% 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_322__3253118_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:13:46.775

% Could-be-implicit typings (8)
thf(ty_n_t__Option__Ooption_It__Com__Ocom_J, type,
    option_com : $tType).
thf(ty_n_t__Com__Ovname, type,
    vname : $tType).
thf(ty_n_t__Com__Ostate, type,
    state : $tType).
thf(ty_n_t__Com__Opname, type,
    pname : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).
thf(ty_n_t__Com__Oloc, type,
    loc : $tType).
thf(ty_n_t__Com__Oglb, type,
    glb : $tType).
thf(ty_n_t__Com__Ocom, type,
    com : $tType).

% Explicit typings (35)
thf(sy_c_Com_OArg, type,
    arg : loc).
thf(sy_c_Com_ORes, type,
    res : loc).
thf(sy_c_Com_OWT, type,
    wt : com > $o).
thf(sy_c_Com_OWT__bodies, type,
    wT_bodies : $o).
thf(sy_c_Com_Obody, type,
    body : pname > option_com).
thf(sy_c_Com_Ocom_OAss, type,
    ass : vname > (state > nat) > com).
thf(sy_c_Com_Ocom_OBODY, type,
    body2 : pname > com).
thf(sy_c_Com_Ocom_OCall, type,
    call : vname > pname > (state > nat) > com).
thf(sy_c_Com_Ocom_OCond, type,
    cond : (state > $o) > com > com > com).
thf(sy_c_Com_Ocom_OLocal, type,
    local : loc > (state > nat) > com > com).
thf(sy_c_Com_Ocom_OSKIP, type,
    skip : com).
thf(sy_c_Com_Ocom_OSemi, type,
    semi : com > com > com).
thf(sy_c_Com_Ocom_OWhile, type,
    while : (state > $o) > com > com).
thf(sy_c_Com_Ocom_Osize__com, type,
    size_com : com > nat).
thf(sy_c_Com_Ovname_OGlb, type,
    glb2 : glb > vname).
thf(sy_c_Com_Ovname_OLoc, type,
    loc2 : loc > vname).
thf(sy_c_Com_Ovname_Osize__vname, type,
    size_vname : vname > nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat, type,
    plus_plus_nat : nat > nat > nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat, type,
    zero_zero_nat : nat).
thf(sy_c_Hoare__Mirabelle__raqjowkjvm_Ostate__not__singleton, type,
    hoare_405891322gleton : $o).
thf(sy_c_Nat_OSuc, type,
    suc : nat > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__Com__Ocom, type,
    size_size_com : com > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__Com__Ovname, type,
    size_size_vname : vname > nat).
thf(sy_c_Natural_Oevalc, type,
    evalc : com > state > state > $o).
thf(sy_c_Natural_Oevaln, type,
    evaln : com > state > nat > state > $o).
thf(sy_c_Natural_Ogetlocs, type,
    getlocs : state > loc > nat).
thf(sy_c_Natural_Onewlocs, type,
    newlocs : loc > nat).
thf(sy_c_Natural_Osetlocs, type,
    setlocs : state > (loc > nat) > state).
thf(sy_c_Natural_Oupdate, type,
    update : state > vname > nat > state).
thf(sy_c_Option_Ooption_ONone_001t__Com__Ocom, type,
    none_com : option_com).
thf(sy_c_Option_Ooption_OSome_001t__Com__Ocom, type,
    some_com : com > option_com).
thf(sy_c_Option_Ooption_Othe_001t__Com__Ocom, type,
    the_com : option_com > com).
thf(sy_v_Z, type,
    z : state).
thf(sy_v_c, type,
    c : com).
thf(sy_v_s_H, type,
    s : state).

% Relevant facts (118)
thf(fact_0_com__det, axiom,
    ((![C : com, S : state, T : state, U : state]: ((evalc @ C @ S @ T) => ((evalc @ C @ S @ U) => (U = T)))))). % com_det
thf(fact_1_single__stateE, axiom,
    ((hoare_405891322gleton => (![T2 : state]: (~ ((![S2 : state]: (S2 = T2)))))))). % single_stateE
thf(fact_2_state__not__singleton__def, axiom,
    ((hoare_405891322gleton = (?[S3 : state]: (?[T3 : state]: (~ ((S3 = T3)))))))). % state_not_singleton_def
thf(fact_3_evalc__elim__cases_I1_J, axiom,
    ((![S : state, T : state]: ((evalc @ skip @ S @ T) => (T = S))))). % evalc_elim_cases(1)
thf(fact_4_evalc_OSkip, axiom,
    ((![S : state]: (evalc @ skip @ S @ S)))). % evalc.Skip
thf(fact_5_evalc__elim__cases_I4_J, axiom,
    ((![C1 : com, C2 : com, S : state, T : state]: ((evalc @ (semi @ C1 @ C2) @ S @ T) => (~ ((![S1 : state]: ((evalc @ C1 @ S @ S1) => (~ ((evalc @ C2 @ S1 @ T))))))))))). % evalc_elim_cases(4)
thf(fact_6_evalc_OSemi, axiom,
    ((![C0 : com, S0 : state, S12 : state, C1 : com, S22 : state]: ((evalc @ C0 @ S0 @ S12) => ((evalc @ C1 @ S12 @ S22) => (evalc @ (semi @ C0 @ C1) @ S0 @ S22)))))). % evalc.Semi
thf(fact_7_evalc__elim__cases_I5_J, axiom,
    ((![B : state > $o, C1 : com, C2 : com, S : state, T : state]: ((evalc @ (cond @ B @ C1 @ C2) @ S @ T) => (((B @ S) => (~ ((evalc @ C1 @ S @ T)))) => (~ (((~ ((B @ S))) => (~ ((evalc @ C2 @ S @ T))))))))))). % evalc_elim_cases(5)
thf(fact_8_evalc_OIfTrue, axiom,
    ((![B : state > $o, S : state, C0 : com, S12 : state, C1 : com]: ((B @ S) => ((evalc @ C0 @ S @ S12) => (evalc @ (cond @ B @ C0 @ C1) @ S @ S12)))))). % evalc.IfTrue
thf(fact_9_evalc_OIfFalse, axiom,
    ((![B : state > $o, S : state, C1 : com, S12 : state, C0 : com]: ((~ ((B @ S))) => ((evalc @ C1 @ S @ S12) => (evalc @ (cond @ B @ C0 @ C1) @ S @ S12)))))). % evalc.IfFalse
thf(fact_10_evalc_OWhileTrue, axiom,
    ((![B : state > $o, S0 : state, C : com, S12 : state, S22 : state]: ((B @ S0) => ((evalc @ C @ S0 @ S12) => ((evalc @ (while @ B @ C) @ S12 @ S22) => (evalc @ (while @ B @ C) @ S0 @ S22))))))). % evalc.WhileTrue
thf(fact_11_evalc_OWhileFalse, axiom,
    ((![B : state > $o, S : state, C : com]: ((~ ((B @ S))) => (evalc @ (while @ B @ C) @ S @ S))))). % evalc.WhileFalse
thf(fact_12_evalc__WHILE__case, axiom,
    ((![B : state > $o, C : com, S : state, T : state]: ((evalc @ (while @ B @ C) @ S @ T) => (((T = S) => (B @ S)) => (~ (((B @ S) => (![S1 : state]: ((evalc @ C @ S @ S1) => (~ ((evalc @ (while @ B @ C) @ S1 @ T))))))))))))). % evalc_WHILE_case
thf(fact_13_com_Oinject_I3_J, axiom,
    ((![X41 : com, X42 : com, Y41 : com, Y42 : com]: (((semi @ X41 @ X42) = (semi @ Y41 @ Y42)) = (((X41 = Y41)) & ((X42 = Y42))))))). % com.inject(3)
thf(fact_14_com_Oinject_I4_J, axiom,
    ((![X51 : state > $o, X52 : com, X53 : com, Y51 : state > $o, Y52 : com, Y53 : com]: (((cond @ X51 @ X52 @ X53) = (cond @ Y51 @ Y52 @ Y53)) = (((X51 = Y51)) & ((((X52 = Y52)) & ((X53 = Y53))))))))). % com.inject(4)
thf(fact_15_com_Oinject_I5_J, axiom,
    ((![X61 : state > $o, X62 : com, Y61 : state > $o, Y62 : com]: (((while @ X61 @ X62) = (while @ Y61 @ Y62)) = (((X61 = Y61)) & ((X62 = Y62))))))). % com.inject(5)
thf(fact_16_com_Odistinct_I5_J, axiom,
    ((![X41 : com, X42 : com]: (~ ((skip = (semi @ X41 @ X42))))))). % com.distinct(5)
thf(fact_17_com_Odistinct_I7_J, axiom,
    ((![X51 : state > $o, X52 : com, X53 : com]: (~ ((skip = (cond @ X51 @ X52 @ X53))))))). % com.distinct(7)
thf(fact_18_com_Odistinct_I37_J, axiom,
    ((![X41 : com, X42 : com, X51 : state > $o, X52 : com, X53 : com]: (~ (((semi @ X41 @ X42) = (cond @ X51 @ X52 @ X53))))))). % com.distinct(37)
thf(fact_19_com_Odistinct_I9_J, axiom,
    ((![X61 : state > $o, X62 : com]: (~ ((skip = (while @ X61 @ X62))))))). % com.distinct(9)
thf(fact_20_com_Odistinct_I39_J, axiom,
    ((![X41 : com, X42 : com, X61 : state > $o, X62 : com]: (~ (((semi @ X41 @ X42) = (while @ X61 @ X62))))))). % com.distinct(39)
thf(fact_21_com_Odistinct_I45_J, axiom,
    ((![X51 : state > $o, X52 : com, X53 : com, X61 : state > $o, X62 : com]: (~ (((cond @ X51 @ X52 @ X53) = (while @ X61 @ X62))))))). % com.distinct(45)
thf(fact_22_evaln__elim__cases_I1_J, axiom,
    ((![S : state, N : nat, T : state]: ((evaln @ skip @ S @ N @ T) => (T = S))))). % evaln_elim_cases(1)
thf(fact_23_evaln__max2, axiom,
    ((![C1 : com, S12 : state, N1 : nat, T1 : state, C2 : com, S22 : state, N2 : nat, T22 : state]: ((evaln @ C1 @ S12 @ N1 @ T1) => ((evaln @ C2 @ S22 @ N2 @ T22) => (?[N3 : nat]: ((evaln @ C1 @ S12 @ N3 @ T1) & (evaln @ C2 @ S22 @ N3 @ T22)))))))). % evaln_max2
thf(fact_24_eval__eq, axiom,
    ((evalc = (^[C3 : com]: (^[S3 : state]: (^[T3 : state]: (?[N4 : nat]: (evaln @ C3 @ S3 @ N4 @ T3)))))))). % eval_eq
thf(fact_25_evalc__evaln, axiom,
    ((![C : com, S : state, T : state]: ((evalc @ C @ S @ T) => (?[N3 : nat]: (evaln @ C @ S @ N3 @ T)))))). % evalc_evaln
thf(fact_26_evaln__evalc, axiom,
    ((![C : com, S : state, N : nat, T : state]: ((evaln @ C @ S @ N @ T) => (evalc @ C @ S @ T))))). % evaln_evalc
thf(fact_27_evaln__WHILE__case, axiom,
    ((![B : state > $o, C : com, S : state, N : nat, T : state]: ((evaln @ (while @ B @ C) @ S @ N @ T) => (((T = S) => (B @ S)) => (~ (((B @ S) => (![S1 : state]: ((evaln @ C @ S @ N @ S1) => (~ ((evaln @ (while @ B @ C) @ S1 @ N @ T))))))))))))). % evaln_WHILE_case
thf(fact_28_evaln_OWhileFalse, axiom,
    ((![B : state > $o, S : state, C : com, N : nat]: ((~ ((B @ S))) => (evaln @ (while @ B @ C) @ S @ N @ S))))). % evaln.WhileFalse
thf(fact_29_evaln_OWhileTrue, axiom,
    ((![B : state > $o, S0 : state, C : com, N : nat, S12 : state, S22 : state]: ((B @ S0) => ((evaln @ C @ S0 @ N @ S12) => ((evaln @ (while @ B @ C) @ S12 @ N @ S22) => (evaln @ (while @ B @ C) @ S0 @ N @ S22))))))). % evaln.WhileTrue
thf(fact_30_evaln_OIfFalse, axiom,
    ((![B : state > $o, S : state, C1 : com, N : nat, S12 : state, C0 : com]: ((~ ((B @ S))) => ((evaln @ C1 @ S @ N @ S12) => (evaln @ (cond @ B @ C0 @ C1) @ S @ N @ S12)))))). % evaln.IfFalse
thf(fact_31_evaln_OIfTrue, axiom,
    ((![B : state > $o, S : state, C0 : com, N : nat, S12 : state, C1 : com]: ((B @ S) => ((evaln @ C0 @ S @ N @ S12) => (evaln @ (cond @ B @ C0 @ C1) @ S @ N @ S12)))))). % evaln.IfTrue
thf(fact_32_evaln__elim__cases_I5_J, axiom,
    ((![B : state > $o, C1 : com, C2 : com, S : state, N : nat, T : state]: ((evaln @ (cond @ B @ C1 @ C2) @ S @ N @ T) => (((B @ S) => (~ ((evaln @ C1 @ S @ N @ T)))) => (~ (((~ ((B @ S))) => (~ ((evaln @ C2 @ S @ N @ T))))))))))). % evaln_elim_cases(5)
thf(fact_33_evaln_OSemi, axiom,
    ((![C0 : com, S0 : state, N : nat, S12 : state, C1 : com, S22 : state]: ((evaln @ C0 @ S0 @ N @ S12) => ((evaln @ C1 @ S12 @ N @ S22) => (evaln @ (semi @ C0 @ C1) @ S0 @ N @ S22)))))). % evaln.Semi
thf(fact_34_evaln__elim__cases_I4_J, axiom,
    ((![C1 : com, C2 : com, S : state, N : nat, T : state]: ((evaln @ (semi @ C1 @ C2) @ S @ N @ T) => (~ ((![S1 : state]: ((evaln @ C1 @ S @ N @ S1) => (~ ((evaln @ C2 @ S1 @ N @ T))))))))))). % evaln_elim_cases(4)
thf(fact_35_evaln_OSkip, axiom,
    ((![S : state, N : nat]: (evaln @ skip @ S @ N @ S)))). % evaln.Skip
thf(fact_36_com_Oinject_I7_J, axiom,
    ((![X81 : vname, X82 : pname, X83 : state > nat, Y81 : vname, Y82 : pname, Y83 : state > nat]: (((call @ X81 @ X82 @ X83) = (call @ Y81 @ Y82 @ Y83)) = (((X81 = Y81)) & ((((X82 = Y82)) & ((X83 = Y83))))))))). % com.inject(7)
thf(fact_37_com_Oinject_I2_J, axiom,
    ((![X31 : loc, X32 : state > nat, X33 : com, Y31 : loc, Y32 : state > nat, Y33 : com]: (((local @ X31 @ X32 @ X33) = (local @ Y31 @ Y32 @ Y33)) = (((X31 = Y31)) & ((((X32 = Y32)) & ((X33 = Y33))))))))). % com.inject(2)
thf(fact_38_com_Oinject_I1_J, axiom,
    ((![X21 : vname, X22 : state > nat, Y21 : vname, Y22 : state > nat]: (((ass @ X21 @ X22) = (ass @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % com.inject(1)
thf(fact_39_com_Odistinct_I35_J, axiom,
    ((![X31 : loc, X32 : state > nat, X33 : com, X81 : vname, X82 : pname, X83 : state > nat]: (~ (((local @ X31 @ X32 @ X33) = (call @ X81 @ X82 @ X83))))))). % com.distinct(35)
thf(fact_40_com_Odistinct_I25_J, axiom,
    ((![X21 : vname, X22 : state > nat, X81 : vname, X82 : pname, X83 : state > nat]: (~ (((ass @ X21 @ X22) = (call @ X81 @ X82 @ X83))))))). % com.distinct(25)
thf(fact_41_com_Odistinct_I15_J, axiom,
    ((![X21 : vname, X22 : state > nat, X31 : loc, X32 : state > nat, X33 : com]: (~ (((ass @ X21 @ X22) = (local @ X31 @ X32 @ X33))))))). % com.distinct(15)
thf(fact_42_com_Odistinct_I21_J, axiom,
    ((![X21 : vname, X22 : state > nat, X61 : state > $o, X62 : com]: (~ (((ass @ X21 @ X22) = (while @ X61 @ X62))))))). % com.distinct(21)
thf(fact_43_com_Odistinct_I31_J, axiom,
    ((![X31 : loc, X32 : state > nat, X33 : com, X61 : state > $o, X62 : com]: (~ (((local @ X31 @ X32 @ X33) = (while @ X61 @ X62))))))). % com.distinct(31)
thf(fact_44_com_Odistinct_I53_J, axiom,
    ((![X61 : state > $o, X62 : com, X81 : vname, X82 : pname, X83 : state > nat]: (~ (((while @ X61 @ X62) = (call @ X81 @ X82 @ X83))))))). % com.distinct(53)
thf(fact_45_com_Odistinct_I19_J, axiom,
    ((![X21 : vname, X22 : state > nat, X51 : state > $o, X52 : com, X53 : com]: (~ (((ass @ X21 @ X22) = (cond @ X51 @ X52 @ X53))))))). % com.distinct(19)
thf(fact_46_com_Odistinct_I29_J, axiom,
    ((![X31 : loc, X32 : state > nat, X33 : com, X51 : state > $o, X52 : com, X53 : com]: (~ (((local @ X31 @ X32 @ X33) = (cond @ X51 @ X52 @ X53))))))). % com.distinct(29)
thf(fact_47_com_Odistinct_I49_J, axiom,
    ((![X51 : state > $o, X52 : com, X53 : com, X81 : vname, X82 : pname, X83 : state > nat]: (~ (((cond @ X51 @ X52 @ X53) = (call @ X81 @ X82 @ X83))))))). % com.distinct(49)
thf(fact_48_com_Odistinct_I17_J, axiom,
    ((![X21 : vname, X22 : state > nat, X41 : com, X42 : com]: (~ (((ass @ X21 @ X22) = (semi @ X41 @ X42))))))). % com.distinct(17)
thf(fact_49_com_Odistinct_I27_J, axiom,
    ((![X31 : loc, X32 : state > nat, X33 : com, X41 : com, X42 : com]: (~ (((local @ X31 @ X32 @ X33) = (semi @ X41 @ X42))))))). % com.distinct(27)
thf(fact_50_com_Odistinct_I43_J, axiom,
    ((![X41 : com, X42 : com, X81 : vname, X82 : pname, X83 : state > nat]: (~ (((semi @ X41 @ X42) = (call @ X81 @ X82 @ X83))))))). % com.distinct(43)
thf(fact_51_com_Odistinct_I1_J, axiom,
    ((![X21 : vname, X22 : state > nat]: (~ ((skip = (ass @ X21 @ X22))))))). % com.distinct(1)
thf(fact_52_com_Odistinct_I3_J, axiom,
    ((![X31 : loc, X32 : state > nat, X33 : com]: (~ ((skip = (local @ X31 @ X32 @ X33))))))). % com.distinct(3)
thf(fact_53_com_Odistinct_I13_J, axiom,
    ((![X81 : vname, X82 : pname, X83 : state > nat]: (~ ((skip = (call @ X81 @ X82 @ X83))))))). % com.distinct(13)
thf(fact_54_com_Oexhaust, axiom,
    ((![Y : com]: ((~ ((Y = skip))) => ((![X212 : vname, X222 : state > nat]: (~ ((Y = (ass @ X212 @ X222))))) => ((![X312 : loc, X322 : state > nat, X332 : com]: (~ ((Y = (local @ X312 @ X322 @ X332))))) => ((![X412 : com, X422 : com]: (~ ((Y = (semi @ X412 @ X422))))) => ((![X512 : state > $o, X522 : com, X532 : com]: (~ ((Y = (cond @ X512 @ X522 @ X532))))) => ((![X612 : state > $o, X622 : com]: (~ ((Y = (while @ X612 @ X622))))) => ((![X7 : pname]: (~ ((Y = (body2 @ X7))))) => (~ ((![X812 : vname, X822 : pname, X832 : state > nat]: (~ ((Y = (call @ X812 @ X822 @ X832))))))))))))))))). % com.exhaust
thf(fact_55_com_Oinduct, axiom,
    ((![P : com > $o, Com : com]: ((P @ skip) => ((![X1 : vname, X2 : state > nat]: (P @ (ass @ X1 @ X2))) => ((![X1 : loc, X2 : state > nat, X3 : com]: ((P @ X3) => (P @ (local @ X1 @ X2 @ X3)))) => ((![X1 : com, X2 : com]: ((P @ X1) => ((P @ X2) => (P @ (semi @ X1 @ X2))))) => ((![X1 : state > $o, X2 : com, X3 : com]: ((P @ X2) => ((P @ X3) => (P @ (cond @ X1 @ X2 @ X3))))) => ((![X1 : state > $o, X2 : com]: ((P @ X2) => (P @ (while @ X1 @ X2)))) => ((![X : pname]: (P @ (body2 @ X))) => ((![X1 : vname, X2 : pname, X3 : state > nat]: (P @ (call @ X1 @ X2 @ X3))) => (P @ Com)))))))))))). % com.induct
thf(fact_56_evalc_OAssign, axiom,
    ((![X4 : vname, A : state > nat, S : state]: (evalc @ (ass @ X4 @ A) @ S @ (update @ S @ X4 @ (A @ S)))))). % evalc.Assign
thf(fact_57_evalc__elim__cases_I2_J, axiom,
    ((![X4 : vname, A : state > nat, S : state, T : state]: ((evalc @ (ass @ X4 @ A) @ S @ T) => (T = (update @ S @ X4 @ (A @ S))))))). % evalc_elim_cases(2)
thf(fact_58_evaln_OAssign, axiom,
    ((![X4 : vname, A : state > nat, S : state, N : nat]: (evaln @ (ass @ X4 @ A) @ S @ N @ (update @ S @ X4 @ (A @ S)))))). % evaln.Assign
thf(fact_59_evaln__elim__cases_I2_J, axiom,
    ((![X4 : vname, A : state > nat, S : state, N : nat, T : state]: ((evaln @ (ass @ X4 @ A) @ S @ N @ T) => (T = (update @ S @ X4 @ (A @ S))))))). % evaln_elim_cases(2)
thf(fact_60_com_Oinject_I6_J, axiom,
    ((![X72 : pname, Y7 : pname]: (((body2 @ X72) = (body2 @ Y7)) = (X72 = Y7))))). % com.inject(6)
thf(fact_61_com_Odistinct_I51_J, axiom,
    ((![X61 : state > $o, X62 : com, X72 : pname]: (~ (((while @ X61 @ X62) = (body2 @ X72))))))). % com.distinct(51)
thf(fact_62_com_Odistinct_I47_J, axiom,
    ((![X51 : state > $o, X52 : com, X53 : com, X72 : pname]: (~ (((cond @ X51 @ X52 @ X53) = (body2 @ X72))))))). % com.distinct(47)
thf(fact_63_com_Odistinct_I41_J, axiom,
    ((![X41 : com, X42 : com, X72 : pname]: (~ (((semi @ X41 @ X42) = (body2 @ X72))))))). % com.distinct(41)
thf(fact_64_com_Odistinct_I23_J, axiom,
    ((![X21 : vname, X22 : state > nat, X72 : pname]: (~ (((ass @ X21 @ X22) = (body2 @ X72))))))). % com.distinct(23)
thf(fact_65_com_Odistinct_I33_J, axiom,
    ((![X31 : loc, X32 : state > nat, X33 : com, X72 : pname]: (~ (((local @ X31 @ X32 @ X33) = (body2 @ X72))))))). % com.distinct(33)
thf(fact_66_com_Odistinct_I55_J, axiom,
    ((![X72 : pname, X81 : vname, X82 : pname, X83 : state > nat]: (~ (((body2 @ X72) = (call @ X81 @ X82 @ X83))))))). % com.distinct(55)
thf(fact_67_com_Odistinct_I11_J, axiom,
    ((![X72 : pname]: (~ ((skip = (body2 @ X72))))))). % com.distinct(11)
thf(fact_68_WT_Oinducts, axiom,
    ((![X5 : com, P : com > $o]: ((wt @ X5) => ((P @ skip) => ((![X6 : vname, A2 : state > nat]: (P @ (ass @ X6 @ A2))) => ((![C4 : com, Y2 : loc, A2 : state > nat]: ((wt @ C4) => ((P @ C4) => (P @ (local @ Y2 @ A2 @ C4))))) => ((![C02 : com, C12 : com]: ((wt @ C02) => ((P @ C02) => ((wt @ C12) => ((P @ C12) => (P @ (semi @ C02 @ C12))))))) => ((![C02 : com, C12 : com, B2 : state > $o]: ((wt @ C02) => ((P @ C02) => ((wt @ C12) => ((P @ C12) => (P @ (cond @ B2 @ C02 @ C12))))))) => ((![C4 : com, B2 : state > $o]: ((wt @ C4) => ((P @ C4) => (P @ (while @ B2 @ C4))))) => ((![Pn : pname]: ((~ (((body @ Pn) = none_com))) => (P @ (body2 @ Pn)))) => ((![Pn : pname, X6 : vname, A2 : state > nat]: ((wt @ (body2 @ Pn)) => ((P @ (body2 @ Pn)) => (P @ (call @ X6 @ Pn @ A2))))) => (P @ X5))))))))))))). % WT.inducts
thf(fact_69_WT_Osimps, axiom,
    ((wt = (^[A3 : com]: (((A3 = skip)) | ((((?[X8 : vname]: (?[B3 : state > nat]: (A3 = (ass @ X8 @ B3))))) | ((((?[C3 : com]: (?[Y3 : loc]: (?[B3 : state > nat]: (((A3 = (local @ Y3 @ B3 @ C3))) & ((wt @ C3))))))) | ((((?[C03 : com]: (?[C13 : com]: (((A3 = (semi @ C03 @ C13))) & ((((wt @ C03)) & ((wt @ C13)))))))) | ((((?[C03 : com]: (?[C13 : com]: (?[B3 : state > $o]: (((A3 = (cond @ B3 @ C03 @ C13))) & ((((wt @ C03)) & ((wt @ C13))))))))) | ((((?[C3 : com]: (?[B3 : state > $o]: (((A3 = (while @ B3 @ C3))) & ((wt @ C3)))))) | ((((?[Pn2 : pname]: (((A3 = (body2 @ Pn2))) & ((~ (((body @ Pn2) = none_com))))))) | ((?[Pn2 : pname]: (?[X8 : vname]: (?[B3 : state > nat]: (((A3 = (call @ X8 @ Pn2 @ B3))) & ((wt @ (body2 @ Pn2))))))))))))))))))))))))). % WT.simps
thf(fact_70_WT_Ocases, axiom,
    ((![A : com]: ((wt @ A) => ((~ ((A = skip))) => ((![X6 : vname, A2 : state > nat]: (~ ((A = (ass @ X6 @ A2))))) => ((![C4 : com]: ((?[Y2 : loc, A2 : state > nat]: (A = (local @ Y2 @ A2 @ C4))) => (~ ((wt @ C4))))) => ((![C02 : com, C12 : com]: ((A = (semi @ C02 @ C12)) => ((wt @ C02) => (~ ((wt @ C12)))))) => ((![C02 : com, C12 : com]: ((?[B2 : state > $o]: (A = (cond @ B2 @ C02 @ C12))) => ((wt @ C02) => (~ ((wt @ C12)))))) => ((![C4 : com]: ((?[B2 : state > $o]: (A = (while @ B2 @ C4))) => (~ ((wt @ C4))))) => ((![Pn : pname]: ((A = (body2 @ Pn)) => ((body @ Pn) = none_com))) => (~ ((![Pn : pname]: ((?[X6 : vname, A2 : state > nat]: (A = (call @ X6 @ Pn @ A2))) => (~ ((wt @ (body2 @ Pn))))))))))))))))))). % WT.cases
thf(fact_71_WTs__elim__cases_I8_J, axiom,
    ((![X4 : vname, P : pname, A : state > nat]: ((wt @ (call @ X4 @ P @ A)) => (wt @ (body2 @ P)))))). % WTs_elim_cases(8)
thf(fact_72_WT_OBody, axiom,
    ((![Pn3 : pname]: ((~ (((body @ Pn3) = none_com))) => (wt @ (body2 @ Pn3)))))). % WT.Body
thf(fact_73_WTs__elim__cases_I6_J, axiom,
    ((![B : state > $o, C : com]: ((wt @ (while @ B @ C)) => (wt @ C))))). % WTs_elim_cases(6)
thf(fact_74_While, axiom,
    ((![C : com, B : state > $o]: ((wt @ C) => (wt @ (while @ B @ C)))))). % While
thf(fact_75_WTs__elim__cases_I5_J, axiom,
    ((![B : state > $o, C1 : com, C2 : com]: ((wt @ (cond @ B @ C1 @ C2)) => (~ (((wt @ C1) => (~ ((wt @ C2)))))))))). % WTs_elim_cases(5)
thf(fact_76_WT_OIf, axiom,
    ((![C0 : com, C1 : com, B : state > $o]: ((wt @ C0) => ((wt @ C1) => (wt @ (cond @ B @ C0 @ C1))))))). % WT.If
thf(fact_77_WTs__elim__cases_I4_J, axiom,
    ((![C1 : com, C2 : com]: ((wt @ (semi @ C1 @ C2)) => (~ (((wt @ C1) => (~ ((wt @ C2)))))))))). % WTs_elim_cases(4)
thf(fact_78_WT_OSemi, axiom,
    ((![C0 : com, C1 : com]: ((wt @ C0) => ((wt @ C1) => (wt @ (semi @ C0 @ C1))))))). % WT.Semi
thf(fact_79_WT_OAssign, axiom,
    ((![X4 : vname, A : state > nat]: (wt @ (ass @ X4 @ A))))). % WT.Assign
thf(fact_80_WT_OLocal, axiom,
    ((![C : com, Y4 : loc, A : state > nat]: ((wt @ C) => (wt @ (local @ Y4 @ A @ C)))))). % WT.Local
thf(fact_81_WTs__elim__cases_I3_J, axiom,
    ((![Y4 : loc, A : state > nat, C : com]: ((wt @ (local @ Y4 @ A @ C)) => (wt @ C))))). % WTs_elim_cases(3)
thf(fact_82_WT_OSkip, axiom,
    ((wt @ skip))). % WT.Skip
thf(fact_83_WT_OCall, axiom,
    ((![Pn3 : pname, X4 : vname, A : state > nat]: ((wt @ (body2 @ Pn3)) => (wt @ (call @ X4 @ Pn3 @ A)))))). % WT.Call
thf(fact_84_evalc_OBody, axiom,
    ((![Pn3 : pname, S0 : state, S12 : state]: ((evalc @ (the_com @ (body @ Pn3)) @ S0 @ S12) => (evalc @ (body2 @ Pn3) @ S0 @ S12))))). % evalc.Body
thf(fact_85_evalc__elim__cases_I6_J, axiom,
    ((![P : pname, S : state, S12 : state]: ((evalc @ (body2 @ P) @ S @ S12) => (evalc @ (the_com @ (body @ P)) @ S @ S12))))). % evalc_elim_cases(6)
thf(fact_86_WTs__elim__cases_I7_J, axiom,
    ((![P : pname]: ((wt @ (body2 @ P)) => (~ ((![Y5 : com]: (~ (((body @ P) = (some_com @ Y5))))))))))). % WTs_elim_cases(7)
thf(fact_87_WT__bodiesD, axiom,
    ((![Pn3 : pname, B : com]: (wT_bodies => (((body @ Pn3) = (some_com @ B)) => (wt @ B)))))). % WT_bodiesD
thf(fact_88_evaln_OBody, axiom,
    ((![Pn3 : pname, S0 : state, N : nat, S12 : state]: ((evaln @ (the_com @ (body @ Pn3)) @ S0 @ N @ S12) => (evaln @ (body2 @ Pn3) @ S0 @ (suc @ N) @ S12))))). % evaln.Body
thf(fact_89_evaln__elim__cases_I6_J, axiom,
    ((![P : pname, S : state, N : nat, S12 : state]: ((evaln @ (body2 @ P) @ S @ N @ S12) => (~ ((![N3 : nat]: ((N = (suc @ N3)) => (~ ((evaln @ (the_com @ (body @ P)) @ S @ N3 @ S12))))))))))). % evaln_elim_cases(6)
thf(fact_90_evaln__Suc, axiom,
    ((![C : com, S : state, N : nat, S4 : state]: ((evaln @ C @ S @ N @ S4) => (evaln @ C @ S @ (suc @ N) @ S4))))). % evaln_Suc
thf(fact_91_evalc__elim__cases_I3_J, axiom,
    ((![Y4 : loc, A : state > nat, C : com, S : state, T : state]: ((evalc @ (local @ Y4 @ A @ C) @ S @ T) => (~ ((![S1 : state]: ((T = (update @ S1 @ (loc2 @ Y4) @ (getlocs @ S @ Y4))) => (~ ((evalc @ C @ (update @ S @ (loc2 @ Y4) @ (A @ S)) @ S1))))))))))). % evalc_elim_cases(3)
thf(fact_92_vname_Oinject_I2_J, axiom,
    ((![X23 : loc, Y23 : loc]: (((loc2 @ X23) = (loc2 @ Y23)) = (X23 = Y23))))). % vname.inject(2)
thf(fact_93_evaln__elim__cases_I3_J, axiom,
    ((![Y4 : loc, A : state > nat, C : com, S : state, N : nat, T : state]: ((evaln @ (local @ Y4 @ A @ C) @ S @ N @ T) => (~ ((![S1 : state]: ((T = (update @ S1 @ (loc2 @ Y4) @ (getlocs @ S @ Y4))) => (~ ((evaln @ C @ (update @ S @ (loc2 @ Y4) @ (A @ S)) @ N @ S1))))))))))). % evaln_elim_cases(3)
thf(fact_94_evaln_OLocal, axiom,
    ((![C : com, S0 : state, Y4 : loc, A : state > nat, N : nat, S12 : state]: ((evaln @ C @ (update @ S0 @ (loc2 @ Y4) @ (A @ S0)) @ N @ S12) => (evaln @ (local @ Y4 @ A @ C) @ S0 @ N @ (update @ S12 @ (loc2 @ Y4) @ (getlocs @ S0 @ Y4))))))). % evaln.Local
thf(fact_95_evalc_OLocal, axiom,
    ((![C : com, S0 : state, Y4 : loc, A : state > nat, S12 : state]: ((evalc @ C @ (update @ S0 @ (loc2 @ Y4) @ (A @ S0)) @ S12) => (evalc @ (local @ Y4 @ A @ C) @ S0 @ (update @ S12 @ (loc2 @ Y4) @ (getlocs @ S0 @ Y4))))))). % evalc.Local
thf(fact_96_evalc_OCall, axiom,
    ((![Pn3 : pname, S0 : state, A : state > nat, S12 : state, X4 : vname]: ((evalc @ (body2 @ Pn3) @ (update @ (setlocs @ S0 @ newlocs) @ (loc2 @ arg) @ (A @ S0)) @ S12) => (evalc @ (call @ X4 @ Pn3 @ A) @ S0 @ (update @ (setlocs @ S12 @ (getlocs @ S0)) @ X4 @ (getlocs @ S12 @ res))))))). % evalc.Call
thf(fact_97_evaln_OCall, axiom,
    ((![Pn3 : pname, S0 : state, A : state > nat, N : nat, S12 : state, X4 : vname]: ((evaln @ (body2 @ Pn3) @ (update @ (setlocs @ S0 @ newlocs) @ (loc2 @ arg) @ (A @ S0)) @ N @ S12) => (evaln @ (call @ X4 @ Pn3 @ A) @ S0 @ N @ (update @ (setlocs @ S12 @ (getlocs @ S0)) @ X4 @ (getlocs @ S12 @ res))))))). % evaln.Call
thf(fact_98_evaln__elim__cases_I7_J, axiom,
    ((![X4 : vname, P : pname, A : state > nat, S : state, N : nat, S12 : state]: ((evaln @ (call @ X4 @ P @ A) @ S @ N @ S12) => (~ ((![S1 : state]: ((S12 = (update @ (setlocs @ S1 @ (getlocs @ S)) @ X4 @ (getlocs @ S1 @ res))) => (~ ((evaln @ (body2 @ P) @ (update @ (setlocs @ S @ newlocs) @ (loc2 @ arg) @ (A @ S)) @ N @ S1))))))))))). % evaln_elim_cases(7)
thf(fact_99_evalc__elim__cases_I7_J, axiom,
    ((![X4 : vname, P : pname, A : state > nat, S : state, S12 : state]: ((evalc @ (call @ X4 @ P @ A) @ S @ S12) => (~ ((![S1 : state]: ((S12 = (update @ (setlocs @ S1 @ (getlocs @ S)) @ X4 @ (getlocs @ S1 @ res))) => (~ ((evalc @ (body2 @ P) @ (update @ (setlocs @ S @ newlocs) @ (loc2 @ arg) @ (A @ S)) @ S1))))))))))). % evalc_elim_cases(7)
thf(fact_100_vname_Osize__gen_I2_J, axiom,
    ((![X23 : loc]: ((size_vname @ (loc2 @ X23)) = zero_zero_nat)))). % vname.size_gen(2)
thf(fact_101_vname_Osize__gen_I1_J, axiom,
    ((![X12 : glb]: ((size_vname @ (glb2 @ X12)) = zero_zero_nat)))). % vname.size_gen(1)
thf(fact_102_vname_Oinject_I1_J, axiom,
    ((![X12 : glb, Y1 : glb]: (((glb2 @ X12) = (glb2 @ Y1)) = (X12 = Y1))))). % vname.inject(1)
thf(fact_103_vname_Oexhaust, axiom,
    ((![Y : vname]: ((![X1 : glb]: (~ ((Y = (glb2 @ X1))))) => (~ ((![X2 : loc]: (~ ((Y = (loc2 @ X2))))))))))). % vname.exhaust
thf(fact_104_vname_Oinduct, axiom,
    ((![P : vname > $o, Vname : vname]: ((![X : glb]: (P @ (glb2 @ X))) => ((![X : loc]: (P @ (loc2 @ X))) => (P @ Vname)))))). % vname.induct
thf(fact_105_vname_Odistinct_I1_J, axiom,
    ((![X12 : glb, X23 : loc]: (~ (((glb2 @ X12) = (loc2 @ X23))))))). % vname.distinct(1)
thf(fact_106_vname_Osize_I3_J, axiom,
    ((![X12 : glb]: ((size_size_vname @ (glb2 @ X12)) = zero_zero_nat)))). % vname.size(3)
thf(fact_107_vname_Osize_I4_J, axiom,
    ((![X23 : loc]: ((size_size_vname @ (loc2 @ X23)) = zero_zero_nat)))). % vname.size(4)
thf(fact_108_com_Osize__gen_I1_J, axiom,
    (((size_com @ skip) = zero_zero_nat))). % com.size_gen(1)
thf(fact_109_com_Osize__gen_I2_J, axiom,
    ((![X21 : vname, X22 : state > nat]: ((size_com @ (ass @ X21 @ X22)) = zero_zero_nat)))). % com.size_gen(2)
thf(fact_110_com_Osize__gen_I7_J, axiom,
    ((![X72 : pname]: ((size_com @ (body2 @ X72)) = zero_zero_nat)))). % com.size_gen(7)
thf(fact_111_com_Osize__gen_I8_J, axiom,
    ((![X81 : vname, X82 : pname, X83 : state > nat]: ((size_com @ (call @ X81 @ X82 @ X83)) = zero_zero_nat)))). % com.size_gen(8)
thf(fact_112_com_Osize__gen_I3_J, axiom,
    ((![X31 : loc, X32 : state > nat, X33 : com]: ((size_com @ (local @ X31 @ X32 @ X33)) = (plus_plus_nat @ (size_com @ X33) @ (suc @ zero_zero_nat)))))). % com.size_gen(3)
thf(fact_113_com_Osize__gen_I4_J, axiom,
    ((![X41 : com, X42 : com]: ((size_com @ (semi @ X41 @ X42)) = (plus_plus_nat @ (plus_plus_nat @ (size_com @ X41) @ (size_com @ X42)) @ (suc @ zero_zero_nat)))))). % com.size_gen(4)
thf(fact_114_com_Osize__gen_I6_J, axiom,
    ((![X61 : state > $o, X62 : com]: ((size_com @ (while @ X61 @ X62)) = (plus_plus_nat @ (size_com @ X62) @ (suc @ zero_zero_nat)))))). % com.size_gen(6)
thf(fact_115_com_Osize__gen_I5_J, axiom,
    ((![X51 : state > $o, X52 : com, X53 : com]: ((size_com @ (cond @ X51 @ X52 @ X53)) = (plus_plus_nat @ (plus_plus_nat @ (size_com @ X52) @ (size_com @ X53)) @ (suc @ zero_zero_nat)))))). % com.size_gen(5)
thf(fact_116_com_Osize_I12_J, axiom,
    ((![X41 : com, X42 : com]: ((size_size_com @ (semi @ X41 @ X42)) = (plus_plus_nat @ (plus_plus_nat @ (size_size_com @ X41) @ (size_size_com @ X42)) @ (suc @ zero_zero_nat)))))). % com.size(12)
thf(fact_117_com_Osize_I11_J, axiom,
    ((![X31 : loc, X32 : state > nat, X33 : com]: ((size_size_com @ (local @ X31 @ X32 @ X33)) = (plus_plus_nat @ (size_size_com @ X33) @ (suc @ zero_zero_nat)))))). % com.size(11)

% Conjectures (4)
thf(conj_0, hypothesis,
    ((![Z : state]: (Z = s)))).
thf(conj_1, hypothesis,
    ((![X9 : state]: (~ ((evalc @ c @ z @ X9)))))).
thf(conj_2, hypothesis,
    ((![T2 : state]: (~ ((![S2 : state]: (S2 = T2))))))).
thf(conj_3, conjecture,
    ($false)).
