), 0.06/0.42 inference(avatar_split_clause,[],[f600,f573,f629])). 0.06/0.42 tff(f632,plain,( 0.06/0.42 min(1,sK4) = 1 | ~spl18_9), 0.06/0.42 inference(resolution,[],[f581,f416])). 0.06/0.42 tff(f633,plain,( 0.06/0.42 max(1,sK4) = sK4 | ~spl18_9), 0.06/0.42 inference(resolution,[],[f581,f417])). 0.06/0.42 tff(f634,plain,( 0.06/0.42 max(sK4,1) = sK4 | ~spl18_9), 0.06/0.42 inference(resolution,[],[f581,f418])). 0.06/0.42 tff(f635,plain,( 0.06/0.42 min(sK4,1) = 1 | ~spl18_9), 0.06/0.42 inference(resolution,[],[f581,f419])). 0.06/0.42 tff(f636,plain,( 0.06/0.42 min(1,sK4) = min(sK4,1) | ~spl18_9), 0.06/0.42 inference(resolution,[],[f581,f420])). 0.06/0.42 tff(f637,plain,( 0.06/0.42 max(1,sK4) = max(sK4,1) | ~spl18_9), 0.06/0.42 inference(resolution,[],[f581,f421])). 0.06/0.42 tff(f645,plain,( 0.06/0.42 spl18_22 <=> min(1,sK4) = 1), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_22])])). 0.06/0.42 tff(f647,plain,( 0.06/0.42 spl18_22 | spl18_9), 0.06/0.42 inference(avatar_split_clause,[],[f632,f580,f645])). 0.06/0.42 tff(f652,plain,( 0.06/0.42 spl18_24 <=> max(1,sK4) = sK4), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_24])])). 0.06/0.42 tff(f653,plain,( 0.06/0.42 max(1,sK4) = sK4 | ~spl18_24), 0.06/0.42 inference(avatar_component_clause,[],[f652])). 0.06/0.42 tff(f654,plain,( 0.06/0.42 spl18_24 | spl18_9), 0.06/0.42 inference(avatar_split_clause,[],[f633,f580,f652])). 0.06/0.42 tff(f659,plain,( 0.06/0.42 spl18_26 <=> max(sK4,1) = sK4), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_26])])). 0.06/0.42 tff(f661,plain,( 0.06/0.42 spl18_26 | spl18_9), 0.06/0.42 inference(avatar_split_clause,[],[f634,f580,f659])). 0.06/0.42 tff(f666,plain,( 0.06/0.42 spl18_28 <=> min(sK4,1) = 1), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_28])])). 0.06/0.42 tff(f668,plain,( 0.06/0.42 spl18_28 | spl18_9), 0.06/0.42 inference(avatar_split_clause,[],[f635,f580,f666])). 0.06/0.42 tff(f673,plain,( 0.06/0.42 spl18_30 <=> min(1,sK4) = min(sK4,1)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_30])])). 0.06/0.42 tff(f675,plain,( 0.06/0.42 spl18_30 | spl18_9), 0.06/0.42 inference(avatar_split_clause,[],[f636,f580,f673])). 0.06/0.42 tff(f680,plain,( 0.06/0.42 spl18_32 <=> max(1,sK4) = max(sK4,1)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_32])])). 0.06/0.42 tff(f682,plain,( 0.06/0.42 spl18_32 | spl18_9), 0.06/0.42 inference(avatar_split_clause,[],[f637,f580,f680])). 0.06/0.42 tff(f683,plain,( 0.06/0.42 abs(sK2) = sK2 | ~spl18_13), 0.06/0.42 inference(resolution,[],[f595,f390])). 0.06/0.42 tff(f684,plain,( 0.06/0.42 min(0,sK2) = 0 | ~spl18_13), 0.06/0.42 inference(resolution,[],[f595,f416])). 0.06/0.42 tff(f685,plain,( 0.06/0.42 max(0,sK2) = sK2 | ~spl18_13), 0.06/0.42 inference(resolution,[],[f595,f417])). 0.06/0.42 tff(f686,plain,( 0.06/0.42 max(sK2,0) = sK2 | ~spl18_13), 0.06/0.42 inference(resolution,[],[f595,f418])). 0.06/0.42 tff(f687,plain,( 0.06/0.42 min(sK2,0) = 0 | ~spl18_13), 0.06/0.42 inference(resolution,[],[f595,f419])). 0.06/0.42 tff(f688,plain,( 0.06/0.42 min(0,sK2) = min(sK2,0) | ~spl18_13), 0.06/0.42 inference(resolution,[],[f595,f420])). 0.06/0.42 tff(f689,plain,( 0.06/0.42 max(0,sK2) = max(sK2,0) | ~spl18_13), 0.06/0.42 inference(resolution,[],[f595,f421])). 0.06/0.42 tff(f697,plain,( 0.06/0.42 spl18_34 <=> abs(sK2) = sK2), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_34])])). 0.06/0.42 tff(f698,plain,( 0.06/0.42 abs(sK2) = sK2 | ~spl18_34), 0.06/0.42 inference(avatar_component_clause,[],[f697])). 0.06/0.42 tff(f699,plain,( 0.06/0.42 spl18_34 | spl18_13), 0.06/0.42 inference(avatar_split_clause,[],[f683,f594,f697])). 0.06/0.42 tff(f704,plain,( 0.06/0.42 spl18_36 <=> min(0,sK2) = 0), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_36])])). 0.06/0.42 tff(f706,plain,( 0.06/0.42 spl18_36 | spl18_13), 0.06/0.42 inference(avatar_split_clause,[],[f684,f594,f704])). 0.06/0.42 tff(f711,plain,( 0.06/0.42 spl18_38 <=> max(0,sK2) = sK2), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_38])])). 0.06/0.42 tff(f712,plain,( 0.06/0.42 max(0,sK2) = sK2 | ~spl18_38), 0.06/0.42 inference(avatar_component_clause,[],[f711])). 0.06/0.42 tff(f713,plain,( 0.06/0.42 spl18_38 | spl18_13), 0.06/0.42 inference(avatar_split_clause,[],[f685,f594,f711])). 0.06/0.42 tff(f718,plain,( 0.06/0.42 spl18_40 <=> max(sK2,0) = sK2), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_40])])). 0.06/0.42 tff(f720,plain,( 0.06/0.42 spl18_40 | spl18_13), 0.06/0.42 inference(avatar_split_clause,[],[f686,f594,f718])). 0.06/0.42 tff(f725,plain,( 0.06/0.42 spl18_42 <=> min(sK2,0) = 0), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_42])])). 0.06/0.42 tff(f727,plain,( 0.06/0.42 spl18_42 | spl18_13), 0.06/0.42 inference(avatar_split_clause,[],[f687,f594,f725])). 0.06/0.42 tff(f732,plain,( 0.06/0.42 spl18_44 <=> min(0,sK2) = min(sK2,0)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_44])])). 0.06/0.42 tff(f734,plain,( 0.06/0.42 spl18_44 | spl18_13), 0.06/0.42 inference(avatar_split_clause,[],[f688,f594,f732])). 0.06/0.42 tff(f739,plain,( 0.06/0.42 spl18_46 <=> max(0,sK2) = max(sK2,0)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_46])])). 0.06/0.42 tff(f741,plain,( 0.06/0.42 spl18_46 | spl18_13), 0.06/0.42 inference(avatar_split_clause,[],[f689,f594,f739])). 0.06/0.42 tff(f742,plain,( 0.06/0.42 abs(sK4) = sK4 | ~spl18_15), 0.06/0.42 inference(resolution,[],[f607,f390])). 0.06/0.42 tff(f743,plain,( 0.06/0.42 min(0,sK4) = 0 | ~spl18_15), 0.06/0.42 inference(resolution,[],[f607,f416])). 0.06/0.42 tff(f744,plain,( 0.06/0.42 max(0,sK4) = sK4 | ~spl18_15), 0.06/0.42 inference(resolution,[],[f607,f417])). 0.06/0.42 tff(f745,plain,( 0.06/0.42 max(sK4,0) = sK4 | ~spl18_15), 0.06/0.42 inference(resolution,[],[f607,f418])). 0.06/0.42 tff(f746,plain,( 0.06/0.42 min(sK4,0) = 0 | ~spl18_15), 0.06/0.42 inference(resolution,[],[f607,f419])). 0.06/0.42 tff(f747,plain,( 0.06/0.42 min(0,sK4) = min(sK4,0) | ~spl18_15), 0.06/0.42 inference(resolution,[],[f607,f420])). 0.06/0.42 tff(f748,plain,( 0.06/0.42 max(0,sK4) = max(sK4,0) | ~spl18_15), 0.06/0.42 inference(resolution,[],[f607,f421])). 0.06/0.42 tff(f756,plain,( 0.06/0.42 spl18_48 <=> abs(sK4) = sK4), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_48])])). 0.06/0.42 tff(f757,plain,( 0.06/0.42 abs(sK4) = sK4 | ~spl18_48), 0.06/0.42 inference(avatar_component_clause,[],[f756])). 0.06/0.42 tff(f758,plain,( 0.06/0.42 spl18_48 | spl18_15), 0.06/0.42 inference(avatar_split_clause,[],[f742,f606,f756])). 0.06/0.42 tff(f763,plain,( 0.06/0.42 spl18_50 <=> min(0,sK4) = 0), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_50])])). 0.06/0.42 tff(f765,plain,( 0.06/0.42 spl18_50 | spl18_15), 0.06/0.42 inference(avatar_split_clause,[],[f743,f606,f763])). 0.06/0.42 tff(f770,plain,( 0.06/0.42 spl18_52 <=> max(0,sK4) = sK4), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_52])])). 0.06/0.42 tff(f772,plain,( 0.06/0.42 spl18_52 | spl18_15), 0.06/0.42 inference(avatar_split_clause,[],[f744,f606,f770])). 0.06/0.42 tff(f777,plain,( 0.06/0.42 spl18_54 <=> max(sK4,0) = sK4), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_54])])). 0.06/0.42 tff(f779,plain,( 0.06/0.42 spl18_54 | spl18_15), 0.06/0.42 inference(avatar_split_clause,[],[f745,f606,f777])). 0.06/0.42 tff(f784,plain,( 0.06/0.42 spl18_56 <=> min(sK4,0) = 0), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_56])])). 0.06/0.42 tff(f786,plain,( 0.06/0.42 spl18_56 | spl18_15), 0.06/0.42 inference(avatar_split_clause,[],[f746,f606,f784])). 0.06/0.42 tff(f791,plain,( 0.06/0.42 spl18_58 <=> min(0,sK4) = min(sK4,0)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_58])])). 0.06/0.42 tff(f793,plain,( 0.06/0.42 spl18_58 | spl18_15), 0.06/0.42 inference(avatar_split_clause,[],[f747,f606,f791])). 0.06/0.42 tff(f798,plain,( 0.06/0.42 spl18_60 <=> max(0,sK4) = max(sK4,0)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_60])])). 0.06/0.42 tff(f800,plain,( 0.06/0.42 spl18_60 | spl18_15), 0.06/0.42 inference(avatar_split_clause,[],[f748,f606,f798])). 0.06/0.42 tff(f802,plain,( 0.06/0.42 mod(sK4,abs(sK2)) = sK4 | $less(sK4,0) | ~spl18_20), 0.06/0.42 inference(resolution,[],[f630,f428])). 0.06/0.42 tff(f803,plain,( 0.06/0.42 div(sK4,abs(sK2)) = 0 | $less(sK4,0) | ~spl18_20), 0.06/0.42 inference(resolution,[],[f630,f429])). 0.06/0.42 tff(f804,plain,( 0.06/0.42 $less(sK4,abs(abs(sK2))) | ~spl18_20), 0.06/0.42 inference(resolution,[],[f630,f432])). 0.06/0.42 tff(f809,plain,( 0.06/0.42 mod(sK4,abs(sK2)) = sK4 | (~spl18_15 | ~spl18_20)), 0.06/0.42 inference(subsumption_resolution,[],[f802,f607])). 0.06/0.42 tff(f814,plain,( 0.06/0.42 spl18_62 <=> mod(sK4,abs(sK2)) = sK4), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_62])])). 0.06/0.42 tff(f816,plain,( 0.06/0.42 spl18_62 | spl18_15 | ~spl18_20), 0.06/0.42 inference(avatar_split_clause,[],[f809,f629,f606,f814])). 0.06/0.42 tff(f817,plain,( 0.06/0.42 div(sK4,abs(sK2)) = 0 | (~spl18_15 | ~spl18_20)), 0.06/0.42 inference(subsumption_resolution,[],[f803,f607])). 0.06/0.42 tff(f822,plain,( 0.06/0.42 spl18_64 <=> div(sK4,abs(sK2)) = 0), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_64])])). 0.06/0.42 tff(f824,plain,( 0.06/0.42 spl18_64 | spl18_15 | ~spl18_20), 0.06/0.42 inference(avatar_split_clause,[],[f817,f629,f606,f822])). 0.06/0.42 tff(f829,plain,( 0.06/0.42 spl18_66 <=> $less(sK4,abs(abs(sK2)))), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_66])])). 0.06/0.42 tff(f831,plain,( 0.06/0.42 spl18_66 | ~spl18_20), 0.06/0.42 inference(avatar_split_clause,[],[f804,f629,f829])). 0.06/0.42 tff(f834,plain,( 0.06/0.42 ( ! [X1:$int] : ($less(mod(X1,sK2),sK2) | 0 = sK2) ) | ~spl18_34), 0.06/0.42 inference(superposition,[],[f413,f698])). 0.06/0.42 tff(f835,plain,( 0.06/0.42 ( ! [X2:$int] : ($less($uminus(sK2),mod(X2,sK2)) | 0 = sK2) ) | ~spl18_34), 0.06/0.42 inference(superposition,[],[f414,f698])). 0.06/0.42 tff(f839,plain,( 0.06/0.42 spl18_69 <=> 0 != sK2), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_69])])). 0.06/0.42 tff(f840,plain,( 0.06/0.42 0 != sK2 | ~spl18_69), 0.06/0.42 inference(avatar_component_clause,[],[f839])). 0.06/0.42 tff(f842,plain,( 0.06/0.42 spl18_68 <=> 0 = sK2), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_68])])). 0.06/0.42 tff(f845,plain,( 0.06/0.42 spl18_70 <=> ! [X1 : $int] : $less(mod(X1,sK2),sK2)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_70])])). 0.06/0.42 tff(f847,plain,( 0.06/0.42 spl18_68 | spl18_70 | ~spl18_34), 0.06/0.42 inference(avatar_split_clause,[],[f834,f697,f845,f842])). 0.06/0.42 tff(f849,plain,( 0.06/0.42 spl18_72 <=> ! [X2 : $int] : $less($uminus(sK2),mod(X2,sK2))), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_72])])). 0.06/0.42 tff(f851,plain,( 0.06/0.42 spl18_68 | spl18_72 | ~spl18_34), 0.06/0.42 inference(avatar_split_clause,[],[f835,f697,f849,f842])). 0.06/0.42 tff(f853,plain,( 0.06/0.42 ( ! [X1:$int] : ($less(mod(X1,sK4),sK4) | 0 = sK4) ) | ~spl18_48), 0.06/0.42 inference(superposition,[],[f413,f757])). 0.06/0.42 tff(f854,plain,( 0.06/0.42 ( ! [X2:$int] : ($less($uminus(sK4),mod(X2,sK4)) | 0 = sK4) ) | ~spl18_48), 0.06/0.42 inference(superposition,[],[f414,f757])). 0.06/0.42 tff(f861,plain,( 0.06/0.42 spl18_74 <=> 0 = sK4), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_74])])). 0.06/0.42 tff(f864,plain,( 0.06/0.42 spl18_76 <=> ! [X1 : $int] : $less(mod(X1,sK4),sK4)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_76])])). 0.06/0.42 tff(f866,plain,( 0.06/0.42 spl18_74 | spl18_76 | ~spl18_48), 0.06/0.42 inference(avatar_split_clause,[],[f853,f756,f864,f861])). 0.06/0.42 tff(f868,plain,( 0.06/0.42 spl18_78 <=> ! [X2 : $int] : $less($uminus(sK4),mod(X2,sK4))), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_78])])). 0.06/0.42 tff(f870,plain,( 0.06/0.42 spl18_74 | spl18_78 | ~spl18_48), 0.06/0.42 inference(avatar_split_clause,[],[f854,f756,f868,f861])). 0.06/0.42 tff(f871,plain,( 0.06/0.42 abs($product(sK6,sK4)) = $product(sK6,sK4) | ~spl18_3), 0.06/0.42 inference(resolution,[],[f560,f390])). 0.06/0.42 tff(f872,plain,( 0.06/0.42 min(0,$product(sK6,sK4)) = 0 | ~spl18_3), 0.06/0.42 inference(resolution,[],[f560,f416])). 0.06/0.42 tff(f873,plain,( 0.06/0.42 max(0,$product(sK6,sK4)) = $product(sK6,sK4) | ~spl18_3), 0.06/0.42 inference(resolution,[],[f560,f417])). 0.06/0.42 tff(f874,plain,( 0.06/0.42 max($product(sK6,sK4),0) = $product(sK6,sK4) | ~spl18_3), 0.06/0.42 inference(resolution,[],[f560,f418])). 0.06/0.42 tff(f875,plain,( 0.06/0.42 min($product(sK6,sK4),0) = 0 | ~spl18_3), 0.06/0.42 inference(resolution,[],[f560,f419])). 0.06/0.42 tff(f876,plain,( 0.06/0.42 min($product(sK6,sK4),0) = min(0,$product(sK6,sK4)) | ~spl18_3), 0.06/0.42 inference(resolution,[],[f560,f420])). 0.06/0.42 tff(f877,plain,( 0.06/0.42 max($product(sK6,sK4),0) = max(0,$product(sK6,sK4)) | ~spl18_3), 0.06/0.42 inference(resolution,[],[f560,f421])). 0.06/0.42 tff(f885,plain,( 0.06/0.42 spl18_80 <=> abs($product(sK6,sK4)) = $product(sK6,sK4)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_80])])). 0.06/0.42 tff(f887,plain,( 0.06/0.42 spl18_80 | spl18_3), 0.06/0.42 inference(avatar_split_clause,[],[f871,f559,f885])). 0.06/0.42 tff(f892,plain,( 0.06/0.42 spl18_82 <=> min(0,$product(sK6,sK4)) = 0), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_82])])). 0.06/0.42 tff(f894,plain,( 0.06/0.42 spl18_82 | spl18_3), 0.06/0.42 inference(avatar_split_clause,[],[f872,f559,f892])). 0.06/0.42 tff(f899,plain,( 0.06/0.42 spl18_84 <=> max(0,$product(sK6,sK4)) = $product(sK6,sK4)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_84])])). 0.06/0.42 tff(f901,plain,( 0.06/0.42 spl18_84 | spl18_3), 0.06/0.42 inference(avatar_split_clause,[],[f873,f559,f899])). 0.06/0.42 tff(f906,plain,( 0.06/0.42 spl18_86 <=> max($product(sK6,sK4),0) = $product(sK6,sK4)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_86])])). 0.06/0.42 tff(f908,plain,( 0.06/0.42 spl18_86 | spl18_3), 0.06/0.42 inference(avatar_split_clause,[],[f874,f559,f906])). 0.06/0.42 tff(f913,plain,( 0.06/0.42 spl18_88 <=> min($product(sK6,sK4),0) = 0), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_88])])). 0.06/0.42 tff(f915,plain,( 0.06/0.42 spl18_88 | spl18_3), 0.06/0.42 inference(avatar_split_clause,[],[f875,f559,f913])). 0.06/0.42 tff(f920,plain,( 0.06/0.42 spl18_90 <=> min($product(sK6,sK4),0) = min(0,$product(sK6,sK4))), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_90])])). 0.06/0.42 tff(f922,plain,( 0.06/0.42 spl18_90 | spl18_3), 0.06/0.42 inference(avatar_split_clause,[],[f876,f559,f920])). 0.06/0.42 tff(f927,plain,( 0.06/0.42 spl18_92 <=> max($product(sK6,sK4),0) = max(0,$product(sK6,sK4))), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_92])])). 0.06/0.42 tff(f929,plain,( 0.06/0.42 spl18_92 | spl18_3), 0.06/0.42 inference(avatar_split_clause,[],[f877,f559,f927])). 0.06/0.42 tff(f930,plain,( 0.06/0.42 mod($product(sK6,sK4),sK2) = $product(sK6,sK4) | $less($product(sK6,sK4),0) | ~spl18_4), 0.06/0.42 inference(resolution,[],[f567,f428])). 0.06/0.42 tff(f931,plain,( 0.06/0.42 div($product(sK6,sK4),sK2) = 0 | $less($product(sK6,sK4),0) | ~spl18_4), 0.06/0.42 inference(resolution,[],[f567,f429])). 0.06/0.42 tff(f937,plain,( 0.06/0.42 mod($product(sK6,sK4),sK2) = $product(sK6,sK4) | (~spl18_3 | ~spl18_4)), 0.06/0.42 inference(subsumption_resolution,[],[f930,f560])). 0.06/0.42 tff(f942,plain,( 0.06/0.42 spl18_94 <=> mod($product(sK6,sK4),sK2) = $product(sK6,sK4)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_94])])). 0.06/0.42 tff(f944,plain,( 0.06/0.42 spl18_94 | spl18_3 | ~spl18_4), 0.06/0.42 inference(avatar_split_clause,[],[f937,f566,f559,f942])). 0.06/0.42 tff(f945,plain,( 0.06/0.42 div($product(sK6,sK4),sK2) = 0 | (~spl18_3 | ~spl18_4)), 0.06/0.42 inference(subsumption_resolution,[],[f931,f560])). 0.06/0.42 tff(f950,plain,( 0.06/0.42 spl18_96 <=> div($product(sK6,sK4),sK2) = 0), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_96])])). 0.06/0.42 tff(f952,plain,( 0.06/0.42 spl18_96 | spl18_3 | ~spl18_4), 0.06/0.42 inference(avatar_split_clause,[],[f945,f566,f559,f950])). 0.06/0.42 tff(f957,plain,( 0.06/0.42 $less($uminus(abs(sK2)),sK4) | 0 = sK2 | ~spl18_16), 0.06/0.42 inference(superposition,[],[f414,f616])). 0.06/0.42 tff(f958,plain,( 0.06/0.42 $sum($product(sK2,div(sK4,sK2)),sK4) = sK4 | 0 = sK2 | ~spl18_16), 0.06/0.42 inference(superposition,[],[f412,f616])). 0.06/0.42 tff(f961,plain,( 0.06/0.42 $less($uminus(abs(sK2)),sK4) | (~spl18_16 | ~spl18_69)), 0.06/0.42 inference(subsumption_resolution,[],[f957,f840])). 0.06/0.42 tff(f962,plain,( 0.06/0.42 $less($uminus(sK2),sK4) | (~spl18_16 | ~spl18_34 | ~spl18_69)), 0.06/0.42 inference(forward_demodulation,[],[f961,f698])). 0.06/0.42 tff(f967,plain,( 0.06/0.42 spl18_98 <=> $less($uminus(sK2),sK4)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_98])])). 0.06/0.42 tff(f968,plain,( 0.06/0.42 $less($uminus(sK2),sK4) | ~spl18_98), 0.06/0.42 inference(avatar_component_clause,[],[f967])). 0.06/0.42 tff(f969,plain,( 0.06/0.42 spl18_98 | ~spl18_16 | ~spl18_34 | spl18_69), 0.06/0.42 inference(avatar_split_clause,[],[f962,f839,f697,f615,f967])). 0.06/0.42 tff(f970,plain,( 0.06/0.42 $sum($product(sK2,div(sK4,sK2)),sK4) = sK4 | (~spl18_16 | ~spl18_69)), 0.06/0.42 inference(subsumption_resolution,[],[f958,f840])). 0.06/0.42 tff(f975,plain,( 0.06/0.42 spl18_100 <=> $sum($product(sK2,div(sK4,sK2)),sK4) = sK4), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_100])])). 0.06/0.42 tff(f977,plain,( 0.06/0.42 spl18_100 | ~spl18_16 | spl18_69), 0.06/0.42 inference(avatar_split_clause,[],[f970,f839,f615,f975])). 0.06/0.42 tff(f978,plain,( 0.06/0.42 mod($uminus(sK2),sK4) = $uminus(sK2) | $less($uminus(sK2),0) | ~spl18_98), 0.06/0.42 inference(resolution,[],[f968,f428])). 0.06/0.42 tff(f979,plain,( 0.06/0.42 div($uminus(sK2),sK4) = 0 | $less($uminus(sK2),0) | ~spl18_98), 0.06/0.42 inference(resolution,[],[f968,f429])). 0.06/0.42 tff(f989,plain,( 0.06/0.42 spl18_102 <=> $less($uminus(sK2),0)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_102])])). 0.06/0.42 tff(f990,plain,( 0.06/0.42 $less($uminus(sK2),0) | ~spl18_102), 0.06/0.42 inference(avatar_component_clause,[],[f989])). 0.06/0.42 tff(f995,plain,( 0.06/0.42 spl18_104 <=> mod($uminus(sK2),sK4) = $uminus(sK2)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_104])])). 0.06/0.42 tff(f997,plain,( 0.06/0.42 spl18_102 | spl18_104 | ~spl18_98), 0.06/0.42 inference(avatar_split_clause,[],[f978,f967,f995,f989])). 0.06/0.42 tff(f1002,plain,( 0.06/0.42 spl18_106 <=> div($uminus(sK2),sK4) = 0), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_106])])). 0.06/0.42 tff(f1004,plain,( 0.06/0.42 spl18_102 | spl18_106 | ~spl18_98), 0.06/0.42 inference(avatar_split_clause,[],[f979,f967,f1002,f989])). 0.06/0.42 tff(f1006,plain,( 0.06/0.42 abs($uminus(sK2)) = $uminus($uminus(sK2)) | ~spl18_102), 0.06/0.42 inference(resolution,[],[f990,f391])). 0.06/0.42 tff(f1009,plain,( 0.06/0.42 $less($uminus(sK2),abs(0)) | ~spl18_102), 0.06/0.42 inference(resolution,[],[f990,f432])). 0.06/0.42 tff(f1020,plain,( 0.06/0.42 spl18_108 <=> abs($uminus(sK2)) = $uminus($uminus(sK2))), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_108])])). 0.06/0.42 tff(f1022,plain,( 0.06/0.42 spl18_108 | ~spl18_102), 0.06/0.42 inference(avatar_split_clause,[],[f1006,f989,f1020])). 0.06/0.42 tff(f1027,plain,( 0.06/0.42 spl18_110 <=> $less($uminus(sK2),abs(0))), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_110])])). 0.06/0.42 tff(f1028,plain,( 0.06/0.42 $less($uminus(sK2),abs(0)) | ~spl18_110), 0.06/0.42 inference(avatar_component_clause,[],[f1027])). 0.06/0.42 tff(f1029,plain,( 0.06/0.42 spl18_110 | ~spl18_102), 0.06/0.42 inference(avatar_split_clause,[],[f1009,f989,f1027])). 0.06/0.42 tff(f1031,plain,( 0.06/0.42 ~$less(abs(sK4),abs($product(0,sK2))) | 0 = sK2 | ~spl18_18), 0.06/0.42 inference(superposition,[],[f411,f623])). 0.06/0.42 tff(f1032,plain,( 0.06/0.42 ~$less(abs(sK4),abs(0)) | 0 = sK2 | ~spl18_18), 0.06/0.42 inference(evaluation,[],[f1031])). 0.06/0.42 tff(f1035,plain,( 0.06/0.42 ~$less(abs(sK4),abs(0)) | (~spl18_18 | ~spl18_69)), 0.06/0.42 inference(subsumption_resolution,[],[f1032,f840])). 0.06/0.42 tff(f1036,plain,( 0.06/0.42 ~$less(sK4,abs(0)) | (~spl18_18 | ~spl18_48 | ~spl18_69)), 0.06/0.42 inference(forward_demodulation,[],[f1035,f757])). 0.06/0.42 tff(f1041,plain,( 0.06/0.42 spl18_113 <=> ~$less(sK4,abs(0))), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_113])])). 0.06/0.42 tff(f1042,plain,( 0.06/0.42 ~$less(sK4,abs(0)) | ~spl18_113), 0.06/0.42 inference(avatar_component_clause,[],[f1041])). 0.06/0.42 tff(f1043,plain,( 0.06/0.42 ~spl18_113 | ~spl18_18 | ~spl18_48 | spl18_69), 0.06/0.42 inference(avatar_split_clause,[],[f1036,f839,f756,f622,f1041])). 0.06/0.42 tff(f1045,plain,( 0.06/0.42 permut2(elt5,elts(elt5,mk_array1(elt5,sK2,t2tb9(sK1))),elts(elt5,mk_array1(elt5,sK2,t2tb9(sK5))),0,length1(elt5,mk_array1(elt5,sK2,t2tb9(sK1)))) | ~spl18_10), 0.06/0.42 inference(resolution,[],[f588,f458])). 0.06/0.42 tff(f1047,plain,( 0.06/0.42 permut2(elt5,elts(elt5,mk_array1(elt5,sK2,t2tb9(sK1))),elts(elt5,mk_array1(elt5,sK2,t2tb9(sK5))),0,sK2) | ~spl18_10), 0.06/0.42 inference(forward_demodulation,[],[f1045,f437])). 0.06/0.42 tff(f1052,plain,( 0.06/0.42 spl18_114 <=> permut2(elt5,elts(elt5,mk_array1(elt5,sK2,t2tb9(sK1))),elts(elt5,mk_array1(elt5,sK2,t2tb9(sK5))),0,sK2)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_114])])). 0.06/0.42 tff(f1054,plain,( 0.06/0.42 spl18_114 | ~spl18_10), 0.06/0.42 inference(avatar_split_clause,[],[f1047,f587,f1052])). 0.06/0.42 tff(f1055,plain,( 0.06/0.42 abs(0) = min(abs(0),sK4) | ~spl18_113), 0.06/0.42 inference(resolution,[],[f1042,f416])). 0.06/0.42 tff(f1056,plain,( 0.06/0.42 max(abs(0),sK4) = sK4 | ~spl18_113), 0.06/0.42 inference(resolution,[],[f1042,f417])). 0.06/0.42 tff(f1057,plain,( 0.06/0.42 max(sK4,abs(0)) = sK4 | ~spl18_113), 0.06/0.42 inference(resolution,[],[f1042,f418])). 0.06/0.42 tff(f1058,plain,( 0.06/0.42 abs(0) = min(sK4,abs(0)) | ~spl18_113), 0.06/0.42 inference(resolution,[],[f1042,f419])). 0.06/0.42 tff(f1059,plain,( 0.06/0.42 min(abs(0),sK4) = min(sK4,abs(0)) | ~spl18_113), 0.06/0.42 inference(resolution,[],[f1042,f420])). 0.06/0.42 tff(f1060,plain,( 0.06/0.42 max(abs(0),sK4) = max(sK4,abs(0)) | ~spl18_113), 0.06/0.42 inference(resolution,[],[f1042,f421])). 0.06/0.42 tff(f1068,plain,( 0.06/0.42 spl18_116 <=> abs(0) = min(abs(0),sK4)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_116])])). 0.06/0.42 tff(f1070,plain,( 0.06/0.42 spl18_116 | spl18_113), 0.06/0.42 inference(avatar_split_clause,[],[f1055,f1041,f1068])). 0.06/0.42 tff(f1075,plain,( 0.06/0.42 spl18_118 <=> max(abs(0),sK4) = sK4), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_118])])). 0.06/0.42 tff(f1077,plain,( 0.06/0.42 spl18_118 | spl18_113), 0.06/0.42 inference(avatar_split_clause,[],[f1056,f1041,f1075])). 0.06/0.42 tff(f1082,plain,( 0.06/0.42 spl18_120 <=> max(sK4,abs(0)) = sK4), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_120])])). 0.06/0.42 tff(f1084,plain,( 0.06/0.42 spl18_120 | spl18_113), 0.06/0.42 inference(avatar_split_clause,[],[f1057,f1041,f1082])). 0.06/0.42 tff(f1089,plain,( 0.06/0.42 spl18_122 <=> abs(0) = min(sK4,abs(0))), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_122])])). 0.06/0.42 tff(f1091,plain,( 0.06/0.42 spl18_122 | spl18_113), 0.06/0.42 inference(avatar_split_clause,[],[f1058,f1041,f1089])). 0.06/0.42 tff(f1096,plain,( 0.06/0.42 spl18_124 <=> min(abs(0),sK4) = min(sK4,abs(0))), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_124])])). 0.06/0.42 tff(f1098,plain,( 0.06/0.42 spl18_124 | spl18_113), 0.06/0.42 inference(avatar_split_clause,[],[f1059,f1041,f1096])). 0.06/0.42 tff(f1103,plain,( 0.06/0.42 spl18_126 <=> max(abs(0),sK4) = max(sK4,abs(0))), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_126])])). 0.06/0.42 tff(f1105,plain,( 0.06/0.42 spl18_126 | spl18_113), 0.06/0.42 inference(avatar_split_clause,[],[f1060,f1041,f1103])). 0.06/0.42 tff(f1113,plain,( 0.06/0.42 ~$less(sK4,sK4) | ~spl18_24), 0.06/0.42 inference(superposition,[],[f405,f653])). 0.06/0.42 tff(f1118,plain,( 0.06/0.42 spl18_129 <=> ~$less(sK4,sK4)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_129])])). 0.06/0.42 tff(f1119,plain,( 0.06/0.42 ~$less(sK4,sK4) | ~spl18_129), 0.06/0.42 inference(avatar_component_clause,[],[f1118])). 0.06/0.42 tff(f1120,plain,( 0.06/0.42 ~spl18_129 | ~spl18_24), 0.06/0.42 inference(avatar_split_clause,[],[f1113,f652,f1118])). 0.06/0.42 tff(f1121,plain,( 0.06/0.42 min(sK4,sK4) = sK4 | ~spl18_129), 0.06/0.42 inference(resolution,[],[f1119,f416])). 0.06/0.42 tff(f1122,plain,( 0.06/0.42 max(sK4,sK4) = sK4 | ~spl18_129), 0.06/0.42 inference(resolution,[],[f1119,f417])). 0.06/0.42 tff(f1123,plain,( 0.06/0.42 max(sK4,sK4) = sK4 | ~spl18_129), 0.06/0.42 inference(resolution,[],[f1119,f418])). 0.06/0.42 tff(f1124,plain,( 0.06/0.42 min(sK4,sK4) = sK4 | ~spl18_129), 0.06/0.42 inference(resolution,[],[f1119,f419])). 0.06/0.42 tff(f1134,plain,( 0.06/0.42 spl18_130 <=> min(sK4,sK4) = sK4), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_130])])). 0.06/0.42 tff(f1136,plain,( 0.06/0.42 spl18_130 | spl18_129), 0.06/0.42 inference(avatar_split_clause,[],[f1121,f1118,f1134])). 0.06/0.42 tff(f1141,plain,( 0.06/0.42 spl18_132 <=> max(sK4,sK4) = sK4), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_132])])). 0.06/0.42 tff(f1143,plain,( 0.06/0.42 spl18_132 | spl18_129), 0.06/0.42 inference(avatar_split_clause,[],[f1122,f1118,f1141])). 0.06/0.42 tff(f1144,plain,( 0.06/0.42 spl18_132 | spl18_129), 0.06/0.42 inference(avatar_split_clause,[],[f1123,f1118,f1141])). 0.06/0.42 tff(f1145,plain,( 0.06/0.42 spl18_130 | spl18_129), 0.06/0.42 inference(avatar_split_clause,[],[f1124,f1118,f1134])). 0.06/0.42 tff(f1154,plain,( 0.06/0.42 ~$less(sK9(tb2t8(mk_array1(elt5,sK2,t2tb9(sK5))),$product(sK6,sK4),min(sK2,$sum($product(sK6,sK4),sK4))),$product(sK6,sK4)) | ~spl18_1), 0.06/0.42 inference(resolution,[],[f553,f452])). 0.06/0.42 tff(f1155,plain,( 0.06/0.42 ~$less(sK10(tb2t8(mk_array1(elt5,sK2,t2tb9(sK5))),$product(sK6,sK4),min(sK2,$sum($product(sK6,sK4),sK4))),sK9(tb2t8(mk_array1(elt5,sK2,t2tb9(sK5))),$product(sK6,sK4),min(sK2,$sum($product(sK6,sK4),sK4)))) | ~spl18_1), 0.06/0.42 inference(resolution,[],[f553,f453])). 0.06/0.42 tff(f1156,plain,( 0.06/0.42 $less(sK10(tb2t8(mk_array1(elt5,sK2,t2tb9(sK5))),$product(sK6,sK4),min(sK2,$sum($product(sK6,sK4),sK4))),min(sK2,$sum($product(sK6,sK4),sK4))) | ~spl18_1), 0.06/0.42 inference(resolution,[],[f553,f454])). 0.06/0.42 tff(f1158,plain,( 0.06/0.42 ~sorted_sub3(tb2t8(mk_array1(elt5,sK2,t2tb9(sK5))),$product(sK6,sK4),$sum($product(sK6,sK4),sK4)) | min(sK2,$sum($product(sK6,sK4),sK4)) = sK2 | ~spl18_1), 0.06/0.42 inference(superposition,[],[f553,f410])). 0.06/0.42 tff(f1163,plain,( 0.06/0.42 spl18_135 <=> ~$less(sK9(tb2t8(mk_array1(elt5,sK2,t2tb9(sK5))),$product(sK6,sK4),min(sK2,$sum($product(sK6,sK4),sK4))),$product(sK6,sK4))), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_135])])). 0.06/0.42 tff(f1165,plain,( 0.06/0.42 ~spl18_135 | spl18_1), 0.06/0.42 inference(avatar_split_clause,[],[f1154,f552,f1163])). 0.06/0.42 tff(f1170,plain,( 0.06/0.42 spl18_137 <=> ~$less(sK10(tb2t8(mk_array1(elt5,sK2,t2tb9(sK5))),$product(sK6,sK4),min(sK2,$sum($product(sK6,sK4),sK4))),sK9(tb2t8(mk_array1(elt5,sK2,t2tb9(sK5))),$product(sK6,sK4),min(sK2,$sum($product(sK6,sK4),sK4))))), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_137])])). 0.06/0.42 tff(f1172,plain,( 0.06/0.42 ~spl18_137 | spl18_1), 0.06/0.42 inference(avatar_split_clause,[],[f1155,f552,f1170])). 0.06/0.42 tff(f1177,plain,( 0.06/0.42 spl18_138 <=> $less(sK10(tb2t8(mk_array1(elt5,sK2,t2tb9(sK5))),$product(sK6,sK4),min(sK2,$sum($product(sK6,sK4),sK4))),min(sK2,$sum($product(sK6,sK4),sK4)))), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_138])])). 0.06/0.42 tff(f1179,plain,( 0.06/0.42 spl18_138 | spl18_1), 0.06/0.42 inference(avatar_split_clause,[],[f1156,f552,f1177])). 0.06/0.42 tff(f1184,plain,( 0.06/0.42 spl18_140 <=> min(sK2,$sum($product(sK6,sK4),sK4)) = sK2), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_140])])). 0.06/0.42 tff(f1190,plain,( 0.06/0.42 spl18_143 <=> ~sorted_sub3(tb2t8(mk_array1(elt5,sK2,t2tb9(sK5))),$product(sK6,sK4),$sum($product(sK6,sK4),sK4))), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_143])])). 0.06/0.42 tff(f1192,plain,( 0.06/0.42 spl18_140 | ~spl18_143 | spl18_1), 0.06/0.42 inference(avatar_split_clause,[],[f1158,f552,f1190,f1184])). 0.06/0.42 tff(f1200,plain,( 0.06/0.42 ~$less(sK2,sK2) | ~spl18_38), 0.06/0.42 inference(superposition,[],[f405,f712])). 0.06/0.42 tff(f1205,plain,( 0.06/0.42 spl18_145 <=> ~$less(sK2,sK2)), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_145])])). 0.06/0.42 tff(f1206,plain,( 0.06/0.42 ~$less(sK2,sK2) | ~spl18_145), 0.06/0.42 inference(avatar_component_clause,[],[f1205])). 0.06/0.42 tff(f1207,plain,( 0.06/0.42 ~spl18_145 | ~spl18_38), 0.06/0.42 inference(avatar_split_clause,[],[f1200,f711,f1205])). 0.06/0.42 tff(f1208,plain,( 0.06/0.42 min(sK2,sK2) = sK2 | ~spl18_145), 0.06/0.42 inference(resolution,[],[f1206,f416])). 0.06/0.42 tff(f1209,plain,( 0.06/0.42 max(sK2,sK2) = sK2 | ~spl18_145), 0.06/0.42 inference(resolution,[],[f1206,f417])). 0.06/0.42 tff(f1210,plain,( 0.06/0.42 max(sK2,sK2) = sK2 | ~spl18_145), 0.06/0.42 inference(resolution,[],[f1206,f418])). 0.06/0.42 tff(f1211,plain,( 0.06/0.42 min(sK2,sK2) = sK2 | ~spl18_145), 0.06/0.42 inference(resolution,[],[f1206,f419])). 0.06/0.42 tff(f1221,plain,( 0.06/0.42 spl18_146 <=> min(sK2,sK2) = sK2), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_146])])). 0.06/0.42 tff(f1223,plain,( 0.06/0.42 spl18_146 | spl18_145), 0.06/0.42 inference(avatar_split_clause,[],[f1208,f1205,f1221])). 0.06/0.42 tff(f1228,plain,( 0.06/0.42 spl18_148 <=> max(sK2,sK2) = sK2), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_148])])). 0.06/0.42 tff(f1230,plain,( 0.06/0.42 spl18_148 | spl18_145), 0.06/0.42 inference(avatar_split_clause,[],[f1209,f1205,f1228])). 0.06/0.42 tff(f1231,plain,( 0.06/0.42 spl18_148 | spl18_145), 0.06/0.42 inference(avatar_split_clause,[],[f1210,f1205,f1228])). 0.06/0.42 tff(f1232,plain,( 0.06/0.42 spl18_146 | spl18_145), 0.06/0.42 inference(avatar_split_clause,[],[f1211,f1205,f1221])). 0.06/0.42 tff(f1245,plain,( 0.06/0.42 ( ! [X8:$int,X9:$int] : (tb2t7(get(elt5,int,t2tb9(sK1),t2tb(X8))) = tb2t7(get(elt5,int,t2tb9(sK3),t2tb(X8))) | $less(X8,0) | ~$less(X8,X9) | sK2 != X9) )), 0.06/0.42 inference(theory_flattening,[],[f364])). 0.06/0.42 tff(f1246,plain,( 0.06/0.42 tb2t7(get(elt5,int,t2tb9(sK1),t2tb(0))) = tb2t7(get(elt5,int,t2tb9(sK3),t2tb(0))) | $less(0,0) | ~$less(0,1) | 1 != sK2), 0.06/0.42 inference(instantiation,[],[f1245])). 0.06/0.42 tff(f1247,plain,( 0.06/0.42 tb2t7(get(elt5,int,t2tb9(sK1),t2tb(0))) = tb2t7(get(elt5,int,t2tb9(sK3),t2tb(0))) | 1 != sK2), 0.06/0.42 inference(interpreted_simplification,[],[f1246])). 0.06/0.42 tff(f1257,plain,( 0.06/0.42 $less($product(sK6,sK4),0) | tb2t7(get(elt5,int,t2tb9(sK1),t2tb($product(sK6,sK4)))) = tb2t7(get(elt5,int,t2tb9(sK3),t2tb($product(sK6,sK4)))) | ~spl18_4), 0.06/0.42 inference(resolution,[],[f364,f567])). 0.06/0.42 tff(f1258,plain,( 0.06/0.42 $less(sK4,0) | tb2t7(get(elt5,int,t2tb9(sK1),t2tb(sK4))) = tb2t7(get(elt5,int,t2tb9(sK3),t2tb(sK4))) | ~spl18_6), 0.06/0.42 inference(resolution,[],[f364,f574])). 0.06/0.42 tff(f1264,plain,( 0.06/0.42 spl18_151 <=> 1 != sK2), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_151])])). 0.06/0.42 tff(f1270,plain,( 0.06/0.42 spl18_152 <=> tb2t7(get(elt5,int,t2tb9(sK1),t2tb(0))) = tb2t7(get(elt5,int,t2tb9(sK3),t2tb(0)))), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_152])])). 0.06/0.42 tff(f1272,plain,( 0.06/0.42 ~spl18_151 | spl18_152), 0.06/0.42 inference(avatar_split_clause,[],[f1247,f1270,f1264])). 0.06/0.42 tff(f1273,plain,( 0.06/0.42 tb2t7(get(elt5,int,t2tb9(sK1),t2tb($product(sK6,sK4)))) = tb2t7(get(elt5,int,t2tb9(sK3),t2tb($product(sK6,sK4)))) | (~spl18_3 | ~spl18_4)), 0.06/0.42 inference(subsumption_resolution,[],[f1257,f560])). 0.06/0.42 tff(f1278,plain,( 0.06/0.42 spl18_154 <=> tb2t7(get(elt5,int,t2tb9(sK1),t2tb($product(sK6,sK4)))) = tb2t7(get(elt5,int,t2tb9(sK3),t2tb($product(sK6,sK4))))), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_154])])). 0.06/0.42 tff(f1280,plain,( 0.06/0.42 spl18_154 | spl18_3 | ~spl18_4), 0.06/0.42 inference(avatar_split_clause,[],[f1273,f566,f559,f1278])). 0.06/0.42 tff(f1281,plain,( 0.06/0.42 tb2t7(get(elt5,int,t2tb9(sK1),t2tb(sK4))) = tb2t7(get(elt5,int,t2tb9(sK3),t2tb(sK4))) | (~spl18_6 | ~spl18_15)), 0.06/0.42 inference(subsumption_resolution,[],[f1258,f607])). 0.06/0.42 tff(f1286,plain,( 0.06/0.42 spl18_156 <=> tb2t7(get(elt5,int,t2tb9(sK1),t2tb(sK4))) = tb2t7(get(elt5,int,t2tb9(sK3),t2tb(sK4)))), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_156])])). 0.06/0.42 tff(f1288,plain,( 0.06/0.42 spl18_156 | ~spl18_6 | spl18_15), 0.06/0.42 inference(avatar_split_clause,[],[f1281,f606,f573,f1286])). 0.06/0.42 tff(f1338,plain,( 0.06/0.42 $less($uminus(sK2),abs(abs(0))) | ~spl18_110), 0.06/0.42 inference(resolution,[],[f1028,f432])). 0.06/0.42 tff(f1347,plain,( 0.06/0.42 spl18_158 <=> $less($uminus(sK2),abs(abs(0)))), 0.06/0.42 introduced(avatar_definition,[new_symbols(naming,[spl18_158])])). 0.06/0.42 tff(f1349,plain,( 0.06/0.42 spl18_158 | ~spl18_110), 0.06/0.42 inference(avatar_split_clause,[],[f1338,f1027,f1347])). 0.06/0.42 tff(f1353,plain,( 0.06/0.42 sorted_sub3(tb2t8(mk_array1(elt5,sK2,t2tb9(sK5))),$product(sK6,sK4),min(sK2,$sum($product(sK6,sK4),sK4))) | $less($product(sK6,sK4),0) | ~spl18_4), 0.06/0.42 inference(resolution,[],[f535,f567])). 0.06/0.42 tff(f1365,plain,( 0.06/0.42 $less($product(sK6,sK4),0) | (~spl18_1 | ~spl18_4)), 0.06/0.42 inference(subsumption_resolution,[],[f1353,f553])). 0.06/0.42 tff(f1366,plain,( 0.06/0.42 $false | (~spl18_1 | ~spl18_3 | ~spl18_4)), 0.06/0.42 inference(subsumption_resolution,[],[f1365,f560])). 0.06/0.42 tff(f1367,plain,( 0.06/0.42 spl18_1 | spl18_3 | ~spl18_4), 0.06/0.42 inference(avatar_contradiction_clause,[],[f1366])). 0.06/0.42 tff(f1368,plain,( 0.06/0.42 $false), 0.06/0.42 inference(avatar_sat_refutation,[],[f554,f561,f568,f575,f582,f589,f596,f597,f617,f624,f631,f647,f654,f661,f668,f675,f682,f699,f706,f713,f720,f727,f734,f741,f758,f765,f772,f779,f786,f793,f800,f816,f824,f831,f847,f851,f866,f870,f887,f894,f901,f908,f915,f922,f929,f944,f952,f969,f977,f997,f1004,f1022,f1029,f1043,f1054,f1070,f1077,f1084,f1091,f1098,f1105,f1120,f1136,f1143,f1144,f1145,f1165,f1172,f1179,f1192,f1207,f1223,f1230,f1231,f1232,f1272,f1280,f1288,f1349,f1367])). 0.06/0.42 % SZS output end Proof for theBenchmark 0.06/0.42 % ------------------------------ 0.06/0.42 % Version: Vampire 4.2.2 (commit 552c234 on 2018-07-02 14:53:33 +0100) 0.06/0.42 % Termination reason: Refutation 0.06/0.42 0.06/0.42 % Memory used [KB]: 6012 0.06/0.42 % Time elapsed: 0.144 s 0.06/0.42 % ------------------------------ 0.06/0.42 % ------------------------------ 0.06/0.42 % Success in time 0.184 s 0.06/0.42 EOF