% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/Hoare/prob_127__3250536_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:12:12.842

% Could-be-implicit typings (6)
thf(ty_n_t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J_J, type,
    set_Ho137910533iple_a : $tType).
thf(ty_n_t__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J, type,
    hoare_1678595023iple_a : $tType).
thf(ty_n_t__Com__Ostate, type,
    state : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).
thf(ty_n_t__Com__Ocom, type,
    com : $tType).
thf(ty_n_tf__a, type,
    a : $tType).

% Explicit typings (16)
thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_Itf__a_M_062_It__Com__Ostate_M_Eo_J_J_M_062_It__Com__Ocom_M_062_I_062_Itf__a_M_062_It__Com__Ostate_M_Eo_J_J_M_Eo_J_J_J_001_062_I_062_Itf__a_M_062_It__Com__Ostate_M_Eo_J_J_M_062_It__Com__Ocom_M_062_I_062_Itf__a_M_062_It__Com__Ostate_M_Eo_J_J_M_Eo_J_J_J_001_062_It__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J_M_Eo_J_001_062_It__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J_M_Eo_J, type,
    bNF_re937587754le_a_o : (((a > state > $o) > com > (a > state > $o) > $o) > ((a > state > $o) > com > (a > state > $o) > $o) > $o) > ((hoare_1678595023iple_a > $o) > (hoare_1678595023iple_a > $o) > $o) > (((a > state > $o) > com > (a > state > $o) > $o) > hoare_1678595023iple_a > $o) > (((a > state > $o) > com > (a > state > $o) > $o) > hoare_1678595023iple_a > $o) > $o).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_It__Com__Ostate_M_Eo_J_J_001_062_Itf__a_M_062_It__Com__Ostate_M_Eo_J_J_001_062_It__Com__Ocom_M_062_I_062_Itf__a_M_062_It__Com__Ostate_M_Eo_J_J_M_Eo_J_J_001_062_It__Com__Ocom_M_062_I_062_Itf__a_M_062_It__Com__Ostate_M_Eo_J_J_M_Eo_J_J, type,
    bNF_re1136346059te_o_o : ((a > state > $o) > (a > state > $o) > $o) > ((com > (a > state > $o) > $o) > (com > (a > state > $o) > $o) > $o) > ((a > state > $o) > com > (a > state > $o) > $o) > ((a > state > $o) > com > (a > state > $o) > $o) > $o).
thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__a_M_062_It__Com__Ostate_M_Eo_J_J_001_062_Itf__a_M_062_It__Com__Ostate_M_Eo_J_J_001_Eo_001_Eo, type,
    bNF_re1473845067_o_o_o : ((a > state > $o) > (a > state > $o) > $o) > ($o > $o > $o) > ((a > state > $o) > $o) > ((a > state > $o) > $o) > $o).
thf(sy_c_BNF__Def_Orel__fun_001t__Com__Ocom_001t__Com__Ocom_001_062_I_062_Itf__a_M_062_It__Com__Ostate_M_Eo_J_J_M_Eo_J_001_062_I_062_Itf__a_M_062_It__Com__Ostate_M_Eo_J_J_M_Eo_J, type,
    bNF_re1858049471te_o_o : (com > com > $o) > (((a > state > $o) > $o) > ((a > state > $o) > $o) > $o) > (com > (a > state > $o) > $o) > (com > (a > state > $o) > $o) > $o).
thf(sy_c_BNF__Def_Orel__fun_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J_001_Eo_001_Eo, type,
    bNF_re797868808_a_o_o : (hoare_1678595023iple_a > hoare_1678595023iple_a > $o) > ($o > $o > $o) > (hoare_1678595023iple_a > $o) > (hoare_1678595023iple_a > $o) > $o).
thf(sy_c_Hoare__Mirabelle__raqjowkjvm_Ohoare__valids_001tf__a, type,
    hoare_1775499016lids_a : set_Ho137910533iple_a > set_Ho137910533iple_a > $o).
thf(sy_c_Hoare__Mirabelle__raqjowkjvm_Ostate__not__singleton, type,
    hoare_405891322gleton : $o).
thf(sy_c_Hoare__Mirabelle__raqjowkjvm_Otriple_Ocase__triple_001tf__a_001_Eo, type,
    hoare_1012081509le_a_o : ((a > state > $o) > com > (a > state > $o) > $o) > hoare_1678595023iple_a > $o).
thf(sy_c_Hoare__Mirabelle__raqjowkjvm_Otriple_Otriple_001tf__a, type,
    hoare_719046530iple_a : (a > state > $o) > com > (a > state > $o) > hoare_1678595023iple_a).
thf(sy_c_Hoare__Mirabelle__raqjowkjvm_Otriple__valid_001tf__a, type,
    hoare_1926814542alid_a : nat > hoare_1678595023iple_a > $o).
thf(sy_c_Natural_Oevaln, type,
    evaln : com > state > nat > state > $o).
thf(sy_c_member_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J, type,
    member1332298086iple_a : hoare_1678595023iple_a > set_Ho137910533iple_a > $o).
thf(sy_v_P, type,
    p : a > state > $o).
thf(sy_v_Q, type,
    q : a > state > $o).
thf(sy_v_c, type,
    c : com).
thf(sy_v_n, type,
    n : nat).

% Relevant facts (11)
thf(fact_0_triple_Oinject, axiom,
    ((![X1 : a > state > $o, X2 : com, X3 : a > state > $o, Y1 : a > state > $o, Y2 : com, Y3 : a > state > $o]: (((hoare_719046530iple_a @ X1 @ X2 @ X3) = (hoare_719046530iple_a @ Y1 @ Y2 @ Y3)) = (((X1 = Y1)) & ((((X2 = Y2)) & ((X3 = Y3))))))))). % triple.inject
thf(fact_1_triple_Ocase, axiom,
    ((![F : (a > state > $o) > com > (a > state > $o) > $o, X1 : a > state > $o, X2 : com, X3 : a > state > $o]: ((hoare_1012081509le_a_o @ F @ (hoare_719046530iple_a @ X1 @ X2 @ X3)) = (F @ X1 @ X2 @ X3))))). % triple.case
thf(fact_2_triple_Oinduct, axiom,
    ((![P : hoare_1678595023iple_a > $o, Triple : hoare_1678595023iple_a]: ((![X1a : a > state > $o, X2a : com, X3a : a > state > $o]: (P @ (hoare_719046530iple_a @ X1a @ X2a @ X3a))) => (P @ Triple))))). % triple.induct
thf(fact_3_triple_Oexhaust, axiom,
    ((![Y : hoare_1678595023iple_a]: (~ ((![X12 : a > state > $o, X22 : com, X32 : a > state > $o]: (~ ((Y = (hoare_719046530iple_a @ X12 @ X22 @ X32)))))))))). % triple.exhaust
thf(fact_4_triple_Ocase__distrib, axiom,
    ((![H : $o > $o, F : (a > state > $o) > com > (a > state > $o) > $o, Triple : hoare_1678595023iple_a]: ((H @ (hoare_1012081509le_a_o @ F @ Triple)) = (hoare_1012081509le_a_o @ (^[X13 : a > state > $o]: (^[X23 : com]: (^[X33 : a > state > $o]: (H @ (F @ X13 @ X23 @ X33))))) @ Triple))))). % triple.case_distrib
thf(fact_5_triple__valid__def, axiom,
    ((hoare_1926814542alid_a = (^[N : nat]: (hoare_1012081509le_a_o @ (^[P2 : a > state > $o]: (^[C : com]: (^[Q : a > state > $o]: (![Z : a]: (![S : state]: (((P2 @ Z @ S)) => ((![S2 : state]: (((evaln @ C @ S @ N @ S2)) => ((Q @ Z @ S2)))))))))))))))). % triple_valid_def
thf(fact_6_evaln__max2, axiom,
    ((![C1 : com, S1 : state, N1 : nat, T1 : state, C2 : com, S22 : state, N2 : nat, T2 : state]: ((evaln @ C1 @ S1 @ N1 @ T1) => ((evaln @ C2 @ S22 @ N2 @ T2) => (?[N3 : nat]: ((evaln @ C1 @ S1 @ N3 @ T1) & (evaln @ C2 @ S22 @ N3 @ T2)))))))). % evaln_max2
thf(fact_7_single__stateE, axiom,
    ((hoare_405891322gleton => (![T : state]: (~ ((![S3 : state]: (S3 = T)))))))). % single_stateE
thf(fact_8_state__not__singleton__def, axiom,
    ((hoare_405891322gleton = (?[S : state]: (?[T3 : state]: (~ ((S = T3)))))))). % state_not_singleton_def
thf(fact_9_triple_Ocase__transfer, axiom,
    ((![S4 : $o > $o > $o]: (bNF_re937587754le_a_o @ (bNF_re1136346059te_o_o @ (^[Y4 : a > state > $o]: (^[Z2 : a > state > $o]: (Y4 = Z2))) @ (bNF_re1858049471te_o_o @ (^[Y4 : com]: (^[Z2 : com]: (Y4 = Z2))) @ (bNF_re1473845067_o_o_o @ (^[Y4 : a > state > $o]: (^[Z2 : a > state > $o]: (Y4 = Z2))) @ S4))) @ (bNF_re797868808_a_o_o @ (^[Y4 : hoare_1678595023iple_a]: (^[Z2 : hoare_1678595023iple_a]: (Y4 = Z2))) @ S4) @ hoare_1012081509le_a_o @ hoare_1012081509le_a_o)))). % triple.case_transfer
thf(fact_10_hoare__valids__def, axiom,
    ((hoare_1775499016lids_a = (^[G : set_Ho137910533iple_a]: (^[Ts : set_Ho137910533iple_a]: (![N : nat]: (((![X : hoare_1678595023iple_a]: (((member1332298086iple_a @ X @ G)) => ((hoare_1926814542alid_a @ N @ X))))) => ((![X : hoare_1678595023iple_a]: (((member1332298086iple_a @ X @ Ts)) => ((hoare_1926814542alid_a @ N @ X)))))))))))). % hoare_valids_def

% Conjectures (1)
thf(conj_0, conjecture,
    (((hoare_1012081509le_a_o @ (^[P2 : a > state > $o]: (^[C : com]: (^[Q : a > state > $o]: (![Z : a]: (![S : state]: (((P2 @ Z @ S)) => ((![S2 : state]: (((evaln @ C @ S @ n @ S2)) => ((Q @ Z @ S2))))))))))) @ (hoare_719046530iple_a @ p @ c @ q)) = (![Z : a]: (![S : state]: (((p @ Z @ S)) => ((![S2 : state]: (((evaln @ c @ S @ n @ S2)) => ((q @ Z @ S2))))))))))).
