TSTP Solution File: SWW471+5 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW471+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %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 : 600s
% DateTime : Thu Jul 21 01:17:07 EDT 2022
% Result : Unknown 211.26s 211.57s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW471+5 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 5 06:12:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.92/1.22 ============================== Prover9 ===============================
% 0.92/1.22 Prover9 (32) version 2009-11A, November 2009.
% 0.92/1.22 Process 23870 was started by sandbox on n027.cluster.edu,
% 0.92/1.22 Sun Jun 5 06:12:08 2022
% 0.92/1.22 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23716_n027.cluster.edu".
% 0.92/1.22 ============================== end of head ===========================
% 0.92/1.22
% 0.92/1.22 ============================== INPUT =================================
% 0.92/1.22
% 0.92/1.22 % Reading from file /tmp/Prover9_23716_n027.cluster.edu
% 0.92/1.22
% 0.92/1.22 set(prolog_style_variables).
% 0.92/1.22 set(auto2).
% 0.92/1.22 % set(auto2) -> set(auto).
% 0.92/1.22 % set(auto) -> set(auto_inference).
% 0.92/1.22 % set(auto) -> set(auto_setup).
% 0.92/1.22 % set(auto_setup) -> set(predicate_elim).
% 0.92/1.22 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.92/1.22 % set(auto) -> set(auto_limits).
% 0.92/1.22 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.92/1.22 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.92/1.22 % set(auto) -> set(auto_denials).
% 0.92/1.22 % set(auto) -> set(auto_process).
% 0.92/1.22 % set(auto2) -> assign(new_constants, 1).
% 0.92/1.22 % set(auto2) -> assign(fold_denial_max, 3).
% 0.92/1.22 % set(auto2) -> assign(max_weight, "200.000").
% 0.92/1.22 % set(auto2) -> assign(max_hours, 1).
% 0.92/1.22 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.92/1.22 % set(auto2) -> assign(max_seconds, 0).
% 0.92/1.22 % set(auto2) -> assign(max_minutes, 5).
% 0.92/1.22 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.92/1.22 % set(auto2) -> set(sort_initial_sos).
% 0.92/1.22 % set(auto2) -> assign(sos_limit, -1).
% 0.92/1.22 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.92/1.22 % set(auto2) -> assign(max_megs, 400).
% 0.92/1.22 % set(auto2) -> assign(stats, some).
% 0.92/1.22 % set(auto2) -> clear(echo_input).
% 0.92/1.22 % set(auto2) -> set(quiet).
% 0.92/1.22 % set(auto2) -> clear(print_initial_clauses).
% 0.92/1.22 % set(auto2) -> clear(print_given).
% 0.92/1.22 assign(lrs_ticks,-1).
% 0.92/1.22 assign(sos_limit,10000).
% 0.92/1.22 assign(order,kbo).
% 0.92/1.22 set(lex_order_vars).
% 0.92/1.22 clear(print_given).
% 0.92/1.22
% 0.92/1.22 % formulas(sos). % not echoed (169 formulas)
% 0.92/1.22
% 0.92/1.22 ============================== end of input ==========================
% 0.92/1.22
% 0.92/1.22 % From the command line: assign(max_seconds, 300).
% 0.92/1.22
% 0.92/1.22 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.92/1.22
% 0.92/1.22 % Formulas that are not ordinary clauses:
% 0.92/1.22 1 (all X_b all X_c all X_a ti(fun(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c))),combb(X_b,X_c,X_a)) = combb(X_b,X_c,X_a)) # label(tsy_c_COMBB_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 2 (all X_a all X_b all X_c ti(fun(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c))),combc(X_a,X_b,X_c)) = combc(X_a,X_b,X_c)) # label(tsy_c_COMBC_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 3 (all X_a ti(fun(X_a,X_a),combi(X_a)) = combi(X_a)) # label(tsy_c_COMBI_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 4 (all X_a all X_b ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b)) = combk(X_a,X_b)) # label(tsy_c_COMBK_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 5 (all X_a all X_b all X_c ti(fun(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c))),combs(X_a,X_b,X_c)) = combs(X_a,X_b,X_c)) # label(tsy_c_COMBS_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 6 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 7 (all X_b ti(fun(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool)),hoare_122391849derivs(X_b)) = hoare_122391849derivs(X_b)) # label(tsy_c_Hoare__Mirabelle__pjuwniqynr_Ohoare__derivs_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 8 (all X_b ti(fun(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool)),hoare_1870528171valids(X_b)) = hoare_1870528171valids(X_b)) # label(tsy_c_Hoare__Mirabelle__pjuwniqynr_Ohoare__valids_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 9 (all X_b ti(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)))),hoare_1008221573triple(X_b)) = hoare_1008221573triple(X_b)) # label(tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 10 (all X_c all X_b ti(fun(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_509422987triple(X_c),X_b)),hoare_885240885e_case(X_c,X_b)) = hoare_885240885e_case(X_c,X_b)) # label(tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__case_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 11 (all X_c all X_b ti(fun(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_509422987triple(X_c),X_b)),hoare_728318379le_rec(X_c,X_b)) = hoare_728318379le_rec(X_c,X_b)) # label(tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__rec_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 12 (all X_b ti(fun(nat,fun(hoare_509422987triple(X_b),bool)),hoare_763665637_valid(X_b)) = hoare_763665637_valid(X_b)) # label(tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple__valid_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 13 (all X_a (semilattice_sup(X_a) -> ti(fun(X_a,fun(X_a,X_a)),semilattice_sup_sup(X_a)) = semilattice_sup_sup(X_a))) # label(tsy_c_Lattices_Osemilattice__sup__class_Osup_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 14 (all X_b ti(fun(X_b,bool),bot_bot(fun(X_b,bool))) = bot_bot(fun(X_b,bool))) # label(tsy_c_Orderings_Obot__class_Obot_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 15 (all X_b ti(fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),powp(X_b)) = powp(X_b)) # label(tsy_c_Predicate_OPowp_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 16 (all X_b ti(fun(fun(X_b,bool),fun(X_b,bool)),collect(X_b)) = collect(X_b)) # label(tsy_c_Set_OCollect_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 17 (all X_c all X_b ti(fun(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool))),image(X_c,X_b)) = image(X_c,X_b)) # label(tsy_c_Set_Oimage_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 18 (all X_b ti(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),insert(X_b)) = insert(X_b)) # label(tsy_c_Set_Oinsert_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 19 (all X_a ti(fun(X_a,fun(X_a,bool)),fequal(X_a)) = fequal(X_a)) # label(tsy_c_fequal_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 20 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_arg1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 21 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_arg2) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 22 (all X_c all X_a all B_1_1 all B_2_1 ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 23 (all B_1_1 (hBOOL(ti(bool,B_1_1)) <-> hBOOL(B_1_1))) # label(tsy_c_hBOOL_arg1) # label(hypothesis) # label(non_clause). [assumption].
% 0.92/1.22 24 (all X_b ti(fun(X_b,fun(fun(X_b,bool),bool)),member(X_b)) = member(X_b)) # label(tsy_c_member_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 25 (all X_b all Fun1_1 all Com_1 all Fun2_1 all Fun1_2 all Com_2 all Fun2_2 (hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Fun1_1),Com_1),Fun2_1) = hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Fun1_2),Com_2),Fun2_2) <-> Fun1_1 = Fun1_2 & Com_1 = Com_2 & Fun2_1 = Fun2_2)) # label(fact_0_triple_Oinject) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 26 (all X_b all Ga all Ts (hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_1870528171valids(X_b),Ga),Ts)) <-> (all N ((all X (hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),bool),member(hoare_509422987triple(X_b)),X),Ga)) -> hBOOL(hAPP(hoare_509422987triple(X_b),bool,hAPP(nat,fun(hoare_509422987triple(X_b),bool),hoare_763665637_valid(X_b),N),X)))) -> (all X (hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),bool),member(hoare_509422987triple(X_b)),X),Ts)) -> hBOOL(hAPP(hoare_509422987triple(X_b),bool,hAPP(nat,fun(hoare_509422987triple(X_b),bool),hoare_763665637_valid(X_b),N),X)))))))) # label(fact_1_hoare__valids__def) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 27 (all X_b all Ga all Pa all Qa all Procsa (hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),semilattice_sup_sup(fun(hoare_509422987triple(X_b),bool)),Ga),hAPP(fun(pname,bool),fun(hoare_509422987triple(X_b),bool),hAPP(fun(pname,hoare_509422987triple(X_b)),fun(fun(pname,bool),fun(hoare_509422987triple(X_b),bool)),image(pname,hoare_509422987triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_509422987triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_509422987triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),pname),hoare_1008221573triple(X_b)),Pa)),body)),Qa)),Procsa))),hAPP(fun(pname,bool),fun(hoare_509422987triple(X_b),bool),hAPP(fun(pname,hoare_509422987triple(X_b)),fun(fun(pname,bool),fun(hoare_509422987triple(X_b),bool)),image(pname,hoare_509422987triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_509422987triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_509422987triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),pname),hoare_1008221573triple(X_b)),Pa)),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body_1))),Qa)),Procsa))) -> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(pname,bool),fun(hoare_509422987triple(X_b),bool),hAPP(fun(pname,hoare_509422987triple(X_b)),fun(fun(pname,bool),fun(hoare_509422987triple(X_b),bool)),image(pname,hoare_509422987triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_509422987triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_509422987triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),pname),hoare_1008221573triple(X_b)),Pa)),body)),Qa)),Procsa))))) # label(fact_2_hoare__derivs_OBody) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 28 (all X_b all C all A_1 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B_1))) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C),B_1))))) # label(fact_3_UnE) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 29 (all X_b all A_1 all B_1 all X_2 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B_1),X_2)) -> (-hBOOL(hAPP(X_b,bool,A_1,X_2)) -> hBOOL(hAPP(X_b,bool,B_1,X_2))))) # label(fact_4_sup1E) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 30 (all X_b all A_1 all B_1 all X_2 ((-hBOOL(hAPP(X_b,bool,B_1,X_2)) -> hBOOL(hAPP(X_b,bool,A_1,X_2))) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B_1),X_2)))) # label(fact_5_sup1CI) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 31 (all X_b all A_1 all C all B_1 ((-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C),B_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C),A_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B_1))))) # label(fact_6_UnCI) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 32 (all X_b all X_c all A_1 all B all F all X_2 (ti(X_b,B) = hAPP(X_c,X_b,F,X_2) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_1)))))) # label(fact_7_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 33 (all X_c all X_b all F1 all Fun1_1 all Com_1 all Fun2_1 hAPP(hoare_509422987triple(X_c),X_b,hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_509422987triple(X_c),X_b),hoare_728318379le_rec(X_c,X_b),F1),hAPP(fun(X_c,fun(state,bool)),hoare_509422987triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_509422987triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_509422987triple(X_c))),hoare_1008221573triple(X_c),Fun1_1),Com_1),Fun2_1)) = hAPP(fun(X_c,fun(state,bool)),X_b,hAPP(com,fun(fun(X_c,fun(state,bool)),X_b),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b)),F1,Fun1_1),Com_1),Fun2_1)) # label(fact_8_triple_Orecs) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 34 (all X_c all X_b all F1 all Fun1_1 all Com_1 all Fun2_1 hAPP(hoare_509422987triple(X_c),X_b,hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_509422987triple(X_c),X_b),hoare_885240885e_case(X_c,X_b),F1),hAPP(fun(X_c,fun(state,bool)),hoare_509422987triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_509422987triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_509422987triple(X_c))),hoare_1008221573triple(X_c),Fun1_1),Com_1),Fun2_1)) = hAPP(fun(X_c,fun(state,bool)),X_b,hAPP(com,fun(fun(X_c,fun(state,bool)),X_b),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b)),F1,Fun1_1),Com_1),Fun2_1)) # label(fact_9_triple_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 35 (all X_c all X_b all F all A_1 all B_1 hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),semilattice_sup_sup(fun(X_c,bool)),A_1),B_1)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_1)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),B_1))) # label(fact_10_image__Un) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 36 (all X_b all X_c (lattice(X_c) -> (all F all G all X hAPP(X_b,X_c,hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),fun(X_b,X_c)),semilattice_sup_sup(fun(X_b,X_c)),F),G),X) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),semilattice_sup_sup(X_c),hAPP(X_b,X_c,F,X)),hAPP(X_b,X_c,G,X))))) # label(fact_11_sup__fun__def) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 37 (all X_c all X_b (lattice(X_b) -> (all F all G all X_2 hAPP(X_c,X_b,hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),semilattice_sup_sup(fun(X_c,X_b)),F),G),X_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),semilattice_sup_sup(X_b),hAPP(X_c,X_b,F,X_2)),hAPP(X_c,X_b,G,X_2))))) # label(fact_12_sup__apply) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 38 (all X_b all Ga all G_1 all Ts (hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),G_1),Ts)) -> (hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),G_1)) -> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),Ts))))) # label(fact_13_cut) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 39 (all X_a (semilattice_sup(X_a) -> (all X_1 all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z_1))))) # label(fact_14_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 40 (all X_a (lattice(X_a) -> (all X_1 all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z_1))))) # label(fact_15_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 41 (all X_a (semilattice_sup(X_a) -> (all A_3 all B_2 all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_3),B_2)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_2),C_1))))) # label(fact_16_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 42 (all X_a (semilattice_sup(X_a) -> (all X_1 all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Z_1))))) # label(fact_17_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 43 (all X_a (lattice(X_a) -> (all X_1 all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Z_1))))) # label(fact_18_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 44 (all X_a (semilattice_sup(X_a) -> (all B_2 all A_3 all C_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_3),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_2),C_1))))) # label(fact_19_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 45 (all X_a (semilattice_sup(X_a) -> (all X_1 all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)))) # label(fact_20_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 46 (all X_a (lattice(X_a) -> (all X_1 all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y)))) # label(fact_21_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 47 (all X_a (semilattice_sup(X_a) -> (all A_3 all B_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_3),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_3),B_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_3),B_2)))) # label(fact_22_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 48 (all X_a (semilattice_sup(X_a) -> (all X_1 all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),X_1)))) # label(fact_23_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 49 (all X_a (lattice(X_a) -> (all X_1 all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),Y),X_1)))) # label(fact_24_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 50 (all X_a (semilattice_sup(X_a) -> (all A_3 all B_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_3),B_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),B_2),A_3)))) # label(fact_25_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 51 (all X_a (semilattice_sup(X_a) -> (all X_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),X_1),X_1) = ti(X_a,X_1)))) # label(fact_26_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 52 (all X_a (semilattice_sup(X_a) -> (all A_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),semilattice_sup_sup(X_a),A_3),A_3) = ti(X_a,A_3)))) # label(fact_27_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 53 (all X_c all X_b all B all F all X_2 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> (ti(X_c,B) = hAPP(X_b,X_c,F,X_2) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),B),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_1)))))) # label(fact_28_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 54 (all X_c all X_b all F all X_2 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),A_1))))) # label(fact_29_imageI) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 55 (all X_b all X_c all Z all F all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_1))) <-> (exists X (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X),A_1)) & ti(X_b,Z) = hAPP(X_c,X_b,F,X))))) # label(fact_30_image__iff) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 56 (all X_b all A_1 all C all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C),B_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B_1))))) # label(fact_31_UnI2) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 57 (all X_b all B_1 all C all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B_1))))) # label(fact_32_UnI1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 58 (all X_b all A_1 all B_1 all X_2 (hBOOL(hAPP(X_b,bool,B_1,X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B_1),X_2)))) # label(fact_33_sup1I2) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 59 (all X_b all B_1 all A_1 all X_2 (hBOOL(hAPP(X_b,bool,A_1,X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B_1),X_2)))) # label(fact_34_sup1I1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 60 (all X_b all Pa all A_1 all B_1 ((all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B_1))) -> hBOOL(hAPP(X_b,bool,Pa,X)))) <-> (all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_1)) -> hBOOL(hAPP(X_b,bool,Pa,X)))) & (all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),B_1)) -> hBOOL(hAPP(X_b,bool,Pa,X)))))) # label(fact_35_ball__Un) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 61 (all X_b all Pa all A_1 all B_1 ((exists X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B_1))) & hBOOL(hAPP(X_b,bool,Pa,X)))) <-> (exists X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_1)) & hBOOL(hAPP(X_b,bool,Pa,X)))) | (exists X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),B_1)) & hBOOL(hAPP(X_b,bool,Pa,X)))))) # label(fact_36_bex__Un) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 62 (all X_b all A_1 all B_1 all C_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B_1)),C_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_1),C_2))) # label(fact_37_Un__assoc) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 63 (all X_b all C all A_1 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B_1))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C),A_1)) | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C),B_1)))) # label(fact_38_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 64 (all X_b all A_1 all B_1 all C_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_1),C_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),C_2))) # label(fact_39_Un__left__commute) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 65 (all X_b all A_1 all B_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B_1)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B_1)) # label(fact_40_Un__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 66 (all X_b all A_1 all B_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B_1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),B_1),A_1)) # label(fact_41_Un__commute) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 67 (all X_b all A_1 all B_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),B_1) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),A_1))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_1)))) # label(fact_42_Un__def) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 68 (all X_b all A_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),A_1),A_1) = ti(fun(X_b,bool),A_1)) # label(fact_43_Un__absorb) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 69 (all X_b all Y_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),combi(X_b)),Y_2) = ti(fun(X_b,bool),Y_2)) # label(fact_44_image__ident) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 70 (all X_c all X_b all X_d all F all G all A_1 hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),hAPP(fun(X_d,bool),fun(X_c,bool),hAPP(fun(X_d,X_c),fun(fun(X_d,bool),fun(X_c,bool)),image(X_d,X_c),G),A_1)) = hAPP(fun(X_d,bool),fun(X_b,bool),hAPP(fun(X_d,X_b),fun(fun(X_d,bool),fun(X_b,bool)),image(X_d,X_b),hAPP(fun(X_d,X_c),fun(X_d,X_b),hAPP(fun(X_c,X_b),fun(fun(X_d,X_c),fun(X_d,X_b)),combb(X_c,X_b,X_d),F),G)),A_1)) # label(fact_45_image__image) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 71 (all X_b all R_1 all S_1 all X (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),R_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),S_1)),X)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),R_1),S_1))))) # label(fact_46_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 72 (all X_b all Pa all Qa hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),Pa)),Qa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Qa))) # label(fact_47_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 73 (all X_b all X_c all B all F all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_1))) -> -(all X (ti(X_b,B) = hAPP(X_c,X_b,F,X) -> -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X),A_1)))))) # label(fact_48_imageE) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 74 (all X_b all N_2 all Pa all Pn_1 all Qa (hBOOL(hAPP(hoare_509422987triple(X_b),bool,hAPP(nat,fun(hoare_509422987triple(X_b),bool),hoare_763665637_valid(X_b),N_2),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn_1))),Qa))) <-> hBOOL(hAPP(hoare_509422987triple(X_b),bool,hAPP(nat,fun(hoare_509422987triple(X_b),bool),hoare_763665637_valid(X_b),hAPP(nat,nat,suc,N_2)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),hAPP(pname,com,body,Pn_1)),Qa))))) # label(fact_49_Body__triple__valid__Suc) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 75 (all X_b all Y_1 -(all Fun1 all Com all Fun2 Y_1 != hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Fun1),Com),Fun2))) # label(fact_50_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 76 (all X_b all Pn_1 all Ga all Pa all Qa all Procsa (hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),semilattice_sup_sup(fun(hoare_509422987triple(X_b),bool)),Ga),hAPP(fun(pname,bool),fun(hoare_509422987triple(X_b),bool),hAPP(fun(pname,hoare_509422987triple(X_b)),fun(fun(pname,bool),fun(hoare_509422987triple(X_b),bool)),image(pname,hoare_509422987triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_509422987triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_509422987triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),pname),hoare_1008221573triple(X_b)),Pa)),body)),Qa)),Procsa))),hAPP(fun(pname,bool),fun(hoare_509422987triple(X_b),bool),hAPP(fun(pname,hoare_509422987triple(X_b)),fun(fun(pname,bool),fun(hoare_509422987triple(X_b),bool)),image(pname,hoare_509422987triple(X_b)),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_509422987triple(X_b)),hAPP(fun(pname,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,hoare_509422987triple(X_b))),combs(pname,fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hAPP(fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)))),fun(fun(pname,com),fun(pname,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)))),combs(pname,com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hAPP(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)))),hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)))),fun(fun(pname,fun(X_b,fun(state,bool))),fun(pname,fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))))),combb(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),pname),hoare_1008221573triple(X_b)),Pa)),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body_1))),Qa)),Procsa))) -> (hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),Pn_1),Procsa)) -> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),hAPP(pname,fun(X_b,fun(state,bool)),Pa,Pn_1)),hAPP(pname,com,body,Pn_1)),hAPP(pname,fun(X_b,fun(state,bool)),Qa,Pn_1))),bot_bot(fun(hoare_509422987triple(X_b),bool)))))))) # label(fact_51_Body1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 77 (all X_c all X_b all F all G all M all N_1 (ti(fun(X_b,bool),M) = ti(fun(X_b,bool),N_1) -> ((all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),N_1)) -> hAPP(X_b,X_c,F,X) = hAPP(X_b,X_c,G,X))) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),M) = hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),G),N_1)))) # label(fact_52_image__cong) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 78 (all X_b all A_1 all X (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),powp(X_b),A_1),X)) <-> (all Xa (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Xa),X)) -> hBOOL(hAPP(X_b,bool,A_1,Xa)))))) # label(fact_53_Powp__def) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 79 (all X_b all Pa all Pn_1 all Qa hBOOL(hAPP(hoare_509422987triple(X_b),bool,hAPP(nat,fun(hoare_509422987triple(X_b),bool),hoare_763665637_valid(X_b),zero_zero(nat)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),hAPP(pname,com,body,Pn_1)),Qa)))) # label(fact_54_Body__triple__valid__0) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 80 (all Pname_1 all Pname (hAPP(pname,com,body,Pname_1) = hAPP(pname,com,body,Pname) <-> ti(pname,Pname_1) = ti(pname,Pname))) # label(fact_55_com_Osimps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 81 (all Pn all S0 all S1 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,Pn))),S0),S1)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(pname,com,body,Pn)),S0),S1)))) # label(fact_56_evalc_OBody) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 82 (all X_b all A_2 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),bot_bot(fun(X_b,bool))))) # label(fact_57_emptyE) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 83 (all X_b all A_2 all B all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),A_1))) -> (ti(X_b,A_2) != ti(X_b,B) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_1))))) # label(fact_58_insertE) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 84 (all X_b all B all A_2 all B_1 ((-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_1)) -> ti(X_b,A_2) = ti(X_b,B)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),B_1))))) # label(fact_59_insertCI) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 85 (all P all S all S1 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(pname,com,body,P)),S),S1)) -> hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,hAPP(option(com),com,the(com),hAPP(pname,option(com),body_1,P))),S),S1)))) # label(fact_60_evalc__elim__cases_I6_J) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 86 (all X_b all A_2 all A_1 bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_1)) # label(fact_61_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 87 (all X_b all A_2 all A_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_1) != bot_bot(fun(X_b,bool))) # label(fact_62_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 88 (all X_b all X (hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),bot_bot(fun(X_b,bool)))))) # label(fact_63_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 89 (all X_b bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse))) # label(fact_64_empty__def) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 90 (all X_b all A_2 all B_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1)))) # label(fact_65_insertI1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 91 (all X_b all A_1 ((all X -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_1))) <-> ti(fun(X_b,bool),A_1) = bot_bot(fun(X_b,bool)))) # label(fact_66_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 92 (all X_b all A_2 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) # label(fact_67_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 93 (all X_b all A_1 ((exists X hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X),A_1))) <-> ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)))) # label(fact_68_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 94 (all X_b all A_2 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) # label(fact_69_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 95 (all X_b all Pa all A_2 ((hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) & (-hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Pa)) = bot_bot(fun(X_b,bool))))) # label(fact_70_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 96 (all X_b all Pa all A_2 ((hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) & (-hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Pa)) = bot_bot(fun(X_b,bool))))) # label(fact_71_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 97 (all X_b all Pa (bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) <-> (all X -hBOOL(hAPP(X_b,bool,Pa,X))))) # label(fact_72_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 98 (all X_b all C -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C),bot_bot(fun(X_b,bool))))) # label(fact_73_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 99 (all X_b all X_c all F all G ((all X hAPP(X_b,X_c,F,X) = hAPP(X_b,X_c,G,X)) -> ti(fun(X_b,X_c),F) = ti(fun(X_b,X_c),G))) # label(fact_74_ext) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 100 (all X_b all X_2 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) <-> hBOOL(hAPP(X_b,bool,A_1,X_2)))) # label(fact_75_mem__def) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 101 (all X_b all Pa hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = ti(fun(X_b,bool),Pa)) # label(fact_76_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 102 (all X_b all A_2 all B_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),B_1) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_1)))) # label(fact_77_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 103 (all X_b all A_2 all A_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),semilattice_sup_sup(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))),A_1)) # label(fact_78_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 104 (all X_b all A_2 all Pa hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fimplies),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2)))),Pa))) # label(fact_79_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 105 (all X_b all B all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) <-> ti(X_b,B) = ti(X_b,A_2))) # label(fact_80_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 106 (all X_b all X_2 all A_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_1)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_1)) # label(fact_81_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 107 (all X_b all X_2 all Y_1 all A_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),A_1)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_1))) # label(fact_82_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 108 (all X_b all A_2 all B all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),A_1))) <-> ti(X_b,A_2) = ti(X_b,B) | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_1)))) # label(fact_83_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 109 (all X_b all Pa (hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = bot_bot(fun(X_b,bool)) <-> (all X -hBOOL(hAPP(X_b,bool,Pa,X))))) # label(fact_84_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 110 (all X_b all A_2 all B all C all D (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),bot_bot(fun(X_b,bool)))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),C),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),D),bot_bot(fun(X_b,bool)))) <-> ti(X_b,A_2) = ti(X_b,C) & ti(X_b,B) = ti(X_b,D) | ti(X_b,A_2) = ti(X_b,D) & ti(X_b,B) = ti(X_b,C))) # label(fact_85_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 111 (all X_b all Y_1 all A_1 all X_2 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),A_1),X_2)) <-> ti(X_b,Y_1) = ti(X_b,X_2) | hBOOL(hAPP(X_b,bool,A_1,X_2)))) # label(fact_86_insert__code) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 112 (all X_b all X all Xa hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X),Xa) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),Xa)))) # label(fact_87_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 113 (all X_b all B_1 all X_2 all A_1 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_1)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),B_1) <-> ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B_1))))) # label(fact_88_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 114 (all X_b all A_2 all A_1 (ti(fun(X_b,bool),A_1) = bot_bot(fun(X_b,bool)) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_1)))) # label(fact_89_equals0D) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 115 (all X_b all B all A_2 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),B_1))))) # label(fact_90_insertI2) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 116 (all X_b all A_2 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_1)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_1) = ti(fun(X_b,bool),A_1))) # label(fact_91_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 117 (all X_b all Ts all Ga all T_4 (hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),T_4),bot_bot(fun(hoare_509422987triple(X_b),bool))))) -> (hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),Ts)) -> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),T_4),Ts)))))) # label(fact_92_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 118 (all X_b all B all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) -> ti(X_b,B) = ti(X_b,A_2))) # label(fact_93_singletonE) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 119 (all X_b all Ga all T_4 all Ts (hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),T_4),Ts))) -> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),T_4),bot_bot(fun(hoare_509422987triple(X_b),bool))))) & hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),Ts)))) # label(fact_94_derivs__insertD) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 120 (all X_b all A_2 all B (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),B),bot_bot(fun(X_b,bool))) -> ti(X_b,A_2) = ti(X_b,B))) # label(fact_95_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 121 (all U all C_1 all S all T_3 (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S),T_3)) -> (hBOOL(hAPP(state,bool,hAPP(state,fun(state,bool),hAPP(com,fun(state,fun(state,bool)),evalc,C_1),S),U)) -> U = T_3))) # label(fact_96_com__det) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 122 (all X_c all X_b all C all A_1 ((ti(fun(X_b,bool),A_1) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),C)),A_1) = bot_bot(fun(X_c,bool))) & (ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),C)),A_1) = hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),C),bot_bot(fun(X_c,bool)))))) # label(fact_97_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 123 (all X_c all X_b all C all X_2 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1)) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),C)),A_1) = hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),C),bot_bot(fun(X_c,bool))))) # label(fact_98_image__constant) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 124 (all T_2 all T_1 (lattice(T_1) -> semilattice_sup(fun(T_2,T_1)))) # label(arity_fun___Lattices_Osemilattice__sup) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 125 (all T_2 all T_1 (lattice(T_1) -> lattice(fun(T_2,T_1)))) # label(arity_fun___Lattices_Olattice) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 126 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 127 (all P (-hBOOL(hAPP(bool,bool,fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 128 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 129 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R) = hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R))) # label(help_COMBB_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 130 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q)) # label(help_COMBC_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 131 (all X_a all P hAPP(X_a,X_a,combi(X_a),P) = ti(X_a,P)) # label(help_COMBI_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 132 (all X_b all X_a all P all Q hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P)) # label(help_COMBK_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 133 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c)),combs(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R))) # label(help_COMBS_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 134 (all Q all P (-hBOOL(P) | -hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 135 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | hBOOL(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 136 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | hBOOL(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 137 (all Q all P (-hBOOL(P) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 138 (all P all Q (-hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 139 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | hBOOL(P) | hBOOL(Q))) # label(help_fdisj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 140 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 141 (all X_a all X_1 all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X_1),Y)) | ti(X_a,X_1) = ti(X_a,Y))) # label(help_fequal_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 142 (all X_a all X_1 all Y (ti(X_a,X_1) != ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X_1),Y)))) # label(help_fequal_2_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 143 (all Q all P (hBOOL(P) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 144 (all P all Q (-hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 145 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)) | -hBOOL(P) | hBOOL(Q))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.24 146 (all N ((all X (hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),bool),member(hoare_509422987triple(x_a)),X),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),semilattice_sup_sup(fun(hoare_509422987triple(x_a),bool)),g),hAPP(fun(pname,bool),fun(hoare_509422987triple(x_a),bool),hAPP(fun(pname,hoare_509422987triple(x_a)),fun(fun(pname,bool),fun(hoare_509422987triple(x_a),bool)),image(pname,hoare_509422987triple(x_a)),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_509422987triple(x_a)),hAPP(fun(pname,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_509422987triple(x_a))),combs(pname,fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hAPP(fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)))),fun(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)))),combs(pname,com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)))),hAPP(fun(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))))),combb(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),pname),hoare_1008221573triple(x_a)),p)),body)),q)),procs)))) -> hBOOL(hAPP(hoare_509422987triple(x_a),bool,hAPP(nat,fun(hoare_509422987triple(x_a),bool),hoare_763665637_valid(x_a),N),X)))) -> (all X (hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),bool),member(hoare_509422987triple(x_a)),X),hAPP(fun(pname,bool),fun(hoare_509422987triple(x_a),bool),hAPP(fun(pname,hoare_509422987triple(x_a)),fun(fun(pname,bool),fun(hoare_509422987triple(x_a),bool)),image(pname,hoare_509422987triple(x_a)),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_509422987triple(x_a)),hAPP(fun(pname,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_509422987triple(x_a))),combs(pname,fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hAPP(fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)))),fun(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)))),combs(pname,com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)))),hAPP(fun(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))))),combb(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),pname),hoare_1008221573triple(x_a)),p)),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body_1))),q)),procs))) -> hBOOL(hAPP(hoare_509422987triple(x_a),bool,hAPP(nat,fun(hoare_509422987triple(x_a),bool),hoare_763665637_valid(x_a),N),X)))))) # label(conj_0) # label(hypothesis) # label(non_clause). [assumption].
% 0.92/1.24 147 -((all X (hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),bool),member(hoare_509422987triple(x_a)),X),g)) -> hBOOL(hAPP(hoare_509422987triple(x_a),bool,hAPP(nat,fun(hoare_509422987triple(x_a),bool),hoare_763665637_valid(x_a),n),X)))) -> (all X (hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),bool),member(hoare_509422987triple(x_a)),X),hAPP(fun(pname,bool),fun(hoare_509422987triple(x_a),bool),hAPP(fun(pname,hoare_509422987triple(x_a)),fun(fun(pname,bool),fun(hoare_509422987triple(x_a),bool)),image(pname,hoare_509422987triple(x_a)),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_509422987triple(x_a)),hAPP(fun(pname,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,hoare_509422987triple(x_a))),combs(pname,fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hAPP(fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)))),fun(fun(pname,com),fun(pname,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)))),combs(pname,com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hAPP(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)))),hAPP(fun(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)))),fun(fun(pname,fun(x_a,fun(state,bool))),fun(pname,fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))))),combb(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),pname),hoare_1008221573triple(x_a)),p)),body)),q)),procs))) -> hBOOL(hAPP(hoare_509422987triple(x_a),bool,hAPP(nat,fun(hoare_509422987triple(x_a),bool),hoare_763665637_valid(x_a),n),X))))) # label(conj_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.92/1.25
% 0.92/1.25 ============================== end of process non-clausal formulas ===
% 0.92/1.25
% 0.92/1.25 ============================== PROCESS INITIAL CLAUSES ===============
% 0.92/1.25
% 0.92/1.25 ============================== PREDICATE ELIMINATION =================
% 0.92/1.25 148 -lattice(A) | semilattice_sup(fun(B,A)) # label(arity_fun___Lattices_Osemilattice__sup) # label(axiom). [clausify(124)].
% 0.92/1.25 149 -semilattice_sup(A) | semilattice_sup_sup(A) = ti(fun(A,fun(A,A)),semilattice_sup_sup(A)) # label(tsy_c_Lattices_Osemilattice__sup__class_Osup_res) # label(axiom). [clausify(13)].
% 0.92/1.25 150 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),D)) # label(fact_14_sup__assoc) # label(axiom). [clausify(39)].
% 0.92/1.25 151 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),D)) # label(fact_16_sup_Oassoc) # label(axiom). [clausify(41)].
% 0.92/1.25 152 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),D)) # label(fact_17_sup__left__commute) # label(axiom). [clausify(42)].
% 0.92/1.25 153 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),D)) # label(fact_19_sup_Oleft__commute) # label(axiom). [clausify(44)].
% 0.92/1.25 154 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) # label(fact_20_sup__left__idem) # label(axiom). [clausify(45)].
% 0.92/1.25 155 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) # label(fact_22_sup_Oleft__idem) # label(axiom). [clausify(47)].
% 0.92/1.25 156 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),B) # label(fact_23_sup__commute) # label(axiom). [clausify(48)].
% 0.92/1.25 157 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),C),B) # label(fact_25_sup_Ocommute) # label(axiom). [clausify(50)].
% 0.92/1.25 158 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),B) = ti(A,B) # label(fact_26_sup__idem) # label(axiom). [clausify(51)].
% 0.92/1.25 159 -semilattice_sup(A) | hAPP(A,A,hAPP(A,fun(A,A),semilattice_sup_sup(A),B),B) = ti(A,B) # label(fact_27_sup_Oidem) # label(axiom). [clausify(52)].
% 0.92/1.25 Derived: -lattice(A) | semilattice_sup_sup(fun(B,A)) = ti(fun(fun(B,A),fun(fun(B,A),fun(B,A))),semilattice_sup_sup(fun(B,A))). [resolve(148,b,149,a)].
% 0.92/1.25 Derived: -lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D)),E) = hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),E)). [resolve(148,b,150,a)].
% 0.92/1.25 Derived: -lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),E)) = hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),E)). [resolve(148,b,152,a)].
% 0.92/1.25 Derived: -lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D)) = hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D). [resolve(148,b,154,a)].
% 0.92/1.25 Derived: -lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),D) = hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),D),C). [resolve(148,b,156,a)].
% 0.92/1.25 Derived: -lattice(A) | hAPP(fun(B,A),fun(B,A),hAPP(fun(B,A),fun(fun(B,A),fun(B,A)),semilattice_sup_sup(fun(B,A)),C),C) = ti(fun(B,A),C). [resolve(148,b,158,a)].
% 0.92/1.25 160 semilattice_sup(nat) # label(arity_Nat_Onat___Lattices_Osemilattice__sup) # label(axiom). [assumption].
% 0.92/1.25 Derived: semilattice_sup_sup(nat) = ti(fun(nat,fun(nat,nat)),semilattice_sup_sup(nat)). [resolve(160,a,149,a)].
% 0.92/1.25 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),B),C)). [resolve(160,a,150,a)].
% 0.92/1.25 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),C)). [resolve(160,a,152,a)].
% 0.92/1.25 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),B). [resolve(160,a,154,a)].
% 0.92/1.25 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),B),A). [resolve(160,a,156,a)].
% 0.92/1.25 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),semilattice_sup_sup(nat),A),A) = ti(nat,A). [resolve(160,a,158,a)].
% 0.92/1.25 161 semilattice_sup(bool) # label(arity_HOL_Obool___Lattices_Osemilattice__sup) # label(axiom). [assumption].
% 0.92/1.25 Derived: semilattice_sup_sup(bool) = ti(fun(bool,fun(bool,bool)),semilattice_sup_sup(bool)). [resolve(161,a,149,a)].
% 0.92/1.25 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B)),C) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),C)). [resolve(161,a,150,a)].
% 0.92/1.25 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),C)) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),C)). [resolve(161,a,152,a)].
% 0.92/1.25 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B)) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B). [resolve(161,a,154,a)].
% 211.26/211.57 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),B) = hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),B),A). [resolve(161,a,156,a)].
% 211.26/211.57 Derived: hAPP(bool,bool,hAPP(bool,fun(bool,bool),semilattice_sup_sup(bool),A),A) = ti(bool,A). [resolve(161,a,158,a)].
% 211.26/211.57
% 211.26/211.57 ============================== end predicate elimination =============
% 211.26/211.57
% 211.26/211.57 Auto_denials: (non-Horn, no changes).
% 211.26/211.57
% 211.26/211.57 Term ordering decisions:
% 211.26/211.57 Function symbol KB weights: bool=1. state=1. pname=1. com=1. x_a=1. nat=1. body=1. body_1=1. fconj=1. fdisj=1. evalc=1. fimplies=1. p=1. procs=1. q=1. fFalse=1. fNot=1. g=1. suc=1. fTrue=1. n=1. c1=1. fun=1. ti=1. image=1. combk=1. hoare_728318379le_rec=1. hoare_885240885e_case=1. f12=1. f13=1. f14=1. f17=1. f18=1. f19=1. f21=1. hoare_509422987triple=1. semilattice_sup_sup=1. member=1. insert=1. bot_bot=1. hoare_1008221573triple=1. option=1. collect=1. hoare_122391849derivs=1. hoare_763665637_valid=1. fequal=1. the=1. hoare_1870528171valids=1. powp=1. combi=1. zero_zero=1. undefined=1. f22=1. combs=1. combb=1. combc=1. f2=1. f3=1. f16=1. hAPP=1. f1=1. f5=1. f6=1. f7=1. f8=1. f9=1. f10=1. f20=1. f4=1. f11=1. f15=1.
% 211.26/211.57
% 211.26/211.57 ============================== end of process initial clauses ========
% 211.26/211.57
% 211.26/211.57 ============================== CLAUSES FOR SEARCH ====================
% 211.26/211.57
% 211.26/211.57 ============================== end of clauses for search =============
% 211.26/211.57
% 211.26/211.57 ============================== SEARCH ================================
% 211.26/211.57
% 211.26/211.57 % Starting search at 0.16 seconds.
% 211.26/211.57
% 211.26/211.57 Low Water (keep): wt=165.000, iters=3353
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% 211.26/211.57 Low Water (keep): wt=65.000, iters=3394
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% 211.26/211.57 Low Water (keep): wt=63.000, iters=3341
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% 211.26/211.57 Low Water (keep): wt=48.000, iters=3381
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% 211.26/211.57 Low Water (keep): wt=46.000, iters=3387
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% 211.26/211.57 Low Water (keep): wt=42.000, iters=3413
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% 211.26/211.57 Low Water (keep): wt=38.000, iters=3369
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% 211.26/211.57 Low Water (keep): wt=35.000, iters=3474
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% 211.26/211.57 Low Water (keep): wt=33.000, iters=3342
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% 211.26/211.57 Low Water (keep): wt=32.000, iters=3354
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% 211.26/211.57 Low Water (keep): wt=31.000, iters=3346
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% 211.26/211.57 Low Water (keep): wt=30.000, iters=3336
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% 211.26/211.57 Low Water (keep): wt=29.000, iters=3336
% 211.26/211.57
% 211.26/211.57 Low Water (displace): id=3080, wt=199.000
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% 211.26/211.57 Low Water (displace): id=3787, wt=198.000
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% 211.26/211.57 Low Water (displace): id=3410, wt=197.000
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% 211.26/211.57 Low Water (displace): id=15077, wt=196.000
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% 211.26/211.57 Low Water (displace): id=14981, wt=195.000
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% 211.26/211.57 Low Water (displace): id=15285, wt=194.000
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% 211.26/211.57 Low Water (displace): id=10789, wt=193.000
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% 211.26/211.57 Low Water (displace): id=14721, wt=192.000
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% 211.26/211.57 Low Water (displace): id=13378, wt=191.000
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% 211.26/211.57 Low Water (displace): id=14842, wt=190.000
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% 211.26/211.57 Low Water (displace): id=15284, wt=189.000
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% 211.26/211.57 Low Water (displace): id=15819, wt=26.000
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% 211.26/211.57 Low Water (displace): id=16225, wt=25.000
% 211.26/211.57
% 211.26/211.57 Low Water (displace): id=16924, wt=24.000
% 211.26/211.57
% 211.26/211.57 Low Water (keep): wt=28.000, iters=3349
% 211.26/211.57
% 211.26/211.57 Low Water (displace): id=20067, wt=23.000
% 211.26/211.57
% 211.26/211.57 Low Water (displace): id=21227, wt=22.000
% 211.26/211.57
% 211.26/211.57 Low Water (keep): wt=27.000, iters=3343
% 211.26/211.57
% 211.26/211.57 Low Water (keep): wt=26.000, iters=3333
% 211.26/211.57
% 211.26/211.57 ============================== STATISTICS ============================
% 211.26/211.57
% 211.26/211.57 Given=8750. Generated=4751367. Kept=138199. proofs=0.
% 211.26/211.57 Usable=7633. Sos=9999. Demods=368. Limbo=1907, Disabled=118906. Hints=0.
% 211.26/211.57 Kept_by_rule=0, Deleted_by_rule=177823.
% 211.26/211.57 Forward_subsumed=1322349. Back_subsumed=2475.
% 211.26/211.57 Sos_limit_deleted=3112996. Sos_displaced=111671. Sos_removed=0.
% 211.26/211.57 New_demodulators=1577 (0 lex), Back_demodulated=4314. Back_unit_deleted=199.
% 211.26/211.57 Demod_attempts=308245249. Demod_rewrites=3832877.
% 211.26/211.57 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
% 211.26/211.57 Nonunit_fsub_feature_tests=3309529. Nonunit_bsub_feature_tests=466954.
% 211.26/211.57 Megabytes=419.43.
% 211.26/211.57 User_CPU=207.31, System_CPU=3.05, Wall_clock=211.
% 211.26/211.57
% 211.26/211.57 Megs malloced by palloc(): 400.
% 211.26/211.57 type (bytes each) gets frees in use bytes
% 211.26/211.57 chunk ( 104) 12976 12976 0 0.0 K
% 211.26/211.57 string_buf ( 8) 11682 11682 0 0.0 K
% 211.26/211.57 token ( 20) 29396 29396 0 0.0 K
% 211.26/211.57 pterm ( 16) 20875 20875 0 0.0 K
% 211.26/211.57 hashtab ( 8) 147 147 0 0.0 K
% 211.26/211.57 hashnode ( 8) 460 460 0 0.0 K
% 211.26/211.57 term ( 20) 458693535 448045669 10647866 207966.1 K
% 211.26/211.57 term arg arrays: 50075.1 K
% 211.26/211.57 attribute ( 12) 1213 32 1181 13.8 K
% 211.26/211.57 ilist ( 8) 674966203 674171699 794504 6207.1 K
% 211.26/211.57 plist ( 8) 6065498 5899765 165733 1294.8 K
% 211.26/211.57 i2list ( 12) 31362141 31362141 0 0.0 K
% 211.26/211.57 just ( 12) 7435319 7264025 171294 2007.4 K
% 211.26/211.57 parajust ( 16) 2707271 2595528 111743 1746.0 K
% 211.26/211.57 instancejust ( 8) 0 0 0 0.0 K
% 211.26/211.57 ivyjust ( 24) 0 0 0 0.0 K
% 211.26/211.57 formula ( 28) 4934 3034 1900 52.0 K
% 211.26/211.57 formula arg arrays: 6.3 K
% 211.26/211.57 topform ( 52) 4751776 4613168 138608 7038.7 K
% 211.26/211.57 clist_pos ( 20) 404184 265371 138813 2711.2 K
% 211.26/211.57 clist ( 16) 8 1 7 0.1 K
% 211.26/211.57 context ( 808) 29237596 29237594 2 1.6 K
% 211.26/211.57 trail ( 12) 31755179 31755175 4 0.0 K
% 211.26/211.57 ac_match_pos (70044) 0 0 0 0.0 K
% 211.26/211.57 ac_match_free_vars_pos (20020)
% 211.26/211.57 0 0 0 0.0 K
% 211.26/211.57 btm_state ( 60) 0 0 0 0.0 K
% 211.26/211.57 btu_state ( 60) 0 0 0 0.0 K
% 211.26/211.57 ac_position (285432) 0 0 0 0.0 K
% 211.26/211.57 fpa_trie ( 20) 5692310 5311884 380426 7430.2 K
% 211.26/211.57 fpa_state ( 28) 11487150 11487150 0 0.0 K
% 211.26/211.57 fpa_index ( 12) 10 0 10 0.1 K
% 211.26/211.57 fpa_chunk ( 20) 7530460 7404372 126088 2462.7 K
% 211.26/211.57 fpa_list ( 16) 5370370 0 5370370 83912.0 K
% 211.26/211.57 fpa_list chunks: 12525.1 K
% 211.26/211.57 discrim ( 12) 3197547 3104215 93332 1093.7 K
% 211.26/211.57 discrim_pos ( 16) 4933333 4933333 0 0.0 K
% 211.26/211.57 flat2 ( 32) 144821851 144821851 0 0.0 K
% 211.26/211.57 flat ( 48) 0 0 0 0.0 K
% 211.26/211.57 flatterm ( 32) 389310576 389310576 0 0.0 K
% 211.26/211.57 mindex ( 28) 13 0 13 0.4 K
% 211.26/211.57 mindex_pos ( 56) 18925802 18925802 0 0.0 K
% 211.26/211.57 lindex ( 12) 5 0 5 0.1 K
% 211.26/211.57 clash ( 40) 0 0 0 0.0 K
% 211.26/211.57 di_tree ( 12) 14500822 12675544 1825278 21390.0 K
% 211.26/211.57 avl_node ( 20) 272251 252253 19998 390.6 K
% 211.26/211.57
% 211.26/211.57 Memory report, 20 @ 20 = 400 megs (400.00 megs used).
% 211.26/211.57 List 1, length 8, 0.0 K
% 211.26/211.57 List 2, length 274, 2.1 K
% 211.26/211.57 List 3, length 8, 0.1 K
% 211.26/211.57 List 8, length 195, 6.1 K
% 211.26/211.57 List 10, length 11, 0.4 K
% 211.26/211.57 List 11, length 7, 0.3 K
% 211.26/211.57 List 14, length 2, 0.1 K
% 211.26/211.57 List 16, length 13, 0.8 K
% 211.26/211.57 List 26, length 767, 77.9 K
% 211.26/211.57 List 128, length 169, 84.5 K
% 211.26/211.57 List 202, length 2, 1.6 K
% 211.26/211.57 List 256, length 1, 1.0 K
% 211.26/211.57
% 211.26/211.57 ============================== SELECTOR REPORT =======================
% 211.26/211.57 Sos_deleted=3112996, Sos_displaced=111671, Sos_size=9999
% 211.26/211.57 SELECTOR PART PRIORITY ORDER SIZE SELECTED
% 211.26/211.57 I 2147483647 high age 0 217
% 211.26/211.57 H 1 high weight 0 0
% 211.26/211.57 A 1 low age 9999 949
% 211.26/211.57 F 4 low weight 893 3792
% 211.26/211.57 T 4 low weight 9106 3792
% 211.26/211.57 ============================== end of selector report ================
% 211.26/211.57
% 211.26/211.57 ============================== end of statistics =====================
% 211.26/211.57
% 211.26/211.57 Exiting with failure.
% 211.26/211.57
% 211.26/211.57 Process 23870 exit (max_megs) Sun Jun 5 06:15:39 2022
% 211.26/211.57 Prover9 interrupted
%------------------------------------------------------------------------------