TSTP Solution File: SWW473+5 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW473+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 01:17:09 EDT 2022
% Result : Theorem 29.87s 30.20s
% Output : Refutation 29.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWW473+5 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 5 09:55:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.80/1.13 ============================== Prover9 ===============================
% 0.80/1.13 Prover9 (32) version 2009-11A, November 2009.
% 0.80/1.13 Process 6433 was started by sandbox2 on n024.cluster.edu,
% 0.80/1.13 Sun Jun 5 09:55:51 2022
% 0.80/1.13 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_6279_n024.cluster.edu".
% 0.80/1.13 ============================== end of head ===========================
% 0.80/1.13
% 0.80/1.13 ============================== INPUT =================================
% 0.80/1.13
% 0.80/1.13 % Reading from file /tmp/Prover9_6279_n024.cluster.edu
% 0.80/1.13
% 0.80/1.13 set(prolog_style_variables).
% 0.80/1.13 set(auto2).
% 0.80/1.13 % set(auto2) -> set(auto).
% 0.80/1.13 % set(auto) -> set(auto_inference).
% 0.80/1.13 % set(auto) -> set(auto_setup).
% 0.80/1.13 % set(auto_setup) -> set(predicate_elim).
% 0.80/1.13 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.80/1.13 % set(auto) -> set(auto_limits).
% 0.80/1.13 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.80/1.13 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.80/1.13 % set(auto) -> set(auto_denials).
% 0.80/1.13 % set(auto) -> set(auto_process).
% 0.80/1.13 % set(auto2) -> assign(new_constants, 1).
% 0.80/1.13 % set(auto2) -> assign(fold_denial_max, 3).
% 0.80/1.13 % set(auto2) -> assign(max_weight, "200.000").
% 0.80/1.13 % set(auto2) -> assign(max_hours, 1).
% 0.80/1.13 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.80/1.13 % set(auto2) -> assign(max_seconds, 0).
% 0.80/1.13 % set(auto2) -> assign(max_minutes, 5).
% 0.80/1.13 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.80/1.13 % set(auto2) -> set(sort_initial_sos).
% 0.80/1.13 % set(auto2) -> assign(sos_limit, -1).
% 0.80/1.13 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.80/1.13 % set(auto2) -> assign(max_megs, 400).
% 0.80/1.13 % set(auto2) -> assign(stats, some).
% 0.80/1.13 % set(auto2) -> clear(echo_input).
% 0.80/1.13 % set(auto2) -> set(quiet).
% 0.80/1.13 % set(auto2) -> clear(print_initial_clauses).
% 0.80/1.13 % set(auto2) -> clear(print_given).
% 0.80/1.13 assign(lrs_ticks,-1).
% 0.80/1.13 assign(sos_limit,10000).
% 0.80/1.13 assign(order,kbo).
% 0.80/1.13 set(lex_order_vars).
% 0.80/1.13 clear(print_given).
% 0.80/1.13
% 0.80/1.13 % formulas(sos). % not echoed (161 formulas)
% 0.80/1.13
% 0.80/1.13 ============================== end of input ==========================
% 0.80/1.13
% 0.80/1.13 % From the command line: assign(max_seconds, 300).
% 0.80/1.13
% 0.80/1.13 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.80/1.13
% 0.80/1.13 % Formulas that are not ordinary clauses:
% 0.80/1.13 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].
% 0.80/1.13 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].
% 0.80/1.13 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].
% 0.80/1.13 4 (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].
% 0.80/1.13 5 (all X_c ti(fun(fun(X_c,bool),nat),finite_card(X_c)) = finite_card(X_c)) # label(tsy_c_Finite__Set_Ocard_res) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 6 (all X_b ti(fun(fun(X_b,bool),bool),finite_finite(X_b)) = finite_finite(X_b)) # label(tsy_c_Finite__Set_Ofinite_res) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 7 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 8 (all X_a (preorder(X_a) -> ti(fun(X_a,fun(X_a,bool)),ord_less_eq(X_a)) = ord_less_eq(X_a))) # label(tsy_c_Orderings_Oord__class_Oless__eq_res) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 9 (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].
% 0.80/1.13 10 (all X_b all X_c ti(fun(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool))),image(X_b,X_c)) = image(X_b,X_c)) # label(tsy_c_Set_Oimage_res) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 11 (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].
% 0.80/1.13 12 (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].
% 0.80/1.13 13 (all X_a all X_c all B_1_1 all B_2 hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2) = hAPP(X_a,X_c,B_1_1,B_2)) # label(tsy_c_hAPP_arg1) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 14 (all X_a all X_c all B_1_1 all B_2 hAPP(X_a,X_c,B_1_1,ti(X_a,B_2)) = hAPP(X_a,X_c,B_1_1,B_2)) # label(tsy_c_hAPP_arg2) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 15 (all X_c all X_a all B_1_1 all B_2 ti(X_c,hAPP(X_a,X_c,B_1_1,B_2)) = hAPP(X_a,X_c,B_1_1,B_2)) # label(tsy_c_hAPP_res) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 16 (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].
% 0.80/1.13 17 (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].
% 0.80/1.13 18 (all Ts all G_1 (hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),Ts),G_1)) -> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,G_1),Ts)))) # label(fact_0_assms_I1_J) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 19 (all X_b all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> hBOOL(hAPP(fun(fun(X_b,bool),bool),bool,finite_finite(fun(X_b,bool)),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,bool),bool),collect(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(fun(X_b,bool),bool)),combc(fun(X_b,bool),fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool))),A_1)))))) # label(fact_1_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 20 (all X_c all X_b all H all F_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),F_1)) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),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),H),F_1))))) # label(fact_2_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 21 (all X_b all A_2 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_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),A_1))))) # label(fact_3_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 22 (all X_c all X_b all F all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_c,bool),nat,finite_card(X_c),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))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1))))) # label(fact_4_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 23 (all X_b all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B)))))) # label(fact_5_card__mono) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 24 (all X_b all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),B)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1))) -> ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B))))) # label(fact_6_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 25 (all X_b all X_2 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1)),hAPP(fun(X_b,bool),nat,finite_card(X_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),X_2),A_1)))))) # label(fact_7_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 26 (all X_b all X_2 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),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),nat,finite_card(X_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),X_2),A_1)) = hAPP(fun(X_b,bool),nat,finite_card(X_b),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),nat,finite_card(X_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),X_2),A_1)) = hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1))))) # label(fact_8_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 27 (all X_b all X_2 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),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),nat,finite_card(X_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),X_2),A_1)) = hAPP(nat,nat,suc,hAPP(fun(X_b,bool),nat,finite_card(X_b),A_1))))) # label(fact_9_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 28 (all X_b all Q_1 all Pa (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) | hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),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),Pa)),Q_1)))))) # label(fact_10_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 29 (all N_1 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_2)),N_1) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),N_1)))) # label(fact_11_Suc__diff__le) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 30 (all K hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),K))))) # label(fact_12_finite__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 31 (all Na hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),Na))) = hAPP(nat,nat,suc,Na)) # label(fact_13_card__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 32 (all X_b (finite_finite_1(X_b) -> (all A_1 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1))))) # label(fact_14_finite__code) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 33 (all X_b (finite_finite_1(X_b) -> (all A_1 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1))))) # label(fact_15_finite) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 34 (all X all Y (hAPP(nat,nat,suc,X) = hAPP(nat,nat,suc,Y) -> X = Y)) # label(fact_16_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 35 (all Nat_1 all Nat (hAPP(nat,nat,suc,Nat_1) = hAPP(nat,nat,suc,Nat) <-> Nat_1 = Nat)) # label(fact_17_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 36 (all N_1 hAPP(nat,nat,suc,N_1) != N_1) # label(fact_18_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 37 (all N_1 N_1 != hAPP(nat,nat,suc,N_1)) # label(fact_19_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.13 38 (all M_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_2)) -> M_2 = N_1))) # label(fact_20_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 39 (all K_1 all I_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),K_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),K_1))))) # label(fact_21_le__trans) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 40 (all M_2 all N_1 (M_2 = N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)))) # label(fact_22_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 41 (all M_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_2)))) # label(fact_23_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 42 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_1))) # label(fact_24_le__refl) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 43 (all I_1 all J all K_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J)),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),K_1)),J)) # label(fact_25_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 44 (all X_b all Pa all Q_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),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)),Q_1)))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_1))))) # label(fact_26_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 45 (all X_b all A_2 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_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),A_1))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)))) # label(fact_27_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 46 (all X_b all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1))))) # label(fact_28_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 47 (all X_b all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1))))) # label(fact_29_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 48 (all M_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_2)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)))) # label(fact_30_Suc__leD) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 49 (all M_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),hAPP(nat,nat,suc,N_1))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) -> M_2 = hAPP(nat,nat,suc,N_1)))) # label(fact_31_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 50 (all M_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),hAPP(nat,nat,suc,N_1))))) # label(fact_32_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 51 (all Na all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),hAPP(nat,nat,suc,M_3))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),M_3)))) # label(fact_33_Suc__le__mono) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 52 (all M_3 all Na (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),hAPP(nat,nat,suc,Na))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),Na)) | M_3 = hAPP(nat,nat,suc,Na))) # label(fact_34_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 53 (all M_3 all Na (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),Na)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Na)),M_3)))) # label(fact_35_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 54 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),N_1))) # label(fact_36_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 55 (all M_2 all N_1 all K_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_2)),N_1)),hAPP(nat,nat,suc,K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),N_1)),K_1)) # label(fact_37_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 56 (all M_2 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M_2)),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),N_1)) # label(fact_38_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 57 (all Na all K all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),M_3)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),Na)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_3),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),Na)))))) # label(fact_39_le__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 58 (all N_1 all K_1 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),N_1)))) # label(fact_40_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 59 (all Na all K all M_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),M_3)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),Na)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_3),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Na),K) <-> M_3 = Na)))) # label(fact_41_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 60 (all I_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),N_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),I_1)) = I_1)) # label(fact_42_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 61 (all L all M_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),L)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),L))))) # label(fact_43_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 62 (all L all M_2 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L),M_2))))) # label(fact_44_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 63 (all M_2 all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_2),N_1)),M_2))) # label(fact_45_diff__le__self) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 64 (all X_c all X_b all B all F all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),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))) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),B))))) # label(fact_46_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 65 (all X_c all X_b all F all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),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))) -> (exists C_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),C_2),A_1)) & hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),C_2)) & ti(fun(X_b,bool),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),C_2)))))) # label(fact_47_finite__subset__image) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 66 (all X_b (order(X_b) -> (all Na all N_3 all F ((all N_2 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,F,N_2)),hAPP(nat,X_b,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Na),N_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,F,Na)),hAPP(nat,X_b,F,N_3)))))))) # label(fact_48_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 67 (all X_c all X_b all F all A_1 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),A_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite(X_c),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))) -> (exists X_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) & -hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),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(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(X_c,fun(X_b,bool),hAPP(fun(X_b,fun(X_c,bool)),fun(X_c,fun(X_b,bool)),combc(X_b,X_c,bool),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,bool)),hAPP(fun(X_c,fun(X_c,bool)),fun(fun(X_b,X_c),fun(X_b,fun(X_c,bool))),combb(X_c,fun(X_c,bool),X_b),fequal(X_c)),F)),hAPP(X_b,X_c,F,X_1))))))))))) # label(fact_49_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 68 (all X_b all X_c all A_1 all B_1 all F all X_2 (ti(X_b,B_1) = 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_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),A_1)))))) # label(fact_50_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 69 (all X_b all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),A_1)) -> ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B)))) # label(fact_51_equalityI) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 70 (all X_b all C_1 all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),C_1),B))))) # label(fact_52_subsetD) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 71 (all X_b all B_1 all A_2 all B ((-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B)) -> ti(X_b,A_2) = ti(X_b,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_1),B))))) # label(fact_53_insertCI) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 72 (all X_b all A_2 all B_1 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_1),A_1))) -> (ti(X_b,A_2) != ti(X_b,B_1) -> 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_54_insertE) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 73 (all X_b all A_2 all 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),A_2),B)))) # label(fact_55_insertI1) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 74 (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),B) = 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)))) # label(fact_56_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 75 (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_57_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 76 (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_58_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 77 (all X_b all X_2 all Y_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),Y_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),Y_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))) # label(fact_59_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 78 (all X_b all A_2 all B_1 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_1),A_1))) <-> ti(X_b,A_2) = ti(X_b,B_1) | 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_60_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 79 (all X_b all Y_2 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_2),A_1),X_2)) <-> ti(X_b,Y_2) = ti(X_b,X_2) | hBOOL(hAPP(X_b,bool,A_1,X_2)))) # label(fact_61_insert__code) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 80 (all X_b all 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(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),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),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) <-> ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B))))) # label(fact_62_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 81 (all X_b all B_1 all A_2 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),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_1),B))))) # label(fact_63_insertI2) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 82 (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_64_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 83 (all X_b all A_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),A_1))) # label(fact_65_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 84 (all X_b all A_1 all B (ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)) & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),A_1)))) # label(fact_66_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 85 (all X_b all A_1 all B (ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)))) # label(fact_67_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 86 (all X_b all A_1 all B (ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),A_1)))) # label(fact_68_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 87 (all X_b all X_2 all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)) -> (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))))) # label(fact_69_in__mono) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 88 (all X_b all 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(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B))))) # label(fact_70_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 89 (all X_b all X_2 all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)) -> (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))))) # label(fact_71_set__mp) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 90 (all X_b all C all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),C)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),C))))) # label(fact_72_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 91 (all X_b all A_1 all B (ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B) -> -(hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),A_1))))) # label(fact_73_equalityE) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 92 (all X_b all X_c all F all G ((all X_1 hAPP(X_b,X_c,F,X_1) = hAPP(X_b,X_c,G,X_1)) -> ti(fun(X_b,X_c),F) = ti(fun(X_b,X_c),G))) # label(fact_74_ext) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 93 (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].
% 0.80/1.14 94 (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].
% 0.80/1.14 95 (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_1 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_1)) & ti(X_b,Z) = hAPP(X_c,X_b,F,X_1))))) # label(fact_77_image__iff) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 96 (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_78_imageI) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 97 (all X_c all X_b all B_1 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_1) = 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_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),F),A_1)))))) # label(fact_79_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 98 (all X_b all X_1 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_1),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_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)),Xa)))) # label(fact_80_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 99 (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_81_image__image) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 100 (all X_b all Y_1 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_1) = ti(fun(X_b,bool),Y_1)) # label(fact_82_image__ident) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 101 (all X_b all B all A_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),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),B)))) # label(fact_83_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 102 (all X_b all X_2 all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(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),X_2),A_1)),B)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B)) & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)))) # label(fact_84_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 103 (all X_b all 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(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),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))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B))))) # label(fact_85_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 104 (all X_b all B_1 all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),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),B_1),B))))) # label(fact_86_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 105 (all X_b all A_2 all C all D (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),C),D)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(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),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),A_2),D))))) # label(fact_87_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 106 (all X_c all X_b all F all A_2 all 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),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),A_2),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),hAPP(X_c,X_b,F,A_2)),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))) # label(fact_88_image__insert) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 107 (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)) -> hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(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)) = 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_89_insert__image) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 108 (all X_b all X_c all B all F all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),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))) <-> (exists AA (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,bool)),AA),A_1)) & ti(fun(X_b,bool),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),AA))))) # label(fact_90_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 109 (all X_c all X_b all F all A_1 all B (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,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),F),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),F),B))))) # label(fact_91_image__mono) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 110 (all X_b all X_c all B_1 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_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),A_1))) -> -(all X_1 (ti(X_b,B_1) = hAPP(X_c,X_b,F,X_1) -> -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_1)))))) # label(fact_92_imageE) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 111 (all X_b all B all A_1 ((all X_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B)))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),A_1),B)))) # label(fact_93_subsetI) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 112 (all I all Pa all K (hBOOL(hAPP(nat,bool,Pa,K)) -> ((all N_2 (hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,suc,N_2))) -> hBOOL(hAPP(nat,bool,Pa,N_2)))) -> hBOOL(hAPP(nat,bool,Pa,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K),I)))))) # label(fact_94_zero__induct__lemma) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 113 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),M_1)) -> (exists M M_1 = hAPP(nat,nat,suc,M)))) # label(fact_95_Suc__le__D) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 114 (all X_c all X_b all F all B all A_1 ((all X_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),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_1)),B)))) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(fun(X_c,bool),fun(fun(X_c,bool),bool),ord_less_eq(fun(X_c,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),F),A_1)),B)))) # label(fact_96_image__subsetI) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 115 (all X_a (preorder(X_a) -> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),X))))) # label(fact_97_order__refl) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 116 (all N (hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),N)) <-> (exists M all X_1 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),M)))))) # label(fact_98_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 117 (all T_2 all T_1 (preorder(T_1) -> preorder(fun(T_2,T_1)))) # label(arity_fun___Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 118 (all T_2 all T_1 (finite_finite_1(T_1) & finite_finite_1(T_2) -> finite_finite_1(fun(T_2,T_1)))) # label(arity_fun___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 119 (all T_2 all T_1 (order(T_1) -> order(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oorder) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 120 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 121 (all P (-hBOOL(hAPP(bool,bool,fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 122 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.14 123 (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].
% 2.05/2.33 124 (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].
% 2.05/2.33 125 (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].
% 2.05/2.33 126 (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].
% 2.05/2.33 127 (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].
% 2.05/2.33 128 (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].
% 2.05/2.33 129 (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].
% 2.05/2.33 130 (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].
% 2.05/2.33 131 (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].
% 2.05/2.33 132 (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].
% 2.05/2.33 133 (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].
% 2.05/2.33 134 (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].
% 2.05/2.33 135 (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].
% 2.05/2.33 136 (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].
% 2.05/2.33 137 (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].
% 2.05/2.33
% 2.05/2.33 ============================== end of process non-clausal formulas ===
% 2.05/2.33
% 2.05/2.33 ============================== PROCESS INITIAL CLAUSES ===============
% 2.05/2.33
% 2.05/2.33 ============================== PREDICATE ELIMINATION =================
% 2.05/2.33
% 2.05/2.33 ============================== end predicate elimination =============
% 2.05/2.33
% 2.05/2.33 Auto_denials: (non-Horn, no changes).
% 2.05/2.33
% 2.05/2.33 Term ordering decisions:
% 2.05/2.33 Function symbol KB weights: bool=1. nat=1. suc=1. x_a=1. pname=1. fdisj=1. fconj=1. u=1. fimplies=1. mgt_call=1. fNot=1. g=1. na=1. p=1. pn=1. fun=1. ti=1. image=1. f10=1. f13=1. ord_less_eq=1. member=1. finite_finite=1. insert=1. minus_minus=1. collect=1. finite_card=1. fequal=1. combi=1. undefined=1. f12=1. combb=1. combc=1. combs=1. f8=1. f9=1. hAPP=1. f2=1. f3=1. f4=1. f1=1. f5=1. f6=1. f7=1. f11=1.
% 2.05/2.33
% 2.05/2.33 ============================== end of process initial clauses ========
% 2.05/2.33
% 2.05/2.33 ============================== CLAUSES FOR SEARCH ====================
% 2.05/2.33
% 2.05/2.33 ============================== end of clauses for search =============
% 2.05/2.33
% 2.05/2.33 ============================== SEARCH ================================
% 2.05/2.33
% 2.05/2.33 % Starting search at 0.10 seconds.
% 2.05/2.33
% 2.05/2.33 Low Water (keep): wt=179.000, iters=3345
% 2.05/2.33
% 2.05/2.33 Low Water (keep): wt=170.000, iters=3405
% 2.05/2.33
% 2.05/2.33 Low Water (keep): wt=146.000, iters=3342
% 2.05/2.33
% 2.05/2.33 Low Water (keep): wt=145.000, iters=3341
% 2.05/2.33
% 2.05/2.33 Low Water (keep): wt=139.000, iters=3381
% 2.05/2.33
% 2.05/2.33 Low Water (keep): wt=123.000, iters=3366
% 2.05/2.33
% 2.05/2.33 Low Water (keep): wt=120.000, iters=3537
% 6.65/6.97
% 6.65/6.97 Low Water (keep): wt=104.000, iters=3488
% 6.65/6.97
% 6.65/6.97 Low Water (keep): wt=90.000, iters=3420
% 6.65/6.97
% 6.65/6.97 Low Water (keep): wt=77.000, iters=3450
% 6.65/6.97
% 6.65/6.97 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 81 (0.00 of 1.30 sec).
% 6.65/6.97
% 6.65/6.97 Low Water (keep): wt=74.000, iters=3596
% 6.65/6.97
% 6.65/6.97 Low Water (keep): wt=66.000, iters=3368
% 6.65/6.97
% 6.65/6.97 Low Water (keep): wt=62.000, iters=3519
% 6.65/6.97
% 6.65/6.97 Low Water (keep): wt=57.000, iters=3399
% 6.65/6.97
% 6.65/6.97 Low Water (keep): wt=49.000, iters=3431
% 6.65/6.97
% 6.65/6.97 Low Water (keep): wt=41.000, iters=3535
% 6.65/6.97
% 6.65/6.97 Low Water (keep): wt=32.000, iters=3355
% 6.65/6.97
% 6.65/6.97 Low Water (keep): wt=31.000, iters=3344
% 6.65/6.97
% 6.65/6.97 Low Water (keep): wt=28.000, iters=3361
% 6.65/6.97
% 6.65/6.97 Low Water (keep): wt=24.000, iters=3424
% 6.65/6.97
% 6.65/6.97 Low Water (keep): wt=22.000, iters=3342
% 6.65/6.97
% 6.65/6.97 Low Water (keep): wt=20.000, iters=3335
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=3509, wt=197.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=3513, wt=193.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=3500, wt=191.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=2588, wt=188.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=9111, wt=187.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=10476, wt=186.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=10477, wt=185.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=10435, wt=184.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=9086, wt=183.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=10408, wt=182.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=10409, wt=181.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=10403, wt=180.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=10365, wt=179.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=10394, wt=178.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=10395, wt=177.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11521, wt=176.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11288, wt=175.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11213, wt=174.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11753, wt=173.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11313, wt=172.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11775, wt=171.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11766, wt=170.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11742, wt=169.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=10568, wt=168.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11738, wt=167.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11722, wt=166.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11734, wt=165.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=10273, wt=164.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11732, wt=163.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=10301, wt=162.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11692, wt=161.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=10267, wt=160.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11730, wt=159.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11041, wt=158.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11686, wt=157.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=10239, wt=156.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11690, wt=155.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=9773, wt=154.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11669, wt=153.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11711, wt=152.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11939, wt=151.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11527, wt=150.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11665, wt=149.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11964, wt=148.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=10938, wt=147.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11869, wt=146.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11861, wt=145.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11855, wt=144.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=10453, wt=143.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=12304, wt=142.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=12283, wt=141.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=12469, wt=140.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=12443, wt=139.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=12285, wt=138.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=12265, wt=137.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=12321, wt=136.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11865, wt=135.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11813, wt=134.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11843, wt=133.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=12890, wt=132.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=12786, wt=131.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=12878, wt=130.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=12902, wt=129.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=12888, wt=128.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=12035, wt=127.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=13010, wt=126.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=12635, wt=125.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=12894, wt=124.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11783, wt=123.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=12241, wt=122.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=12895, wt=121.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=13408, wt=120.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=12835, wt=119.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=13001, wt=118.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=12623, wt=117.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=12322, wt=116.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=11765, wt=115.000
% 6.65/6.97
% 6.65/6.97 Low Water (displace): id=13616, wt=114.000
% 29.87/30.20
% 29.87/30.20 Low Water (displace): id=12865, wt=113.000
% 29.87/30.20
% 29.87/30.20 Low Water (displace): id=13896, wt=112.000
% 29.87/30.20
% 29.87/30.20 Low Water (displace): id=14041, wt=111.000
% 29.87/30.20
% 29.87/30.20 Low Water (displace): id=14065, wt=110.000
% 29.87/30.20
% 29.87/30.20 Low Water (displace): id=14502, wt=109.000
% 29.87/30.20
% 29.87/30.20 Low Water (displace): id=14040, wt=108.000
% 29.87/30.20
% 29.87/30.20 Low Water (displace): id=14498, wt=107.000
% 29.87/30.20
% 29.87/30.20 Low Water (displace): id=14623, wt=106.000
% 29.87/30.20
% 29.87/30.20 Low Water (displace): id=14994, wt=105.000
% 29.87/30.20
% 29.87/30.20 Low Water (displace): id=15038, wt=104.000
% 29.87/30.20
% 29.87/30.20 Low Water (displace): id=15135, wt=103.000
% 29.87/30.20
% 29.87/30.20 Low Water (displace): id=15229, wt=102.000
% 29.87/30.20
% 29.87/30.20 Low Water (displace): id=15438, wt=101.000
% 29.87/30.20
% 29.87/30.20 Low Water (displace): id=15403, wt=100.000
% 29.87/30.20
% 29.87/30.20 Low Water (displace): id=15695, wt=99.000
% 29.87/30.20
% 29.87/30.20 Low Water (displace): id=15735, wt=98.000
% 29.87/30.20
% 29.87/30.20 Low Water (displace): id=16010, wt=97.000
% 29.87/30.20
% 29.87/30.20 Low Water (displace): id=16193, wt=96.000
% 29.87/30.20
% 29.87/30.20 Low Water (displace): id=16968, wt=89.000
% 29.87/30.20
% 29.87/30.20 Low Water (displace): id=19595, wt=20.000
% 29.87/30.20
% 29.87/30.20 ============================== PROOF =================================
% 29.87/30.20 % SZS status Theorem
% 29.87/30.20 % SZS output start Refutation
% 29.87/30.20
% 29.87/30.20 % Proof 1 at 28.41 (+ 0.68) seconds.
% 29.87/30.20 % Length of proof is 10.
% 29.87/30.20 % Level of proof is 3.
% 29.87/30.20 % Maximum clause weight is 87.000.
% 29.87/30.20 % Given clauses 4841.
% 29.87/30.20
% 29.87/30.20 105 (all X_b all A_2 all C all D (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),C),D)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(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),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),A_2),D))))) # label(fact_87_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 29.87/30.20 107 (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)) -> hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(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)) = 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_89_insert__image) # label(axiom) # label(non_clause). [assumption].
% 29.87/30.20 279 -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),B),C)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),C))) # label(fact_87_insert__mono) # label(axiom). [clausify(105)].
% 29.87/30.20 281 -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C)) | hAPP(fun(D,bool),fun(D,bool),hAPP(D,fun(fun(D,bool),fun(D,bool)),insert(D),hAPP(A,D,E,B)),hAPP(fun(A,bool),fun(D,bool),hAPP(fun(A,D),fun(fun(A,bool),fun(D,bool)),image(A,D),E),C)) = hAPP(fun(A,bool),fun(D,bool),hAPP(fun(A,D),fun(fun(A,bool),fun(D,bool)),image(A,D),E),C) # label(fact_89_insert__image) # label(axiom). [clausify(107)].
% 29.87/30.20 329 hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) # label(conj_1) # label(hypothesis). [assumption].
% 29.87/30.20 333 hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)) # label(conj_4) # label(hypothesis). [assumption].
% 29.87/30.20 335 -hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(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),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) # label(conj_6) # label(negated_conjecture). [assumption].
% 29.87/30.20 907 hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(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),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),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))). [resolve(329,a,279,a)].
% 29.87/30.20 956 hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),hAPP(pname,A,B,pn)),hAPP(fun(pname,bool),fun(A,bool),hAPP(fun(pname,A),fun(fun(pname,bool),fun(A,bool)),image(pname,A),B),u)) = hAPP(fun(pname,bool),fun(A,bool),hAPP(fun(pname,A),fun(fun(pname,bool),fun(A,bool)),image(pname,A),B),u). [resolve(333,a,281,a)].
% 29.87/30.20 22157 $F. [para(956(a,1),907(a,1,4)),unit_del(a,335)].
% 29.87/30.20
% 29.87/30.20 % SZS output end Refutation
% 29.87/30.20 ============================== end of proof ==========================
% 29.87/30.20
% 29.87/30.20 ============================== STATISTICS ============================
% 29.87/30.20
% 29.87/30.20 Given=4841. Generated=1167481. Kept=21999. proofs=1.
% 29.87/30.20 Usable=4831. Sos=9999. Demods=234. Limbo=43, Disabled=7326. Hints=0.
% 29.87/30.20 Megabytes=59.71.
% 29.87/30.20 User_CPU=28.41, System_CPU=0.68, Wall_clock=29.
% 29.87/30.20
% 29.87/30.20 ============================== end of statistics =====================
% 29.87/30.20
% 29.87/30.20 ============================== end of search =========================
% 29.87/30.20
% 29.87/30.20 THEOREM PROVED
% 29.87/30.20 % SZS status Theorem
% 29.87/30.20
% 29.87/30.20 Exiting with 1 proof.
% 29.87/30.20
% 29.87/30.20 Process 6433 exit (max_proofs) Sun Jun 5 09:56:20 2022
% 29.87/30.20 Prover9 interrupted
%------------------------------------------------------------------------------