TSTP Solution File: SWW472+5 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW472+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 01:17:08 EDT 2022
% Result : Timeout 300.04s 300.34s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW472+5 : TPTP v8.1.0. Released v5.3.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 5 23:58:35 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.92/1.21 ============================== Prover9 ===============================
% 0.92/1.21 Prover9 (32) version 2009-11A, November 2009.
% 0.92/1.21 Process 21011 was started by sandbox on n024.cluster.edu,
% 0.92/1.21 Sun Jun 5 23:58:36 2022
% 0.92/1.21 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_20858_n024.cluster.edu".
% 0.92/1.21 ============================== end of head ===========================
% 0.92/1.21
% 0.92/1.21 ============================== INPUT =================================
% 0.92/1.21
% 0.92/1.21 % Reading from file /tmp/Prover9_20858_n024.cluster.edu
% 0.92/1.21
% 0.92/1.21 set(prolog_style_variables).
% 0.92/1.21 set(auto2).
% 0.92/1.21 % set(auto2) -> set(auto).
% 0.92/1.21 % set(auto) -> set(auto_inference).
% 0.92/1.21 % set(auto) -> set(auto_setup).
% 0.92/1.21 % set(auto_setup) -> set(predicate_elim).
% 0.92/1.21 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.92/1.21 % set(auto) -> set(auto_limits).
% 0.92/1.21 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.92/1.21 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.92/1.21 % set(auto) -> set(auto_denials).
% 0.92/1.21 % set(auto) -> set(auto_process).
% 0.92/1.21 % set(auto2) -> assign(new_constants, 1).
% 0.92/1.21 % set(auto2) -> assign(fold_denial_max, 3).
% 0.92/1.21 % set(auto2) -> assign(max_weight, "200.000").
% 0.92/1.21 % set(auto2) -> assign(max_hours, 1).
% 0.92/1.21 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.92/1.21 % set(auto2) -> assign(max_seconds, 0).
% 0.92/1.21 % set(auto2) -> assign(max_minutes, 5).
% 0.92/1.21 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.92/1.21 % set(auto2) -> set(sort_initial_sos).
% 0.92/1.21 % set(auto2) -> assign(sos_limit, -1).
% 0.92/1.21 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.92/1.21 % set(auto2) -> assign(max_megs, 400).
% 0.92/1.21 % set(auto2) -> assign(stats, some).
% 0.92/1.21 % set(auto2) -> clear(echo_input).
% 0.92/1.21 % set(auto2) -> set(quiet).
% 0.92/1.21 % set(auto2) -> clear(print_initial_clauses).
% 0.92/1.21 % set(auto2) -> clear(print_given).
% 0.92/1.21 assign(lrs_ticks,-1).
% 0.92/1.21 assign(sos_limit,10000).
% 0.92/1.21 assign(order,kbo).
% 0.92/1.21 set(lex_order_vars).
% 0.92/1.21 clear(print_given).
% 0.92/1.21
% 0.92/1.21 % formulas(sos). % not echoed (165 formulas)
% 0.92/1.21
% 0.92/1.21 ============================== end of input ==========================
% 0.92/1.21
% 0.92/1.21 % From the command line: assign(max_seconds, 300).
% 0.92/1.21
% 0.92/1.21 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.92/1.21
% 0.92/1.21 % Formulas that are not ordinary clauses:
% 0.92/1.21 1 (all X_a ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool)),big_semilattice_big(X_a)) = big_semilattice_big(X_a)) # label(tsy_c_Big__Operators_Osemilattice__big_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 2 (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].
% 0.92/1.21 3 (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].
% 0.92/1.21 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].
% 0.92/1.21 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].
% 0.92/1.21 6 (all X_a ti(fun(X_a,fun(fun(vname,fun(fun(state,nat),X_a)),fun(fun(loc,fun(fun(state,nat),fun(com,X_a))),fun(fun(com,fun(com,X_a)),fun(fun(fun(state,bool),fun(com,fun(com,X_a))),fun(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a))))))))),com_case(X_a)) = com_case(X_a)) # label(tsy_c_Com_Ocom_Ocom__case_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 7 (all X_a ti(fun(fun(X_a,bool),bool),finite_finite_1(X_a)) = finite_finite_1(X_a)) # label(tsy_c_Finite__Set_Ofinite_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 8 (all X_a ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a)),finite_fold1(X_a)) = finite_fold1(X_a)) # label(tsy_c_Finite__Set_Ofold1_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 9 (all X_a ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),fun(X_a,bool))),finite_fold1Set(X_a)) = finite_fold1Set(X_a)) # label(tsy_c_Finite__Set_Ofold1Set_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 10 (all X_a all X_b ti(fun(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool)))),finite_fold_graph(X_a,X_b)) = finite_fold_graph(X_a,X_b)) # label(tsy_c_Finite__Set_Ofold__graph_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 11 (all X_a all X_b ti(fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)))),finite908156982e_idem(X_a,X_b)) = finite908156982e_idem(X_a,X_b)) # label(tsy_c_Finite__Set_Ofolding__image__simple__idem_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 12 (all X_a ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool)),finite_folding_one(X_a)) = finite_folding_one(X_a)) # label(tsy_c_Finite__Set_Ofolding__one_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 13 (all X_a ti(fun(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool)),finite2073411215e_idem(X_a)) = finite2073411215e_idem(X_a)) # label(tsy_c_Finite__Set_Ofolding__one__idem_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 14 (all X_a ti(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool))),minus_minus(fun(X_a,bool))) = minus_minus(fun(X_a,bool))) # label(tsy_c_Groups_Ominus__class_Ominus_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 15 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 16 (all X_a ti(fun(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool)),hoare_122391849derivs(X_a)) = hoare_122391849derivs(X_a)) # label(tsy_c_Hoare__Mirabelle__pjuwniqynr_Ohoare__derivs_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 17 (all X_a ti(fun(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool)),hoare_1870528171valids(X_a)) = hoare_1870528171valids(X_a)) # label(tsy_c_Hoare__Mirabelle__pjuwniqynr_Ohoare__valids_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 18 (all X_a ti(fun(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a)))),hoare_1008221573triple(X_a)) = hoare_1008221573triple(X_a)) # label(tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 19 (all X_b all X_a ti(fun(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a))),fun(hoare_509422987triple(X_b),X_a)),hoare_885240885e_case(X_b,X_a)) = hoare_885240885e_case(X_b,X_a)) # label(tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__case_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 20 (all X_b all X_a ti(fun(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a))),fun(hoare_509422987triple(X_b),X_a)),hoare_728318379le_rec(X_b,X_a)) = hoare_728318379le_rec(X_b,X_a)) # label(tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__rec_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 21 (all X_a (bot(X_a) -> ti(X_a,bot_bot(X_a)) = bot_bot(X_a))) # label(tsy_c_Orderings_Obot__class_Obot_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 22 (all X_a ti(fun(fun(X_a,bool),fun(X_a,bool)),collect(X_a)) = collect(X_a)) # label(tsy_c_Set_OCollect_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 23 (all X_a ti(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),insert(X_a)) = insert(X_a)) # label(tsy_c_Set_Oinsert_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 24 (all X_a ti(fun(fun(X_a,bool),X_a),the_elem(X_a)) = the_elem(X_a)) # label(tsy_c_Set_Othe__elem_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 25 (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].
% 0.92/1.21 26 (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].
% 0.92/1.21 27 (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].
% 0.92/1.21 28 (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].
% 0.92/1.21 29 (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].
% 0.92/1.21 30 (all X_a ti(fun(X_a,fun(fun(X_a,bool),bool)),member(X_a)) = member(X_a)) # label(tsy_c_member_res) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 31 (all X_a all G_1 hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_1),bot_bot(fun(hoare_509422987triple(X_a),bool))))) # label(fact_0_empty) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 32 (all X_a all Fun1_1 all Com_1 all Fun2_1 all Fun1_2 all Com_2 all Fun2_2 (hAPP(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a))),hoare_1008221573triple(X_a),Fun1_1),Com_1),Fun2_1) = hAPP(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a))),hoare_1008221573triple(X_a),Fun1_2),Com_2),Fun2_2) <-> Fun1_1 = Fun1_2 & Com_1 = Com_2 & Fun2_1 = Fun2_2)) # label(fact_1_triple_Oinject) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 33 (all X_a all G_1 all Ts (hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_1),Ts)) -> hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_1870528171valids(X_a),G_1),Ts)))) # label(fact_2_hoare__sound) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 34 (all X_a all G_1 all G_2 all Ts (hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_2),Ts)) -> (hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_1),G_2)) -> hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_1),Ts))))) # label(fact_3_cut) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 35 (all X_a all Ts all G_1 all T_3 (hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_1),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),T_3),bot_bot(fun(hoare_509422987triple(X_a),bool))))) -> (hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_1),Ts)) -> hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_1),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),T_3),Ts)))))) # label(fact_4_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 36 (all X_a all G_1 all T_3 all Ts (hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_1),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),T_3),Ts))) -> hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_1),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),T_3),bot_bot(fun(hoare_509422987triple(X_a),bool))))) & hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_1),Ts)))) # label(fact_5_derivs__insertD) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 37 (all X_a all Qa all G_1 all Pa all Ca all Q_2 (hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_1),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a))),hoare_1008221573triple(X_a),Pa),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_a),bool))))) -> ((all Z_1 all S (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Q_2,Z_1),S)) -> hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Qa,Z_1),S)))) -> hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_1),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a))),hoare_1008221573triple(X_a),Pa),Ca),Qa)),bot_bot(fun(hoare_509422987triple(X_a),bool)))))))) # label(fact_6_conseq2) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 38 (all X_a all Pa all G_1 all P_2 all Ca all Qa (hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_1),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a))),hoare_1008221573triple(X_a),P_2),Ca),Qa)),bot_bot(fun(hoare_509422987triple(X_a),bool))))) -> ((all Z_1 all S (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Pa,Z_1),S)) -> hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),P_2,Z_1),S)))) -> hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_1),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a))),hoare_1008221573triple(X_a),Pa),Ca),Qa)),bot_bot(fun(hoare_509422987triple(X_a),bool)))))))) # label(fact_7_conseq1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 39 (all X_a all A_1 all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),A_2))) -> (ti(X_a,A_1) != ti(X_a,B_1) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2))))) # label(fact_8_insertE) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 40 (all X_a all B_1 all A_1 all B ((-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),B)) -> ti(X_a,A_1) = ti(X_a,B_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),B))))) # label(fact_9_insertCI) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 41 (all X_a all Qa all Pa all G_1 all P_2 all Ca all Q_2 (hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_1),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a))),hoare_1008221573triple(X_a),P_2),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_a),bool))))) -> ((all Z_1 all S (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Pa,Z_1),S)) -> (all S_1 ((all Z_2 (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),P_2,Z_2),S)) -> hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Q_2,Z_2),S_1)))) -> hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Qa,Z_1),S_1)))))) -> hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_1),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a))),hoare_1008221573triple(X_a),Pa),Ca),Qa)),bot_bot(fun(hoare_509422987triple(X_a),bool)))))))) # label(fact_10_conseq12) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 42 (all X_a all A_1 -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),bot_bot(fun(X_a,bool))))) # label(fact_11_emptyE) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 43 (all X_b all X_a all F1 all Fun1_1 all Com_1 all Fun2_1 hAPP(hoare_509422987triple(X_b),X_a,hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a))),fun(hoare_509422987triple(X_b),X_a),hoare_728318379le_rec(X_b,X_a),F1),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)),X_a,hAPP(com,fun(fun(X_b,fun(state,bool)),X_a),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a)),F1,Fun1_1),Com_1),Fun2_1)) # label(fact_12_triple_Orecs) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 44 (all X_b all X_a all F1 all Fun1_1 all Com_1 all Fun2_1 hAPP(hoare_509422987triple(X_b),X_a,hAPP(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a))),fun(hoare_509422987triple(X_b),X_a),hoare_885240885e_case(X_b,X_a),F1),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)),X_a,hAPP(com,fun(fun(X_b,fun(state,bool)),X_a),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),X_a)),F1,Fun1_1),Com_1),Fun2_1)) # label(fact_13_triple_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 45 (all X_a all A_1 all A_2 bot_bot(fun(X_a,bool)) != hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2)) # label(fact_14_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 46 (all X_a all A_1 all A_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2) != bot_bot(fun(X_a,bool))) # label(fact_15_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 47 (all X_a all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool))))) <-> ti(X_a,B_1) = ti(X_a,A_1))) # label(fact_16_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 48 (all X_a all A_1 all B_1 all Ca all D (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),bot_bot(fun(X_a,bool)))) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),D),bot_bot(fun(X_a,bool)))) <-> ti(X_a,A_1) = ti(X_a,Ca) & ti(X_a,B_1) = ti(X_a,D) | ti(X_a,A_1) = ti(X_a,D) & ti(X_a,B_1) = ti(X_a,Ca))) # label(fact_17_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 49 (all X_a all A_1 all A_2 (ti(fun(X_a,bool),A_2) = bot_bot(fun(X_a,bool)) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)))) # label(fact_18_equals0D) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 50 (all X_a all Pa (hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa) = bot_bot(fun(X_a,bool)) <-> (all X_2 -hBOOL(hAPP(X_a,bool,Pa,X_2))))) # label(fact_19_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 51 (all X_a all Ca -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),bot_bot(fun(X_a,bool))))) # label(fact_20_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 52 (all X_a all Pa (bot_bot(fun(X_a,bool)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa) <-> (all X_2 -hBOOL(hAPP(X_a,bool,Pa,X_2))))) # label(fact_21_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 53 (all X_a all A_2 ((exists X_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2))) <-> ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)))) # label(fact_22_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 54 (all X_a all A_2 ((all X_2 -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_2))) <-> ti(fun(X_a,bool),A_2) = bot_bot(fun(X_a,bool)))) # label(fact_23_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 55 (all X_a bot_bot(fun(X_a,bool)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(bool,fun(X_a,bool),combk(bool,X_a),fFalse))) # label(fact_24_empty__def) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 56 (all X_a all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2) = ti(fun(X_a,bool),A_2))) # label(fact_25_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.21 57 (all X_a all B_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),B)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),B))))) # label(fact_26_insertI2) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 58 (all X_a all B all X_1 all A_2 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),A_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),B) <-> ti(fun(X_a,bool),A_2) = ti(fun(X_a,bool),B))))) # label(fact_27_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 59 (all X_a all Y_2 all A_2 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_2),A_2),X_1)) <-> ti(X_a,Y_2) = ti(X_a,X_1) | hBOOL(hAPP(X_a,bool,A_2,X_1)))) # label(fact_28_insert__code) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 60 (all X_a all A_1 all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),A_2))) <-> ti(X_a,A_1) = ti(X_a,B_1) | hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)))) # label(fact_29_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 61 (all X_a all X_1 all Y_2 all A_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_2),A_2)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),A_2))) # label(fact_30_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 62 (all X_a all X_1 all A_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),A_2)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),A_2)) # label(fact_31_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 63 (all X_a all A_1 all Pa hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fimplies),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_1)))),Pa))) # label(fact_32_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 64 (all X_a all A_1 all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),B) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B)))) # label(fact_33_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 65 (all X_a all A_1 all B hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),B)))) # label(fact_34_insertI1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 66 (all X_a all A_1 all B_1 (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool))) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),bot_bot(fun(X_a,bool))) -> ti(X_a,A_1) = ti(X_a,B_1))) # label(fact_35_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 67 (all X_a all B_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool))))) -> ti(X_a,B_1) = ti(X_a,A_1))) # label(fact_36_singletonE) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 68 (all X_a all X_1 hAPP(fun(X_a,bool),X_a,the_elem(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),bot_bot(fun(X_a,bool)))) = ti(X_a,X_1)) # label(fact_37_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 69 (all X_b all X_a (bot(X_a) -> (all X_1 hAPP(X_b,X_a,bot_bot(fun(X_b,X_a)),X_1) = bot_bot(X_a)))) # label(fact_38_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 70 (all X_a all X_b (bot(X_b) -> (all X_2 hAPP(X_a,X_b,bot_bot(fun(X_a,X_b)),X_2) = bot_bot(X_b)))) # label(fact_39_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 71 (all X_a all G_1 all Pa hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_1),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a))),hoare_1008221573triple(X_a),Pa),skip),Pa)),bot_bot(fun(hoare_509422987triple(X_a),bool)))))) # label(fact_40_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 72 (all X_a all D all R_1 all G_1 all Pa all Ca all Qa (hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_1),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a))),hoare_1008221573triple(X_a),Pa),Ca),Qa)),bot_bot(fun(hoare_509422987triple(X_a),bool))))) -> (hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_1),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a))),hoare_1008221573triple(X_a),Qa),D),R_1)),bot_bot(fun(hoare_509422987triple(X_a),bool))))) -> hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_1),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a))),hoare_1008221573triple(X_a),Pa),hAPP(com,com,hAPP(com,fun(com,com),semi,Ca),D)),R_1)),bot_bot(fun(hoare_509422987triple(X_a),bool)))))))) # label(fact_41_Comp) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 73 (all X_a all Y_2 -(all Fun1 all Com all Fun2 Y_2 != hAPP(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a))),hoare_1008221573triple(X_a),Fun1),Com),Fun2))) # label(fact_42_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 74 (all X_a all X_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> -(all B_2 (ti(fun(X_a,bool),A_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),B_2) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_2)))))) # label(fact_43_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 75 (all X_a all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> (exists B_2 (ti(fun(X_a,bool),A_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),B_2) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),B_2)))))) # label(fact_44_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 76 (all Com1_2 all Com2_2 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2) != skip) # label(fact_45_com_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 77 (all Com1_2 all Com2_2 skip != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2)) # label(fact_46_com_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 78 (all X_a all A_2 ((all Y_1 -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_2))) -> ti(fun(X_a,bool),A_2) = bot_bot(fun(X_a,bool)))) # label(fact_47_equals0I) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 79 (all X_a all Qa all G_1 all Ca all Pa ((all Z_1 all S (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Pa,Z_1),S)) -> (exists P_1 exists Q_1 (hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_1),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a))),hoare_1008221573triple(X_a),P_1),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_a),bool))))) & (all S_1 ((all Z_2 (hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),P_1,Z_2),S)) -> hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Q_1,Z_2),S_1)))) -> hBOOL(hAPP(state,bool,hAPP(X_a,fun(state,bool),Qa,Z_1),S_1)))))))) -> hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_1),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a),hAPP(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a)),hAPP(fun(X_a,fun(state,bool)),fun(com,fun(fun(X_a,fun(state,bool)),hoare_509422987triple(X_a))),hoare_1008221573triple(X_a),Pa),Ca),Qa)),bot_bot(fun(hoare_509422987triple(X_a),bool))))))) # label(fact_48_conseq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 80 (all Com1 all Com2 all Com1_1 all Com2_1 (hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2) = hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1) <-> Com1 = Com1_1 & Com2 = Com2_1)) # label(fact_49_com_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 81 (all X_a all A_2 (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) <-> (exists X_2 exists B_2 (ti(fun(X_a,bool),A_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),B_2) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B_2)))))) # label(fact_50_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 82 (all X_a all X_2 (hBOOL(hAPP(X_a,bool,bot_bot(fun(X_a,bool)),X_2)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),bot_bot(fun(X_a,bool)))))) # label(fact_51_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 83 (all X_a all F1 all F2 all F3 all F4 all F5 all F6 all F7 all F8 hAPP(com,X_a,hAPP(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a),hAPP(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a)),hAPP(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a))),hAPP(fun(fun(state,bool),fun(com,fun(com,X_a))),fun(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a)))),hAPP(fun(com,fun(com,X_a)),fun(fun(fun(state,bool),fun(com,fun(com,X_a))),fun(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a))))),hAPP(fun(loc,fun(fun(state,nat),fun(com,X_a))),fun(fun(com,fun(com,X_a)),fun(fun(fun(state,bool),fun(com,fun(com,X_a))),fun(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a)))))),hAPP(fun(vname,fun(fun(state,nat),X_a)),fun(fun(loc,fun(fun(state,nat),fun(com,X_a))),fun(fun(com,fun(com,X_a)),fun(fun(fun(state,bool),fun(com,fun(com,X_a))),fun(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a))))))),hAPP(X_a,fun(fun(vname,fun(fun(state,nat),X_a)),fun(fun(loc,fun(fun(state,nat),fun(com,X_a))),fun(fun(com,fun(com,X_a)),fun(fun(fun(state,bool),fun(com,fun(com,X_a))),fun(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a)))))))),com_case(X_a),F1),F2),F3),F4),F5),F6),F7),F8),skip) = ti(X_a,F1)) # label(fact_52_com_Osimps_I64_J) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 84 (all X_a all F1 all F2 all F3 all F4 all F5 all F6 all F7 all F8 all Com1 all Com2 hAPP(com,X_a,hAPP(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a),hAPP(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a)),hAPP(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a))),hAPP(fun(fun(state,bool),fun(com,fun(com,X_a))),fun(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a)))),hAPP(fun(com,fun(com,X_a)),fun(fun(fun(state,bool),fun(com,fun(com,X_a))),fun(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a))))),hAPP(fun(loc,fun(fun(state,nat),fun(com,X_a))),fun(fun(com,fun(com,X_a)),fun(fun(fun(state,bool),fun(com,fun(com,X_a))),fun(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a)))))),hAPP(fun(vname,fun(fun(state,nat),X_a)),fun(fun(loc,fun(fun(state,nat),fun(com,X_a))),fun(fun(com,fun(com,X_a)),fun(fun(fun(state,bool),fun(com,fun(com,X_a))),fun(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a))))))),hAPP(X_a,fun(fun(vname,fun(fun(state,nat),X_a)),fun(fun(loc,fun(fun(state,nat),fun(com,X_a))),fun(fun(com,fun(com,X_a)),fun(fun(fun(state,bool),fun(com,fun(com,X_a))),fun(fun(fun(state,bool),fun(com,X_a)),fun(fun(pname,X_a),fun(fun(vname,fun(pname,fun(fun(state,nat),X_a))),fun(com,X_a)))))))),com_case(X_a),F1),F2),F3),F4),F5),F6),F7),F8),hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2)) = hAPP(com,X_a,hAPP(com,fun(com,X_a),F4,Com1),Com2)) # label(fact_53_com_Osimps_I67_J) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 85 (all X_a all F_1 all A_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),fun(X_a,bool)),finite_fold1Set(X_a),F_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool)))),B_1)) <-> ti(X_a,A_1) = ti(X_a,B_1))) # label(fact_54_fold1Set__sing) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 86 (all X_a all X_1 all F_1 all F (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F_1),F)) -> hAPP(fun(X_a,bool),X_a,F,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),bot_bot(fun(X_a,bool)))) = ti(X_a,X_1))) # label(fact_55_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 87 (all X_a all F_1 all A_1 hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),F_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool)))) = ti(X_a,A_1)) # label(fact_56_fold1__singleton) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 88 (all X_a all A_1 all G all F_1 (G = hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),F_1) -> hAPP(fun(X_a,bool),X_a,G,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool)))) = ti(X_a,A_1))) # label(fact_57_fold1__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 89 (all X_a all F_1 all X_1 -hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),fun(X_a,bool)),finite_fold1Set(X_a),F_1),bot_bot(fun(X_a,bool))),X_1))) # label(fact_58_empty__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 90 (all X_a all F_1 all A_2 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),fun(X_a,bool)),finite_fold1Set(X_a),F_1),A_2),X_1)) -> ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)))) # label(fact_59_fold1Set__nonempty) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 91 (all X_a all F_1 all A_1 all A_2 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),finite_fold_graph(X_a,X_a),F_1),A_1),A_2),X_1)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),fun(X_a,bool)),finite_fold1Set(X_a),F_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2)),X_1))))) # label(fact_60_fold1Set_Ointros) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 92 (all X_a all X_1 all A_2 all F_1 all F (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F_1),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,F,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F_1,X_1),hAPP(fun(X_a,bool),X_a,F,A_2))))))) # label(fact_61_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 93 (all X_a all A_2 all F_1 all F (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F_1),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_a,F,A_2) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),F_1),A_2)))) # label(fact_62_folding__one_Oeq__fold) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 94 (all X_a hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),bot_bot(fun(X_a,bool))))) # label(fact_63_finite_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 95 (all X_a all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2))))) # label(fact_64_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 96 (all X_b all X_a all F_1 all Z hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),finite_fold_graph(X_a,X_b),F_1),Z),bot_bot(fun(X_a,bool))),Z))) # label(fact_65_fold__graph_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 97 (all X_b all X_a all F_1 all Z all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),finite_fold_graph(X_a,X_b),F_1),Z),bot_bot(fun(X_a,bool))),X_1)) -> ti(X_b,X_1) = ti(X_b,Z))) # label(fact_66_empty__fold__graphE) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 98 (all X_b all X_a all F_1 all Z all Y_2 all X_1 all A_2 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),finite_fold_graph(X_a,X_b),F_1),Z),A_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),finite_fold_graph(X_a,X_b),F_1),Z),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),A_2)),hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F_1,X_1),Y_2)))))) # label(fact_67_fold__graph_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 99 (all X_a (finite_finite(X_a) -> (all A_2 hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2))))) # label(fact_68_finite) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 100 (all X_a (finite_finite(X_a) -> (all A_2 hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2))))) # label(fact_69_finite__code) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 101 (all X_a all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)))) # label(fact_70_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 102 (all X_a all A_2 all F_1 all F (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F_1),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> ((all X_2 all Y_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F_1,X_2),Y_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_1),bot_bot(fun(X_a,bool))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(fun(X_a,bool),X_a,F,A_2)),A_2))))))) # label(fact_71_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 103 (all X_a all F_1 all A_1 all X_3 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),fun(X_a,bool)),finite_fold1Set(X_a),F_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),X_3)),X_1)) -> -(all A_4 all A_3 (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),X_3) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_4),A_3) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),finite_fold_graph(X_a,X_a),F_1),A_4),A_3),X_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_4),A_3))))))) # label(fact_72_insert__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 104 (all X_a all F_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> (exists X1 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),fun(X_a,bool)),finite_fold1Set(X_a),F_1),A_2),X1)))))) # label(fact_73_finite__nonempty__imp__fold1Set) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 105 (all X_a all Pa all F (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,Pa,bot_bot(fun(X_a,bool)))) -> ((all X_2 all F_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),F_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,Pa,F_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,Pa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),F_2))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,Pa,F)))))) # label(fact_74_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 106 (all X_a all X_b all F_1 all G ((all X_2 hAPP(X_a,X_b,F_1,X_2) = hAPP(X_a,X_b,G,X_2)) -> ti(fun(X_a,X_b),F_1) = ti(fun(X_a,X_b),G))) # label(fact_75_ext) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 107 (all X_a all X_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) <-> hBOOL(hAPP(X_a,bool,A_2,X_1)))) # label(fact_76_mem__def) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 108 (all X_a all Pa hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa) = ti(fun(X_a,bool),Pa)) # label(fact_77_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 109 (all X_a all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_1)) <-> ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)) | (exists A_3 exists A_4 (ti(fun(X_a,bool),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_4),A_3) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)))))) # label(fact_78_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 110 (all X_b all X_a all F_1 all Z all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (exists X1 hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),finite_fold_graph(X_a,X_b),F_1),Z),A_2),X1))))) # label(fact_79_finite__imp__fold__graph) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 111 (all X_a all F_1 all A1 all A2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),fun(X_a,bool)),finite_fold1Set(X_a),F_1),A1),A2)) <-> (exists A_4 exists A_3 exists X_2 (ti(fun(X_a,bool),A1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_4),A_3) & ti(X_a,A2) = ti(X_a,X_2) & hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),finite_fold_graph(X_a,X_a),F_1),A_4),A_3),X_2)) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_4),A_3)))))) # label(fact_80_fold1Set_Osimps) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 112 (all X_b all X_a all F_1 all Z all A1 all A2 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),finite_fold_graph(X_a,X_b),F_1),Z),A1),A2)) <-> ti(fun(X_a,bool),A1) = bot_bot(fun(X_a,bool)) & ti(X_b,A2) = ti(X_b,Z) | (exists X_2 exists A_3 exists Y_1 (ti(fun(X_a,bool),A1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_3) & ti(X_b,A2) = hAPP(X_b,X_b,hAPP(X_a,fun(X_b,X_b),F_1,X_2),Y_1) & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) & hBOOL(hAPP(X_b,bool,hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(fun(X_a,bool),fun(X_b,bool))),finite_fold_graph(X_a,X_b),F_1),Z),A_3),Y_1)))))) # label(fact_81_fold__graph_Osimps) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 113 (all X_a all X_1 all A_2 all F_1 all F (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite2073411215e_idem(X_a),F_1),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (ti(fun(X_a,bool),A_2) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,F,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F_1,X_1),hAPP(fun(X_a,bool),X_a,F,A_2)))))) # label(fact_82_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 114 (all X_a all X_1 all F_1 all F (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite2073411215e_idem(X_a),F_1),F)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F_1,X_1),X_1) = ti(X_a,X_1))) # label(fact_83_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 115 (all X_a all X_1 all A_2 all F_1 all F (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite2073411215e_idem(X_a),F_1),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F_1,X_1),hAPP(fun(X_a,bool),X_a,F,A_2)) = hAPP(fun(X_a,bool),X_a,F,A_2))))) # label(fact_84_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 116 (all X_a all Pa all F (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F)) -> (ti(fun(X_a,bool),F) != bot_bot(fun(X_a,bool)) -> ((all X_2 hBOOL(hAPP(fun(X_a,bool),bool,Pa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))))) -> ((all X_2 all F_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_2)) -> (ti(fun(X_a,bool),F_2) != bot_bot(fun(X_a,bool)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),F_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,Pa,F_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,Pa,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),F_2)))))))) -> hBOOL(hAPP(fun(X_a,bool),bool,Pa,F))))))) # label(fact_85_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 117 (all X_b all X_a all X_1 all A_2 all F_1 all Z all G all F (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F_1),Z),G),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_2)) -> hAPP(fun(X_b,bool),X_a,F,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_1),A_2)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F_1,hAPP(X_b,X_a,G,X_1)),hAPP(fun(X_b,bool),X_a,F,A_2))))) # label(fact_86_folding__image__simple__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.22 118 (all X_b all X_a all X_1 all F_1 all Z all G all F (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F_1),Z),G),F)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F_1,X_1),X_1) = ti(X_a,X_1))) # label(fact_87_folding__image__simple__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 119 (all X_b all X_a all X_1 all A_2 all F_1 all Z all G all F (hBOOL(hAPP(fun(fun(X_b,bool),X_a),bool,hAPP(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool),hAPP(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool)),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(fun(X_b,X_a),fun(fun(fun(X_b,bool),X_a),bool))),finite908156982e_idem(X_a,X_b),F_1),Z),G),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_2)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F_1,hAPP(X_b,X_a,G,X_1)),hAPP(fun(X_b,bool),X_a,F,A_2)) = hAPP(fun(X_b,bool),X_a,F,A_2))))) # label(fact_88_folding__image__simple__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 120 (all X_a all A_2 all F_1 all F (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),big_semilattice_big(X_a),F_1),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hAPP(fun(X_a,bool),X_a,F,A_2) = hAPP(fun(X_a,bool),X_a,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,bool),X_a),finite_fold1(X_a),F_1),A_2)))) # label(fact_89_semilattice__big_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 121 (all X_a all X_1 all A_2 all F_1 all F (hBOOL(hAPP(fun(fun(X_a,bool),X_a),bool,hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(fun(X_a,bool),X_a),bool),finite_folding_one(X_a),F_1),F)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),bot_bot(fun(X_a,bool)))) = bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,F,A_2) = ti(X_a,X_1)) & (hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),bot_bot(fun(X_a,bool)))) != bot_bot(fun(X_a,bool)) -> hAPP(fun(X_a,bool),X_a,F,A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),F_1,X_1),hAPP(fun(X_a,bool),X_a,F,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),bot_bot(fun(X_a,bool))))))))))) # label(fact_90_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 122 (all X_a all B all Ca all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_2)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B)))))) # label(fact_91_DiffI) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 123 (all X_a all Ca all A_2 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B))) -> -(hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B))))) # label(fact_92_DiffE) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 124 (all X_a all B all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B))))) # label(fact_93_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 125 (all X_a all A_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_1),A_2)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool))))) = ti(fun(X_a,bool),A_2))) # label(fact_94_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 126 (all X_a all X_1 all A_2 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_2)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),A_2)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),bot_bot(fun(X_a,bool)))) = ti(fun(X_a,bool),A_2))) # label(fact_95_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 127 (all X_a all A_1 all A_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool))))) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),A_2)) # label(fact_96_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 128 (all X_a all A_2 all A_1 all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),B)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool))))),B)) # label(fact_97_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 129 (all X_a all A_2 all A_1 all B hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),B)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),bot_bot(fun(X_a,bool))))) # label(fact_98_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 130 (all X_a all A_2 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_1),B)))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_2),B))))) # label(fact_99_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 131 (all T_2 all T_1 (finite_finite(T_1) & finite_finite(T_2) -> finite_finite(fun(T_2,T_1)))) # label(arity_fun___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 132 (all T_2 all T_1 (bot(T_1) -> bot(fun(T_2,T_1)))) # label(arity_fun___Orderings_Obot) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.23 133 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.33 134 (all P (-hBOOL(hAPP(bool,bool,fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.33 135 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.33 136 (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].
% 0.92/1.33 137 (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].
% 0.92/1.33 138 (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].
% 0.92/1.33 139 (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].
% 0.92/1.33 140 (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].
% 0.92/1.33 141 (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].
% 0.92/1.33 142 (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].
% 0.92/1.33 143 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.33 144 (all X_a all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)) | ti(X_a,X) = ti(X_a,Y))) # label(help_fequal_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.33 145 (all X_a all X all Y (ti(X_a,X) != ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)))) # label(help_fequal_2_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.33 146 (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].
% 0.92/1.33 147 (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].
% 0.92/1.33 148 (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].
% 0.92/1.33
% 0.92/1.33 ============================== end of process non-clausal formulas ===
% 0.92/1.33
% 0.92/1.33 ============================== PROCESS INITIAL CLAUSES ===============
% 0.92/1.33
% 0.92/1.33 ============================== PREDICATE ELIMINATION =================
% 0.92/1.33
% 0.92/1.33 ============================== end predicate elimination =============
% 0.92/1.33
% 0.92/1.33 Auto_denials: (non-Horn, no changes).
% 0.92/1.33
% 0.92/1.33 Term ordering decisions:
% 0.92/1.33 Function symbol KB weights: bool=1. state=1. com=1. pname=1. nat=1. vname=1. semi=1. loc=1. fdisj=1. fimplies=1. c=1. fFalse=1. fNot=1. skip=1. fTrue=1. hoare_Mirabelle_MGT=1. p=1. q=1. fun=1. ti=1. finite_fold_graph=1. finite908156982e_idem=1. combk=1. hoare_728318379le_rec=1. hoare_885240885e_case=1. f8=1. f9=1. f10=1. f11=1. f12=1. f13=1. f14=1. f17=1. f21=1. f22=1. f31=1. f32=1. hoare_509422987triple=1. insert=1. bot_bot=1. member=1. finite_finite_1=1. hoare_122391849derivs=1. hoare_1008221573triple=1. minus_minus=1. finite_fold1Set=1. collect=1. finite_folding_one=1. fequal=1. finite_fold1=1. finite2073411215e_idem=1. com_case=1. hoare_1870528171valids=1. big_semilattice_big=1. the_elem=1. undefined=1. combb=1. combc=1. combs=1. f15=1. f16=1. f27=1. f28=1. f29=1. f40=1. f41=1. f42=1. hAPP=1. f23=1. f24=1. f30=1. f34=1. f35=1. f36=Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------