TSTP Solution File: ITP366_1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 10:44:33 EDT 2023
% Result : Theorem 17.31s 5.01s
% Output : CNFRefutation 17.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 19:05:09 EDT 2023
% 0.14/0.35 % CPUTime :
% 17.31/5.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.31/5.01
% 17.31/5.01 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.31/5.03 %$ semantics_ltln$ > member$ > gF_advice_congruent_axioms$ > gF_advice_congruent$ > fun_app$o > fun_app$l > fun_app$d > fun_app$c > fun_app$b > fun_app$ > idx_sequence$ > af_congruent_axioms$ > subsequence$ > foldl$ > def_9 > def_7 > def_5 > def_4 > uuh$ > uug$ > uuf$ > uue$ > suffix$ > sub$ > plus$ > g_F$ > gF_advice$ > g$ > fun_app$p > fun_app$n > fun_app$m > fun_app$k > fun_app$j > fun_app$i > fun_app$h > fun_app$g > fun_app$f > fun_app$e > fun_app$a > f_G$ > fG_advice$ > f$ > def_8 > def_6 > def_3 > def_2 > def_10 > def_1 > conc$ > case_nat$a > case_nat$ > build$ > #nlpp > uuc$ > uub$ > uua$ > uu$ > sgn$ > numeral$ > nu_stable$ > nat$ > mu_stable$ > less$ > language_ltln$ > inc$ > dbl_inc$ > dbl_dec$ > dbl$ > collect$ > bit1$ > bit0$ > x$ > w$ > uuj$ > uui$ > uud$ > unf$ > tltrue > tlfalse > pred$ > phi$ > one$ > of_nat$ > num_of_nat$ > next_ltln$ > id$ > af_letter$ > #skF_15 > #skF_61 > #skF_20 > #skF_23 > #skF_17 > #skF_5 > #skF_30 > #skF_67 > #skF_48 > #skF_59 > #skF_64 > #skF_11 > #skF_39 > #skF_41 > #skF_75 > #skF_72 > #skF_35 > #skF_27 > #skF_58 > #skF_42 > #skF_53 > #skF_26 > #skF_14 > #skF_57 > #skF_18 > #skF_63 > #skF_43 > #skF_78 > #skF_21 > #skF_70 > #skF_16 > #skF_46 > #skF_60 > #skF_9 > #skF_29 > #skF_12 > #skF_33 > #skF_8 > #skF_6 > #skF_68 > #skF_62 > #skF_2 > #skF_47 > #skF_74 > #skF_1 > #skF_7 > #skF_13 > #skF_65 > #skF_32 > #skF_4 > #skF_76 > #skF_49 > #skF_52 > #skF_31 > #skF_50 > #skF_25 > #skF_44 > #skF_55 > #skF_38 > #skF_54 > #skF_45 > #skF_3 > #skF_71 > #skF_51 > #skF_40 > #skF_37 > #skF_10 > #skF_19 > #skF_56 > #skF_77 > #skF_34 > #skF_28 > #skF_69 > #skF_66 > #skF_36 > #skF_22 > #skF_73 > #skF_24
% 17.31/5.03
% 17.31/5.03 %Foreground sorts:
% 17.31/5.03 tff(A_set_list$, type, A_set_list$: $tType ).
% 17.31/5.03 tff(Nat_nat_bool_fun_fun$, type, Nat_nat_bool_fun_fun$: $tType ).
% 17.31/5.03 tff(Nat$, type, Nat$: $tType ).
% 17.31/5.03 tff(A_set_a_ltln_fun$, type, A_set_a_ltln_fun$: $tType ).
% 17.31/5.03 tff(Nat_a_set_fun_set$, type, Nat_a_set_fun_set$: $tType ).
% 17.31/5.03 tff(A_set$, type, A_set$: $tType ).
% 17.31/5.03 tff(tlbool, type, tlbool: $tType ).
% 17.31/5.03 tff(Int_int_fun$, type, Int_int_fun$: $tType ).
% 17.31/5.03 tff(Nat_nat_fun$, type, Nat_nat_fun$: $tType ).
% 17.31/5.03 tff(Nat_int_fun$, type, Nat_int_fun$: $tType ).
% 17.31/5.03 tff(Nat_a_set_fun$, type, Nat_a_set_fun$: $tType ).
% 17.31/5.03 tff(Num_bool_fun$, type, Num_bool_fun$: $tType ).
% 17.31/5.03 tff(A_ltln_bool_fun$, type, A_ltln_bool_fun$: $tType ).
% 17.31/5.03 tff(A_ltln_a_set_a_ltln_fun_fun$, type, A_ltln_a_set_a_ltln_fun_fun$: $tType ).
% 17.31/5.03 tff(Bool_bool_fun$, type, Bool_bool_fun$: $tType ).
% 17.31/5.03 tff(Nat_num_fun$, type, Nat_num_fun$: $tType ).
% 17.31/5.03 tff(Nat_bool_fun$, type, Nat_bool_fun$: $tType ).
% 17.31/5.03 tff(Bool_nat_fun$, type, Bool_nat_fun$: $tType ).
% 17.31/5.03 tff(A_ltln_set$, type, A_ltln_set$: $tType ).
% 17.31/5.03 tff(A_ltln_a_ltln_bool_fun_fun$, type, A_ltln_a_ltln_bool_fun_fun$: $tType ).
% 17.31/5.03 tff(Nat_a_set_fun_bool_fun$, type, Nat_a_set_fun_bool_fun$: $tType ).
% 17.31/5.03 tff(A_ltln$, type, A_ltln$: $tType ).
% 17.31/5.03 tff(Int_bool_fun$, type, Int_bool_fun$: $tType ).
% 17.31/5.03 tff(A_ltln_a_ltln_fun$, type, A_ltln_a_ltln_fun$: $tType ).
% 17.31/5.03 tff(Num$, type, Num$: $tType ).
% 17.31/5.03
% 17.31/5.03 %Background operators:
% 17.31/5.03 tff('#skE_2', type, '#skE_2': $int).
% 17.31/5.03 tff('#skE_1', type, '#skE_1': $int).
% 17.31/5.03
% 17.31/5.03 %Foreground operators:
% 17.31/5.03 tff('#skF_15', type, '#skF_15': (Nat$ * Nat$ * Nat_nat_bool_fun_fun$) > Nat$).
% 17.31/5.03 tff(uuj$, type, uuj$: Nat_bool_fun$).
% 17.31/5.03 tff('#skF_61', type, '#skF_61': (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_a_ltln_fun$) > Nat_a_set_fun$).
% 17.31/5.03 tff(af_congruent_axioms$, type, af_congruent_axioms$: A_ltln_a_ltln_bool_fun_fun$ > $o).
% 17.31/5.03 tff('#skF_20', type, '#skF_20': (Nat$ * Nat_bool_fun$) > Nat$).
% 17.31/5.03 tff('#skF_23', type, '#skF_23': (Nat$ * Nat$) > Nat$).
% 17.31/5.03 tff(def_6, type, def_6: (Bool_bool_fun$ * tlbool) > tlbool).
% 17.31/5.03 tff(fun_app$g, type, fun_app$g: (A_set_a_ltln_fun$ * A_set$) > A_ltln$).
% 17.31/5.03 tff('#skF_17', type, '#skF_17': (Nat$ * Nat$ * Nat_nat_bool_fun_fun$) > Nat$).
% 17.31/5.03 tff(uug$, type, uug$: (Bool_nat_fun$ * Nat_bool_fun$) > Nat_nat_fun$).
% 17.31/5.03 tff('#skF_5', type, '#skF_5': A_ltln_a_ltln_bool_fun_fun$ > A_ltln$).
% 17.31/5.03 tff('#skF_30', type, '#skF_30': Nat$ > Nat$).
% 17.31/5.03 tff(fun_app$d, type, fun_app$d: (Bool_bool_fun$ * tlbool) > $o).
% 17.31/5.03 tff('#skF_67', type, '#skF_67': (Nat_a_set_fun$ * A_ltln$ * A_ltln_set$ * A_ltln$) > Nat$).
% 17.31/5.03 tff(def_1, type, def_1: (Nat_bool_fun$ * Nat$) > tlbool).
% 17.31/5.03 tff(def_5, type, def_5: (tlbool * Nat_bool_fun$ * Nat$) > tlbool).
% 17.31/5.03 tff('#skF_48', type, '#skF_48': (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_a_ltln_fun$) > A_ltln$).
% 17.31/5.03 tff(uua$, type, uua$: Nat_a_set_fun_set$ > Nat_a_set_fun_bool_fun$).
% 17.31/5.03 tff('#skF_59', type, '#skF_59': (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_a_ltln_fun$) > A_ltln$).
% 17.31/5.03 tff('#skF_64', type, '#skF_64': (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_a_ltln_fun$) > A_ltln$).
% 17.31/5.03 tff(next_ltln$, type, next_ltln$: A_ltln_a_ltln_fun$).
% 17.31/5.03 tff('#skF_11', type, '#skF_11': (Nat$ * Nat$ * Nat_bool_fun$) > Nat$).
% 17.31/5.03 tff('#skF_39', type, '#skF_39': (Nat_nat_bool_fun_fun$ * Nat$ * Nat$) > Nat$).
% 17.31/5.03 tff('#skF_41', type, '#skF_41': (Nat_nat_bool_fun_fun$ * Nat$ * Nat$) > Nat$).
% 17.31/5.03 tff('#skF_75', type, '#skF_75': (Nat$ * Nat$) > Nat$).
% 17.31/5.03 tff('#skF_72', type, '#skF_72': (Num_bool_fun$ * Num$) > Num$).
% 17.31/5.03 tff(def_7, type, def_7: (tlbool * Nat_bool_fun$ * Nat$) > tlbool).
% 17.31/5.03 tff('#skF_35', type, '#skF_35': (Nat$ * Nat_bool_fun$) > Nat$).
% 17.31/5.03 tff(one$, type, one$: Num$).
% 17.31/5.03 tff(uu$, type, uu$: A_ltln$ > Nat_a_set_fun_bool_fun$).
% 17.31/5.03 tff('#skF_27', type, '#skF_27': (Nat_num_fun$ * Nat$ * Nat$) > Nat$).
% 17.31/5.03 tff(def_4, type, def_4: (tlbool * Nat_bool_fun$ * Nat$) > tlbool).
% 17.31/5.03 tff(def_3, type, def_3: (Nat_bool_fun$ * Nat$) > tlbool).
% 17.31/5.03 tff(uub$, type, uub$: $int > Int_bool_fun$).
% 17.31/5.03 tff('#skF_58', type, '#skF_58': (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_a_ltln_fun$) > Nat_a_set_fun$).
% 17.31/5.03 tff(foldl$, type, foldl$: (A_ltln_a_set_a_ltln_fun_fun$ * A_ltln$ * A_set_list$) > A_ltln$).
% 17.31/5.03 tff('#skF_42', type, '#skF_42': (Nat_nat_bool_fun_fun$ * Nat$ * Nat$) > Nat$).
% 17.31/5.03 tff('#skF_53', type, '#skF_53': (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_a_ltln_fun$) > A_ltln$).
% 17.31/5.03 tff('#skF_26', type, '#skF_26': (Nat_int_fun$ * Nat$ * Nat$) > Nat$).
% 17.31/5.03 tff(tlfalse, type, tlfalse: tlbool).
% 17.31/5.03 tff('#skF_14', type, '#skF_14': (Nat$ * Nat$ * Nat_nat_bool_fun_fun$) > Nat$).
% 17.31/5.03 tff('#skF_57', type, '#skF_57': (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_a_ltln_fun$) > A_ltln$).
% 17.31/5.03 tff(fun_app$e, type, fun_app$e: (Nat_nat_fun$ * Nat$) > Nat$).
% 17.31/5.03 tff('#skF_18', type, '#skF_18': (Nat$ * Nat$) > Nat$).
% 17.31/5.03 tff('#skF_63', type, '#skF_63': (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_a_ltln_fun$) > A_ltln_set$).
% 17.31/5.03 tff('#skF_43', type, '#skF_43': (Nat_bool_fun$ * Nat$) > Nat$).
% 17.31/5.03 tff('#skF_78', type, '#skF_78': (Nat$ * Nat$) > Nat$).
% 17.31/5.03 tff('#skF_21', type, '#skF_21': (Nat$ * Nat_bool_fun$) > Nat$).
% 17.31/5.03 tff(fun_app$k, type, fun_app$k: (Nat_int_fun$ * Nat$) > $int).
% 17.31/5.03 tff('#skF_70', type, '#skF_70': A_ltln_a_ltln_fun$ > A_ltln$).
% 17.31/5.03 tff(fun_app$n, type, fun_app$n: (Nat_nat_bool_fun_fun$ * Nat$) > Nat_bool_fun$).
% 17.31/5.03 tff(uud$, type, uud$: Nat_nat_fun$).
% 17.31/5.03 tff('#skF_16', type, '#skF_16': (Nat$ * Nat$ * Nat_nat_bool_fun_fun$) > Nat$).
% 17.31/5.03 tff(numeral$, type, numeral$: Num$ > $int).
% 17.31/5.03 tff(dbl$, type, dbl$: $int > $int).
% 17.31/5.03 tff('#skF_46', type, '#skF_46': (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_a_ltln_fun$) > A_ltln$).
% 17.31/5.03 tff(pred$, type, pred$: Nat_nat_fun$).
% 17.31/5.03 tff(plus$, type, plus$: (Num$ * Num$) > Num$).
% 17.31/5.03 tff(gF_advice$, type, gF_advice$: (A_ltln$ * A_ltln_set$) > A_ltln$).
% 17.31/5.03 tff(id$, type, id$: A_ltln_a_ltln_fun$).
% 17.31/5.03 tff(bit0$, type, bit0$: Num$ > Num$).
% 17.31/5.03 tff(inc$, type, inc$: Num$ > Num$).
% 17.31/5.03 tff('#skF_60', type, '#skF_60': (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_a_ltln_fun$) > A_ltln_set$).
% 17.31/5.03 tff('#skF_9', type, '#skF_9': (Nat_a_set_fun_bool_fun$ * Nat_a_set_fun_bool_fun$) > Nat_a_set_fun$).
% 17.31/5.03 tff(case_nat$a, type, case_nat$a: (tlbool * Nat_bool_fun$) > Nat_bool_fun$).
% 17.31/5.03 tff(build$, type, build$: (A_set$ * Nat_a_set_fun$) > Nat_a_set_fun$).
% 17.31/5.03 tff(bit1$, type, bit1$: Num$ > Num$).
% 17.31/5.03 tff(subsequence$, type, subsequence$: (Nat_a_set_fun$ * Nat$ * Nat$) > A_set_list$).
% 17.31/5.03 tff('#skF_29', type, '#skF_29': (Nat$ * Nat$) > Nat$).
% 17.31/5.03 tff('#skF_12', type, '#skF_12': (Nat_bool_fun$ * Nat$) > Nat$).
% 17.31/5.03 tff(fun_app$l, type, fun_app$l: (A_ltln_bool_fun$ * A_ltln$) > $o).
% 17.31/5.03 tff('#skF_33', type, '#skF_33': Nat$ > Nat$).
% 17.31/5.03 tff('#skF_8', type, '#skF_8': (Nat_a_set_fun_bool_fun$ * Nat_a_set_fun_bool_fun$) > Nat_a_set_fun$).
% 17.31/5.03 tff('#skF_6', type, '#skF_6': A_ltln_a_ltln_bool_fun_fun$ > A_set$).
% 17.31/5.03 tff(of_nat$, type, of_nat$: Nat_int_fun$).
% 17.31/5.03 tff('#skF_68', type, '#skF_68': (Nat_a_set_fun$ * A_ltln$ * A_ltln_set$) > Nat$).
% 17.31/5.03 tff('#skF_62', type, '#skF_62': (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_a_ltln_fun$) > A_ltln$).
% 17.31/5.03 tff('#skF_2', type, '#skF_2': A_ltln_a_ltln_bool_fun_fun$ > A_ltln$).
% 17.31/5.03 tff(conc$, type, conc$: (A_set_list$ * Nat_a_set_fun$) > Nat_a_set_fun$).
% 17.31/5.03 tff('#skF_47', type, '#skF_47': (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_a_ltln_fun$) > Nat_a_set_fun$).
% 17.31/5.03 tff(semantics_ltln$, type, semantics_ltln$: (Nat_a_set_fun$ * A_ltln$) > $o).
% 17.31/5.03 tff(g_F$, type, g_F$: (A_ltln$ * Nat_a_set_fun$) > A_ltln_set$).
% 17.31/5.03 tff(fun_app$j, type, fun_app$j: (Nat_a_set_fun$ * Nat$) > A_set$).
% 17.31/5.03 tff('#skF_74', type, '#skF_74': Num$ > Num$).
% 17.31/5.03 tff(uue$, type, uue$: (Nat_nat_fun$ * Nat_nat_fun$) > Nat_nat_fun$).
% 17.31/5.03 tff('#skF_1', type, '#skF_1': A_ltln_a_ltln_bool_fun_fun$ > A_ltln$).
% 17.31/5.03 tff(uuc$, type, uuc$: $int > Int_int_fun$).
% 17.31/5.03 tff('#skF_7', type, '#skF_7': (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_set$ * A_ltln$ * A_ltln_a_ltln_fun$ * Nat_a_set_fun$) > Nat$).
% 17.31/5.03 tff('#skF_13', type, '#skF_13': (Nat_bool_fun$ * Nat$) > Nat$).
% 17.31/5.03 tff(fun_app$o, type, fun_app$o: (Num_bool_fun$ * Num$) > $o).
% 17.31/5.03 tff('#skF_65', type, '#skF_65': (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_a_ltln_fun$) > A_ltln$).
% 17.31/5.03 tff('#skF_32', type, '#skF_32': (Nat$ * Nat_bool_fun$) > Nat$).
% 17.31/5.03 tff('#skF_4', type, '#skF_4': A_ltln_a_ltln_bool_fun_fun$ > A_ltln$).
% 17.31/5.03 tff(af_letter$, type, af_letter$: A_ltln_a_set_a_ltln_fun_fun$).
% 17.31/5.03 tff('#skF_76', type, '#skF_76': (Nat$ * Nat$) > Nat$).
% 17.31/5.03 tff('#skF_49', type, '#skF_49': (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_a_ltln_fun$) > A_ltln_set$).
% 17.31/5.03 tff(f$, type, f$: (A_ltln$ * Nat_a_set_fun$) > A_ltln_set$).
% 17.31/5.03 tff('#skF_52', type, '#skF_52': (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_a_ltln_fun$) > A_ltln_set$).
% 17.31/5.03 tff(mu_stable$, type, mu_stable$: A_ltln$ > Nat_a_set_fun_bool_fun$).
% 17.31/5.03 tff('#skF_31', type, '#skF_31': (Nat$ * Nat_bool_fun$) > Nat$).
% 17.31/5.03 tff(fun_app$b, type, fun_app$b: (Nat_a_set_fun_bool_fun$ * Nat_a_set_fun$) > $o).
% 17.31/5.03 tff('#skF_50', type, '#skF_50': (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_a_ltln_fun$) > Nat_a_set_fun$).
% 17.31/5.03 tff(fun_app$a, type, fun_app$a: (Int_int_fun$ * $int) > $int).
% 17.31/5.03 tff(fun_app$i, type, fun_app$i: (A_ltln_a_ltln_fun$ * A_ltln$) > A_ltln$).
% 17.31/5.03 tff(f_G$, type, f_G$: (A_ltln$ * Nat_a_set_fun$) > A_ltln_set$).
% 17.31/5.03 tff(member$, type, member$: (Nat_a_set_fun$ * Nat_a_set_fun_set$) > $o).
% 17.31/5.03 tff('#skF_25', type, '#skF_25': (Nat_num_fun$ * Nat$ * Nat$) > Nat$).
% 17.31/5.03 tff(fun_app$h, type, fun_app$h: (A_ltln_a_set_a_ltln_fun_fun$ * A_ltln$) > A_set_a_ltln_fun$).
% 17.31/5.03 tff('#skF_44', type, '#skF_44': Nat$ > Nat$).
% 17.31/5.03 tff(gF_advice_congruent_axioms$, type, gF_advice_congruent_axioms$: (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_a_ltln_fun$) > $o).
% 17.31/5.03 tff(unf$, type, unf$: A_ltln_a_ltln_fun$).
% 17.31/5.03 tff(uuh$, type, uuh$: (Bool_bool_fun$ * Nat_bool_fun$) > Nat_bool_fun$).
% 17.31/5.03 tff(gF_advice_congruent$, type, gF_advice_congruent$: (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_a_ltln_fun$) > $o).
% 17.31/5.03 tff(fG_advice$, type, fG_advice$: (A_ltln$ * A_ltln_set$) > A_ltln$).
% 17.31/5.03 tff('#skF_55', type, '#skF_55': (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_a_ltln_fun$) > A_ltln_set$).
% 17.31/5.03 tff('#skF_38', type, '#skF_38': (Nat_bool_fun$ * Nat$) > Nat$).
% 17.31/5.03 tff('#skF_54', type, '#skF_54': (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_a_ltln_fun$) > A_ltln$).
% 17.31/5.03 tff(dbl_inc$, type, dbl_inc$: $int > $int).
% 17.31/5.03 tff(fun_app$c, type, fun_app$c: (Nat_bool_fun$ * Nat$) > $o).
% 17.31/5.03 tff(def_10, type, def_10: (Nat_bool_fun$ * Nat$) > tlbool).
% 17.31/5.03 tff(case_nat$, type, case_nat$: (Nat$ * Nat_nat_fun$) > Nat_nat_fun$).
% 17.31/5.03 tff(nat$, type, nat$: $int > Nat$).
% 17.31/5.03 tff(num_of_nat$, type, num_of_nat$: Nat_num_fun$).
% 17.31/5.03 tff(g$, type, g$: (A_ltln$ * Nat_a_set_fun$) > A_ltln_set$).
% 17.31/5.03 tff('#skF_45', type, '#skF_45': (Nat_bool_fun$ * Nat$) > Nat$).
% 17.31/5.03 tff('#skF_3', type, '#skF_3': A_ltln_a_ltln_bool_fun_fun$ > A_set$).
% 17.31/5.03 tff(language_ltln$, type, language_ltln$: A_ltln$ > Nat_a_set_fun_set$).
% 17.31/5.03 tff('#skF_71', type, '#skF_71': (Nat_bool_fun$ * Nat$ * Nat$) > Nat$).
% 17.31/5.03 tff(collect$, type, collect$: Nat_a_set_fun_bool_fun$ > Nat_a_set_fun_set$).
% 17.31/5.03 tff('#skF_51', type, '#skF_51': (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_a_ltln_fun$) > A_ltln$).
% 17.31/5.03 tff('#skF_40', type, '#skF_40': (Nat_nat_bool_fun_fun$ * Nat$ * Nat$) > Nat$).
% 17.31/5.03 tff(suffix$, type, suffix$: (Nat$ * Nat_a_set_fun$) > Nat_a_set_fun$).
% 17.31/5.03 tff(sgn$, type, sgn$: $int > $int).
% 17.31/5.03 tff('#skF_37', type, '#skF_37': Nat$ > Nat$).
% 17.31/5.03 tff('#skF_10', type, '#skF_10': (Nat$ * Nat$ * Nat_bool_fun$) > Nat$).
% 17.31/5.03 tff('#skF_19', type, '#skF_19': (Nat$ * Nat_bool_fun$) > Nat$).
% 17.31/5.03 tff(less$, type, less$: Num$ > Num_bool_fun$).
% 17.31/5.03 tff(fun_app$, type, fun_app$: (Int_bool_fun$ * $int) > $o).
% 17.31/5.03 tff(uui$, type, uui$: Nat_bool_fun$).
% 17.31/5.03 tff(tltrue, type, tltrue: tlbool).
% 17.31/5.03 tff('#skF_56', type, '#skF_56': (A_ltln_a_ltln_bool_fun_fun$ * Nat_a_set_fun$ * A_ltln_set$ * A_ltln_a_ltln_fun$ * A_ltln$) > Nat$).
% 17.31/5.03 tff(def_8, type, def_8: (Nat_bool_fun$ * Nat$) > tlbool).
% 17.31/5.03 tff('#skF_77', type, '#skF_77': (Nat$ * Nat$) > Nat$).
% 17.31/5.03 tff(idx_sequence$, type, idx_sequence$: Nat_nat_fun$ > $o).
% 17.31/5.03 tff('#skF_34', type, '#skF_34': (Nat$ * Nat_bool_fun$) > Nat$).
% 17.31/5.03 tff(def_2, type, def_2: (Nat_bool_fun$ * Nat$) > tlbool).
% 17.31/5.03 tff(fun_app$p, type, fun_app$p: (Nat_num_fun$ * Nat$) > Num$).
% 17.31/5.03 tff(uuf$, type, uuf$: (Nat_bool_fun$ * Nat_nat_fun$) > Nat_bool_fun$).
% 17.31/5.03 tff('#skF_28', type, '#skF_28': (Nat_int_fun$ * Nat$ * Nat$) > Nat$).
% 17.31/5.03 tff(fun_app$m, type, fun_app$m: (A_ltln_a_ltln_bool_fun_fun$ * A_ltln$) > A_ltln_bool_fun$).
% 17.31/5.03 tff('#skF_69', type, '#skF_69': Nat_nat_fun$ > Nat$).
% 17.31/5.03 tff('#skF_66', type, '#skF_66': (A_ltln_a_ltln_bool_fun_fun$ * A_ltln_a_ltln_fun$) > A_ltln_set$).
% 17.31/5.03 tff(w$, type, w$: Nat_a_set_fun$).
% 17.31/5.03 tff('#skF_36', type, '#skF_36': (Nat$ * Nat_bool_fun$) > Nat$).
% 17.31/5.03 tff(sub$, type, sub$: (Num$ * Num$) > $int).
% 17.31/5.03 tff('#skF_22', type, '#skF_22': (Nat$ * Nat_bool_fun$) > Nat$).
% 17.31/5.03 tff(fun_app$f, type, fun_app$f: (Bool_nat_fun$ * tlbool) > Nat$).
% 17.31/5.03 tff(phi$, type, phi$: A_ltln$).
% 17.31/5.03 tff(def_9, type, def_9: (tlbool * Nat_bool_fun$ * Nat$) > tlbool).
% 17.31/5.03 tff('#skF_73', type, '#skF_73': Num$ > Num$).
% 17.31/5.03 tff(x$, type, x$: A_ltln_set$).
% 17.31/5.03 tff(dbl_dec$, type, dbl_dec$: $int > $int).
% 17.31/5.03 tff(nu_stable$, type, nu_stable$: A_ltln$ > Nat_a_set_fun_bool_fun$).
% 17.31/5.03 tff('#skF_24', type, '#skF_24': (Nat$ * Nat$) > Nat$).
% 17.31/5.03
% 17.31/5.04 tff(f_109, axiom, (![A__questionmark_v0:A_ltln$, A__questionmark_v1:A_ltln_set$]: (gF_advice$(fun_app$i(next_ltln$, A__questionmark_v0), A__questionmark_v1) = fun_app$i(next_ltln$, gF_advice$(A__questionmark_v0, A__questionmark_v1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', axiom18)).
% 17.31/5.04 tff(f_118, axiom, (![A__questionmark_v0:A_ltln$]: (fun_app$i(unf$, fun_app$i(next_ltln$, A__questionmark_v0)) = fun_app$i(next_ltln$, A__questionmark_v0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', axiom21)).
% 17.31/5.04 tff(f_84, axiom, semantics_ltln$(w$, gF_advice$(fun_app$i(unf$, fun_app$i(next_ltln$, phi$)), x$)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', axiom12)).
% 17.31/5.04 tff(f_96, axiom, (![A__questionmark_v0:Nat_a_set_fun$, A__questionmark_v1:A_ltln$]: (semantics_ltln$(A__questionmark_v0, fun_app$i(next_ltln$, A__questionmark_v1)) <=> semantics_ltln$(suffix$(nat$(1), A__questionmark_v0), A__questionmark_v1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', axiom15)).
% 17.31/5.04 tff(f_112, axiom, (![A__questionmark_v0:A_ltln$, A__questionmark_v1:A_set$]: (fun_app$g(fun_app$h(af_letter$, fun_app$i(next_ltln$, A__questionmark_v0)), A__questionmark_v1) = A__questionmark_v0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', axiom19)).
% 17.31/5.04 tff(f_82, negated_conjecture, ~semantics_ltln$(suffix$(nat$(1), w$), gF_advice$(fun_app$g(fun_app$h(af_letter$, fun_app$i(next_ltln$, phi$)), fun_app$j(w$, nat$(0))), x$)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conjecture11)).
% 17.31/5.04 tff(c_52, plain, (![A__questionmark_v0_32:A_ltln$, A__questionmark_v1_33:A_ltln_set$]: (gF_advice$(fun_app$i(next_ltln$, A__questionmark_v0_32), A__questionmark_v1_33)=fun_app$i(next_ltln$, gF_advice$(A__questionmark_v0_32, A__questionmark_v1_33)))), inference(cnfTransformation, [status(thm)], [f_109])).
% 17.31/5.04 tff(c_58, plain, (![A__questionmark_v0_36:A_ltln$]: (fun_app$i(unf$, fun_app$i(next_ltln$, A__questionmark_v0_36))=fun_app$i(next_ltln$, A__questionmark_v0_36))), inference(cnfTransformation, [status(thm)], [f_118])).
% 17.31/5.04 tff(c_35, plain, (semantics_ltln$(w$, gF_advice$(fun_app$i(unf$, fun_app$i(next_ltln$, phi$)), x$))), inference(cnfTransformation, [status(thm)], [f_84])).
% 17.31/5.04 tff(c_3028, plain, (semantics_ltln$(w$, fun_app$i(next_ltln$, gF_advice$(phi$, x$)))), inference(demodulation, [status(thm), theory('equality')], [c_52, c_58, c_35])).
% 17.31/5.04 tff(c_12145, plain, (![A__questionmark_v0_9439:Nat_a_set_fun$, A__questionmark_v1_9440:A_ltln$]: (semantics_ltln$(suffix$(nat$(1), A__questionmark_v0_9439), A__questionmark_v1_9440) | ~semantics_ltln$(A__questionmark_v0_9439, fun_app$i(next_ltln$, A__questionmark_v1_9440)))), inference(cnfTransformation, [status(thm)], [f_96])).
% 17.31/5.04 tff(c_54, plain, (![A__questionmark_v0_34:A_ltln$, A__questionmark_v1_35:A_set$]: (fun_app$g(fun_app$h(af_letter$, fun_app$i(next_ltln$, A__questionmark_v0_34)), A__questionmark_v1_35)=A__questionmark_v0_34)), inference(cnfTransformation, [status(thm)], [f_112])).
% 17.31/5.04 tff(c_2909, plain, (~semantics_ltln$(suffix$(nat$(1), w$), gF_advice$(fun_app$g(fun_app$h(af_letter$, fun_app$i(next_ltln$, phi$)), fun_app$j(w$, nat$(0))), x$))), inference(cnfTransformation, [status(thm)], [f_82])).
% 17.31/5.04 tff(c_3030, plain, (~semantics_ltln$(suffix$(nat$(1), w$), gF_advice$(phi$, x$))), inference(demodulation, [status(thm), theory('equality')], [c_54, c_2909])).
% 17.31/5.04 tff(c_12161, plain, (~semantics_ltln$(w$, fun_app$i(next_ltln$, gF_advice$(phi$, x$)))), inference(resolution, [status(thm)], [c_12145, c_3030])).
% 17.31/5.04 tff(c_12179, plain, $false, inference(demodulation, [status(thm), theory('equality')], [c_3028, c_12161])).
% 17.31/5.04 % SZS output end CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.31/5.04
% 17.31/5.04 Inference rules
% 17.31/5.04 ----------------------
% 17.31/5.04 #Ref : 9
% 17.31/5.04 #Sup : 1930
% 17.31/5.04 #Fact : 1
% 17.31/5.04 #Define : 2
% 17.31/5.04 #Split : 0
% 17.31/5.04 #Chain : 0
% 17.31/5.04 #Close : 0
% 17.31/5.04
% 17.31/5.04 Ordering : LPO
% 17.31/5.04
% 17.31/5.04 Simplification rules
% 17.31/5.04 ----------------------
% 17.31/5.04 #Subsume : 293
% 17.31/5.04 #Demod : 479
% 17.31/5.04 #Tautology : 1176
% 17.31/5.04 #SimpNegUnit : 117
% 17.31/5.04 #BackRed : 10
% 17.31/5.04
% 17.31/5.04 #Partial instantiations: 315
% 17.31/5.04 #Strategies tried : 1
% 17.31/5.04
% 17.31/5.04 Timing (in seconds)
% 17.31/5.04 ----------------------
% 17.31/5.04 Preprocessing : 1.77
% 17.31/5.04 Parsing : 0.79
% 17.31/5.04 CNF conversion : 0.14
% 17.31/5.04 Main loop : 2.23
% 17.31/5.04 Inferencing : 0.56
% 17.31/5.04 Reduction : 0.81
% 17.31/5.04 Demodulation : 0.56
% 17.31/5.04 BG Simplification : 0.37
% 17.31/5.04 Subsumption : 0.52
% 17.31/5.04 Abstraction : 0.07
% 17.31/5.04 MUC search : 0.00
% 17.31/5.04 Cooper : 0.07
% 17.31/5.04 Total : 4.05
% 17.31/5.04 Index Insertion : 0.00
% 17.31/5.04 Index Deletion : 0.00
% 17.31/5.04 Index Matching : 0.00
% 17.31/5.04 BG Taut test : 0.00
%------------------------------------------------------------------------------