0.08/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.34 % Computer : n013.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1200 0.13/0.34 % DateTime : Wed Jul 14 16:41:48 EDT 2021 0.13/0.34 % CPUTime : 2.21/2.42 ============================== Prover9 =============================== 2.21/2.42 Prover9 (32) version 2009-11A, November 2009. 2.21/2.42 Process 11003 was started by sandbox on n013.cluster.edu, 2.21/2.42 Wed Jul 14 16:41:50 2021 2.21/2.42 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_10850_n013.cluster.edu". 2.21/2.42 ============================== end of head =========================== 2.21/2.42 2.21/2.42 ============================== INPUT ================================= 2.21/2.42 2.21/2.42 % Reading from file /tmp/Prover9_10850_n013.cluster.edu 2.21/2.42 2.21/2.42 set(prolog_style_variables). 2.21/2.42 set(auto2). 2.21/2.42 % set(auto2) -> set(auto). 2.21/2.42 % set(auto) -> set(auto_inference). 2.21/2.42 % set(auto) -> set(auto_setup). 2.21/2.42 % set(auto_setup) -> set(predicate_elim). 2.21/2.42 % set(auto_setup) -> assign(eq_defs, unfold). 2.21/2.42 % set(auto) -> set(auto_limits). 2.21/2.42 % set(auto_limits) -> assign(max_weight, "100.000"). 2.21/2.42 % set(auto_limits) -> assign(sos_limit, 20000). 2.21/2.42 % set(auto) -> set(auto_denials). 2.21/2.42 % set(auto) -> set(auto_process). 2.21/2.42 % set(auto2) -> assign(new_constants, 1). 2.21/2.42 % set(auto2) -> assign(fold_denial_max, 3). 2.21/2.42 % set(auto2) -> assign(max_weight, "200.000"). 2.21/2.42 % set(auto2) -> assign(max_hours, 1). 2.21/2.42 % assign(max_hours, 1) -> assign(max_seconds, 3600). 2.21/2.42 % set(auto2) -> assign(max_seconds, 0). 2.21/2.42 % set(auto2) -> assign(max_minutes, 5). 2.21/2.42 % assign(max_minutes, 5) -> assign(max_seconds, 300). 2.21/2.42 % set(auto2) -> set(sort_initial_sos). 2.21/2.42 % set(auto2) -> assign(sos_limit, -1). 2.21/2.42 % set(auto2) -> assign(lrs_ticks, 3000). 2.21/2.42 % set(auto2) -> assign(max_megs, 400). 2.21/2.42 % set(auto2) -> assign(stats, some). 2.21/2.42 % set(auto2) -> clear(echo_input). 2.21/2.42 % set(auto2) -> set(quiet). 2.21/2.42 % set(auto2) -> clear(print_initial_clauses). 2.21/2.42 % set(auto2) -> clear(print_given). 2.21/2.42 assign(lrs_ticks,-1). 2.21/2.42 assign(sos_limit,10000). 2.21/2.42 assign(order,kbo). 2.21/2.42 set(lex_order_vars). 2.21/2.42 clear(print_given). 2.21/2.42 2.21/2.42 % formulas(sos). % not echoed (1194 formulas) 2.21/2.42 2.21/2.42 ============================== end of input ========================== 2.21/2.42 2.21/2.42 % From the command line: assign(max_seconds, 1200). 2.21/2.42 2.21/2.42 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 2.21/2.42 2.21/2.42 % Formulas that are not ordinary clauses: 2.21/2.42 1 (all X_b all X_c all F all A_3 (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_3) = bot_bot(fun(X_b,bool)) <-> ti(fun(X_c,bool),A_3) = bot_bot(fun(X_c,bool)))) # label(fact_81_empty__is__image) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 2 (all X_a (linorder(X_a) -> (all X ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),X)))) # label(fact_536_Max_Oidem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 3 (all X_b all A_3 hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),hAPP(nat,fun(X_b,nat),combk(nat,X_b),one_one(nat))),A_3) = hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)) # label(fact_646_card__eq__setsum) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 4 (all X_b (linordered_semidom(X_b) -> (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),M_1)),hAPP(nat,X_b,semiring_1_of_nat(X_b),N))))))) # label(fact_817_of__nat__less__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 5 (all N_1 all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),N_1))),hAPP(nat,int,semiring_1_of_nat(int),M)))) # label(fact_680_negative__zle) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 6 (all X_b finite_folding_one(X_b) = ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),finite_folding_one(X_b))) # label(tsy_c_Finite__Set_Ofolding__one_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 7 (all X_b (linorder(X_b) -> (all X_1 hAPP(fun(X_b,bool),X_b,big_linorder_Min(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_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1)))) # label(fact_385_Min_Osingleton) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 8 (all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)),N_1) = M) # label(fact_426_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 9 (all X_b all X_c (comm_monoid_mult(X_c) -> (all Ba all A_2 all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),S_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(X_c,fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(X_b,X_c)),combc(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_b,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combs(X_b,X_c,fun(X_c,X_c)),hAPP(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c))),hAPP(fun(bool,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c)))),combb(bool,fun(X_c,fun(X_c,X_c)),X_b),if(X_c)),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))),Ba)),one_one(X_c))),S_1) = hAPP(X_b,X_c,Ba,A_2)) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),S_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(X_c,fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(X_b,X_c)),combc(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_b,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combs(X_b,X_c,fun(X_c,X_c)),hAPP(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c))),hAPP(fun(bool,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c)))),combb(bool,fun(X_c,fun(X_c,X_c)),X_b),if(X_c)),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))),Ba)),one_one(X_c))),S_1) = one_one(X_c)))))) # label(fact_645_setprod__delta) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 10 (all X_a (ord(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Least),X) = ti(X_a,X))))) # label(fact_584_max__leastL) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 11 (all Q all P (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | -hBOOL(P))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 12 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)))))) # label(fact_751_leI) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 13 (all X_a (comm_semiring_1(X_a) -> (all M all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M)))) # label(fact_636_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 14 (all X_b all X_1 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),X_1) = ti(X_b,X_1))) # label(fact_130_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 15 (all X_b all A_3 all B_2 (ti(fun(X_b,bool),B_2) = ti(fun(X_b,bool),A_3) -> -(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_3),B_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_2),A_3))))) # label(fact_281_equalityE) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 16 (all Z Z = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),one_one(int))) # label(fact_707_zmult__1__right) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 17 (all I all J all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),K)))) # label(fact_715_add__lessD1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 18 (all Z all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))))) # label(fact_804_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 19 (all N all Q_3 all Pa ((all X_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,Q_3,X_2)),hAPP(nat,nat,Pa,X_2)))) -> hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),minus_minus(nat)),Pa)),Q_3)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),Pa),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),Q_3),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N))))) # label(fact_337_sum__diff__distrib) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 20 (all X_a (comm_monoid_mult(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a))))) # label(fact_627_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 21 (all P all Q (-hBOOL(P) | hBOOL(Q) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 22 (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),Y)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X)) | Y = X)) # label(fact_891_zless__linear) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 23 (all X_b all X_c all Z_2 all X_1 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite_comp_fun_idem(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_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_1),A_3)) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2)),A_3)))) # label(fact_201_comp__fun__idem_Ofold__insert__idem2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 24 (all X_b all A_3 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool))))) # label(fact_852_not__psubset__empty) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 25 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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)),A_3),B_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))) -> ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2))))) # label(fact_614_card__seteq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 26 (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_1_1_T) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 27 (all X_b all X_c (comm_monoid_mult(X_c) -> (all F all F_2 ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_2)) -> one_one(X_c) = hAPP(X_b,X_c,F,X_2))) -> one_one(X_c) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),F_2))))) # label(fact_655_setprod__1_H) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 28 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = ti(fun(X_b,bool),A_3))) # label(fact_148_insert__Diff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 29 (all X_a (order(X_a) -> (all Z all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X))))))) # label(fact_765_xt1_I8_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 30 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(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_1),A_3))) & (bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(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_1),A_3)) = ti(X_b,X_1)))))) # label(fact_519_Max_Oinsert__remove) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 31 (all X_a (linorder(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),C))))) # label(fact_538_min__max_Osup_Oassoc) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 32 (all X_b all Fun1_1 all Com_1 all Fun2_1 all Fun1_2 all Com_2 all Fun2_2 (hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1_1),Com_1),Fun2_1) = hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1_2),Com_2),Fun2_2) <-> Fun1_1 = Fun1_2 & Fun2_1 = Fun2_2 & Com_1 = Com_2)) # label(fact_1_triple_Oinject) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 33 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),I)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),J))))) # label(fact_404_mult__le__mono2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 34 (all X_b all A_3 all B_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)),A_3),B_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_2),A_3)) <-> ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2))) # label(fact_288_set__eq__subset) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 35 (all X_a (linorder(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),C))))) # label(fact_349_min__max_Oinf_Oassoc) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 36 (all X_c all X_b all X_d all F all G all A_3 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_3) = 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_3))) # label(fact_70_image__image) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 37 (all X_b (boolean_algebra(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),X_1)),hAPP(X_b,X_b,uminus_uminus(X_b),Y_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)))))) # label(fact_813_compl__less__compl__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 38 (all X_a (order(X_a) -> (all Z all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X))))))) # label(fact_763_xt1_I7_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 39 (all X_c all X_b all F1 all Fun1_1 all Com_1 all Fun2_1 hAPP(hoare_2118899576triple(X_c),X_b,hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_2118899576triple(X_c),X_b),hoare_225284258e_case(X_c,X_b),F1),hAPP(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hoare_759811442triple(X_c),Fun1_1),Com_1),Fun2_1)) = hAPP(fun(X_c,fun(state,bool)),X_b,hAPP(com,fun(fun(X_c,fun(state,bool)),X_b),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b)),F1,Fun1_1),Com_1),Fun2_1)) # label(fact_42_triple_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 40 (all X_b all A_3 (bot_bot(fun(X_b,bool)) = ti(fun(X_b,bool),A_3) <-> (all X_2 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))))) # label(fact_22_all__not__in__conv) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 41 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))) # label(fact_959_zero__less__int__conv) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 42 (all X_b (linord2061991079up_add(X_b) -> (all K_1 all N_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),N_3) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),K_1),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),N_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b)),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combs(X_b,bool,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool))),hAPP(fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),combb(fun(X_b,bool),fun(X_b,fun(bool,bool)),X_b),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,X_b),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,X_b),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,X_b),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool)),X_b),combb(X_b,bool,X_b)),fequal(X_b))),hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),K_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)),N_3)))))))))) # label(fact_601_add__Min__commute) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 43 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z))))) # label(fact_539_min__max_Osup__left__commute) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 44 (all X_b all Pa ((exists X_2 ((all Y_1 (hBOOL(hAPP(X_b,bool,Pa,Y_1)) -> ti(X_b,Y_1) = ti(X_b,X_2))) & hBOOL(hAPP(X_b,bool,Pa,X_2)))) -> hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa))))) # label(fact_117_theI_H) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 45 (all M all N_1 all K all L_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),L_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))))) # label(fact_716_less__add__eq__less) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 46 (all X_b all Q_3 all Pa ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> hBOOL(hAPP(X_b,bool,Q_3,X_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)),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),Q_3))))) # label(fact_340_Collect__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 47 (all X_b all Pa all A_2 (hBOOL(hAPP(X_b,bool,Pa,A_2)) -> ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> ti(X_b,X_2) = ti(X_b,A_2))) -> hAPP(fun(X_b,bool),X_b,the(X_b),Pa) = ti(X_b,A_2)))) # label(fact_93_the__equality) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 48 (all X_b all Ca all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) -> -(hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B_2))))) # label(fact_128_DiffE) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 49 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))) # label(fact_237_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 50 (all Pa all K_1 all I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),I_1)) -> (hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_1),one_one(int)))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),I_2)) -> (hBOOL(hAPP(int,bool,Pa,I_2)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,Pa,I_1)))))) # label(fact_909_int__gr__induct) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 51 (all Z all W_2 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),Z)),W_2) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),W_2))) # label(fact_687_zmult__zminus) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 52 (all X_c all X_d all X_b (semiring_0(X_b) -> (all F all A_3 all G all B_2 hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_d,bool),fun(X_c,X_b),hAPP(fun(X_c,fun(fun(X_d,bool),X_b)),fun(fun(X_d,bool),fun(X_c,X_b)),combc(X_c,fun(X_d,bool),X_b),hAPP(fun(X_c,fun(X_d,X_b)),fun(X_c,fun(fun(X_d,bool),X_b)),hAPP(fun(fun(X_d,X_b),fun(fun(X_d,bool),X_b)),fun(fun(X_c,fun(X_d,X_b)),fun(X_c,fun(fun(X_d,bool),X_b))),combb(fun(X_d,X_b),fun(fun(X_d,bool),X_b),X_c),big_co1399186613setsum(X_d,X_b)),hAPP(fun(X_d,X_b),fun(X_c,fun(X_d,X_b)),hAPP(fun(X_c,fun(fun(X_d,X_b),fun(X_d,X_b))),fun(fun(X_d,X_b),fun(X_c,fun(X_d,X_b))),combc(X_c,fun(X_d,X_b),fun(X_d,X_b)),hAPP(fun(X_c,fun(X_b,X_b)),fun(X_c,fun(fun(X_d,X_b),fun(X_d,X_b))),hAPP(fun(fun(X_b,X_b),fun(fun(X_d,X_b),fun(X_d,X_b))),fun(fun(X_c,fun(X_b,X_b)),fun(X_c,fun(fun(X_d,X_b),fun(X_d,X_b)))),combb(fun(X_b,X_b),fun(fun(X_d,X_b),fun(X_d,X_b)),X_c),combb(X_b,X_b,X_d)),hAPP(fun(X_c,X_b),fun(X_c,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_c),times_times(X_b)),F))),G))),B_2)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),F),A_3)),hAPP(fun(X_d,bool),X_b,hAPP(fun(X_d,X_b),fun(fun(X_d,bool),X_b),big_co1399186613setsum(X_d,X_b),G),B_2))))) # label(fact_187_setsum__product) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 53 (all X_b all X_c all X_1 all Z_2 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite_comp_fun_idem(X_b,X_c),F)) -> hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2)) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2))) # label(fact_162_comp__fun__idem_Ofun__left__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 54 (all X_b (ab_group_add(X_b) -> (all A_2 all Ba all Ca all D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Ca),D) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),Ba) -> (ti(X_b,Ca) = ti(X_b,D) <-> ti(X_b,Ba) = ti(X_b,A_2)))))) # label(fact_247_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 55 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> ((exists X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),X_1)))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3)),X_1)))))))) # label(fact_390_fold1__below__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 56 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) | ti(X_a,X) = ti(X_a,Y))))) # label(fact_759_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 57 (all X_b all X_c (comm_monoid_mult(X_c) -> (all F all S_1 all T_4 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),T_4)) -> (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)),S_1),T_4)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),T_4),S_1))) -> one_one(X_c) = hAPP(X_b,X_c,F,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),T_4) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),S_1))))))) # label(fact_652_setprod__mono__one__right) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 58 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3))) <-> (all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),X_2)))))))))) # label(fact_840_strict__below__fold1__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 59 (all X_b (linorder(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),B_2) != bot_bot(fun(X_b,bool)) -> (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_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),B_2)),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3))))))) # label(fact_376_Min_Osubset__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 60 (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1)))) # label(fact_676_zdiff__int) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 61 (all X_a (order(X_a) -> (all Z all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),X))))))) # label(fact_267_xt1_I6_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 62 (all X_b all Q_3 all Pa all Ga all P_4 all Ca all Q_5 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),P_4),Ca),Q_5)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> ((all Z_4 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_4),S_3)) -> (all S_4 ((all Z_5 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_4,Z_5),S_3)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_5,Z_5),S_4)))) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_3,Z_4),S_4)))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))))) # label(fact_8_conseq12) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 63 (all X_b (linorder(X_b) -> hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_b,X_b),ord_min(X_b))))) # label(fact_373_min__max_Ocomp__fun__idem__inf) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 64 (all X_b all X_c all Z_2 all X_1 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2)),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_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_1),A_3)))))) # label(fact_183_comp__fun__commute_Ofold__insert2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 65 (all X_b all F all A_2 all X_3 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),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),A_2),X_3)),X_1)) -> -(all A_5 all A_4 (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_5),A_4) = 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),X_3) -> (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)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),F),A_5),A_4),X_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_5),A_4))))))) # label(fact_108_insert__fold1SetE) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 66 (all X_c all X_b all X_1 all A_3 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),bot_bot(fun(X_c,bool)))))) = hAPP(fun(X_c,bool),X_b,F_2,A_3))))) # label(fact_158_folding__image__simple_Oremove) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 67 (all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)) # label(fact_461_nat__add__commute) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 68 (all X_a (order(X_a) -> (all A_1 all B (ti(X_a,B) != ti(X_a,A_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_755_xt1_I12_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 69 (all X_a (ordere236663937imp_le(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z)))) # label(fact_534_max__add__distrib__left) # label(axiom) # label(non_clause). [assumption]. 2.21/2.42 70 (all X_c all X_b (semiring_1(X_b) & comm_monoid_mult(X_b) -> (all F all A_3 hAPP(nat,X_b,semiring_1_of_nat(X_b),hAPP(fun(X_c,bool),nat,hAPP(fun(X_c,nat),fun(fun(X_c,bool),nat),big_co302546470etprod(X_c,nat),F),A_3)) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),hAPP(fun(X_c,nat),fun(X_c,X_b),hAPP(fun(nat,X_b),fun(fun(X_c,nat),fun(X_c,X_b)),combb(nat,X_b,X_c),semiring_1_of_nat(X_b)),F)),A_3)))) # label(fact_666_of__nat__setprod) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 71 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(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_1),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),X_1),A_3)))))) # label(fact_577_Max_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 72 (all X_b all X_c (comm_monoid_add(X_c) -> (all G all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),plus_plus(X_c),hAPP(X_b,X_c,G,X_1)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),A_3)) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),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_3))))))) # label(fact_218_setsum_Oinsert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 73 (all X_b (linorder(X_b) -> (all X_1 ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(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_1),bot_bot(fun(X_b,bool))))))) # label(fact_471_min__max_OInf__fin_Osingleton) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 74 (all X_c all X_b (semiring_1(X_b) -> (all F all A_3 hAPP(nat,X_b,semiring_1_of_nat(X_b),hAPP(fun(X_c,bool),nat,hAPP(fun(X_c,nat),fun(fun(X_c,bool),nat),big_co1399186613setsum(X_c,nat),F),A_3)) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_c,nat),fun(X_c,X_b),hAPP(fun(nat,X_b),fun(fun(X_c,nat),fun(X_c,X_b)),combb(nat,X_b,X_c),semiring_1_of_nat(X_b)),F)),A_3)))) # label(fact_667_of__nat__setsum) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 75 (all X_c all X_b all F all Z_2 all Y_2 all X_1 all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),Y_2)) -> hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_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_1),A_3)),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Y_2)))))) # label(fact_107_fold__graph_OinsertI) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 76 (all X_b (linorder(X_b) -> (all Ba all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),Ba),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_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),A_2),hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),Ba),A_3)))))) # label(fact_569_min__max_Ofold__sup__insert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 77 (all X_b all A_2 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),bot_bot(fun(X_b,bool))))) # label(fact_11_emptyE) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 78 (all N_3 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3)) <-> (exists M_2 all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),M_2)))))) # label(fact_806_finite__nat__set__iff__bounded) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 79 (all K all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1))) # label(fact_431_diff__cancel) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 80 (all X_a (linorder(X_a) -> (all B all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)))))))) # label(fact_361_min__max_Ole__infI) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 81 (all X_b (linorder(X_b) -> ord_max(X_b) = hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,X_b)),min(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),ord_less_eq(X_b))))) # label(fact_573_dual__min) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 82 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) <-> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),Y_2) = ti(X_b,Y_2))))) # label(fact_549_min__max_Ole__iff__sup) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 83 (all X_b all A_3 bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),A_3)) # label(fact_139_Diff__cancel) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 84 (all X_b (linorder(X_b) -> (all X_1 all Y_2 all Z_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),Y_2)),Z_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),Z_2)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Z_2)))))) # label(fact_736_min__less__iff__disj) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 85 (all X_a (linordered_semidom(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))))))) # label(fact_822_less__add__one) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 86 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(X_b,X_c,G,X_1)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),A_3)) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),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_3))))))) # label(fact_198_setprod_Oinsert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 87 (all X_d all X_b all X_c (comm_monoid_add(X_c) -> (all G all F all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),S_1) = hAPP(fun(X_d,bool),X_c,hAPP(fun(X_d,X_c),fun(fun(X_d,bool),X_c),big_co1399186613setsum(X_d,X_c),hAPP(fun(X_d,fun(X_b,bool)),fun(X_d,X_c),hAPP(fun(fun(X_b,bool),X_c),fun(fun(X_d,fun(X_b,bool)),fun(X_d,X_c)),combb(fun(X_b,bool),X_c,X_d),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G)),hAPP(fun(X_d,fun(X_b,bool)),fun(X_d,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_d,fun(X_b,bool)),fun(X_d,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_d),collect(X_b)),hAPP(fun(X_d,fun(X_b,bool)),fun(X_d,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_d,fun(X_b,bool)),fun(X_d,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_d),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)),S_1)))),hAPP(fun(X_b,fun(X_d,bool)),fun(X_d,fun(X_b,bool)),combc(X_b,X_d,bool),hAPP(fun(X_b,X_d),fun(X_b,fun(X_d,bool)),hAPP(fun(X_d,fun(X_d,bool)),fun(fun(X_b,X_d),fun(X_b,fun(X_d,bool))),combb(X_d,fun(X_d,bool),X_b),fequal(X_d)),F)))))),hAPP(fun(X_b,bool),fun(X_d,bool),hAPP(fun(X_b,X_d),fun(fun(X_b,bool),fun(X_d,bool)),image(X_b,X_d),F),S_1)))))) # label(fact_208_setsum__image__gen) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 88 (all X_b all A_3 all A_2 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))),B_2)) # label(fact_145_Diff__insert2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 89 (all X_b all A_2 all Ba all Ca all D (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),bot_bot(fun(X_b,bool)))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),D),bot_bot(fun(X_b,bool)))) <-> ti(X_b,A_2) = ti(X_b,D) & ti(X_b,Ba) = ti(X_b,Ca) | ti(X_b,A_2) = ti(X_b,Ca) & ti(X_b,Ba) = ti(X_b,D))) # label(fact_37_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 90 (all W_1 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_2),one_one(int)))))) # label(fact_869_zle__diff1__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 91 (all X_a (monoid_mult(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1)))) # label(fact_632_mult__1__left) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 92 (all M all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J))))) # label(fact_719_trans__less__add2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 93 (all X_b all X_c ti(fun(fun(X_b,fun(X_c,X_c)),bool),finite100568337ommute(X_b,X_c)) = finite100568337ommute(X_b,X_c)) # label(tsy_c_Finite__Set_Ocomp__fun__commute_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 94 (all X_b all B_2 all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))),one_one(nat)) = hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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_2))))))) # label(fact_648_card__Diff__insert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 95 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(X_b,X_c,G,X_2) = hAPP(X_b,X_c,H,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),H),A_3)))))) # label(fact_209_setprod_Ocong) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 96 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_747_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 97 (all X_a (linord20386208strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))))) # label(fact_992_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 98 (all K_1 all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)))) # label(fact_420_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 99 (all X_b (linorder(X_b) -> (all X_1 all Y_2 all Z_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),Z_2)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Z_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),Y_2)),Z_2)))))) # label(fact_357_min__le__iff__disj) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 100 (all X_b all X_a all P all Q ti(X_a,P) = hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q)) # label(help_COMBK_1_1_U) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 101 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) -> (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) <-> ti(X_b,Y_2) = ti(X_b,X_1)))))) # label(fact_758_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 102 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))) # label(fact_936_less__zeroE) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 103 (all X_b all Ca all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3))) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)))) # label(fact_527_ComplE) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 104 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))) # label(fact_970_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 105 (all X_a (ord(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (ti(X_a,C) = ti(X_a,B) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))))))) # label(fact_272_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 106 (all X_b all Pa all Ga all P_4 all Ca all Q_3 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),P_4),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> ((all Z_4 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_4),S_3)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_4,Z_4),S_3)))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))))) # label(fact_7_conseq1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 107 (all X_c (ord(X_c) -> ord_less_eq(X_c) = ti(fun(X_c,fun(X_c,bool)),ord_less_eq(X_c)))) # label(tsy_c_Orderings_Oord__class_Oless__eq_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 108 (all K all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1))) # label(fact_425_diff__mult__distrib2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 109 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_771_order__less__asym) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 110 (all X_b all X_c (ordere779506340up_add(X_c) & semiring_1(X_c) -> (all F all K_2 all A_3 ((all I_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),I_2),A_3)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,I_2)),K_2)))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3)),hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(nat,X_c,semiring_1_of_nat(X_c),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))),K_2))))))) # label(fact_665_setsum__bounded) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 111 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (ti(X_b,X_1) = ti(X_b,Y_2) <-> hAPP(X_b,fun(X_b,bool),ord_greaterThan(X_b),X_1) = hAPP(X_b,fun(X_b,bool),ord_greaterThan(X_b),Y_2))))) # label(fact_546_greaterThan__eq__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 112 (all K all I all J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),J)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J),K)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),K))))) # label(fact_693_zle__trans) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 113 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B)),hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))) # label(fact_502_minus__add) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 114 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)) = ti(X_a,X)))) # label(fact_533_min__max_Osup__inf__absorb) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 115 (all N_1 all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M)),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N_1),M)) # label(fact_565_nat__minus__add__max) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 116 (all X_a all X_c all X_b all P all Q all R hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q) = 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)) # label(help_COMBC_1_1_U) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 117 (all X_b (linorder(X_b) -> (all N_3 all H ((all X_2 all Y_1 hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_1)) = hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_2),Y_1))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),N_3) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),N_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),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),H),N_3)))))))) # label(fact_392_Min_Ohom__commute) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 118 (all X_a (ord(X_a) -> (all C all A_1 all B (ti(X_a,A_1) = ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))))))) # label(fact_777_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 119 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ly)))) # label(fact_241_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 120 (all X_b all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),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(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_3))) = hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3)) # label(fact_522_Compl__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 121 (all X_b all R_1 all S_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)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),R_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),S_1))) <-> 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)),R_1),S_1)))) # label(fact_264_pred__subset__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 122 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))) # label(fact_508_minus__mult__minus) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 123 (all X_a (cancel_semigroup_add(X_a) -> (all B all A_1 all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),A_1) -> ti(X_a,B) = ti(X_a,C))))) # label(fact_226_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 124 (all X_a (order(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (ti(X_a,B) != ti(X_a,A_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_760_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 125 (all X_b all Q_3 all Pa ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> hBOOL(hAPP(X_b,bool,Q_3,X_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)),Pa),Q_3)))) # label(fact_339_predicate1I) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 126 (all X_b (linord581940658strict(X_b) -> (all A_2 all Ca all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),Ca)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),zero_zero(X_b))) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),A_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),Ca))))))) # label(fact_981_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 127 (all X_b ti(fun(fun(X_b,bool),nat),finite_card(X_b)) = finite_card(X_b)) # label(tsy_c_Finite__Set_Ocard_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 128 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)))) # label(fact_802_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 129 (all K all I all J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),J)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),J)))))) # label(fact_961_zmult__zless__mono2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 130 (all I all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),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)) = I)) # label(fact_439_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 131 (all X_c all X_b all H all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2)) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(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_2))))) # label(fact_100_finite__imageI) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 132 (all X_a (boolean_algebra(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y)),hAPP(X_a,X_a,uminus_uminus(X_a),X))))))) # label(fact_499_compl__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 133 (all X_b all X_c (bot(X_c) -> (all X_2 bot_bot(X_c) = hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2)))) # label(fact_44_bot__fun__def) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 134 (all X_b all A_2 all Ba (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),bot_bot(fun(X_b,bool))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))) -> ti(X_b,Ba) = ti(X_b,A_2))) # label(fact_35_singleton__inject) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 135 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),M)))) # label(fact_635_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 136 (all X_a (semiring(X_a) -> (all A_1 all E_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),E_1)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),E_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),E_1)),C))))) # label(fact_224_combine__common__factor) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 137 (all X_b all X_c ti(fun(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool)))),finite_fold_graph(X_b,X_c)) = finite_fold_graph(X_b,X_c)) # label(tsy_c_Finite__Set_Ofold__graph_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 138 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Rx))))) # label(fact_242_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 139 (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M)) -> N_1 != M)) # label(fact_797_less__not__refl2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 140 (all X_c all X_b (bot(X_b) -> (all X_1 hAPP(X_c,X_b,bot_bot(fun(X_c,X_b)),X_1) = bot_bot(X_b)))) # label(fact_43_bot__apply) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 141 (all X_b all Ca all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3))))) # label(fact_520_ComplI) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 142 (all X_a (linordered_semidom(X_a) -> (all A_1 all N_1 all N_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_4)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_4)))))))) # label(fact_886_power__increasing) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 143 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z)))) # label(fact_348_min__max_Oinf__assoc) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 144 (all X_b all Ts all Ga (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),ord_less_eq(fun(hoare_2118899576triple(X_b),bool)),Ts),Ga)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts)))) # label(fact_319_asm) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 145 (all X_b (linordered_semidom(X_b) -> (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(nat,X_b,semiring_1_of_nat(X_b),N))))))) # label(fact_973_of__nat__0__less__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 146 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_511_diff__minus__eq__add) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 147 (all X_a (ordere779506340up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))))))) # label(fact_297_add__left__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 148 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z))))) # label(fact_537_min__max_Osup__assoc) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 149 (all X_c all X_b (uminus(X_b) -> (all A_3 all X_1 hAPP(X_b,X_b,uminus_uminus(X_b),hAPP(X_c,X_b,A_3,X_1)) = hAPP(X_c,X_b,hAPP(fun(X_c,X_b),fun(X_c,X_b),uminus_uminus(fun(X_c,X_b)),A_3),X_1)))) # label(fact_484_uminus__apply) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 150 (all Z all W_2 hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),W_2)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),Z)),hAPP(int,int,uminus_uminus(int),W_2))) # label(fact_690_zminus__zadd__distrib) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 151 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N_1))) # label(fact_937_le0) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 152 (all X_b (linorder(X_b) -> hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_b,X_b),ord_max(X_b))))) # label(fact_560_min__max_Ocomp__fun__idem__sup) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 153 (all X_b all A_3 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(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_3))),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(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_2))))) # label(fact_131_set__diff__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 154 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)))))) # label(fact_346_Min_Oin__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 155 (all X_c all X_b all F all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> 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_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_3)) = 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_3))) # label(fact_82_insert__image) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 156 (all X_b all X_c (ab_group_add(X_c) -> (all F all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))) & (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3)),hAPP(X_b,X_c,F,A_2)) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))))))) # label(fact_173_setsum__diff1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 157 (all X_b hoare_1301688828derivs(X_b) = ti(fun(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool)),hoare_1301688828derivs(X_b))) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Ohoare__derivs_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 158 (all M_1 all K_1 all F ((all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M_2)),hAPP(nat,nat,F,N_2))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,F,M_1)),K_1)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)))))) # label(fact_911_mono__nat__linear__lb) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 159 (all X_b all X_c (comm_monoid_add(X_c) & ordere223160158up_add(X_c) -> (all F all G all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),A_3))))))))) # label(fact_847_setsum__strict__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 160 (all U all M_1 all N all J_1 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),I_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M_1)),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),N)))))) # label(fact_841_nat__less__add__iff1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 161 (all X_a (linord581940658strict(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))))) # label(fact_995_mult__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 162 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)))) # label(fact_441_add__diff__assoc) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 163 (all P (fFalse = ti(bool,P) | ti(bool,P) = fTrue)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 164 (all X_a (linord20386208strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_993_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 165 (all X_a (ord(X_a) -> (all C all A_1 all B (ti(X_a,B) = ti(X_a,A_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))))))) # label(fact_274_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 166 (all X_b all Q_3 all Ga all Ca all Pa ((all Z_4 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_4),S_3)) -> (exists P_3 exists Q_4 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),P_3),Ca),Q_4)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) & (all S_4 ((all Z_5 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_3,Z_5),S_3)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_4,Z_5),S_4)))) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_3,Z_4),S_4)))))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))) # label(fact_51_conseq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 167 (all X_b all X_c (comm_monoid_mult(X_c) -> big_co302546470etprod(X_b,X_c) = ti(fun(fun(X_b,X_c),fun(fun(X_b,bool),X_c)),big_co302546470etprod(X_b,X_c)))) # label(tsy_c_Big__Operators_Ocomm__monoid__mult__class_Osetprod_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 168 (all X_b all Ba all A_2 all B_2 ((-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_2)) -> ti(X_b,Ba) = ti(X_b,A_2)) -> 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),Ba),B_2))))) # label(fact_10_insertCI) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 169 (all X_b all D_2 all B_2 all A_3 all C_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_3),C_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)),D_2),B_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)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),C_1),D_2)))))) # label(fact_316_Diff__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 170 (all X_b (power(X_b) -> ti(fun(X_b,fun(nat,X_b)),power_power(X_b)) = power_power(X_b))) # label(tsy_c_Power_Opower__class_Opower_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 171 (all X_a (linorder(X_a) -> (all X all Y ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y))))) # label(fact_532_min__max_Oinf__sup__absorb) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 172 (all X_a (linorder(X_a) -> (all A_1 all B all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_734_min__max_Oless__infI2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 173 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)),I) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I)),K))) # label(fact_447_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 174 (all X_a (comm_monoid_mult(X_a) -> (all A_1 all B all N_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),N_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N_1))))) # label(fact_872_power__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 175 (all X_c all X_b (ab_group_add(X_b) -> (all F all G all A_3 hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),F),A_3)),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),G),A_3)) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,X_b)),combs(X_c,X_b,X_b),hAPP(fun(X_c,X_b),fun(X_c,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_c),minus_minus(X_b)),F)),G)),A_3)))) # label(fact_190_setsum__subtractf) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 176 (all X_a (linorder(X_a) -> (all X ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),X)))) # label(fact_347_Min_Oidem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 177 (all N_1 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)))) # label(fact_423_le__add2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 178 (all X_a all P ti(X_a,P) = hAPP(X_a,X_a,combi(X_a),P)) # label(help_COMBI_1_1_U) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 179 (all X_b (order(X_b) -> (all A_2 all Ba all Ca (ti(X_b,A_2) = ti(X_b,Ba) & ti(X_b,Ca) = ti(X_b,Ba) <-> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ca),bot_bot(fun(X_b,bool))) = hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),Ba))))) # label(fact_832_atLeastAtMost__singleton__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 180 (all X_b (linorder(X_b) -> ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b)),big_Sup_fin(X_b)) = big_Sup_fin(X_b))) # label(tsy_c_Big__Operators_Olattice_OSup__fin_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 181 (all X_b (order(X_b) -> (all K_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),K_1),bot_bot(fun(X_b,bool))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(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),K_1),bot_bot(fun(X_b,bool)))),hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),K_1))))) # label(fact_257_single__Diff__lessThan) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 182 (all X_b (ab_sem1668676832m_mult(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(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_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),times_times(X_b)),A_2),A_3))))) # label(fact_206_fold1__eq__fold__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 183 (all X_a (group_add(X_a) -> (all A_1 all B ti(X_a,B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B))))) # label(fact_503_add__minus__cancel) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 184 (all Y all X all Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))))) # label(fact_803_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 185 (all X_c all X_b all R_1 all K_1 all T_4 all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),T_4)) -> ((all X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),T_4)) -> K_1 = hAPP(fun(X_b,bool),nat,finite_card(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)),S_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),R_1),X_2)))))) -> hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,nat),hAPP(fun(fun(X_c,bool),nat),fun(fun(X_b,fun(X_c,bool)),fun(X_b,nat)),combb(fun(X_c,bool),nat,X_b),finite_card(X_c)),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool)),hAPP(fun(fun(X_c,bool),fun(X_c,bool)),fun(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool))),combb(fun(X_c,bool),fun(X_c,bool),X_b),collect(X_c)),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool)),hAPP(fun(fun(X_c,bool),fun(X_c,bool)),fun(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool))),combb(fun(X_c,bool),fun(X_c,bool),X_b),hAPP(fun(X_c,fun(bool,bool)),fun(fun(X_c,bool),fun(X_c,bool)),combs(X_c,bool,bool),hAPP(fun(X_c,bool),fun(X_c,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_c,bool),fun(X_c,fun(bool,bool))),combb(bool,fun(bool,bool),X_c),fconj),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,fun(fun(X_c,bool),bool)),fun(fun(X_c,bool),fun(X_c,bool)),combc(X_c,fun(X_c,bool),bool),member(X_c)),T_4)))),R_1)))),S_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_1),hAPP(fun(X_c,bool),nat,finite_card(X_c),T_4)))))) # label(fact_619_setsum__multicount) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 186 (all X_b all A_3 all X_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_3),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),bot_bot(fun(X_b,bool))))) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))) = ti(fun(X_b,bool),A_3) | bot_bot(fun(X_b,bool)) = ti(fun(X_b,bool),A_3))) # label(fact_320_subset__singletonD) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 187 (all X_c all X_b (comm_monoid_mult(X_b) -> (all G one_one(X_b) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),G),bot_bot(fun(X_c,bool)))))) # label(fact_640_setprod_Oempty) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 188 (all X_b all X_c all Z_2 all X_1 all A_3 all V all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_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_1),A_3)),V)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> -(all Y_1 (ti(X_c,V) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Y_1) -> -hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),Y_1)))))))) # label(fact_207_comp__fun__commute_Ofold__graph__insertE) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 189 (all X_b all X_c (comm_monoid_add(X_c) -> (all G all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),plus_plus(X_c),hAPP(X_b,X_c,G,X_1)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),A_3)))))) # label(fact_212_setsum_Oremove) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 190 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_max(X_b)),A_3))))) # label(fact_596_min__max_OSup__fin_OF__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 191 (all K -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K)),zero_zero(int)))) # label(fact_958_int__less__0__conv) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 192 (all X_b all A_3 all A_2 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) # label(fact_144_Diff__insert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 193 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> (exists B_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_3)) & ti(fun(X_b,bool),A_3) = 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_3))))) # label(fact_49_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 194 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y))))) # label(fact_363_min__max_Oinf__absorb1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 195 (all L all U hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),L),U)))) # label(fact_890_finite__atLeastAtMost__int) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 196 (all K all I all J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),J)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),I)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),J))))) # label(fact_706_zadd__left__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.43 197 (all X_a (ordere223160158up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))))) # label(fact_729_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 198 (all T_2 all T_1 (minus(T_1) -> minus(fun(T_2,T_1)))) # label(arity_fun___Groups_Ominus) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 199 (all X_b all X_c all Z_2 all X_1 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_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_1),A_3))))) # label(fact_196_comp__fun__commute_Ofold__insert__remove) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 200 (all X_c all X_b (ord(X_c) & order(X_b) -> (all Ca all F all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,Ba)),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Ca),Ba)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Y_1),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,Y_1)),hAPP(X_c,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,Ca)),A_2)))))))) # label(fact_610_xt2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 201 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 202 (all X_b (ord(X_b) -> (all I_1 all K_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),I_1),hAPP(X_b,fun(X_b,bool),ord_greaterThan(X_b),K_1))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),K_1),I_1)))))) # label(fact_807_greaterThan__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 203 (all X_a (linorder(X_a) -> (all Y all Z all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Z),X)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z)),X)))) # label(fact_529_min__max_Osup__inf__distrib2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 204 (all X_b (ab_group_add(X_b) -> ti(X_b,zero_zero(X_b)) = zero_zero(X_b))) # label(tsy_c_Groups_Ozero__class_Ozero_1_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 205 (all X_a (linord219039673up_add(X_a) -> (all X all Y hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))) # label(fact_563_minus__min__eq__max) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 206 (all Com1 all Com2 all Vname_1 all Fun_1 hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2) != hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname_1),Fun_1)) # label(fact_73_com_Osimps_I25_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 207 (all X_c all X_b all F all Z_2 all Y_2 all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),fold_graph(X_b,X_c),F),Z_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool))))),Y_2)) -> hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),fold_graph(X_b,X_c),F),Z_2),A_3),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Y_2)))))) # label(fact_172_fold__graph_H_Ointros_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 208 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) -> M = N_1))) # label(fact_412_le__antisym) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 209 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_3))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)))) # label(fact_104_finite__insert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 210 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)) = ti(X_a,A_1)))) # label(fact_486_minus__minus) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 211 (all X_a (linorder(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y))))) # label(fact_554_min__max_Osup__absorb1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 212 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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)),A_3),B_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)))))) # label(fact_615_card__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 213 (all M_1 all N (M_1 = one_one(nat) & N = one_one(nat) <-> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N))) # label(fact_625_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 214 (all X_b all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,F_2,A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),A_3)))) # label(fact_95_folding__one_Oeq__fold) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 215 (all X_b (linord219039673up_add(X_b) -> (all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),S_1) -> hAPP(X_b,X_b,uminus_uminus(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),S_1)) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),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),uminus_uminus(X_b)),S_1))))))) # label(fact_481_minus__Min__eq__Max) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 216 (all X_a (linorder(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),A_1)))) # label(fact_356_min__max_Oinf_Oidem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 217 (all X_c all X_b all A_3 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3)) -> hAPP(X_c,X_b,G,X_2) = ti(X_b,Z_2))) -> hAPP(fun(X_c,bool),X_b,F_2,A_3) = ti(X_b,Z_2))))) # label(fact_170_folding__image__simple_Oneutral) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 218 (all X_a (monoid_mult(X_a) -> (all A_1 all M all N_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),N_1)))) # label(fact_876_power__mult) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 219 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> 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_1),A_3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))))))) # label(fact_649_card_Oinsert__remove) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 220 (all M all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)))) # label(fact_824_add__diff__inverse) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 221 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_max(X_b)),A_3))))) # label(fact_572_Max_OF__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 222 (all X_b (comm_semiring_1(X_b) -> (all N hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),N)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),N)),one_one(X_b))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),one_one(X_b)),one_one(X_b))),hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),semiring_1_of_nat(X_b)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),N)))))) # label(fact_677_gauss__sum) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 223 (all X_b all X_c (comm_monoid_add(X_c) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(X_b,X_c,G,X_2) = hAPP(X_b,X_c,H,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),H),A_3)))))) # label(fact_210_setsum_Ocong) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 224 (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)) = M)) # label(fact_440_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 225 (all X_a (cancel_semigroup_add(X_a) -> ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)) = plus_plus(X_a))) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 226 (all X_b (ord(X_b) -> ti(fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,X_b))),max(X_b)) = max(X_b))) # label(tsy_c_Orderings_Oord_Omax_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 227 (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]. 2.21/2.44 228 (all X_b (linorder(X_b) -> (all M_3 all N_3 (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)),M_3),N_3)) -> (ti(fun(X_b,bool),M_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),N_3)),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),M_3))))))))) # label(fact_341_Min__antimono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 229 (all X_b all F all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),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),A_2),bot_bot(fun(X_b,bool)))),Ba)) <-> ti(X_b,A_2) = ti(X_b,Ba))) # label(fact_57_fold1Set__sing) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 230 (all X_a (linordered_semidom(X_a) -> (all N_1 all M (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),M)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),M),N_1)))))))) # label(fact_823_less__1__mult) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 231 (all X_b (linorder(X_b) -> (all Ba all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),A_2),Ba)),hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),Ba),A_3)))))))) # label(fact_567_min__max_Osup__le__fold__sup) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 232 (all X_b all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_2)) <-> ti(fun(X_b,bool),A_2) = bot_bot(fun(X_b,bool)) | (exists A_4 exists A_5 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_4)) & ti(fun(X_b,bool),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_5),A_4))))) # label(fact_110_finite_Osimps) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 233 (all X_b all A_3 ((all Y_1 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_3))) -> bot_bot(fun(X_b,bool)) = ti(fun(X_b,bool),A_3))) # label(fact_50_equals0I) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 234 (all X_b (ring(X_b) -> (all A_2 all E all Ca all Ba all D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),E)),D) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),Ca) <-> ti(X_b,Ca) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Ba),A_2)),E)),D))))) # label(fact_219_eq__add__iff2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 235 (all X_b all X_1 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> hAPP(fun(X_b,bool),X_b,F_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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,A_3))))))) # label(fact_94_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 236 (all X_a (linorder(X_a) -> (all A_1 all X all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_552_min__max_Ole__supI2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 237 (all X_a (ordere223160158up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_727_add__strict__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 238 (all U all M_1 all N all I_1 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)),U)),N)))))) # label(fact_452_nat__le__add__iff2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 239 (all X_b all Y_2 -(all Fun1 all Com all Fun2 hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Fun1),Com),Fun2) != Y_2)) # label(fact_47_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 240 (all X_b all X_c (comm_monoid_mult(X_c) -> (all Ba all Ca all A_2 all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),S_1)) -> hAPP(nat,X_c,hAPP(X_c,fun(nat,X_c),power_power(X_c),Ca),hAPP(fun(X_b,bool),nat,finite_card(X_b),S_1)) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(X_c,fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(X_b,X_c)),combc(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_b,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combs(X_b,X_c,fun(X_c,X_c)),hAPP(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c))),hAPP(fun(bool,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c)))),combb(bool,fun(X_c,fun(X_c,X_c)),X_b),if(X_c)),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))),Ba)),Ca)),S_1)) & (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),S_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(X_c,fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(X_b,X_c)),combc(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_b,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combs(X_b,X_c,fun(X_c,X_c)),hAPP(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c))),hAPP(fun(bool,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c)))),combb(bool,fun(X_c,fun(X_c,X_c)),X_b),if(X_c)),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))),Ba)),Ca)),S_1) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(X_b,X_c,Ba,A_2)),hAPP(nat,X_c,hAPP(X_c,fun(nat,X_c),power_power(X_c),Ca),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),S_1)),one_one(nat))))))))) # label(fact_678_setprod__gen__delta) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 241 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ti(X_a,Y) != ti(X_a,X))))) # label(fact_782_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 242 (all X_b all X_1 all A_3 all B_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)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))))) # label(fact_283_set__mp) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 243 (all X_c all X_b all F all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(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_3))) -> (exists X_2 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_3))),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_2)))))) & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))))))) # label(fact_112_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 244 (all X_b all A_3 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)),bot_bot(fun(X_b,bool))),A_3))) # label(fact_262_empty__subsetI) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 245 (all X_a (ab_sem1668676832m_mult(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)))) # label(fact_166_times_Oidem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 246 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_757_order__less__imp__le) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 247 (all X_a (linordered_semidom(X_a) -> (all N_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)))))))) # label(fact_881_power__less__power__Suc) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 248 (all X_b all A_3 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)) # label(fact_133_Diff__idemp) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 249 (all X_b all X_c (order(X_b) & order(X_c) -> (all Ca all A_2 all F all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),hAPP(X_c,X_b,F,Ba))) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Ba),Ca)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),X_2),Y_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,X_2)),hAPP(X_c,X_b,F,Y_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,Ca))))))))) # label(fact_930_order__le__less__subst1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 250 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) | N = M_1)) # label(fact_738_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 251 (all J_1 all I_1 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J_1),I_1)) -> hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),I_1),J_1) = hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),I_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_1),one_one(int))),J_1))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J_1),I_1)) -> bot_bot(fun(int,bool)) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),I_1),J_1)))) # label(fact_892_simp__from__to) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 252 (all X_b all X_c all F all G ((all X_2 hAPP(X_b,X_c,G,X_2) = hAPP(X_b,X_c,F,X_2)) -> ti(fun(X_b,X_c),F) = ti(fun(X_b,X_c),G))) # label(fact_75_ext) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 253 (all N all K_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)))))) # label(fact_826_less__diff__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 254 (all X_b all X_1 all A_3 (hBOOL(hAPP(X_b,bool,A_3,X_1)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)))) # label(fact_76_mem__def) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 255 (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]. 2.21/2.44 256 (all S all T_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3)) -> T_3 != S)) # label(fact_796_less__not__refl3) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 257 (all N_1 all M M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M)),N_1)) # label(fact_427_diff__add__inverse) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 258 (all X_b all X_c (order(X_b) & order(X_c) -> (all F all Ca all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,Ba)),Ca)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_1)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,F,Y_1))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,A_2)),Ca)))))))) # label(fact_925_order__less__le__subst2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 259 (all X_a (linorder(X_a) -> (all B all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),C))))) # label(fact_540_min__max_Osup_Oleft__commute) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 260 (all X_a (dense_linorder(X_a) -> (all Z all Y ((all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z)))))) # label(fact_917_dense__le) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 261 (all X_b (order(X_b) -> (all A_2 all Ba (hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),Ba) = bot_bot(fun(X_b,bool)) <-> -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)))))) # label(fact_828_atLeastatMost__empty__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 262 (all X_b (linorder(X_b) -> (all N_3 all H ((all X_2 all Y_1 hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_2),Y_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_1))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),N_3) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),N_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),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),H),N_3)))))))) # label(fact_478_min__max_OInf__fin_Ohom__commute) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 263 (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]. 2.21/2.44 264 (all X_b (order(X_b) -> (all Ca all A_2 all F all Ba (ti(X_b,A_2) = hAPP(X_b,X_b,F,Ba) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),Ba)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,F,Y_1)),hAPP(X_b,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,F,Ca)),A_2)))))))) # label(fact_611_xt1_I15_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 265 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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)),A_3),B_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)))))) # label(fact_871_card__psubset) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 266 (all X_a (order(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> ti(X_a,X) = ti(X_a,Y)))))) # label(fact_268_xt1_I5_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 267 (all Z1 all Z2 all Z3 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),Z3)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),Z2)),Z3)) # label(fact_695_zmult__assoc) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 268 (all X_b all Q_3 all Pa (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3))) | hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_3)))))) # label(fact_97_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 269 (all X_b all Pa all A_2 ((hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Pa))) & (-hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2))),Pa)) = bot_bot(fun(X_b,bool))))) # label(fact_15_Collect__conv__if) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 270 (all M all I all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),I)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),I)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),M),N_1)),I)) # label(fact_424_min__diff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 271 (all M all N_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1))) # label(fact_672_int__mult) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 272 (all N_1 (zero_zero(nat) != N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)))) # label(fact_968_gr0I) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 273 (all M_1 all N (N != M_1 & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)))) # label(fact_737_nat__less__le) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 274 (all X_b all F all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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_2),A_3)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),A_3)),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),B_2)) = hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))))) # label(fact_258_setsum__diff__nat) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 275 (all T_2 all T_1 (boolean_algebra(T_1) -> boolean_algebra(fun(T_2,T_1)))) # label(arity_fun___Lattices_Oboolean__algebra) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 276 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))))) # label(fact_547_le__maxI1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 277 (all X_b (idom(X_b) -> (all A_2 all Ba (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),A_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),Ba) <-> hAPP(X_b,X_b,uminus_uminus(X_b),Ba) = ti(X_b,A_2) | ti(X_b,Ba) = ti(X_b,A_2))))) # label(fact_509_square__eq__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 278 (all X_b all X_c all F all A_3 all B_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)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3)),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_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),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),B_2))))) # label(fact_322_image__diff__subset) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 279 (all Vname all Fun hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname),Fun) != skip) # label(fact_74_com_Osimps_I8_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 280 (all X_b all A_3 all B_2 (ti(fun(X_b,bool),A_3) != ti(fun(X_b,bool),B_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)),A_3),B_2)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)))) # label(fact_853_psubset__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 281 (all X_b all X_c (ord(X_c) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(X_b,X_c,G,X_1))))))) # label(fact_276_le__funD) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 282 (all X_b (linord219039673up_add(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b))))))) # label(fact_975_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 283 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 284 (all X_b (ab_sem1668676832m_mult(X_b) -> (all X_1 all A_3 (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3))))))) # label(fact_126_fold1__insert__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 285 (all X_a (linorder(X_a) -> (all Y all X (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_752_not__leE) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 286 (all X_b all X_c (comm_monoid_mult(X_c) -> (all Y_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),Y_2)),A_3) = hAPP(nat,X_c,hAPP(X_c,fun(nat,X_c),power_power(X_c),Y_2),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))))) # label(fact_838_setprod__constant) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 287 (all X_a (linordered_idom(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),X)),X)))))))) # label(fact_941_mult__left__le__one__le) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 288 (all X_a (linorder(X_a) -> (all X all Y all Z hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z))))))) # label(fact_562_min__max_Odistrib__sup__le) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 289 (all X_b (ordered_ring(X_b) -> (all A_2 all E all Ca all Ba all D (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),E)),D))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Ba),A_2)),E)),D))))))) # label(fact_837_less__add__iff2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 290 (all X_b all A_2 all Ba all A_3 (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),Ba),A_3))) -> (ti(X_b,Ba) != ti(X_b,A_2) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3))))) # label(fact_9_insertE) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 291 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (ti(X_a,Y) != ti(X_a,X) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_770_linorder__cases) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 292 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3))))))) # label(fact_470_min__max_OInf__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 293 (all X_b (linordered_idom(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),zero_zero(X_b))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2)),zero_zero(X_b))))))) # label(fact_979_even__less__0__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 294 (all M all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M))))) # label(fact_720_trans__less__add1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 295 (all X_a (cancel146912293up_add(X_a) -> (all A_1 all B all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) -> ti(X_a,B) = ti(X_a,C))))) # label(fact_227_add__imp__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 296 (all I_1 all Pa all K_1 (hBOOL(hAPP(int,bool,Pa,K_1)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_1),I_2)) -> (hBOOL(hAPP(int,bool,Pa,I_2)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),K_1)) -> (hBOOL(hAPP(int,bool,Pa,I_2)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,Pa,I_1)))))) # label(fact_931_int__induct) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 297 (all X_b all F all A_3 hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co302546470etprod(X_b,nat),F),A_3)) = hAPP(fun(X_b,bool),int,hAPP(fun(X_b,int),fun(fun(X_b,bool),int),big_co302546470etprod(X_b,int),hAPP(fun(X_b,nat),fun(X_b,int),hAPP(fun(nat,int),fun(fun(X_b,nat),fun(X_b,int)),combb(nat,int,X_b),semiring_1_of_nat(int)),F)),A_3)) # label(fact_675_int__setprod) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 298 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool))))))) & (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3) = ti(X_b,X_1))))))) # label(fact_380_Min_Oremove) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 299 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)))))) # label(fact_844_card__Diff1__less) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 300 (all X_c all X_b all Ba all F all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (ti(X_c,Ba) = hAPP(X_b,X_c,F,X_1) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Ba),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_3)))))) # label(fact_67_rev__image__eqI) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 301 (all X_a (preorder(X_a) -> (all X -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),X))))) # label(fact_791_order__less__irrefl) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 302 (all X_b (linordered_semidom(X_b) -> (all M_1 all N all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),one_one(X_b)),A_2)) -> (N = M_1 <-> hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),A_2),M_1) = hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),A_2),N)))))) # label(fact_879_power__inject__exp) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 303 (all X_a (ord(X_a) -> ord_min(X_a) = ti(fun(X_a,fun(X_a,X_a)),ord_min(X_a)))) # label(tsy_c_Orderings_Oord__class_Omin_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 304 (all X_b all F all A_3 hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),A_3)) # label(fact_65_fold1__def) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 305 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z))))) # label(fact_531_min__max_Osup__inf__distrib1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 306 (all X_a (linorder(X_a) -> (all A_1 all B all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_364_min__max_Ole__infI2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 307 (all X_b (ord(X_b) -> ord_less(X_b) = ti(fun(X_b,fun(X_b,bool)),ord_less(X_b)))) # label(tsy_c_Orderings_Oord__class_Oless_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 308 (all X_b all Pa all A_2 (hBOOL(hAPP(X_b,bool,Pa,A_2)) -> ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> ti(X_b,A_2) = ti(X_b,X_2))) -> hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa)))))) # label(fact_115_theI) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 309 (all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)) # label(fact_456_nat__mult__commute) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 310 (all X_b (ordered_ring(X_b) -> (all A_2 all E all Ca all Ba all D (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),E)),D))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Ba),A_2)),E)),D))))))) # label(fact_325_le__add__iff2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 311 (all M_1 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_1),N) = one_one(nat) <-> one_one(nat) = M_1 & N = one_one(nat))) # label(fact_623_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 312 (all X_b all A_3 all Ba ((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_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),bot_bot(fun(X_b,bool))))) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),partial_flat_lub(X_b),Ba),A_3) = ti(X_b,Ba)) & (-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_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),bot_bot(fun(X_b,bool))))) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),partial_flat_lub(X_b),Ba),A_3) = hAPP(fun(X_b,bool),X_b,the(X_b),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)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),bot_bot(fun(X_b,bool))))))))) # label(fact_336_flat__lub__def) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 313 (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_259_order__refl) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 314 (all X_b (minus(X_b) -> minus_minus(X_b) = ti(fun(X_b,fun(X_b,X_b)),minus_minus(X_b)))) # label(tsy_c_Groups_Ominus__class_Ominus_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 315 (all X_a (ring_1(X_a) -> (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)))))) # label(fact_663_of__nat__diff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 316 (all X_a (linordered_semidom(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)))))) # label(fact_942_zero__less__two) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 317 (all X_a (comm_semiring_1(X_a) -> (all M hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),M) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),M)))) # label(fact_637_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 318 (all U_1 all M all N_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I)),U_1)),N_1)))) # label(fact_451_nat__diff__add__eq2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 319 (all X_b (ab_sem1668676832m_mult(X_b) -> (all N_3 all H ((all X_2 all Y_1 hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_1)) = hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),Y_1))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),N_3) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),N_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),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),H),N_3)))))))) # label(fact_153_hom__fold1__commute) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 320 (all X_b all Ca -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),bot_bot(fun(X_b,bool))))) # label(fact_19_empty__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 321 (all X all Y all Z hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Y)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Z)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))) # label(fact_703_zpower__zadd__distrib) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 322 (all X_a (linord219039673up_add(X_a) -> (all X all Y hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))) # label(fact_564_minus__max__eq__min) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 323 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),one_one(nat)) = hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))))))) # label(fact_651_card__Diff__singleton__if) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 324 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_1)) <-> M_1 != N)) # label(fact_800_nat__neq__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 325 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all Ba all Ca all D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),Ba) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Ca),D) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),D))))))) # label(fact_304_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.44 326 (all M_1 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)))) # label(fact_670_zle__int) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 327 (all X_a (linorder(X_a) -> (all Y all Z all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z)),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Z),X))))) # label(fact_528_min__max_Oinf__sup__distrib2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 328 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Y))))) # label(fact_368_min__max_Oinf__le2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 329 (all X_b all X_c all Z_2 all X_1 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),A_3))))) # label(fact_195_comp__fun__commute_Ofold__rec) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 330 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))))) # label(fact_239_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 331 (all X_b all X_c (comm_monoid_mult(X_c) -> (all F all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),A_3) = one_one(X_c))))) # label(fact_642_setprod__infinite) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 332 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_949_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 333 (all X_a (preorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z))))))) # label(fact_762_order__less__le__trans) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 334 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_b,X_b,uminus_uminus(X_b),Ba))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),hAPP(X_b,X_b,uminus_uminus(X_b),A_2))))))) # label(fact_810_less__minus__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 335 (all X_b all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),B_2),C_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_1))))) # label(fact_858_psubset__trans) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 336 (all Z all W_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),W_2)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_2),Z)))) # label(fact_692_zle__linear) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 337 (all X_b (order(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) <-> ti(X_b,X_1) = ti(X_b,Y_2) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)))))) # label(fact_750_order__le__less) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 338 (all Com1_1 all Com2_1 all Com1 all Com2 (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_56_com_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 339 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> 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_1),A_3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))) # label(fact_647_card_Oinsert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 340 (all X_b all X_1 ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),X_1))) # label(fact_88_the__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 341 (all Pa ((all X_2 hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),X_2)))) <-> (all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hBOOL(hAPP(int,bool,Pa,X_2)))))) # label(fact_951_transfer__int__nat__quantifiers_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 342 (all X_b (ab_semigroup_mult(X_b) -> (all X_1 all A_3 (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3)))))))) # label(fact_125_fold1__insert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 343 (all X_c all X_b all F all Z_2 hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),fold_graph(X_b,X_c),F),Z_2),bot_bot(fun(X_b,bool))),Z_2))) # label(fact_191_fold__graph_H_Ointros_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 344 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_976_add__pos__pos) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 345 (all X_b all A_2 all Pa ((exists X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) & (all Y_1 (hBOOL(hAPP(X_b,bool,Pa,Y_1)) -> ti(X_b,X_2) = ti(X_b,Y_1))))) -> (hBOOL(hAPP(X_b,bool,Pa,A_2)) -> ti(X_b,A_2) = hAPP(fun(X_b,bool),X_b,the(X_b),Pa)))) # label(fact_116_the1__equality) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 346 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b)),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combs(X_b,bool,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool))),hAPP(fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),combb(fun(X_b,bool),fun(X_b,fun(bool,bool)),X_b),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,X_b),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,X_b),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,X_b),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool)),X_b),combb(X_b,bool,X_b)),fequal(X_b))),hAPP(X_b,fun(X_b,X_b),ord_max(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)),A_3))))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3))))))) # label(fact_588_min__max_Osup__Inf1__distrib) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 347 (all X_b all A_3 all X_1 all B_2 ((hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(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_1),A_3)),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(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_1),A_3)),B_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_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))))) # label(fact_141_insert__Diff__if) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 348 (all X_c all X_b all B_2 all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (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_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_3))) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),B_2))))) # label(fact_321_finite__surj) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 349 (all T_2 all T_1 (uminus(T_1) -> uminus(fun(T_2,T_1)))) # label(arity_fun___Groups_Ouminus) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 350 (all X_b all X_c all X_1 all Z_2 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),A_3)) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2)),A_3)))) # label(fact_178_comp__fun__commute_Ofold__fun__comm) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 351 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))))) # label(fact_238_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 352 (all X_b (linorder(X_b) -> (all Ba all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),Ba),A_3)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),A_2),Ba)))))))) # label(fact_387_min__max_Ofold__inf__le__inf) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 353 (all X_b all B_2 all X_1 all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_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_1),A_3) = 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),B_2) <-> ti(fun(X_b,bool),B_2) = ti(fun(X_b,bool),A_3))))) # label(fact_26_insert__ident) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 354 (all X_a (linordered_semidom(X_a) -> (all A_1 all N_1 all B (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> ti(X_a,A_1) = ti(X_a,B)))))))) # label(fact_966_power__eq__imp__eq__base) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 355 (all X_c all X_b all X_1 all A_3 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3)) -> (-hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3)) -> hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_2,A_3)))))) # label(fact_169_folding__image__simple_Oinsert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 356 (all X_a (order(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (ti(X_a,C) = ti(X_a,B) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1))))))) # label(fact_774_xt1_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 357 (all X_b (linorder(X_b) -> (all X_1 all Y_2 all Z_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),Y_2),Z_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Z_2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)))))) # label(fact_366_min__max_Ole__inf__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 358 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3))))) # label(fact_472_min__max_OInf__fin_OF__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 359 (all X_b all X_c (ordere779506340up_add(X_c) & comm_monoid_add(X_c) -> (all F all G all K_2 ((all I_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),I_2),K_2)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,I_2)),hAPP(X_b,X_c,G,I_2))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),K_2)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),K_2))))))) # label(fact_333_setsum__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 360 (all X_b all Ca all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)))) # label(fact_134_DiffD1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 361 (all X_a (linorder(X_a) -> (all B all A_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_365_min__max_Ole__infI1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 362 (all X_b all B_2 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_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_2)))) # label(fact_312_subset__insertI) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 363 (all X_a (ordere223160158up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))))))) # label(fact_728_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 364 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3))))) # label(fact_372_Min_OF__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 365 (all X_c all X_b (order(X_b) & order(X_c) -> (all Ca all F all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,Ba)),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Ca),Ba)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Y_1),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,Y_1)),hAPP(X_c,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,Ca)),A_2)))))))) # label(fact_927_xt4) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 366 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y))))) # label(fact_541_min__max_Osup__left__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 367 (all N_1 all K all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),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),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)))) # label(fact_449_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 368 (all X_c all X_b all Q_3 all Pa (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),hAPP(fun(X_c,bool),fun(X_c,bool),collect(X_c),hAPP(fun(X_c,fun(X_b,bool)),fun(X_c,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_c,fun(X_b,bool)),fun(X_c,bool)),combb(fun(X_b,bool),bool,X_c),fEx(X_b)),hAPP(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_c),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_3))))) <-> (all Y_1 (hBOOL(hAPP(X_b,bool,Pa,Y_1)) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),hAPP(fun(X_c,bool),fun(X_c,bool),collect(X_c),hAPP(X_b,fun(X_c,bool),hAPP(fun(X_c,fun(X_b,bool)),fun(X_b,fun(X_c,bool)),combc(X_c,X_b,bool),Q_3),Y_1))))))))) # label(fact_589_finite__Collect__bounded__ex) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 369 (all U all F ((all N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),hAPP(nat,nat,F,N_2)))) -> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(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),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),F)),U)))))) # label(fact_398_finite__less__ub) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 370 (all X_b (linorder(X_b) -> (all Z_2 all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Z_2),X_1)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Z_2),Y_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Z_2),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),Y_2))))))) # label(fact_711_less__max__iff__disj) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 371 (all X_b all X_c (comm_monoid_add(X_c) -> (all F all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),plus_plus(X_c),hAPP(X_b,X_c,F,A_2)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))))))))) # label(fact_213_setsum__diff1_H) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 372 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),A_2)),Ba)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),Ba)),A_2)))))) # label(fact_809_minus__less__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 373 (all Q all P (-hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | -hBOOL(P))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 374 (all X_a (ordere779506340up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))))) # label(fact_298_add__right__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 375 (all X_c all X_b all B_2 all A_3 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3)) -> (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_2),A_3)) -> hAPP(fun(X_c,bool),X_b,F_2,A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_c,bool),X_b,F_2,B_2)),hAPP(fun(X_c,bool),X_b,F_2,A_3)))))) # label(fact_323_folding__image__simple__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 376 (all X_a (order(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (ti(X_a,B) != ti(X_a,A_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_761_xt1_I11_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 377 (all Com1_2 all Com2_2 skip != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2)) # label(fact_53_com_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 378 (all M_1 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),M_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),N))) -> hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),M_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),N)) = hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),N)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),M_1),N)))) # label(fact_864_atLeastAtMostPlus1__int__conv) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 379 (all X_b all Ts all Ga all Ts_1 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts_1)) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),ord_less_eq(fun(hoare_2118899576triple(X_b),bool)),Ts),Ts_1)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts))))) # label(fact_318_weaken) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 380 (all Y all X all Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Z)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))))) # label(fact_467_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 381 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))) -> ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(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_1),A_3))) & (bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool))))))))))) # label(fact_605_min__max_OSup__fin_Oinsert__remove) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 382 (all Vname all Fun hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname),Fun) != skip) # label(fact_78_com_Osimps_I9_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 383 (all X_b all A_3 ti(fun(X_b,bool),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3))) # label(fact_523_double__complement) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 384 (all I all J all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),K)),J)) # label(fact_429_diff__commute) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 385 (all X_a (linordered_idom(X_a) -> (all X all Y (ti(X_a,Y) != ti(X_a,X) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_769_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 386 (all X_b (ord(X_b) -> hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,X_b)),min(X_b),ord_less_eq(X_b)) = ord_min(X_b))) # label(fact_401_min__ord__min) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 387 (all X_c all X_b all F all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> 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)),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_3))))) # label(fact_68_imageI) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 388 (all X_b (linorder(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),A_2),A_3) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(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_3)))))) # label(fact_578_Max_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 389 (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]. 2.21/2.45 390 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),K))) # label(fact_445_diff__add__assoc) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 391 (all X_b all X_c all B_2 all F all A_3 (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_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),A_3))) <-> (exists AA (ti(fun(X_b,bool),B_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),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_3)))))) # label(fact_314_subset__image__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 392 (all X_a (ab_group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1)))) # label(fact_492_minus__diff__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 393 (all X_b (ordered_ab_group_add(X_b) -> (all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),Ba)),hAPP(X_b,X_b,uminus_uminus(X_b),A_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)))))) # label(fact_494_neg__le__iff__le) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 394 (all X all Y all Z hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Z))) # label(fact_460_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 395 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)))))) # label(fact_745_linorder__not__less) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 396 (all X_b all A_2 all A_3 bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) # label(fact_40_empty__not__insert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 397 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> ((all X_2 all Y_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_2),Y_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)),A_3)))))))) # label(fact_607_min__max_OSup__fin_Oclosed) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 398 (all X_b all X_1 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) -> ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,F_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_1),bot_bot(fun(X_b,bool)))))) # label(fact_58_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 399 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)))) # label(fact_507_minus__mult__commute) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 400 (all N all N_3 ((all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),N)))) -> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3)))) # label(fact_912_bounded__nat__set__is__finite) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 401 (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]. 2.21/2.45 402 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all Ba all Ca all D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),Ca),D) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),Ba) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),D)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba))))))) # label(fact_768_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 403 (all A_3 all B_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_2))) <-> hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A_3),B_2)))) # label(fact_895_transfer__nat__int__set__relations_I5_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 404 (all X_a (linordered_semidom(X_a) -> (all N_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))))))) # label(fact_964_zero__less__power) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 405 (all X_c all X_b (comm_monoid_mult(X_b) -> (all H all G all S_1 all R_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,one_one(X_b)),one_one(X_b))) -> ((all X1 all Y1 all X2 all Y2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,Y1),Y2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,X1),X2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X1),Y1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X2),Y2))))) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),S_1)) -> ((all X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),S_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(X_c,X_b,H,X_2)),hAPP(X_c,X_b,G,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),R_1,hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),H),S_1)),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),G),S_1)))))))))) # label(fact_657_setprod_Orelated) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 406 (all X_b (ordered_ab_group_add(X_b) -> (all X_1 hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),X_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),uminus_uminus(X_b)),hAPP(X_b,fun(X_b,bool),ord_greaterThan(X_b),X_1))))) # label(fact_517_image__uminus__greaterThan) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 407 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) -> (ti(X_b,X_1) = ti(X_b,Y_2) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2))))))) # label(fact_753_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 408 (all X_a (linorder(X_a) -> (all X all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B))) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B))))))) # label(fact_358_min__max_Ole__infE) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 409 (all X_b all A_3 ((exists X_2 exists B_3 (ti(fun(X_b,bool),A_3) = 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_3) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_3)))) <-> ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)))) # label(fact_52_nonempty__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 410 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ti(X_a,X) != ti(X_a,Y))))) # label(fact_781_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 411 (all X_a (ordere216010020id_add(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_946_add__strict__increasing) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 412 (all X_b all X_1 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,A_3)))))) # label(fact_119_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 413 (all X_b all A_3 all B_2 (ti(fun(X_b,bool),B_2) = ti(fun(X_b,bool),A_3) -> 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_2),A_3)))) # label(fact_286_equalityD2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 414 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),M)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),M)))) # label(fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 415 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)),I) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I)),K))) # label(fact_446_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 416 (all X_b all X_1 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),F),X_1),A_3) = hAPP(fun(X_b,bool),X_b,F_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_1),A_3)))))) # label(fact_203_folding__one_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 417 (all X_b all Pa all A_2 ((hBOOL(hAPP(X_b,bool,Pa,A_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Pa))) & (-hBOOL(hAPP(X_b,bool,Pa,A_2)) -> bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Pa))))) # label(fact_14_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 418 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y))) # label(fact_906_Nat__Transfer_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 419 (all Pa all I_1 all K_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_1),K_1)) -> (hBOOL(hAPP(int,bool,Pa,K_1)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),K_1)) -> (hBOOL(hAPP(int,bool,Pa,I_2)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,Pa,I_1)))))) # label(fact_889_int__le__induct) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 420 (all I_1 all K_1 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),J_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_1))))) # label(fact_442_le__diff__conv2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 421 (all X_a (linord581940658strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_991_mult__neg__neg) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 422 (all X_b all Y_2 all A_3 all X_1 (hBOOL(hAPP(X_b,bool,A_3,X_1)) | ti(X_b,X_1) = ti(X_b,Y_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_3),X_1)))) # label(fact_27_insert__code) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 423 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3))) <-> (all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),X_2)))))))))) # label(fact_391_min__max_Obelow__fold1__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 424 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))) -> ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(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_1),A_3))) & (bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(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_1),A_3))))))) # label(fact_379_Min_Oinsert__remove) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 425 (all X_b all X_c (ab_group_add(X_c) -> (all F all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (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_2),A_3)) -> hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),B_2)) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))))))) # label(fact_329_setsum__diff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 426 (all X_b (power(X_b) -> times_times(X_b) = ti(fun(X_b,fun(X_b,X_b)),times_times(X_b)))) # label(tsy_c_Groups_Otimes__class_Otimes_0_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 427 (all X_b all X_1 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,F_2,A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,A_3)))))) # label(fact_151_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 428 (all X_a (preorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z))))))) # label(fact_764_order__le__less__trans) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 429 (all I all J all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),K)) # label(fact_428_diff__diff__left) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 430 (all X_a (ab_semigroup_add(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))) # label(fact_233_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 431 (all X_b all A_3 all X_1 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(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_1),A_3)),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) # label(fact_142_insert__Diff1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.45 432 (all X_b (linorder(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),B_2) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b)),hAPP(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,bool)),hAPP(fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),fun(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,bool))),combb(fun(X_b,fun(X_b,bool)),fun(X_b,bool),X_b),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b))),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(X_b,bool)))),combc(X_b,fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),fun(X_b,fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)))),hAPP(fun(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),fun(X_b,fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool))))),combb(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool))),X_b),combs(X_b,fun(X_b,bool),fun(X_b,bool))),hAPP(fun(X_b,fun(X_b,fun(X_b,fun(bool,bool)))),fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),hAPP(fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),fun(fun(X_b,fun(X_b,fun(X_b,fun(bool,bool)))),fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))))),combb(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),X_b),hAPP(fun(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combs(X_b,bool,bool))),hAPP(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,fun(X_b,fun(bool,bool)))),hAPP(fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),fun(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,fun(X_b,fun(bool,bool))))),combb(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool))),X_b),hAPP(fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),combb(fun(X_b,bool),fun(X_b,fun(bool,bool)),X_b),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,fun(X_b,X_b)),fun(X_b,fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,fun(X_b,bool)))),combc(X_b,fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool)))),hAPP(fun(fun(fun(X_b,X_b),fun(X_b,bool)),fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool))))),combb(fun(fun(X_b,X_b),fun(X_b,bool)),fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool))),X_b),combb(fun(X_b,X_b),fun(X_b,bool),X_b)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool)),X_b),combb(X_b,bool,X_b)),fequal(X_b)))),ord_min(X_b)))))),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(bool,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(bool,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combb(bool,bool,X_b)),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_3)))),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_2))))))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),B_2))))))))) # label(fact_592_min__max_Oinf__Sup2__distrib) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 433 (all X_b (ab_group_add(X_b) -> (all F all M_1 all N ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) -> hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(fun(nat,fun(X_b,X_b)),fun(fun(nat,X_b),fun(nat,X_b)),combs(nat,X_b,X_b),hAPP(fun(nat,X_b),fun(nat,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(nat,X_b),fun(nat,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),nat),minus_minus(X_b)),F)),hAPP(fun(nat,nat),fun(nat,X_b),hAPP(fun(nat,X_b),fun(fun(nat,nat),fun(nat,X_b)),combb(nat,X_b,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M_1),N)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(nat,X_b,F,M_1)),hAPP(nat,X_b,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))))) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) -> zero_zero(X_b) = hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(fun(nat,fun(X_b,X_b)),fun(fun(nat,X_b),fun(nat,X_b)),combs(nat,X_b,X_b),hAPP(fun(nat,X_b),fun(nat,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(nat,X_b),fun(nat,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),nat),minus_minus(X_b)),F)),hAPP(fun(nat,nat),fun(nat,X_b),hAPP(fun(nat,X_b),fun(fun(nat,nat),fun(nat,X_b)),combb(nat,X_b,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M_1),N))))))) # label(fact_934_setsum__natinterval__difff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 434 (all X_b all Ca all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B_2))))) # label(fact_859_psubsetD) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 435 (all X_a (ring_1(X_a) -> (all A_1 all N_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),N_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))))) # label(fact_887_power__minus) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 436 (all X_b (order(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) <-> ti(X_b,Y_2) = ti(X_b,X_1))))) # label(fact_278_order__eq__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 437 (all X_c all X_b (semiring_1(X_b) -> (all Y_2 all A_3 hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(X_b,fun(X_c,X_b),combk(X_b,X_c),Y_2)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),hAPP(fun(X_c,bool),nat,finite_card(X_c),A_3))),Y_2)))) # label(fact_664_setsum__constant) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 438 (all X_b all Pa all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))) -> ((all X_2 all F_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,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),X_2),F_3))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2)))))) # label(fact_111_finite__induct) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 439 (all X_b (group_add(X_b) -> (all A_2 all Ba (ti(X_b,Ba) = hAPP(X_b,X_b,uminus_uminus(X_b),A_2) <-> ti(X_b,A_2) = hAPP(X_b,X_b,uminus_uminus(X_b),Ba))))) # label(fact_487_equation__minus__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 440 (all X_b all Pa all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_3)) -> ((all A_5 all A_4 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_4)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_5),A_4)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_4)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_4),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_5),bot_bot(fun(X_b,bool)))))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))))))) # label(fact_156_finite__empty__induct) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 441 (all X_b all X_1 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))) -> hAPP(fun(X_b,bool),X_b,F_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_1),A_3)) = ti(X_b,X_1)) & (bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_b,F_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_1),A_3)))))) # label(fact_124_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 442 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)) | ti(X_b,Y_2) = ti(X_b,X_1) <-> -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)))))) # label(fact_789_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 443 (all X_b (boolean_algebra(X_b) -> (all X_1 all Y_2 (ti(X_b,X_1) = ti(X_b,Y_2) <-> hAPP(X_b,X_b,uminus_uminus(X_b),Y_2) = hAPP(X_b,X_b,uminus_uminus(X_b),X_1))))) # label(fact_485_compl__eq__compl__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 444 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))))) # label(fact_417_add__le__mono1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 445 (all I all J -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),I))) # label(fact_723_not__add__less1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 446 (all X_a all X all Y ti(X_a,Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fFalse),X),Y)) # label(help_If_2_1_T) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 447 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> ti(X_a,X) = ti(X_a,Y)))))) # label(fact_270_order__antisym) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 448 (all X_b all D all R_1 all Ga all Pa all Ca all Q_3 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Q_3),D),R_1)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),hAPP(com,com,hAPP(com,fun(com,com),semi,Ca),D)),R_1)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))))) # label(fact_46_Comp) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 449 (all X_a all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fTrue),X),Y) = ti(X_a,X)) # label(help_If_1_1_T) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 450 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),one_one(nat)) = hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))))))) # label(fact_621_card__Diff__singleton) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 451 (all X_a (linordered_semidom(X_a) -> (all M all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)))))) # label(fact_819_of__nat__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 452 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z))))) # label(fact_530_min__max_Oinf__sup__distrib1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 453 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)))) # label(fact_739_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 454 (all Z hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Z)))) # label(fact_953_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 455 (all X_a (monoid_mult(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a))))) # label(fact_629_mult__1__right) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 456 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3)))))))) # label(fact_381_Max__ge) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 457 (all X_a (ordere223160158up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_821_add__le__less__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 458 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool))))))))) # label(fact_650_card_Oremove) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 459 (all N 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(nat)),N))) = N) # label(fact_815_card__Collect__less__nat) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 460 (all A_3 hAPP(fun(nat,bool),nat,finite_card(nat),A_3) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))) # label(fact_901_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 461 (all N_1 N_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),one_one(nat))) # label(fact_624_nat__mult__1__right) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 462 (all X_c all X_b all F all Z_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (exists X1 hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),X1))))) # label(fact_113_finite__imp__fold__graph) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 463 (all X_b all F all A_2 hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),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),A_2),bot_bot(fun(X_b,bool)))) = ti(X_b,A_2)) # label(fact_61_fold1__singleton) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 464 (all X_1 all Y_2 all Pa ((-hBOOL(Pa) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),Pa),X_1),Y_2)) = hAPP(nat,int,semiring_1_of_nat(int),Y_2)) & (hBOOL(Pa) -> hAPP(nat,int,semiring_1_of_nat(int),X_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),Pa),X_1),Y_2))))) # label(fact_898_int__if__cong) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 465 (all X_a (linordered_semidom(X_a) -> (all M all N_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))))))) # label(fact_884_power__less__imp__less__exp) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 466 (all I all U_1 all J all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),J)),U_1)),K)) # label(fact_464_left__add__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 467 (all X_b all F all A_2 all A_3 ((hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),A_3)),hAPP(X_b,nat,F,A_2)) = hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),A_3)))) # label(fact_199_setsum__diff1__nat) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 468 (all M all N_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1))) # label(fact_671_zmult__int) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 469 (all X_a (linord581940658strict(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_996_mult__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 470 (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]. 2.21/2.46 471 (all N all K_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) <-> 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_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K_1))))))) # label(fact_402_le__diff__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 472 (all X_b all X_1 all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(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_1),A_3)),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),bot_bot(fun(X_b,bool)))) = ti(fun(X_b,bool),A_3))) # label(fact_147_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 473 (all L all U hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),L),U)))) # label(fact_938_finite__greaterThanAtMost) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 474 (all K_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),ord_lessThan(nat),K_1)))) # label(fact_343_finite__lessThan) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 475 (all W_1 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int)))) <-> W_1 = Z_2 | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)))) # label(fact_863_zless__add1__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 476 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,X_c)),combs(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combb(X_c,fun(X_c,X_c),X_b),times_times(X_c)),G)),H)),A_3) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),A_3)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),H),A_3)))))) # label(fact_194_setprod_Odistrib) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 477 (all X_b all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),bot_bot(fun(X_b,bool))) = ti(fun(X_b,bool),A_3)) # label(fact_138_Diff__empty) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 478 (all X_b (linordered_semidom(X_b) -> (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),M_1)),hAPP(nat,X_b,semiring_1_of_nat(X_b),N))))))) # label(fact_659_of__nat__le__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 479 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),J))) # label(fact_434_diff__diff__right) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 480 (all X_a (ordered_ab_group_add(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z)))) # label(fact_371_min__diff__distrib__left) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 481 (all X_b (ordered_ab_group_add(X_b) -> (all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),Ba)),hAPP(X_b,X_b,uminus_uminus(X_b),A_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba)))))) # label(fact_808_neg__less__iff__less) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 482 (all X_c all X_b all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_2)) -> hAPP(fun(X_c,bool),X_b,F_2,bot_bot(fun(X_c,bool))) = ti(X_b,Z_2))) # label(fact_165_folding__image__simple_Oempty) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 483 (all X_b all X_c ti(fun(fun(X_b,fun(X_c,X_c)),bool),finite_comp_fun_idem(X_b,X_c)) = finite_comp_fun_idem(X_b,X_c)) # label(tsy_c_Finite__Set_Ocomp__fun__idem_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 484 (all L_1 all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),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),L_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),L_1))))) # label(fact_438_diff__le__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 485 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)),A_3))))))) # label(fact_384_Min__in) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 486 (all X_b (comm_semiring_1(X_b) -> (all A_2 all D all N hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),one_one(X_b)),one_one(X_b))),hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),hAPP(fun(nat,X_b),fun(nat,X_b),hAPP(fun(X_b,X_b),fun(fun(nat,X_b),fun(nat,X_b)),combb(X_b,X_b,nat),hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2)),hAPP(X_b,fun(nat,X_b),hAPP(fun(nat,fun(X_b,X_b)),fun(X_b,fun(nat,X_b)),combc(nat,X_b,X_b),hAPP(fun(nat,X_b),fun(nat,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(nat,X_b),fun(nat,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),nat),times_times(X_b)),semiring_1_of_nat(X_b))),D))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),N)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))),D))))))) # label(fact_656_arith__series__general) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 487 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> one_one(X_c) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),A_3))))) # label(fact_643_setprod_Oinfinite) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 488 (all X_b hBOOL(hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),bool,finite_comp_fun_idem(X_b,fun(X_b,bool)),insert(X_b)))) # label(fact_163_comp__fun__idem__insert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 489 (all X_b (order(X_b) -> (all A_2 all Ba all Ca all D (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),Ba)),hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),Ca),D))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),D)) & (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),A_2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),D)) & (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),D)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),A_2))) | -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba))))))) # label(fact_794_atLeastatMost__psubset__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 490 (all X_b all A_3 all B_2 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_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)),A_3),B_2)))) # label(fact_287_equalityD1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 491 (all X_c all X_b all R_1 all K_1 all T_5 all S_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),T_5)) -> ((all X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),T_5)) -> hAPP(X_c,nat,K_1,X_2) = hAPP(fun(X_b,bool),nat,finite_card(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)),S_2))),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),R_1),X_2)))))) -> hAPP(fun(X_c,bool),nat,hAPP(fun(X_c,nat),fun(fun(X_c,bool),nat),big_co1399186613setsum(X_c,nat),K_1),T_5) = hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,nat),hAPP(fun(fun(X_c,bool),nat),fun(fun(X_b,fun(X_c,bool)),fun(X_b,nat)),combb(fun(X_c,bool),nat,X_b),finite_card(X_c)),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool)),hAPP(fun(fun(X_c,bool),fun(X_c,bool)),fun(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool))),combb(fun(X_c,bool),fun(X_c,bool),X_b),collect(X_c)),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool)),hAPP(fun(fun(X_c,bool),fun(X_c,bool)),fun(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool))),combb(fun(X_c,bool),fun(X_c,bool),X_b),hAPP(fun(X_c,fun(bool,bool)),fun(fun(X_c,bool),fun(X_c,bool)),combs(X_c,bool,bool),hAPP(fun(X_c,bool),fun(X_c,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_c,bool),fun(X_c,fun(bool,bool))),combb(bool,fun(bool,bool),X_c),fconj),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,fun(fun(X_c,bool),bool)),fun(fun(X_c,bool),fun(X_c,bool)),combc(X_c,fun(X_c,bool),bool),member(X_c)),T_5)))),R_1)))),S_2))))) # label(fact_620_setsum__multicount__gen) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 492 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K))))) # label(fact_718_add__less__mono1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 493 (all X_a ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a)) = if(X_a)) # label(tsy_c_If_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 494 (all X_a (linorder(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y) = ti(X_a,Y))))) # label(fact_362_min__max_Oinf__absorb2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 495 (all M all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N_1)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1))))) # label(fact_413_add__leE) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 496 (all X_b (linord219039673up_add(X_b) -> (all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),A_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),A_2))))))) # label(fact_974_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 497 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> ti(X_a,Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y))))) # label(fact_553_min__max_Osup__absorb2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 498 (all X_a (linordered_semidom(X_a) -> (all N_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N_1))))))))) # label(fact_967_power__strict__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 499 (all X_b (ordere236663937imp_le(X_b) -> (all A_2 all Ca all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ba),Ca))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)))))) # label(fact_300_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 500 (all X_b all X_c ti(fun(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c))),finite_fold(X_b,X_c)) = finite_fold(X_b,X_c)) # label(tsy_c_Finite__Set_Ofold_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 501 (all X_b (preorder(X_b) -> (all X_1 all Y_2 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)))))) # label(fact_749_less__le__not__le) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 502 (all X_b (order(X_b) -> (all A_2 all Ba all Ca all D (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),D)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ca),A_2)) | -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)) <-> 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(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),Ba)),hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),Ca),D))))))) # label(fact_830_atLeastatMost__subset__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 503 (all K_1 all I_1 all J_1 hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_1),K_1)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),I_1),J_1))) # label(fact_805_image__add__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 504 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_944_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 505 (all X_b (ring(X_b) -> (all A_2 all E all Ca all Ba all D (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),Ca) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),E)),D) <-> ti(X_b,D) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),Ba)),E)),Ca))))) # label(fact_220_eq__add__iff1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 506 (all X_b all A_2 all A_3 (ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)))) # label(fact_17_equals0D) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 507 (all X_b (ab_semigroup_mult(X_b) -> (all Z_2 all Ba all A_3 all Y_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)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),times_times(X_b)),Ba),A_3),Y_2)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),A_3)) -> 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)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),times_times(X_b)),Z_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),Ba),A_3)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Z_2),Y_2)))))))) # label(fact_150_fold__graph__insert__swap) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 508 (all T_2 all T_1 (finite_finite(T_2) & finite_finite(T_1) -> finite_finite(fun(T_2,T_1)))) # label(arity_fun___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 509 (all X_b all Ga all Ca all Q_3 all Pa ((all Z_4 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_4),S_3)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),hAPP(fun(state,bool),fun(X_b,fun(state,bool)),combk(fun(state,bool),X_b),hAPP(state,fun(state,bool),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),S_3))),Ca),hAPP(fun(state,bool),fun(X_b,fun(state,bool)),combk(fun(state,bool),X_b),hAPP(X_b,fun(state,bool),Q_3,Z_4)))),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))) # label(fact_5_escape) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 510 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> ((exists X_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),X_1)) & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3)),X_1)))))))) # label(fact_839_fold1__strict__below__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 511 (all X_a (linorder(X_a) -> (all T_3 exists Z_1 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),T_3),X_2)))))) # label(fact_919_pinf_I8_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 512 (all X_b (linorder(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),A_2),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)) = ti(X_b,A_2)))))) # label(fact_595_min__max_Oinf__Sup__absorb) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 513 (all X_a (ab_sem1668676832m_mult(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))) # label(fact_168_mult__left__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 514 (all X_c all X_b all F all A_3 all B_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)),A_3),B_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)),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_3)),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_2))))) # label(fact_313_image__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 515 (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]. 2.21/2.46 516 (all X_a (order(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (ti(X_a,B) = ti(X_a,C) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1))))))) # label(fact_271_xt1_I4_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 517 (all X_b (linord219039673up_add(X_b) -> (all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),S_1) -> hAPP(X_b,X_b,uminus_uminus(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),S_1)) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),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),uminus_uminus(X_b)),S_1))))))) # label(fact_480_minus__Max__eq__Min) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 518 (all Vname_1 all Fun_1 all Vname all Fun (Fun_1 = Fun & ti(vname,Vname_1) = ti(vname,Vname) <-> hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname),Fun) = hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname_1),Fun_1))) # label(fact_66_com_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 519 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),B) = ti(X_a,A_1)))) # label(fact_222_add__diff__cancel) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 520 (all X_c all X_b all X_1 all A_3 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite1357897459simple(X_b,X_c),F),Z_2),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3)) -> hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,bool),fun(fun(X_c,bool),fun(X_c,bool)),minus_minus(fun(X_c,bool)),A_3),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),bot_bot(fun(X_c,bool))))))))) # label(fact_157_folding__image__simple_Oinsert__remove) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 521 (all X_b (semiri456707255roduct(X_b) -> (all W_1 all Y_2 all X_1 all Z_2 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W_1),Y_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Z_2)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),W_1),Z_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),Y_2)) <-> ti(X_b,X_1) = ti(X_b,W_1) | ti(X_b,Z_2) = ti(X_b,Y_2))))) # label(fact_223_crossproduct__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 522 (all X_b all B_2 all X_1 all A_3 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (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_3),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),B_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)),A_3),B_2))))) # label(fact_310_subset__insert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 523 (all X_a all X_b combk(X_a,X_b) = ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b))) # label(tsy_c_COMBK_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 524 (all X_b (comm_monoid_add(X_b) -> (all F all P_1 all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat)))) -> hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),P_1))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M_1),N))),hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),P_1)))))))) # label(fact_843_setsum__ub__add__nat) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 525 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> 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_3) = ti(fun(X_b,bool),A_3))) # label(fact_24_insert__absorb) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 526 (all X_a (ord(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> ti(X_a,Least) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Least),X))))) # label(fact_400_min__leastL) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 527 (all X_a (comm_ring_1(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)))) # label(fact_512_comm__ring__1__class_Onormalizing__ring__rules_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 528 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)) <-> ti(X_b,X_1) != ti(X_b,Y_2))))) # label(fact_790_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 529 (all X_1 all Y_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2))))) # label(fact_903_transfer__int__nat__relations_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 530 (all K all L_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K),L_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L_1)))))) # label(fact_717_add__less__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 531 (all X_a (order(X_a) -> (all C all A_1 all B (ti(X_a,A_1) = ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1))))))) # label(fact_776_xt1_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 532 (all X_b all C_1 all A_3 all B_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)),A_3),B_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_2),C_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_3),C_1))))) # label(fact_282_subset__trans) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 533 (all X all N_1 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),X)),N_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N_1))) # label(fact_908_Nat__Transfer_Otransfer__int__nat__functions_I4_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 534 (all P all Q (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)) | -hBOOL(Q))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 535 (all N_1 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M)))) # label(fact_422_le__add1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 536 (all X_a (ordere236663937imp_le(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_294_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 537 (all X_b all X_c finite1357897459simple(X_b,X_c) = ti(fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)))),finite1357897459simple(X_b,X_c))) # label(tsy_c_Finite__Set_Ofolding__image__simple_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 538 (all X_a (linorder(X_a) -> (all T_3 exists Z_1 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),T_3)))))) # label(fact_922_minf_I6_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 539 (all X_b all Ba all A_3 all B_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)),A_3),B_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)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),B_2))))) # label(fact_309_subset__insertI2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 540 (all X_b all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))))) # label(fact_129_finite__Diff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 541 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> hAPP(fun(X_b,bool),X_b,big_linorder_Min(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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)))))))) # label(fact_375_Min_Oinsert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 542 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)),zero_zero(X_a)))))))) # label(fact_986_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 543 (all X_b (linorder(X_b) -> (all X_1 ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(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_1),bot_bot(fun(X_b,bool))))))) # label(fact_594_min__max_OSup__fin_Osingleton) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 544 (all W_2 all Z1 all Z2 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_2),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_2),Z2)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2))) # label(fact_704_zadd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 545 (all M all N_1 (M = N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)))) # label(fact_410_eq__imp__le) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 546 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(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_1),A_3))))))) # label(fact_473_min__max_OInf__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 547 (all X_a (ordere236663937imp_le(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_725_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 548 (all X all Y all Z hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Y)),Z) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Y),Z))) # label(fact_696_zpower__zpower) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 549 (all X_b all X_c (comm_monoid_mult(X_c) -> (all F all G all A_3 all B_2 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)) -> hAPP(X_b,X_c,G,X_2) = hAPP(X_b,X_c,F,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),B_2)))))) # label(fact_252_setprod__cong) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 550 (all X_a (preorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z))))))) # label(fact_269_order__trans) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 551 (all X_c all X_b (comm_monoid_mult(X_b) -> (all F all G all A_3 hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,X_b)),combs(X_c,X_b,X_b),hAPP(fun(X_c,X_b),fun(X_c,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_c),times_times(X_b)),F)),G)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),F),A_3)),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),G),A_3))))) # label(fact_186_setprod__timesf) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 552 (all W_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_2),W_2))) # label(fact_691_zle__refl) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 553 (all X_b (linorder(X_b) -> (all X_1 all Y_2 all Z_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),Y_2)),Z_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),Z_2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Z_2)))))) # label(fact_550_min__max_Ole__sup__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.46 554 (all X_b (linorder(X_b) -> (all Z_2 all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Z_2),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),Y_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Z_2),X_1)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Z_2),Y_2)))))) # label(fact_735_min__less__iff__conj) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 555 (all X_b all Pa ((all Q_2 ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> hBOOL(Q_2))) -> hBOOL(Q_2))) <-> (exists X1 hBOOL(hAPP(X_b,bool,Pa,X1))))) # label(fact_608_Ex__def) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 556 (all M_1 all N (M_1 = N <-> hAPP(nat,int,semiring_1_of_nat(int),N) = hAPP(nat,int,semiring_1_of_nat(int),M_1))) # label(fact_686_int__int__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 557 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))))) # label(fact_140_finite__Diff2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 558 (all X_b (order(X_b) -> (all A_2 all Ba (ti(X_b,A_2) = ti(X_b,Ba) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))) = hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),Ba))))) # label(fact_831_atLeastAtMost__singleton_H) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 559 (all X_b (ab_semigroup_mult(X_b) -> times_times(X_b) = ti(fun(X_b,fun(X_b,X_b)),times_times(X_b)))) # label(tsy_c_Groups_Otimes__class_Otimes_2_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 560 (all L all U hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),L),U)))) # label(fact_681_finite__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 561 (all X_b all Ba all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) -> ti(X_b,A_2) = ti(X_b,Ba))) # label(fact_36_singletonE) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 562 (all W_1 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_2)) <-> (exists N_2 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),N_2)) = Z_2))) # label(fact_683_zle__iff__zadd) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 563 (all X_b (linorder(X_b) -> (all B_2 all A_3 (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (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_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),B_2)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3))))))))) # label(fact_338_fold1__antimono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 564 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))))) # label(fact_240_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 565 (all X_b all A_3 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_3),A_3))) # label(fact_289_subset__refl) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 566 (all X_b all X_c (uminus(X_c) -> (all A_3 all X_2 hAPP(X_c,X_c,uminus_uminus(X_c),hAPP(X_b,X_c,A_3,X_2)) = hAPP(X_b,X_c,hAPP(fun(X_b,X_c),fun(X_b,X_c),uminus_uminus(fun(X_b,X_c)),A_3),X_2)))) # label(fact_482_fun__Compl__def) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 567 (all X_b all X_2 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_2),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_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)),Xa)))) # label(fact_34_insert__compr__raw) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 568 (all X_b finite_finite_1(X_b) = ti(fun(fun(X_b,bool),bool),finite_finite_1(X_b))) # label(tsy_c_Finite__Set_Ofinite_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 569 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)))) # label(fact_544_min__max_Osup_Ocommute) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 570 (all X_b all X_c (ord(X_c) -> (all F all G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) <-> (all X_2 hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2)))))))) # label(fact_280_le__fun__def) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 571 (all L_1 all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),M)))))) # label(fact_743_diff__less__mono2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 572 (all X_b (linorder(X_b) -> (all Ba all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),A_2),hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),Ba),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),Ba),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_3)))))) # label(fact_388_min__max_Ofold__inf__insert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 573 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))) # label(fact_251_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 574 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,B_1_1,B_2_1) = hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1))) # label(tsy_c_hAPP_arg2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 575 (all X_b all F all A_3 hAPP(fun(X_b,bool),int,hAPP(fun(X_b,int),fun(fun(X_b,bool),int),big_co1399186613setsum(X_b,int),hAPP(fun(X_b,nat),fun(X_b,int),hAPP(fun(nat,int),fun(fun(X_b,nat),fun(X_b,int)),combb(nat,int,X_b),semiring_1_of_nat(int)),F)),A_3) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),A_3))) # label(fact_674_int__setsum) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 576 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) <-> N != zero_zero(nat))) # label(fact_971_neq0__conv) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 577 (all X_a (comm_monoid_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_630_mult__1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 578 (all X_a all X_b all X_c combc(X_a,X_b,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))) # label(tsy_c_COMBC_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 579 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> -(all B_3 (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),B_3) = ti(fun(X_b,bool),A_3) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_3)))))) # label(fact_48_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 580 (all X_a (linorder(X_a) -> (all B all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),C))))) # label(fact_351_min__max_Oinf_Oleft__commute) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 581 (all K_1 all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),L)),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_1),L)))) # label(fact_960_less__bin__lemma) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 582 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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)),A_3),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))))) # label(fact_307_rev__finite__subset) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 583 (all X_b (linorder(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),B_2) != bot_bot(fun(X_b,bool)) -> (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_2),A_3)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),B_2)),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3)))))))) # label(fact_576_Max_Osubset__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 584 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),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_1),A_3)))))) # label(fact_613_card__insert__le) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 585 (all X_b all X_c all Z_2 all X_1 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),A_3)) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_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_1),A_3)))))) # label(fact_184_comp__fun__commute_Ofold__insert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 586 (all X_b all N_3 all H all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) -> ((all X_2 all Y_1 hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_1)) = hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),Y_1))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (ti(fun(X_b,bool),N_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,F_2,N_3)) = hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,X_b),fun(fun(X_b,bool),fun(X_b,bool)),image(X_b,X_b),H),N_3))))))) # label(fact_155_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 587 (all K_1 all I_1 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1) = K_1 <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),I_1) = J_1))) # label(fact_444_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 588 (all Z all W_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),W_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_2),Z)) -> Z = W_2))) # label(fact_694_zle__antisym) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 589 (all X_b (ordered_ring(X_b) -> (all A_2 all E all Ca all Ba all D (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),E)),D))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),Ba)),E)),Ca)),D)))))) # label(fact_324_le__add__iff1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 590 (all X_a (order(X_a) -> (all C all A_1 all B (ti(X_a,A_1) = ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1))))))) # label(fact_273_xt1_I3_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 591 (all X_c all X_b (minus(X_b) -> (all A_3 all B_2 all X_1 hAPP(X_c,X_b,hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),minus_minus(fun(X_c,X_b)),A_3),B_2),X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_c,X_b,A_3,X_1)),hAPP(X_c,X_b,B_2,X_1))))) # label(fact_159_minus__apply) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 592 (all X_b all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_3))))) # label(fact_99_finite_OinsertI) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 593 (all X_b (bot(X_b) -> (all A_2 (bot_bot(X_b) != ti(X_b,A_2) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),bot_bot(X_b)),A_2)))))) # label(fact_767_bot__less) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 594 (all X_b (linorder(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),B_2) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),B_2)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b)),hAPP(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,bool)),hAPP(fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),fun(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,bool))),combb(fun(X_b,fun(X_b,bool)),fun(X_b,bool),X_b),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b))),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(X_b,bool)))),combc(X_b,fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),fun(X_b,fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)))),hAPP(fun(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),fun(X_b,fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool))))),combb(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool))),X_b),combs(X_b,fun(X_b,bool),fun(X_b,bool))),hAPP(fun(X_b,fun(X_b,fun(X_b,fun(bool,bool)))),fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),hAPP(fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),fun(fun(X_b,fun(X_b,fun(X_b,fun(bool,bool)))),fun(X_b,fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))))),combb(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),X_b),hAPP(fun(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combs(X_b,bool,bool))),hAPP(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,fun(X_b,fun(bool,bool)))),hAPP(fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),fun(fun(X_b,fun(X_b,fun(X_b,bool))),fun(X_b,fun(X_b,fun(X_b,fun(bool,bool))))),combb(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool))),X_b),hAPP(fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),combb(fun(X_b,bool),fun(X_b,fun(bool,bool)),X_b),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,fun(X_b,X_b)),fun(X_b,fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,fun(X_b,bool)))),combc(X_b,fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool))),hAPP(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool)))),hAPP(fun(fun(fun(X_b,X_b),fun(X_b,bool)),fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool)))),fun(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool))))),combb(fun(fun(X_b,X_b),fun(X_b,bool)),fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(X_b,bool))),X_b),combb(fun(X_b,X_b),fun(X_b,bool),X_b)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool)),X_b),combb(X_b,bool,X_b)),fequal(X_b)))),ord_max(X_b)))))),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(bool,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(bool,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combb(bool,bool,X_b)),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_3)))),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_2)))))))))))))) # label(fact_587_min__max_Osup__Inf2__distrib) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 595 (all X_a (linorder(X_a) -> (all B all D_1 all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),C),D_1)))))))) # label(fact_557_min__max_Osup__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 596 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))))))) # label(fact_988_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 597 (all X_c all X_b all F1 all Fun1_1 all Com_1 all Fun2_1 hAPP(fun(X_c,fun(state,bool)),X_b,hAPP(com,fun(fun(X_c,fun(state,bool)),X_b),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b)),F1,Fun1_1),Com_1),Fun2_1) = hAPP(hoare_2118899576triple(X_c),X_b,hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_2118899576triple(X_c),X_b),hoare_1759541758le_rec(X_c,X_b),F1),hAPP(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_2118899576triple(X_c))),hoare_759811442triple(X_c),Fun1_1),Com_1),Fun2_1))) # label(fact_16_triple_Orecs) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 598 (all P (ti(bool,P) = fFalse | fTrue = ti(bool,P))) # label(help_If_3_1_T) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 599 (all Z1 all Z2 all Z3 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z2),Z3)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)),Z3)) # label(fact_700_zadd__assoc) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 600 (all X_a (linorder(X_a) -> (all Y all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))))) # label(fact_548_le__maxI2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 601 (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]. 2.21/2.47 602 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_295_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 603 (all W_2 all Z1 all Z2 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_2),Z1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_2),Z2)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z1),Z2))) # label(fact_699_zdiff__zmult__distrib2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 604 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_784_order__less__not__sym) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 605 (all Pa all M_1 all N ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N),M_1))) -> ((M_1 = N -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N),M_1))) -> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N),M_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N),M_1)))))) # label(fact_795_nat__less__cases) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 606 (all X_a (preorder(X_a) -> (all X all Y (Y = X -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_277_order__eq__refl) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 607 (all T all A ti(T,A) = ti(T,ti(T,A))) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 608 (all X_b (linorder(X_b) -> hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,X_b)),max(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),ord_less_eq(X_b))) = ord_min(X_b))) # label(fact_397_dual__max) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 609 (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]. 2.21/2.47 610 (all X_b (linorder(X_b) -> ti(fun(fun(X_b,bool),X_b),big_linorder_Min(X_b)) = big_linorder_Min(X_b))) # label(tsy_c_Big__Operators_Olinorder__class_OMin_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 611 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b)),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combs(X_b,bool,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool))),hAPP(fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),combb(fun(X_b,bool),fun(X_b,fun(bool,bool)),X_b),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,X_b),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,X_b),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,X_b),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool)),X_b),combb(X_b,bool,X_b)),fequal(X_b))),hAPP(X_b,fun(X_b,X_b),ord_min(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)),A_3)))))))))) # label(fact_591_min__max_Oinf__Sup1__distrib) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 612 (all X_b all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> ((all X_2 all Y_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_2),Y_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,F_2,A_3)),A_3))))))) # label(fact_96_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 613 (all X_b all A_3 all B_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)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)),A_3))) # label(fact_317_Diff__subset) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 614 (all X_b (ord(X_b) -> ord_lessThan(X_b) = ti(fun(X_b,fun(X_b,bool)),ord_lessThan(X_b)))) # label(tsy_c_SetInterval_Oord__class_OlessThan_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 615 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),zero_zero(nat)))) # label(fact_972_not__less0) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 616 (all K all I all J (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),J)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I),K)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),J),K))))) # label(fact_850_zadd__strict__right__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 617 (all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M))))) # label(fact_406_le__cube) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 618 (all X_b all X_c (comm_monoid_mult(X_c) -> (all F all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(X_b,X_c,F,A_2)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),A_3)) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),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),A_2),A_3))))))) # label(fact_197_setprod__insert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 619 (all X_c all X_b all F all A_2 all B_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),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_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),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_2))) # label(fact_83_image__insert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 620 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,B_1_1,B_2_1) = hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1)) # label(tsy_c_hAPP_arg1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 621 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),B) = ti(X_a,A_1)))) # label(fact_221_diff__add__cancel) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 622 (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]. 2.21/2.47 623 (all X_b all X_1 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))) -> hAPP(fun(X_b,bool),X_b,F_2,A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),hAPP(fun(X_b,bool),X_b,F_2,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool))))))) & (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F_2,A_3) = ti(X_b,X_1)))))) # label(fact_123_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 624 (all Z_2 all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),W_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),W_1)) & W_1 != Z_2)) # label(fact_849_zless__le) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 625 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)))) # label(fact_355_min__max_Oinf_Ocommute) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 626 (all X_b all B_2 all A_3 ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_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)),A_3),B_2)))) # label(fact_331_subsetI) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 627 (all X_b all Ga all Pa all Ca all Q_3 all C_1 ((hBOOL(C_1) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),hAPP(bool,fun(X_b,fun(state,bool)),hAPP(fun(X_b,fun(bool,fun(state,bool))),fun(bool,fun(X_b,fun(state,bool))),combc(X_b,bool,fun(state,bool)),hAPP(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(bool,fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(bool,fun(state,bool))),fun(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(bool,fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(bool,fun(state,bool)),X_b),combc(state,bool,bool)),hAPP(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),Pa))),C_1)),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))))) # label(fact_4_constant) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 628 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Y))) # label(fact_905_Nat__Transfer_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 629 (all X_b all X_1 hAPP(fun(X_b,bool),X_b,the_elem(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_1),bot_bot(fun(X_b,bool)))) = ti(X_b,X_1)) # label(fact_41_the__elem__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 630 (all X_b all Ga hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) # label(fact_0_empty) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 631 (all A_3 all B_2 (B_2 = A_3 <-> hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_2) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))) # label(fact_897_transfer__nat__int__set__relations_I3_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 632 (all N_3 ((exists M_2 all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_2),M_2)))) <-> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_3)))) # label(fact_345_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 633 (all X_c all X_b (order(X_c) & order(X_b) -> (all Ca all F all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Ca),hAPP(X_b,X_c,F,Ba))) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_1),X_2)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,Y_1)),hAPP(X_b,X_c,F,X_2))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Ca),hAPP(X_b,X_c,F,A_2))))))))) # label(fact_921_xt5) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 634 (all X_a (linordered_semidom(X_a) -> (all M all N_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1))))))) # label(fact_845_power__le__imp__le__exp) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 635 (all X_b (order(X_b) -> (all Y_2 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)) -> (ti(X_b,Y_2) = ti(X_b,X_1) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2))))))) # label(fact_275_order__antisym__conv) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 636 (all X_c all X_b all F all Z_2 all A_3 hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,bool),X_b)),finite_fold(X_c,X_b),F),Z_2),A_3) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_c,bool),fun(X_b,bool)),hAPP(fun(X_c,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,bool),fun(X_b,bool))),finite_fold_graph(X_c,X_b),F),Z_2),A_3))) # label(fact_200_fold__def) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 637 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),Y_2) = ti(X_b,X_1) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)))))) # label(fact_367_min__max_Ole__iff__inf) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 638 (all Pa ((exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) & hBOOL(hAPP(int,bool,Pa,X_2)))) <-> (exists X_2 hBOOL(hAPP(int,bool,Pa,hAPP(nat,int,semiring_1_of_nat(int),X_2)))))) # label(fact_952_transfer__int__nat__quantifiers_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 639 (all K all L_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),L_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),L_1)))))) # label(fact_416_add__le__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 640 (all W_1 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z_2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_2),one_one(int)))))) # label(fact_868_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 641 (all M_1 all K_1 all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K_1) <-> M_1 = N)) # label(fact_457_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 642 (all U all M_1 all N all I_1 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)),U)),N) = M_1 <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)))) # label(fact_450_nat__eq__add__iff2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 643 (all Pa all K_1 all I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_1),I_1)) -> (hBOOL(hAPP(int,bool,Pa,K_1)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K_1),I_2)) -> (hBOOL(hAPP(int,bool,Pa,I_2)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,Pa,I_1)))))) # label(fact_910_int__ge__induct) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 644 (all X_b (ord(X_b) -> (all I_1 all K_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),I_1),K_1)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),I_1),hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),K_1))))))) # label(fact_744_lessThan__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 645 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)))))))) # label(fact_474_min__max_OInf__fin_Oinsert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 646 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_945_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 647 (all M all N_1 all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)),K)) # label(fact_459_nat__add__assoc) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 648 (all M all K all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K))) # label(fact_432_diff__cancel2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 649 (all X_b all Ga all Pa hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),skip),Pa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))) # label(fact_45_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 650 (all X_c all X_b all X_d (comm_monoid_add(X_d) -> (all F all R_1 all T_4 all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),T_4)) -> hAPP(fun(X_c,bool),X_d,hAPP(fun(X_c,X_d),fun(fun(X_c,bool),X_d),big_co1399186613setsum(X_c,X_d),hAPP(fun(X_c,fun(X_b,bool)),fun(X_c,X_d),hAPP(fun(X_c,fun(fun(X_b,bool),X_d)),fun(fun(X_c,fun(X_b,bool)),fun(X_c,X_d)),combs(X_c,fun(X_b,bool),X_d),hAPP(fun(X_c,fun(X_b,X_d)),fun(X_c,fun(fun(X_b,bool),X_d)),hAPP(fun(fun(X_b,X_d),fun(fun(X_b,bool),X_d)),fun(fun(X_c,fun(X_b,X_d)),fun(X_c,fun(fun(X_b,bool),X_d))),combb(fun(X_b,X_d),fun(fun(X_b,bool),X_d),X_c),big_co1399186613setsum(X_b,X_d)),hAPP(fun(X_b,fun(X_c,X_d)),fun(X_c,fun(X_b,X_d)),combc(X_b,X_c,X_d),F))),hAPP(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_c),collect(X_b)),hAPP(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_c),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)),S_1)))),hAPP(fun(X_b,fun(X_c,bool)),fun(X_c,fun(X_b,bool)),combc(X_b,X_c,bool),R_1))))),T_4) = hAPP(fun(X_b,bool),X_d,hAPP(fun(X_b,X_d),fun(fun(X_b,bool),X_d),big_co1399186613setsum(X_b,X_d),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,X_d),hAPP(fun(X_b,fun(fun(X_c,bool),X_d)),fun(fun(X_b,fun(X_c,bool)),fun(X_b,X_d)),combs(X_b,fun(X_c,bool),X_d),hAPP(fun(X_b,fun(X_c,X_d)),fun(X_b,fun(fun(X_c,bool),X_d)),hAPP(fun(fun(X_c,X_d),fun(fun(X_c,bool),X_d)),fun(fun(X_b,fun(X_c,X_d)),fun(X_b,fun(fun(X_c,bool),X_d))),combb(fun(X_c,X_d),fun(fun(X_c,bool),X_d),X_b),big_co1399186613setsum(X_c,X_d)),F)),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool)),hAPP(fun(fun(X_c,bool),fun(X_c,bool)),fun(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool))),combb(fun(X_c,bool),fun(X_c,bool),X_b),collect(X_c)),hAPP(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool)),hAPP(fun(fun(X_c,bool),fun(X_c,bool)),fun(fun(X_b,fun(X_c,bool)),fun(X_b,fun(X_c,bool))),combb(fun(X_c,bool),fun(X_c,bool),X_b),hAPP(fun(X_c,fun(bool,bool)),fun(fun(X_c,bool),fun(X_c,bool)),combs(X_c,bool,bool),hAPP(fun(X_c,bool),fun(X_c,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_c,bool),fun(X_c,fun(bool,bool))),combb(bool,fun(bool,bool),X_c),fconj),hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(fun(X_c,fun(fun(X_c,bool),bool)),fun(fun(X_c,bool),fun(X_c,bool)),combc(X_c,fun(X_c,bool),bool),member(X_c)),T_4)))),R_1)))),S_1)))))) # label(fact_211_setsum__setsum__restrict) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 651 (all X_b (semiri456707255roduct(X_b) -> (all Ca all D all A_2 all Ba (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),D)) != hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),D)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),Ca)) <-> ti(X_b,A_2) != ti(X_b,Ba) & ti(X_b,D) != ti(X_b,Ca))))) # label(fact_249_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 652 (all X_b all A_2 all A_3 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),A_3)) # label(fact_146_insert__Diff__single) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 653 (all M all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),M))))) # label(fact_419_trans__le__add1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 654 (all X_a (ab_group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_513_ab__diff__minus) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 655 (all X_a (linordered_semidom(X_a) -> (all N_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))))))) # label(fact_878_one__le__power) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 656 (all X_a (ordere779506340up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_296_add__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 657 (all X_b all Y_4 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_4) = ti(fun(X_b,bool),Y_4)) # label(fact_71_image__ident) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 658 (all K_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(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(nat)),K_1))))) # label(fact_682_finite__Collect__less__nat) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 659 (all K all M all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1))) # label(fact_462_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 660 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))) # label(fact_543_min__max_Osup__commute) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 661 (all X_b (ordered_ab_group_add(X_b) -> (all X_1 all Y_2 hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),Y_2)),hAPP(X_b,X_b,uminus_uminus(X_b),X_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),uminus_uminus(X_b)),hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),X_1),Y_2))))) # label(fact_834_image__uminus__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 2.21/2.47 662 (all X_b (ordere236663937imp_le(X_b) -> (all Ca all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ca),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ca),Ba))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)))))) # label(fact_299_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 663 (all X_b all X_c all Ba all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),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_3))) -> -(all X_2 (hAPP(X_c,X_b,F,X_2) = ti(X_b,Ba) -> -hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3)))))) # label(fact_87_imageE) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 664 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)))) # label(fact_353_min__max_Oinf_Oleft__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 665 (all X_c all X_b all X_1 all A_3 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3)) -> (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_1),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_2,A_3)) = hAPP(fun(X_c,bool),X_b,F_2,A_3))))) # label(fact_152_folding__image__simple__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 666 (all X_b all Ba all A_2 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),B_2)) -> 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),Ba),B_2))))) # label(fact_25_insertI2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 667 (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]. 2.21/2.48 668 (all X_b (linorder(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),B_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_2),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),B_2)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)))))))) # label(fact_475_min__max_OInf__fin_Osubset__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 669 (all X_b (power(X_b) -> hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(nat,X_b)),hAPP(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(nat,X_b))),power_1(X_b),one_one(X_b)),times_times(X_b)) = power_power(X_b))) # label(fact_916_power__power__power) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 670 (all X_b all X_c (order(X_c) & order(X_b) -> (all F all Ca all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,Ba)),Ca)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_1)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,F,Y_1))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),hAPP(X_b,X_c,F,A_2)),Ca)))))))) # label(fact_928_order__le__less__subst2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 671 (all X_a (semiring_1(X_a) -> semiring_1_of_nat(X_a) = ti(fun(nat,X_a),semiring_1_of_nat(X_a)))) # label(tsy_c_Nat_Osemiring__1__class_Oof__nat_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 672 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_1))) # label(fact_408_le__refl) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 673 (all X_b all Pa (bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) <-> (all X_2 -hBOOL(hAPP(X_b,bool,Pa,X_2))))) # label(fact_20_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 674 (all X_b all A_2 all C_1 all D_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)),C_1),D_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)),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_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),D_2))))) # label(fact_308_insert__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 675 (all X_b (linord2061991079up_add(X_b) -> (all K_1 all N_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),N_3) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),fEx(X_b)),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,fun(bool,bool))),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),X_b),combs(X_b,bool,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool))),hAPP(fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,fun(bool,bool)))),combb(fun(X_b,bool),fun(X_b,fun(bool,bool)),X_b),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,X_b),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,X_b),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,X_b),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,X_b),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,X_b),fun(X_b,bool)),X_b),combb(X_b,bool,X_b)),fequal(X_b))),hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),K_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)),N_3))))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),K_1),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),N_3))))))) # label(fact_600_add__Max__commute) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 676 (all X_c all X_b (comm_monoid_mult(X_b) -> (all A_3 hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),hAPP(X_b,fun(X_c,X_b),combk(X_b,X_c),one_one(X_b))),A_3) = one_one(X_b)))) # label(fact_622_setprod__1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 677 (all X_b (bot(X_b) -> (all A_2 (ti(X_b,A_2) = bot_bot(X_b) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),bot_bot(X_b))))))) # label(fact_302_bot__unique) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 678 (all X_b all Ga all Pa all X_3 all A_2 hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),hAPP(fun(state,state),fun(X_b,fun(state,bool)),hAPP(fun(X_b,fun(fun(state,state),fun(state,bool))),fun(fun(state,state),fun(X_b,fun(state,bool))),combc(X_b,fun(state,state),fun(state,bool)),hAPP(fun(X_b,fun(state,bool)),fun(X_b,fun(fun(state,state),fun(state,bool))),hAPP(fun(fun(state,bool),fun(fun(state,state),fun(state,bool))),fun(fun(X_b,fun(state,bool)),fun(X_b,fun(fun(state,state),fun(state,bool)))),combb(fun(state,bool),fun(fun(state,state),fun(state,bool)),X_b),combb(state,bool,state)),Pa)),hAPP(fun(state,nat),fun(state,state),hAPP(fun(state,fun(nat,state)),fun(fun(state,nat),fun(state,state)),combs(state,nat,state),hAPP(vname,fun(state,fun(nat,state)),hAPP(fun(state,fun(vname,fun(nat,state))),fun(vname,fun(state,fun(nat,state))),combc(state,vname,fun(nat,state)),update),X_3)),A_2))),hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,X_3),A_2)),Pa)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))) # label(fact_60_Ass) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 679 (all K_1 all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)))) # label(fact_721_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 680 (all X_b big_semilattice_big(X_b) = ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),big_semilattice_big(X_b))) # label(tsy_c_Big__Operators_Osemilattice__big_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 681 (all X_b all A_3 all B_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)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))))) # label(fact_306_finite__subset) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 682 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3)))))) # label(fact_566_Max_Oin__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 683 (all X_b all C_1 all A_3 all B_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)),A_3),B_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_2),C_1)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),C_1),A_3)) = ti(fun(X_b,bool),A_3)))) # label(fact_315_double__diff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 684 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))) # label(fact_234_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 685 (all X_b all X_c ti(fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)))),finite908156982e_idem(X_b,X_c)) = finite908156982e_idem(X_b,X_c)) # label(tsy_c_Finite__Set_Ofolding__image__simple__idem_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 686 (all X_c all X_b all F all Z_2 all A1 all A2 (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A1),A2)) <-> ti(fun(X_b,bool),A1) = bot_bot(fun(X_b,bool)) & ti(X_c,A2) = ti(X_c,Z_2) | (exists X_2 exists A_4 exists Y_1 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_4) = ti(fun(X_b,bool),A1) & hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_2),Y_1) = ti(X_c,A2) & hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_4),Y_1)) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_4)))))) # label(fact_118_fold__graph_Osimps) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 687 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Min(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_1),A_3))))))) # label(fact_374_Min__insert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 688 (all X_a (comm_semiring_1(X_a) -> (all X all P_2 all Q_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_2),Q_1)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),P_2)),Q_1)))) # label(fact_724_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 689 (all X_c all X_b all F all Pa (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) -> hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),hAPP(fun(X_c,bool),fun(X_c,bool),collect(X_c),hAPP(fun(X_c,fun(X_b,bool)),fun(X_c,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_c,fun(X_b,bool)),fun(X_c,bool)),combb(fun(X_b,bool),bool,X_c),fEx(X_b)),hAPP(fun(X_b,bool),fun(X_c,fun(X_b,bool)),hAPP(fun(X_c,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_c,fun(X_b,bool))),combc(X_c,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_c,fun(X_b,fun(bool,bool))),fun(X_c,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_c,fun(X_b,fun(bool,bool))),fun(X_c,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),X_c),combs(X_b,bool,bool)),hAPP(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,fun(bool,bool))),hAPP(fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),fun(fun(X_c,fun(X_b,bool)),fun(X_c,fun(X_b,fun(bool,bool)))),combb(fun(X_b,bool),fun(X_b,fun(bool,bool)),X_c),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,X_c),fun(X_c,fun(X_b,bool)),hAPP(fun(X_c,fun(fun(X_b,X_c),fun(X_b,bool))),fun(fun(X_b,X_c),fun(X_c,fun(X_b,bool))),combc(X_c,fun(X_b,X_c),fun(X_b,bool)),hAPP(fun(X_c,fun(X_c,bool)),fun(X_c,fun(fun(X_b,X_c),fun(X_b,bool))),hAPP(fun(fun(X_c,bool),fun(fun(X_b,X_c),fun(X_b,bool))),fun(fun(X_c,fun(X_c,bool)),fun(X_c,fun(fun(X_b,X_c),fun(X_b,bool)))),combb(fun(X_c,bool),fun(fun(X_b,X_c),fun(X_b,bool)),X_c),combb(X_c,bool,X_b)),fequal(X_c))),F)))),Pa))))))) # label(fact_590_finite__image__set) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 690 (all X_b (ring_11004092258visors(X_b) -> (all X_1 (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),X_1) = one_one(X_b) <-> hAPP(X_b,X_b,uminus_uminus(X_b),one_one(X_b)) = ti(X_b,X_1) | one_one(X_b) = ti(X_b,X_1))))) # label(fact_638_square__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 691 (all X_a (ordere216010020id_add(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_947_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 692 (all X_b all A_3 all A_2 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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_2)))))) # label(fact_149_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 693 (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]. 2.21/2.48 694 (all X_b all X_c (minus(X_c) -> (all A_3 all B_2 all X_2 hAPP(X_b,X_c,hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),fun(X_b,X_c)),minus_minus(fun(X_b,X_c)),A_3),B_2),X_2) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(X_b,X_c,A_3,X_2)),hAPP(X_b,X_c,B_2,X_2))))) # label(fact_160_fun__diff__def) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 695 (all X_b all X_1 all Y_2 all A_3 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),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_3)) = 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_1),A_3))) # label(fact_29_insert__commute) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 696 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2))),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)))))) # label(fact_618_diff__card__le__card__Diff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 697 (all X_a (linorder(X_a) -> (all X all Y (ti(X_a,Y) != ti(X_a,X) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_786_linorder__neqE) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 698 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)))) # label(fact_352_min__max_Oinf__left__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 699 (all Pa all I_1 all K_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),K_1)) -> (hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_1),one_one(int)))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),K_1)) -> (hBOOL(hAPP(int,bool,Pa,I_2)) -> hBOOL(hAPP(int,bool,Pa,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,Pa,I_1)))))) # label(fact_893_int__less__induct) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 700 (all X_b (linorder(X_b) -> (all X_1 all Y_2 all Z_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),Z_2)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Z_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),Y_2)),Z_2)))))) # label(fact_710_max__less__iff__conj) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 701 (all X_b all X_c (comm_monoid_add(X_c) -> (all G all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),plus_plus(X_c),hAPP(X_b,X_c,G,X_1)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),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_3)))))) # label(fact_214_setsum_Oinsert__remove) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 702 (all X_b (linorder(X_b) -> (all Pa all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))) -> ((all B_1 all A_4 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_4)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_4)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),B_1)))) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_4)) -> hBOOL(hAPP(fun(X_b,bool),bool,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),B_1),A_4))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_3)))))))) # label(fact_932_finite__linorder__max__induct) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 703 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)) -> (N_1 != M -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))))) # label(fact_740_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 704 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(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_1),A_3))))))) # label(fact_574_Max__insert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 705 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)))))))) # label(fact_586_min__max_OInf__le__Sup) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 706 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(X_b,X_c,G,X_2) = one_one(X_c))) -> one_one(X_c) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),A_3)))))) # label(fact_654_setprod_Oneutral) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 707 (all X_b all A_2 all Ba all A_3 (ti(X_b,Ba) = ti(X_b,A_2) | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) <-> 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),Ba),A_3))))) # label(fact_28_insert__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 708 (all X_b (ab_semigroup_mult(X_b) -> (all A_2 all Ba all A_3 all X_1 (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)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),times_times(X_b)),Ba),A_3),X_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),A_3)) -> 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)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),times_times(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),Ba),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))),X_1)))))))) # label(fact_143_fold__graph__permute__diff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 709 (all X_b all Pa (hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = bot_bot(fun(X_b,bool)) <-> (all X_2 -hBOOL(hAPP(X_b,bool,Pa,X_2))))) # label(fact_18_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 710 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_955_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 711 (all X_c all X_b all F all A_3 (bot_bot(fun(X_c,bool)) = ti(fun(X_c,bool),A_3) <-> bot_bot(fun(X_b,bool)) = hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),F),A_3))) # label(fact_79_image__is__empty) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 712 (all X_b all X_c all Y_2 all Z_2 all A_3 all X_1 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),X_1)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),Y_2)) -> ti(X_c,Y_2) = ti(X_c,X_1))))) # label(fact_193_comp__fun__commute_Ofold__graph__determ) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 713 (all X_a (linordered_semidom(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_977_pos__add__strict) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 714 (all X_c all X_b all F all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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_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),A_3))) -> (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_3)) & 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) = ti(fun(X_b,bool),B_2) & hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),C_2))))))) # label(fact_332_finite__subset__image) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 715 (all X_a (linordered_semidom(X_a) -> (all N_1 all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)))))))) # label(fact_882_power__gt1__lemma) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 716 (all X_b (linorder(X_b) -> (all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),B_2) != bot_bot(fun(X_b,bool)) -> (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_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),B_2)),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3))))))) # label(fact_599_min__max_OSup__fin_Osubset__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 717 (all X_b all X_c (comm_monoid_add(X_c) -> (all F all G all A_3 ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hAPP(X_b,X_c,G,X_2) = hAPP(X_b,X_c,F,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),A_3))))) # label(fact_254_setsum__cong2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 718 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3))))))) # label(fact_593_min__max_OSup__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 719 (all X_b all Pa all Q_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(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_3)))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_3))) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))))) # label(fact_103_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 720 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)),X_1))))))) # label(fact_382_Min__le) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 721 (all X_b all X_c all Z_2 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),A_3)))))) # label(fact_185_comp__fun__commute_Ofold__graph__fold) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 722 (all X_b all X_c (comm_monoid_mult(X_c) -> (all Ba all A_2 all S_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),S_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(X_c,fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(X_b,X_c)),combc(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_b,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combs(X_b,X_c,fun(X_c,X_c)),hAPP(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c))),hAPP(fun(bool,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c)))),combb(bool,fun(X_c,fun(X_c,X_c)),X_b),if(X_c)),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Ba)),one_one(X_c))),S_1) = hAPP(X_b,X_c,Ba,A_2)) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),S_1)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),hAPP(X_c,fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(X_b,X_c)),combc(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_b,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combs(X_b,X_c,fun(X_c,X_c)),hAPP(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c))),hAPP(fun(bool,fun(X_c,fun(X_c,X_c))),fun(fun(X_b,bool),fun(X_b,fun(X_c,fun(X_c,X_c)))),combb(bool,fun(X_c,fun(X_c,X_c)),X_b),if(X_c)),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2))),Ba)),one_one(X_c))),S_1) = one_one(X_c)))))) # label(fact_644_setprod__delta_H) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 723 (all X_c all X_b all F all Z_2 ti(X_b,Z_2) = hAPP(fun(X_c,bool),X_b,hAPP(X_b,fun(fun(X_c,bool),X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,bool),X_b)),finite_fold(X_c,X_b),F),Z_2),bot_bot(fun(X_c,bool)))) # label(fact_182_fold__empty) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 724 (all Com1_2 all Com2_2 skip != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2)) # label(fact_54_com_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 725 (all Z all W_2 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_2),Z) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),W_2)) # label(fact_702_zadd__commute) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 726 (all X_a (linordered_semidom(X_a) -> (all A_1 all N_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_939_power__less__imp__less__base) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 727 (all X_b all X_c (ring(X_c) -> (all F all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3)),hAPP(X_b,X_c,F,A_2))))))) # label(fact_174_setsum__diff1__ring) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 728 (all X_b (ord(X_b) -> ti(fun(X_b,fun(X_b,bool)),ord_greaterThan(X_b)) = ord_greaterThan(X_b))) # label(tsy_c_SetInterval_Oord__class_OgreaterThan_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 729 (all X_b all X_c (order(X_b) & order(X_c) -> (all Ca all A_2 all F all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,Ba))) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),Ba),Ca)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),X_2),Y_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,X_2)),hAPP(X_c,X_b,F,Y_1))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),hAPP(X_c,X_b,F,Ca))))))))) # label(fact_929_order__less__le__subst1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 730 (all X_b all X_c (comm_monoid_add(X_c) -> (all H all G all A_3 all B_2 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)) -> hAPP(X_b,X_c,G,X_2) = hAPP(X_b,X_c,H,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),B_2) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),H),A_3)))))) # label(fact_256_setsum_OF__cong) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 731 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> ((all Y_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_1)))) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3))))))) # label(fact_396_Max__eqI) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 732 (all X_b all Pa hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),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),Pa))) # label(fact_521_Collect__neg__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 733 (all X_b (group_add(X_b) -> (all A_2 all Ba (ti(X_b,A_2) = hAPP(X_b,X_b,uminus_uminus(X_b),Ba) <-> ti(X_b,Ba) = hAPP(X_b,X_b,uminus_uminus(X_b),A_2))))) # label(fact_488_minus__equation__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 734 (all X_b all B_2 all Ca all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2)))))) # label(fact_127_DiffI) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 735 (all X_a (linorder(X_a) -> (all T_3 exists Z_1 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),T_3),X_2)))))) # label(fact_918_minf_I8_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 736 (all X_b (order(X_b) -> ti(fun(X_b,fun(X_b,fun(X_b,bool))),ord_atLeastAtMost(X_b)) = ord_atLeastAtMost(X_b))) # label(tsy_c_SetInterval_Oord__class_OatLeastAtMost_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 737 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (ti(X_b,X_1) = ti(X_b,Y_2) <-> hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),X_1) = hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),Y_2))))) # label(fact_293_lessThan__eq__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 738 (all X_b (group_add(X_b) -> (all A_2 all Ba (hAPP(X_b,X_b,uminus_uminus(X_b),A_2) = hAPP(X_b,X_b,uminus_uminus(X_b),Ba) <-> ti(X_b,Ba) = ti(X_b,A_2))))) # label(fact_489_neg__equal__iff__equal) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 739 (all X_c all X_b all F all B_2 all A_3 ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> 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)),B_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)),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_3)),B_2)))) # label(fact_334_image__subsetI) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 740 (all X_a (comm_semiring_1(X_a) -> (all X all P_2 all Q_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),P_2),Q_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),P_2)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_1))))) # label(fact_816_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 741 (all X_b all Q_3 all Ga all Pa all Ca all Q_5 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_5)),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> ((all Z_4 all S_3 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_5,Z_4),S_3)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_3,Z_4),S_3)))) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b))),hoare_759811442triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_2118899576triple(X_b),bool)))))))) # label(fact_6_conseq2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 742 (all X_a (ordered_ab_group_add(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z)))) # label(fact_535_max__diff__distrib__left) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 743 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),D_1)))) # label(fact_235_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 744 (all X_b all F all A_2 all A_3 all X_1 (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)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),F),A_2),A_3),X_1)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),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),A_2),A_3)),X_1))))) # label(fact_92_fold1Set_Ointros) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 745 (all X_b (linorder(X_b) -> (all X_1 ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(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_1),bot_bot(fun(X_b,bool))))))) # label(fact_386_Max_Osingleton) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 746 (all P (-hBOOL(hAPP(bool,bool,fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 747 (all X_b (semiring_char_0(X_b) -> (all M_1 all N (M_1 = N <-> hAPP(nat,X_b,semiring_1_of_nat(X_b),M_1) = hAPP(nat,X_b,semiring_1_of_nat(X_b),N))))) # label(fact_658_of__nat__eq__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 748 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),K))))) # label(fact_411_le__trans) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 749 (all X_b all A_3 all B_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)),A_3),B_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_2),A_3)) -> ti(fun(X_b,bool),B_2) = ti(fun(X_b,bool),A_3)))) # label(fact_260_equalityI) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 750 (all X_a (linorder(X_a) -> (all A_1 all X all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_712_min__max_Oless__supI2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 751 (all N all K_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N)) -> (N = M_1 <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M_1),K_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K_1))))) # label(fact_448_eq__diff__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 752 (all X_c all X_b all F 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),bot_bot(fun(X_c,bool))) = bot_bot(fun(X_b,bool))) # label(fact_80_image__empty) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 753 (all X_b all A_3 all B_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)),A_3),B_2)) <-> ti(fun(X_b,bool),B_2) = ti(fun(X_b,bool),A_3) | hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)))) # label(fact_854_subset__iff__psubset__eq) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 754 (all X_b all X_1 all Y_2 all Pa ((-hBOOL(Pa) -> hAPP(fun(X_b,bool),X_b,the(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(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,Pa)),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(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,Pa))),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)),Y_2)))) = ti(X_b,Y_2)) & (hBOOL(Pa) -> hAPP(fun(X_b,bool),X_b,the(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(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,Pa)),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(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,Pa))),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)),Y_2)))) = ti(X_b,X_1)))) # label(fact_90_If__def) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 755 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(X_b,X_c,G,X_1)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),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_3)))))) # label(fact_175_setprod_Oinsert__remove) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 756 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)))) # label(fact_354_min__max_Oinf__commute) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 757 (all X_a (ordere216010020id_add(X_a) -> zero_zero(X_a) = ti(X_a,zero_zero(X_a)))) # label(tsy_c_Groups_Ozero__class_Ozero_0_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 758 (all X_a (ab_semigroup_add(X_a) -> plus_plus(X_a) = ti(fun(X_a,fun(X_a,X_a)),plus_plus(X_a)))) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 759 (all Z -(all M_2 all N_2 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M_2)),hAPP(nat,int,semiring_1_of_nat(int),N_2)) != Z)) # label(fact_914_int__diff__cases) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 760 (all X_b all A_2 all B_2 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_2)))) # label(fact_33_insertI1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 761 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)))))) # label(fact_865_psubset__card__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 762 (all M all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)))) # label(fact_414_add__leD1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 763 (all X_b all X_c all Z_2 all A_3 all Y_2 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),Y_2)) -> ti(X_c,Y_2) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),A_3)))) # label(fact_181_comp__fun__commute_Ofold__equality) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 764 (all X_b all A_2 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,F_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),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),F),A_2),A_3)))) # label(fact_204_folding__one__idem_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 765 (all X all Y all Z hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Y),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Z)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Y),Z))) # label(fact_701_zadd__left__commute) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 766 (all M 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),N_1)),M))) # label(fact_433_diff__le__self) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 767 (all X_b ti(fun(fun(X_b,bool),X_b),the(X_b)) = the(X_b)) # label(tsy_c_HOL_OThe_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 768 (all X_a (linordered_semidom(X_a) -> (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))))))) # label(fact_818_less__imp__of__nat__less) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 769 (all X_a (preorder(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)))))) # label(fact_779_order__less__asym_H) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 770 (all X_b all A_2 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) # label(fact_12_singleton__conv2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 771 (all X_a (linordered_idom(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),X)))))))) # label(fact_940_mult__right__le__one__le) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 772 (all X_c all X_b hoare_225284258e_case(X_c,X_b) = ti(fun(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_2118899576triple(X_c),X_b)),hoare_225284258e_case(X_c,X_b))) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Otriple_Otriple__case_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 773 (all X_b power_1(X_b) = ti(fun(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(nat,X_b)))),power_1(X_b))) # label(tsy_c_Power_Opower_Opower_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 774 (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]. 2.21/2.48 775 (all X_a all X_c all X_b all P all Q all R hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,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)) # label(help_COMBB_1_1_U) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 776 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(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_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)))))))) # label(fact_597_min__max_OSup__fin_Oinsert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 777 (all X_b all X_c (ord(X_c) -> (all F all G ((all X_2 hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_2)),hAPP(X_b,X_c,G,X_2)))) -> hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)))))) # label(fact_335_le__funI) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 778 (all P all Q (hBOOL(Q) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 779 (all X_a (ab_sem1668676832m_mult(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X) = ti(X_a,X)))) # label(fact_167_mult__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.48 780 (all X_b (linorder(X_b) -> (all X_1 all Y_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)),hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),X_1)),hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),Y_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)))))) # label(fact_292_lessThan__subset__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 781 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))) # label(fact_542_min__max_Osup_Oleft__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 782 (all N_1 all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N_1))))) # label(fact_950_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 783 (all X_b all X_c all A_2 all Z_2 all A_3 all Y_2 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),A_3),Y_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> (exists Y_3 (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))),Y_3)) & ti(X_c,Y_2) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,A_2),Y_3))))))) # label(fact_171_comp__fun__commute_Ofold__graph__insertE__aux) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 784 (all X_a (linorder(X_a) -> (all T_3 exists Z_1 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X_2)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),T_3)))))) # label(fact_923_pinf_I6_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 785 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),B)))) # label(fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 786 (all Z all W_2 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z),W_2) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),hAPP(int,int,uminus_uminus(int),W_2))) # label(fact_688_diff__int__def__symmetric) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 787 (all X_b all X_c (comm_monoid_add(X_c) -> (all F all A_2 all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),F_2)) -> hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),plus_plus(X_c),hAPP(X_b,X_c,F,A_2)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),F_2)) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),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),A_2),F_2))))))) # label(fact_217_setsum__insert) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 788 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),hAPP(X_b,X_b,uminus_uminus(X_b),A_2))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),hAPP(X_b,X_b,uminus_uminus(X_b),Ba))))))) # label(fact_496_le__minus__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 789 (all X_b all A_3 bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),bot_bot(fun(X_b,bool))),A_3)) # label(fact_137_empty__Diff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 790 (all X_c all X_b hoare_1759541758le_rec(X_c,X_b) = ti(fun(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_2118899576triple(X_c),X_b)),hoare_1759541758le_rec(X_c,X_b))) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Otriple_Otriple__rec_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 791 (all X_c all X_b (order(X_c) & order(X_b) -> (all Ca all F all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Ca),hAPP(X_b,X_c,F,Ba))) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_1),X_2)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,Y_1)),hAPP(X_b,X_c,F,X_2))))) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Ca),hAPP(X_b,X_c,F,A_2))))))))) # label(fact_924_xt7) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 792 (all X_b all One all Times all A_2 hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(nat,X_b)),hAPP(X_b,fun(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(nat,X_b))),power_1(X_b),One),Times),A_2),zero_zero(nat)) = ti(X_b,One)) # label(fact_943_power_Opower_Opower__0) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 793 (all X_b (cancel_semigroup_add(X_b) -> (all Ba all A_2 all Ca (ti(X_b,Ba) = ti(X_b,Ca) <-> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ca),A_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ba),A_2))))) # label(fact_230_add__right__cancel) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 794 (all M all N_1 all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),I)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I),N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1))))) # label(fact_965_nat__power__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 795 (all U_1 all M all N_1 all J all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),I)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),U_1)),M)),N_1))) # label(fact_454_nat__diff__add__eq1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 796 (all X_b (order(X_b) -> (all A_2 hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),A_2) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))))) # label(fact_833_atLeastAtMost__singleton) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 797 (all X_b all A_2 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) # label(fact_13_singleton__conv) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 798 (all Z1 all Z2 all W_2 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)),W_2) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W_2))) # label(fact_705_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 799 (all X_b all Ca all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3))) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)))) # label(fact_526_ComplD) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 800 (all X_b all Ca all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3))) <-> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)))) # label(fact_524_Compl__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 801 (all X_c all X_b (comm_monoid_add(X_b) -> big_co1399186613setsum(X_c,X_b) = ti(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),big_co1399186613setsum(X_c,X_b)))) # label(tsy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 802 (all X_b all F all X_1 -hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),bot_bot(fun(X_b,bool))),X_1))) # label(fact_85_empty__fold1SetE) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 803 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> ((all X_2 all Y_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_2),Y_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3)),A_3)))))))) # label(fact_479_min__max_OInf__fin_Oclosed) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 804 (all X_c all X_b (semiring_0(X_b) -> (all F all A_3 all R_2 hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),F),A_3)),R_2) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(X_b,fun(X_c,X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(X_b,fun(X_c,X_b)),combc(X_c,X_b,X_b),hAPP(fun(X_c,X_b),fun(X_c,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_c),times_times(X_b)),F)),R_2)),A_3)))) # label(fact_188_setsum__left__distrib) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 805 (all A_3 all B_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_2))) <-> hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),A_3),B_2)))) # label(fact_900_transfer__nat__int__set__relations_I4_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 806 (all Z hAPP(int,int,uminus_uminus(int),hAPP(int,int,uminus_uminus(int),Z)) = Z) # label(fact_860_zminus__zminus) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 807 (all X_b (ord(X_b) -> ti(fun(X_b,fun(X_b,X_b)),ord_max(X_b)) = ord_max(X_b))) # label(tsy_c_Orderings_Oord__class_Omax_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 808 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b)),finite_fold1(X_b)) = finite_fold1(X_b)) # label(tsy_c_Finite__Set_Ofold1_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 809 (all X_b (boolean_algebra(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_1)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),X_1)),hAPP(X_b,X_b,uminus_uminus(X_b),Y_2))))))) # label(fact_500_compl__le__compl__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 810 (all X_b all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) <-> (exists N_2 exists F_1 ti(fun(X_b,bool),A_3) = hAPP(fun(nat,bool),fun(X_b,bool),hAPP(fun(nat,X_b),fun(fun(nat,bool),fun(X_b,bool)),image(nat,X_b),F_1),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(nat)),N_2)))))) # label(fact_888_finite__conv__nat__seg__image) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 811 (all X_b (linorder(X_b) -> (all Y_2 all X_1 (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)) -> (ti(X_b,Y_2) = ti(X_b,X_1) <-> -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2))))))) # label(fact_787_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 812 (all U all M_1 all N all J_1 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),I_1)) -> (N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M_1) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),N)))) # label(fact_453_nat__eq__add__iff1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 813 (all Z1 all Z2 all W_2 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W_2)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z1),Z2)),W_2)) # label(fact_698_zdiff__zmult__distrib) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 814 (all X_b all X_c ti(fun(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool)))),fold_graph(X_b,X_c)) = fold_graph(X_b,X_c)) # label(tsy_c_Nitpick_Ofold__graph_H_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 815 (all Z_3 all Z all W_3 all W_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_3),W_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_3),Z)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_3),Z_3)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_2),Z)))))) # label(fact_861_zadd__zless__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 816 (all X_a all P all X (hBOOL(hAPP(fun(X_a,bool),bool,fEx(X_a),P)) | -hBOOL(hAPP(X_a,bool,P,X)))) # label(help_fEx_1_1_U) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 817 (all X_a (ordered_ab_group_add(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B)),hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))))) # label(fact_493_le__imp__neg__le) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 818 (all X_b all F all A_3 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A_3),X_1)) -> ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)))) # label(fact_84_fold1Set__nonempty) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 819 (all A_3 (hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))) <-> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A_3)))) # label(fact_894_transfer__nat__int__set__relations_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 820 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,uminus_uminus(X_a),X))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))))) # label(fact_498_compl__le__swap1) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 821 (all X_a (linorder(X_a) -> (all B all A_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),X))))))) # label(fact_555_min__max_Ole__supI) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 822 (all X_a (linorder(X_a) -> (all Z all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z)),X))))))) # label(fact_556_min__max_Osup__least) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 823 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_990_mult__neg__pos) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 824 (all X_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),N))) <-> N = zero_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_1)))) # label(fact_963_nat__zero__less__power__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 825 (all X_a (bot(X_a) -> (all A_1 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),bot_bot(X_a)))))) # label(fact_766_not__less__bot) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 826 (all X_b all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))) # label(fact_609_card__Diff1__le) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 827 (all X_b (comm_monoid_add(X_b) -> (all Pa all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) -> hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),Pa),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M_1),N)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(nat,X_b,Pa,M_1)),hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),Pa),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),M_1),N))))))) # label(fact_935_setsum__head) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 828 (all X_1 all A_3 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),A_3)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))))) # label(fact_896_transfer__nat__int__set__relations_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 829 (all X_b all C_1 all A_3 all B_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)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),B_2),C_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_1))))) # label(fact_857_subset__psubset__trans) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 830 (all X_1 all Y_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_2))))) # label(fact_904_transfer__int__nat__relations_I3_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 831 (all X_b (ab_semigroup_mult(X_b) -> hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite100568337ommute(X_b,X_b),times_times(X_b))))) # label(fact_192_comp__fun__commute) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 832 (all X_a (order(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_778_xt1_I9_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 833 (all X_b (linorder(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),A_2),A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(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_3)))))) # label(fact_602_min__max_OSup__fin_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 834 (all X_b all Ca all A_3 all B_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)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B_2))))) # label(fact_261_subsetD) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 835 (all X_a (dense_linorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ((all W (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W),Z))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z))))))) # label(fact_920_dense__le__bounded) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 836 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1))) # label(fact_798_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 837 (all X_b (linorder(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Min(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_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),A_2),A_3))))) # label(fact_378_Min_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 838 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) | M = N_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)))) # label(fact_741_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 839 (all X_a (linorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z)))))))) # label(fact_360_min__max_Oinf__greatest) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 840 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) <-> (exists K_3 N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_3)))) # label(fact_421_le__iff__add) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 841 (all X_c all X_b (comm_monoid_mult(X_b) -> (all F hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co302546470etprod(X_c,X_b),F),bot_bot(fun(X_c,bool))) = one_one(X_b)))) # label(fact_641_setprod__empty) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 842 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))) = bot_bot(fun(X_b,bool)) -> ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3)) & (bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))))))))))) # label(fact_518_Max_Oremove) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 843 (all X_c (uminus(X_c) -> uminus_uminus(X_c) = ti(fun(X_c,X_c),uminus_uminus(X_c)))) # label(tsy_c_Groups_Ouminus__class_Ouminus_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 844 (all X_a (ordere236663937imp_le(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z))))) # label(fact_370_min__add__distrib__left) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 845 (all X_c all X_b (order(X_b) & ord(X_c) -> (all Ca all F all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_c,X_b,F,Ba)),A_2)) -> (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Ca),Ba)) -> ((all X_2 all Y_1 (hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less(X_c),Y_1),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,Y_1)),hAPP(X_c,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_c,X_b,F,Ca)),A_2)))))))) # label(fact_926_xt6) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 846 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_506_minus__mult__left) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 847 (all Vname_1 all Fun_1 all Com1 all Com2 hAPP(fun(state,nat),com,hAPP(vname,fun(fun(state,nat),com),ass,Vname_1),Fun_1) != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2)) # label(fact_72_com_Osimps_I24_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 848 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_783_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 849 (all X_b all X_c all Z_2 all F all A_3 ((exists X_2 (hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),X_2),A_3)) & hAPP(X_c,X_b,F,X_2) = ti(X_b,Z_2))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Z_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),A_3))))) # label(fact_69_image__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 850 (all X_b all Ga all G_1 all Ts (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),G_1),Ts)) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),G_1)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts))))) # label(fact_2_cut) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 851 (all X_b all A_3 all X_1 all B_2 ((hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool))))),B_2))) & (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> 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_3),B_2)))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),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),B_2))))) # label(fact_870_psubset__insert__iff) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 852 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)))))) # label(fact_956_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 853 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),X_1),A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(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_1),A_3))))))) # label(fact_603_min__max_OSup__fin_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 854 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y)),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y)))))) # label(fact_497_compl__le__swap2) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 855 (all X_a (order(X_a) -> (all A_1 all B (ti(X_a,A_1) != ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_754_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 856 (all X_b (ord(X_b) -> ord_max(X_b) = hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,X_b)),max(X_b),ord_less_eq(X_b)))) # label(fact_568_max__ord__max) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 857 (all X_b bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse))) # label(fact_23_empty__def) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 858 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_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_2),A_3)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)) = hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))))) # label(fact_617_card__Diff__subset) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 859 (all X_a (linorder(X_a) -> (all X all Y all Z hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z))))))) # label(fact_561_min__max_Odistrib__inf__le) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 860 (all X_b all X_c all Z_2 all X_1 all A_3 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite_comp_fun_idem(X_b,X_c),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_2),A_3)) = hAPP(fun(X_b,bool),X_c,hAPP(X_c,fun(fun(X_b,bool),X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),X_c)),finite_fold(X_b,X_c),F),Z_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_1),A_3))))) # label(fact_202_comp__fun__idem_Ofold__insert__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 861 (all X_b ti(fun(fun(X_b,bool),X_b),the_elem(X_b)) = the_elem(X_b)) # label(tsy_c_Set_Othe__elem_res) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 862 (all X_a (linorder(X_a) -> (all A_1 all B all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),X)) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),X)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X))))))) # label(fact_558_min__max_Ole__supE) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 863 (all X_1 all Y_2 (hAPP(nat,int,semiring_1_of_nat(int),X_1) = hAPP(nat,int,semiring_1_of_nat(int),Y_2) <-> X_1 = Y_2)) # label(fact_899_transfer__int__nat__relations_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 864 (all X_b (cancel_semigroup_add(X_b) -> (all A_2 all Ba all Ca (hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),Ba) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),Ca) <-> ti(X_b,Ca) = ti(X_b,Ba))))) # label(fact_231_add__left__cancel) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 865 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> ((all Y_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_1)))) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3) = ti(X_b,X_1))))))) # label(fact_395_Min__eqI) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 866 (all X_b (finite_finite(X_b) -> (all A_3 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))))) # label(fact_102_finite__code) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 867 (all X_b all F all A1 all A2 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A1),A2)) <-> (exists A_5 exists A_4 exists 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),A_5),A_4) = ti(fun(X_b,bool),A1) & 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)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),F),A_5),A_4),X_2)) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_5),A_4)) & ti(X_b,A2) = ti(X_b,X_2))))) # label(fact_114_fold1Set_Osimps) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 868 (all X_a (comm_ring_1(X_a) -> (all X hAPP(X_a,X_a,uminus_uminus(X_a),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),X)))) # label(fact_639_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 869 (all N_1 all J all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),N_1)),K)))) # label(fact_742_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 870 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_1),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),C)))))) # label(fact_827_diff__less__mono) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 871 (all P all Q (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | -hBOOL(Q))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 872 (all X_b all B_2 all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),B_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_2),A_3)) -> hAPP(fun(X_b,bool),X_b,F_2,A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(fun(X_b,bool),X_b,F_2,B_2)),hAPP(fun(X_b,bool),X_b,F_2,A_3))))))) # label(fact_328_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 873 (all X_a (linordered_semidom(X_a) -> (all A_1 all N_1 all N_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_4)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_4)))))))) # label(fact_883_power__strict__increasing) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 874 (all X_c all X_b all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> 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_3))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))) # label(fact_616_card__image__le) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 875 (all X_b all X_c all X_1 all Y_2 all Z_2 all F (hBOOL(hAPP(fun(X_b,fun(X_c,X_c)),bool,finite100568337ommute(X_b,X_c),F)) -> hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,Y_2),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),Z_2)) = hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,X_1),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F,Y_2),Z_2)))) # label(fact_179_comp__fun__commute_Ofun__left__comm) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 876 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,big_linorder_Min(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_1),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),X_1),A_3)))))) # label(fact_377_Min_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption]. 2.21/2.49 877 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),X))))) # label(fact_369_min__max_Oinf__le1) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 878 (all X_b all X_c (comm_monoid_add(X_c) -> (all F all G all A_3 all B_2 (ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)) -> hAPP(X_b,X_c,G,X_2) = hAPP(X_b,X_c,F,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),B_2) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),F),A_3)))))) # label(fact_255_setsum__cong) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 879 (all X_c all X_b (comm_monoid_add(X_b) -> (all F all G all A_3 hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),F),A_3)),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),G),A_3)) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_c,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,X_b)),combs(X_c,X_b,X_b),hAPP(fun(X_c,X_b),fun(X_c,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_c,X_b),fun(X_c,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_c),plus_plus(X_b)),F)),G)),A_3)))) # label(fact_215_setsum__addf) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 880 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N_1)) -> N_1 != zero_zero(nat))) # label(fact_969_gr__implies__not0) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 881 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))) # label(fact_246_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 882 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3)),A_3))))))) # label(fact_383_Max__in) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 883 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> ((all X_2 all Y_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_2),Y_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Min(X_b),A_3)),A_3)))))))) # label(fact_393_Min_Oclosed) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 884 (all X_b (ab_sem1668676832m_mult(X_b) -> hBOOL(hAPP(fun(X_b,fun(X_b,X_b)),bool,finite_comp_fun_idem(X_b,X_b),times_times(X_b))))) # label(fact_164_comp__fun__idem) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 885 (all X_b (linordered_semidom(X_b) -> (all X_1 all Y_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),one_one(X_b)),Ba)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),Ba),X_1)),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),Ba),Y_2)))))))) # label(fact_846_power__increasing__iff) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 886 (all X_b (preorder(X_b) -> (all Pa all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)) -> hBOOL(Pa)))))) # label(fact_780_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 887 (all X_a (boolean_algebra(X_a) -> (all X ti(X_a,X) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X))))) # label(fact_483_double__compl) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 888 (all M all N_1 all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K))) # label(fact_463_add__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 889 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1))))) # label(fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 890 (all X_a (linorder(X_a) -> (all B all D_1 all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),C),D_1)))))))) # label(fact_359_min__max_Oinf__mono) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 891 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1))) # label(fact_801_less__not__refl) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 892 (all X_a (order(X_a) -> (all Z all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X))))))) # label(fact_772_xt1_I10_J) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 893 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_978_add__neg__neg) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 894 (all X_b all A_3 (ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) <-> 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_3),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3))))) # label(fact_515_subset__Compl__self__eq) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 895 (all X_a (semiring_1(X_a) -> (all M all N_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))))) # label(fact_660_of__nat__add) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 896 (all X_c all X_b all Ca all A_3 ((bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),Ca)),A_3) = hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),Ca),bot_bot(fun(X_c,bool)))) & (ti(fun(X_b,bool),A_3) = bot_bot(fun(X_b,bool)) -> bot_bot(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),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),Ca)),A_3)))) # label(fact_63_image__constant__conv) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 897 (all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M)))) # label(fact_407_le__square) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 898 (all U U = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),ord_lessThan(nat),U))) # label(fact_612_card__lessThan) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 899 (all X_b all A_3 all X_1 all B_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)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool))))),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> 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_3),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),B_2)))))) # label(fact_326_diff__single__insert) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 900 (all N_1 all M -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),M))))) # label(fact_848_not__int__zless__negative) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 901 (all X_a (monoid_mult(X_a) -> (all A_1 all M all N_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))))) # label(fact_880_power__add) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 902 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_726_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 903 (all X_b (one(X_b) -> ti(X_b,one_one(X_b)) = one_one(X_b))) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 904 (all X_a (order(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Least))))) # label(fact_585_max__leastR) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 905 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool))))))) & (bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3) = ti(X_b,X_1))))))) # label(fact_468_min__max_OInf__fin_Oremove) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 906 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y)),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y)))))) # label(fact_811_compl__less__swap2) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 907 (all Z Z = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),Z)) # label(fact_708_zmult__1) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 908 (all X_c all X_b (semiring_0(X_b) -> (all R_2 all F all A_3 hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),R_2),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),F),A_3)) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_b,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),combb(X_b,X_b,X_c),hAPP(X_b,fun(X_b,X_b),times_times(X_b),R_2)),F)),A_3)))) # label(fact_189_setsum__right__distrib) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 909 (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]. 2.29/2.49 910 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),hAPP(X_a,X_a,uminus_uminus(X_a),X))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))))) # label(fact_812_compl__less__swap1) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 911 (all X_b all A_3 ((exists X_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3))) <-> bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3))) # label(fact_21_ex__in__conv) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 912 (all M all N_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N_1)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))) # label(fact_669_zadd__int) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 913 (all X_a (linord20386208strict(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))))))) # label(fact_987_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 914 (all X_a (order(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> ti(X_a,Least) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Least))))) # label(fact_399_min__leastR) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 915 (all X_a (comm_semiring_1(X_a) -> (all Lx all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ry) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))))) # label(fact_244_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 916 (all X_b all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_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_2),C_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),C_1))))) # label(fact_856_psubset__subset__trans) # label(axiom) # label(non_clause). [assumption]. 2.29/2.49 917 (all X_b (linord581940658strict(X_b) -> (all A_2 all Ba all Ca (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),Ca)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ca),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ca),Ba)))))))) # label(fact_983_mult__less__cancel__left__pos) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 918 (all X_b all A_3 all F all N (hAPP(fun(nat,bool),fun(X_b,bool),hAPP(fun(nat,X_b),fun(fun(nat,bool),fun(X_b,bool)),image(nat,X_b),F),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(nat)),N))) = ti(fun(X_b,bool),A_3) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)))) # label(fact_714_nat__seg__image__imp__finite) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 919 (all X_a (semiring_1(X_a) -> (all M all N_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1))))) # label(fact_661_of__nat__mult) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 920 (all X_b all X_1 all A_3 all B_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)),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_3)),B_2)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_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)),A_3),B_2)))) # label(fact_311_insert__subset) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 921 (all Z all W_2 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W_2),Z) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z),W_2)) # label(fact_697_zmult__commute) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 922 (all X_b (linorder(X_b) -> (all Ca all Ba all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Ba)))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_max(X_b)),Ca),A_3)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),Ba),Ca)))))))) # label(fact_581_min__max_Ofold__sup__le__sup) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 923 (all X_b (linorder(X_b) -> ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b)),big_Inf_fin(X_b)) = big_Inf_fin(X_b))) # label(tsy_c_Big__Operators_Olattice_OInf__fin_res) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 924 (all M all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),M)),K))))) # label(fact_436_le__add__diff) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 925 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3)) = hAPP(fun(X_b,bool),X_b,big_linorder_Max(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_1),A_3)))))))) # label(fact_575_Max_Oinsert) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 926 (all L_1 all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),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_1),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_1),M))))) # label(fact_437_diff__le__mono2) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 927 (all X_b all Ca all A_3 all B_2 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B_2)) & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),A_3)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))))) # label(fact_132_Diff__iff) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 928 (all K_1 all M_1 all N (M_1 = N <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),M_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),N))) # label(fact_458_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 929 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_985_mult__pos__neg) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 930 (all M all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1)))) # label(fact_415_add__leD2) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 931 (all X_c all X_b all F all Z_2 hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),bot_bot(fun(X_b,bool))),Z_2))) # label(fact_105_fold__graph_OemptyI) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 932 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)) = ti(X_a,B)))) # label(fact_504_minus__add__cancel) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 933 (all M all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N_1)))) # label(fact_409_nat__le__linear) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 934 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(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_1),A_3))))))) # label(fact_598_min__max_OSup__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 935 (all X_b (ab_semigroup_mult(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> ((all X_2 all Y_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_2),Y_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(X_b)),A_3)),A_3)))))))) # label(fact_154_fold1__in) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 936 (all X_b all Ts all Ga all T_5 (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),T_5),bot_bot(fun(hoare_2118899576triple(X_b),bool))))) -> (hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),Ts)) -> hBOOL(hAPP(fun(hoare_2118899576triple(X_b),bool),bool,hAPP(fun(hoare_2118899576triple(X_b),bool),fun(fun(hoare_2118899576triple(X_b),bool),bool),hoare_1301688828derivs(X_b),Ga),hAPP(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool),hAPP(hoare_2118899576triple(X_b),fun(fun(hoare_2118899576triple(X_b),bool),fun(hoare_2118899576triple(X_b),bool)),insert(hoare_2118899576triple(X_b)),T_5),Ts)))))) # label(fact_3_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 937 (all X_b all A_3 all B_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_2),A_3)) <-> 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),uminus_uminus(fun(X_b,bool)),A_3)),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),B_2))))) # label(fact_491_Compl__subset__Compl__iff) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 938 (all X_b all B_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),finite_fold(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_b),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),combc(fun(X_b,bool),fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)))),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool))))),B_2),A_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_2),A_3))) # label(fact_177_minus__fold__remove) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 939 (all X_b all X_c (comm_monoid_mult(X_c) -> (all H all G all A_3 all B_2 (ti(fun(X_b,bool),B_2) = ti(fun(X_b,bool),A_3) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B_2)) -> hAPP(X_b,X_c,H,X_2) = hAPP(X_b,X_c,G,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),H),A_3) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),B_2)))))) # label(fact_253_setprod_OF__cong) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 940 (all X_b all A_3 (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_3),bot_bot(fun(X_b,bool)))) <-> bot_bot(fun(X_b,bool)) = ti(fun(X_b,bool),A_3))) # label(fact_305_subset__empty) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 941 (all X_a (semiring_1(X_a) -> (all M all N_1 hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N_1)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),N_1)))) # label(fact_875_of__nat__power) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 942 (all X_a (linordered_ring(X_a) -> (all A_1 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)),zero_zero(X_a)))))) # label(fact_980_not__square__less__zero) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 943 (all X_a (linorder(X_a) -> (all B all A_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_733_min__max_Oless__infI1) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 944 (all P all Q (hBOOL(Q) | hBOOL(P) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)))) # label(help_fdisj_3_1_U) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 945 (all X_a (ord(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (ti(X_a,B) = ti(X_a,C) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))))))) # label(fact_775_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 946 (all M all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J))))) # label(fact_418_trans__le__add2) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 947 (all X_c all X_b all X_1 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_2)) -> ti(X_b,X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,X_1),X_1))) # label(fact_136_folding__image__simple__idem_Oidem) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 948 (all X_b (comm_monoid_add(X_b) -> (all F all M_1 all K_1 all N hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M_1),K_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K_1))) = hAPP(fun(nat,bool),X_b,hAPP(fun(nat,X_b),fun(fun(nat,bool),X_b),big_co1399186613setsum(nat,X_b),hAPP(fun(nat,nat),fun(nat,X_b),hAPP(fun(nat,X_b),fun(fun(nat,nat),fun(nat,X_b)),combb(nat,X_b,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),M_1),N))))) # label(fact_835_setsum__shift__bounds__cl__nat__ivl) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 949 (all X_b (one(X_b) -> (all X_1 (one_one(X_b) = ti(X_b,X_1) <-> ti(X_b,X_1) = one_one(X_b))))) # label(fact_634_one__reorient) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 950 (all X_b hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),bot_bot(fun(X_b,bool))))) # label(fact_98_finite_OemptyI) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 951 (all X_b ti(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_2118899576triple(X_b)))),hoare_759811442triple(X_b)) = hoare_759811442triple(X_b)) # label(tsy_c_Hoare__Mirabelle__lcrcocijdw_Otriple_Otriple_res) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 952 (all X_a (linorder(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),A_1)))) # label(fact_545_min__max_Osup_Oidem) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 953 (all M all N_1 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),M)),N_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N_1))) # label(fact_685_zpower__int) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 954 (all X_b all A_3 all B_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)),A_3),B_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)),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),B_2)),hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3))))) # label(fact_490_Compl__anti__mono) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 955 (all X_b (order(X_b) -> (all X_1 all Y_2 (ti(X_b,X_1) != ti(X_b,Y_2) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_1),Y_2)))))) # label(fact_748_order__less__le) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 956 (all X_b all A_3 all F all F_2 (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),big_semilattice_big(X_b),F),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,F_2,A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F),A_3)))) # label(fact_122_semilattice__big_OF__eq) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 957 (all X_c all X_b all F all G all M_3 all N_3 (ti(fun(X_b,bool),M_3) = ti(fun(X_b,bool),N_3) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),N_3)) -> hAPP(X_b,X_c,F,X_2) = hAPP(X_b,X_c,G,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),G),N_3) = hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),F),M_3)))) # label(fact_91_image__cong) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 958 (all X_b all A_2 all G all F (G = hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F) -> hAPP(fun(X_b,bool),X_b,G,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool)))) = ti(X_b,A_2))) # label(fact_62_fold1__singleton__def) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 959 (all X_b partial_flat_lub(X_b) = ti(fun(X_b,fun(fun(X_b,bool),X_b)),partial_flat_lub(X_b))) # label(tsy_c_Partial__Function_Oflat__lub_res) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 960 (all X_b (ordere236663937imp_le(X_b) -> (all Ca all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ca),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ca),Ba))))))) # label(fact_730_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 961 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)))))) # label(fact_279_linorder__linear) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 962 (all X_b all X_1 all A_3 all B_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)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))))) # label(fact_285_in__mono) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 963 (all X_b all Pa all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2)) -> (ti(fun(X_b,bool),F_2) != bot_bot(fun(X_b,bool)) -> ((all X_2 hBOOL(hAPP(fun(X_b,bool),bool,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),X_2),bot_bot(fun(X_b,bool)))))) -> ((all X_2 all F_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_3)) -> (ti(fun(X_b,bool),F_3) != bot_bot(fun(X_b,bool)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,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),X_2),F_3)))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2))))))) # label(fact_120_finite__ne__induct) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 964 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool))),finite_fold1Set(X_b)) = finite_fold1Set(X_b)) # label(tsy_c_Finite__Set_Ofold1Set_res) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 965 (all X_b (order(X_b) -> (all A_2 all Ba (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),A_2),Ba)) <-> bot_bot(fun(X_b,bool)) = hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),Ba))))) # label(fact_829_atLeastatMost__empty__iff2) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 966 (all X_b (linorder(X_b) -> (all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_3) -> ((all X_2 all Y_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_2),Y_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),A_3)),A_3)))))))) # label(fact_580_Max_Oclosed) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 967 (all X all Y (X != Y -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X))))) # label(fact_799_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 968 (all X_b all Ca all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),B_2)))) # label(fact_135_DiffD2) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 969 (all T_2 all T_1 (ord(T_1) -> ord(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oord) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 970 (all X_b all A_2 hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_2)) = ti(X_b,A_2)) # label(fact_89_the__eq__trivial) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 971 (all X_b all B_2 all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (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_3),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_2))))) # label(fact_284_set__rev__mp) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 972 (all X_b (ordered_ring(X_b) -> (all A_2 all E all Ca all Ba all D (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),E)),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ba),E)),D))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),Ba)),E)),Ca)),D)))))) # label(fact_836_less__add__iff1) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 973 (all X_a (bot(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),bot_bot(X_a)),A_1))))) # label(fact_303_bot__least) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 974 (all X_b all F all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (ti(fun(X_b,bool),A_3) != bot_bot(fun(X_b,bool)) -> (exists X1 hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F),A_3),X1)))))) # label(fact_109_finite__nonempty__imp__fold1Set) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 975 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_948_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 976 (all U all M_1 all N all I_1 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),I_1)),U)),N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),N)))))) # label(fact_842_nat__less__add__iff2) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 977 (all X_b all X_c (comm_monoid_mult(X_c) -> (all G all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),A_3) = hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),times_times(X_c),hAPP(X_b,X_c,G,X_1)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),G),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool))))))))))) # label(fact_176_setprod_Oremove) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 978 (all X_a ti(fun(fun(X_a,bool),bool),fEx(X_a)) = fEx(X_a)) # label(tsy_c_fEx_res) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 979 (all X_a (comm_semiring_1(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z))))) # label(fact_248_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 980 (all X_b (linord581940658strict(X_b) -> (all A_2 all Ba all Ca (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),zero_zero(X_b))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ca),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ca),Ba))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),A_2))))))) # label(fact_989_mult__less__cancel__left__neg) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 981 (all X_b all X_c (comm_monoid_add(X_c) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),plus_plus(X_c),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),G),A_3)),hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),H),A_3)) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),hAPP(fun(X_b,X_c),fun(X_b,X_c),hAPP(fun(X_b,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,X_c)),combs(X_b,X_c,X_c),hAPP(fun(X_b,X_c),fun(X_b,fun(X_c,X_c)),hAPP(fun(X_c,fun(X_c,X_c)),fun(fun(X_b,X_c),fun(X_b,fun(X_c,X_c))),combb(X_c,fun(X_c,X_c),X_b),plus_plus(X_c)),G)),H)),A_3))))) # label(fact_216_setsum_Odistrib) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 982 (all I_1 all J_1 all F ((all I_2 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I_2)),hAPP(nat,nat,F,J_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,F,I_1)),hAPP(nat,nat,F,J_1)))))) # label(fact_915_less__mono__imp__le__mono) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 983 (all J all I -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),I)),I))) # label(fact_722_not__add__less2) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 984 (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_31_insert__Collect) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 985 (all X_b (linorder(X_b) -> (all Ca all Ba all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Ba),X_2)))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),Ba),Ca)),hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),Ca),A_3)))))))) # label(fact_394_min__max_Oinf__le__fold__inf) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 986 (all X_b all A_2 all A_3 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_3) != bot_bot(fun(X_b,bool))) # label(fact_39_insert__not__empty) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 987 (all X_b (ord(X_b) -> ti(fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,X_b))),min(X_b)) = min(X_b))) # label(tsy_c_Orderings_Oord_Omin_res) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 988 (all X_b (ordered_ab_group_add(X_b) -> (all X_1 hAPP(X_b,fun(X_b,bool),ord_greaterThan(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),X_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),uminus_uminus(X_b)),hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),X_1))))) # label(fact_516_image__uminus__lessThan) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 989 (all X_a (linorder(X_a) -> (all B all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_713_min__max_Oless__supI1) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 990 (all X_a all X all Y (ti(X_a,Y) != ti(X_a,X) | 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]. 2.29/2.50 991 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_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)),hAPP(X_b,fun(X_b,bool),ord_greaterThan(X_b),X_1)),hAPP(X_b,fun(X_b,bool),ord_greaterThan(X_b),Y_2))))))) # label(fact_571_greaterThan__subset__iff) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 992 (all X_b all A_3 all B_2 (hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),B_2) = hAPP(fun(X_b,bool),fun(X_b,bool),uminus_uminus(fun(X_b,bool)),A_3) <-> ti(fun(X_b,bool),A_3) = ti(fun(X_b,bool),B_2))) # label(fact_525_Compl__eq__Compl__iff) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 993 (all X_a (monoid_mult(X_a) -> (all A_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),one_one(nat)) = ti(X_a,A_1)))) # label(fact_877_power__one__right) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 994 (all X_b all Pa all A_3 all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_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)),F_2),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))) -> ((all A_5 all F_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_5),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_5),F_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,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_5),F_3)))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2))))))) # label(fact_330_finite__subset__induct) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 995 (all X_a (comm_semiring_1(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a))))) # label(fact_628_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 996 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),X_1),A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(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_1),A_3))))))) # label(fact_476_min__max_OInf__fin_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 997 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C all D_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),D_1))))) # label(fact_236_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 998 (all X_b all A_3 all X_1 all B_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)),A_3),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),B_2))) <-> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> 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_3),B_2))) & (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> 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(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool))))),B_2))))) # label(fact_327_subset__insert__iff) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 999 (all X_a (monoid_mult(X_a) -> (all A_1 all N_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1)),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_1))))) # label(fact_873_power__commutes) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1000 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)))))) # label(fact_265_linorder__le__cases) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1001 (all X_a (comm_semiring_1(X_a) -> (all X ti(X_a,X) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),one_one(nat))))) # label(fact_709_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1002 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),K))))) # label(fact_405_mult__le__mono1) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1003 (all X_a (comm_semiring_1(X_a) -> (all X all Y all Q_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),Q_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),Q_1))))) # label(fact_732_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1004 (all X_b all X_2 (hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X_2)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),bot_bot(fun(X_b,bool)))))) # label(fact_59_bot__empty__eq) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1005 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),finite2073411215e_idem(X_b)) = finite2073411215e_idem(X_b)) # label(tsy_c_Finite__Set_Ofolding__one__idem_res) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1006 (all X_b (linord581940658strict(X_b) -> (all Ca all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),Ca)) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ca),zero_zero(X_b))) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),A_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ca),A_2)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),Ca),Ba))))))) # label(fact_982_mult__less__cancel__left__disj) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1007 (all X_a (monoid_mult(X_a) -> (all N_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),one_one(X_a)),N_1) = one_one(X_a)))) # label(fact_874_power__one) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1008 (all X_c all X_b all Ca all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(fun(X_b,X_c),fun(fun(X_b,bool),fun(X_c,bool)),image(X_b,X_c),hAPP(X_c,fun(X_b,X_c),combk(X_c,X_b),Ca)),A_3) = hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),Ca),bot_bot(fun(X_c,bool))))) # label(fact_86_image__constant) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1009 (all X_b (linorder(X_b) -> (all M_1 all N (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),M_1)),hAPP(X_b,fun(X_b,bool),ord_lessThan(X_b),N))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),M_1),N)))))) # label(fact_793_lessThan__strict__subset__iff) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1010 (all X_a (bot(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),bot_bot(X_a))) -> bot_bot(X_a) = ti(X_a,A_1))))) # label(fact_301_le__bot) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1011 (all W_2 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_2),Z)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_2),one_one(int))),Z)))) # label(fact_866_zless__imp__add1__zle) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1012 (all X_a (semiring_1(X_a) -> one_one(X_a) = hAPP(nat,X_a,semiring_1_of_nat(X_a),one_one(nat)))) # label(fact_662_of__nat__1) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1013 (all Z all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z))))) # label(fact_466_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1014 (all M all N_1 all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N_1)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K))) # label(fact_455_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1015 (all X_b (finite_finite(X_b) -> (all A_3 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3))))) # label(fact_101_finite) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1016 (all X_b (linorder(X_b) -> (all M_3 all N_3 (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)),M_3),N_3)) -> (ti(fun(X_b,bool),M_3) != bot_bot(fun(X_b,bool)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),M_3)),hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),N_3))))))))) # label(fact_342_Max__mono) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1017 (all X_b all Ba all A_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_2),bot_bot(fun(X_b,bool))))) <-> ti(X_b,A_2) = ti(X_b,Ba))) # label(fact_38_singleton__iff) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1018 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) | ti(X_a,X) = ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_788_linorder__less__linear) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1019 (all X_b all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(fun(fun(X_b,bool),bool),bool,finite_finite_1(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_3)))))) # label(fact_263_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1020 (all X_c all X_b all X_1 all A_3 all F all Z_2 all G all F_2 (hBOOL(hAPP(fun(fun(X_c,bool),X_b),bool,hAPP(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool),hAPP(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_c,X_b),fun(fun(fun(X_c,bool),X_b),bool))),finite908156982e_idem(X_b,X_c),F),Z_2),G),F_2)) -> (hBOOL(hAPP(fun(X_c,bool),bool,finite_finite_1(X_c),A_3)) -> hAPP(fun(X_c,bool),X_b,F_2,hAPP(fun(X_c,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_c,bool),fun(X_c,bool)),insert(X_c),X_1),A_3)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F,hAPP(X_c,X_b,G,X_1)),hAPP(fun(X_c,bool),X_b,F_2,A_3))))) # label(fact_121_folding__image__simple__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1021 (all X_b (order(X_b) -> (all Ba all A_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Ba),A_2)) -> bot_bot(fun(X_b,bool)) = hAPP(X_b,fun(X_b,bool),hAPP(X_b,fun(X_b,fun(X_b,bool)),ord_atLeastAtMost(X_b),A_2),Ba))))) # label(fact_792_atLeastatMost__empty) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1022 (all X_b (bot(X_b) -> bot_bot(X_b) = ti(X_b,bot_bot(X_b)))) # label(tsy_c_Orderings_Obot__class_Obot_res) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1023 (all X_b (linorder(X_b) -> (all Z_2 all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Z_2),Y_2)) | hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Z_2),X_1)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Z_2),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),Y_2))))))) # label(fact_559_le__max__iff__disj) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1024 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3)) & (bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))) -> ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),A_3))))))) # label(fact_604_min__max_OSup__fin_Oremove) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1025 (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_77_Collect__def) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1026 (all X_a (linorder(X_a) -> (all X all Y all Z ((all X_2 all Y_1 all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y_1),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_2),Z_1))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z)))))) # label(fact_582_min__max_Odistrib__imp1) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1027 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_505_minus__mult__right) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1028 (all X_b (ordered_ab_group_add(X_b) -> (all A_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),Ba)),A_2)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_b,X_b,uminus_uminus(X_b),A_2)),Ba)))))) # label(fact_495_minus__le__iff) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1029 (all X_b all X_c (comm_monoid_mult(X_c) -> (all F all S_1 all T_4 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),T_4)) -> (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)),S_1),T_4)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),T_4),S_1))) -> one_one(X_c) = hAPP(X_b,X_c,F,X_2))) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),S_1) = hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co302546470etprod(X_b,X_c),F),T_4))))))) # label(fact_653_setprod__mono__one__left) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1030 (all W_1 all Z_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z_2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),one_one(int))),Z_2)))) # label(fact_867_add1__zle__eq) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1031 (all X_c all X_d all X_b (comm_monoid_add(X_b) -> (all F all B_2 all A_3 hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_d,bool),fun(X_c,X_b),hAPP(fun(X_c,fun(fun(X_d,bool),X_b)),fun(fun(X_d,bool),fun(X_c,X_b)),combc(X_c,fun(X_d,bool),X_b),hAPP(fun(X_c,fun(X_d,X_b)),fun(X_c,fun(fun(X_d,bool),X_b)),hAPP(fun(fun(X_d,X_b),fun(fun(X_d,bool),X_b)),fun(fun(X_c,fun(X_d,X_b)),fun(X_c,fun(fun(X_d,bool),X_b))),combb(fun(X_d,X_b),fun(fun(X_d,bool),X_b),X_c),big_co1399186613setsum(X_d,X_b)),F)),B_2)),A_3) = hAPP(fun(X_d,bool),X_b,hAPP(fun(X_d,X_b),fun(fun(X_d,bool),X_b),big_co1399186613setsum(X_d,X_b),hAPP(fun(X_c,bool),fun(X_d,X_b),hAPP(fun(X_d,fun(fun(X_c,bool),X_b)),fun(fun(X_c,bool),fun(X_d,X_b)),combc(X_d,fun(X_c,bool),X_b),hAPP(fun(X_d,fun(X_c,X_b)),fun(X_d,fun(fun(X_c,bool),X_b)),hAPP(fun(fun(X_c,X_b),fun(fun(X_c,bool),X_b)),fun(fun(X_d,fun(X_c,X_b)),fun(X_d,fun(fun(X_c,bool),X_b))),combb(fun(X_c,X_b),fun(fun(X_c,bool),X_b),X_d),big_co1399186613setsum(X_c,X_b)),hAPP(fun(X_c,fun(X_d,X_b)),fun(X_d,fun(X_c,X_b)),combc(X_c,X_d,X_b),F))),A_3)),B_2)))) # label(fact_180_setsum__commute) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1032 (all M all N_1 all K hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K))) # label(fact_430_diff__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1033 (all X_a fequal(X_a) = ti(fun(X_a,fun(X_a,bool)),fequal(X_a))) # label(tsy_c_fequal_res) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1034 (all X_b all X_1 all Pa all Q_3 (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)),Pa),Q_3)) -> (hBOOL(hAPP(X_b,bool,Pa,X_1)) -> hBOOL(hAPP(X_b,bool,Q_3,X_1))))) # label(fact_290_predicate1D) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1035 (all X_a (linorder(X_a) -> (all X all Y all Z ((all X_2 all Y_1 all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y_1),Z_1))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z)))))) # label(fact_583_min__max_Odistrib__imp2) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1036 (all K all L_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),L_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),L_1)))))) # label(fact_403_mult__le__mono) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1037 (all X_b (linorder(X_b) -> (all X_1 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_1)) <-> -hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_1),Y_2)))))) # label(fact_746_linorder__not__le) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1038 (all X_b (linorder(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(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_3)) = hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),ord_min(X_b)),A_2),A_3))))) # label(fact_477_min__max_OInf__fin_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1039 (all X_b (ab_semigroup_mult(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hAPP(fun(X_b,bool),X_b,hAPP(X_b,fun(fun(X_b,bool),X_b),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),X_b)),finite_fold(X_b,X_b),times_times(X_b)),A_2),A_3) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),times_times(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_3))))))) # label(fact_205_fold1__eq__fold) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1040 (all X_b (linorder(X_b) -> (all Pa all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))) -> ((all B_1 all A_4 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_4)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_4)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_1),X_2)))) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_4)) -> hBOOL(hAPP(fun(X_b,bool),bool,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),B_1),A_4))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,A_3)))))))) # label(fact_933_finite__linorder__min__induct) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1041 (all K_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(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_1))))) # label(fact_344_finite__Collect__le__nat) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1042 (all X_a (linorder(X_a) -> (all B all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_551_min__max_Ole__supI1) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1043 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_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)),A_3),B_2)))) # label(fact_855_psubset__imp__subset) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1044 (all M_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),M_1)),hAPP(nat,int,semiring_1_of_nat(int),N))))) # label(fact_862_zless__int) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1045 (all U all M_1 all N all J_1 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),I_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_1)),U)),M_1)),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_1),U)),N)))))) # label(fact_465_nat__le__add__iff1) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1046 (all M all N_1 all Z hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N_1))),Z) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)),Z))) # label(fact_668_zadd__int__left) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1047 (all X_a (cancel_semigroup_add(X_a) -> (all A_1 all B all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) -> ti(X_a,B) = ti(X_a,C))))) # label(fact_228_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption]. 2.29/2.50 1048 (all X_b (linordered_semidom(X_b) -> (all X_1 all Y_2 all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),one_one(X_b)),Ba)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),Ba),X_1)),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),Ba),Y_2))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_2))))))) # label(fact_885_power__strict__increasing__iff) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1049 (all X_c all X_b (ab_group_add(X_b) -> (all F all A_3 hAPP(X_b,X_b,uminus_uminus(X_b),hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),F),A_3)) = hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_c,X_b),fun(X_c,X_b),hAPP(fun(X_b,X_b),fun(fun(X_c,X_b),fun(X_c,X_b)),combb(X_b,X_b,X_c),uminus_uminus(X_b)),F)),A_3)))) # label(fact_510_setsum__negf) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1050 (all X_b all X_3 hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),fequal(fun(X_b,bool)),X_3)),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool))))) = hAPP(fun(X_b,bool),X_b,the_elem(X_b),X_3)) # label(fact_55_the__elem__def) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1051 (all X_b (linorder(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),ord_min(X_b)),A_3)),A_2))))))) # label(fact_389_min__max_Ofold1__belowI) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1052 (all X_b all Y_2 all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),A_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool))))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),bot_bot(fun(X_b,bool)))))),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))))))) # label(fact_679_card__Diff2__less) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1053 (all X_a (linorder(X_a) -> (all X all Y all Z hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z))))) # label(fact_350_min__max_Oinf__left__commute) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1054 (all X_b all X_c (ord(X_c) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) -> hBOOL(hAPP(X_c,bool,hAPP(X_c,fun(X_c,bool),ord_less_eq(X_c),hAPP(X_b,X_c,F,X_1)),hAPP(X_b,X_c,G,X_1))))))) # label(fact_266_le__funE) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1055 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ti(X_a,X) != ti(X_a,Y))))) # label(fact_785_less__imp__neq) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1056 (all X_a (preorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z))))))) # label(fact_773_order__less__trans) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1057 (all N_1 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N_1)),N_1) = M)) # label(fact_443_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1058 (all X_b (linorder(X_b) -> (all N_3 all H ((all X_2 all Y_1 hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_2),Y_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_1))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),N_3) -> hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),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),H),N_3)) = hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,big_linorder_Max(X_b),N_3)))))))) # label(fact_579_Max_Ohom__commute) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1059 (all X_a (semiring(X_a) -> times_times(X_a) = ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)))) # label(tsy_c_Groups_Otimes__class_Otimes_1_res) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1060 (all X_b all F all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2)) -> (hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co302546470etprod(X_b,nat),F),F_2) = one_one(nat) <-> (all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_2)) -> one_one(nat) = hAPP(X_b,nat,F,X_2)))))) # label(fact_633_setprod__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1061 (all N_1 N_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N_1)) # label(fact_626_nat__mult__1) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1062 (all X_a (ab_semigroup_mult(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))) # label(fact_243_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1063 (all X_a (comm_semiring_1(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1)))) # label(fact_631_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1064 (all X_b all X_1 all A_3 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),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_3)) = 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_3)) # label(fact_30_insert__absorb2) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1065 (all J_1 all K_1 all I_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),J_1),K_1)),I_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1))))) # label(fact_435_le__diff__conv) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1066 (all X_a (linorder(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_756_leD) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1067 (all X_a (ordere223160158up_add(X_a) -> (all C all D_1 all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D_1)))))))) # label(fact_820_add__less__le__mono) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1068 (all Z all W_2 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z),W_2) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),hAPP(int,int,uminus_uminus(int),W_2))) # label(fact_689_diff__int__def) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1069 (all X_b all A_2 all B_2 hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),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_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_2)) # label(fact_32_insert__compr) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1070 (all X_b all Q_3 all Pa all X_1 (hBOOL(hAPP(X_b,bool,Pa,X_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)),Pa),Q_3)) -> hBOOL(hAPP(X_b,bool,Q_3,X_1))))) # label(fact_291_rev__predicate1D) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1071 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_514_diff__def) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1072 (all X_b all A_3 all B_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less(fun(X_b,bool)),A_3),B_2)) -> (exists B_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_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),B_2),A_3)))))) # label(fact_913_psubset__imp__ex__mem) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1073 (all X_b (ordere236663937imp_le(X_b) -> (all A_2 all Ca all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),Ca)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),Ba),Ca))) <-> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),A_2),Ba)))))) # label(fact_731_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1074 (all Pa all I_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),Pa)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I_1)))))) # label(fact_814_finite__M__bounded__by__nat) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1075 (all X_b collect(X_b) = ti(fun(fun(X_b,bool),fun(X_b,bool)),collect(X_b))) # label(tsy_c_Set_OCollect_res) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1076 (all I_1 all J_1 all K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_1),K_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1)),J_1)))) # label(fact_825_less__diff__conv) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1077 (all X_b (linorder(X_b) -> (all A_2 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_2),A_3)) -> ti(X_b,A_2) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),A_2),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),A_3))))))) # label(fact_570_min__max_Osup__Inf__absorb) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1078 (all M all N_1 hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N_1)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),M)),N_1)) # label(fact_684_int__power) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1079 (all X_a (comm_semiring_1(X_a) -> (all Lx all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))))) # label(fact_245_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1080 (all X_c all X_b all F all Z_2 all X_1 (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F),Z_2),bot_bot(fun(X_b,bool))),X_1)) -> ti(X_c,X_1) = ti(X_c,Z_2))) # label(fact_106_empty__fold__graphE) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1081 (all X_a (comm_semiring(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))) # label(fact_250_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1082 (all X_b all X_c (ord(X_c) -> (all F all G (hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less(fun(X_b,X_c)),F),G)) <-> hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),F),G)) & -hBOOL(hAPP(fun(X_b,X_c),bool,hAPP(fun(X_b,X_c),fun(fun(X_b,X_c),bool),ord_less_eq(fun(X_b,X_c)),G),F)))))) # label(fact_851_less__fun__def) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1083 (all X_b (linorder(X_b) -> ti(fun(fun(X_b,bool),X_b),big_linorder_Max(X_b)) = big_linorder_Max(X_b))) # label(tsy_c_Big__Operators_Olinorder__class_OMax_res) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1084 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_984_mult__pos__pos) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1085 (all X_a (ab_group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))))) # label(fact_501_minus__add__distrib) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1086 (all X_b (linorder(X_b) -> (all N_3 all H ((all X_2 all Y_1 hAPP(X_b,X_b,H,hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),X_2),Y_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(X_b,X_b,H,X_2)),hAPP(X_b,X_b,H,Y_1))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),N_3)) -> (ti(fun(X_b,bool),N_3) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),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),H),N_3)) = hAPP(X_b,X_b,H,hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Sup_fin(X_b),ord_max(X_b)),N_3)))))))) # label(fact_606_min__max_OSup__fin_Ohom__commute) # label(axiom) # label(non_clause). [assumption]. 2.29/2.51 1087 (all X_b all X_c all A_3 all Ba all F all X_1 (ti(X_b,Ba) = 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_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),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_3)))))) # label(fact_64_image__eqI) # label(axiom) # label(non_clause). [assumption]. 2.37/2.58 1088 (all X_b (linorder(X_b) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> (bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(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_1),A_3)) = ti(X_b,X_1)) & (bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),X_1),hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(X_b)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),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),bot_bot(fun(X_b,bool)))))) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),big_Inf_fin(X_b),ord_min(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_1),A_3))))))) # label(fact_469_min__max_OInf__fin_Oinsert__remove) # label(axiom) # label(non_clause). [assumption]. 2.37/2.58 1089 (all X_b hBOOL(hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),bool,finite_comp_fun_idem(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_b),hAPP(fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool))),combc(fun(X_b,bool),fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)))),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool))))))) # label(fact_161_comp__fun__idem__remove) # label(axiom) # label(non_clause). [assumption]. 2.37/2.58 1090 (all X_a (linord893533164strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_994_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption]. 2.37/2.58 2.37/2.58 ============================== end of process non-clausal formulas === 2.37/2.58 2.37/2.58 ============================== PROCESS INITIAL CLAUSES =============== 2.37/2.58 2.37/2.58 ============================== PREDICATE ELIMINATION ================= 2.37/2.58 1091 -ab_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_233_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom). [clausify(430)]. 2.37/2.58 1092 ab_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__add) # label(axiom). [assumption]. 2.37/2.58 1093 ab_semigroup_add(int) # label(arity_Int_Oint___Groups_Oab__semigroup__add) # label(axiom). [assumption]. 2.37/2.58 1094 -ab_semigroup_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom). [clausify(758)]. 2.41/2.67 Derived: plus_plus(nat) = ti(fun(nat,fun(nat,nat)),plus_plus(nat)). [resolve(1094,a,1092,a)]. 2.41/2.67 Derived: plus_plus(int) = ti(fun(int,fun(int,int)),plus_plus(int)). [resolve(1094,a,1093,a)]. 2.41/2.67 1095 linorder(nat) # label(arity_Nat_Onat___Orderings_Olinorder) # label(axiom). [assumption]. 2.41/2.67 1096 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),B) # label(fact_536_Max_Oidem) # label(axiom). [clausify(2)]. 2.41/2.67 1097 -linorder(A) | ti(A,B) = hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),bot_bot(fun(A,bool)))) # label(fact_385_Min_Osingleton) # label(axiom). [clausify(7)]. 2.41/2.67 1098 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_751_leI) # label(axiom). [clausify(12)]. 2.41/2.67 1099 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_519_Max_Oinsert__remove) # label(axiom). [clausify(30)]. 2.41/2.67 1100 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) != hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | ti(A,C) = hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) # label(fact_519_Max_Oinsert__remove) # label(axiom). [clausify(30)]. 2.41/2.67 1101 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) # label(fact_538_min__max_Osup_Oassoc) # label(axiom). [clausify(31)]. 2.41/2.67 1102 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_349_min__max_Oinf_Oassoc) # label(axiom). [clausify(35)]. 2.41/2.67 1103 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)) # label(fact_539_min__max_Osup__left__commute) # label(axiom). [clausify(43)]. 2.41/2.67 1104 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B)),D)) # label(fact_390_fold1__below__iff) # label(axiom). [clausify(55)]. 2.41/2.67 1105 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f9(A,C,B)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B)),C)) # label(fact_390_fold1__below__iff) # label(axiom). [clausify(55)]. 2.41/2.67 1106 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f9(A,C,B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B)),C)) # label(fact_390_fold1__below__iff) # label(axiom). [clausify(55)]. 2.41/2.67 1107 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_840_strict__below__fold1__iff) # label(axiom). [clausify(58)]. 2.41/2.67 1108 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f11(A,C,B)),B)) # label(fact_840_strict__below__fold1__iff) # label(axiom). [clausify(58)]. 2.41/2.67 1109 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),f11(A,C,B))) # label(fact_840_strict__below__fold1__iff) # label(axiom). [clausify(58)]. 2.41/2.67 1110 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),C) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),A,big_linorder_Min(A),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(fun(A,bool),A,big_linorder_Min(A),C)),hAPP(fun(A,bool),A,big_linorder_Min(A),B)) # label(fact_376_Min_Osubset__idem) # label(axiom). [clausify(59)]. 2.41/2.67 1111 -linorder(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite_comp_fun_idem(A,A),ord_min(A))) # label(fact_373_min__max_Ocomp__fun__idem__inf) # label(axiom). [clausify(63)]. 2.41/2.67 1112 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),B) # label(fact_577_Max_Oeq__fold_H) # label(axiom). [clausify(71)]. 2.41/2.67 1113 -linorder(A) | ti(A,B) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),bot_bot(fun(A,bool)))) # label(fact_471_min__max_OInf__fin_Osingleton) # label(axiom). [clausify(73)]. 2.41/2.67 1114 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),B)) # label(fact_569_min__max_Ofold__sup__insert) # label(axiom). [clausify(76)]. 2.41/2.67 1115 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) # label(fact_361_min__max_Ole__infI) # label(axiom). [clausify(80)]. 2.41/2.67 1116 -linorder(A) | ord_max(A) = hAPP(fun(A,fun(A,bool)),fun(A,fun(A,A)),min(A),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),ord_less_eq(A))) # label(fact_573_dual__min) # label(axiom). [clausify(81)]. 2.41/2.67 1117 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) # label(fact_549_min__max_Ole__iff__sup) # label(axiom). [clausify(82)]. 2.41/2.67 1118 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) != hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) # label(fact_549_min__max_Ole__iff__sup) # label(axiom). [clausify(82)]. 2.41/2.67 1119 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_736_min__less__iff__disj) # label(axiom). [clausify(84)]. 2.41/2.67 1120 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_736_min__less__iff__disj) # label(axiom). [clausify(84)]. 2.41/2.67 1121 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_736_min__less__iff__disj) # label(axiom). [clausify(84)]. 2.41/2.67 1122 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_747_linorder__le__less__linear) # label(axiom). [clausify(96)]. 2.41/2.67 1123 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),B)),C)) # label(fact_357_min__le__iff__disj) # label(axiom). [clausify(99)]. 2.41/2.67 1124 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C)) # label(fact_357_min__le__iff__disj) # label(axiom). [clausify(99)]. 2.41/2.67 1125 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),B)),C)) # label(fact_357_min__le__iff__disj) # label(axiom). [clausify(99)]. 2.41/2.67 1126 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) # label(fact_758_linorder__antisym__conv2) # label(axiom). [clausify(101)]. 2.41/2.67 1127 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_758_linorder__antisym__conv2) # label(axiom). [clausify(101)]. 2.41/2.67 1128 -linorder(A) | ti(A,B) != ti(A,C) | hAPP(A,fun(A,bool),ord_greaterThan(A),B) = hAPP(A,fun(A,bool),ord_greaterThan(A),C) # label(fact_546_greaterThan__eq__iff) # label(axiom). [clausify(111)]. 2.41/2.67 1129 -linorder(A) | ti(A,B) = ti(A,C) | hAPP(A,fun(A,bool),ord_greaterThan(A),B) != hAPP(A,fun(A,bool),ord_greaterThan(A),C) # label(fact_546_greaterThan__eq__iff) # label(axiom). [clausify(111)]. 2.41/2.67 1130 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) # label(fact_533_min__max_Osup__inf__absorb) # label(axiom). [clausify(114)]. 2.41/2.67 1131 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,B,f23(A,C,B))),hAPP(A,A,B,f24(A,C,B))) != hAPP(A,A,B,hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f23(A,C,B)),f24(A,C,B))) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | ti(fun(A,bool),C) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),B),C)) = hAPP(A,A,B,hAPP(fun(A,bool),A,big_linorder_Min(A),C)) # label(fact_392_Min_Ohom__commute) # label(axiom). [clausify(117)]. 2.41/2.67 1132 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_348_min__max_Oinf__assoc) # label(axiom). [clausify(143)]. 2.41/2.67 1133 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) # label(fact_537_min__max_Osup__assoc) # label(axiom). [clausify(148)]. 2.41/2.67 1134 -linorder(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite_comp_fun_idem(A,A),ord_max(A))) # label(fact_560_min__max_Ocomp__fun__idem__sup) # label(axiom). [clausify(152)]. 2.41/2.67 1135 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,big_linorder_Min(A),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,big_linorder_Min(A),B)) # label(fact_346_Min_Oin__idem) # label(axiom). [clausify(154)]. 2.41/2.67 1136 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) # label(fact_532_min__max_Oinf__sup__absorb) # label(axiom). [clausify(171)]. 2.41/2.67 1137 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),B)),C)) # label(fact_734_min__max_Oless__infI2) # label(axiom). [clausify(172)]. 2.41/2.67 1138 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),B) # label(fact_347_Min_Oidem) # label(axiom). [clausify(176)]. 2.41/2.67 1139 -linorder(A) | big_Sup_fin(A) = ti(fun(fun(A,fun(A,A)),fun(fun(A,bool),A)),big_Sup_fin(A)) # label(tsy_c_Big__Operators_Olattice_OSup__fin_res) # label(axiom). [clausify(180)]. 2.41/2.67 1140 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_max(A)),B) # label(fact_596_min__max_OSup__fin_OF__eq) # label(axiom). [clausify(190)]. 2.41/2.67 1141 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) # label(fact_363_min__max_Oinf__absorb1) # label(axiom). [clausify(194)]. 2.41/2.67 1142 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C) # label(fact_529_min__max_Osup__inf__distrib2) # label(axiom). [clausify(203)]. 2.41/2.67 1143 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B) # label(fact_554_min__max_Osup__absorb1) # label(axiom). [clausify(211)]. 2.41/2.67 1144 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),B) # label(fact_356_min__max_Oinf_Oidem) # label(axiom). [clausify(216)]. 2.41/2.67 1145 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,big_linorder_Max(A),B) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_max(A)),B) # label(fact_572_Max_OF__eq) # label(axiom). [clausify(221)]. 2.41/2.67 1146 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),B),C)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,big_linorder_Min(A),C)),hAPP(fun(A,bool),A,big_linorder_Min(A),B))) # label(fact_341_Min__antimono) # label(axiom). [clausify(228)]. 2.41/2.67 1147 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),D),B))) # label(fact_567_min__max_Osup__le__fold__sup) # label(axiom). [clausify(231)]. 2.41/2.67 1148 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_552_min__max_Ole__supI2) # label(axiom). [clausify(236)]. 2.41/2.67 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),A). [resolve(1095,a,1096,a)]. 2.41/2.67 Derived: ti(nat,A) = hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),A),bot_bot(fun(nat,bool)))). [resolve(1095,a,1097,a)]. 2.41/2.68 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(1095,a,1098,a)]. 2.41/2.68 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))). [resolve(1095,a,1099,a)]. 2.41/2.68 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) != hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | ti(nat,B) = hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)). [resolve(1095,a,1100,a)]. 2.41/2.68 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)). [resolve(1095,a,1101,a)]. 2.41/2.68 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)). [resolve(1095,a,1102,a)]. 2.41/2.68 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)). [resolve(1095,a,1103,a)]. 2.41/2.68 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A)),C)). [resolve(1095,a,1104,a)]. 2.41/2.68 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f9(nat,B,A)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A)),B)). [resolve(1095,a,1105,a)]. 2.41/2.68 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f9(nat,B,A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A)),B)). [resolve(1095,a,1106,a)]. 2.41/2.68 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A))) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),C),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(1095,a,1107,a)]. 2.41/2.68 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A))) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f11(nat,B,A)),A)). [resolve(1095,a,1108,a)]. 2.41/2.68 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),f11(nat,B,A))). [resolve(1095,a,1109,a)]. 2.41/2.68 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),B) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),B),A)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),B)),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A)). [resolve(1095,a,1110,a)]. 2.41/2.68 Derived: hBOOL(hAPP(fun(nat,fun(nat,nat)),bool,finite_comp_fun_idem(nat,nat),ord_min(nat))). [resolve(1095,a,1111,a)]. 2.41/2.68 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_max(nat)),B),A). [resolve(1095,a,1112,a)]. 2.41/2.68 Derived: ti(nat,A) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),A),bot_bot(fun(nat,bool)))). [resolve(1095,a,1113,a)]. 2.41/2.68 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_max(nat)),B),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),C),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_max(nat)),B),A)). [resolve(1095,a,1114,a)]. 2.41/2.68 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))). [resolve(1095,a,1115,a)]. 2.41/2.68 Derived: ord_max(nat) = hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,nat)),min(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat))). [resolve(1095,a,1116,a)]. 2.41/2.68 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B). [resolve(1095,a,1117,a)]. 2.41/2.68 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B). [resolve(1095,a,1118,a)]. 2.41/2.68 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(1095,a,1119,a)]. 2.41/2.68 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(1095,a,1120,a)]. 2.41/2.68 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(1095,a,1121,a)]. 2.41/2.68 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),C),A)),B)). [resolve(1095,a,1123,a)]. 2.41/2.68 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),B)). [resolve(1095,a,1124,a)]. 2.41/2.68 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),C),A)),B)). [resolve(1095,a,1125,a)]. 2.41/2.68 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) = ti(nat,A). [resolve(1095,a,1126,a)]. 2.41/2.68 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) != ti(nat,A). [resolve(1095,a,1127,a)]. 2.41/2.68 Derived: ti(nat,A) != ti(nat,B) | hAPP(nat,fun(nat,bool),ord_greaterThan(nat),A) = hAPP(nat,fun(nat,bool),ord_greaterThan(nat),B). [resolve(1095,a,1128,a)]. 2.41/2.68 Derived: ti(nat,A) = ti(nat,B) | hAPP(nat,fun(nat,bool),ord_greaterThan(nat),A) != hAPP(nat,fun(nat,bool),ord_greaterThan(nat),B). [resolve(1095,a,1129,a)]. 2.41/2.68 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)). [resolve(1095,a,1130,a)]. 2.41/2.68 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,A,f23(nat,B,A))),hAPP(nat,nat,A,f24(nat,B,A))) != hAPP(nat,nat,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),f23(nat,B,A)),f24(nat,B,A))) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | ti(fun(nat,bool),B) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),A),B)) = hAPP(nat,nat,A,hAPP(fun(nat,bool),nat,big_linorder_Min(nat),B)). [resolve(1095,a,1131,a)]. 2.41/2.68 Derived: hBOOL(hAPP(fun(nat,fun(nat,nat)),bool,finite_comp_fun_idem(nat,nat),ord_max(nat))). [resolve(1095,a,1134,a)]. 2.41/2.68 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A)). [resolve(1095,a,1135,a)]. 2.41/2.68 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)). [resolve(1095,a,1136,a)]. 2.41/2.68 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),A). [resolve(1095,a,1138,a)]. 2.41/2.68 Derived: big_Sup_fin(nat) = ti(fun(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat)),big_Sup_fin(nat)). [resolve(1095,a,1139,a)]. 2.41/2.68 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_max(nat)),A). [resolve(1095,a,1140,a)]. 2.41/2.68 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B). [resolve(1095,a,1141,a)]. 2.41/2.68 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),B). [resolve(1095,a,1142,a)]. 2.41/2.68 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),A). [resolve(1095,a,1143,a)]. 2.41/2.69 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_max(nat)),A). [resolve(1095,a,1145,a)]. 2.41/2.69 Derived: -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A),B)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),B)),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A))). [resolve(1095,a,1146,a)]. 2.41/2.69 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_max(nat)),C),A))). [resolve(1095,a,1147,a)]. 2.41/2.69 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B))). [resolve(1095,a,1148,a)]. 2.41/2.69 1149 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)) # label(fact_540_min__max_Osup_Oleft__commute) # label(axiom). [clausify(259)]. 2.41/2.69 1150 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,B,f52(A,C,B))),hAPP(A,A,B,f53(A,C,B))) != hAPP(A,A,B,hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f52(A,C,B)),f53(A,C,B))) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | ti(fun(A,bool),C) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),B),C)) = hAPP(A,A,B,hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),C)) # label(fact_478_min__max_OInf__fin_Ohom__commute) # label(axiom). [clausify(262)]. 2.41/2.69 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,A,f52(nat,B,A))),hAPP(nat,nat,A,f53(nat,B,A))) != hAPP(nat,nat,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),f52(nat,B,A)),f53(nat,B,A))) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | ti(fun(nat,bool),B) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),A),B)) = hAPP(nat,nat,A,hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),B)). [resolve(1150,a,1095,a)]. 2.41/2.69 1151 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C))) # label(fact_547_le__maxI1) # label(axiom). [clausify(276)]. 2.41/2.69 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B))). [resolve(1151,a,1095,a)]. 2.41/2.69 1152 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_752_not__leE) # label(axiom). [clausify(285)]. 2.41/2.69 1153 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)))) # label(fact_562_min__max_Odistrib__sup__le) # label(axiom). [clausify(288)]. 2.41/2.69 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)))). [resolve(1153,a,1095,a)]. 2.41/2.69 1154 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_770_linorder__cases) # label(axiom). [clausify(291)]. 2.41/2.69 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) = ti(nat,A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). [resolve(1154,a,1095,a)]. 2.41/2.69 1155 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)) # label(fact_470_min__max_OInf__fin_Oin__idem) # label(axiom). [clausify(292)]. 2.41/2.69 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)). [resolve(1155,a,1095,a)]. 2.41/2.69 1156 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | bot_bot(fun(A,bool)) = hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | hAPP(fun(A,bool),A,big_linorder_Min(A),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_380_Min_Oremove) # label(axiom). [clausify(298)]. 2.41/2.69 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | bot_bot(fun(nat,bool)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))). [resolve(1156,a,1095,a)]. 2.41/2.69 1157 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | bot_bot(fun(A,bool)) != hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | ti(A,C) = hAPP(fun(A,bool),A,big_linorder_Min(A),B) # label(fact_380_Min_Oremove) # label(axiom). [clausify(298)]. 2.41/2.69 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | bot_bot(fun(nat,bool)) != hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | ti(nat,B) = hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A). [resolve(1157,a,1095,a)]. 2.41/2.69 1158 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_531_min__max_Osup__inf__distrib1) # label(axiom). [clausify(305)]. 2.41/2.69 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)). [resolve(1158,a,1095,a)]. 2.41/2.69 1159 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),B)),C)) # label(fact_364_min__max_Ole__infI2) # label(axiom). [clausify(306)]. 2.41/2.69 1160 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_528_min__max_Oinf__sup__distrib2) # label(axiom). [clausify(327)]. 2.41/2.69 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)). [resolve(1160,a,1095,a)]. 2.41/2.69 1161 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),C)) # label(fact_368_min__max_Oinf__le2) # label(axiom). [clausify(328)]. 2.41/2.69 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),B)). [resolve(1161,a,1095,a)]. 2.41/2.69 1162 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,fun(A,bool)),fun(A,bool),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A)),hAPP(fun(A,bool),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,bool),fun(A,fun(A,bool))),combc(A,fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool))),hAPP(fun(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),A),combs(A,bool,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool))),hAPP(fun(fun(A,bool),fun(A,fun(bool,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),combb(fun(A,bool),fun(A,fun(bool,bool)),A),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj)),hAPP(fun(A,A),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,A),fun(A,bool))),fun(fun(A,A),fun(A,fun(A,bool))),combc(A,fun(A,A),fun(A,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool))),hAPP(fun(fun(A,bool),fun(fun(A,A),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool)))),combb(fun(A,bool),fun(fun(A,A),fun(A,bool)),A),combb(A,bool,A)),fequal(A))),hAPP(A,fun(A,A),ord_max(A),C))))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))))) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)) # label(fact_588_min__max_Osup__Inf1__distrib) # label(axiom). [clausify(346)]. 2.41/2.69 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,bool),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat)),hAPP(fun(nat,bool),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(nat,fun(nat,bool))),combc(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combc(nat,fun(nat,nat),fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool))),hAPP(fun(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool)))),combb(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool)),nat),combb(nat,bool,nat)),fequal(nat))),hAPP(nat,fun(nat,nat),ord_max(nat),B))))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),A))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)). [resolve(1162,a,1095,a)]. 2.41/2.70 1163 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),D),B)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) # label(fact_387_min__max_Ofold__inf__le__inf) # label(axiom). [clausify(352)]. 2.41/2.70 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_min(nat)),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))). [resolve(1163,a,1095,a)]. 2.41/2.70 1164 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_366_min__max_Ole__inf__iff) # label(axiom). [clausify(357)]. 2.41/2.70 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1164,a,1095,a)]. 2.41/2.70 1165 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_366_min__max_Ole__inf__iff) # label(axiom). [clausify(357)]. 2.41/2.70 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1165,a,1095,a)]. 2.41/2.70 1166 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_366_min__max_Ole__inf__iff) # label(axiom). [clausify(357)]. 2.41/2.70 1167 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B) # label(fact_472_min__max_OInf__fin_OF__eq) # label(axiom). [clausify(358)]. 2.41/2.70 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A). [resolve(1167,a,1095,a)]. 2.41/2.70 1168 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C)) # label(fact_365_min__max_Ole__infI1) # label(axiom). [clausify(361)]. 2.41/2.70 1169 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,big_linorder_Min(A),B) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B) # label(fact_372_Min_OF__eq) # label(axiom). [clausify(364)]. 2.41/2.70 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A). [resolve(1169,a,1095,a)]. 2.41/2.70 1170 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) # label(fact_541_min__max_Osup__left__idem) # label(axiom). [clausify(366)]. 2.41/2.70 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B). [resolve(1170,a,1095,a)]. 2.41/2.70 1171 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) # label(fact_711_less__max__iff__disj) # label(axiom). [clausify(370)]. 2.41/2.70 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))). [resolve(1171,a,1095,a)]. 2.41/2.70 1172 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_711_less__max__iff__disj) # label(axiom). [clausify(370)]. 2.41/2.70 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B))). [resolve(1172,a,1095,a)]. 2.41/2.70 1173 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) # label(fact_711_less__max__iff__disj) # label(axiom). [clausify(370)]. 2.41/2.70 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))). [resolve(1173,a,1095,a)]. 2.41/2.70 1174 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) != hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | ti(A,C) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) # label(fact_605_min__max_OSup__fin_Oinsert__remove) # label(axiom). [clausify(381)]. 2.41/2.70 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) != hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | ti(nat,B) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)). [resolve(1174,a,1095,a)]. 2.41/2.70 1175 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_605_min__max_OSup__fin_Oinsert__remove) # label(axiom). [clausify(381)]. 2.41/2.70 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))). [resolve(1175,a,1095,a)]. 2.41/2.70 1176 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),B) # label(fact_578_Max_Oeq__fold__idem_H) # label(axiom). [clausify(388)]. 2.41/2.70 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_max(nat)),B),A). [resolve(1176,a,1095,a)]. 2.41/2.70 1177 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_745_linorder__not__less) # label(axiom). [clausify(395)]. 2.41/2.70 1178 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_745_linorder__not__less) # label(axiom). [clausify(395)]. 2.41/2.70 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(1178,a,1095,a)]. 2.41/2.70 1179 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f70(A,B)),f71(A,B))),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f70(A,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f71(A,B)),bot_bot(fun(A,bool)))))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B)),B)) # label(fact_607_min__max_OSup__fin_Oclosed) # label(axiom). [clausify(397)]. 2.41/2.70 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),f70(nat,A)),f71(nat,A))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f70(nat,A)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f71(nat,A)),bot_bot(fun(nat,bool)))))) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A)),A)). [resolve(1179,a,1095,a)]. 2.41/2.70 1180 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_753_linorder__antisym__conv1) # label(axiom). [clausify(407)]. 2.41/2.70 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) != ti(nat,A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1180,a,1095,a)]. 2.41/2.70 1181 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_753_linorder__antisym__conv1) # label(axiom). [clausify(407)]. 2.41/2.70 1182 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_358_min__max_Ole__infE) # label(axiom). [clausify(408)]. 2.41/2.70 1183 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_358_min__max_Ole__infE) # label(axiom). [clausify(408)]. 2.41/2.70 1184 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_391_min__max_Obelow__fold1__iff) # label(axiom). [clausify(423)]. 2.41/2.70 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A))) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),C),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1184,a,1095,a)]. 2.41/2.70 1185 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f81(A,C,B)),B)) # label(fact_391_min__max_Obelow__fold1__iff) # label(axiom). [clausify(423)]. 2.41/2.70 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A))) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f81(nat,B,A)),A)). [resolve(1185,a,1095,a)]. 2.41/2.70 1186 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),f81(A,C,B))) # label(fact_391_min__max_Obelow__fold1__iff) # label(axiom). [clausify(423)]. 2.41/2.70 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f81(nat,B,A))). [resolve(1186,a,1095,a)]. 2.41/2.71 1187 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) != hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | ti(A,C) = hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) # label(fact_379_Min_Oinsert__remove) # label(axiom). [clausify(424)]. 2.41/2.71 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) != hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | ti(nat,B) = hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)). [resolve(1187,a,1095,a)]. 2.41/2.71 1188 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_379_Min_Oinsert__remove) # label(axiom). [clausify(424)]. 2.41/2.71 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))). [resolve(1188,a,1095,a)]. 2.41/2.71 1189 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | ti(fun(A,bool),C) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,fun(A,bool)),fun(A,bool),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A)),hAPP(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,bool)),hAPP(fun(fun(A,fun(A,bool)),fun(A,bool)),fun(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,bool))),combb(fun(A,fun(A,bool)),fun(A,bool),A),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A))),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,fun(A,bool))),hAPP(fun(A,fun(fun(A,fun(A,bool)),fun(A,fun(A,bool)))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(A,bool)))),combc(A,fun(A,fun(A,bool)),fun(A,fun(A,bool))),hAPP(fun(A,fun(A,fun(fun(A,bool),fun(A,bool)))),fun(A,fun(fun(A,fun(A,bool)),fun(A,fun(A,bool)))),hAPP(fun(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,bool)))),fun(fun(A,fun(A,fun(fun(A,bool),fun(A,bool)))),fun(A,fun(fun(A,fun(A,bool)),fun(A,fun(A,bool))))),combb(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,bool))),A),combs(A,fun(A,bool),fun(A,bool))),hAPP(fun(A,fun(A,fun(A,fun(bool,bool)))),fun(A,fun(A,fun(fun(A,bool),fun(A,bool)))),hAPP(fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),fun(fun(A,fun(A,fun(A,fun(bool,bool)))),fun(A,fun(A,fun(fun(A,bool),fun(A,bool))))),combb(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool))),A),hAPP(fun(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),A),combs(A,bool,bool))),hAPP(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,fun(A,fun(bool,bool)))),hAPP(fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),fun(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,fun(A,fun(bool,bool))))),combb(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool))),A),hAPP(fun(fun(A,bool),fun(A,fun(bool,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),combb(fun(A,bool),fun(A,fun(bool,bool)),A),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj))),hAPP(fun(A,fun(A,A)),fun(A,fun(A,fun(A,bool))),hAPP(fun(A,fun(fun(A,fun(A,A)),fun(A,fun(A,bool)))),fun(fun(A,fun(A,A)),fun(A,fun(A,fun(A,bool)))),combc(A,fun(A,fun(A,A)),fun(A,fun(A,bool))),hAPP(fun(A,fun(fun(A,A),fun(A,bool))),fun(A,fun(fun(A,fun(A,A)),fun(A,fun(A,bool)))),hAPP(fun(fun(fun(A,A),fun(A,bool)),fun(fun(A,fun(A,A)),fun(A,fun(A,bool)))),fun(fun(A,fun(fun(A,A),fun(A,bool))),fun(A,fun(fun(A,fun(A,A)),fun(A,fun(A,bool))))),combb(fun(fun(A,A),fun(A,bool)),fun(fun(A,fun(A,A)),fun(A,fun(A,bool))),A),combb(fun(A,A),fun(A,bool),A)),hAPP(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool))),hAPP(fun(fun(A,bool),fun(fun(A,A),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool)))),combb(fun(A,bool),fun(fun(A,A),fun(A,bool)),A),combb(A,bool,A)),fequal(A)))),ord_min(A)))))),hAPP(fun(A,bool),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,bool),fun(A,fun(A,bool))),combc(A,fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(bool,bool)),fun(A,fun(fun(A,bool),fun(A,bool))),hAPP(fun(fun(bool,bool),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(bool,bool)),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(bool,bool),fun(fun(A,bool),fun(A,bool)),A),combb(bool,bool,A)),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),C))))))) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B)),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),C)) # label(fact_592_min__max_Oinf__Sup2__distrib) # label(axiom). [clausify(432)]. 2.41/2.71 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | ti(fun(nat,bool),B) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,bool),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,bool)),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,bool)),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,bool))),combb(fun(nat,fun(nat,bool)),fun(nat,bool),nat),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat))),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(nat,bool)))),combc(nat,fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool)))),fun(nat,fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)))),hAPP(fun(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool)))),fun(nat,fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))))),combb(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),nat),combs(nat,fun(nat,bool),fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,fun(bool,bool)))),fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool)))),hAPP(fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,fun(nat,fun(nat,fun(bool,bool)))),fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),nat),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,fun(bool,bool)))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,fun(bool,bool))))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),nat),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combc(nat,fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(nat,fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool)))),hAPP(fun(fun(fun(nat,nat),fun(nat,bool)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(nat,fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool))))),combb(fun(fun(nat,nat),fun(nat,bool)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool))),nat),combb(fun(nat,nat),fun(nat,bool),nat)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool))),hAPP(fun(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool)))),combb(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool)),nat),combb(nat,bool,nat)),fequal(nat)))),ord_min(nat)))))),hAPP(fun(nat,bool),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(nat,fun(nat,bool))),combc(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(bool,bool)),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(bool,bool)),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),nat),combb(bool,bool,nat)),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),A)))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),B))))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),B)). [resolve(1189,a,1095,a)]. 2.41/2.71 1190 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_789_not__less__iff__gr__or__eq) # label(axiom). [clausify(442)]. 2.52/2.71 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). [resolve(1190,a,1095,a)]. 2.52/2.71 1191 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_789_not__less__iff__gr__or__eq) # label(axiom). [clausify(442)]. 2.52/2.71 Derived: ti(nat,A) != ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). [resolve(1191,a,1095,a)]. 2.52/2.71 1192 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_789_not__less__iff__gr__or__eq) # label(axiom). [clausify(442)]. 2.52/2.71 1193 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)) # label(fact_530_min__max_Oinf__sup__distrib1) # label(axiom). [clausify(452)]. 2.52/2.71 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)). [resolve(1193,a,1095,a)]. 2.52/2.71 1194 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(fun(A,bool),A,big_linorder_Max(A),B))) # label(fact_381_Max__ge) # label(axiom). [clausify(456)]. 2.52/2.71 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A))). [resolve(1194,a,1095,a)]. 2.52/2.71 1195 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,big_linorder_Min(A),B)),B)) # label(fact_384_Min__in) # label(axiom). [clausify(485)]. 2.52/2.71 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A)),A)). [resolve(1195,a,1095,a)]. 2.52/2.71 1196 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),B) # label(fact_362_min__max_Oinf__absorb2) # label(axiom). [clausify(494)]. 2.52/2.71 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),A). [resolve(1196,a,1095,a)]. 2.52/2.71 1197 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) # label(fact_553_min__max_Osup__absorb2) # label(axiom). [clausify(497)]. 2.52/2.71 1198 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B)),D)) # label(fact_839_fold1__strict__below__iff) # label(axiom). [clausify(510)]. 2.52/2.71 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A)),C)). [resolve(1198,a,1095,a)]. 2.52/2.71 1199 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f90(A,C,B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B)),C)) # label(fact_839_fold1__strict__below__iff) # label(axiom). [clausify(510)]. 2.52/2.72 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f90(nat,B,A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A)),B)). [resolve(1199,a,1095,a)]. 2.52/2.72 1200 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f90(A,C,B)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B)),C)) # label(fact_839_fold1__strict__below__iff) # label(axiom). [clausify(510)]. 2.52/2.72 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f90(nat,B,A)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A)),B)). [resolve(1200,a,1095,a)]. 2.52/2.72 1201 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f91(A,B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_919_pinf_I8_J) # label(axiom). [clausify(511)]. 2.52/2.72 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f91(nat,A)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1201,a,1095,a)]. 2.52/2.72 1202 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B)) # label(fact_595_min__max_Oinf__Sup__absorb) # label(axiom). [clausify(512)]. 2.52/2.72 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | ti(nat,B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A)). [resolve(1202,a,1095,a)]. 2.52/2.72 1203 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_790_linorder__neq__iff) # label(axiom). [clausify(528)]. 2.52/2.72 1204 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,B) != ti(A,C) # label(fact_790_linorder__neq__iff) # label(axiom). [clausify(528)]. 2.52/2.72 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,A) != ti(nat,B). [resolve(1204,a,1095,a)]. 2.52/2.72 1205 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | ti(A,C) = ti(A,B) # label(fact_790_linorder__neq__iff) # label(axiom). [clausify(528)]. 2.52/2.72 1206 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),f93(A,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_922_minf_I6_J) # label(axiom). [clausify(538)]. 2.52/2.72 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),f93(nat,B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1206,a,1095,a)]. 2.52/2.72 1207 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,big_linorder_Min(A),B)) # label(fact_375_Min_Oinsert) # label(axiom). [clausify(541)]. 2.52/2.72 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A)). [resolve(1207,a,1095,a)]. 2.52/2.72 1208 -linorder(A) | ti(A,B) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),bot_bot(fun(A,bool)))) # label(fact_594_min__max_OSup__fin_Osingleton) # label(axiom). [clausify(543)]. 2.52/2.72 Derived: ti(nat,A) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),A),bot_bot(fun(nat,bool)))). [resolve(1208,a,1095,a)]. 2.52/2.72 1209 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)) # label(fact_473_min__max_OInf__fin_Oinsert__idem) # label(axiom). [clausify(546)]. 2.52/2.72 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)). [resolve(1209,a,1095,a)]. 2.52/2.72 1210 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_550_min__max_Ole__sup__iff) # label(axiom). [clausify(553)]. 2.52/2.72 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1210,a,1095,a)]. 2.52/2.72 1211 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_550_min__max_Ole__sup__iff) # label(axiom). [clausify(553)]. 2.52/2.72 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1211,a,1095,a)]. 2.52/2.72 1212 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_550_min__max_Ole__sup__iff) # label(axiom). [clausify(553)]. 2.52/2.72 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1212,a,1095,a)]. 2.52/2.72 1213 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_735_min__less__iff__conj) # label(axiom). [clausify(554)]. 2.52/2.72 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1213,a,1095,a)]. 2.52/2.72 1214 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_735_min__less__iff__conj) # label(axiom). [clausify(554)]. 2.52/2.72 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(1214,a,1095,a)]. 2.52/2.72 1215 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_735_min__less__iff__conj) # label(axiom). [clausify(554)]. 2.52/2.72 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(1215,a,1095,a)]. 2.52/2.72 1216 -linorder(A) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -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,finite_finite_1(A),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),C)),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B))) # label(fact_338_fold1__antimono) # label(axiom). [clausify(563)]. 2.52/2.72 Derived: ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A),B)) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),B)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A))). [resolve(1216,a,1095,a)]. 2.52/2.72 1217 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B) # label(fact_544_min__max_Osup_Ocommute) # label(axiom). [clausify(569)]. 2.52/2.72 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),A). [resolve(1217,a,1095,a)]. 2.52/2.72 1218 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),C),B)) # label(fact_388_min__max_Ofold__inf__insert) # label(axiom). [clausify(572)]. 2.52/2.72 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_min(nat)),B),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),C),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),C),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_min(nat)),B),A)). [resolve(1218,a,1095,a)]. 2.52/2.72 1219 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)) # label(fact_351_min__max_Oinf_Oleft__commute) # label(axiom). [clausify(580)]. 2.52/2.72 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)). [resolve(1219,a,1095,a)]. 2.52/2.73 1220 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),C) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),A,big_linorder_Max(A),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(fun(A,bool),A,big_linorder_Max(A),C)),hAPP(fun(A,bool),A,big_linorder_Max(A),B)) # label(fact_576_Max_Osubset__idem) # label(axiom). [clausify(583)]. 2.52/2.73 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),B) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),B),A)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),B)),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A)). [resolve(1220,a,1095,a)]. 2.52/2.73 1221 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | ti(fun(A,bool),C) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,fun(A,bool)),fun(A,bool),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A)),hAPP(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,bool)),hAPP(fun(fun(A,fun(A,bool)),fun(A,bool)),fun(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,bool))),combb(fun(A,fun(A,bool)),fun(A,bool),A),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A))),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,fun(A,bool))),hAPP(fun(A,fun(fun(A,fun(A,bool)),fun(A,fun(A,bool)))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(A,bool)))),combc(A,fun(A,fun(A,bool)),fun(A,fun(A,bool))),hAPP(fun(A,fun(A,fun(fun(A,bool),fun(A,bool)))),fun(A,fun(fun(A,fun(A,bool)),fun(A,fun(A,bool)))),hAPP(fun(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,bool)))),fun(fun(A,fun(A,fun(fun(A,bool),fun(A,bool)))),fun(A,fun(fun(A,fun(A,bool)),fun(A,fun(A,bool))))),combb(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,bool))),A),combs(A,fun(A,bool),fun(A,bool))),hAPP(fun(A,fun(A,fun(A,fun(bool,bool)))),fun(A,fun(A,fun(fun(A,bool),fun(A,bool)))),hAPP(fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),fun(fun(A,fun(A,fun(A,fun(bool,bool)))),fun(A,fun(A,fun(fun(A,bool),fun(A,bool))))),combb(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool))),A),hAPP(fun(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),A),combs(A,bool,bool))),hAPP(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,fun(A,fun(bool,bool)))),hAPP(fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),fun(fun(A,fun(A,fun(A,bool))),fun(A,fun(A,fun(A,fun(bool,bool))))),combb(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool))),A),hAPP(fun(fun(A,bool),fun(A,fun(bool,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),combb(fun(A,bool),fun(A,fun(bool,bool)),A),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj))),hAPP(fun(A,fun(A,A)),fun(A,fun(A,fun(A,bool))),hAPP(fun(A,fun(fun(A,fun(A,A)),fun(A,fun(A,bool)))),fun(fun(A,fun(A,A)),fun(A,fun(A,fun(A,bool)))),combc(A,fun(A,fun(A,A)),fun(A,fun(A,bool))),hAPP(fun(A,fun(fun(A,A),fun(A,bool))),fun(A,fun(fun(A,fun(A,A)),fun(A,fun(A,bool)))),hAPP(fun(fun(fun(A,A),fun(A,bool)),fun(fun(A,fun(A,A)),fun(A,fun(A,bool)))),fun(fun(A,fun(fun(A,A),fun(A,bool))),fun(A,fun(fun(A,fun(A,A)),fun(A,fun(A,bool))))),combb(fun(fun(A,A),fun(A,bool)),fun(fun(A,fun(A,A)),fun(A,fun(A,bool))),A),combb(fun(A,A),fun(A,bool),A)),hAPP(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool))),hAPP(fun(fun(A,bool),fun(fun(A,A),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool)))),combb(fun(A,bool),fun(fun(A,A),fun(A,bool)),A),combb(A,bool,A)),fequal(A)))),ord_max(A)))))),hAPP(fun(A,bool),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,bool),fun(A,fun(A,bool))),combc(A,fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(bool,bool)),fun(A,fun(fun(A,bool),fun(A,bool))),hAPP(fun(fun(bool,bool),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(bool,bool)),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(bool,bool),fun(fun(A,bool),fun(A,bool)),A),combb(bool,bool,A)),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),C))))))) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),C)) # label(fact_587_min__max_Osup__Inf2__distrib) # label(axiom). [clausify(594)]. 2.52/2.73 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | ti(fun(nat,bool),B) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,bool),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,bool)),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,bool)),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,bool))),combb(fun(nat,fun(nat,bool)),fun(nat,bool),nat),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat))),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(nat,bool)))),combc(nat,fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool)))),fun(nat,fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)))),hAPP(fun(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool)))),fun(nat,fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))))),combb(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),nat),combs(nat,fun(nat,bool),fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,fun(bool,bool)))),fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool)))),hAPP(fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),fun(fun(nat,fun(nat,fun(nat,fun(bool,bool)))),fun(nat,fun(nat,fun(fun(nat,bool),fun(nat,bool))))),combb(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),nat),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,fun(bool,bool)))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,fun(bool,bool))))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),nat),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combc(nat,fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(nat,fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool)))),hAPP(fun(fun(fun(nat,nat),fun(nat,bool)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool)))),fun(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(nat,fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool))))),combb(fun(fun(nat,nat),fun(nat,bool)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,bool))),nat),combb(fun(nat,nat),fun(nat,bool),nat)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool))),hAPP(fun(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool)))),combb(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool)),nat),combb(nat,bool,nat)),fequal(nat)))),ord_max(nat)))))),hAPP(fun(nat,bool),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(nat,fun(nat,bool))),combc(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(bool,bool)),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(bool,bool)),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),nat),combb(bool,bool,nat)),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),A)))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),B))))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),B)). [resolve(1221,a,1095,a)]. 2.52/2.73 1222 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),E))) # label(fact_557_min__max_Osup__mono) # label(axiom). [clausify(595)]. 2.52/2.73 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),D))). [resolve(1222,a,1095,a)]. 2.52/2.73 1223 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B))) # label(fact_548_le__maxI2) # label(axiom). [clausify(600)]. 2.52/2.73 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),A))). [resolve(1223,a,1095,a)]. 2.52/2.73 1224 -linorder(A) | ord_min(A) = hAPP(fun(A,fun(A,bool)),fun(A,fun(A,A)),max(A),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),ord_less_eq(A))) # label(fact_397_dual__max) # label(axiom). [clausify(608)]. 2.52/2.73 Derived: ord_min(nat) = hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,nat)),max(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat))). [resolve(1224,a,1095,a)]. 2.52/2.73 1225 -linorder(A) | big_linorder_Min(A) = ti(fun(fun(A,bool),A),big_linorder_Min(A)) # label(tsy_c_Big__Operators_Olinorder__class_OMin_res) # label(axiom). [clausify(610)]. 2.52/2.73 Derived: big_linorder_Min(nat) = ti(fun(fun(nat,bool),nat),big_linorder_Min(nat)). [resolve(1225,a,1095,a)]. 2.52/2.73 1226 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,fun(A,bool)),fun(A,bool),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A)),hAPP(fun(A,bool),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,bool),fun(A,fun(A,bool))),combc(A,fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool))),hAPP(fun(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),A),combs(A,bool,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool))),hAPP(fun(fun(A,bool),fun(A,fun(bool,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),combb(fun(A,bool),fun(A,fun(bool,bool)),A),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj)),hAPP(fun(A,A),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,A),fun(A,bool))),fun(fun(A,A),fun(A,fun(A,bool))),combc(A,fun(A,A),fun(A,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool))),hAPP(fun(fun(A,bool),fun(fun(A,A),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool)))),combb(fun(A,bool),fun(fun(A,A),fun(A,bool)),A),combb(A,bool,A)),fequal(A))),hAPP(A,fun(A,A),ord_min(A),C))))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))))) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B)) # label(fact_591_min__max_Oinf__Sup1__distrib) # label(axiom). [clausify(611)]. 2.52/2.73 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,bool),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat)),hAPP(fun(nat,bool),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(nat,fun(nat,bool))),combc(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combc(nat,fun(nat,nat),fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool))),hAPP(fun(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool)))),combb(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool)),nat),combb(nat,bool,nat)),fequal(nat))),hAPP(nat,fun(nat,nat),ord_min(nat),B))))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),A))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A)). [resolve(1226,a,1095,a)]. 2.52/2.73 1227 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),B) # label(fact_355_min__max_Oinf_Ocommute) # label(axiom). [clausify(625)]. 2.52/2.73 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),A). [resolve(1227,a,1095,a)]. 2.52/2.73 1228 -linorder(A) | ti(A,B) != hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_367_min__max_Ole__iff__inf) # label(axiom). [clausify(637)]. 2.52/2.73 Derived: ti(nat,A) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1228,a,1095,a)]. 2.52/2.74 1229 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_367_min__max_Ole__iff__inf) # label(axiom). [clausify(637)]. 2.52/2.74 1230 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)) # label(fact_474_min__max_OInf__fin_Oinsert) # label(axiom). [clausify(645)]. 2.52/2.74 1231 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B) # label(fact_543_min__max_Osup__commute) # label(axiom). [clausify(660)]. 2.52/2.74 1232 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) # label(fact_353_min__max_Oinf_Oleft__idem) # label(axiom). [clausify(664)]. 2.52/2.74 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B). [resolve(1232,a,1095,a)]. 2.52/2.74 1233 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),C) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),C)),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)) # label(fact_475_min__max_OInf__fin_Osubset__idem) # label(axiom). [clausify(668)]. 2.52/2.74 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),B) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),B),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),B)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)). [resolve(1233,a,1095,a)]. 2.52/2.74 1234 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,big_linorder_Max(A),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,big_linorder_Max(A),B)) # label(fact_566_Max_Oin__idem) # label(axiom). [clausify(682)]. 2.52/2.74 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A)). [resolve(1234,a,1095,a)]. 2.52/2.74 1235 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,big_linorder_Min(A),B)) # label(fact_374_Min__insert) # label(axiom). [clausify(687)]. 2.52/2.74 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A)). [resolve(1235,a,1095,a)]. 2.52/2.74 1236 -linorder(A) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_786_linorder__neqE) # label(axiom). [clausify(697)]. 2.52/2.74 1237 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) # label(fact_352_min__max_Oinf__left__idem) # label(axiom). [clausify(698)]. 2.52/2.74 1238 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),B)),C)) # label(fact_710_max__less__iff__conj) # label(axiom). [clausify(700)]. 2.52/2.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),A)),B)). [resolve(1238,a,1095,a)]. 2.52/2.74 1239 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),B)),C)) # label(fact_710_max__less__iff__conj) # label(axiom). [clausify(700)]. 2.52/2.74 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),A)),B)). [resolve(1239,a,1095,a)]. 2.52/2.74 1240 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C)) # label(fact_710_max__less__iff__conj) # label(axiom). [clausify(700)]. 2.52/2.74 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)),B)). [resolve(1240,a,1095,a)]. 2.52/2.74 1241 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f122(A,C,B))) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_932_finite__linorder__max__induct) # label(axiom). [clausify(702)]. 2.52/2.74 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),f122(nat,B,A))) | hBOOL(hAPP(fun(nat,bool),bool,B,A)). [resolve(1241,a,1095,a)]. 2.52/2.74 1242 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),f122(A,C,B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),f121(A,C,B))) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_932_finite__linorder__max__induct) # label(axiom). [clausify(702)]. 2.52/2.74 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),C),f122(nat,B,A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),f121(nat,B,A))) | hBOOL(hAPP(fun(nat,bool),bool,B,A)). [resolve(1242,a,1095,a)]. 2.52/2.74 1243 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | hBOOL(hAPP(fun(A,bool),bool,C,f122(A,C,B))) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_932_finite__linorder__max__induct) # label(axiom). [clausify(702)]. 2.52/2.74 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | hBOOL(hAPP(fun(nat,bool),bool,B,f122(nat,B,A))) | hBOOL(hAPP(fun(nat,bool),bool,B,A)). [resolve(1243,a,1095,a)]. 2.52/2.74 1244 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | -hBOOL(hAPP(fun(A,bool),bool,C,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f121(A,C,B)),f122(A,C,B)))) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_932_finite__linorder__max__induct) # label(axiom). [clausify(702)]. 2.52/2.75 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | -hBOOL(hAPP(fun(nat,bool),bool,B,hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f121(nat,B,A)),f122(nat,B,A)))) | hBOOL(hAPP(fun(nat,bool),bool,B,A)). [resolve(1244,a,1095,a)]. 2.52/2.75 1245 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,big_linorder_Max(A),B)) # label(fact_574_Max__insert) # label(axiom). [clausify(704)]. 2.52/2.75 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A)). [resolve(1245,a,1095,a)]. 2.52/2.75 1246 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B))) # label(fact_586_min__max_OInf__le__Sup) # label(axiom). [clausify(705)]. 2.52/2.75 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A))). [resolve(1246,a,1095,a)]. 2.52/2.75 1247 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),C) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),C)),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B)) # label(fact_599_min__max_OSup__fin_Osubset__idem) # label(axiom). [clausify(716)]. 2.52/2.75 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),B) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),B),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),B)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A)). [resolve(1247,a,1095,a)]. 2.52/2.75 1248 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B)) # label(fact_593_min__max_OSup__fin_Oin__idem) # label(axiom). [clausify(718)]. 2.52/2.75 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A)). [resolve(1248,a,1095,a)]. 2.52/2.75 1249 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,big_linorder_Min(A),B)),C)) # label(fact_382_Min__le) # label(axiom). [clausify(720)]. 2.52/2.75 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A)),B)). [resolve(1249,a,1095,a)]. 2.52/2.75 1250 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f130(A,C,B)),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | ti(A,C) = hAPP(fun(A,bool),A,big_linorder_Max(A),B) # label(fact_396_Max__eqI) # label(axiom). [clausify(731)]. 2.52/2.75 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f130(nat,B,A)),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | ti(nat,B) = hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A). [resolve(1250,a,1095,a)]. 2.52/2.75 1251 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f130(A,C,B)),C)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | ti(A,C) = hAPP(fun(A,bool),A,big_linorder_Max(A),B) # label(fact_396_Max__eqI) # label(axiom). [clausify(731)]. 2.52/2.75 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f130(nat,B,A)),B)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | ti(nat,B) = hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A). [resolve(1251,a,1095,a)]. 2.52/2.75 1252 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),f131(A,C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_918_minf_I8_J) # label(axiom). [clausify(735)]. 2.52/2.75 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),f131(nat,B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(1252,a,1095,a)]. 2.52/2.75 1253 -linorder(A) | ti(A,B) != ti(A,C) | hAPP(A,fun(A,bool),ord_lessThan(A),B) = hAPP(A,fun(A,bool),ord_lessThan(A),C) # label(fact_293_lessThan__eq__iff) # label(axiom). [clausify(737)]. 2.52/2.75 Derived: ti(nat,A) != ti(nat,B) | hAPP(nat,fun(nat,bool),ord_lessThan(nat),A) = hAPP(nat,fun(nat,bool),ord_lessThan(nat),B). [resolve(1253,a,1095,a)]. 2.52/2.75 1254 -linorder(A) | ti(A,B) = ti(A,C) | hAPP(A,fun(A,bool),ord_lessThan(A),B) != hAPP(A,fun(A,bool),ord_lessThan(A),C) # label(fact_293_lessThan__eq__iff) # label(axiom). [clausify(737)]. 2.52/2.75 Derived: ti(nat,A) = ti(nat,B) | hAPP(nat,fun(nat,bool),ord_lessThan(nat),A) != hAPP(nat,fun(nat,bool),ord_lessThan(nat),B). [resolve(1254,a,1095,a)]. 2.52/2.75 1255 linorder(int) # label(arity_Int_Oint___Orderings_Olinorder) # label(axiom). [assumption]. 2.52/2.75 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),A). [resolve(1255,a,1096,a)]. 2.52/2.75 Derived: ti(int,A) = hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),A),bot_bot(fun(int,bool)))). [resolve(1255,a,1097,a)]. 2.52/2.75 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1255,a,1098,a)]. 2.52/2.75 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))). [resolve(1255,a,1099,a)]. 2.52/2.75 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) != hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | ti(int,B) = hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)). [resolve(1255,a,1100,a)]. 2.52/2.75 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)). [resolve(1255,a,1101,a)]. 2.52/2.75 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C)). [resolve(1255,a,1102,a)]. 2.52/2.75 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)). [resolve(1255,a,1103,a)]. 2.52/2.75 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A)),C)). [resolve(1255,a,1104,a)]. 2.52/2.75 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f9(int,B,A)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A)),B)). [resolve(1255,a,1105,a)]. 2.52/2.75 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),f9(int,B,A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A)),B)). [resolve(1255,a,1106,a)]. 2.52/2.75 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A))) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),C),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). [resolve(1255,a,1107,a)]. 2.52/2.75 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f11(int,B,A)),A)). [resolve(1255,a,1108,a)]. 2.52/2.75 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),f11(int,B,A))). [resolve(1255,a,1109,a)]. 2.52/2.75 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),B) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),B),A)) | hAPP(fun(int,bool),int,big_linorder_Min(int),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(fun(int,bool),int,big_linorder_Min(int),B)),hAPP(fun(int,bool),int,big_linorder_Min(int),A)). [resolve(1255,a,1110,a)]. 2.52/2.75 Derived: hBOOL(hAPP(fun(int,fun(int,int)),bool,finite_comp_fun_idem(int,int),ord_min(int))). [resolve(1255,a,1111,a)]. 2.52/2.75 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),B),A). [resolve(1255,a,1112,a)]. 2.52/2.75 Derived: ti(int,A) = hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),A),bot_bot(fun(int,bool)))). [resolve(1255,a,1113,a)]. 2.52/2.75 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),B),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),C),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),B),A)). [resolve(1255,a,1114,a)]. 2.52/2.75 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))). [resolve(1255,a,1115,a)]. 2.52/2.75 Derived: ord_max(int) = hAPP(fun(int,fun(int,bool)),fun(int,fun(int,int)),min(int),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int))). [resolve(1255,a,1116,a)]. 2.52/2.75 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B). [resolve(1255,a,1117,a)]. 2.52/2.75 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,B) != hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B). [resolve(1255,a,1118,a)]. 2.52/2.75 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(1255,a,1119,a)]. 2.52/2.75 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). [resolve(1255,a,1120,a)]. 2.52/2.75 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(1255,a,1121,a)]. 2.52/2.75 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),C),A)),B)). [resolve(1255,a,1123,a)]. 2.52/2.75 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),B)). [resolve(1255,a,1124,a)]. 2.52/2.76 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),C),A)),B)). [resolve(1255,a,1125,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,B) = ti(int,A). [resolve(1255,a,1126,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,B) != ti(int,A). [resolve(1255,a,1127,a)]. 2.52/2.76 Derived: ti(int,A) != ti(int,B) | hAPP(int,fun(int,bool),ord_greaterThan(int),A) = hAPP(int,fun(int,bool),ord_greaterThan(int),B). [resolve(1255,a,1128,a)]. 2.52/2.76 Derived: ti(int,A) = ti(int,B) | hAPP(int,fun(int,bool),ord_greaterThan(int),A) != hAPP(int,fun(int,bool),ord_greaterThan(int),B). [resolve(1255,a,1129,a)]. 2.52/2.76 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)). [resolve(1255,a,1130,a)]. 2.52/2.76 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,A,f23(int,B,A))),hAPP(int,int,A,f24(int,B,A))) != hAPP(int,int,A,hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),f23(int,B,A)),f24(int,B,A))) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | ti(fun(int,bool),B) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),A),B)) = hAPP(int,int,A,hAPP(fun(int,bool),int,big_linorder_Min(int),B)). [resolve(1255,a,1131,a)]. 2.52/2.76 Derived: hBOOL(hAPP(fun(int,fun(int,int)),bool,finite_comp_fun_idem(int,int),ord_max(int))). [resolve(1255,a,1134,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,big_linorder_Min(int),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,big_linorder_Min(int),A)). [resolve(1255,a,1135,a)]. 2.52/2.76 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)). [resolve(1255,a,1136,a)]. 2.52/2.76 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),A). [resolve(1255,a,1138,a)]. 2.52/2.76 Derived: big_Sup_fin(int) = ti(fun(fun(int,fun(int,int)),fun(fun(int,bool),int)),big_Sup_fin(int)). [resolve(1255,a,1139,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A) = hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_max(int)),A). [resolve(1255,a,1140,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B). [resolve(1255,a,1141,a)]. 2.52/2.76 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),B). [resolve(1255,a,1142,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),A). [resolve(1255,a,1143,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,big_linorder_Max(int),A) = hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_max(int)),A). [resolve(1255,a,1145,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),A),B)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,big_linorder_Min(int),B)),hAPP(fun(int,bool),int,big_linorder_Min(int),A))). [resolve(1255,a,1146,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),C),A))). [resolve(1255,a,1147,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),B))). [resolve(1255,a,1148,a)]. 2.52/2.76 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,A,f52(int,B,A))),hAPP(int,int,A,f53(int,B,A))) != hAPP(int,int,A,hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),f52(int,B,A)),f53(int,B,A))) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | ti(fun(int,bool),B) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),A),B)) = hAPP(int,int,A,hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),B)). [resolve(1255,a,1150,a)]. 2.52/2.76 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B))). [resolve(1255,a,1151,a)]. 2.52/2.76 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)))). [resolve(1255,a,1153,a)]. 2.52/2.76 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,B) = ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)). [resolve(1255,a,1154,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)). [resolve(1255,a,1155,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | bot_bot(fun(int,bool)) = hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | hAPP(fun(int,bool),int,big_linorder_Min(int),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))). [resolve(1255,a,1156,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | bot_bot(fun(int,bool)) != hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | ti(int,B) = hAPP(fun(int,bool),int,big_linorder_Min(int),A). [resolve(1255,a,1157,a)]. 2.52/2.76 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C)). [resolve(1255,a,1158,a)]. 2.52/2.76 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C)). [resolve(1255,a,1160,a)]. 2.52/2.76 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),B)). [resolve(1255,a,1161,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,fun(int,bool)),fun(int,bool),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int)),hAPP(fun(int,bool),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,bool),fun(int,fun(int,bool))),combc(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),int),combs(int,bool,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool))),hAPP(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),int),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj)),hAPP(fun(int,int),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,int),fun(int,bool))),fun(fun(int,int),fun(int,fun(int,bool))),combc(int,fun(int,int),fun(int,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),hAPP(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int))),hAPP(int,fun(int,int),ord_max(int),B))))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),A))))) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)). [resolve(1255,a,1162,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),C),A)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))). [resolve(1255,a,1163,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)). [resolve(1255,a,1164,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1255,a,1165,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A) = hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A). [resolve(1255,a,1167,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,big_linorder_Min(int),A) = hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A). [resolve(1255,a,1169,a)]. 2.52/2.76 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B). [resolve(1255,a,1170,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C))). [resolve(1255,a,1171,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),B))). [resolve(1255,a,1172,a)]. 2.52/2.76 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C))). [resolve(1255,a,1173,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) != hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | ti(int,B) = hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)). [resolve(1255,a,1174,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))). [resolve(1255,a,1175,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),B),A). [resolve(1255,a,1176,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1255,a,1178,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),f70(int,A)),f71(int,A))),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f70(int,A)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f71(int,A)),bot_bot(fun(int,bool)))))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)),A)). [resolve(1255,a,1179,a)]. 2.52/2.76 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,B) != ti(int,A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1255,a,1180,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A))) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),C),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)). [resolve(1255,a,1184,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f81(int,B,A)),A)). [resolve(1255,a,1185,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),f81(int,B,A))). [resolve(1255,a,1186,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) != hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | ti(int,B) = hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)). [resolve(1255,a,1187,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))). [resolve(1255,a,1188,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | ti(fun(int,bool),B) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,fun(int,bool)),fun(int,bool),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int)),hAPP(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,bool)),hAPP(fun(fun(int,fun(int,bool)),fun(int,bool)),fun(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,bool))),combb(fun(int,fun(int,bool)),fun(int,bool),int),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int))),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,fun(int,bool))),hAPP(fun(int,fun(fun(int,fun(int,bool)),fun(int,fun(int,bool)))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(int,bool)))),combc(int,fun(int,fun(int,bool)),fun(int,fun(int,bool))),hAPP(fun(int,fun(int,fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(int,fun(int,bool)),fun(int,fun(int,bool)))),hAPP(fun(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,bool)))),fun(fun(int,fun(int,fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(int,fun(int,bool)),fun(int,fun(int,bool))))),combb(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,bool))),int),combs(int,fun(int,bool),fun(int,bool))),hAPP(fun(int,fun(int,fun(int,fun(bool,bool)))),fun(int,fun(int,fun(fun(int,bool),fun(int,bool)))),hAPP(fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(int,fun(int,fun(bool,bool)))),fun(int,fun(int,fun(fun(int,bool),fun(int,bool))))),combb(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool))),int),hAPP(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),int),combs(int,bool,bool))),hAPP(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,fun(int,fun(bool,bool)))),hAPP(fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),fun(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,fun(int,fun(bool,bool))))),combb(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool))),int),hAPP(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),int),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),hAPP(fun(int,fun(int,int)),fun(int,fun(int,fun(int,bool))),hAPP(fun(int,fun(fun(int,fun(int,int)),fun(int,fun(int,bool)))),fun(fun(int,fun(int,int)),fun(int,fun(int,fun(int,bool)))),combc(int,fun(int,fun(int,int)),fun(int,fun(int,bool))),hAPP(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(int,fun(int,int)),fun(int,fun(int,bool)))),hAPP(fun(fun(fun(int,int),fun(int,bool)),fun(fun(int,fun(int,int)),fun(int,fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(int,fun(int,int)),fun(int,fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(int,fun(int,int)),fun(int,fun(int,bool))),int),combb(fun(int,int),fun(int,bool),int)),hAPP(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),hAPP(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),ord_min(int)))))),hAPP(fun(int,bool),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,bool),fun(int,fun(int,bool))),combc(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(bool,bool)),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(bool,bool),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(bool,bool)),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(bool,bool),fun(fun(int,bool),fun(int,bool)),int),combb(bool,bool,int)),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),A)))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),B))))))) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),B)). [resolve(1255,a,1189,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)). [resolve(1255,a,1190,a)]. 2.52/2.76 Derived: ti(int,A) != ti(int,B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)). [resolve(1255,a,1191,a)]. 2.52/2.76 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)). [resolve(1255,a,1193,a)]. 2.52/2.76 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(fun(int,bool),int,big_linorder_Max(int),A))). [resolve(1255,a,1194,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(fun(int,bool),int,big_linorder_Min(int),A)),A)). [resolve(1255,a,1195,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),A). [resolve(1255,a,1196,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A)),C)). [resolve(1255,a,1198,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f90(int,B,A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A)),B)). [resolve(1255,a,1199,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f90(int,B,A)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A)),B)). [resolve(1255,a,1200,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f91(int,A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1255,a,1201,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)). [resolve(1255,a,1202,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,A) != ti(int,B). [resolve(1255,a,1204,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),f93(int,B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1255,a,1206,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,big_linorder_Min(int),A)). [resolve(1255,a,1207,a)]. 2.52/2.77 Derived: ti(int,A) = hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),A),bot_bot(fun(int,bool)))). [resolve(1255,a,1208,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)). [resolve(1255,a,1209,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)). [resolve(1255,a,1210,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)). [resolve(1255,a,1211,a)]. 2.52/2.77 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)). [resolve(1255,a,1212,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(1255,a,1213,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(1255,a,1214,a)]. 2.52/2.77 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(1255,a,1215,a)]. 2.52/2.77 Derived: ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),A),B)) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),B)),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A))). [resolve(1255,a,1216,a)]. 2.52/2.77 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),A). [resolve(1255,a,1217,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),B),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),C),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),C),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),B),A)). [resolve(1255,a,1218,a)]. 2.52/2.77 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)). [resolve(1255,a,1219,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),B) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),B),A)) | hAPP(fun(int,bool),int,big_linorder_Max(int),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(fun(int,bool),int,big_linorder_Max(int),B)),hAPP(fun(int,bool),int,big_linorder_Max(int),A)). [resolve(1255,a,1220,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | ti(fun(int,bool),B) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,fun(int,bool)),fun(int,bool),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int)),hAPP(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,bool)),hAPP(fun(fun(int,fun(int,bool)),fun(int,bool)),fun(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,bool))),combb(fun(int,fun(int,bool)),fun(int,bool),int),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int))),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,fun(int,bool))),hAPP(fun(int,fun(fun(int,fun(int,bool)),fun(int,fun(int,bool)))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(int,bool)))),combc(int,fun(int,fun(int,bool)),fun(int,fun(int,bool))),hAPP(fun(int,fun(int,fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(int,fun(int,bool)),fun(int,fun(int,bool)))),hAPP(fun(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,bool)))),fun(fun(int,fun(int,fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(int,fun(int,bool)),fun(int,fun(int,bool))))),combb(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,bool))),int),combs(int,fun(int,bool),fun(int,bool))),hAPP(fun(int,fun(int,fun(int,fun(bool,bool)))),fun(int,fun(int,fun(fun(int,bool),fun(int,bool)))),hAPP(fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(int,fun(int,fun(bool,bool)))),fun(int,fun(int,fun(fun(int,bool),fun(int,bool))))),combb(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool))),int),hAPP(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),int),combs(int,bool,bool))),hAPP(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,fun(int,fun(bool,bool)))),hAPP(fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),fun(fun(int,fun(int,fun(int,bool))),fun(int,fun(int,fun(int,fun(bool,bool))))),combb(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool))),int),hAPP(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),int),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),hAPP(fun(int,fun(int,int)),fun(int,fun(int,fun(int,bool))),hAPP(fun(int,fun(fun(int,fun(int,int)),fun(int,fun(int,bool)))),fun(fun(int,fun(int,int)),fun(int,fun(int,fun(int,bool)))),combc(int,fun(int,fun(int,int)),fun(int,fun(int,bool))),hAPP(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(int,fun(int,int)),fun(int,fun(int,bool)))),hAPP(fun(fun(fun(int,int),fun(int,bool)),fun(fun(int,fun(int,int)),fun(int,fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(int,fun(int,int)),fun(int,fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(int,fun(int,int)),fun(int,fun(int,bool))),int),combb(fun(int,int),fun(int,bool),int)),hAPP(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),hAPP(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),ord_max(int)))))),hAPP(fun(int,bool),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,bool),fun(int,fun(int,bool))),combc(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(bool,bool)),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(bool,bool),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(bool,bool)),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(bool,bool),fun(fun(int,bool),fun(int,bool)),int),combb(bool,bool,int)),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),A)))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),B))))))) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),B)). [resolve(1255,a,1221,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),D))). [resolve(1255,a,1222,a)]. 2.52/2.77 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),A))). [resolve(1255,a,1223,a)]. 2.52/2.77 Derived: ord_min(int) = hAPP(fun(int,fun(int,bool)),fun(int,fun(int,int)),max(int),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int))). [resolve(1255,a,1224,a)]. 2.52/2.77 Derived: big_linorder_Min(int) = ti(fun(fun(int,bool),int),big_linorder_Min(int)). [resolve(1255,a,1225,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,fun(int,bool)),fun(int,bool),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int)),hAPP(fun(int,bool),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,bool),fun(int,fun(int,bool))),combc(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),int),combs(int,bool,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool))),hAPP(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),int),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj)),hAPP(fun(int,int),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,int),fun(int,bool))),fun(fun(int,int),fun(int,fun(int,bool))),combc(int,fun(int,int),fun(int,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),hAPP(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int))),hAPP(int,fun(int,int),ord_min(int),B))))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),A))))) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)). [resolve(1255,a,1226,a)]. 2.52/2.77 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),A). [resolve(1255,a,1227,a)]. 2.52/2.77 Derived: ti(int,A) != hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1255,a,1228,a)]. 2.52/2.77 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B). [resolve(1255,a,1232,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),B) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),B),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),B)),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)). [resolve(1255,a,1233,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,big_linorder_Max(int),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,big_linorder_Max(int),A)). [resolve(1255,a,1234,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,big_linorder_Min(int),A)). [resolve(1255,a,1235,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),A)),B)). [resolve(1255,a,1238,a)]. 2.52/2.77 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),A)),B)). [resolve(1255,a,1239,a)]. 2.52/2.77 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)),B)). [resolve(1255,a,1240,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),f122(int,B,A))) | hBOOL(hAPP(fun(int,bool),bool,B,A)). [resolve(1255,a,1241,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),C),f122(int,B,A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),f121(int,B,A))) | hBOOL(hAPP(fun(int,bool),bool,B,A)). [resolve(1255,a,1242,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | hBOOL(hAPP(fun(int,bool),bool,B,f122(int,B,A))) | hBOOL(hAPP(fun(int,bool),bool,B,A)). [resolve(1255,a,1243,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | -hBOOL(hAPP(fun(int,bool),bool,B,hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f121(int,B,A)),f122(int,B,A)))) | hBOOL(hAPP(fun(int,bool),bool,B,A)). [resolve(1255,a,1244,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,big_linorder_Max(int),A)). [resolve(1255,a,1245,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A))). [resolve(1255,a,1246,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),B) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),B),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),B)),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)). [resolve(1255,a,1247,a)]. 2.52/2.77 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)). [resolve(1255,a,1248,a)]. 2.52/2.78 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,big_linorder_Min(int),A)),B)). [resolve(1255,a,1249,a)]. 2.52/2.78 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f130(int,B,A)),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | ti(int,B) = hAPP(fun(int,bool),int,big_linorder_Max(int),A). [resolve(1255,a,1250,a)]. 2.52/2.78 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),f130(int,B,A)),B)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | ti(int,B) = hAPP(fun(int,bool),int,big_linorder_Max(int),A). [resolve(1255,a,1251,a)]. 2.52/2.78 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),f131(int,B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1255,a,1252,a)]. 2.52/2.78 Derived: ti(int,A) != ti(int,B) | hAPP(int,fun(int,bool),ord_lessThan(int),A) = hAPP(int,fun(int,bool),ord_lessThan(int),B). [resolve(1255,a,1253,a)]. 2.52/2.78 Derived: ti(int,A) = ti(int,B) | hAPP(int,fun(int,bool),ord_lessThan(int),A) != hAPP(int,fun(int,bool),ord_lessThan(int),B). [resolve(1255,a,1254,a)]. 2.52/2.78 1256 -linorder(A) | ti(A,B) = hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),bot_bot(fun(A,bool)))) # label(fact_386_Max_Osingleton) # label(axiom). [clausify(745)]. 2.52/2.78 Derived: ti(nat,A) = hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),A),bot_bot(fun(nat,bool)))). [resolve(1256,a,1095,a)]. 2.52/2.78 Derived: ti(int,A) = hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),A),bot_bot(fun(int,bool)))). [resolve(1256,a,1255,a)]. 2.52/2.78 1257 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_712_min__max_Oless__supI2) # label(axiom). [clausify(750)]. 2.52/2.78 1258 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),B) # label(fact_354_min__max_Oinf__commute) # label(axiom). [clausify(756)]. 2.52/2.78 1259 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B)) # label(fact_597_min__max_OSup__fin_Oinsert) # label(axiom). [clausify(776)]. 2.52/2.78 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A)). [resolve(1259,a,1095,a)]. 2.52/2.78 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)). [resolve(1259,a,1255,a)]. 2.52/2.78 1260 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),ord_lessThan(A),B)),hAPP(A,fun(A,bool),ord_lessThan(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_292_lessThan__subset__iff) # label(axiom). [clausify(780)]. 2.52/2.78 Derived: -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1260,a,1095,a)]. 2.52/2.78 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(int,fun(int,bool),ord_lessThan(int),A)),hAPP(int,fun(int,bool),ord_lessThan(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1260,a,1255,a)]. 2.52/2.78 1261 -linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),ord_lessThan(A),B)),hAPP(A,fun(A,bool),ord_lessThan(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_292_lessThan__subset__iff) # label(axiom). [clausify(780)]. 2.52/2.78 Derived: hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(1261,a,1095,a)]. 2.52/2.78 Derived: hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(int,fun(int,bool),ord_lessThan(int),A)),hAPP(int,fun(int,bool),ord_lessThan(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1261,a,1255,a)]. 2.52/2.78 1262 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) # label(fact_542_min__max_Osup_Oleft__idem) # label(axiom). [clausify(781)]. 2.52/2.78 1263 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f139(A,B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_923_pinf_I6_J) # label(axiom). [clausify(784)]. 2.52/2.78 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f139(nat,A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(1263,a,1095,a)]. 2.52/2.78 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f139(int,A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1263,a,1255,a)]. 2.52/2.78 1264 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f142(A,B)),f143(A,B))),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f142(A,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f143(A,B)),bot_bot(fun(A,bool)))))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)),B)) # label(fact_479_min__max_OInf__fin_Oclosed) # label(axiom). [clausify(803)]. 2.52/2.78 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),f142(nat,A)),f143(nat,A))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f142(nat,A)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f143(nat,A)),bot_bot(fun(nat,bool)))))) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)),A)). [resolve(1264,a,1095,a)]. 2.52/2.79 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),f142(int,A)),f143(int,A))),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f142(int,A)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f143(int,A)),bot_bot(fun(int,bool)))))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)),A)). [resolve(1264,a,1255,a)]. 2.52/2.79 1265 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_787_linorder__antisym__conv3) # label(axiom). [clausify(811)]. 2.52/2.79 1266 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_787_linorder__antisym__conv3) # label(axiom). [clausify(811)]. 2.52/2.79 1267 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C)) # label(fact_555_min__max_Ole__supI) # label(axiom). [clausify(821)]. 2.52/2.79 1268 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C)) # label(fact_556_min__max_Osup__least) # label(axiom). [clausify(822)]. 2.52/2.79 1269 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),B) # label(fact_602_min__max_OSup__fin_Oeq__fold__idem_H) # label(axiom). [clausify(833)]. 2.52/2.79 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_max(nat)),B),A). [resolve(1269,a,1095,a)]. 2.52/2.79 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),B),A). [resolve(1269,a,1255,a)]. 2.52/2.79 1270 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),C),B) # label(fact_378_Min_Oeq__fold__idem_H) # label(axiom). [clausify(837)]. 2.52/2.79 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_min(nat)),B),A). [resolve(1270,a,1095,a)]. 2.52/2.79 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),B),A). [resolve(1270,a,1255,a)]. 2.52/2.79 1271 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) # label(fact_360_min__max_Oinf__greatest) # label(axiom). [clausify(839)]. 2.52/2.79 1272 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | bot_bot(fun(A,bool)) != hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | ti(A,C) = hAPP(fun(A,bool),A,big_linorder_Max(A),B) # label(fact_518_Max_Oremove) # label(axiom). [clausify(842)]. 2.52/2.79 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | bot_bot(fun(nat,bool)) != hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | ti(nat,B) = hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A). [resolve(1272,a,1095,a)]. 2.52/2.79 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | bot_bot(fun(int,bool)) != hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | ti(int,B) = hAPP(fun(int,bool),int,big_linorder_Max(int),A). [resolve(1272,a,1255,a)]. 2.52/2.79 1273 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | bot_bot(fun(A,bool)) = hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | hAPP(fun(A,bool),A,big_linorder_Max(A),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_518_Max_Oremove) # label(axiom). [clausify(842)]. 2.52/2.79 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | bot_bot(fun(nat,bool)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))). [resolve(1273,a,1095,a)]. 2.52/2.79 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | bot_bot(fun(int,bool)) = hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | hAPP(fun(int,bool),int,big_linorder_Max(int),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))). [resolve(1273,a,1255,a)]. 2.60/2.80 1274 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),B) # label(fact_603_min__max_OSup__fin_Oeq__fold_H) # label(axiom). [clausify(853)]. 2.60/2.80 1275 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D))),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)))) # label(fact_561_min__max_Odistrib__inf__le) # label(axiom). [clausify(859)]. 2.60/2.80 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)))). [resolve(1275,a,1095,a)]. 2.60/2.80 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C))),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)))). [resolve(1275,a,1255,a)]. 2.60/2.80 1276 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_558_min__max_Ole__supE) # label(axiom). [clausify(862)]. 2.60/2.80 1277 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_558_min__max_Ole__supE) # label(axiom). [clausify(862)]. 2.60/2.80 1278 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f151(A,C,B)),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | ti(A,C) = hAPP(fun(A,bool),A,big_linorder_Min(A),B) # label(fact_395_Min__eqI) # label(axiom). [clausify(865)]. 2.60/2.80 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f151(nat,B,A)),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | ti(nat,B) = hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A). [resolve(1278,a,1095,a)]. 2.60/2.80 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f151(int,B,A)),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | ti(int,B) = hAPP(fun(int,bool),int,big_linorder_Min(int),A). [resolve(1278,a,1255,a)]. 2.60/2.80 1279 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),f151(A,C,B))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | ti(A,C) = hAPP(fun(A,bool),A,big_linorder_Min(A),B) # label(fact_395_Min__eqI) # label(axiom). [clausify(865)]. 2.60/2.80 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f151(nat,B,A))) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | ti(nat,B) = hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A). [resolve(1279,a,1095,a)]. 2.60/2.80 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),f151(int,B,A))) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | ti(int,B) = hAPP(fun(int,bool),int,big_linorder_Min(int),A). [resolve(1279,a,1255,a)]. 2.60/2.80 1280 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),C),B) # label(fact_377_Min_Oeq__fold_H) # label(axiom). [clausify(876)]. 2.60/2.80 1281 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),B)) # label(fact_369_min__max_Oinf__le1) # label(axiom). [clausify(877)]. 2.60/2.80 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),A)). [resolve(1281,a,1095,a)]. 2.60/2.80 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),A)). [resolve(1281,a,1255,a)]. 2.60/2.80 1282 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,big_linorder_Max(A),B)),B)) # label(fact_383_Max__in) # label(axiom). [clausify(882)]. 2.60/2.80 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A)),A)). [resolve(1282,a,1095,a)]. 2.60/2.80 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(fun(int,bool),int,big_linorder_Max(int),A)),A)). [resolve(1282,a,1255,a)]. 2.60/2.80 1283 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f156(A,B)),f157(A,B))),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f156(A,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f157(A,B)),bot_bot(fun(A,bool)))))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,big_linorder_Min(A),B)),B)) # label(fact_393_Min_Oclosed) # label(axiom). [clausify(883)]. 2.60/2.80 1284 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),E))) # label(fact_359_min__max_Oinf__mono) # label(axiom). [clausify(890)]. 2.60/2.80 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),D))). [resolve(1284,a,1095,a)]. 2.60/2.80 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),D))). [resolve(1284,a,1255,a)]. 2.60/2.80 1285 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | bot_bot(fun(A,bool)) = hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_468_min__max_OInf__fin_Oremove) # label(axiom). [clausify(905)]. 2.60/2.80 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | bot_bot(fun(nat,bool)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))). [resolve(1285,a,1095,a)]. 2.60/2.80 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | bot_bot(fun(int,bool)) = hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))). [resolve(1285,a,1255,a)]. 2.60/2.80 1286 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | bot_bot(fun(A,bool)) != hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | ti(A,C) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B) # label(fact_468_min__max_OInf__fin_Oremove) # label(axiom). [clausify(905)]. 2.60/2.80 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | bot_bot(fun(nat,bool)) != hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | ti(nat,B) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A). [resolve(1286,a,1095,a)]. 2.60/2.80 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | bot_bot(fun(int,bool)) != hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | ti(int,B) = hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A). [resolve(1286,a,1255,a)]. 2.60/2.81 1287 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f161(A,C,D,B)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),B)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_581_min__max_Ofold__sup__le__sup) # label(axiom). [clausify(922)]. 2.60/2.81 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f161(nat,B,C,A)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_max(nat)),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B))). [resolve(1287,a,1095,a)]. 2.60/2.81 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f161(int,B,C,A)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),B),A)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),B))). [resolve(1287,a,1255,a)]. 2.60/2.81 1288 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f161(A,C,D,B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_max(A)),C),B)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_581_min__max_Ofold__sup__le__sup) # label(axiom). [clausify(922)]. 2.60/2.81 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f161(nat,B,C,A)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_max(nat)),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B))). [resolve(1288,a,1095,a)]. 2.60/2.81 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),f161(int,B,C,A)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_max(int)),B),A)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),B))). [resolve(1288,a,1255,a)]. 2.60/2.81 1289 -linorder(A) | big_Inf_fin(A) = ti(fun(fun(A,fun(A,A)),fun(fun(A,bool),A)),big_Inf_fin(A)) # label(tsy_c_Big__Operators_Olattice_OInf__fin_res) # label(axiom). [clausify(923)]. 2.60/2.81 Derived: big_Inf_fin(nat) = ti(fun(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat)),big_Inf_fin(nat)). [resolve(1289,a,1095,a)]. 2.60/2.81 Derived: big_Inf_fin(int) = ti(fun(fun(int,fun(int,int)),fun(fun(int,bool),int)),big_Inf_fin(int)). [resolve(1289,a,1255,a)]. 2.60/2.81 1290 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,big_linorder_Max(A),B)) # label(fact_575_Max_Oinsert) # label(axiom). [clausify(925)]. 2.60/2.82 1291 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B)) # label(fact_598_min__max_OSup__fin_Oinsert__idem) # label(axiom). [clausify(934)]. 2.60/2.82 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A)). [resolve(1291,a,1095,a)]. 2.60/2.82 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A)). [resolve(1291,a,1255,a)]. 2.60/2.82 1292 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C)) # label(fact_733_min__max_Oless__infI1) # label(axiom). [clausify(943)]. 2.60/2.82 1293 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),B) # label(fact_545_min__max_Osup_Oidem) # label(axiom). [clausify(952)]. 2.60/2.82 1294 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_279_linorder__linear) # label(axiom). [clausify(961)]. 2.60/2.82 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(1294,a,1095,a)]. 2.60/2.82 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1294,a,1255,a)]. 2.60/2.82 1295 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f169(A,B)),f170(A,B))),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f169(A,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f170(A,B)),bot_bot(fun(A,bool)))))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,big_linorder_Max(A),B)),B)) # label(fact_580_Max_Oclosed) # label(axiom). [clausify(966)]. 2.60/2.82 1296 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f174(A,C,D,B)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),C)),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),C),B))) # label(fact_394_min__max_Oinf__le__fold__inf) # label(axiom). [clausify(985)]. 2.60/2.82 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f174(nat,B,C,A)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),C),B)),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_min(nat)),B),A))). [resolve(1296,a,1095,a)]. 2.60/2.82 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),f174(int,B,C,A)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),C),B)),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),B),A))). [resolve(1296,a,1255,a)]. 2.60/2.82 1297 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),f174(A,D,C,B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)),hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),D),B))) # label(fact_394_min__max_Oinf__le__fold__inf) # label(axiom). [clausify(985)]. 2.60/2.82 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f174(nat,C,B,A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)),hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_min(nat)),C),A))). [resolve(1297,a,1095,a)]. 2.60/2.82 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),f174(int,C,B,A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C)),hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),C),A))). [resolve(1297,a,1255,a)]. 2.60/2.82 1298 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) # label(fact_713_min__max_Oless__supI1) # label(axiom). [clausify(989)]. 2.60/2.82 1299 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),ord_greaterThan(A),C)),hAPP(A,fun(A,bool),ord_greaterThan(A),B))) # label(fact_571_greaterThan__subset__iff) # label(axiom). [clausify(991)]. 2.60/2.82 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_greaterThan(nat),B)),hAPP(nat,fun(nat,bool),ord_greaterThan(nat),A))). [resolve(1299,a,1095,a)]. 2.60/2.82 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(int,fun(int,bool),ord_greaterThan(int),B)),hAPP(int,fun(int,bool),ord_greaterThan(int),A))). [resolve(1299,a,1255,a)]. 2.60/2.82 1300 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),ord_greaterThan(A),C)),hAPP(A,fun(A,bool),ord_greaterThan(A),B))) # label(fact_571_greaterThan__subset__iff) # label(axiom). [clausify(991)]. 2.60/2.82 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_greaterThan(nat),B)),hAPP(nat,fun(nat,bool),ord_greaterThan(nat),A))). [resolve(1300,a,1095,a)]. 2.60/2.82 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(int,fun(int,bool),ord_greaterThan(int),B)),hAPP(int,fun(int,bool),ord_greaterThan(int),A))). [resolve(1300,a,1255,a)]. 2.60/2.82 1301 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),C),B) # label(fact_476_min__max_OInf__fin_Oeq__fold_H) # label(axiom). [clausify(996)]. 2.60/2.82 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_min(nat)),B),A). [resolve(1301,a,1095,a)]. 2.60/2.82 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),B),A). [resolve(1301,a,1255,a)]. 2.60/2.82 1302 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_265_linorder__le__cases) # label(axiom). [clausify(1000)]. 2.60/2.82 1303 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less(fun(A,bool)),hAPP(A,fun(A,bool),ord_lessThan(A),B)),hAPP(A,fun(A,bool),ord_lessThan(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_793_lessThan__strict__subset__iff) # label(axiom). [clausify(1009)]. 2.60/2.82 Derived: -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1303,a,1095,a)]. 2.60/2.82 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(int,fun(int,bool),ord_lessThan(int),A)),hAPP(int,fun(int,bool),ord_lessThan(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(1303,a,1255,a)]. 2.60/2.82 1304 -linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less(fun(A,bool)),hAPP(A,fun(A,bool),ord_lessThan(A),B)),hAPP(A,fun(A,bool),ord_lessThan(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_793_lessThan__strict__subset__iff) # label(axiom). [clausify(1009)]. 2.60/2.82 Derived: hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(1304,a,1095,a)]. 2.60/2.82 Derived: hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(int,fun(int,bool),ord_lessThan(int),A)),hAPP(int,fun(int,bool),ord_lessThan(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(1304,a,1255,a)]. 2.60/2.82 1305 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),B),C)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,big_linorder_Max(A),B)),hAPP(fun(A,bool),A,big_linorder_Max(A),C))) # label(fact_342_Max__mono) # label(axiom). [clausify(1016)]. 2.60/2.82 Derived: -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A),B)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A)),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),B))). [resolve(1305,a,1095,a)]. 2.60/2.83 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),A),B)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,big_linorder_Max(int),A)),hAPP(fun(int,bool),int,big_linorder_Max(int),B))). [resolve(1305,a,1255,a)]. 2.60/2.83 1306 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_788_linorder__less__linear) # label(axiom). [clausify(1018)]. 2.60/2.83 1307 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_559_le__max__iff__disj) # label(axiom). [clausify(1023)]. 2.60/2.83 1308 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) # label(fact_559_le__max__iff__disj) # label(axiom). [clausify(1023)]. 2.60/2.83 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))). [resolve(1308,a,1095,a)]. 2.60/2.83 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C))). [resolve(1308,a,1255,a)]. 2.60/2.83 1309 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_559_le__max__iff__disj) # label(axiom). [clausify(1023)]. 2.60/2.83 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B))). [resolve(1309,a,1095,a)]. 2.60/2.83 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),B))). [resolve(1309,a,1255,a)]. 2.60/2.83 1310 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | bot_bot(fun(A,bool)) = hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_604_min__max_OSup__fin_Oremove) # label(axiom). [clausify(1024)]. 2.60/2.83 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | bot_bot(fun(nat,bool)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))). [resolve(1310,a,1095,a)]. 2.60/2.83 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | bot_bot(fun(int,bool)) = hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))). [resolve(1310,a,1255,a)]. 2.60/2.83 1311 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | bot_bot(fun(A,bool)) != hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | ti(A,C) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),B) # label(fact_604_min__max_OSup__fin_Oremove) # label(axiom). [clausify(1024)]. 2.60/2.83 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | bot_bot(fun(nat,bool)) != hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | ti(nat,B) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),A). [resolve(1311,a,1095,a)]. 2.60/2.83 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | bot_bot(fun(int,bool)) != hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | ti(int,B) = hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),A). [resolve(1311,a,1255,a)]. 2.60/2.83 1312 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f177(A,B,C,D)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f178(A,B,C,D)),f179(A,B,C,D))) != hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f177(A,B,C,D)),f178(A,B,C,D))),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f177(A,B,C,D)),f179(A,B,C,D))) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_582_min__max_Odistrib__imp1) # label(axiom). [clausify(1026)]. 2.60/2.83 1313 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f181(A,B,C,D)),f182(A,B,C,D))),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f181(A,B,C,D)),f183(A,B,C,D))) != hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f181(A,B,C,D)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),f182(A,B,C,D)),f183(A,B,C,D))) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)) # label(fact_583_min__max_Odistrib__imp2) # label(axiom). [clausify(1035)]. 2.60/2.83 1314 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_746_linorder__not__le) # label(axiom). [clausify(1037)]. 2.60/2.83 1315 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_746_linorder__not__le) # label(axiom). [clausify(1037)]. 2.60/2.83 1316 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),ord_min(A)),C),B) # label(fact_477_min__max_OInf__fin_Oeq__fold__idem_H) # label(axiom). [clausify(1038)]. 2.60/2.83 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),ord_min(nat)),B),A). [resolve(1316,a,1095,a)]. 2.60/2.83 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),ord_min(int)),B),A). [resolve(1316,a,1255,a)]. 2.60/2.83 1317 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),f185(A,C,B))) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_933_finite__linorder__min__induct) # label(axiom). [clausify(1040)]. 2.60/2.83 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),f185(nat,B,A))) | hBOOL(hAPP(fun(nat,bool),bool,B,A)). [resolve(1317,a,1095,a)]. 2.60/2.83 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),f185(int,B,A))) | hBOOL(hAPP(fun(int,bool),bool,B,A)). [resolve(1317,a,1255,a)]. 2.60/2.83 1318 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),f185(A,C,B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f184(A,C,B)),D)) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_933_finite__linorder__min__induct) # label(axiom). [clausify(1040)]. 2.60/2.83 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),C),f185(nat,B,A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f184(nat,B,A)),C)) | hBOOL(hAPP(fun(nat,bool),bool,B,A)). [resolve(1318,a,1095,a)]. 2.60/2.83 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),C),f185(int,B,A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f184(int,B,A)),C)) | hBOOL(hAPP(fun(int,bool),bool,B,A)). [resolve(1318,a,1255,a)]. 2.60/2.83 1319 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | hBOOL(hAPP(fun(A,bool),bool,C,f185(A,C,B))) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_933_finite__linorder__min__induct) # label(axiom). [clausify(1040)]. 2.60/2.84 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | hBOOL(hAPP(fun(nat,bool),bool,B,f185(nat,B,A))) | hBOOL(hAPP(fun(nat,bool),bool,B,A)). [resolve(1319,a,1095,a)]. 2.60/2.84 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | hBOOL(hAPP(fun(int,bool),bool,B,f185(int,B,A))) | hBOOL(hAPP(fun(int,bool),bool,B,A)). [resolve(1319,a,1255,a)]. 2.60/2.84 1320 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,C,bot_bot(fun(A,bool)))) | -hBOOL(hAPP(fun(A,bool),bool,C,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f184(A,C,B)),f185(A,C,B)))) | hBOOL(hAPP(fun(A,bool),bool,C,B)) # label(fact_933_finite__linorder__min__induct) # label(axiom). [clausify(1040)]. 2.60/2.84 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,B,bot_bot(fun(nat,bool)))) | -hBOOL(hAPP(fun(nat,bool),bool,B,hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f184(nat,B,A)),f185(nat,B,A)))) | hBOOL(hAPP(fun(nat,bool),bool,B,A)). [resolve(1320,a,1095,a)]. 2.60/2.84 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,B,bot_bot(fun(int,bool)))) | -hBOOL(hAPP(fun(int,bool),bool,B,hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f184(int,B,A)),f185(int,B,A)))) | hBOOL(hAPP(fun(int,bool),bool,B,A)). [resolve(1320,a,1255,a)]. 2.60/2.84 1321 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) # label(fact_551_min__max_Ole__supI1) # label(axiom). [clausify(1042)]. 2.60/2.84 1322 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),ord_min(A)),B)),C)) # label(fact_389_min__max_Ofold1__belowI) # label(axiom). [clausify(1051)]. 2.60/2.84 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),ord_min(nat)),A)),B)). [resolve(1322,a,1095,a)]. 2.60/2.84 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),ord_min(int)),A)),B)). [resolve(1322,a,1255,a)]. 2.60/2.84 1323 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)) # label(fact_350_min__max_Oinf__left__commute) # label(axiom). [clausify(1053)]. 2.60/2.84 1324 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,B,f186(A,C,B))),hAPP(A,A,B,f187(A,C,B))) != hAPP(A,A,B,hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f186(A,C,B)),f187(A,C,B))) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | ti(fun(A,bool),C) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),B),C)) = hAPP(A,A,B,hAPP(fun(A,bool),A,big_linorder_Max(A),C)) # label(fact_579_Max_Ohom__commute) # label(axiom). [clausify(1058)]. 2.60/2.84 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,A,f186(nat,B,A))),hAPP(nat,nat,A,f187(nat,B,A))) != hAPP(nat,nat,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),f186(nat,B,A)),f187(nat,B,A))) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | ti(fun(nat,bool),B) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),A),B)) = hAPP(nat,nat,A,hAPP(fun(nat,bool),nat,big_linorder_Max(nat),B)). [resolve(1324,a,1095,a)]. 2.60/2.84 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,A,f186(int,B,A))),hAPP(int,int,A,f187(int,B,A))) != hAPP(int,int,A,hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),f186(int,B,A)),f187(int,B,A))) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | ti(fun(int,bool),B) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),A),B)) = hAPP(int,int,A,hAPP(fun(int,bool),int,big_linorder_Max(int),B)). [resolve(1324,a,1255,a)]. 2.60/2.84 1325 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_756_leD) # label(axiom). [clausify(1066)]. 2.60/2.84 1326 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),B)) # label(fact_570_min__max_Osup__Inf__absorb) # label(axiom). [clausify(1077)]. 2.60/2.84 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | ti(nat,B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),A)). [resolve(1326,a,1095,a)]. 2.60/2.84 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),A)). [resolve(1326,a,1255,a)]. 2.60/2.84 1327 -linorder(A) | big_linorder_Max(A) = ti(fun(fun(A,bool),A),big_linorder_Max(A)) # label(tsy_c_Big__Operators_Olinorder__class_OMax_res) # label(axiom). [clausify(1083)]. 2.60/2.84 Derived: big_linorder_Max(nat) = ti(fun(fun(nat,bool),nat),big_linorder_Max(nat)). [resolve(1327,a,1095,a)]. 2.60/2.84 Derived: big_linorder_Max(int) = ti(fun(fun(int,bool),int),big_linorder_Max(int)). [resolve(1327,a,1255,a)]. 2.60/2.84 1328 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,B,f190(A,C,B))),hAPP(A,A,B,f191(A,C,B))) != hAPP(A,A,B,hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),f190(A,C,B)),f191(A,C,B))) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),C)) | ti(fun(A,bool),C) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),B),C)) = hAPP(A,A,B,hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Sup_fin(A),ord_max(A)),C)) # label(fact_606_min__max_OSup__fin_Ohom__commute) # label(axiom). [clausify(1086)]. 2.60/2.84 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,A,f190(nat,B,A))),hAPP(nat,nat,A,f191(nat,B,A))) != hAPP(nat,nat,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),f190(nat,B,A)),f191(nat,B,A))) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),B)) | ti(fun(nat,bool),B) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),A),B)) = hAPP(nat,nat,A,hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Sup_fin(nat),ord_max(nat)),B)). [resolve(1328,a,1095,a)]. 2.60/2.84 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,A,f190(int,B,A))),hAPP(int,int,A,f191(int,B,A))) != hAPP(int,int,A,hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),f190(int,B,A)),f191(int,B,A))) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),B)) | ti(fun(int,bool),B) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),A),B)) = hAPP(int,int,A,hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Sup_fin(int),ord_max(int)),B)). [resolve(1328,a,1255,a)]. 2.60/2.84 1329 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) != hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | ti(A,C) = hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) # label(fact_469_min__max_OInf__fin_Oinsert__remove) # label(axiom). [clausify(1088)]. 2.60/2.84 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) != hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | ti(nat,B) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)). [resolve(1329,a,1095,a)]. 2.60/2.84 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) != hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | ti(int,B) = hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)). [resolve(1329,a,1255,a)]. 2.60/2.84 1330 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | bot_bot(fun(A,bool)) = hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),big_Inf_fin(A),ord_min(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))) # label(fact_469_min__max_OInf__fin_Oinsert__remove) # label(axiom). [clausify(1088)]. 2.60/2.84 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | bot_bot(fun(nat,bool)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),big_Inf_fin(nat),ord_min(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),bot_bot(fun(nat,bool)))))). [resolve(1330,a,1095,a)]. 2.60/2.84 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | bot_bot(fun(int,bool)) = hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),big_Inf_fin(int),ord_min(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),A),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),bot_bot(fun(int,bool)))))). [resolve(1330,a,1255,a)]. 2.68/2.94 1331 linordered_semidom(nat) # label(arity_Nat_Onat___Rings_Olinordered__semidom) # label(axiom). [assumption]. 2.68/2.94 1332 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) # label(fact_817_of__nat__less__iff) # label(axiom). [clausify(4)]. 2.68/2.94 1333 -linordered_semidom(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) # label(fact_817_of__nat__less__iff) # label(axiom). [clausify(4)]. 2.68/2.94 1334 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A)))) # label(fact_822_less__add__one) # label(axiom). [clausify(85)]. 2.68/2.94 1335 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C))) # label(fact_886_power__increasing) # label(axiom). [clausify(142)]. 2.68/2.94 1336 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))) # label(fact_973_of__nat__0__less__iff) # label(axiom). [clausify(145)]. 2.68/2.94 1337 -linordered_semidom(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))) # label(fact_973_of__nat__0__less__iff) # label(axiom). [clausify(145)]. 2.68/2.94 1338 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_823_less__1__mult) # label(axiom). [clausify(230)]. 2.68/2.94 1339 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)))) # label(fact_881_power__less__power__Suc) # label(axiom). [clausify(247)]. 2.68/2.94 1340 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | C != D | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D) # label(fact_879_power__inject__exp) # label(axiom). [clausify(302)]. 2.68/2.94 1341 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | C = D | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) != hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D) # label(fact_879_power__inject__exp) # label(axiom). [clausify(302)]. 2.68/2.94 1342 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A)))) # label(fact_942_zero__less__two) # label(axiom). [clausify(316)]. 2.68/2.94 1343 -linordered_semidom(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) != hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | ti(A,B) = ti(A,D) # label(fact_966_power__eq__imp__eq__base) # label(axiom). [clausify(354)]. 2.68/2.94 1344 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_964_zero__less__power) # label(axiom). [clausify(404)]. 2.68/2.94 1345 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) # label(fact_819_of__nat__less__imp__less) # label(axiom). [clausify(451)]. 2.68/2.94 1346 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) # label(fact_884_power__less__imp__less__exp) # label(axiom). [clausify(465)]. 2.68/2.94 1347 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) # label(fact_659_of__nat__le__iff) # label(axiom). [clausify(478)]. 2.68/2.94 1348 -linordered_semidom(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) # label(fact_659_of__nat__le__iff) # label(axiom). [clausify(478)]. 2.68/2.94 1349 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),D))) # label(fact_967_power__strict__mono) # label(axiom). [clausify(498)]. 2.68/2.94 1350 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) # label(fact_845_power__le__imp__le__exp) # label(axiom). [clausify(634)]. 2.68/2.94 1351 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_878_one__le__power) # label(axiom). [clausify(655)]. 2.68/2.94 1352 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_977_pos__add__strict) # label(axiom). [clausify(713)]. 2.68/2.94 1353 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)))) # label(fact_882_power__gt1__lemma) # label(axiom). [clausify(715)]. 2.68/2.94 1354 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_939_power__less__imp__less__base) # label(axiom). [clausify(726)]. 2.68/2.94 1355 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) # label(fact_818_less__imp__of__nat__less) # label(axiom). [clausify(768)]. 2.68/2.94 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))). [resolve(1331,a,1332,a)]. 2.68/2.94 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))). [resolve(1331,a,1333,a)]. 2.68/2.94 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),one_one(nat)))). [resolve(1331,a,1334,a)]. 2.68/2.94 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B))). [resolve(1331,a,1335,a)]. 2.68/2.94 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,semiring_1_of_nat(nat),A))). [resolve(1331,a,1336,a)]. 2.68/2.94 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,semiring_1_of_nat(nat),A))). [resolve(1331,a,1337,a)]. 2.68/2.94 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))). [resolve(1331,a,1338,a)]. 2.68/2.94 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)))). [resolve(1331,a,1339,a)]. 2.68/2.94 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | B != C | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C). [resolve(1331,a,1340,a)]. 2.68/2.94 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | B = C | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C). [resolve(1331,a,1341,a)]. 2.68/2.94 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat)))). [resolve(1331,a,1342,a)]. 2.68/2.94 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | ti(nat,A) = ti(nat,C). [resolve(1331,a,1343,a)]. 2.68/2.94 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(1331,a,1346,a)]. 2.68/2.94 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))). [resolve(1331,a,1347,a)]. 2.73/2.95 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))). [resolve(1331,a,1348,a)]. 2.73/2.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),C))). [resolve(1331,a,1349,a)]. 2.73/2.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1331,a,1350,a)]. 2.73/2.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B))). [resolve(1331,a,1351,a)]. 2.73/2.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))). [resolve(1331,a,1352,a)]. 2.73/2.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)))). [resolve(1331,a,1353,a)]. 2.73/2.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(1331,a,1354,a)]. 2.73/2.95 1356 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C))) # label(fact_883_power__strict__increasing) # label(axiom). [clausify(873)]. 2.73/2.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B))). [resolve(1356,a,1331,a)]. 2.73/2.95 1357 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) # label(fact_846_power__increasing__iff) # label(axiom). [clausify(885)]. 2.73/2.95 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C))). [resolve(1357,a,1331,a)]. 2.73/2.95 1358 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) # label(fact_846_power__increasing__iff) # label(axiom). [clausify(885)]. 2.76/2.96 1359 linordered_semidom(int) # label(arity_Int_Oint___Rings_Olinordered__semidom) # label(axiom). [assumption]. 2.76/2.96 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int)))). [resolve(1359,a,1334,a)]. 2.76/2.96 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),A)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B))). [resolve(1359,a,1335,a)]. 2.76/2.96 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),A))). [resolve(1359,a,1336,a)]. 2.76/2.96 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),A))). [resolve(1359,a,1337,a)]. 2.76/2.96 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(1359,a,1338,a)]. 2.76/2.96 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)))). [resolve(1359,a,1339,a)]. 2.76/2.96 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | B != C | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C). [resolve(1359,a,1340,a)]. 2.76/2.96 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | B = C | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C). [resolve(1359,a,1341,a)]. 2.76/2.96 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int)))). [resolve(1359,a,1342,a)]. 2.76/2.96 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | ti(int,A) = ti(int,C). [resolve(1359,a,1343,a)]. 2.76/2.96 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B))). [resolve(1359,a,1344,a)]. 2.76/2.96 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(1359,a,1346,a)]. 2.76/2.96 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B))). [resolve(1359,a,1347,a)]. 2.76/2.96 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B))). [resolve(1359,a,1348,a)]. 2.86/3.06 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),C))). [resolve(1359,a,1349,a)]. 2.86/3.06 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1359,a,1350,a)]. 2.86/3.06 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B))). [resolve(1359,a,1351,a)]. 2.86/3.06 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))). [resolve(1359,a,1352,a)]. 2.86/3.06 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)))). [resolve(1359,a,1353,a)]. 2.86/3.06 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(1359,a,1354,a)]. 2.86/3.06 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),A)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B))). [resolve(1359,a,1356,a)]. 2.86/3.06 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C))). [resolve(1359,a,1357,a)]. 2.86/3.06 1360 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) # label(fact_885_power__strict__increasing__iff) # label(axiom). [clausify(1048)]. 2.86/3.06 1361 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) # label(fact_885_power__strict__increasing__iff) # label(axiom). [clausify(1048)]. 2.86/3.06 1362 comm_monoid_mult(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 2.86/3.06 1363 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),hAPP(fun(B,fun(B,bool)),fun(B,fun(B,bool)),combc(B,B,bool),fequal(B)),D))),E)),one_one(A))),C) = hAPP(B,A,E,D) # label(fact_645_setprod__delta) # label(axiom). [clausify(9)]. 2.86/3.06 1364 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),hAPP(fun(B,fun(B,bool)),fun(B,fun(B,bool)),combc(B,B,bool),fequal(B)),D))),E)),one_one(A))),C) # label(fact_645_setprod__delta) # label(axiom). [clausify(9)]. 2.86/3.06 1365 -comm_monoid_mult(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) # label(fact_627_mult_Ocomm__neutral) # label(axiom). [clausify(20)]. 2.86/3.06 1366 -comm_monoid_mult(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f3(B,A,C,D)),D)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D) # label(fact_655_setprod__1_H) # label(axiom). [clausify(27)]. 2.86/3.06 1367 -comm_monoid_mult(A) | one_one(A) != hAPP(B,A,C,f3(B,A,C,D)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D) # label(fact_655_setprod__1_H) # label(axiom). [clausify(27)]. 2.86/3.06 1368 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f10(B,A,E,D,C)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D))) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) # label(fact_652_setprod__mono__one__right) # label(axiom). [clausify(57)]. 2.86/3.06 1369 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | one_one(A) != hAPP(B,A,E,f10(B,A,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) # label(fact_652_setprod__mono__one__right) # label(axiom). [clausify(57)]. 2.86/3.06 1370 -semiring_1(A) | -comm_monoid_mult(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(fun(B,nat),fun(B,A),hAPP(fun(nat,A),fun(fun(B,nat),fun(B,A)),combb(nat,A,B),semiring_1_of_nat(A)),C)),D) = hAPP(nat,A,semiring_1_of_nat(A),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),D)) # label(fact_666_of__nat__setprod) # label(axiom). [clausify(70)]. 2.86/3.06 1371 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(B,A,E,D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C)) # label(fact_198_setprod_Oinsert) # label(axiom). [clausify(86)]. 2.86/3.06 1372 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f19(B,A,D,E,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) # label(fact_209_setprod_Ocong) # label(axiom). [clausify(95)]. 2.86/3.06 1373 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(B,A,D,f19(B,A,E,D,C)) != hAPP(B,A,E,f19(B,A,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) # label(fact_209_setprod_Ocong) # label(axiom). [clausify(95)]. 2.86/3.06 1374 -comm_monoid_mult(A) | big_co302546470etprod(B,A) = ti(fun(fun(B,A),fun(fun(B,bool),A)),big_co302546470etprod(B,A)) # label(tsy_c_Big__Operators_Ocomm__monoid__mult__class_Osetprod_res) # label(axiom). [clausify(167)]. 2.86/3.06 1375 -comm_monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_872_power__mult__distrib) # label(axiom). [clausify(174)]. 2.86/3.06 1376 -comm_monoid_mult(A) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),bot_bot(fun(B,bool))) # label(fact_640_setprod_Oempty) # label(axiom). [clausify(187)]. 2.86/3.06 1377 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),hAPP(fun(B,fun(B,bool)),fun(B,fun(B,bool)),combc(B,B,bool),fequal(B)),D))),E)),F)),C) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),F),hAPP(fun(B,bool),nat,finite_card(B),C)) # label(fact_678_setprod__gen__delta) # label(axiom). [clausify(240)]. 2.86/3.06 1378 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),hAPP(fun(B,fun(B,bool)),fun(B,fun(B,bool)),combc(B,B,bool),fequal(B)),D))),E)),F)),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(B,A,E,D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),F),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(B,bool),nat,finite_card(B),C)),one_one(nat)))) # label(fact_678_setprod__gen__delta) # label(axiom). [clausify(240)]. 2.86/3.06 1379 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),combk(A,B),D)),C) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),hAPP(fun(B,bool),nat,finite_card(B),C)) # label(fact_838_setprod__constant) # label(axiom). [clausify(286)]. 2.86/3.06 1380 -comm_monoid_mult(A) | hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) # label(fact_642_setprod__infinite) # label(axiom). [clausify(331)]. 2.86/3.06 1381 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f74(C,A,D,E,F,B)),f76(C,A,D,E,F,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f77(C,A,D,E,F,B)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_657_setprod_Orelated) # label(axiom). [clausify(405)]. 2.86/3.06 1382 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f74(C,A,D,E,F,B)),f76(C,A,D,E,F,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(C,A,D,f77(C,A,D,E,F,B))),hAPP(C,A,E,f77(C,A,D,E,F,B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_657_setprod_Orelated) # label(axiom). [clausify(405)]. 2.86/3.06 1383 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f73(C,A,D,E,F,B)),f75(C,A,D,E,F,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f77(C,A,D,E,F,B)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_657_setprod_Orelated) # label(axiom). [clausify(405)]. 2.86/3.06 1384 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,f73(C,A,D,E,F,B)),f75(C,A,D,E,F,B))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(C,A,D,f77(C,A,D,E,F,B))),hAPP(C,A,E,f77(C,A,D,E,F,B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_657_setprod_Orelated) # label(axiom). [clausify(405)]. 2.86/3.06 1385 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f73(C,A,D,E,F,B)),f74(C,A,D,E,F,B))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f75(C,A,D,E,F,B)),f76(C,A,D,E,F,B)))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | hBOOL(hAPP(fun(C,bool),bool,hAPP(C,fun(fun(C,bool),bool),member(C),f77(C,A,D,E,F,B)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_657_setprod_Orelated) # label(axiom). [clausify(405)]. 2.86/3.06 1386 -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,one_one(A)),one_one(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f73(C,A,D,E,F,B)),f74(C,A,D,E,F,B))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f75(C,A,D,E,F,B)),f76(C,A,D,E,F,B)))) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),F)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(C,A,D,f77(C,A,D,E,F,B))),hAPP(C,A,E,f77(C,A,D,E,F,B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_657_setprod_Orelated) # label(axiom). [clausify(405)]. 2.86/3.06 1387 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),D)),E)),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C)) # label(fact_194_setprod_Odistrib) # label(axiom). [clausify(476)]. 2.86/3.06 1388 -comm_monoid_mult(A) | hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) # label(fact_643_setprod_Oinfinite) # label(axiom). [clausify(487)]. 2.86/3.06 1389 -comm_monoid_mult(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f94(B,A,E,F,D,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),F),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) # label(fact_252_setprod__cong) # label(axiom). [clausify(549)]. 2.86/3.06 1390 -comm_monoid_mult(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hAPP(B,A,E,f94(B,A,F,E,D,C)) != hAPP(B,A,F,f94(B,A,F,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),F),D) # label(fact_252_setprod__cong) # label(axiom). [clausify(549)]. 2.86/3.06 1391 -comm_monoid_mult(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E)) # label(fact_186_setprod__timesf) # label(axiom). [clausify(551)]. 2.86/3.06 1392 -comm_monoid_mult(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) # label(fact_630_mult__1) # label(axiom). [clausify(577)]. 2.86/3.06 1393 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(B,A,E,D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C)) # label(fact_197_setprod__insert) # label(axiom). [clausify(618)]. 2.86/3.06 1394 -comm_monoid_mult(A) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),combk(A,B),one_one(A))),C) # label(fact_622_setprod__1) # label(axiom). [clausify(676)]. 2.86/3.06 1395 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f123(B,A,D,C)),C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) # label(fact_654_setprod_Oneutral) # label(axiom). [clausify(706)]. 2.86/3.06 1396 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | one_one(A) != hAPP(B,A,D,f123(B,A,D,C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) # label(fact_654_setprod_Oneutral) # label(axiom). [clausify(706)]. 2.86/3.06 1397 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),fequal(B),D))),E)),one_one(A))),C) = hAPP(B,A,E,D) # label(fact_644_setprod__delta_H) # label(axiom). [clausify(722)]. 2.86/3.06 1398 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),fequal(B),D))),E)),one_one(A))),C) # label(fact_644_setprod__delta_H) # label(axiom). [clausify(722)]. 2.86/3.07 1399 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),E),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(B,A,D,E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),E),bot_bot(fun(B,bool)))))) # label(fact_175_setprod_Oinsert__remove) # label(axiom). [clausify(755)]. 2.86/3.07 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(nat))),B) = hAPP(A,nat,D,C). [resolve(1362,a,1363,a)]. 2.86/3.07 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(nat))),B). [resolve(1362,a,1364,a)]. 2.86/3.07 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),one_one(nat)). [resolve(1362,a,1365,a)]. 2.86/3.07 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f3(A,nat,B,C)),C)) | one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C). [resolve(1362,a,1366,a)]. 2.86/3.07 Derived: one_one(nat) != hAPP(A,nat,B,f3(A,nat,B,C)) | one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C). [resolve(1362,a,1367,a)]. 2.86/3.07 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f10(A,nat,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C). [resolve(1362,a,1368,a)]. 2.86/3.07 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(nat) != hAPP(A,nat,D,f10(A,nat,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C). [resolve(1362,a,1369,a)]. 2.86/3.07 Derived: -semiring_1(nat) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(fun(A,nat),fun(A,nat),hAPP(fun(nat,nat),fun(fun(A,nat),fun(A,nat)),combb(nat,nat,A),semiring_1_of_nat(nat)),B)),C) = hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C)). [resolve(1362,a,1370,b)]. 2.86/3.07 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(A,nat,D,C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B)). [resolve(1362,a,1371,a)]. 2.86/3.07 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f19(A,nat,C,D,B)),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B). [resolve(1362,a,1372,a)]. 2.86/3.07 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,nat,C,f19(A,nat,D,C,B)) != hAPP(A,nat,D,f19(A,nat,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B). [resolve(1362,a,1373,a)]. 2.86/3.07 Derived: big_co302546470etprod(A,nat) = ti(fun(fun(A,nat),fun(fun(A,bool),nat)),big_co302546470etprod(A,nat)). [resolve(1362,a,1374,a)]. 2.86/3.07 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),B). [resolve(1362,a,1375,a)]. 2.86/3.07 Derived: one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),bot_bot(fun(A,bool))). [resolve(1362,a,1376,a)]. 2.86/3.07 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),E),hAPP(fun(A,bool),nat,finite_card(A),B)). [resolve(1362,a,1377,a)]. 2.86/3.07 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(A,nat,D,C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),E),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(A,bool),nat,finite_card(A),B)),one_one(nat)))). [resolve(1362,a,1378,a)]. 2.86/3.07 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),combk(nat,A),C)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),hAPP(fun(A,bool),nat,finite_card(A),B)). [resolve(1362,a,1379,a)]. 2.86/3.07 Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B). [resolve(1362,a,1380,a)]. 2.86/3.07 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f74(B,nat,C,D,E,A)),f76(B,nat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f77(B,nat,C,D,E,A)),E)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))). [resolve(1362,a,1381,a)]. 2.86/3.07 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f74(B,nat,C,D,E,A)),f76(B,nat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(B,nat,C,f77(B,nat,C,D,E,A))),hAPP(B,nat,D,f77(B,nat,C,D,E,A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))). [resolve(1362,a,1382,a)]. 2.86/3.07 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f73(B,nat,C,D,E,A)),f75(B,nat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f77(B,nat,C,D,E,A)),E)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))). [resolve(1362,a,1383,a)]. 2.86/3.07 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,f73(B,nat,C,D,E,A)),f75(B,nat,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(B,nat,C,f77(B,nat,C,D,E,A))),hAPP(B,nat,D,f77(B,nat,C,D,E,A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))). [resolve(1362,a,1384,a)]. 2.86/3.07 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f73(B,nat,C,D,E,A)),f74(B,nat,C,D,E,A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f75(B,nat,C,D,E,A)),f76(B,nat,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f77(B,nat,C,D,E,A)),E)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))). [resolve(1362,a,1385,a)]. 2.86/3.07 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,one_one(nat)),one_one(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f73(B,nat,C,D,E,A)),f74(B,nat,C,D,E,A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f75(B,nat,C,D,E,A)),f76(B,nat,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(B,nat,C,f77(B,nat,C,D,E,A))),hAPP(B,nat,D,f77(B,nat,C,D,E,A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),A,hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),C),E)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co302546470etprod(B,nat),D),E))). [resolve(1362,a,1386,a)]. 2.86/3.07 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(fun(A,nat),fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(fun(A,nat),fun(A,nat)),combs(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(A,fun(nat,nat))),combb(nat,fun(nat,nat),A),times_times(nat)),C)),D)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B)). [resolve(1362,a,1387,a)]. 2.86/3.07 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f94(A,nat,D,E,C,B)),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),E),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C). [resolve(1362,a,1389,a)]. 2.86/3.07 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,nat,D,f94(A,nat,E,D,C,B)) != hAPP(A,nat,E,f94(A,nat,E,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),E),C). [resolve(1362,a,1390,a)]. 2.86/3.07 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(fun(A,nat),fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(fun(A,nat),fun(A,nat)),combs(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(A,fun(nat,nat))),combb(nat,fun(nat,nat),A),times_times(nat)),B)),C)),D) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),D)). [resolve(1362,a,1391,a)]. 2.86/3.07 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),A). [resolve(1362,a,1392,a)]. 2.86/3.07 Derived: one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),combk(nat,A),one_one(nat))),B). [resolve(1362,a,1394,a)]. 2.86/3.07 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f123(A,nat,C,B)),B)) | one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B). [resolve(1362,a,1395,a)]. 2.86/3.07 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(nat) != hAPP(A,nat,C,f123(A,nat,C,B)) | one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B). [resolve(1362,a,1396,a)]. 2.86/3.07 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(nat))),B) = hAPP(A,nat,D,C). [resolve(1362,a,1397,a)]. 2.86/3.07 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(nat) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(A,fun(nat,fun(nat,nat))),fun(fun(A,nat),fun(A,fun(nat,nat))),combs(A,nat,fun(nat,nat)),hAPP(fun(A,bool),fun(A,fun(nat,fun(nat,nat))),hAPP(fun(bool,fun(nat,fun(nat,nat))),fun(fun(A,bool),fun(A,fun(nat,fun(nat,nat)))),combb(bool,fun(nat,fun(nat,nat)),A),if(nat)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(nat))),B). [resolve(1362,a,1398,a)]. 2.86/3.08 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(A,nat,C,D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),bot_bot(fun(A,bool)))))). [resolve(1362,a,1399,a)]. 2.86/3.08 1400 -comm_monoid_mult(A) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),bot_bot(fun(B,bool))) # label(fact_641_setprod__empty) # label(axiom). [clausify(841)]. 2.86/3.08 1401 -comm_monoid_mult(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f164(B,A,E,F,D,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),F),C) # label(fact_253_setprod_OF__cong) # label(axiom). [clausify(939)]. 2.86/3.08 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f164(A,nat,D,E,C,B)),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),E),B). [resolve(1401,a,1362,a)]. 2.86/3.08 1402 -comm_monoid_mult(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hAPP(B,A,E,f164(B,A,E,F,D,C)) != hAPP(B,A,F,f164(B,A,E,F,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),F),C) # label(fact_253_setprod_OF__cong) # label(axiom). [clausify(939)]. 2.86/3.08 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,nat,D,f164(A,nat,D,E,C,B)) != hAPP(A,nat,E,f164(A,nat,D,E,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),E),B). [resolve(1402,a,1362,a)]. 2.86/3.08 1403 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(B,A,E,D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),bot_bot(fun(B,bool)))))) # label(fact_176_setprod_Oremove) # label(axiom). [clausify(977)]. 2.86/3.08 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(A,nat,D,C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))). [resolve(1403,a,1362,a)]. 2.86/3.09 1404 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f180(B,A,E,D,C)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D))) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) # label(fact_653_setprod__mono__one__left) # label(axiom). [clausify(1029)]. 2.86/3.09 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f180(A,nat,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C). [resolve(1404,a,1362,a)]. 2.86/3.09 1405 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | one_one(A) != hAPP(B,A,E,f180(B,A,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) # label(fact_653_setprod__mono__one__left) # label(axiom). [clausify(1029)]. 2.86/3.09 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(nat) != hAPP(A,nat,D,f180(A,nat,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),C). [resolve(1405,a,1362,a)]. 2.86/3.09 1406 comm_monoid_mult(int) # label(arity_Int_Oint___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 2.86/3.09 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(int))),B) = hAPP(A,int,D,C). [resolve(1406,a,1363,a)]. 2.86/3.09 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),one_one(int))),B). [resolve(1406,a,1364,a)]. 2.86/3.09 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),one_one(int)). [resolve(1406,a,1365,a)]. 2.86/3.09 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f3(A,int,B,C)),C)) | one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C). [resolve(1406,a,1366,a)]. 2.86/3.09 Derived: one_one(int) != hAPP(A,int,B,f3(A,int,B,C)) | one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C). [resolve(1406,a,1367,a)]. 2.86/3.09 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f10(A,int,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C). [resolve(1406,a,1368,a)]. 2.86/3.09 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(int) != hAPP(A,int,D,f10(A,int,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C). [resolve(1406,a,1369,a)]. 2.86/3.09 Derived: -semiring_1(int) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(fun(A,nat),fun(A,int),hAPP(fun(nat,int),fun(fun(A,nat),fun(A,int)),combb(nat,int,A),semiring_1_of_nat(int)),B)),C) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),B),C)). [resolve(1406,a,1370,b)]. 2.86/3.09 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(A,int,D,C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B)). [resolve(1406,a,1371,a)]. 2.86/3.09 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f19(A,int,C,D,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B). [resolve(1406,a,1372,a)]. 2.86/3.09 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,int,C,f19(A,int,D,C,B)) != hAPP(A,int,D,f19(A,int,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B). [resolve(1406,a,1373,a)]. 2.86/3.09 Derived: big_co302546470etprod(A,int) = ti(fun(fun(A,int),fun(fun(A,bool),int)),big_co302546470etprod(A,int)). [resolve(1406,a,1374,a)]. 2.86/3.09 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),B)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),B). [resolve(1406,a,1375,a)]. 2.86/3.09 Derived: one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),bot_bot(fun(A,bool))). [resolve(1406,a,1376,a)]. 2.86/3.09 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),E),hAPP(fun(A,bool),nat,finite_card(A),B)). [resolve(1406,a,1377,a)]. 2.86/3.09 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),fequal(A)),C))),D)),E)),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(A,int,D,C)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),E),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(A,bool),nat,finite_card(A),B)),one_one(nat)))). [resolve(1406,a,1378,a)]. 2.86/3.09 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),combk(int,A),C)),B) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),hAPP(fun(A,bool),nat,finite_card(A),B)). [resolve(1406,a,1379,a)]. 2.86/3.09 Derived: hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B). [resolve(1406,a,1380,a)]. 2.86/3.09 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f74(B,int,C,D,E,A)),f76(B,int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f77(B,int,C,D,E,A)),E)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))). [resolve(1406,a,1381,a)]. 2.86/3.09 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f74(B,int,C,D,E,A)),f76(B,int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(B,int,C,f77(B,int,C,D,E,A))),hAPP(B,int,D,f77(B,int,C,D,E,A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))). [resolve(1406,a,1382,a)]. 2.86/3.09 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f73(B,int,C,D,E,A)),f75(B,int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f77(B,int,C,D,E,A)),E)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))). [resolve(1406,a,1383,a)]. 2.86/3.09 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,f73(B,int,C,D,E,A)),f75(B,int,C,D,E,A))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(B,int,C,f77(B,int,C,D,E,A))),hAPP(B,int,D,f77(B,int,C,D,E,A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))). [resolve(1406,a,1384,a)]. 2.90/3.09 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f73(B,int,C,D,E,A)),f74(B,int,C,D,E,A))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f75(B,int,C,D,E,A)),f76(B,int,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f77(B,int,C,D,E,A)),E)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))). [resolve(1406,a,1385,a)]. 2.90/3.09 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,one_one(int)),one_one(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f73(B,int,C,D,E,A)),f74(B,int,C,D,E,A))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f75(B,int,C,D,E,A)),f76(B,int,C,D,E,A)))) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),E)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(B,int,C,f77(B,int,C,D,E,A))),hAPP(B,int,D,f77(B,int,C,D,E,A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),A,hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),C),E)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co302546470etprod(B,int),D),E))). [resolve(1406,a,1386,a)]. 2.90/3.09 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(A,fun(int,int)),fun(fun(A,int),fun(A,int)),combs(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),times_times(int)),C)),D)),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B)). [resolve(1406,a,1387,a)]. 2.90/3.09 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f94(A,int,D,E,C,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),E),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C). [resolve(1406,a,1389,a)]. 2.90/3.09 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,int,D,f94(A,int,E,D,C,B)) != hAPP(A,int,E,f94(A,int,E,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),E),C). [resolve(1406,a,1390,a)]. 2.90/3.09 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(A,fun(int,int)),fun(fun(A,int),fun(A,int)),combs(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),times_times(int)),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),D)). [resolve(1406,a,1391,a)]. 2.90/3.09 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),A). [resolve(1406,a,1392,a)]. 2.90/3.09 Derived: one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),combk(int,A),one_one(int))),B). [resolve(1406,a,1394,a)]. 2.90/3.09 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f123(A,int,C,B)),B)) | one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B). [resolve(1406,a,1395,a)]. 2.90/3.09 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(int) != hAPP(A,int,C,f123(A,int,C,B)) | one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B). [resolve(1406,a,1396,a)]. 2.90/3.09 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(int))),B) = hAPP(A,int,D,C). [resolve(1406,a,1397,a)]. 2.90/3.09 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(int) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(A,fun(int,fun(int,int))),fun(fun(A,int),fun(A,fun(int,int))),combs(A,int,fun(int,int)),hAPP(fun(A,bool),fun(A,fun(int,fun(int,int))),hAPP(fun(bool,fun(int,fun(int,int))),fun(fun(A,bool),fun(A,fun(int,fun(int,int)))),combb(bool,fun(int,fun(int,int)),A),if(int)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(int))),B). [resolve(1406,a,1398,a)]. 2.90/3.09 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(A,int,C,D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),bot_bot(fun(A,bool)))))). [resolve(1406,a,1399,a)]. 2.90/3.09 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f164(A,int,D,E,C,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),E),B). [resolve(1406,a,1401,a)]. 2.90/3.09 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,int,D,f164(A,int,D,E,C,B)) != hAPP(A,int,E,f164(A,int,D,E,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),E),B). [resolve(1406,a,1402,a)]. 2.90/3.09 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(A,int,D,C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))). [resolve(1406,a,1403,a)]. 2.90/3.09 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f180(A,int,D,C,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C))) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C). [resolve(1406,a,1404,a)]. 2.95/3.17 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | one_one(int) != hAPP(A,int,D,f180(A,int,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),D),C). [resolve(1406,a,1405,a)]. 2.95/3.17 1407 comm_semiring_1(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 2.95/3.17 1408 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_636_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom). [clausify(13)]. 2.95/3.17 1409 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B) # label(fact_237_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom). [clausify(49)]. 2.95/3.17 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),one_one(nat))),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)). [resolve(1407,a,1408,a)]. 2.95/3.17 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),A). [resolve(1407,a,1409,a)]. 2.95/3.17 1410 comm_semiring_1(int) # label(arity_Int_Oint___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 2.95/3.17 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int))),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)). [resolve(1410,a,1408,a)]. 2.95/3.17 1411 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_241_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom). [clausify(119)]. 2.95/3.17 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),B). [resolve(1411,a,1407,a)]. 2.95/3.17 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),B). [resolve(1411,a,1410,a)]. 2.95/3.17 1412 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),C) # label(fact_635_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom). [clausify(135)]. 2.95/3.17 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),one_one(nat))),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),B). [resolve(1412,a,1407,a)]. 2.95/3.17 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int))),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),B). [resolve(1412,a,1410,a)]. 2.95/3.17 1413 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_242_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom). [clausify(138)]. 2.95/3.18 1414 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,semiring_1_of_nat(A),B)),one_one(A))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A))),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),semiring_1_of_nat(A)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),B))) # label(fact_677_gauss__sum) # label(axiom). [clausify(222)]. 2.95/3.18 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),one_one(nat))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),semiring_1_of_nat(nat)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),A))). [resolve(1414,a,1407,a)]. 2.95/3.18 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),A)),one_one(int))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),semiring_1_of_nat(int)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),A))). [resolve(1414,a,1410,a)]. 2.95/3.18 1415 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A))),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) # label(fact_637_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom). [clausify(317)]. 2.95/3.18 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat))),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),A). [resolve(1415,a,1407,a)]. 2.95/3.18 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int))),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A). [resolve(1415,a,1410,a)]. 2.95/3.18 1416 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),E)) # label(fact_239_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom). [clausify(330)]. 2.95/3.18 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),D)). [resolve(1416,a,1407,a)]. 2.95/3.18 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),D)). [resolve(1416,a,1410,a)]. 2.95/3.18 1417 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)) # label(fact_238_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom). [clausify(351)]. 2.95/3.18 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D)). [resolve(1417,a,1407,a)]. 2.95/3.18 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)). [resolve(1417,a,1410,a)]. 2.95/3.18 1418 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom). [clausify(414)]. 2.95/3.18 1419 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),one_one(nat)))),D)))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A))),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),plus_plus(A),C)),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),semiring_1_of_nat(A))),D))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))) # label(fact_656_arith__series__general) # label(axiom). [clausify(486)]. 2.95/3.18 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),C)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),plus_plus(nat),B)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),times_times(nat)),semiring_1_of_nat(nat))),C))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A))). [resolve(1419,a,1407,a)]. 2.95/3.18 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),C)))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(int,int),fun(fun(nat,int),fun(nat,int)),combb(int,int,nat),hAPP(int,fun(int,int),plus_plus(int),B)),hAPP(int,fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(int,fun(nat,int)),combc(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),semiring_1_of_nat(int))),C))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A))). [resolve(1419,a,1410,a)]. 2.95/3.20 1420 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E))) # label(fact_240_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom). [clausify(564)]. 2.95/3.20 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D))). [resolve(1420,a,1410,a)]. 2.95/3.20 1421 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_251_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom). [clausify(573)]. 2.95/3.20 1422 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_234_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom). [clausify(684)]. 2.95/3.20 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)). [resolve(1422,a,1407,a)]. 2.95/3.20 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)). [resolve(1422,a,1410,a)]. 2.95/3.20 1423 -comm_semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),D) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) # label(fact_724_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom). [clausify(688)]. 2.95/3.20 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(1423,a,1407,a)]. 2.95/3.20 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),C) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(1423,a,1410,a)]. 2.95/3.20 1424 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),D)) # label(fact_816_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom). [clausify(740)]. 2.95/3.20 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)). [resolve(1424,a,1407,a)]. 2.95/3.20 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)). [resolve(1424,a,1410,a)]. 3.01/3.22 1425 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_235_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom). [clausify(743)]. 3.01/3.22 1426 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom). [clausify(785)]. 3.01/3.22 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),B). [resolve(1426,a,1407,a)]. 3.01/3.22 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),B). [resolve(1426,a,1410,a)]. 3.01/3.22 1427 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B) # label(fact_246_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom). [clausify(881)]. 3.01/3.22 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A). [resolve(1427,a,1407,a)]. 3.01/3.22 1428 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E)) # label(fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom). [clausify(889)]. 3.01/3.22 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D)). [resolve(1428,a,1407,a)]. 3.01/3.22 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D)). [resolve(1428,a,1410,a)]. 3.01/3.22 1429 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_244_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom). [clausify(915)]. 3.01/3.22 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)). [resolve(1429,a,1410,a)]. 3.01/3.22 1430 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_248_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom). [clausify(979)]. 3.01/3.22 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)). [resolve(1430,a,1407,a)]. 3.01/3.22 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)). [resolve(1430,a,1410,a)]. 3.07/3.31 1431 -comm_semiring_1(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) # label(fact_628_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom). [clausify(995)]. 3.07/3.31 1432 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)) # label(fact_236_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom). [clausify(997)]. 3.07/3.31 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)). [resolve(1432,a,1407,a)]. 3.07/3.31 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)). [resolve(1432,a,1410,a)]. 3.07/3.31 1433 -comm_semiring_1(A) | ti(A,B) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),one_one(nat)) # label(fact_709_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom). [clausify(1001)]. 3.07/3.31 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),one_one(nat)). [resolve(1433,a,1407,a)]. 3.07/3.31 Derived: ti(int,A) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),one_one(nat)). [resolve(1433,a,1410,a)]. 3.07/3.31 1434 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_732_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom). [clausify(1003)]. 3.07/3.31 1435 -comm_semiring_1(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) # label(fact_631_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom). [clausify(1063)]. 3.07/3.31 1436 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_245_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom). [clausify(1079)]. 3.07/3.31 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)). [resolve(1436,a,1407,a)]. 3.07/3.31 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)). [resolve(1436,a,1410,a)]. 3.07/3.31 1437 linord2061991079up_add(int) # label(arity_Int_Oint___Groups_Olinordered__ab__semigroup__add) # label(axiom). [assumption]. 3.07/3.31 1438 -linord2061991079up_add(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,fun(A,bool)),fun(A,bool),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A)),hAPP(fun(A,bool),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,bool),fun(A,fun(A,bool))),combc(A,fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool))),hAPP(fun(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),A),combs(A,bool,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool))),hAPP(fun(fun(A,bool),fun(A,fun(bool,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),combb(fun(A,bool),fun(A,fun(bool,bool)),A),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj)),hAPP(fun(A,A),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,A),fun(A,bool))),fun(fun(A,A),fun(A,fun(A,bool))),combc(A,fun(A,A),fun(A,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool))),hAPP(fun(fun(A,bool),fun(fun(A,A),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool)))),combb(fun(A,bool),fun(fun(A,A),fun(A,bool)),A),combb(A,bool,A)),fequal(A))),hAPP(A,fun(A,A),plus_plus(A),C))))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))))) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(fun(A,bool),A,big_linorder_Min(A),B)) # label(fact_601_add__Min__commute) # label(axiom). [clausify(42)]. 3.07/3.31 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,fun(int,bool)),fun(int,bool),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int)),hAPP(fun(int,bool),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,bool),fun(int,fun(int,bool))),combc(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),int),combs(int,bool,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool))),hAPP(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),int),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj)),hAPP(fun(int,int),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,int),fun(int,bool))),fun(fun(int,int),fun(int,fun(int,bool))),combc(int,fun(int,int),fun(int,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),hAPP(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int))),hAPP(int,fun(int,int),plus_plus(int),B))))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),A))))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(fun(int,bool),int,big_linorder_Min(int),A)). [resolve(1437,a,1438,a)]. 3.07/3.31 1439 linord2061991079up_add(nat) # label(arity_Nat_Onat___Groups_Olinordered__ab__semigroup__add) # label(axiom). [assumption]. 3.07/3.31 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Min(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,bool),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat)),hAPP(fun(nat,bool),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(nat,fun(nat,bool))),combc(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combc(nat,fun(nat,nat),fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool))),hAPP(fun(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool)))),combb(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool)),nat),combb(nat,bool,nat)),fequal(nat))),hAPP(nat,fun(nat,nat),plus_plus(nat),B))))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),A))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Min(nat),A)). [resolve(1439,a,1438,a)]. 3.07/3.32 1440 -linord2061991079up_add(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(fun(A,fun(A,bool)),fun(A,bool),hAPP(fun(fun(A,bool),bool),fun(fun(A,fun(A,bool)),fun(A,bool)),combb(fun(A,bool),bool,A),fEx(A)),hAPP(fun(A,bool),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,bool),fun(A,bool))),fun(fun(A,bool),fun(A,fun(A,bool))),combc(A,fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool))),hAPP(fun(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool))),fun(fun(A,fun(A,fun(bool,bool))),fun(A,fun(fun(A,bool),fun(A,bool)))),combb(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),A),combs(A,bool,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool))),hAPP(fun(fun(A,bool),fun(A,fun(bool,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(A,fun(bool,bool)))),combb(fun(A,bool),fun(A,fun(bool,bool)),A),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj)),hAPP(fun(A,A),fun(A,fun(A,bool)),hAPP(fun(A,fun(fun(A,A),fun(A,bool))),fun(fun(A,A),fun(A,fun(A,bool))),combc(A,fun(A,A),fun(A,bool)),hAPP(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool))),hAPP(fun(fun(A,bool),fun(fun(A,A),fun(A,bool))),fun(fun(A,fun(A,bool)),fun(A,fun(fun(A,A),fun(A,bool)))),combb(fun(A,bool),fun(fun(A,A),fun(A,bool)),A),combb(A,bool,A)),fequal(A))),hAPP(A,fun(A,A),plus_plus(A),C))))),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B))))) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(fun(A,bool),A,big_linorder_Max(A),B)) # label(fact_600_add__Max__commute) # label(axiom). [clausify(675)]. 3.07/3.32 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,fun(int,bool)),fun(int,bool),hAPP(fun(fun(int,bool),bool),fun(fun(int,fun(int,bool)),fun(int,bool)),combb(fun(int,bool),bool,int),fEx(int)),hAPP(fun(int,bool),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,bool),fun(int,fun(int,bool))),combc(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),int),combs(int,bool,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool))),hAPP(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),int),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj)),hAPP(fun(int,int),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,int),fun(int,bool))),fun(fun(int,int),fun(int,fun(int,bool))),combc(int,fun(int,int),fun(int,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),hAPP(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int))),hAPP(int,fun(int,int),plus_plus(int),B))))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),A))))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(fun(int,bool),int,big_linorder_Max(int),A)). [resolve(1440,a,1437,a)]. 3.21/3.42 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | hAPP(fun(nat,bool),nat,big_linorder_Max(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,bool),hAPP(fun(fun(nat,bool),bool),fun(fun(nat,fun(nat,bool)),fun(nat,bool)),combb(fun(nat,bool),bool,nat),fEx(nat)),hAPP(fun(nat,bool),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,bool),fun(nat,fun(nat,bool))),combc(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combc(nat,fun(nat,nat),fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool))),hAPP(fun(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(fun(nat,nat),fun(nat,bool)))),combb(fun(nat,bool),fun(fun(nat,nat),fun(nat,bool)),nat),combb(nat,bool,nat)),fequal(nat))),hAPP(nat,fun(nat,nat),plus_plus(nat),B))))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),A))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(fun(nat,bool),nat,big_linorder_Max(nat),A)). [resolve(1440,a,1439,a)]. 3.21/3.42 1441 semiring_0(nat) # label(arity_Nat_Onat___Rings_Osemiring__0) # label(axiom). [assumption]. 3.21/3.42 1442 -semiring_0(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(C,bool),fun(B,A),hAPP(fun(B,fun(fun(C,bool),A)),fun(fun(C,bool),fun(B,A)),combc(B,fun(C,bool),A),hAPP(fun(B,fun(C,A)),fun(B,fun(fun(C,bool),A)),hAPP(fun(fun(C,A),fun(fun(C,bool),A)),fun(fun(B,fun(C,A)),fun(B,fun(fun(C,bool),A))),combb(fun(C,A),fun(fun(C,bool),A),B),big_co1399186613setsum(C,A)),hAPP(fun(C,A),fun(B,fun(C,A)),hAPP(fun(B,fun(fun(C,A),fun(C,A))),fun(fun(C,A),fun(B,fun(C,A))),combc(B,fun(C,A),fun(C,A)),hAPP(fun(B,fun(A,A)),fun(B,fun(fun(C,A),fun(C,A))),hAPP(fun(fun(A,A),fun(fun(C,A),fun(C,A))),fun(fun(B,fun(A,A)),fun(B,fun(fun(C,A),fun(C,A)))),combb(fun(A,A),fun(fun(C,A),fun(C,A)),B),combb(A,A,C)),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),D))),E))),F)),V6) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),V6)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),E),F)) # label(fact_187_setsum__product) # label(axiom). [clausify(52)]. 3.21/3.42 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(fun(B,bool),fun(A,nat),hAPP(fun(A,fun(fun(B,bool),nat)),fun(fun(B,bool),fun(A,nat)),combc(A,fun(B,bool),nat),hAPP(fun(A,fun(B,nat)),fun(A,fun(fun(B,bool),nat)),hAPP(fun(fun(B,nat),fun(fun(B,bool),nat)),fun(fun(A,fun(B,nat)),fun(A,fun(fun(B,bool),nat))),combb(fun(B,nat),fun(fun(B,bool),nat),A),big_co1399186613setsum(B,nat)),hAPP(fun(B,nat),fun(A,fun(B,nat)),hAPP(fun(A,fun(fun(B,nat),fun(B,nat))),fun(fun(B,nat),fun(A,fun(B,nat))),combc(A,fun(B,nat),fun(B,nat)),hAPP(fun(A,fun(nat,nat)),fun(A,fun(fun(B,nat),fun(B,nat))),hAPP(fun(fun(nat,nat),fun(fun(B,nat),fun(B,nat))),fun(fun(A,fun(nat,nat)),fun(A,fun(fun(B,nat),fun(B,nat)))),combb(fun(nat,nat),fun(fun(B,nat),fun(B,nat)),A),combb(nat,nat,B)),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(A,fun(nat,nat))),combb(nat,fun(nat,nat),A),times_times(nat)),C))),D))),E)),F) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),F)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),D),E)). [resolve(1441,a,1442,a)]. 3.25/3.45 1443 semiring_0(int) # label(arity_Int_Oint___Rings_Osemiring__0) # label(axiom). [assumption]. 3.25/3.45 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(B,bool),fun(A,int),hAPP(fun(A,fun(fun(B,bool),int)),fun(fun(B,bool),fun(A,int)),combc(A,fun(B,bool),int),hAPP(fun(A,fun(B,int)),fun(A,fun(fun(B,bool),int)),hAPP(fun(fun(B,int),fun(fun(B,bool),int)),fun(fun(A,fun(B,int)),fun(A,fun(fun(B,bool),int))),combb(fun(B,int),fun(fun(B,bool),int),A),big_co1399186613setsum(B,int)),hAPP(fun(B,int),fun(A,fun(B,int)),hAPP(fun(A,fun(fun(B,int),fun(B,int))),fun(fun(B,int),fun(A,fun(B,int))),combc(A,fun(B,int),fun(B,int)),hAPP(fun(A,fun(int,int)),fun(A,fun(fun(B,int),fun(B,int))),hAPP(fun(fun(int,int),fun(fun(B,int),fun(B,int))),fun(fun(A,fun(int,int)),fun(A,fun(fun(B,int),fun(B,int)))),combb(fun(int,int),fun(fun(B,int),fun(B,int)),A),combb(int,int,B)),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),times_times(int)),C))),D))),E)),F) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),F)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),D),E)). [resolve(1443,a,1442,a)]. 3.25/3.45 1444 -semiring_0(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),D) # label(fact_188_setsum__left__distrib) # label(axiom). [clausify(804)]. 3.25/3.45 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(A,fun(nat,nat))),combb(nat,fun(nat,nat),A),times_times(nat)),B)),C)),D) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D)),C). [resolve(1444,a,1441,a)]. 3.25/3.45 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),times_times(int)),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),C). [resolve(1444,a,1443,a)]. 3.25/3.45 1445 -semiring_0(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),hAPP(A,fun(A,A),times_times(A),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E)) # label(fact_189_setsum__right__distrib) # label(axiom). [clausify(908)]. 3.35/3.55 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(fun(A,nat),fun(A,nat),hAPP(fun(nat,nat),fun(fun(A,nat),fun(A,nat)),combb(nat,nat,A),hAPP(nat,fun(nat,nat),times_times(nat),B)),C)),D) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),D)). [resolve(1445,a,1441,a)]. 3.35/3.55 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(int,int),fun(fun(A,int),fun(A,int)),combb(int,int,A),hAPP(int,fun(int,int),times_times(int),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D)). [resolve(1445,a,1443,a)]. 3.35/3.55 1446 ab_group_add(int) # label(arity_Int_Oint___Groups_Oab__group__add) # label(axiom). [assumption]. 3.35/3.55 1447 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | ti(A,C) != ti(A,B) | ti(A,D) = ti(A,E) # label(fact_247_diff__eq__diff__eq) # label(axiom). [clausify(54)]. 3.35/3.55 1448 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | ti(A,C) = ti(A,B) | ti(A,D) != ti(A,E) # label(fact_247_diff__eq__diff__eq) # label(axiom). [clausify(54)]. 3.35/3.55 1449 -ab_group_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),bot_bot(fun(B,bool))))) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) # label(fact_173_setsum__diff1) # label(axiom). [clausify(156)]. 3.35/3.55 1450 -ab_group_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),bot_bot(fun(B,bool))))) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C)),hAPP(B,A,E,D)) # label(fact_173_setsum__diff1) # label(axiom). [clausify(156)]. 3.35/3.55 1451 -ab_group_add(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),minus_minus(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E)) # label(fact_190_setsum__subtractf) # label(axiom). [clausify(175)]. 3.35/3.55 1452 -ab_group_add(A) | zero_zero(A) = ti(A,zero_zero(A)) # label(tsy_c_Groups_Ozero__class_Ozero_1_res) # label(axiom). [clausify(204)]. 3.35/3.55 1453 -ab_group_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B) # label(fact_492_minus__diff__eq) # label(axiom). [clausify(392)]. 3.35/3.55 1454 -ab_group_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D)) # label(fact_329_setsum__diff) # label(axiom). [clausify(425)]. 3.35/3.55 1455 -ab_group_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),D)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),D),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(nat,A,D,B)),hAPP(nat,A,D,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),one_one(nat)))) # label(fact_934_setsum__natinterval__difff) # label(axiom). [clausify(433)]. 3.35/3.55 1456 -ab_group_add(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | zero_zero(A) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),D)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),D),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) # label(fact_934_setsum__natinterval__difff) # label(axiom). [clausify(433)]. 3.35/3.55 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | ti(int,B) != ti(int,A) | ti(int,C) = ti(int,D). [resolve(1446,a,1447,a)]. 3.35/3.55 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | ti(int,B) = ti(int,A) | ti(int,C) != ti(int,D). [resolve(1446,a,1448,a)]. 3.35/3.55 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool))))) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B). [resolve(1446,a,1449,a)]. 3.35/3.55 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool))))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B)),hAPP(A,int,D,C)). [resolve(1446,a,1450,a)]. 3.35/3.55 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(A,fun(int,int)),fun(fun(A,int),fun(A,int)),combs(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),minus_minus(int)),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D)). [resolve(1446,a,1451,a)]. 3.35/3.58 Derived: zero_zero(int) = ti(int,zero_zero(int)). [resolve(1446,a,1452,a)]. 3.35/3.58 Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),A). [resolve(1446,a,1453,a)]. 3.35/3.58 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C)). [resolve(1446,a,1454,a)]. 3.35/3.58 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),minus_minus(int)),C)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,C,A)),hAPP(nat,int,C,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))). [resolve(1446,a,1455,a)]. 3.35/3.58 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | zero_zero(int) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),minus_minus(int)),C)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)). [resolve(1446,a,1456,a)]. 3.35/3.58 1457 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_513_ab__diff__minus) # label(axiom). [clausify(654)]. 3.35/3.58 1458 -ab_group_add(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),uminus_uminus(A)),C)),D) = hAPP(A,A,uminus_uminus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D)) # label(fact_510_setsum__negf) # label(axiom). [clausify(1049)]. 3.35/3.58 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(int,int),fun(fun(A,int),fun(A,int)),combb(int,int,A),uminus_uminus(int)),B)),C) = hAPP(int,int,uminus_uminus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C)). [resolve(1458,a,1446,a)]. 3.35/3.58 1459 -ab_group_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) # label(fact_501_minus__add__distrib) # label(axiom). [clausify(1085)]. 3.35/3.58 Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)). [resolve(1459,a,1446,a)]. 3.47/3.67 1460 ordere236663937imp_le(int) # label(arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption]. 3.47/3.67 1461 -ordere236663937imp_le(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_534_max__add__distrib__left) # label(axiom). [clausify(69)]. 3.47/3.67 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)). [resolve(1460,a,1461,a)]. 3.47/3.67 1462 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_300_add__le__cancel__right) # label(axiom). [clausify(499)]. 3.47/3.67 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)). [resolve(1462,a,1460,a)]. 3.47/3.67 1463 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_300_add__le__cancel__right) # label(axiom). [clausify(499)]. 3.47/3.67 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)). [resolve(1463,a,1460,a)]. 3.47/3.67 1464 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_294_add__le__imp__le__left) # label(axiom). [clausify(536)]. 3.47/3.67 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)). [resolve(1464,a,1460,a)]. 3.47/3.67 1465 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_725_add__less__imp__less__left) # label(axiom). [clausify(547)]. 3.47/3.67 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). [resolve(1465,a,1460,a)]. 3.47/3.67 1466 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_295_add__le__imp__le__right) # label(axiom). [clausify(602)]. 3.47/3.67 1467 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_299_add__le__cancel__left) # label(axiom). [clausify(662)]. 3.47/3.67 1468 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_299_add__le__cancel__left) # label(axiom). [clausify(662)]. 3.47/3.69 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)). [resolve(1468,a,1460,a)]. 3.47/3.69 1469 ordere236663937imp_le(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption]. 3.47/3.69 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)). [resolve(1469,a,1461,a)]. 3.47/3.69 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1469,a,1462,a)]. 3.47/3.69 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(1469,a,1463,a)]. 3.47/3.69 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1469,a,1464,a)]. 3.47/3.69 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(1469,a,1465,a)]. 3.47/3.69 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(1469,a,1468,a)]. 3.47/3.69 1470 -ordere236663937imp_le(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C) # label(fact_370_min__add__distrib__left) # label(axiom). [clausify(844)]. 3.47/3.69 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),B). [resolve(1470,a,1460,a)]. 3.47/3.69 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),B). [resolve(1470,a,1469,a)]. 3.47/3.69 1471 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_726_add__less__imp__less__right) # label(axiom). [clausify(902)]. 3.47/3.69 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(1471,a,1460,a)]. 3.47/3.69 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(1471,a,1469,a)]. 3.47/3.69 1472 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) # label(fact_730_add__less__cancel__left) # label(axiom). [clausify(960)]. 3.56/3.78 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))). [resolve(1472,a,1460,a)]. 3.56/3.78 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))). [resolve(1472,a,1469,a)]. 3.56/3.78 1473 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) # label(fact_730_add__less__cancel__left) # label(axiom). [clausify(960)]. 3.56/3.78 1474 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_731_add__less__cancel__right) # label(axiom). [clausify(1073)]. 3.56/3.78 1475 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_731_add__less__cancel__right) # label(axiom). [clausify(1073)]. 3.56/3.78 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(1475,a,1460,a)]. 3.56/3.78 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(1475,a,1469,a)]. 3.56/3.78 1476 comm_monoid_add(int) # label(arity_Int_Oint___Groups_Ocomm__monoid__add) # label(axiom). [assumption]. 3.56/3.78 1477 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(B,A,E,D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C)) # label(fact_218_setsum_Oinsert) # label(axiom). [clausify(72)]. 3.56/3.78 1478 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(D,bool),A,hAPP(fun(D,A),fun(fun(D,bool),A),big_co1399186613setsum(D,A),hAPP(fun(D,fun(B,bool)),fun(D,A),hAPP(fun(fun(B,bool),A),fun(fun(D,fun(B,bool)),fun(D,A)),combb(fun(B,bool),A,D),hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E)),hAPP(fun(D,fun(B,bool)),fun(D,fun(B,bool)),hAPP(fun(fun(B,bool),fun(B,bool)),fun(fun(D,fun(B,bool)),fun(D,fun(B,bool))),combb(fun(B,bool),fun(B,bool),D),collect(B)),hAPP(fun(D,fun(B,bool)),fun(D,fun(B,bool)),hAPP(fun(fun(B,bool),fun(B,bool)),fun(fun(D,fun(B,bool)),fun(D,fun(B,bool))),combb(fun(B,bool),fun(B,bool),D),hAPP(fun(B,fun(bool,bool)),fun(fun(B,bool),fun(B,bool)),combs(B,bool,bool),hAPP(fun(B,bool),fun(B,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(B,bool),fun(B,fun(bool,bool))),combb(bool,fun(bool,bool),B),fconj),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,fun(fun(B,bool),bool)),fun(fun(B,bool),fun(B,bool)),combc(B,fun(B,bool),bool),member(B)),C)))),hAPP(fun(B,fun(D,bool)),fun(D,fun(B,bool)),combc(B,D,bool),hAPP(fun(B,D),fun(B,fun(D,bool)),hAPP(fun(D,fun(D,bool)),fun(fun(B,D),fun(B,fun(D,bool))),combb(D,fun(D,bool),B),fequal(D)),F)))))),hAPP(fun(B,bool),fun(D,bool),hAPP(fun(B,D),fun(fun(B,bool),fun(D,bool)),image(B,D),F),C)) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) # label(fact_208_setsum__image__gen) # label(axiom). [clausify(87)]. 3.56/3.78 1479 -comm_monoid_add(A) | -ordere223160158up_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | ti(fun(B,bool),C) = bot_bot(fun(B,bool)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f28(B,A,D,E,C)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C))) # label(fact_847_setsum__strict__mono) # label(axiom). [clausify(159)]. 3.56/3.78 1480 -comm_monoid_add(A) | -ordere223160158up_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | ti(fun(B,bool),C) = bot_bot(fun(B,bool)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(B,A,D,f28(B,A,D,E,C))),hAPP(B,A,E,f28(B,A,D,E,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C))) # label(fact_847_setsum__strict__mono) # label(axiom). [clausify(159)]. 3.56/3.78 1481 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(B,A,E,D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),bot_bot(fun(B,bool)))))) # label(fact_212_setsum_Oremove) # label(axiom). [clausify(189)]. 3.56/3.78 1482 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f38(B,A,D,E,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C) # label(fact_210_setsum_Ocong) # label(axiom). [clausify(223)]. 3.56/3.78 1483 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(B,A,D,f38(B,A,E,D,C)) != hAPP(B,A,E,f38(B,A,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) # label(fact_210_setsum_Ocong) # label(axiom). [clausify(223)]. 3.56/3.78 1484 -ordere779506340up_add(A) | -comm_monoid_add(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f64(B,A,C,D,E)),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E))) # label(fact_333_setsum__mono) # label(axiom). [clausify(359)]. 3.56/3.78 1485 -ordere779506340up_add(A) | -comm_monoid_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,C,f64(B,A,C,D,E))),hAPP(B,A,D,f64(B,A,C,D,E)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E))) # label(fact_333_setsum__mono) # label(axiom). [clausify(359)]. 3.56/3.78 1486 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(B,A,E,D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),bot_bot(fun(B,bool)))))) # label(fact_213_setsum__diff1_H) # label(axiom). [clausify(371)]. 3.56/3.78 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,D,C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B)). [resolve(1476,a,1477,a)]. 3.56/3.78 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(C,bool),int,hAPP(fun(C,int),fun(fun(C,bool),int),big_co1399186613setsum(C,int),hAPP(fun(C,fun(A,bool)),fun(C,int),hAPP(fun(fun(A,bool),int),fun(fun(C,fun(A,bool)),fun(C,int)),combb(fun(A,bool),int,C),hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),collect(A)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),hAPP(fun(A,C),fun(A,fun(C,bool)),hAPP(fun(C,fun(C,bool)),fun(fun(A,C),fun(A,fun(C,bool))),combb(C,fun(C,bool),A),fequal(C)),E)))))),hAPP(fun(A,bool),fun(C,bool),hAPP(fun(A,C),fun(fun(A,bool),fun(C,bool)),image(A,C),E),B)) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B). [resolve(1476,a,1478,a)]. 3.56/3.78 Derived: -ordere223160158up_add(int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f28(A,int,C,D,B)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B))). [resolve(1476,a,1479,a)]. 3.56/3.78 Derived: -ordere223160158up_add(int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,C,f28(A,int,C,D,B))),hAPP(A,int,D,f28(A,int,C,D,B)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B))). [resolve(1476,a,1480,a)]. 3.56/3.78 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,D,C)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))). [resolve(1476,a,1481,a)]. 3.56/3.78 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f38(A,int,C,D,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B). [resolve(1476,a,1482,a)]. 3.60/3.79 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,int,C,f38(A,int,D,C,B)) != hAPP(A,int,D,f38(A,int,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B). [resolve(1476,a,1483,a)]. 3.60/3.79 Derived: -ordere779506340up_add(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f64(A,int,B,C,D)),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D))). [resolve(1476,a,1484,b)]. 3.60/3.79 Derived: -ordere779506340up_add(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,B,f64(A,int,B,C,D))),hAPP(A,int,C,f64(A,int,B,C,D)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D))). [resolve(1476,a,1485,b)]. 3.60/3.79 1487 -comm_monoid_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),one_one(nat)))) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),E))) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C))),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),E)))) # label(fact_843_setsum__ub__add__nat) # label(axiom). [clausify(524)]. 3.60/3.79 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D)))). [resolve(1487,a,1476,a)]. 3.60/3.79 1488 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(D,bool),bool,finite_finite_1(D),E)) | hAPP(fun(D,bool),A,hAPP(fun(D,A),fun(fun(D,bool),A),big_co1399186613setsum(D,A),hAPP(fun(D,fun(B,bool)),fun(D,A),hAPP(fun(D,fun(fun(B,bool),A)),fun(fun(D,fun(B,bool)),fun(D,A)),combs(D,fun(B,bool),A),hAPP(fun(D,fun(B,A)),fun(D,fun(fun(B,bool),A)),hAPP(fun(fun(B,A),fun(fun(B,bool),A)),fun(fun(D,fun(B,A)),fun(D,fun(fun(B,bool),A))),combb(fun(B,A),fun(fun(B,bool),A),D),big_co1399186613setsum(B,A)),hAPP(fun(B,fun(D,A)),fun(D,fun(B,A)),combc(B,D,A),F))),hAPP(fun(D,fun(B,bool)),fun(D,fun(B,bool)),hAPP(fun(fun(B,bool),fun(B,bool)),fun(fun(D,fun(B,bool)),fun(D,fun(B,bool))),combb(fun(B,bool),fun(B,bool),D),collect(B)),hAPP(fun(D,fun(B,bool)),fun(D,fun(B,bool)),hAPP(fun(fun(B,bool),fun(B,bool)),fun(fun(D,fun(B,bool)),fun(D,fun(B,bool))),combb(fun(B,bool),fun(B,bool),D),hAPP(fun(B,fun(bool,bool)),fun(fun(B,bool),fun(B,bool)),combs(B,bool,bool),hAPP(fun(B,bool),fun(B,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(B,bool),fun(B,fun(bool,bool))),combb(bool,fun(bool,bool),B),fconj),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,fun(fun(B,bool),bool)),fun(fun(B,bool),fun(B,bool)),combc(B,fun(B,bool),bool),member(B)),C)))),hAPP(fun(B,fun(D,bool)),fun(D,fun(B,bool)),combc(B,D,bool),V6))))),E) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,fun(D,bool)),fun(B,A),hAPP(fun(B,fun(fun(D,bool),A)),fun(fun(B,fun(D,bool)),fun(B,A)),combs(B,fun(D,bool),A),hAPP(fun(B,fun(D,A)),fun(B,fun(fun(D,bool),A)),hAPP(fun(fun(D,A),fun(fun(D,bool),A)),fun(fun(B,fun(D,A)),fun(B,fun(fun(D,bool),A))),combb(fun(D,A),fun(fun(D,bool),A),B),big_co1399186613setsum(D,A)),F)),hAPP(fun(B,fun(D,bool)),fun(B,fun(D,bool)),hAPP(fun(fun(D,bool),fun(D,bool)),fun(fun(B,fun(D,bool)),fun(B,fun(D,bool))),combb(fun(D,bool),fun(D,bool),B),collect(D)),hAPP(fun(B,fun(D,bool)),fun(B,fun(D,bool)),hAPP(fun(fun(D,bool),fun(D,bool)),fun(fun(B,fun(D,bool)),fun(B,fun(D,bool))),combb(fun(D,bool),fun(D,bool),B),hAPP(fun(D,fun(bool,bool)),fun(fun(D,bool),fun(D,bool)),combs(D,bool,bool),hAPP(fun(D,bool),fun(D,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(D,bool),fun(D,fun(bool,bool))),combb(bool,fun(bool,bool),D),fconj),hAPP(fun(D,bool),fun(D,bool),hAPP(fun(D,fun(fun(D,bool),bool)),fun(fun(D,bool),fun(D,bool)),combc(D,fun(D,bool),bool),member(D)),E)))),V6)))),C) # label(fact_211_setsum__setsum__restrict) # label(axiom). [clausify(650)]. 3.60/3.80 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),D)) | hAPP(fun(C,bool),int,hAPP(fun(C,int),fun(fun(C,bool),int),big_co1399186613setsum(C,int),hAPP(fun(C,fun(A,bool)),fun(C,int),hAPP(fun(C,fun(fun(A,bool),int)),fun(fun(C,fun(A,bool)),fun(C,int)),combs(C,fun(A,bool),int),hAPP(fun(C,fun(A,int)),fun(C,fun(fun(A,bool),int)),hAPP(fun(fun(A,int),fun(fun(A,bool),int)),fun(fun(C,fun(A,int)),fun(C,fun(fun(A,bool),int))),combb(fun(A,int),fun(fun(A,bool),int),C),big_co1399186613setsum(A,int)),hAPP(fun(A,fun(C,int)),fun(C,fun(A,int)),combc(A,C,int),E))),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),collect(A)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),F))))),D) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,fun(C,bool)),fun(A,int),hAPP(fun(A,fun(fun(C,bool),int)),fun(fun(A,fun(C,bool)),fun(A,int)),combs(A,fun(C,bool),int),hAPP(fun(A,fun(C,int)),fun(A,fun(fun(C,bool),int)),hAPP(fun(fun(C,int),fun(fun(C,bool),int)),fun(fun(A,fun(C,int)),fun(A,fun(fun(C,bool),int))),combb(fun(C,int),fun(fun(C,bool),int),A),big_co1399186613setsum(C,int)),E)),hAPP(fun(A,fun(C,bool)),fun(A,fun(C,bool)),hAPP(fun(fun(C,bool),fun(C,bool)),fun(fun(A,fun(C,bool)),fun(A,fun(C,bool))),combb(fun(C,bool),fun(C,bool),A),collect(C)),hAPP(fun(A,fun(C,bool)),fun(A,fun(C,bool)),hAPP(fun(fun(C,bool),fun(C,bool)),fun(fun(A,fun(C,bool)),fun(A,fun(C,bool))),combb(fun(C,bool),fun(C,bool),A),hAPP(fun(C,fun(bool,bool)),fun(fun(C,bool),fun(C,bool)),combs(C,bool,bool),hAPP(fun(C,bool),fun(C,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(C,bool),fun(C,fun(bool,bool))),combb(bool,fun(bool,bool),C),fconj),hAPP(fun(C,bool),fun(C,bool),hAPP(fun(C,fun(fun(C,bool),bool)),fun(fun(C,bool),fun(C,bool)),combc(C,fun(C,bool),bool),member(C)),D)))),F)))),B). [resolve(1488,a,1476,a)]. 3.60/3.80 1489 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),E),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(B,A,D,E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),E),bot_bot(fun(B,bool)))))) # label(fact_214_setsum_Oinsert__remove) # label(axiom). [clausify(701)]. 3.60/3.80 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,C,D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),bot_bot(fun(A,bool)))))). [resolve(1489,a,1476,a)]. 3.60/3.80 1490 -comm_monoid_add(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f126(B,A,C,D,E)),E)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E) # label(fact_254_setsum__cong2) # label(axiom). [clausify(717)]. 3.60/3.80 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f126(A,int,B,C,D)),D)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D). [resolve(1490,a,1476,a)]. 3.60/3.80 1491 -comm_monoid_add(A) | hAPP(B,A,C,f126(B,A,D,C,E)) != hAPP(B,A,D,f126(B,A,D,C,E)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E) # label(fact_254_setsum__cong2) # label(axiom). [clausify(717)]. 3.60/3.80 Derived: hAPP(A,int,B,f126(A,int,C,B,D)) != hAPP(A,int,C,f126(A,int,C,B,D)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D). [resolve(1491,a,1476,a)]. 3.60/3.80 1492 -comm_monoid_add(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f129(B,A,E,F,D,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),F),C) # label(fact_256_setsum_OF__cong) # label(axiom). [clausify(730)]. 3.60/3.80 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f129(A,int,D,E,C,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),E),B). [resolve(1492,a,1476,a)]. 3.60/3.80 1493 -comm_monoid_add(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hAPP(B,A,E,f129(B,A,E,F,D,C)) != hAPP(B,A,F,f129(B,A,E,F,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),F),C) # label(fact_256_setsum_OF__cong) # label(axiom). [clausify(730)]. 3.60/3.80 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,int,D,f129(A,int,D,E,C,B)) != hAPP(A,int,E,f129(A,int,D,E,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),E),B). [resolve(1493,a,1476,a)]. 3.60/3.80 1494 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(B,A,E,D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C)) # label(fact_217_setsum__insert) # label(axiom). [clausify(787)]. 3.60/3.81 1495 -comm_monoid_add(A) | big_co1399186613setsum(B,A) = ti(fun(fun(B,A),fun(fun(B,bool),A)),big_co1399186613setsum(B,A)) # label(tsy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_res) # label(axiom). [clausify(801)]. 3.60/3.81 Derived: big_co1399186613setsum(A,int) = ti(fun(fun(A,int),fun(fun(A,bool),int)),big_co1399186613setsum(A,int)). [resolve(1495,a,1476,a)]. 3.60/3.81 1496 -comm_monoid_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,D,B)),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),B),C))) # label(fact_935_setsum__head) # label(axiom). [clausify(827)]. 3.60/3.81 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,C,A)),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),A),B))). [resolve(1496,a,1476,a)]. 3.60/3.81 1497 -comm_monoid_add(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f155(B,A,E,F,D,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),F),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D) # label(fact_255_setsum__cong) # label(axiom). [clausify(878)]. 3.60/3.81 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f155(A,int,D,E,C,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),E),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C). [resolve(1497,a,1476,a)]. 3.60/3.81 1498 -comm_monoid_add(A) | ti(fun(B,bool),C) != ti(fun(B,bool),D) | hAPP(B,A,E,f155(B,A,F,E,D,C)) != hAPP(B,A,F,f155(B,A,F,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),F),D) # label(fact_255_setsum__cong) # label(axiom). [clausify(878)]. 3.60/3.81 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,int,D,f155(A,int,E,D,C,B)) != hAPP(A,int,E,f155(A,int,E,D,C,B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B) = hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),E),C). [resolve(1498,a,1476,a)]. 3.60/3.81 1499 -comm_monoid_add(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),plus_plus(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E)) # label(fact_215_setsum__addf) # label(axiom). [clausify(879)]. 3.60/3.81 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(A,fun(int,int)),fun(fun(A,int),fun(A,int)),combs(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),plus_plus(int)),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D)). [resolve(1499,a,1476,a)]. 3.60/3.82 1500 -comm_monoid_add(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),B),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),D),E)) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),E),C))) # label(fact_835_setsum__shift__bounds__cl__nat__ivl) # label(axiom). [clausify(948)]. 3.60/3.82 Derived: hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),C),D)) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),B))). [resolve(1500,a,1476,a)]. 3.60/3.82 1501 -comm_monoid_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),plus_plus(A)),D)),E)),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C)) # label(fact_216_setsum_Odistrib) # label(axiom). [clausify(981)]. 3.60/3.82 1502 -comm_monoid_add(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(C,bool),fun(B,A),hAPP(fun(B,fun(fun(C,bool),A)),fun(fun(C,bool),fun(B,A)),combc(B,fun(C,bool),A),hAPP(fun(B,fun(C,A)),fun(B,fun(fun(C,bool),A)),hAPP(fun(fun(C,A),fun(fun(C,bool),A)),fun(fun(B,fun(C,A)),fun(B,fun(fun(C,bool),A))),combb(fun(C,A),fun(fun(C,bool),A),B),big_co1399186613setsum(C,A)),hAPP(fun(C,fun(B,A)),fun(B,fun(C,A)),combc(C,B,A),D))),E)),F) = hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),hAPP(fun(B,bool),fun(C,A),hAPP(fun(C,fun(fun(B,bool),A)),fun(fun(B,bool),fun(C,A)),combc(C,fun(B,bool),A),hAPP(fun(C,fun(B,A)),fun(C,fun(fun(B,bool),A)),hAPP(fun(fun(B,A),fun(fun(B,bool),A)),fun(fun(C,fun(B,A)),fun(C,fun(fun(B,bool),A))),combb(fun(B,A),fun(fun(B,bool),A),C),big_co1399186613setsum(B,A)),D)),F)),E) # label(fact_180_setsum__commute) # label(axiom). [clausify(1031)]. 3.60/3.82 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(B,bool),fun(A,int),hAPP(fun(A,fun(fun(B,bool),int)),fun(fun(B,bool),fun(A,int)),combc(A,fun(B,bool),int),hAPP(fun(A,fun(B,int)),fun(A,fun(fun(B,bool),int)),hAPP(fun(fun(B,int),fun(fun(B,bool),int)),fun(fun(A,fun(B,int)),fun(A,fun(fun(B,bool),int))),combb(fun(B,int),fun(fun(B,bool),int),A),big_co1399186613setsum(B,int)),hAPP(fun(B,fun(A,int)),fun(A,fun(B,int)),combc(B,A,int),C))),D)),E) = hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),hAPP(fun(A,bool),fun(B,int),hAPP(fun(B,fun(fun(A,bool),int)),fun(fun(A,bool),fun(B,int)),combc(B,fun(A,bool),int),hAPP(fun(B,fun(A,int)),fun(B,fun(fun(A,bool),int)),hAPP(fun(fun(A,int),fun(fun(A,bool),int)),fun(fun(B,fun(A,int)),fun(B,fun(fun(A,bool),int))),combb(fun(A,int),fun(fun(A,bool),int),B),big_co1399186613setsum(A,int)),C)),E)),D). [resolve(1502,a,1476,a)]. 3.60/3.82 1503 comm_monoid_add(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__add) # label(axiom). [assumption]. 3.60/3.82 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(A,nat,D,C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B)). [resolve(1503,a,1477,a)]. 3.60/3.82 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(C,bool),nat,hAPP(fun(C,nat),fun(fun(C,bool),nat),big_co1399186613setsum(C,nat),hAPP(fun(C,fun(A,bool)),fun(C,nat),hAPP(fun(fun(A,bool),nat),fun(fun(C,fun(A,bool)),fun(C,nat)),combb(fun(A,bool),nat,C),hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),collect(A)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),hAPP(fun(A,C),fun(A,fun(C,bool)),hAPP(fun(C,fun(C,bool)),fun(fun(A,C),fun(A,fun(C,bool))),combb(C,fun(C,bool),A),fequal(C)),E)))))),hAPP(fun(A,bool),fun(C,bool),hAPP(fun(A,C),fun(fun(A,bool),fun(C,bool)),image(A,C),E),B)) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B). [resolve(1503,a,1478,a)]. 3.60/3.82 Derived: -ordere223160158up_add(nat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f28(A,nat,C,D,B)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),B)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B))). [resolve(1503,a,1479,a)]. 3.60/3.82 Derived: -ordere223160158up_add(nat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(A,nat,C,f28(A,nat,C,D,B))),hAPP(A,nat,D,f28(A,nat,C,D,B)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),B)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B))). [resolve(1503,a,1480,a)]. 3.60/3.82 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(A,nat,D,C)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),bot_bot(fun(A,bool)))))). [resolve(1503,a,1481,a)]. 3.60/3.82 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f38(A,nat,C,D,B)),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),B). [resolve(1503,a,1482,a)]. 3.60/3.82 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,nat,C,f38(A,nat,D,C,B)) != hAPP(A,nat,D,f38(A,nat,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B). [resolve(1503,a,1483,a)]. 3.60/3.82 Derived: -ordere779506340up_add(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f64(A,nat,B,C,D)),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),D))). [resolve(1503,a,1484,b)]. 3.60/3.82 Derived: -ordere779506340up_add(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(A,nat,B,f64(A,nat,B,C,D))),hAPP(A,nat,C,f64(A,nat,B,C,D)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),D))). [resolve(1503,a,1485,b)]. 3.60/3.82 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D)))). [resolve(1503,a,1487,a)]. 3.60/3.83 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(C,bool),bool,finite_finite_1(C),D)) | hAPP(fun(C,bool),nat,hAPP(fun(C,nat),fun(fun(C,bool),nat),big_co1399186613setsum(C,nat),hAPP(fun(C,fun(A,bool)),fun(C,nat),hAPP(fun(C,fun(fun(A,bool),nat)),fun(fun(C,fun(A,bool)),fun(C,nat)),combs(C,fun(A,bool),nat),hAPP(fun(C,fun(A,nat)),fun(C,fun(fun(A,bool),nat)),hAPP(fun(fun(A,nat),fun(fun(A,bool),nat)),fun(fun(C,fun(A,nat)),fun(C,fun(fun(A,bool),nat))),combb(fun(A,nat),fun(fun(A,bool),nat),C),big_co1399186613setsum(A,nat)),hAPP(fun(A,fun(C,nat)),fun(C,fun(A,nat)),combc(A,C,nat),E))),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),collect(A)),hAPP(fun(C,fun(A,bool)),fun(C,fun(A,bool)),hAPP(fun(fun(A,bool),fun(A,bool)),fun(fun(C,fun(A,bool)),fun(C,fun(A,bool))),combb(fun(A,bool),fun(A,bool),C),hAPP(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),hAPP(fun(A,bool),fun(A,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B)))),hAPP(fun(A,fun(C,bool)),fun(C,fun(A,bool)),combc(A,C,bool),F))))),D) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(fun(A,fun(C,bool)),fun(A,nat),hAPP(fun(A,fun(fun(C,bool),nat)),fun(fun(A,fun(C,bool)),fun(A,nat)),combs(A,fun(C,bool),nat),hAPP(fun(A,fun(C,nat)),fun(A,fun(fun(C,bool),nat)),hAPP(fun(fun(C,nat),fun(fun(C,bool),nat)),fun(fun(A,fun(C,nat)),fun(A,fun(fun(C,bool),nat))),combb(fun(C,nat),fun(fun(C,bool),nat),A),big_co1399186613setsum(C,nat)),E)),hAPP(fun(A,fun(C,bool)),fun(A,fun(C,bool)),hAPP(fun(fun(C,bool),fun(C,bool)),fun(fun(A,fun(C,bool)),fun(A,fun(C,bool))),combb(fun(C,bool),fun(C,bool),A),collect(C)),hAPP(fun(A,fun(C,bool)),fun(A,fun(C,bool)),hAPP(fun(fun(C,bool),fun(C,bool)),fun(fun(A,fun(C,bool)),fun(A,fun(C,bool))),combb(fun(C,bool),fun(C,bool),A),hAPP(fun(C,fun(bool,bool)),fun(fun(C,bool),fun(C,bool)),combs(C,bool,bool),hAPP(fun(C,bool),fun(C,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(C,bool),fun(C,fun(bool,bool))),combb(bool,fun(bool,bool),C),fconj),hAPP(fun(C,bool),fun(C,bool),hAPP(fun(C,fun(fun(C,bool),bool)),fun(fun(C,bool),fun(C,bool)),combc(C,fun(C,bool),bool),member(C)),D)))),F)))),B). [resolve(1503,a,1488,a)]. 3.60/3.83 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(A,nat,C,D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),D),bot_bot(fun(A,bool)))))). [resolve(1503,a,1489,a)]. 3.60/3.83 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f126(A,nat,B,C,D)),D)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),D) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D). [resolve(1503,a,1490,a)]. 3.60/3.83 Derived: hAPP(A,nat,B,f126(A,nat,C,B,D)) != hAPP(A,nat,C,f126(A,nat,C,B,D)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),D). [resolve(1503,a,1491,a)]. 3.60/3.83 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f129(A,nat,D,E,C,B)),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),E),B). [resolve(1503,a,1492,a)]. 3.60/3.83 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,nat,D,f129(A,nat,D,E,C,B)) != hAPP(A,nat,E,f129(A,nat,D,E,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),E),B). [resolve(1503,a,1493,a)]. 3.60/3.83 Derived: big_co1399186613setsum(A,nat) = ti(fun(fun(A,nat),fun(fun(A,bool),nat)),big_co1399186613setsum(A,nat)). [resolve(1503,a,1495,a)]. 3.60/3.83 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,C,A)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr1471790799AtMost(nat),A),B))). [resolve(1503,a,1496,a)]. 3.60/3.83 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f155(A,nat,D,E,C,B)),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),E),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),C). [resolve(1503,a,1497,a)]. 3.60/3.83 Derived: ti(fun(A,bool),B) != ti(fun(A,bool),C) | hAPP(A,nat,D,f155(A,nat,E,D,C,B)) != hAPP(A,nat,E,f155(A,nat,E,D,C,B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),E),C). [resolve(1503,a,1498,a)]. 3.71/3.91 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(fun(A,nat),fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(fun(A,nat),fun(A,nat)),combs(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(A,fun(nat,nat))),combb(nat,fun(nat,nat),A),plus_plus(nat)),B)),C)),D) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D)),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),D)). [resolve(1503,a,1499,a)]. 3.71/3.91 Derived: hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),C),D)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),B))). [resolve(1503,a,1500,a)]. 3.71/3.91 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(fun(B,bool),fun(A,nat),hAPP(fun(A,fun(fun(B,bool),nat)),fun(fun(B,bool),fun(A,nat)),combc(A,fun(B,bool),nat),hAPP(fun(A,fun(B,nat)),fun(A,fun(fun(B,bool),nat)),hAPP(fun(fun(B,nat),fun(fun(B,bool),nat)),fun(fun(A,fun(B,nat)),fun(A,fun(fun(B,bool),nat))),combb(fun(B,nat),fun(fun(B,bool),nat),A),big_co1399186613setsum(B,nat)),hAPP(fun(B,fun(A,nat)),fun(A,fun(B,nat)),combc(B,A,nat),C))),D)),E) = hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),hAPP(fun(A,bool),fun(B,nat),hAPP(fun(B,fun(fun(A,bool),nat)),fun(fun(A,bool),fun(B,nat)),combc(B,fun(A,bool),nat),hAPP(fun(B,fun(A,nat)),fun(B,fun(fun(A,bool),nat)),hAPP(fun(fun(A,nat),fun(fun(A,bool),nat)),fun(fun(B,fun(A,nat)),fun(B,fun(fun(A,bool),nat))),combb(fun(A,nat),fun(fun(A,bool),nat),B),big_co1399186613setsum(A,nat)),C)),E)),D). [resolve(1503,a,1502,a)]. 3.71/3.91 1504 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_981_mult__less__cancel__right__disj) # label(axiom). [clausify(126)]. 3.71/3.91 1505 linord581940658strict(int) # label(arity_Int_Oint___Rings_Olinordered__ring__strict) # label(axiom). [assumption]. 3.71/3.91 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A))). [resolve(1504,a,1505,a)]. 3.71/3.91 1506 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) # label(fact_981_mult__less__cancel__right__disj) # label(axiom). [clausify(126)]. 3.71/3.91 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A))). [resolve(1506,a,1505,a)]. 3.71/3.92 1507 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_981_mult__less__cancel__right__disj) # label(axiom). [clausify(126)]. 3.71/3.92 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A))). [resolve(1507,a,1505,a)]. 3.71/3.92 1508 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) # label(fact_981_mult__less__cancel__right__disj) # label(axiom). [clausify(126)]. 3.71/3.92 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A))). [resolve(1508,a,1505,a)]. 3.71/3.92 1509 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_981_mult__less__cancel__right__disj) # label(axiom). [clausify(126)]. 3.71/3.92 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))). [resolve(1509,a,1505,a)]. 3.71/3.92 1510 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_981_mult__less__cancel__right__disj) # label(axiom). [clausify(126)]. 3.71/3.92 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))). [resolve(1510,a,1505,a)]. 3.71/3.92 1511 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_995_mult__strict__right__mono__neg) # label(axiom). [clausify(161)]. 3.71/3.92 1512 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_991_mult__neg__neg) # label(axiom). [clausify(421)]. 3.71/3.92 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(1512,a,1505,a)]. 3.71/3.95 1513 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_996_mult__strict__left__mono__neg) # label(axiom). [clausify(469)]. 3.71/3.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A))). [resolve(1513,a,1505,a)]. 3.71/3.95 1514 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_983_mult__less__cancel__left__pos) # label(axiom). [clausify(917)]. 3.71/3.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))). [resolve(1514,a,1505,a)]. 3.71/3.95 1515 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_983_mult__less__cancel__left__pos) # label(axiom). [clausify(917)]. 3.71/3.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))). [resolve(1515,a,1505,a)]. 3.71/3.95 1516 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)) # label(fact_989_mult__less__cancel__left__neg) # label(axiom). [clausify(980)]. 3.71/3.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),B)). [resolve(1516,a,1505,a)]. 3.71/3.95 1517 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),C)) # label(fact_989_mult__less__cancel__left__neg) # label(axiom). [clausify(980)]. 3.71/3.95 1518 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_982_mult__less__cancel__left__disj) # label(axiom). [clausify(1006)]. 3.71/3.95 1519 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_982_mult__less__cancel__left__disj) # label(axiom). [clausify(1006)]. 3.86/4.06 1520 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_982_mult__less__cancel__left__disj) # label(axiom). [clausify(1006)]. 3.86/4.06 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))). [resolve(1520,a,1505,a)]. 3.86/4.06 1521 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_982_mult__less__cancel__left__disj) # label(axiom). [clausify(1006)]. 3.86/4.06 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(1521,a,1505,a)]. 3.86/4.06 1522 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_982_mult__less__cancel__left__disj) # label(axiom). [clausify(1006)]. 3.86/4.06 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))). [resolve(1522,a,1505,a)]. 3.86/4.06 1523 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_982_mult__less__cancel__left__disj) # label(axiom). [clausify(1006)]. 3.86/4.06 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))). [resolve(1523,a,1505,a)]. 3.86/4.06 1524 monoid_mult(int) # label(arity_Int_Oint___Groups_Omonoid__mult) # label(axiom). [assumption]. 3.86/4.06 1525 -monoid_mult(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) # label(fact_632_mult__1__left) # label(axiom). [clausify(91)]. 3.86/4.06 1526 -monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),D) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) # label(fact_876_power__mult) # label(axiom). [clausify(218)]. 3.86/4.06 1527 -monoid_mult(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) # label(fact_629_mult__1__right) # label(axiom). [clausify(455)]. 3.86/4.06 1528 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),D)) # label(fact_880_power__add) # label(axiom). [clausify(901)]. 3.93/4.16 1529 -monoid_mult(A) | ti(A,B) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),one_one(nat)) # label(fact_877_power__one__right) # label(axiom). [clausify(993)]. 3.93/4.16 1530 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) # label(fact_873_power__commutes) # label(axiom). [clausify(999)]. 3.93/4.16 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)). [resolve(1530,a,1524,a)]. 3.93/4.16 1531 -monoid_mult(A) | one_one(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),one_one(A)),B) # label(fact_874_power__one) # label(axiom). [clausify(1007)]. 3.93/4.16 Derived: one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),one_one(int)),A). [resolve(1531,a,1524,a)]. 3.93/4.16 1532 monoid_mult(nat) # label(arity_Nat_Onat___Groups_Omonoid__mult) # label(axiom). [assumption]. 3.93/4.16 Derived: one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),one_one(nat)),A). [resolve(1532,a,1531,a)]. 3.93/4.16 1533 linord20386208strict(nat) # label(arity_Nat_Onat___Rings_Olinordered__semiring__strict) # label(axiom). [assumption]. 3.93/4.16 1534 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_992_mult__strict__right__mono) # label(axiom). [clausify(97)]. 3.93/4.16 1535 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_993_mult__strict__left__mono) # label(axiom). [clausify(164)]. 3.93/4.16 1536 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),zero_zero(A))) # label(fact_986_mult__pos__neg2) # label(axiom). [clausify(542)]. 3.93/4.16 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))). [resolve(1533,a,1534,a)]. 3.93/4.16 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))). [resolve(1533,a,1535,a)]. 3.93/4.16 1537 linord20386208strict(int) # label(arity_Int_Oint___Rings_Olinordered__semiring__strict) # label(axiom). [assumption]. 3.93/4.16 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)),zero_zero(int))). [resolve(1537,a,1536,a)]. 3.93/4.16 1538 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_988_zero__less__mult__pos2) # label(axiom). [clausify(596)]. 3.93/4.16 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)). [resolve(1538,a,1533,a)]. 3.99/4.19 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)). [resolve(1538,a,1537,a)]. 3.99/4.19 1539 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_990_mult__neg__pos) # label(axiom). [clausify(823)]. 3.99/4.19 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),zero_zero(nat))). [resolve(1539,a,1533,a)]. 3.99/4.19 1540 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_987_zero__less__mult__pos) # label(axiom). [clausify(913)]. 3.99/4.19 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)). [resolve(1540,a,1533,a)]. 3.99/4.19 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)). [resolve(1540,a,1537,a)]. 3.99/4.19 1541 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_985_mult__pos__neg) # label(axiom). [clausify(929)]. 3.99/4.19 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),zero_zero(nat))). [resolve(1541,a,1533,a)]. 3.99/4.19 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),zero_zero(int))). [resolve(1541,a,1537,a)]. 3.99/4.19 1542 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_984_mult__pos__pos) # label(axiom). [clausify(1084)]. 3.99/4.19 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B))). [resolve(1542,a,1533,a)]. 3.99/4.19 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(1542,a,1537,a)]. 4.03/4.30 1543 group_add(int) # label(arity_Int_Oint___Groups_Ogroup__add) # label(axiom). [assumption]. 4.03/4.30 1544 -group_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B)) # label(fact_502_minus__add) # label(axiom). [clausify(113)]. 4.03/4.30 1545 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),hAPP(A,A,uminus_uminus(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) # label(fact_511_diff__minus__eq__add) # label(axiom). [clausify(146)]. 4.03/4.30 1546 -group_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_503_add__minus__cancel) # label(axiom). [clausify(183)]. 4.03/4.30 1547 -group_add(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,uminus_uminus(A),B)) # label(fact_486_minus__minus) # label(axiom). [clausify(210)]. 4.03/4.30 Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),B)),hAPP(int,int,uminus_uminus(int),A)). [resolve(1543,a,1544,a)]. 4.03/4.30 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B). [resolve(1543,a,1545,a)]. 4.03/4.30 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),B)),A)). [resolve(1543,a,1546,a)]. 4.03/4.30 Derived: ti(int,A) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,uminus_uminus(int),A)). [resolve(1543,a,1547,a)]. 4.03/4.30 1548 -group_add(A) | ti(A,B) != hAPP(A,A,uminus_uminus(A),C) | ti(A,C) = hAPP(A,A,uminus_uminus(A),B) # label(fact_487_equation__minus__iff) # label(axiom). [clausify(439)]. 4.03/4.30 Derived: ti(int,A) != hAPP(int,int,uminus_uminus(int),B) | ti(int,B) = hAPP(int,int,uminus_uminus(int),A). [resolve(1548,a,1543,a)]. 4.03/4.30 1549 -group_add(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),C) | ti(A,C) != hAPP(A,A,uminus_uminus(A),B) # label(fact_487_equation__minus__iff) # label(axiom). [clausify(439)]. 4.03/4.30 1550 -group_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),C) # label(fact_222_add__diff__cancel) # label(axiom). [clausify(519)]. 4.03/4.30 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),B). [resolve(1550,a,1543,a)]. 4.03/4.30 1551 -group_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),C) # label(fact_221_diff__add__cancel) # label(axiom). [clausify(621)]. 4.03/4.30 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),B). [resolve(1551,a,1543,a)]. 4.03/4.30 1552 -group_add(A) | ti(A,B) != hAPP(A,A,uminus_uminus(A),C) | ti(A,C) = hAPP(A,A,uminus_uminus(A),B) # label(fact_488_minus__equation__iff) # label(axiom). [clausify(733)]. 4.03/4.30 1553 -group_add(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),C) | ti(A,C) != hAPP(A,A,uminus_uminus(A),B) # label(fact_488_minus__equation__iff) # label(axiom). [clausify(733)]. 4.03/4.30 1554 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) != hAPP(A,A,uminus_uminus(A),C) | ti(A,B) = ti(A,C) # label(fact_489_neg__equal__iff__equal) # label(axiom). [clausify(738)]. 4.03/4.30 Derived: hAPP(int,int,uminus_uminus(int),A) != hAPP(int,int,uminus_uminus(int),B) | ti(int,A) = ti(int,B). [resolve(1554,a,1543,a)]. 4.03/4.30 1555 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,uminus_uminus(A),C) | ti(A,B) != ti(A,C) # label(fact_489_neg__equal__iff__equal) # label(axiom). [clausify(738)]. 4.03/4.30 Derived: hAPP(int,int,uminus_uminus(int),A) = hAPP(int,int,uminus_uminus(int),B) | ti(int,A) != ti(int,B). [resolve(1555,a,1543,a)]. 4.03/4.30 1556 -group_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B)) # label(fact_504_minus__add__cancel) # label(axiom). [clausify(932)]. 4.20/4.40 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A)). [resolve(1556,a,1543,a)]. 4.20/4.40 1557 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_514_diff__def) # label(axiom). [clausify(1071)]. 4.20/4.40 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),B)). [resolve(1557,a,1543,a)]. 4.20/4.40 1558 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,B) = ti(A,D) | ti(A,C) = ti(A,E) # label(fact_223_crossproduct__eq) # label(axiom). [clausify(521)]. 4.20/4.40 1559 semiri456707255roduct(nat) # label(arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption]. 4.20/4.40 1560 semiri456707255roduct(int) # label(arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption]. 4.20/4.40 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)) | ti(nat,A) = ti(nat,C) | ti(nat,B) = ti(nat,D). [resolve(1558,a,1559,a)]. 4.20/4.40 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)) | ti(int,A) = ti(int,C) | ti(int,B) = ti(int,D). [resolve(1558,a,1560,a)]. 4.20/4.40 1561 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,B) != ti(A,D) # label(fact_223_crossproduct__eq) # label(axiom). [clausify(521)]. 4.20/4.40 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)) | ti(nat,A) != ti(nat,C). [resolve(1561,a,1559,a)]. 4.20/4.40 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)) | ti(int,A) != ti(int,C). [resolve(1561,a,1560,a)]. 4.20/4.40 1562 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,C) != ti(A,E) # label(fact_223_crossproduct__eq) # label(axiom). [clausify(521)]. 4.20/4.40 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)) | ti(nat,B) != ti(nat,D). [resolve(1562,a,1559,a)]. 4.31/4.51 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)) | ti(int,B) != ti(int,D). [resolve(1562,a,1560,a)]. 4.31/4.51 1563 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,B) != ti(A,D) # label(fact_249_crossproduct__noteq) # label(axiom). [clausify(651)]. 4.31/4.51 1564 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,C) != ti(A,E) # label(fact_249_crossproduct__noteq) # label(axiom). [clausify(651)]. 4.31/4.51 1565 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,B) = ti(A,D) | ti(A,C) = ti(A,E) # label(fact_249_crossproduct__noteq) # label(axiom). [clausify(651)]. 4.31/4.51 1566 -ab_semigroup_mult(A) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),times_times(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),times_times(A)),B)) # label(fact_125_fold1__insert) # label(axiom). [clausify(342)]. 4.31/4.51 1567 ab_semigroup_mult(int) # label(arity_Int_Oint___Groups_Oab__semigroup__mult) # label(axiom). [assumption]. 4.31/4.51 1568 ab_semigroup_mult(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__mult) # label(axiom). [assumption]. 4.31/4.51 Derived: ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),times_times(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),times_times(int)),A)). [resolve(1566,a,1567,a)]. 4.31/4.51 Derived: ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),times_times(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),times_times(nat)),A)). [resolve(1566,a,1568,a)]. 4.31/4.51 1569 -ab_semigroup_mult(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),fun(A,bool))),finite_fold_graph(A,A),times_times(A)),B),C),D)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),fun(A,bool))),finite_fold_graph(A,A),times_times(A)),E),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),D))) # label(fact_150_fold__graph__insert__swap) # label(axiom). [clausify(507)]. 4.33/4.52 Derived: -hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),fun(int,bool))),finite_fold_graph(int,int),times_times(int)),A),B),C)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),fun(int,bool))),finite_fold_graph(int,int),times_times(int)),D),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),C))). [resolve(1569,a,1567,a)]. 4.33/4.52 Derived: -hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),fun(nat,bool))),finite_fold_graph(nat,nat),times_times(nat)),A),B),C)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),fun(nat,bool))),finite_fold_graph(nat,nat),times_times(nat)),D),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D),C))). [resolve(1569,a,1568,a)]. 4.33/4.52 1570 -ab_semigroup_mult(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_2_res) # label(axiom). [clausify(559)]. 4.33/4.52 Derived: times_times(int) = ti(fun(int,fun(int,int)),times_times(int)). [resolve(1570,a,1567,a)]. 4.33/4.52 Derived: times_times(nat) = ti(fun(nat,fun(nat,nat)),times_times(nat)). [resolve(1570,a,1568,a)]. 4.33/4.52 1571 -ab_semigroup_mult(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),fun(A,bool))),finite_fold_graph(A,A),times_times(A)),B),C),D)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),E),C)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),fun(A,bool))),finite_fold_graph(A,A),times_times(A)),E),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),C),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),E),bot_bot(fun(A,bool)))))),D)) # label(fact_143_fold__graph__permute__diff) # label(axiom). [clausify(708)]. 4.33/4.52 Derived: -hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),fun(int,bool))),finite_fold_graph(int,int),times_times(int)),A),B),C)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),D),B)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),fun(int,bool))),finite_fold_graph(int,int),times_times(int)),D),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),A),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,bool),fun(int,bool)),minus_minus(fun(int,bool)),B),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),D),bot_bot(fun(int,bool)))))),C)). [resolve(1571,a,1567,a)]. 4.33/4.52 Derived: -hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),fun(nat,bool))),finite_fold_graph(nat,nat),times_times(nat)),A),B),C)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),D),B)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),fun(nat,bool))),finite_fold_graph(nat,nat),times_times(nat)),D),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),A),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,bool),fun(fun(nat,bool),fun(nat,bool)),minus_minus(fun(nat,bool)),B),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),D),bot_bot(fun(nat,bool)))))),C)). [resolve(1571,a,1568,a)]. 4.33/4.54 1572 -ab_semigroup_mult(A) | hBOOL(hAPP(fun(A,fun(A,A)),bool,finite100568337ommute(A,A),times_times(A))) # label(fact_192_comp__fun__commute) # label(axiom). [clausify(831)]. 4.33/4.54 Derived: hBOOL(hAPP(fun(int,fun(int,int)),bool,finite100568337ommute(int,int),times_times(int))). [resolve(1572,a,1567,a)]. 4.33/4.54 Derived: hBOOL(hAPP(fun(nat,fun(nat,nat)),bool,finite100568337ommute(nat,nat),times_times(nat))). [resolve(1572,a,1568,a)]. 4.33/4.54 1573 -ab_semigroup_mult(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f162(A,B)),f163(A,B))),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f162(A,B)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),f163(A,B)),bot_bot(fun(A,bool)))))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),times_times(A)),B)),B)) # label(fact_154_fold1__in) # label(axiom). [clausify(935)]. 4.33/4.54 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f162(int,A)),f163(int,A))),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f162(int,A)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),f163(int,A)),bot_bot(fun(int,bool)))))) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),times_times(int)),A)),A)). [resolve(1573,a,1567,a)]. 4.33/4.54 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | ti(fun(nat,bool),A) = bot_bot(fun(nat,bool)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f162(nat,A)),f163(nat,A))),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f162(nat,A)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),f163(nat,A)),bot_bot(fun(nat,bool)))))) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),times_times(nat)),A)),A)). [resolve(1573,a,1568,a)]. 4.33/4.54 1574 -ab_semigroup_mult(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),A,hAPP(fun(A,fun(A,A)),fun(fun(A,bool),A),finite_fold1(A),times_times(A)),hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),C),B)) = hAPP(fun(A,bool),A,hAPP(A,fun(fun(A,bool),A),hAPP(fun(A,fun(A,A)),fun(A,fun(fun(A,bool),A)),finite_fold(A,A),times_times(A)),C),B) # label(fact_205_fold1__eq__fold) # label(axiom). [clausify(1039)]. 4.33/4.54 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B),A)) | hAPP(fun(int,bool),int,hAPP(fun(int,fun(int,int)),fun(fun(int,bool),int),finite_fold1(int),times_times(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(int,fun(fun(int,bool),fun(int,bool)),insert(int),B),A)) = hAPP(fun(int,bool),int,hAPP(int,fun(fun(int,bool),int),hAPP(fun(int,fun(int,int)),fun(int,fun(fun(int,bool),int)),finite_fold(int,int),times_times(int)),B),A). [resolve(1574,a,1567,a)]. 4.33/4.63 Derived: -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),A)) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,bool),nat),finite_fold1(nat),times_times(nat)),hAPP(fun(nat,bool),fun(nat,bool),hAPP(nat,fun(fun(nat,bool),fun(nat,bool)),insert(nat),B),A)) = hAPP(fun(nat,bool),nat,hAPP(nat,fun(fun(nat,bool),nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(fun(nat,bool),nat)),finite_fold(nat,nat),times_times(nat)),B),A). [resolve(1574,a,1568,a)]. 4.33/4.63 1575 -ab_semigroup_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_243_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom). [clausify(1062)]. 4.33/4.63 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(1575,a,1568,a)]. 4.33/4.63 1576 ring(int) # label(arity_Int_Oint___Rings_Oring) # label(axiom). [assumption]. 4.33/4.63 1577 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) # label(fact_508_minus__mult__minus) # label(axiom). [clausify(122)]. 4.33/4.63 1578 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F) | ti(A,D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F) # label(fact_219_eq__add__iff2) # label(axiom). [clausify(234)]. 4.33/4.63 1579 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F) | ti(A,D) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F) # label(fact_219_eq__add__iff2) # label(axiom). [clausify(234)]. 4.33/4.63 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B). [resolve(1576,a,1577,a)]. 4.33/4.63 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E) | ti(int,C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),D),A)),B)),E). [resolve(1576,a,1578,a)]. 4.33/4.63 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E) | ti(int,C) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),D),A)),B)),E). [resolve(1576,a,1579,a)]. 4.33/4.63 1580 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,uminus_uminus(A),B)),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_507_minus__mult__commute) # label(axiom). [clausify(399)]. 4.33/4.63 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),A)),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,uminus_uminus(int),B)). [resolve(1580,a,1576,a)]. 4.54/4.76 1581 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F) | ti(A,F) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),C)),D) # label(fact_220_eq__add__iff1) # label(axiom). [clausify(505)]. 4.54/4.76 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E) | ti(int,E) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),B)),C). [resolve(1581,a,1576,a)]. 4.54/4.76 1582 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F) | ti(A,F) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),C)),D) # label(fact_220_eq__add__iff1) # label(axiom). [clausify(505)]. 4.54/4.76 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E) | ti(int,E) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),B)),C). [resolve(1582,a,1576,a)]. 4.54/4.76 1583 -ring(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),hAPP(fun(B,bool),fun(B,bool),hAPP(B,fun(fun(B,bool),fun(B,bool)),insert(B),D),bot_bot(fun(B,bool))))) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C)),hAPP(B,A,E,D)) # label(fact_174_setsum__diff1__ring) # label(axiom). [clausify(727)]. 4.54/4.76 1584 -ring(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,uminus_uminus(A),B)),C) # label(fact_506_minus__mult__left) # label(axiom). [clausify(846)]. 4.54/4.76 Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),A)),B). [resolve(1584,a,1576,a)]. 4.54/4.76 1585 -ring(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_505_minus__mult__right) # label(axiom). [clausify(1027)]. 4.54/4.76 Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,uminus_uminus(int),B)). [resolve(1585,a,1576,a)]. 4.54/4.76 1586 cancel_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 4.54/4.76 1587 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C) | ti(A,B) = ti(A,D) # label(fact_226_add__right__imp__eq) # label(axiom). [clausify(123)]. 4.54/4.76 1588 -cancel_semigroup_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_1_res) # label(axiom). [clausify(225)]. 4.54/4.76 1589 -cancel_semigroup_add(A) | ti(A,B) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D) # label(fact_230_add__right__cancel) # label(axiom). [clausify(793)]. 4.79/4.99 1590 -cancel_semigroup_add(A) | ti(A,B) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D) # label(fact_230_add__right__cancel) # label(axiom). [clausify(793)]. 4.79/4.99 1591 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) = ti(A,D) # label(fact_231_add__left__cancel) # label(axiom). [clausify(864)]. 4.79/4.99 1592 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) != ti(A,D) # label(fact_231_add__left__cancel) # label(axiom). [clausify(864)]. 4.79/4.99 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B) | ti(nat,A) = ti(nat,C). [resolve(1586,a,1587,a)]. 4.79/4.99 Derived: ti(nat,A) != ti(nat,B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C). [resolve(1586,a,1589,a)]. 4.79/4.99 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C) | ti(nat,B) = ti(nat,C). [resolve(1586,a,1591,a)]. 4.79/4.99 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C) | ti(nat,B) != ti(nat,C). [resolve(1586,a,1592,a)]. 4.79/4.99 1593 cancel_semigroup_add(int) # label(arity_Int_Oint___Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 4.79/4.99 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B) | ti(int,A) = ti(int,C). [resolve(1593,a,1587,a)]. 4.79/4.99 Derived: ti(int,A) != ti(int,B) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C). [resolve(1593,a,1589,a)]. 4.79/4.99 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C) | ti(int,B) = ti(int,C). [resolve(1593,a,1591,a)]. 4.79/4.99 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C) | ti(int,B) != ti(int,C). [resolve(1593,a,1592,a)]. 4.79/4.99 1594 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) = ti(A,D) # label(fact_228_add__left__imp__eq) # label(axiom). [clausify(1047)]. 4.79/4.99 1595 semiring(nat) # label(arity_Nat_Onat___Rings_Osemiring) # label(axiom). [assumption]. 4.79/4.99 1596 -semiring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),E)) # label(fact_224_combine__common__factor) # label(axiom). [clausify(136)]. 4.79/4.99 1597 semiring(int) # label(arity_Int_Oint___Rings_Osemiring) # label(axiom). [assumption]. 4.79/4.99 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),D)). [resolve(1597,a,1596,a)]. 4.79/4.99 1598 -semiring(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_1_res) # label(axiom). [clausify(1059)]. 4.79/4.99 1599 -comm_semiring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_250_comm__semiring__class_Odistrib) # label(axiom). [clausify(1081)]. 4.79/4.99 1600 comm_semiring(int) # label(arity_Int_Oint___Rings_Ocomm__semiring) # label(axiom). [assumption]. 4.79/4.99 1601 comm_semiring(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring) # label(axiom). [assumption]. 4.84/5.08 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)). [resolve(1599,a,1600,a)]. 4.84/5.08 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(1599,a,1601,a)]. 4.84/5.08 1602 -linord219039673up_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) # label(fact_563_minus__min__eq__max) # label(axiom). [clausify(205)]. 4.84/5.08 1603 linord219039673up_add(int) # label(arity_Int_Oint___Groups_Olinordered__ab__group__add) # label(axiom). [assumption]. 4.84/5.08 Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)). [resolve(1602,a,1603,a)]. 4.84/5.08 1604 -linord219039673up_add(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Max(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),uminus_uminus(A)),B)) = hAPP(A,A,uminus_uminus(A),hAPP(fun(A,bool),A,big_linorder_Min(A),B)) # label(fact_481_minus__Min__eq__Max) # label(axiom). [clausify(215)]. 4.84/5.08 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Max(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),uminus_uminus(int)),A)) = hAPP(int,int,uminus_uminus(int),hAPP(fun(int,bool),int,big_linorder_Min(int),A)). [resolve(1604,a,1603,a)]. 4.84/5.08 1605 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) # label(fact_975_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(282)]. 4.84/5.08 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A)),zero_zero(int))). [resolve(1605,a,1603,a)]. 4.84/5.08 1606 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) # label(fact_975_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(282)]. 4.84/5.08 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A)),zero_zero(int))). [resolve(1606,a,1603,a)]. 4.84/5.08 1607 -linord219039673up_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) # label(fact_564_minus__max__eq__min) # label(axiom). [clausify(322)]. 4.84/5.08 Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)). [resolve(1607,a,1603,a)]. 4.84/5.08 1608 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B))) # label(fact_974_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(496)]. 5.33/5.54 1609 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B))) # label(fact_974_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(496)]. 5.33/5.54 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A))). [resolve(1609,a,1603,a)]. 5.33/5.54 1610 -linord219039673up_add(A) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | ti(fun(A,bool),B) = bot_bot(fun(A,bool)) | hAPP(fun(A,bool),A,big_linorder_Min(A),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),uminus_uminus(A)),B)) = hAPP(A,A,uminus_uminus(A),hAPP(fun(A,bool),A,big_linorder_Max(A),B)) # label(fact_480_minus__Max__eq__Min) # label(axiom). [clausify(517)]. 5.33/5.54 Derived: -hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A)) | ti(fun(int,bool),A) = bot_bot(fun(int,bool)) | hAPP(fun(int,bool),int,big_linorder_Min(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),uminus_uminus(int)),A)) = hAPP(int,int,uminus_uminus(int),hAPP(fun(int,bool),int,big_linorder_Max(int),A)). [resolve(1610,a,1603,a)]. 5.33/5.54 1611 power(int) # label(arity_Int_Oint___Power_Opower) # label(axiom). [assumption]. 5.33/5.54 1612 -power(A) | power_power(A) = ti(fun(A,fun(nat,A)),power_power(A)) # label(tsy_c_Power_Opower__class_Opower_res) # label(axiom). [clausify(170)]. 5.33/5.54 Derived: power_power(int) = ti(fun(int,fun(nat,int)),power_power(int)). [resolve(1611,a,1612,a)]. 5.33/5.54 1613 -power(A) | times_times(A) = ti(fun(A,fun(A,A)),times_times(A)) # label(tsy_c_Groups_Otimes__class_Otimes_0_res) # label(axiom). [clausify(426)]. 5.33/5.54 1614 -power(A) | power_power(A) = hAPP(fun(A,fun(A,A)),fun(A,fun(nat,A)),hAPP(A,fun(fun(A,fun(A,A)),fun(A,fun(nat,A))),power_1(A),one_one(A)),times_times(A)) # label(fact_916_power__power__power) # label(axiom). [clausify(669)]. 5.33/5.54 Derived: power_power(int) = hAPP(fun(int,fun(int,int)),fun(int,fun(nat,int)),hAPP(int,fun(fun(int,fun(int,int)),fun(int,fun(nat,int))),power_1(int),one_one(int)),times_times(int)). [resolve(1614,a,1611,a)]. 5.33/5.54 1615 power(nat) # label(arity_Nat_Onat___Power_Opower) # label(axiom). [assumption]. 5.33/5.54 Derived: power_power(nat) = ti(fun(nat,fun(nat,nat)),power_power(nat)). [resolve(1615,a,1612,a)]. 5.33/5.54 Derived: power_power(nat) = hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),hAPP(nat,fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat))),power_1(nat),one_one(nat)),times_times(nat)). [resolve(1615,a,1614,a)]. 5.33/5.54 1616 -idom(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C) | ti(A,B) = hAPP(A,A,uminus_uminus(A),C) | ti(A,B) = ti(A,C) # label(fact_509_square__eq__iff) # label(axiom). [clausify(277)]. 5.33/5.54 1617 idom(int) # label(arity_Int_Oint___Rings_Oidom) # label(axiom). [assumption]. 5.33/5.54 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B) | ti(int,A) = hAPP(int,int,uminus_uminus(int),B) | ti(int,A) = ti(int,B). [resolve(1616,a,1617,a)]. 5.33/5.54 1618 -idom(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C) | ti(A,B) != hAPP(A,A,uminus_uminus(A),C) # label(fact_509_square__eq__iff) # label(axiom). [clausify(277)]. 5.33/5.54 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B) | ti(int,A) != hAPP(int,int,uminus_uminus(int),B). [resolve(1618,a,1617,a)]. 5.33/5.54 1619 -idom(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C) | ti(A,B) != ti(A,C) # label(fact_509_square__eq__iff) # label(axiom). [clausify(277)]. 5.33/5.54 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B) | ti(int,A) != ti(int,B). [resolve(1619,a,1617,a)]. 5.33/5.54 1620 -linordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),zero_zero(A))) # label(fact_980_not__square__less__zero) # label(axiom). [clausify(942)]. 5.73/5.95 1621 linordered_ring(int) # label(arity_Int_Oint___Rings_Olinordered__ring) # label(axiom). [assumption]. 5.73/5.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),zero_zero(int))). [resolve(1620,a,1621,a)]. 5.73/5.95 1622 -one(A) | one_one(A) = ti(A,one_one(A)) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom). [clausify(903)]. 5.73/5.95 1623 one(nat) # label(arity_Nat_Onat___Groups_Oone) # label(axiom). [assumption]. 5.73/5.95 1624 one(int) # label(arity_Int_Oint___Groups_Oone) # label(axiom). [assumption]. 5.73/5.95 Derived: one_one(nat) = ti(nat,one_one(nat)). [resolve(1622,a,1623,a)]. 5.73/5.95 Derived: one_one(int) = ti(int,one_one(int)). [resolve(1622,a,1624,a)]. 5.73/5.95 1625 -semiring_char_0(A) | B != C | hAPP(nat,A,semiring_1_of_nat(A),B) = hAPP(nat,A,semiring_1_of_nat(A),C) # label(fact_658_of__nat__eq__iff) # label(axiom). [clausify(747)]. 5.73/5.95 1626 semiring_char_0(int) # label(arity_Int_Oint___Nat_Osemiring__char__0) # label(axiom). [assumption]. 5.73/5.95 1627 semiring_char_0(nat) # label(arity_Nat_Onat___Nat_Osemiring__char__0) # label(axiom). [assumption]. 5.73/5.95 Derived: A != B | hAPP(nat,nat,semiring_1_of_nat(nat),A) = hAPP(nat,nat,semiring_1_of_nat(nat),B). [resolve(1625,a,1627,a)]. 5.73/5.95 1628 -semiring_char_0(A) | B = C | hAPP(nat,A,semiring_1_of_nat(A),B) != hAPP(nat,A,semiring_1_of_nat(A),C) # label(fact_658_of__nat__eq__iff) # label(axiom). [clausify(747)]. 5.73/5.95 Derived: A = B | hAPP(nat,nat,semiring_1_of_nat(nat),A) != hAPP(nat,nat,semiring_1_of_nat(nat),B). [resolve(1628,a,1627,a)]. 5.73/5.95 1629 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F))) # label(fact_837_less__add__iff2) # label(axiom). [clausify(289)]. 5.73/5.95 1630 ordered_ring(int) # label(arity_Int_Oint___Rings_Oordered__ring) # label(axiom). [assumption]. 5.73/5.95 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),D),A)),B)),E))). [resolve(1629,a,1630,a)]. 5.73/5.95 1631 -ordered_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F))) # label(fact_837_less__add__iff2) # label(axiom). [clausify(289)]. 5.73/5.95 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),D),A)),B)),E))). [resolve(1631,a,1630,a)]. 5.73/5.95 1632 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F))) # label(fact_325_le__add__iff2) # label(axiom). [clausify(310)]. 5.73/5.96 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),D),A)),B)),E))). [resolve(1632,a,1630,a)]. 5.73/5.96 1633 -ordered_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F))) # label(fact_325_le__add__iff2) # label(axiom). [clausify(310)]. 5.73/5.96 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),D),A)),B)),E))). [resolve(1633,a,1630,a)]. 5.73/5.96 1634 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),C)),D)),F)) # label(fact_324_le__add__iff1) # label(axiom). [clausify(589)]. 5.73/5.96 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),B)),C)),E)). [resolve(1634,a,1630,a)]. 5.73/5.96 1635 -ordered_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),C)),D)),F)) # label(fact_324_le__add__iff1) # label(axiom). [clausify(589)]. 5.73/5.96 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),B)),C)),E)). [resolve(1635,a,1630,a)]. 5.80/6.07 1636 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),C)),D)),F)) # label(fact_836_less__add__iff1) # label(axiom). [clausify(972)]. 5.80/6.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),B)),C)),E)). [resolve(1636,a,1630,a)]. 5.80/6.07 1637 -ordered_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),C)),D)),F)) # label(fact_836_less__add__iff1) # label(axiom). [clausify(972)]. 5.80/6.07 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),B)),C)),E)). [resolve(1637,a,1630,a)]. 5.80/6.07 1638 linordered_idom(int) # label(arity_Int_Oint___Rings_Olinordered__idom) # label(axiom). [assumption]. 5.80/6.07 1639 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),B)) # label(fact_941_mult__left__le__one__le) # label(axiom). [clausify(287)]. 5.80/6.07 1640 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) # label(fact_979_even__less__0__iff) # label(axiom). [clausify(293)]. 5.80/6.07 1641 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) # label(fact_979_even__less__0__iff) # label(axiom). [clausify(293)]. 5.80/6.07 1642 -linordered_idom(A) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_769_linorder__neqE__linordered__idom) # label(axiom). [clausify(385)]. 5.80/6.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)),A)). [resolve(1638,a,1639,a)]. 5.80/6.07 1643 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),B)) # label(fact_940_mult__right__le__one__le) # label(axiom). [clausify(771)]. 6.19/6.38 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),one_one(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),A)). [resolve(1643,a,1638,a)]. 6.19/6.38 1644 cancel146912293up_add(int) # label(arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption]. 6.19/6.38 1645 -cancel146912293up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) = ti(A,D) # label(fact_227_add__imp__eq) # label(axiom). [clausify(295)]. 6.19/6.38 1646 cancel146912293up_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption]. 6.19/6.38 1647 ring_1(int) # label(arity_Int_Oint___Rings_Oring__1) # label(axiom). [assumption]. 6.19/6.38 1648 -ring_1(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(nat,A,semiring_1_of_nat(A),C)),hAPP(nat,A,semiring_1_of_nat(A),B)) = hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),B)) # label(fact_663_of__nat__diff) # label(axiom). [clausify(315)]. 6.19/6.38 1649 -ring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),one_one(A))),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),C)),B) # label(fact_887_power__minus) # label(axiom). [clausify(435)]. 6.19/6.38 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),B)),hAPP(nat,int,semiring_1_of_nat(int),A)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A)). [resolve(1647,a,1648,a)]. 6.19/6.38 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),one_one(int))),A)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),B)),A). [resolve(1647,a,1649,a)]. 6.19/6.38 1650 ordered_ab_group_add(int) # label(arity_Int_Oint___Groups_Oordered__ab__group__add) # label(axiom). [assumption]. 6.19/6.38 1651 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_304_diff__eq__diff__less__eq) # label(axiom). [clausify(325)]. 6.19/6.38 1652 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_304_diff__eq__diff__less__eq) # label(axiom). [clausify(325)]. 6.19/6.38 1653 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_810_less__minus__iff) # label(axiom). [clausify(334)]. 6.19/6.38 1654 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_810_less__minus__iff) # label(axiom). [clausify(334)]. 6.19/6.38 1655 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_809_minus__less__iff) # label(axiom). [clausify(372)]. 6.19/6.38 1656 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_809_minus__less__iff) # label(axiom). [clausify(372)]. 6.19/6.38 1657 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_494_neg__le__iff__le) # label(axiom). [clausify(393)]. 6.19/6.38 1658 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_494_neg__le__iff__le) # label(axiom). [clausify(393)]. 6.19/6.38 1659 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) # label(fact_768_diff__eq__diff__less) # label(axiom). [clausify(402)]. 6.19/6.38 1660 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) # label(fact_768_diff__eq__diff__less) # label(axiom). [clausify(402)]. 6.19/6.38 1661 -ordered_ab_group_add(A) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),uminus_uminus(A)),hAPP(A,fun(A,bool),ord_greaterThan(A),B)) = hAPP(A,fun(A,bool),ord_lessThan(A),hAPP(A,A,uminus_uminus(A),B)) # label(fact_517_image__uminus__greaterThan) # label(axiom). [clausify(406)]. 6.19/6.38 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1650,a,1651,a)]. 6.19/6.38 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(1650,a,1652,a)]. 6.19/6.38 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,uminus_uminus(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,uminus_uminus(int),A))). [resolve(1650,a,1653,a)]. 6.19/6.38 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),B)),A)). [resolve(1650,a,1655,a)]. 6.19/6.38 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1650,a,1657,a)]. 6.19/6.38 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(1650,a,1658,a)]. 6.19/6.38 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)). [resolve(1650,a,1659,a)]. 6.19/6.38 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)). [resolve(1650,a,1660,a)]. 6.19/6.38 Derived: hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),uminus_uminus(int)),hAPP(int,fun(int,bool),ord_greaterThan(int),A)) = hAPP(int,fun(int,bool),ord_lessThan(int),hAPP(int,int,uminus_uminus(int),A)). [resolve(1650,a,1661,a)]. 6.19/6.40 1662 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C) # label(fact_371_min__diff__distrib__left) # label(axiom). [clausify(480)]. 6.19/6.40 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),B). [resolve(1662,a,1650,a)]. 6.19/6.40 1663 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_808_neg__less__iff__less) # label(axiom). [clausify(481)]. 6.19/6.40 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)). [resolve(1663,a,1650,a)]. 6.19/6.40 1664 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_808_neg__less__iff__less) # label(axiom). [clausify(481)]. 6.19/6.40 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)). [resolve(1664,a,1650,a)]. 6.19/6.40 1665 -ordered_ab_group_add(A) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),uminus_uminus(A)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),B),C)) = hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B)) # label(fact_834_image__uminus__atLeastAtMost) # label(axiom). [clausify(661)]. 6.19/6.40 Derived: hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),uminus_uminus(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),A),B)) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),hAPP(int,int,uminus_uminus(int),B)),hAPP(int,int,uminus_uminus(int),A)). [resolve(1665,a,1650,a)]. 6.19/6.40 1666 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)) # label(fact_535_max__diff__distrib__left) # label(axiom). [clausify(742)]. 6.19/6.40 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),C)). [resolve(1666,a,1650,a)]. 6.19/6.40 1667 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_496_le__minus__iff) # label(axiom). [clausify(788)]. 6.19/6.40 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,uminus_uminus(int),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,uminus_uminus(int),A))). [resolve(1667,a,1650,a)]. 6.19/6.40 1668 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_496_le__minus__iff) # label(axiom). [clausify(788)]. 6.19/6.40 1669 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B))) # label(fact_493_le__imp__neg__le) # label(axiom). [clausify(817)]. 6.27/6.50 1670 -ordered_ab_group_add(A) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),uminus_uminus(A)),hAPP(A,fun(A,bool),ord_lessThan(A),B)) = hAPP(A,fun(A,bool),ord_greaterThan(A),hAPP(A,A,uminus_uminus(A),B)) # label(fact_516_image__uminus__lessThan) # label(axiom). [clausify(988)]. 6.27/6.50 Derived: hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),uminus_uminus(int)),hAPP(int,fun(int,bool),ord_lessThan(int),A)) = hAPP(int,fun(int,bool),ord_greaterThan(int),hAPP(int,int,uminus_uminus(int),A)). [resolve(1670,a,1650,a)]. 6.27/6.50 1671 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_495_minus__le__iff) # label(axiom). [clausify(1028)]. 6.27/6.50 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),B)),A)). [resolve(1671,a,1650,a)]. 6.27/6.50 1672 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_495_minus__le__iff) # label(axiom). [clausify(1028)]. 6.27/6.50 1673 ordere216010020id_add(int) # label(arity_Int_Oint___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption]. 6.27/6.50 1674 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_949_add__nonpos__neg) # label(axiom). [clausify(332)]. 6.27/6.50 1675 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_976_add__pos__pos) # label(axiom). [clausify(344)]. 6.27/6.50 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),zero_zero(int))). [resolve(1673,a,1674,a)]. 6.27/6.50 1676 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_946_add__strict__increasing) # label(axiom). [clausify(411)]. 6.27/6.50 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))). [resolve(1676,a,1673,a)]. 6.27/6.50 1677 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_944_add__pos__nonneg) # label(axiom). [clausify(504)]. 6.27/6.50 1678 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_945_add__nonneg__pos) # label(axiom). [clausify(646)]. 6.27/6.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))). [resolve(1678,a,1673,a)]. 6.27/6.52 1679 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_947_add__strict__increasing2) # label(axiom). [clausify(691)]. 6.27/6.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))). [resolve(1679,a,1673,a)]. 6.27/6.52 1680 -ordere216010020id_add(A) | zero_zero(A) = ti(A,zero_zero(A)) # label(tsy_c_Groups_Ozero__class_Ozero_0_res) # label(axiom). [clausify(757)]. 6.27/6.52 1681 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_978_add__neg__neg) # label(axiom). [clausify(893)]. 6.27/6.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),zero_zero(int))). [resolve(1681,a,1673,a)]. 6.27/6.52 1682 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_948_add__neg__nonpos) # label(axiom). [clausify(975)]. 6.27/6.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),zero_zero(int))). [resolve(1682,a,1673,a)]. 6.27/6.52 1683 ordere216010020id_add(nat) # label(arity_Nat_Onat___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption]. 6.27/6.52 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),zero_zero(nat))). [resolve(1683,a,1674,a)]. 6.27/6.52 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))). [resolve(1683,a,1676,a)]. 6.27/6.52 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B))). [resolve(1683,a,1678,a)]. 6.27/6.52 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))). [resolve(1683,a,1679,a)]. 6.27/6.52 Derived: zero_zero(nat) = ti(nat,zero_zero(nat)). [resolve(1683,a,1680,a)]. 6.27/6.52 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),zero_zero(nat))). [resolve(1683,a,1681,a)]. 7.22/7.42 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),zero_zero(nat))). [resolve(1683,a,1682,a)]. 7.22/7.42 1684 -ring_11004092258visors(A) | one_one(A) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) | ti(A,B) = hAPP(A,A,uminus_uminus(A),one_one(A)) | one_one(A) = ti(A,B) # label(fact_638_square__eq__1__iff) # label(axiom). [clausify(690)]. 7.22/7.42 1685 ring_11004092258visors(int) # label(arity_Int_Oint___Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption]. 7.22/7.42 Derived: one_one(int) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A) | ti(int,A) = hAPP(int,int,uminus_uminus(int),one_one(int)) | one_one(int) = ti(int,A). [resolve(1684,a,1685,a)]. 7.22/7.42 1686 -ring_11004092258visors(A) | one_one(A) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) | ti(A,B) != hAPP(A,A,uminus_uminus(A),one_one(A)) # label(fact_638_square__eq__1__iff) # label(axiom). [clausify(690)]. 7.22/7.42 Derived: one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A) | ti(int,A) != hAPP(int,int,uminus_uminus(int),one_one(int)). [resolve(1686,a,1685,a)]. 7.22/7.42 1687 -ring_11004092258visors(A) | one_one(A) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) | one_one(A) != ti(A,B) # label(fact_638_square__eq__1__iff) # label(axiom). [clausify(690)]. 7.22/7.42 Derived: one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A) | one_one(int) != ti(int,A). [resolve(1687,a,1685,a)]. 7.22/7.42 1688 -linord893533164strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_994_comm__mult__strict__left__mono) # label(axiom). [clausify(1090)]. 7.22/7.42 1689 linord893533164strict(nat) # label(arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption]. 7.22/7.42 1690 linord893533164strict(int) # label(arity_Int_Oint___Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption]. 7.22/7.42 1691 comm_ring_1(int) # label(arity_Int_Oint___Rings_Ocomm__ring__1) # label(axiom). [assumption]. 7.22/7.42 1692 -comm_ring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_512_comm__ring__1__class_Onormalizing__ring__rules_I2_J) # label(axiom). [clausify(527)]. 7.22/7.42 1693 -comm_ring_1(A) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,uminus_uminus(A),one_one(A))),B) # label(fact_639_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom). [clausify(868)]. 7.22/7.42 Derived: hAPP(int,int,uminus_uminus(int),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),one_one(int))),A). [resolve(1693,a,1691,a)]. 7.22/7.42 7.22/7.42 ============================== end predicate elimination ============= 7.22/7.42 7.22/7.42 Auto_denials: (non-Horn, no changes). 7.22/7.42 7.22/7.42 Term ordering decisions: 7.22/7.42 Function symbol KB weights: bool=1. nat=1. int=1. state=1. com=1. fconj=1. vname=1. fdisj=1. fimplies=1. ass=1. fNot=1. semi=1. fFalse=1. fTrue=1. skip=1. update=1. b=1. c=1. g=1. p=1. x_a=1. fun=1. ti=1. big_co1399186613setsum=1. big_co302546470etprod=1. image=1. finite_fold=1. finite_fold_graph=1. finite100568337ommute=1. combk=1. finite_comp_fun_idem=1. finite1357897459simple=1. finite908156982e_idem=1. fold_graph=1. hoare_1759541758le_rec=1. hoare_225284258e_case=1. f4=1. f18=1. f39=1. f40=1. f41=1. f42=1. f43=1. f44=1. f68=1. f70=1. f71=1. f72=1. f78=1. f79=1. f91=1. f93=1. f95=1. f96=1. f98=1. f106=1. f116=1. f124=1. f131=1. f139=1. f142=1. f143=1. f144=1. f145=1. f147=1. f159=1. f162=1. f163=1. ord_less_eq=1. ord_less=1. hoare_2118899576triple=1. plus_plus=1. finite_finite_1=1. bot_bot=1. times_times=1. insert=1. member=1. minus_minus=1. ord_min=1. ord_max=1. one_one=1. zero_zero=1. semiring_1_of_nat=1. uminus_uminus=1. power_power=1. collect=1. big_linorder_Min=1. finite_card=1. big_Sup_fin=1. big_linorder_Max=1. ord_atLeastAtMost=1. big_Inf_fin=1. finite_fold1=1. fequal=1. hoare_759811442triple=1. hoare_1301688828derivs=1. ord_lessThan=1. fEx=1. ord_greaterThan=1. if=1. the=1. finite_fold1Set=1. finite_folding_one=1. finite2073411215e_idem=1. max=1. min=1. ord_gr1471790799AtMost=1. power_1=1. combi=1. partial_flat_lub=1. the_elem=1. big_semilattice_big=1. undefined=1. f17=1. f61=1. f62=1. f107=1. f110=1. f111=1. f135=1. f136=1. combb=1. combc=1. combs=1. f1=1. f2=1. f5=1. f6=1. f7=1. f8=1. f9=1. f11=1. f23=1. f24=1. f25=1. f26=1. f27=1. f34=1. f52=1. f53=1. f56=1. f57=1. f58=1. f80=1. f81=1. f82=1. f83=1. f84=1. f85=1. f90=1. f92=1. f97=1. f100=1. f105=1. f112=1. f120=1. f121=1. f122=1. f130=1. f151=1. f158=1. f160=1. f166=1. f167=1. f168=1. f171=1. f172=1. f173=1. f184=1. f185=1. f186=1. f187=1. f188=1. f189=1. f190=1. f191=1. hAPP=1. f3=1. f45=1. f48=1. f63=1. f67=1. f99=1. f103=1. f104=1. f123=1. f137=1. f152=1. f153=1. f154=1. f161=1. f174=1. f175=1. f176=1. f10=1. f15=1. f16=1. f19=1. f22=1. f28=1. f29=1. f30=1. f38=1. f54=1. f55=1. f64=1. f69=1. f86=1. f88=1. f89=1. f101=1. f102=1. f113=1. f125=1. f126=1. f132=1. f150=1. f180=1. f20=1. f21=1. f32=1. f35=1. f36=1. f46=1. f47=1. f49=1. f50=1. f65=1. f66=1. f73=1. f74=1. f75=1. f76=1. f77=1. f87=1. f94=1. f108=1. f109=1. f114=1. f115=1. f117=1. f118=1. f119=1. f127=1. f128=1. f129=1. f133=1. f134=1. f140=1. f141=1. f148=1. f149=1. f155=1. f164=1. f165=1. f12=1. f13=1. f14=1. f31=1. f33=1. f37=1. f138=1. 9.62/9.82 9.62/9.82 ============================== end of process initial clauses ======== 9.62/9.82 9.62/9.82 ============================== CLAUSES FOR SEARCH ==================== 9.62/9.82 9.62/9.82 ============================== end of clauses for search ============= 9.62/9.82 9.62/9.82 ============================== SEARCH ================================ 9.62/9.82 9.62/9.82 % Starting search at 5.21 seconds. 9.62/9.82 9.62/9.82 Low Water (keep): wt=163.000, iters=3453 9.62/9.82 9.62/9.82 Low Water (keep): wt=151.000, iters=3353 9.62/9.82 9.62/9.82 Low Water (keep): wt=147.000, iters=3437 9.62/9.82 9.62/9.82 Low Water (keep): wt=144.000, iters=3373 9.62/9.82 9.62/9.82 Low Water (keep): wt=141.000, iters=3387 9.62/9.82 9.62/9.82 Low Water (keep): wt=140.000, iters=3405 9.62/9.82 9.62/9.82 Low Water (keep): wt=130.000, iters=3336 9.62/9.82 9.62/9.82 Low Water (keep): wt=129.000, iters=3338 9.62/9.82 9.62/9.82 Low Water (keep): wt=125.000, iters=3369 9.62/9.82 9.62/9.82 Low Water (keep): wt=123.000, iters=3376 9.62/9.82 9.62/9.82 Low Water (keep): wt=122.000, iters=3373 9.62/9.82 9.62/9.82 Low Water (keep): wt=117.000, iters=3386 9.62/9.82 9.62/9.82 Low Water (keep): wt=116.000, iters=3417 9.62/9.82 9.62/9.82 Low Water (keep): wt=111.000, iters=3393 9.62/9.82 9.62/9.82 Low Water (keep): wt=110.000, iters=3438 9.62/9.82 9.62/9.82 Low Water (keep): wt=109.000, iters=3396 9.62/9.82 9.62/9.82 Low Water (keep): wt=108.000, iters=3365 9.62/9.82 9.62/9.82 Low Water (keep): wt=106.000, iters=3381 9.62/9.82 9.62/9.82 Low Water (keep): wt=105.000, iters=3426 9.62/9.82 9.62/9.82 Low Water (keep): wt=104.000, iters=3402 9.62/9.82 9.62/9.82 Low Water (keep): wt=102.000, iters=3397 9.62/9.82 9.62/9.82 Low Water (keep): wt=101.000, iters=3394 9.62/9.82 9.62/9.82 Low Water (keep): wt=100.000, iters=3376 9.62/9.82 9.62/9.82 Low Water (keep): wt=99.000, iters=3459 9.62/9.82 9.62/9.82 Low Water (keep): wt=98.000, iters=3539 9.62/9.82 9.62/9.82 Low Water (keep): wt=91.000, iters=3333 9.62/9.82 9.62/9.82 Low Water (keep): wt=87.000, iters=3403 9.62/9.82 9.62/9.82 Low Water (keep): wt=86.000, iters=3334 9.62/9.82 9.62/9.82 Low Water (keep): wt=83.000, iters=3373 9.62/9.82 9.62/9.82 Low Water (keep): wt=82.000, iters=3393 9.62/9.82 9.62/9.82 Low Water (keep): wt=80.000, iters=3335 9.62/9.82 9.62/9.82 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 74 (0.00 of 6.93 sec). 9.62/9.82 9.62/9.82 Low Water (keep): wt=78.000, iters=3404 9.62/9.82 9.62/9.82 Low Water (keep): wt=77.000, iters=3422 9.62/9.82 9.62/9.82 Low Water (keep): wt=76.000, iters=3414 9.62/9.82 9.62/9.82 Low Water (keep): wt=75.000, iters=3380 9.62/9.82 9.62/9.82 Low Water (keep): wt=74.000, iters=3435 9.62/9.82 9.62/9.82 Low Water (keep): wt=73.000, iters=3369 9.62/9.82 9.62/9.82 Low Water (keep): wt=72.000, iters=3444 9.62/9.82 9.62/9.82 Low Water (keep): wt=71.000, iters=3405 9.62/9.82 9.62/9.82 Low Water (keep): wt=70.000, iters=3367 9.62/9.82 9.62/9.82 Low Water (keep): wt=69.000, iters=3392 9.62/9.82 9.62/9.82 Low Water (keep): wt=68.000, iters=3388 9.62/9.82 9.62/9.82 Low Water (keep): wt=67.000, iters=3338 9.62/9.82 9.62/9.82 Low Water (keep): wt=66.000, iters=3401 9.62/9.82 9.62/9.82 Low Water (keep): wt=65.000, iters=3426 9.62/9.82 9.62/9.82 Low Water (keep): wt=64.000, iters=3368 116.94/117.16 116.94/117.16 Low Water (keep): wt=62.000, iters=3375 116.94/117.16 116.94/117.16 Low Water (keep): wt=61.000, iters=3350 116.94/117.16 116.94/117.16 Low Water (keep): wt=60.000, iters=3334 116.94/117.16 116.94/117.16 Low Water (keep): wt=59.000, iters=3338 116.94/117.16 116.94/117.16 Low Water (keep): wt=57.000, iters=3378 116.94/117.16 116.94/117.16 Low Water (keep): wt=56.000, iters=3353 116.94/117.16 116.94/117.16 Low Water (keep): wt=55.000, iters=3342 116.94/117.16 116.94/117.16 Low Water (keep): wt=54.000, iters=3334 116.94/117.16 116.94/117.16 Low Water (keep): wt=52.000, iters=3344 116.94/117.16 116.94/117.16 Low Water (keep): wt=51.000, iters=3339 116.94/117.16 116.94/117.16 Low Water (keep): wt=50.000, iters=3345 116.94/117.16 116.94/117.16 Low Water (keep): wt=49.000, iters=3342 116.94/117.16 116.94/117.16 Low Water (keep): wt=48.000, iters=3362 116.94/117.16 116.94/117.16 Low Water (keep): wt=47.000, iters=3356 116.94/117.16 116.94/117.16 Low Water (keep): wt=46.000, iters=3384 116.94/117.16 116.94/117.16 Low Water (keep): wt=44.000, iters=3353 116.94/117.16 116.94/117.16 Low Water (keep): wt=42.000, iters=3888 116.94/117.16 116.94/117.16 Low Water (keep): wt=40.000, iters=3670 116.94/117.16 116.94/117.16 Low Water (keep): wt=39.000, iters=3469 116.94/117.16 116.94/117.16 Low Water (keep): wt=38.000, iters=3479 116.94/117.16 116.94/117.16 Low Water (keep): wt=36.000, iters=3335 116.94/117.16 116.94/117.16 Low Water (keep): wt=35.000, iters=3530 116.94/117.16 116.94/117.16 Low Water (keep): wt=34.000, iters=3397 116.94/117.16 116.94/117.16 Low Water (keep): wt=33.000, iters=3370 116.94/117.16 116.94/117.16 Low Water (keep): wt=32.000, iters=3375 116.94/117.16 116.94/117.16 Low Water (keep): wt=31.000, iters=3352 116.94/117.16 116.94/117.16 Low Water (displace): id=16662, wt=22.000 116.94/117.16 116.94/117.16 Low Water (displace): id=16666, wt=20.000 116.94/117.16 116.94/117.16 Low Water (displace): id=16670, wt=18.000 116.94/117.16 116.94/117.16 Low Water (keep): wt=29.000, iters=3387 116.94/117.16 116.94/117.16 Low Water (displace): id=23441, wt=16.000 116.94/117.16 116.94/117.16 Low Water (keep): wt=28.000, iters=3333 116.94/117.16 116.94/117.16 Low Water (keep): wt=27.000, iters=3333 116.94/117.16 116.94/117.16 Low Water (keep): wt=26.000, iters=3333 116.94/117.16 116.94/117.16 Low Water (keep): wt=25.000, iters=3341 116.94/117.16 116.94/117.16 Low Water (keep): wt=24.000, iters=3373 116.94/117.16 116.94/117.16 Low Water (keep): wt=23.000, iters=3333 116.94/117.16 116.94/117.16 ============================== STATISTICS ============================ 116.94/117.16 116.94/117.16 Given=11532. Generated=2962721. Kept=160990. proofs=0. 116.94/117.16 Usable=9908. Sos=9992. Demods=1284. Limbo=3324, Disabled=140140. Hints=0. 116.94/117.16 Kept_by_rule=0, Deleted_by_rule=73939. 116.94/117.16 Forward_subsumed=360121. Back_subsumed=84. 116.94/117.16 Sos_limit_deleted=2367670. Sos_displaced=131980. Sos_removed=0. 116.94/117.16 New_demodulators=2413 (0 lex), Back_demodulated=5315. Back_unit_deleted=387. 116.94/117.16 Demod_attempts=163883974. Demod_rewrites=892571. 116.94/117.16 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 116.94/117.16 Nonunit_fsub_feature_tests=2517229. Nonunit_bsub_feature_tests=18023. 116.94/117.16 Megabytes=419.43. 116.94/117.16 User_CPU=113.09, System_CPU=1.84, Wall_clock=115. 116.94/117.16 116.94/117.16 Megs malloced by palloc(): 400. 116.94/117.16 type (bytes each) gets frees in use bytes 116.94/117.16 chunk ( 104) 105015 105015 0 0.0 K 116.94/117.16 string_buf ( 8) 91081 91081 0 0.0 K 116.94/117.16 token ( 20) 228364 228364 0 0.0 K 116.94/117.16 pterm ( 16) 161428 161428 0 0.0 K 116.94/117.16 hashtab ( 8) 1090 1090 0 0.0 K 116.94/117.16 hashnode ( 8) 4982 4982 0 0.0 K 116.94/117.16 term ( 20) 237705721 228305091 9400630 183606.1 K 116.94/117.16 term arg arrays: 39822.6 K 116.94/117.16 attribute ( 12) 7818 148 7670 89.9 K 116.94/117.16 ilist ( 8) 681338277 680520638 817639 6387.8 K 116.94/117.16 plist ( 8) 7567351 7367222 200129 1563.5 K 116.94/117.16 i2list ( 12) 11815066 11815066 0 0.0 K 116.94/117.16 just ( 12) 3709270 3526622 182648 2140.4 K 116.94/117.16 parajust ( 16) 646106 555239 90867 1419.8 K 116.94/117.16 instancejust ( 8) 0 0 0 0.0 K 116.94/117.16 ivyjust ( 24) 0 0 0 0.0 K 116.94/117.16 formula ( 28) 52499 34581 17918 489.9 K 116.94/117.16 formula arg arrays: 61.5 K 116.94/117.16 topform ( 52) 2966403 2801730 164673 8362.3 K 116.94/117.16 clist_pos ( 20) 476109 311461 164648 3215.8 K 116.94/117.16 clist ( 16) 8 1 7 0.1 K 116.94/117.16 context ( 808) 15350956 15350954 2 1.6 K 116.94/117.16 trail ( 12) 17946701 17946697 4 0.0 K 116.94/117.16 ac_match_pos (70044) 0 0 0 0.0 K 116.94/117.16 ac_match_free_vars_pos (20020) 116.94/117.16 0 0 0 0.0 K 116.94/117.16 btm_state ( 60) 0 0 0 0.0 K 116.94/117.16 btu_state ( 60) 0 0 0 0.0 K 116.94/117.17 ac_position (285432) 0 0 0 0.0 K 116.94/117.17 fpa_trie ( 20) 3088060 2844213 243847 4762.6 K 116.94/117.17 fpa_state ( 28) 12808794 12808794 0 0.0 K 116.94/117.17 fpa_index ( 12) 10 0 10 0.1 K 116.94/117.17 fpa_chunk ( 20) 4275893 4127827 148066 2891.9 K 116.94/117.17 fpa_list ( 16) 2915017 0 2915017 45547.1 K 116.94/117.17 fpa_list chunks: 13286.8 K 116.94/117.17 discrim ( 12) 3075391 2865408 209983 2460.7 K 116.94/117.17 discrim_pos ( 16) 1098557 1098557 0 0.0 K 116.94/117.17 flat2 ( 32) 65268698 65268698 0 0.0 K 116.94/117.17 flat ( 48) 0 0 0 0.0 K 116.94/117.17 flatterm ( 32) 194323829 194323829 0 0.0 K 116.94/117.17 mindex ( 28) 13 0 13 0.4 K 116.94/117.17 mindex_pos ( 56) 7786937 7786937 0 0.0 K 116.94/117.17 lindex ( 12) 5 0 5 0.1 K 116.94/117.17 clash ( 40) 0 0 0 0.0 K 116.94/117.17 di_tree ( 12) 28664518 20814560 7849958 91991.7 K 116.94/117.17 avl_node ( 20) 313435 293451 19984 390.3 K 116.94/117.17 116.94/117.17 Memory report, 20 @ 20 = 400 megs (400.00 megs used). 116.94/117.17 List 1, length 9, 0.0 K 116.94/117.17 List 2, length 1075, 8.4 K 116.94/117.17 List 3, length 6, 0.1 K 116.94/117.17 List 7, length 4, 0.1 K 116.94/117.17 List 8, length 406, 12.7 K 116.94/117.17 List 10, length 6, 0.2 K 116.94/117.17 List 11, length 12, 0.5 K 116.94/117.17 List 12, length 4, 0.2 K 116.94/117.17 List 14, length 2, 0.1 K 116.94/117.17 List 16, length 4095, 255.9 K 116.94/117.17 List 26, length 1087, 110.4 K 116.94/117.17 List 128, length 52, 26.0 K 116.94/117.17 List 202, length 2, 1.6 K 116.94/117.17 List 256, length 3, 3.0 K 116.94/117.17 116.94/117.17 ============================== SELECTOR REPORT ======================= 116.94/117.17 Sos_deleted=2367670, Sos_displaced=131980, Sos_size=9992 116.94/117.17 SELECTOR PART PRIORITY ORDER SIZE SELECTED 116.94/117.17 I 2147483647 high age 0 1406 116.94/117.17 H 1 high weight 0 0 116.94/117.17 A 1 low age 9992 1126 116.94/117.17 F 4 low weight 522 4500 116.94/117.17 T 4 low weight 9470 4500 116.94/117.17 ============================== end of selector report ================ 116.94/117.17 116.94/117.17 ============================== end of statistics ===================== 116.94/117.17 116.94/117.17 Exiting with failure. 116.94/117.17 116.94/117.17 Process 11003 exit (max_megs) Wed Jul 14 16:43:45 2021 116.94/117.17 Prover9 interrupted 116.94/117.17 EOF