0.05/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.10 % Command : tptp2X_and_run_prover9 %d %s 0.09/0.30 % Computer : n006.cluster.edu 0.09/0.30 % Model : x86_64 x86_64 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.30 % Memory : 8042.1875MB 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.31 % CPULimit : 1200 0.09/0.31 % DateTime : Tue Jul 13 16:49:10 EDT 2021 0.09/0.31 % CPUTime : 2.14/2.52 ============================== Prover9 =============================== 2.14/2.52 Prover9 (32) version 2009-11A, November 2009. 2.14/2.52 Process 18943 was started by sandbox2 on n006.cluster.edu, 2.14/2.52 Tue Jul 13 16:49:12 2021 2.14/2.52 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_18790_n006.cluster.edu". 2.14/2.52 ============================== end of head =========================== 2.14/2.52 2.14/2.52 ============================== INPUT ================================= 2.14/2.52 2.14/2.52 % Reading from file /tmp/Prover9_18790_n006.cluster.edu 2.14/2.52 2.14/2.52 set(prolog_style_variables). 2.14/2.52 set(auto2). 2.14/2.52 % set(auto2) -> set(auto). 2.14/2.52 % set(auto) -> set(auto_inference). 2.14/2.52 % set(auto) -> set(auto_setup). 2.14/2.52 % set(auto_setup) -> set(predicate_elim). 2.14/2.52 % set(auto_setup) -> assign(eq_defs, unfold). 2.14/2.52 % set(auto) -> set(auto_limits). 2.14/2.52 % set(auto_limits) -> assign(max_weight, "100.000"). 2.14/2.52 % set(auto_limits) -> assign(sos_limit, 20000). 2.14/2.52 % set(auto) -> set(auto_denials). 2.14/2.52 % set(auto) -> set(auto_process). 2.14/2.52 % set(auto2) -> assign(new_constants, 1). 2.14/2.52 % set(auto2) -> assign(fold_denial_max, 3). 2.14/2.52 % set(auto2) -> assign(max_weight, "200.000"). 2.14/2.52 % set(auto2) -> assign(max_hours, 1). 2.14/2.52 % assign(max_hours, 1) -> assign(max_seconds, 3600). 2.14/2.52 % set(auto2) -> assign(max_seconds, 0). 2.14/2.52 % set(auto2) -> assign(max_minutes, 5). 2.14/2.52 % assign(max_minutes, 5) -> assign(max_seconds, 300). 2.14/2.52 % set(auto2) -> set(sort_initial_sos). 2.14/2.52 % set(auto2) -> assign(sos_limit, -1). 2.14/2.52 % set(auto2) -> assign(lrs_ticks, 3000). 2.14/2.52 % set(auto2) -> assign(max_megs, 400). 2.14/2.52 % set(auto2) -> assign(stats, some). 2.14/2.52 % set(auto2) -> clear(echo_input). 2.14/2.52 % set(auto2) -> set(quiet). 2.14/2.52 % set(auto2) -> clear(print_initial_clauses). 2.14/2.52 % set(auto2) -> clear(print_given). 2.14/2.52 assign(lrs_ticks,-1). 2.14/2.52 assign(sos_limit,10000). 2.14/2.52 assign(order,kbo). 2.14/2.52 set(lex_order_vars). 2.14/2.52 clear(print_given). 2.14/2.52 2.14/2.52 % formulas(sos). % not echoed (617 formulas) 2.14/2.52 2.14/2.52 ============================== end of input ========================== 2.14/2.52 2.14/2.52 % From the command line: assign(max_seconds, 1200). 2.14/2.52 2.14/2.52 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 2.14/2.52 2.14/2.52 % Formulas that are not ordinary clauses: 2.14/2.52 1 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,suc,N_1))))) # label(fact_483_le__SucI) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 2 (all X_a all Pa all Xs_1 hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Xs_1))),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Xs_1)) # label(fact_322_takeWhile__eq__take) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 3 (all X_a listrelp(X_a) = ti(fun(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool))),listrelp(X_a))) # label(tsy_c_List_Olistrelp_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 4 (all X_a ti(fun(fun(product_prod(X_a,X_a),bool),fun(nat,fun(product_prod(list(X_a),list(X_a)),bool))),lexn(X_a)) = lexn(X_a)) # label(tsy_c_List_Olexn_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 5 (all X_a all N_1 all Xs Xs = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs))) # label(fact_321_append__take__drop__id) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 6 (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_433_not__leE) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 7 (all X_a all Xs (nil(X_a) != Xs -> hAPP(list(X_a),list(X_a),rotate1(X_a),Xs) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),tl(X_a),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(list(X_a),X_a,hd(X_a),Xs)),nil(X_a))))) # label(fact_228_rotate1__hd__tl) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 8 (all X_a all Pa all Xs_1 all Yes all No (hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Yes),No) = hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(fun(X_a,bool),fun(list(X_a),product_prod(list(X_a),list(X_a))),partition(X_a),Pa),Xs_1) -> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Yes))) -> hBOOL(hAPP(X_a,bool,Pa,X_2)))) & (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),No))) -> -hBOOL(hAPP(X_a,bool,Pa,X_2)))))) # label(fact_294_partition__P) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 9 (all X_b all X_a maps(X_b,X_a) = ti(fun(fun(X_b,list(X_a)),fun(list(X_b),list(X_a))),maps(X_b,X_a))) # label(tsy_c_List_Omaps_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 10 (all X_a (order(X_a) -> (all X_1 all Y_1 (ti(X_a,X_1) = ti(X_a,Y_1) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)))))) # label(fact_435_order__le__less) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 11 (all X_a all X_b all X_1 all F all A_1 all B (hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,fun(X_b,bool),B,X_1)))))) # label(fact_55_Pi__mem) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 12 (all X_a all X_1 all Xs_1 all Y_1 all Ys_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_1))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lex(X_a),R_2))) <-> ti(X_a,X_1) = ti(X_a,Y_1) & hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lex(X_a),R_2))) | hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),R_2)) & hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1))) # label(fact_175_Cons__in__lex) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 13 (all X_a all X_b all X_c product_curry(X_a,X_b,X_c) = ti(fun(fun(product_prod(X_a,X_b),X_c),fun(X_a,fun(X_b,X_c))),product_curry(X_a,X_b,X_c))) # label(tsy_c_Product__Type_Ocurry_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 14 (all X_a (order(X_a) -> (all C_1 all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2)) -> (ti(X_a,C_1) = ti(X_a,B_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2))))))) # label(fact_337_xt1_I4_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 15 (all X_a (cl_HOL_Oequal(X_a) -> fequal(X_a) = equal_equal(X_a))) # label(fact_240_eq__equal) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 16 (all N_1 hAPP(nat,nat,suc,N_1) != N_1) # label(fact_452_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 17 (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_406_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 18 (all X_a all Pa all X_1 all Xs_1 hAPP(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a)),hAPP(fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a)))),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a))),product_prod_case(list(X_a),list(X_a),product_prod(list(X_a),list(X_a))),hAPP(fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a)))),fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a)))),hAPP(fun(list(X_a),fun(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(list(X_a),product_prod(list(X_a),list(X_a))))),fun(fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a)))),fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))))),combs(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(list(X_a),product_prod(list(X_a),list(X_a)))),hAPP(fun(list(X_a),fun(list(X_a),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a))))),fun(list(X_a),fun(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(list(X_a),product_prod(list(X_a),list(X_a))))),hAPP(fun(fun(list(X_a),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a)))),fun(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(list(X_a),product_prod(list(X_a),list(X_a))))),fun(fun(list(X_a),fun(list(X_a),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a))))),fun(list(X_a),fun(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(list(X_a),product_prod(list(X_a),list(X_a)))))),combb(fun(list(X_a),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a)))),fun(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(list(X_a),product_prod(list(X_a),list(X_a)))),list(X_a)),combs(list(X_a),product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a)))),hAPP(fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a)))),fun(list(X_a),fun(list(X_a),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a))))),hAPP(fun(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(list(X_a),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a))))),fun(fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a)))),fun(list(X_a),fun(list(X_a),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a)))))),combb(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(list(X_a),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a)))),list(X_a)),hAPP(fun(product_prod(list(X_a),list(X_a)),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a)))),fun(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(list(X_a),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a))))),combb(product_prod(list(X_a),list(X_a)),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a))),list(X_a)),hAPP(bool,fun(product_prod(list(X_a),list(X_a)),fun(product_prod(list(X_a),list(X_a)),product_prod(list(X_a),list(X_a)))),if(product_prod(list(X_a),list(X_a))),hAPP(X_a,bool,Pa,X_1)))),hAPP(fun(list(X_a),list(X_a)),fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a)))),hAPP(fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a)))),fun(fun(list(X_a),list(X_a)),fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))))),combb(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),list(X_a)),product_Pair(list(X_a),list(X_a))),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1))))),hAPP(fun(list(X_a),list(X_a)),fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a)))),hAPP(fun(list(X_a),fun(fun(list(X_a),list(X_a)),fun(list(X_a),product_prod(list(X_a),list(X_a))))),fun(fun(list(X_a),list(X_a)),fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))))),combc(list(X_a),fun(list(X_a),list(X_a)),fun(list(X_a),product_prod(list(X_a),list(X_a)))),hAPP(fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a)))),fun(list(X_a),fun(fun(list(X_a),list(X_a)),fun(list(X_a),product_prod(list(X_a),list(X_a))))),hAPP(fun(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(fun(list(X_a),list(X_a)),fun(list(X_a),product_prod(list(X_a),list(X_a))))),fun(fun(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a)))),fun(list(X_a),fun(fun(list(X_a),list(X_a)),fun(list(X_a),product_prod(list(X_a),list(X_a)))))),combb(fun(list(X_a),product_prod(list(X_a),list(X_a))),fun(fun(list(X_a),list(X_a)),fun(list(X_a),product_prod(list(X_a),list(X_a)))),list(X_a)),combb(list(X_a),product_prod(list(X_a),list(X_a)),list(X_a))),product_Pair(list(X_a),list(X_a)))),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1)))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(fun(X_a,bool),fun(list(X_a),product_prod(list(X_a),list(X_a))),partition(X_a),Pa),Xs_1)) = hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(fun(X_a,bool),fun(list(X_a),product_prod(list(X_a),list(X_a))),partition(X_a),Pa),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))) # label(fact_177_partition_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 19 (all X_b all X_a all F all Xs_1 all Pa all S_2 (hBOOL(hAPP(X_a,bool,Pa,S_2)) -> ((all S_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),hAPP(list(X_b),fun(X_b,bool),set(X_b),Xs_1))) -> (hBOOL(hAPP(X_a,bool,Pa,S_3)) -> hBOOL(hAPP(X_a,bool,Pa,hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),F,S_3),X_2)))))) -> hBOOL(hAPP(X_a,bool,Pa,hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),S_2),Xs_1)))))) # label(fact_306_foldl__weak__invariant) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 20 (all X_c all X_a all X_b all F all Aa all Ba hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),hAPP(fun(product_prod(X_b,X_c),X_a),fun(X_b,fun(X_c,X_a)),product_curry(X_b,X_c,X_a),F),Aa),Ba) = hAPP(product_prod(X_b,X_c),X_a,F,hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba))) # label(fact_89_curry__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 21 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (exists Ys exists Zs_2 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys))) & hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs_2)) = Xs_1)))) # label(fact_312_split__list__first) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 22 (all X_a all X_b all A_1 hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),top_top(fun(X_b,bool)))) = top_top(fun(fun(X_a,X_b),bool))) # label(fact_102_Pi__UNIV) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 23 (all X_a all Xs_1 all Pa all X_1 ((-hBOOL(hAPP(X_a,bool,Pa,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)) = nil(X_a)) & (hBOOL(hAPP(X_a,bool,Pa,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Xs_1))))) # label(fact_118_takeWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 24 (all X_a all N_1 hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),nil(X_a)) = nil(X_a)) # label(fact_250_drop__Nil) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 25 (all X_a all V_1 all Va hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),V_1),Va)),nil(X_a)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),V_1),Va)) # label(fact_49_splice_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 26 (all X_a all Xs all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),N_1)) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),Xs) = Xs)) # label(fact_353_take__all) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 27 (all X_a all Ws (-hBOOL(hAPP(list(X_a),bool,distinct(X_a),Ws)) -> (exists Xs_2 exists Ys exists Zs_2 exists Y_2 Ws = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_2),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),nil(X_a))),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),nil(X_a))),Zs_2))))))) # label(fact_213_not__distinct__decomp) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 28 (all X_b all X_c all X_a all F1 all Aa all Ba hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,Aa),Ba) = hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_rec(X_b,X_c,X_a),F1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba))) # label(fact_32_prod_Orecs) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 29 (all X_b all X_c all X_a all F1 all Aa all Ba hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,Aa),Ba)) # label(fact_181_prod_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 30 (all X_a ti(fun(nat,fun(list(X_a),list(X_a))),take(X_a)) = take(X_a)) # label(tsy_c_List_Otake_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 31 (all X_a all X_c all X_b all Z_2 all Ca all Aa all Ba (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z_2),hAPP(X_c,fun(X_a,bool),hAPP(X_b,fun(X_c,fun(X_a,bool)),Ca,Aa),Ba))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z_2),hAPP(product_prod(X_b,X_c),fun(X_a,bool),hAPP(fun(X_b,fun(X_c,fun(X_a,bool))),fun(product_prod(X_b,X_c),fun(X_a,bool)),product_prod_case(X_b,X_c,fun(X_a,bool)),Ca),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)))))) # label(fact_202_mem__splitI) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 32 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_arg1) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 33 (all X_a all X_1 all Pa all Q_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),Pa),Q_1)) -> (hBOOL(hAPP(X_a,bool,Pa,X_1)) -> hBOOL(hAPP(X_a,bool,Q_1,X_1))))) # label(fact_380_predicate1D) # label(axiom) # label(non_clause). [assumption]. 2.14/2.52 34 (all L_1 all X_1 all Y_1 (ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_1) -> (hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_1),arrow_2064824852le_Lin)) -> hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,L_1),X_1),Y_1)),arrow_2064824852le_Lin))))) # label(fact_41_above__Lin) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 35 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | hBOOL(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 36 (all X_a all Xs Xs = hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs))) # label(fact_254_rev__rev__ident) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 37 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),M)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)))) # label(fact_498_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 38 (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_401_linorder__neqE) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 39 (all X_a all Pa all Xs_1 (nil(X_a) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),Xs_1) <-> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,Pa,X_2)))))) # label(fact_288_dropWhile__eq__Nil__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 40 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> M_1 = N_1))) # label(fact_470_less__SucE) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 41 (all X_a if(X_a) = ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a))) # label(tsy_c_If_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 42 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (exists Ys exists Zs_2 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs_2)) = Xs_1 & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Zs_2))))))) # label(fact_313_split__list__last) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 43 (all N_1 all M_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1)) -> N_1 != M_1)) # label(fact_460_less__not__refl2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 44 (all X_a all R_2 all A1 all A2 (hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_2),A1),A2)) <-> (exists X_2 exists Y_2 exists Xs_2 exists Ys (A1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2) & hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys) = A2 & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,X_2),Y_2)) & hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_2),Xs_2),Ys)))) | nil(X_a) = A2 & A1 = nil(X_a))) # label(fact_236_listrelp_Osimps) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 45 (all Fa (hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,Fa)) <-> (all X_2 (hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof)) -> (all Xa (hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Xa),arrow_1111136790e_Prof)) -> (all A_4 all B_2 ((all I (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_4),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Xa,I))) <-> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_4),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I))))) -> (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_4),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2))) <-> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_4),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,Xa)))))))))))) # label(fact_28_IIA__def) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 46 (all X_a all R_2 all S_2 (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(fun(product_prod(X_a,X_a),bool),fun(fun(product_prod(X_a,X_a),bool),bool),ord_less_eq(fun(product_prod(X_a,X_a),bool)),R_2),S_2)) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(fun(product_prod(list(X_a),list(X_a)),bool),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),ord_less_eq(fun(product_prod(list(X_a),list(X_a)),bool)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),S_2))))) # label(fact_368_listrel1__mono) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 47 (all X_a all Xs all Ys_2 all Zs_1 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_2)),Zs_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_2),Zs_1))) # label(fact_131_append__assoc) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 48 (all X_a all Ys_2 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),nil(X_a)),Ys_2) = Ys_2) # label(fact_134_append__Nil) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 49 (all T_2 all T_1 (enum(T_2) & enum(T_1) -> enum(product_prod(T_2,T_1)))) # label(arity_prod___Enum_Oenum) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 50 (all X_b all X_a all F all G all L all K_1 all Aa all Ba (ti(X_a,Ba) = ti(X_a,Aa) -> (K_1 = L -> ((all 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),hAPP(list(X_b),fun(X_b,bool),set(X_b),L))) -> hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),G,A_4),X_2) = hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),F,A_4),X_2))) -> hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),G),Ba),K_1) = hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),Aa),L))))) # label(fact_305_foldl__cong) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 51 (all X_a all Pa hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa) = ti(fun(X_a,bool),Pa)) # label(fact_77_Collect__def) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 52 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> ti(X_a,X_1) != ti(X_a,Y_1))))) # label(fact_397_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 53 (all X_a all X_b ti(fun(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool))),pi(X_a,X_b)) = pi(X_a,X_b)) # label(tsy_c_FuncSet_OPi_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 54 (all X_b all X_c all X_a all Ca all Aa all Ba hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),Ca,Aa),Ba) = hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),produc1605651328_split(X_b,X_c,X_a),Ca),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba))) # label(fact_72_internal__split__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 55 (all X_a (order(X_a) -> (all C_1 all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) -> (ti(X_a,B_1) = ti(X_a,C_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),A_2))))))) # label(fact_413_xt1_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 56 (all X_a all Xs all Ys_2 ((all I hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I),Ys_2) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I),Xs)) -> Ys_2 = Xs)) # label(fact_325_take__equalityI) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 57 (all P (ti(bool,P) = fFalse | fTrue = ti(bool,P))) # label(help_fTrue_1_1_T) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 58 (all X_a all Xs Xs = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),nil(X_a))) # label(fact_136_append__Nil2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 59 (all X_a all Xs all Ys_2 (nil(X_a) != Ys_2 -> hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_2)) = hAPP(list(X_a),X_a,last(X_a),Ys_2))) # label(fact_149_last__appendR) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 60 (all X_a all N_1 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),Xs))) # label(fact_442_take__butlast) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 61 (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]. 2.14/2.53 62 (all X_a all Xs (Xs != nil(X_a) -> hAPP(list(X_a),X_a,hd(X_a),Xs) = hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs)))) # label(fact_241_last__rev) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 63 (all X_a all Us_1 all Vs_1 all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))) & Us_1 = Vs_1 | Ys_1 = Xs_1 & hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Us_1),Vs_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Us_1)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Vs_1))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))))) # label(fact_168_append__listrel1I) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 64 (all X_b all X_a all F1 all F2 ti(X_a,F1) = hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a)),list_rec(X_a,X_b),F1),F2),nil(X_b))) # label(fact_79_list_Orecs_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 65 (all X_a all Ca all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Ca),B))))) # label(fact_376_subsetD) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 66 (all X_a all X_b all X_c all X_1 all Pa ((all A_4 all B_2 all C_2 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,Pa,hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),A_4),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),B_2),C_2))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,Pa,X_1)))) # label(fact_64_prod__induct3) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 67 (all X_a set(X_a) = ti(fun(list(X_a),fun(X_a,bool)),set(X_a))) # label(tsy_c_List_Oset_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 68 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)))) # label(fact_485_Suc__leD) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 69 (all X_a distinct(X_a) = ti(fun(list(X_a),bool),distinct(X_a))) # label(tsy_c_List_Odistinct_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 70 (all X_a all X_b all X_1 all F all A_1 all B (hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,fun(X_b,bool),B,X_1))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))))) # label(fact_43_PiE) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 71 (all X_b all X_c all X_a all X_2 all Xa all Xb hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),hAPP(fun(product_prod(X_a,X_b),X_c),fun(X_a,fun(X_b,X_c)),product_curry(X_a,X_b,X_c),X_2),Xa),Xb) = hAPP(product_prod(X_a,X_b),X_c,X_2,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Xa),Xb))) # label(fact_81_curry__def) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 72 (all X_a all Xs_1 (Xs_1 = nil(X_a) <-> hAPP(list(X_a),list(X_a),rotate1(X_a),Xs_1) = nil(X_a))) # label(fact_163_rotate1__is__Nil__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 73 (all X_a tl(X_a) = ti(fun(list(X_a),list(X_a)),tl(X_a))) # label(tsy_c_List_Otl_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 74 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_1))),Xs_1))) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_1))),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1))))) # label(fact_269_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 75 (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]. 2.14/2.53 76 (all X_a all Xs all Ys_2 hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_2)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Ys_2)),hAPP(list(X_a),list(X_a),rev(X_a),Xs))) # label(fact_256_rev__append) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 77 (all X_a all X_b all X_c all X_d all X_e all X_1 all Pa ((all A_4 all B_2 all C_2 all D all E hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,Pa,hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),A_4),hAPP(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,X_e))),B_2),hAPP(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e)),hAPP(X_c,fun(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e))),product_Pair(X_c,product_prod(X_d,X_e)),C_2),hAPP(X_e,product_prod(X_d,X_e),hAPP(X_d,fun(X_e,product_prod(X_d,X_e)),product_Pair(X_d,X_e),D),E))))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,Pa,X_1)))) # label(fact_67_prod__induct5) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 78 (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,Y) = ti(X_a,X)))))) # label(fact_338_order__antisym) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 79 (all X_b all X_a all A_2 all B_1 all A_6 all B_4 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_6),B_4) -> -(ti(X_a,A_6) = ti(X_a,A_2) -> ti(X_b,B_1) != ti(X_b,B_4)))) # label(fact_15_Pair__inject) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 80 (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_423_order__less__le__trans) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 81 (all X_a ti(fun(fun(X_a,bool),fun(list(X_a),product_prod(list(X_a),list(X_a)))),partition(X_a)) = partition(X_a)) # label(tsy_c_List_Opartition_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 82 (all X_a lexord(X_a) = ti(fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool)),lexord(X_a))) # label(tsy_c_List_Olexord_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 83 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) <-> M = N | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_489_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 84 (all X_a all Xs_1 hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)) = hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)) # label(fact_274_set__rev) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 85 (all P (-hBOOL(hAPP(bool,bool,fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 86 (all X_a all Xs all Ys_2 (Ys_2 = nil(X_a) -> hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_2)) = hAPP(list(X_a),X_a,last(X_a),Xs))) # label(fact_150_last__appendL) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 87 (all X_a ti(fun(fun(X_a,bool),fun(X_a,bool)),collect(X_a)) = collect(X_a)) # label(tsy_c_Set_OCollect_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 88 (all X_a all Pa all Xs_1 ((exists X_2 (hBOOL(hAPP(X_a,bool,Pa,X_2)) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) -> -(all Ys all X_2 ((exists Zs_2 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs_2)) = Xs_1) -> -hBOOL(hAPP(X_a,bool,Pa,X_2)))))) # label(fact_298_split__list__propE) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 89 (all X_b all X_a all F nil(X_a) = hAPP(list(X_b),list(X_a),hAPP(fun(X_b,list(X_a)),fun(list(X_b),list(X_a)),maps(X_b,X_a),F),nil(X_b))) # label(fact_93_maps__simps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 90 (all X_a all X_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),top_top(fun(X_a,bool))))) # label(fact_111_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 91 (all X_a ti(fun(list(X_a),X_a),hd(X_a)) = hd(X_a)) # label(tsy_c_List_Ohd_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 92 (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),Y),X)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_329_linorder__linear) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 93 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),hAPP(nat,nat,suc,M))))) # label(fact_482_Suc__le__mono) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 94 (all X_a all P hAPP(X_a,X_a,combi(X_a),P) = ti(X_a,P)) # label(help_COMBI_1_1_U) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 95 (all X_a (linorder(X_a) -> (all Y_1 all X_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) -> (ti(X_a,X_1) = ti(X_a,Y_1) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1))))))) # label(fact_400_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 96 (all X_a all N_1 all X all Xs hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X)),Xs)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))) # label(fact_266_replicate__app__Cons__same) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 97 (all X_a ti(fun(fun(X_a,bool),fun(list(X_a),list(X_a))),dropWhile(X_a)) = dropWhile(X_a)) # label(tsy_c_List_OdropWhile_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 98 (all I_2 all Fa (hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Fa),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) -> ((all X_2 (hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof)) -> (all A_4 all B_2 (ti(arrow_490897120le_alt,B_2) != ti(arrow_490897120le_alt,A_4) -> (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_4),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I_2))) -> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_4),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2)))))))) -> hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,Fa),I_2))))) # label(fact_42_dictatorI) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 99 (all X_a (linorder(X_a) -> (all X_1 all Xs_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),X_2)))) -> (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)))))))) # label(fact_363_sorted_OCons) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 100 (all I (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p_1,I))) <-> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I))))) # label(fact_5_iff) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 101 (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_341_xt1_I6_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 102 (all X_a all X_1 all Xs_1 all Y_1 all Ys_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_1))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))) <-> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))) & ti(X_a,Y_1) = ti(X_a,X_1) | hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),R_2)) & Xs_1 = Ys_1)) # label(fact_169_Cons__listrel1__Cons) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 103 (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_428_order__less__imp__le) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 104 (all X_a all Xs_1 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),M),Xs_1))),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs_1)))))) # label(fact_373_set__take__subset__set__take) # label(axiom) # label(non_clause). [assumption]. 2.14/2.53 105 (all X_a all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))) -> -(all X_2 all Y_2 (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),Y_2)),R_2)) -> (all Us all Vs (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Vs)) = Xs_1 -> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Vs)) != Ys_1)))))) # label(fact_172_listrel1E) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 106 (all X_a all N_1 all Xs hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),hAPP(list(X_a),list(X_a),butlast(X_a),Xs))) # label(fact_245_butlast__drop) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 107 (all X_a all Xs hAPP(list(X_a),nat,size_size(list(X_a)),Xs) = hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),rotate1(X_a),Xs))) # label(fact_183_length__rotate1) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 108 (all M all N (hAPP(nat,nat,suc,N) = M | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,N))))) # label(fact_481_le__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 109 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> (N_1 != hAPP(nat,nat,suc,M_1) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),N_1))))) # label(fact_472_Suc__lessI) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 110 (all X_a all X_1 all U all V all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),X_1),U)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),X_1),V))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))) -> ((all A_4 -hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),A_4),A_4)),R_2))) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),U),V)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2)))))) # label(fact_157_lexord__append__leftD) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 111 (all X_a all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2))) -> hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1) = hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) # label(fact_223_listrel__eq__len) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 112 (all X_a all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))) -> hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1) = hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) # label(fact_191_listrel1__eq__len) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 113 (all X_a all N_1 exists Xs_2 hAPP(list(X_a),nat,size_size(list(X_a)),Xs_2) = N_1) # label(fact_212_Ex__list__of__length) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 114 (all X_a all X_b ti(fun(X_a,fun(X_b,product_prod(X_a,X_b))),product_Pair(X_a,X_b)) = product_Pair(X_a,X_b)) # label(tsy_c_Product__Type_OPair_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 115 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> ti(X_a,Y_1) = ti(X_a,X_1)))))) # label(fact_427_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 116 (all X_a all Xs all Ys_2 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs) != hAPP(list(X_a),nat,size_size(list(X_a)),Ys_2) -> Xs != Ys_2)) # label(fact_179_neq__if__length__neq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 117 (all X_a all N_1 all X all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,N_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))) # label(fact_349_drop__Suc__Cons) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 118 (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_422_xt1_I7_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 119 (all X_a all X_b all S_1 all R_1 (ti(fun(product_prod(X_a,X_b),bool),S_1) = ti(fun(product_prod(X_a,X_b),bool),R_1) <-> (all X_2 all Xa (hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Xa)),R_1)) <-> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Xa)),S_1)))))) # label(fact_60_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 120 (all T_2 all T_1 (top(T_1) -> top(fun(T_2,T_1)))) # label(arity_fun___Orderings_Otop) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 121 (all X_b all X_a all F all B all A_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),B)))) -> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B)))))) # label(fact_57_funcsetI) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 122 (all X_a (order(X_a) -> (all A_2 all B_1 (ti(X_a,A_2) != ti(X_a,B_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))))))) # label(fact_431_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 123 (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]. 2.14/2.54 124 (all X_a all Xs_1 all X_1 all Ys_1 all Y_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),nil(X_a))) <-> ti(X_a,X_1) = ti(X_a,Y_1) & Xs_1 = Ys_1)) # label(fact_145_append1__eq__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 125 (all X_b all X_a all Q_1 all Pa ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_2),Y_2)))) -> hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),Pa),Q_1)))) # label(fact_392_predicate2I) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 126 (all X_a all X all Xs ti(X_a,X) = hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))) # label(fact_230_hd_Osimps) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 127 (all T_2 all T_1 (enum(T_2) & cl_HOL_Oequal(T_1) -> cl_HOL_Oequal(fun(T_2,T_1)))) # label(arity_fun___HOL_Oequal) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 128 (all X_a all N all X_1 all Xs_1 hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)) = hAPP(nat,list(X_a),hAPP(fun(nat,list(X_a)),fun(nat,list(X_a)),hAPP(list(X_a),fun(fun(nat,list(X_a)),fun(nat,list(X_a))),nat_case(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),hAPP(list(X_a),fun(nat,list(X_a)),hAPP(fun(nat,fun(list(X_a),list(X_a))),fun(list(X_a),fun(nat,list(X_a))),combc(nat,list(X_a),list(X_a)),drop(X_a)),Xs_1)),N)) # label(fact_271_drop__Cons) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 129 (all X_a all N_1 all X N_1 = hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X))) # label(fact_262_length__replicate) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 130 (all X_a (linorder(X_a) -> linorder_sorted(X_a) = ti(fun(list(X_a),bool),linorder_sorted(X_a)))) # label(tsy_c_List_Olinorder__class_Osorted_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 131 (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]. 2.14/2.54 132 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),hAPP(nat,nat,suc,N_1))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> hAPP(nat,nat,suc,N_1) = M_1))) # label(fact_484_le__SucE) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 133 (all X_a all Xs_1 all N ((exists Y_2 exists Ys (hAPP(list(X_a),nat,size_size(list(X_a)),Ys) = N & Xs_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys))) <-> hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(nat,nat,suc,N))) # label(fact_375_length__Suc__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 134 (all X_a all Xs_1 all Y_1 all Ys_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_1))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2))) -> -(all X_2 all Xs_2 (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2) -> (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),Y_1)),R_2)) -> -hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_2),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2)))))))) # label(fact_225_listrel__Cons2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 135 (all X_a all X_b all P_2 -(all X_2 all Y_2 hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2) != ti(product_prod(X_a,X_b),P_2))) # label(fact_62_PairE) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 136 (all X_a all A_1 all B (ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1)))) # label(fact_386_equalityD2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 137 (all X_c all X_a all X_b all Z_2 all Ca all P_1 ((all A_4 all B_2 (ti(product_prod(X_a,X_b),P_1) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_2) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Z_2),hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),Ca,A_4),B_2))))) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Z_2),hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),Ca),P_1))))) # label(fact_207_mem__splitI2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 138 (all X_a all X_1 all Xs_1 all Ys_1 all Zs (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Zs) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1) <-> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1) = Zs & nil(X_a) = Ys_1 | (exists Ys_3 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Ys_3) = Ys_1 & Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),Zs))))) # label(fact_144_Cons__eq__append__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 139 (all X_a all X_b all X_c all X_d all X_e all X_f all Y -(all A_4 all B_2 all C_2 all D all E all F_1 hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),A_4),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),B_2),hAPP(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),hAPP(X_c,fun(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_Pair(X_c,product_prod(X_d,product_prod(X_e,X_f))),C_2),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),D),hAPP(X_f,product_prod(X_e,X_f),hAPP(X_e,fun(X_f,product_prod(X_e,X_f)),product_Pair(X_e,X_f),E),F_1))))) != ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),Y))) # label(fact_66_prod__cases6) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 140 (all X_a exists X_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),top_top(fun(X_a,bool))))) # label(fact_121_UNIV__witness) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 141 (all X_a all X_b in_rel(X_a,X_b) = ti(fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),in_rel(X_a,X_b))) # label(tsy_c_FunDef_Oin__rel_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 142 (all X_a all Y_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),nil(X_a)),Y_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))) <-> (exists A_4 exists X_2 hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_4),X_2) = Y_1))) # label(fact_107_lexord__Nil__left) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 143 (all X_a all X all Xs Xs = hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))) # label(fact_218_tl_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 144 (all X_a all Xs all X hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a)))) = Xs) # label(fact_153_butlast__snoc) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 145 (all X_a all Xs_1 all Ys_1 (nil(X_a) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1) <-> Ys_1 = nil(X_a) & nil(X_a) = Xs_1)) # label(fact_135_Nil__is__append__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 146 (all X_a all Pa all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),Xs_1))))) # label(fact_186_distinct__dropWhile) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 147 (all X_a all X_1 all Y_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),X_1),Y_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))) & hAPP(list(X_a),nat,size_size(list(X_a)),Y_1) = hAPP(list(X_a),nat,size_size(list(X_a)),X_1) <-> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),X_1),Y_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lex(X_a),R_2))))) # label(fact_194_lexord__lex) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 148 (all X_a all X_1 all N all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs_1)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_317_in__set__takeD) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 149 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)) -> M_1 = N_1))) # label(fact_467_le__antisym) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 150 (all X_a all X_b all Pa ((exists X1 hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,X1))) <-> (exists A_4 exists B_2 hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_2)))))) # label(fact_71_split__paired__Ex) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 151 (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]. 2.14/2.54 152 (all X_a (top(X_a) -> (all Aa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),top_top(X_a)),Aa)) <-> top_top(X_a) = ti(X_a,Aa))))) # label(fact_345_top__unique) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 153 (all S all T_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S),T_3)) -> S != T_3)) # label(fact_461_less__not__refl3) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 154 (all X_a all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) <-> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1))))) # label(fact_263_distinct__rev) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 155 (all X_a (linorder(X_a) -> (all N_1 all Xs (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),Xs))))))) # label(fact_320_sorted__take) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 156 (all X_a all U all X_1 all Y_1 all Aa all Ba all R_2 (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),Aa),Ba)),R_2)) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),U),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Aa),X_1))),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),U),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Ba),Y_1)))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))))) # label(fact_155_lexord__append__left__rightI) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 157 (all X_a all Zs all Ys_1 all R_2 all Xs_1 ((all X_2 all Y_2 all Z_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),Y_2)),R_2)) -> (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),Y_2),Z_1)),R_2)) -> hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),Z_1)),R_2)))))) -> (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))) -> (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Ys_1),Zs)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Zs)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))))))) # label(fact_295_lexord__partial__trans) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 158 (all X_a all X_b all Pa all Xs_1 all Ys_1 (hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = hAPP(list(X_b),nat,size_size(list(X_b)),Ys_1) -> (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),Pa,nil(X_a)),nil(X_b))) -> ((all X_2 all Xs_2 all Y_2 all Ys (hAPP(list(X_b),nat,size_size(list(X_b)),Ys) = hAPP(list(X_a),nat,size_size(list(X_a)),Xs_2) -> (hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),Pa,Xs_2),Ys)) -> hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),Pa,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2)),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Y_2),Ys)))))) -> hBOOL(hAPP(list(X_b),bool,hAPP(list(X_a),fun(list(X_b),bool),Pa,Xs_1),Ys_1)))))) # label(fact_195_list__induct2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 159 (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]. 2.14/2.54 160 (all X_a all N_1 all Xs hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),hAPP(list(X_a),list(X_a),tl(X_a),Xs))) # label(fact_247_tl__drop) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 161 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)))))) # label(fact_439_linorder__not__le) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 162 (all X_a all Ys_1 all Pa all Xs_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,Pa,X_2)))) -> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Ys_1)) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)))) # label(fact_297_takeWhile__append2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 163 (all M_1 all N_1 (N_1 = M_1 | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)))) # label(fact_486_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 164 (all X_a all X_b all X_c all Q_1 all Pa all Z_2 (hBOOL(hAPP(X_a,bool,Q_1,hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),Pa),Z_2))) -> -(all X_2 all Y_2 (hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),X_2),Y_2) = ti(product_prod(X_b,X_c),Z_2) -> -hBOOL(hAPP(X_a,bool,Q_1,hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),Pa,X_2),Y_2))))))) # label(fact_198_splitE2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 165 (all X_a all Xs all Zs_1 all X all Xs1 all Ys_2 (Ys_2 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs1) -> (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs1),Zs_1) = Xs -> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_2),Zs_1) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)))) # label(fact_133_Cons__eq__appendI) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 166 (all X_a top_top(fun(X_a,bool)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(bool,fun(X_a,bool),combk(bool,X_a),fTrue))) # label(fact_119_UNIV__def) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 167 (all X_a all X_b all Pa ((all A_4 all B_2 hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_2)))) <-> (all X1 hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,X1))))) # label(fact_13_split__paired__All) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 168 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q)) # label(help_COMBC_1_1_U) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 169 (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_434_leI) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 170 (all X_a all X all Xs ((nil(X_a) = Xs -> nil(X_a) = hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))) & (nil(X_a) != Xs -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)) = hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))))) # label(fact_105_butlast_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 171 (all X_b all X_a all F all Aa all Xs_1 all Ys_1 hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),Aa),Xs_1)),Ys_1) = hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),Aa),hAPP(list(X_b),list(X_b),hAPP(list(X_b),fun(list(X_b),list(X_b)),append(X_b),Xs_1),Ys_1))) # label(fact_278_foldl__append) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 172 (all X_a ti(fun(list(X_a),nat),size_size(list(X_a))) = size_size(list(X_a))) # label(tsy_c_Nat_Osize__class_Osize_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 173 (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_421_order__le__less__trans) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 174 (all X_a all Xs_1 all X_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))))) # label(fact_370_set__subset__Cons) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 175 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) & M != N <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_490_nat__less__le) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 176 (all T_2 all T_1 (enum(T_2) & enum(T_1) -> enum(fun(T_2,T_1)))) # label(arity_fun___Enum_Oenum) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 177 (all X_a all X all Xs (nil(X_a) = Xs -> hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = ti(X_a,X))) # label(fact_96_last__ConsL) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 178 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (exists Ys exists Zs_2 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs_2)) = Xs_1))) # label(fact_310_split__list) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 179 (all X_a all Ys_1 all R_2 -hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),nil(X_a)),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lex(X_a),R_2)))) # label(fact_126_Nil__notin__lex) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 180 (all X_a all X_1 all R_2 all Y_1 ((exists B_2 exists Z_1 Y_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),B_2),Z_1)) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),X_1),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),X_1),Y_1))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))))) # label(fact_156_lexord__append__rightI) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 181 (all X_a all Ys_1 all Pa all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (-hBOOL(hAPP(X_a,bool,Pa,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1))))) # label(fact_286_takeWhile__append1) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 182 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) <-> (exists Ys exists Zs_2 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Zs_2))) & Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs_2)))))) # label(fact_300_in__set__conv__decomp__last) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 183 (all X_a all N_1 all X hAPP(list(X_a),list(X_a),rev(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X)) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X)) # label(fact_253_rev__replicate) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 184 (all X_b all X_a all F all Aa all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),F,Aa),Ba)) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),F),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))))) # label(fact_200_splitI) # label(axiom) # label(non_clause). [assumption]. 2.14/2.54 185 (all X_a all X_b (ord(X_b) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))))) # label(fact_332_le__funD) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 186 -(all C_2 -hBOOL(hAPP(list(arrow_490897120le_alt),bool,distinct(arrow_490897120le_alt),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),a),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),b),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),C_2),nil(arrow_490897120le_alt))))))) # label(fact_6__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 187 (all X_a all Xs_1 all Pa all X_1 ((-hBOOL(hAPP(X_a,bool,Pa,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)) & (hBOOL(hAPP(X_a,bool,Pa,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),Xs_1)))) # label(fact_184_dropWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 188 (all X_a all Pa all Xs_1 ((exists X_2 (hBOOL(hAPP(X_a,bool,Pa,X_2)) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) -> -(all Ys all X_2 all Zs_2 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs_2)) = Xs_1 -> (hBOOL(hAPP(X_a,bool,Pa,X_2)) -> -(all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Zs_2))) -> -hBOOL(hAPP(X_a,bool,Pa,Xa))))))))) # label(fact_311_split__list__last__propE) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 189 (all X_c all X_a all X_b all R_1 all Aa all Ba all Ca (hBOOL(hAPP(X_c,bool,hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),R_1),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba)),Ca)) -> hBOOL(hAPP(X_c,bool,hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),R_1,Aa),Ba),Ca)))) # label(fact_204_splitD_H) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 190 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_476_Suc__less__eq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 191 (all X_a all Pa all Xs_1 ((exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(X_a,bool,Pa,X_2)))) -> -(all Ys all X_2 ((exists Zs_2 Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs_2))) -> (hBOOL(hAPP(X_a,bool,Pa,X_2)) -> -(all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys))) -> -hBOOL(hAPP(X_a,bool,Pa,Xa))))))))) # label(fact_307_split__list__first__propE) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 192 (all X_b all X_a all Q_1 all Pa all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,X_1),Y_1)) -> (hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),Pa),Q_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_1),Y_1))))) # label(fact_382_rev__predicate2D) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 193 (all X_a all X_b all X_c all Y -(all A_4 all B_2 all C_2 hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),A_4),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),B_2),C_2)) != ti(product_prod(X_a,product_prod(X_b,X_c)),Y))) # label(fact_63_prod__cases3) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 194 (all X_a (cl_HOL_Oequal(X_a) -> fequal(X_a) = equal_equal(X_a))) # label(fact_237_equal) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 195 (all X_a all Xs_1 (Xs_1 != nil(X_a) -> (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> hAPP(list(X_a),list(X_a),butlast(X_a),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),hAPP(list(X_a),X_a,last(X_a),Xs_1)))),Xs_1)))) # label(fact_113_takeWhile__not__last) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 196 (all X_a (linorder(X_a) -> (all Ys_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)) -> (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Ys_1)) -> (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Ys_1)) -> (hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1) = hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys_1) -> Ys_1 = Xs_1)))))))) # label(fact_285_sorted__distinct__set__unique) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 197 (all X_a all Xs_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),nil(X_a))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2))) -> Xs_1 = nil(X_a))) # label(fact_216_listrel__Nil2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 198 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)))))) # label(fact_398_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 199 (all X_a all N_1 all Xs hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),hAPP(list(X_a),list(X_a),tl(X_a),Xs))) # label(fact_248_drop__tl) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 200 (all X_c all X_b all X_a all P_1 all F all G all Q_2 ((all X_2 all Y_2 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2) = ti(product_prod(X_a,X_b),Q_2) -> hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),G,X_2),Y_2) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),F,X_2),Y_2))) -> (ti(product_prod(X_a,X_b),Q_2) = ti(product_prod(X_a,X_b),P_1) -> hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),G),Q_2) = hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),F),P_1)))) # label(fact_197_split__cong) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 201 (all X_b all X_a all X all Xs (hAPP(list(X_a),list(X_a),rotate1(X_a),nil(X_a)) = nil(X_a) & hAPP(list(X_b),list(X_b),hAPP(list(X_b),fun(list(X_b),list(X_b)),append(X_b),Xs),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),X),nil(X_b))) = hAPP(list(X_b),list(X_b),rotate1(X_b),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),X),Xs)))) # label(fact_162_rotate__simps) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 202 (all X_a all X all Xs -hBOOL(hAPP(list(X_a),bool,null(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)))) # label(fact_86_null__rec_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 203 (all X_b all X_a all F all Aa all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba)) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))))) # label(fact_87_curryD) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 204 (all X_a (top(X_a) -> (all Aa (top_top(X_a) != ti(X_a,Aa) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),top_top(X_a))))))) # label(fact_418_less__top) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 205 (all X_a all X_b all Ca all P_1 (hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),Ca),P_1)) -> -(all X_2 all Y_2 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2) = ti(product_prod(X_a,X_b),P_1) -> -hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Ca,X_2),Y_2)))))) # label(fact_206_splitE) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 206 (all X_a all X_b all F all Aa all Ba (hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),F),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),F,Aa),Ba)))) # label(fact_203_splitD) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 207 (all X_a all X_b foldl(X_a,X_b) = ti(fun(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a))),foldl(X_a,X_b))) # label(tsy_c_List_Ofoldl_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 208 (all X_a butlast(X_a) = ti(fun(list(X_a),list(X_a)),butlast(X_a))) # label(tsy_c_List_Obutlast_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 209 (all X_a all Xs_1 (hAPP(list(X_a),list(X_a),rev(X_a),Xs_1) = nil(X_a) <-> nil(X_a) = Xs_1)) # label(fact_258_rev__is__Nil__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 210 (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_405_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 211 (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]. 2.14/2.55 212 (all X_a all X_1 all Xs_1 ((exists Ys exists Zs_2 Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs_2))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_299_in__set__conv__decomp) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 213 (all X_a all X_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),top_top(fun(X_a,bool))))) # label(fact_110_UNIV__I) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 214 (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_429_leD) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 215 (all X_a all Xs_1 all L all Pa all X_1 (-hBOOL(hAPP(X_a,bool,Pa,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),L))))) # label(fact_146_takeWhile__tail) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 216 (all X_a all X_b ti(fun(X_a,fun(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a))),list_case(X_a,X_b)) = list_case(X_a,X_b)) # label(tsy_c_List_Olist_Olist__case_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 217 (all X_b all X_c all X_a all X_d all X_e all F all G all P_1 hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F),hAPP(product_prod(X_d,X_e),product_prod(X_b,X_c),hAPP(fun(X_d,fun(X_e,product_prod(X_b,X_c))),fun(product_prod(X_d,X_e),product_prod(X_b,X_c)),product_prod_case(X_d,X_e,product_prod(X_b,X_c)),G),P_1)) = hAPP(product_prod(X_d,X_e),X_a,hAPP(fun(X_d,fun(X_e,X_a)),fun(product_prod(X_d,X_e),X_a),product_prod_case(X_d,X_e,X_a),hAPP(fun(X_d,fun(X_e,product_prod(X_b,X_c))),fun(X_d,fun(X_e,X_a)),hAPP(fun(fun(X_e,product_prod(X_b,X_c)),fun(X_e,X_a)),fun(fun(X_d,fun(X_e,product_prod(X_b,X_c))),fun(X_d,fun(X_e,X_a))),combb(fun(X_e,product_prod(X_b,X_c)),fun(X_e,X_a),X_d),hAPP(fun(product_prod(X_b,X_c),X_a),fun(fun(X_e,product_prod(X_b,X_c)),fun(X_e,X_a)),combb(product_prod(X_b,X_c),X_a,X_e),hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F))),G)),P_1)) # label(fact_178_split__twice) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 218 (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_416_order__less__asym) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 219 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,bool)),ord_less(X_a)) = ord_less(X_a))) # label(tsy_c_Orderings_Oord__class_Oless_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 220 (all X_a all A_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),top_top(fun(X_a,bool))))) # label(fact_365_subset__UNIV) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 221 (all X_a all I_1 all Xs (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),I_1),Xs))))) # label(fact_319_distinct__take) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 222 (all X_a all Xs_1 all Ys_1 all Zs (Ys_1 = Zs <-> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Zs) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1))) # label(fact_129_same__append__eq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 223 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1))) # label(fact_459_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 224 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_1)))) # label(fact_464_nat__le__linear) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 225 (all X_a all X_b (ord(X_b) -> (all F all G ((all X_2 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2)))) <-> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)))))) # label(fact_328_le__fun__def) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 226 (all X_a all Xs_1 all Y_1 all Ys_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_1))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))) -> ((all X_2 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Ys_1) = Xs_1 -> -hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),Y_1)),R_2)))) -> -(all Zs_2 (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Zs_2) -> -hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Zs_2),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2)))))))) # label(fact_174_Cons__listrel1E2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 227 (all X_a all X_b (ord(X_b) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))))) # label(fact_342_le__funE) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 228 (all X_a all Pa all Xs_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),Xs_1))),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))) # label(fact_356_length__dropWhile__le) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 229 (all X_a all Xs_1 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),hAPP(fun(list(X_a),fun(X_a,list(X_a))),fun(list(X_a),fun(list(X_a),list(X_a))),foldl(list(X_a),X_a),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),fun(X_a,list(X_a))),combc(X_a,list(X_a),list(X_a)),cons(X_a))),nil(X_a)),Xs_1) = hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)) # label(fact_272_rev__foldl__cons) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 230 (all X_b all X_a all B all A_3 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),A_1)) -> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(fun(X_a,X_b),bool),fun(fun(fun(X_a,X_b),bool),bool),ord_less_eq(fun(fun(X_a,X_b),bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_3),B))))) # label(fact_367_Pi__anti__mono) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 231 (all X_b member(X_b) = ti(fun(X_b,fun(fun(X_b,bool),bool)),member(X_b))) # label(tsy_c_member_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 232 (all M all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),M)))) # label(fact_480_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 233 (all X_a all C all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),C)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C))))) # label(fact_390_subset__trans) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 234 (all X_a all Xs_1 all X_1 all Ys_1 all Y_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))) & ti(X_a,X_1) = ti(X_a,Y_1) | hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),R_2)) & Ys_1 = Xs_1 <-> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)))),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),nil(X_a))))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))))) # label(fact_160_snoc__listrel1__snoc__iff) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 235 (all X_a all X_1 all Y_1 all R_2 ((all A_4 all B_2 (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),B_2),A_4)),R_2)) | ti(X_a,B_2) = ti(X_a,A_4) | hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),A_4),B_2)),R_2)))) -> X_1 = Y_1 | hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Y_1),X_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))) | hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),X_1),Y_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))))) # label(fact_109_lexord__linear) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 236 (all X_a all Pa all Xs_1 (nil(X_a) != Xs_1 -> ((all X_2 hBOOL(hAPP(list(X_a),bool,Pa,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),nil(X_a))))) -> ((all X_2 all Xs_2 (nil(X_a) != Xs_2 -> (hBOOL(hAPP(list(X_a),bool,Pa,Xs_2)) -> hBOOL(hAPP(list(X_a),bool,Pa,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2)))))) -> hBOOL(hAPP(list(X_a),bool,Pa,Xs_1)))))) # label(fact_78_list__nonempty__induct) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 237 (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_420_xt1_I8_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 238 (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]. 2.14/2.55 239 (all X all Y (Y != X -> (-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_458_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 240 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_497_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 241 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)))) # label(fact_492_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 242 (all X_a cons(X_a) = ti(fun(X_a,fun(list(X_a),list(X_a))),cons(X_a))) # label(tsy_c_List_Olist_OCons_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 243 (all X_a all N_1 all X all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),Xs))) # label(fact_348_take__Suc__Cons) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 244 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)))) # label(fact_488_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 245 (all X_1 all Y_1 all L_1 all Z_2 ((ti(arrow_490897120le_alt,Y_1) = ti(arrow_490897120le_alt,Z_2) -> ti(arrow_490897120le_alt,Y_1) != ti(arrow_490897120le_alt,X_1)) & (ti(arrow_490897120le_alt,Z_2) != ti(arrow_490897120le_alt,Y_1) -> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_1)),L_1))) & ti(arrow_490897120le_alt,Z_2) != ti(arrow_490897120le_alt,X_1) <-> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,L_1),Z_2))))) # label(fact_11_in__mktop) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 246 (all X_a (top(X_a) -> ti(X_a,top_top(X_a)) = top_top(X_a))) # label(tsy_c_Orderings_Otop__class_Otop_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 247 (all X_b hBOOL(hAPP(list(X_b),bool,null(X_b),nil(X_b)))) # label(fact_83_null__rec_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 248 (all X_a ti(fun(X_a,fun(X_a,bool)),fequal(X_a)) = fequal(X_a)) # label(tsy_c_fequal_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 249 (all X_1 all L_1 (hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_1),arrow_2064824852le_Lin)) -> hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,L_1),X_1)),arrow_2064824852le_Lin)))) # label(fact_23_mkbot__Lin) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 250 (all P_a all Pa all A_5 all B_3 all Aa all Ba (ti(arrow_490897120le_alt,Ba) != ti(arrow_490897120le_alt,Aa) -> (ti(arrow_490897120le_alt,B_3) != ti(arrow_490897120le_alt,A_5) -> (ti(arrow_490897120le_alt,B_3) != ti(arrow_490897120le_alt,Aa) -> (ti(arrow_490897120le_alt,Ba) != ti(arrow_490897120le_alt,A_5) -> (hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Pa),arrow_1111136790e_Prof)) -> (hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),P_a),arrow_1111136790e_Prof)) -> ((all I (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_a,I))) <-> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I))))) -> (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa))) -> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_a)))))))))))) # label(fact_19__C1_C) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 251 (all X_a all X_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B))))) # label(fact_389_set__mp) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 252 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)))) # label(fact_468_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 253 (all X_a all X_1 all U all V all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),U),V)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),X_1),U)),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),X_1),V))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))))) # label(fact_151_lexord__append__leftI) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 254 (all P_a all Pa all A_5 all B_3 all Aa all Ba (ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Ba) -> (ti(arrow_490897120le_alt,B_3) != ti(arrow_490897120le_alt,A_5) -> (ti(arrow_490897120le_alt,B_3) != ti(arrow_490897120le_alt,Aa) -> (ti(arrow_490897120le_alt,A_5) != ti(arrow_490897120le_alt,Ba) -> (hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),Pa),arrow_1111136790e_Prof)) -> (hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),P_a),arrow_1111136790e_Prof)) -> ((all I (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),P_a,I))) <-> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Pa,I))))) -> (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,Pa))) <-> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_5),B_3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,P_a)))))))))))) # label(fact_20__C2_C) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 255 (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]. 2.14/2.55 256 (all X_a (cl_HOL_Oequal(X_a) -> (all X_1 all Y_1 (ti(X_a,Y_1) = ti(X_a,X_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),equal_equal(X_a),X_1),Y_1)))))) # label(fact_239_equal__eq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 257 (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_327_order__refl) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 258 (all X_a (top(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),top_top(X_a)),A_2)) -> ti(X_a,A_2) = top_top(X_a))))) # label(fact_344_top__le) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 259 (all K all I_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J)) -> (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,suc,I_1)),K))))) # label(fact_471_less__trans__Suc) # label(axiom) # label(non_clause). [assumption]. 2.14/2.55 260 (all X_a all Ys_1 all Xs_1 all Us_1 all Vs_1 all X_1 all Y_1 all R_2 (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),R_2)) -> (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Vs_1)) = Xs_1 -> (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Vs_1)) = Ys_1 -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))))))) # label(fact_171_listrel1I) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 261 (all X_a all Pa all Xs_1 hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Xs_1))),Xs_1)) # label(fact_244_dropWhile__eq__drop) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 262 (all X_a all Xs all Ys_2 ((Ys_2 = nil(X_a) -> hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_2)) = hAPP(list(X_a),X_a,last(X_a),Xs)) & (nil(X_a) != Ys_2 -> hAPP(list(X_a),X_a,last(X_a),Ys_2) = hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_2))))) # label(fact_148_last__append) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 263 (all X_b (ord(X_b) -> ord_less_eq(X_b) = ti(fun(X_b,fun(X_b,bool)),ord_less_eq(X_b)))) # label(tsy_c_Orderings_Oord__class_Oless__eq_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 264 (all X_b all X_a all F all Aa hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),Aa),nil(X_b)) = ti(X_a,Aa)) # label(fact_281_foldl__Nil) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 265 (all X_b all X_a all F all Aa all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba)) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))))) # label(fact_88_curryE) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 266 (all X_a last(X_a) = ti(fun(list(X_a),X_a),last(X_a))) # label(tsy_c_List_Olast_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 267 (all X_a all Ys_1 all Zs all X_1 all Xs_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Zs) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1) <-> Ys_1 = nil(X_a) & hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1) = Zs | (exists Ys_3 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Ys_3) = Ys_1 & hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),Zs) = Xs_1)))) # label(fact_143_append__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 268 (all X_a all Pa all Xs_1 all Y_1 all Ys_1 (-hBOOL(hAPP(X_a,bool,Pa,Y_1)) & Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_1)) <-> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_1))) # label(fact_176_dropWhile__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 269 (all X_a all F1 all F2 all Nat hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),F1),F2),hAPP(nat,nat,suc,Nat)) = hAPP(nat,X_a,F2,Nat)) # label(fact_491_nat__case__Suc) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 270 (all X_a all X_b all X_c all Z_2 all Ca all P_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z_2),hAPP(product_prod(X_b,X_c),fun(X_a,bool),hAPP(fun(X_b,fun(X_c,fun(X_a,bool))),fun(product_prod(X_b,X_c),fun(X_a,bool)),product_prod_case(X_b,X_c,fun(X_a,bool)),Ca),P_1))) -> -(all X_2 all Y_2 (ti(product_prod(X_b,X_c),P_1) = hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),X_2),Y_2) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z_2),hAPP(X_c,fun(X_a,bool),hAPP(X_b,fun(X_c,fun(X_a,bool)),Ca,X_2),Y_2))))))) # label(fact_209_mem__splitE) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 271 (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_402_less__imp__neq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 272 (all X_a all Pa hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),nil(X_a)),nil(X_a)) = hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(fun(X_a,bool),fun(list(X_a),product_prod(list(X_a),list(X_a))),partition(X_a),Pa),nil(X_a))) # label(fact_114_partition_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 273 (all X_a ti(fun(list(X_a),list(X_a)),rev(X_a)) = rev(X_a)) # label(tsy_c_List_Orev_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 274 (all X_a all Xs_1_1 all Xs_2_1 all Ys_1_1 all Ys_2_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1_1),Xs_2_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1_1),Ys_2_1) <-> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1_1)),hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1_1))) -> Ys_2_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1_1)),Xs_1_1)),Xs_2_1) & Ys_1_1 = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1_1)),Xs_1_1)) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1_1)),hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1_1))) -> Xs_1_1 = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1_1)),Ys_1_1) & hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1_1)),Ys_1_1)),Ys_2_1) = Xs_2_1))) # label(fact_326_append__eq__append__conv__if) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 275 (all X_a all X_1 all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B))))) # label(fact_387_in__mono) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 276 (all X_a all A_1 all B (ti(fun(X_a,bool),B) = ti(fun(X_a,bool),A_1) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)))) # label(fact_385_equalityD1) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 277 (all X_a (order(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)))))) # label(fact_409_xt1_I9_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 278 (all X_b all X_a (top(X_a) -> (all X_1 top_top(X_a) = hAPP(X_b,X_a,top_top(fun(X_b,X_a)),X_1)))) # label(fact_112_top__apply) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 279 (all X_a all N all X_1 all Xs_1 hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)) = hAPP(nat,list(X_a),hAPP(fun(nat,list(X_a)),fun(nat,list(X_a)),hAPP(list(X_a),fun(fun(nat,list(X_a)),fun(nat,list(X_a))),nat_case(list(X_a)),nil(X_a)),hAPP(fun(nat,list(X_a)),fun(nat,list(X_a)),hAPP(fun(list(X_a),list(X_a)),fun(fun(nat,list(X_a)),fun(nat,list(X_a))),combb(list(X_a),list(X_a),nat),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1)),hAPP(list(X_a),fun(nat,list(X_a)),hAPP(fun(nat,fun(list(X_a),list(X_a))),fun(list(X_a),fun(nat,list(X_a))),combc(nat,list(X_a),list(X_a)),take(X_a)),Xs_1))),N)) # label(fact_316_take__Cons) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 280 (all X_a (cl_HOL_Oequal(X_a) -> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),equal_equal(X_a),X),X))))) # label(fact_238_equal__refl) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 281 (all X_a all X_1 all Xs_1 ((exists Ys exists Zs_2 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs_2)) = Xs_1 & -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys))))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_301_in__set__conv__decomp__first) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 282 (all X_a all Xs_1 all Ys_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1) = Xs_1 <-> Ys_1 = nil(X_a))) # label(fact_140_append__self__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 283 (all X_b all X_c all X_a all F all Aa all Ba hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F,Aa),Ba)) # label(fact_182_split__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 284 (all L_1 all X_1 all Y_1 (ti(arrow_490897120le_alt,Y_1) != ti(arrow_490897120le_alt,X_1) -> (hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_1),arrow_2064824852le_Lin)) -> hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,L_1),X_1),Y_1)),arrow_2064824852le_Lin))))) # label(fact_17_below__Lin) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 285 (all X_a all Xs_1 (nil(X_a) = Xs_1 <-> hBOOL(hAPP(list(X_a),bool,null(X_a),Xs_1)))) # label(fact_84_List_Onull__def) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 286 (all X_a (preorder(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)))))) # label(fact_408_order__less__asym_H) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 287 (all X all Y (hAPP(nat,nat,suc,X) = hAPP(nat,nat,suc,Y) -> X = Y)) # label(fact_455_Suc__inject) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 288 (all X_a all N_1 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs))),nil(X_a))) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N_1)),Xs))) # label(fact_395_take__hd__drop) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 289 (all X_a all X_b all S_2 all Xs_1 all F ((all X_2 all Y_2 all S_3 hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,S_3),X_2)),Y_2) = hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,S_3),Y_2)),X_2)) -> hAPP(list(X_a),X_b,hAPP(X_b,fun(list(X_a),X_b),hAPP(fun(X_b,fun(X_a,X_b)),fun(X_b,fun(list(X_a),X_b)),foldl(X_b,X_a),F),S_2),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)) = hAPP(list(X_a),X_b,hAPP(X_b,fun(list(X_a),X_b),hAPP(fun(X_b,fun(X_a,X_b)),fun(X_b,fun(list(X_a),X_b)),foldl(X_b,X_a),F),S_2),Xs_1))) # label(fact_302_foldl__rev) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 290 (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_339_order__trans) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 291 (all X_a all C all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),B),C)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),C))))) # label(fact_446_subset__psubset__trans) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 292 (all X_a (linorder(X_a) -> (all Zs_1 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(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Zs_1))) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Zs_1))))))))) # label(fact_351_sorted__many) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 293 (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_414_order__less__trans) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 294 (all X_a all Xs (nil(X_a) != Xs -> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(list(X_a),X_a,last(X_a),Xs)),nil(X_a))) = Xs)) # label(fact_123_append__butlast__last__id) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 295 (all X_a all X_b all X_1 all F all A_1 all B (hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B)))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),B))))) # label(fact_48_funcset__mem) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 296 (all X_a all Xs hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),rev(X_a),Xs)) = hAPP(list(X_a),nat,size_size(list(X_a)),Xs)) # label(fact_257_length__rev) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 297 (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]. 2.14/2.56 298 (all Aa all Ba all L_1 (hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_1),arrow_2064824852le_Lin)) -> (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),L_1)) -> -hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Aa)),L_1))))) # label(fact_25_Lin__irrefl) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 299 (all X_a all X_b all X_c all X_d all X_e all X_f all X_1 all Pa ((all A_4 all B_2 all C_2 all D all E all F_1 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),bool,Pa,hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),A_4),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),B_2),hAPP(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),hAPP(X_c,fun(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_Pair(X_c,product_prod(X_d,product_prod(X_e,X_f))),C_2),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),D),hAPP(X_f,product_prod(X_e,X_f),hAPP(X_e,fun(X_f,product_prod(X_e,X_f)),product_Pair(X_e,X_f),E),F_1)))))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),bool,Pa,X_1)))) # label(fact_65_prod__induct6) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 300 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1))))) # label(fact_473_less__SucI) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 301 (all X_a all Xs_1 all Ys_1 all Zs (Ys_1 = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)),Zs) & hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)),Zs) = Xs_1 <-> Zs = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1))) # label(fact_323_append__eq__conv__conj) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 302 (all X_b null(X_b) = ti(fun(list(X_b),bool),null(X_b))) # label(tsy_c_List_Onull_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 303 (all X_a all R_2 all S_2 (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(fun(product_prod(X_a,X_a),bool),fun(fun(product_prod(X_a,X_a),bool),bool),ord_less_eq(fun(product_prod(X_a,X_a),bool)),R_2),S_2)) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(fun(product_prod(list(X_a),list(X_a)),bool),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),ord_less_eq(fun(product_prod(list(X_a),list(X_a)),bool)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),S_2))))) # label(fact_369_listrel__mono) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 304 (all X_a all X_b all Pa all Q_1 all X_2 (hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),Q_1),X_2)) & hBOOL(Pa) <-> hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fconj,Pa))),Q_1)),X_2)))) # label(fact_210_split__part) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 305 (all X_a all Pa all Xs_1 (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Xs_1) <-> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,Pa,X_2)))))) # label(fact_277_takeWhile__eq__all__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 306 (all X_a all X all Xs all Y all Ys_2 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Ys_2)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),Xs),Ys_2)))) # label(fact_52_splice_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 307 (all X_a all N_1 all Xs (Xs != nil(X_a) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),hAPP(list(X_a),X_a,hd(X_a),Xs)),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),hAPP(list(X_a),list(X_a),tl(X_a),Xs))) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N_1)),Xs))) # label(fact_324_take__Suc) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 308 (all X_a all Xs_1 all R_2 -hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),nil(X_a)),Xs_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2)))) # label(fact_167_not__Nil__listrel1) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 309 (all T all A ti(T,A) = ti(T,ti(T,A))) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 310 (all X_a (order(X_a) -> (all Y_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) -> (ti(X_a,Y_1) = ti(X_a,X_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1))))))) # label(fact_333_order__antisym__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 311 (all X_a all Xs_1 all X_1 all Ys_1 (nil(X_a) != Ys_1 & Xs_1 = hAPP(list(X_a),list(X_a),butlast(X_a),Ys_1) & ti(X_a,X_1) = hAPP(list(X_a),X_a,last(X_a),Ys_1) <-> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a))) = Ys_1)) # label(fact_124_snoc__eq__iff__butlast) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 312 (all X_a all A_1 ((all X_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))) -> ti(fun(X_a,bool),A_1) = top_top(fun(X_a,bool)))) # label(fact_120_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 313 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Xs_1)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_279_in__set__butlastD) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 314 (all X_a all Xs all Ys_2 (Xs = Ys_2 -> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),nil(X_a)),Ys_2) = Xs)) # label(fact_142_eq__Nil__appendI) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 315 (all X_a all X_1 all R_2 -hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),X_1),nil(X_a))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2)))) # label(fact_104_lexord__Nil__right) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 316 (all X_a all N_1 all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)) = hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs))) # label(fact_246_drop__butlast) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 317 (all X_a all Xs_1 all Ys_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1) = nil(X_a) <-> nil(X_a) = Xs_1 & nil(X_a) = Ys_1)) # label(fact_139_append__is__Nil__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 318 (all X_a all X_1 all Xs_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) <-> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))))) # label(fact_284_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 319 (all X_a all X all Xs (Xs != nil(X_a) -> hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)) = hAPP(list(X_a),X_a,last(X_a),Xs))) # label(fact_97_last__ConsR) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 320 (all X_a all Xs_1 all Ys_1 (hAPP(list(X_a),list(X_a),rev(X_a),Xs_1) = hAPP(list(X_a),list(X_a),rev(X_a),Ys_1) <-> Ys_1 = Xs_1)) # label(fact_251_rev__is__rev__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 321 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))) <-> N = M | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_477_less__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 322 (all X_a all Pa all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Xs_1))))) # label(fact_116_distinct__takeWhile) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 323 (all X_a (order(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) -> (ti(X_a,B_1) != ti(X_a,A_2) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))))))) # label(fact_425_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 324 (all X_a all A_1 hBOOL(hAPP(fun(fun(X_a,X_a),bool),bool,hAPP(fun(X_a,X_a),fun(fun(fun(X_a,X_a),bool),bool),member(fun(X_a,X_a)),combi(X_a)),hAPP(fun(X_a,fun(X_a,bool)),fun(fun(X_a,X_a),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_a,bool)),fun(fun(X_a,X_a),bool)),pi(X_a,X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,fun(X_a,bool)),combk(fun(X_a,bool),X_a),A_1))))) # label(fact_47_funcset__id) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 325 (all M_1 all N_1 (N_1 = M_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)))) # label(fact_465_eq__imp__le) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 326 (all X_a listrel(X_a) = ti(fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool)),listrel(X_a))) # label(tsy_c_List_Olistrel_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 327 (all X_a all Aa all X_1 all Ba all Y_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Aa),X_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Ba),Y_1))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))) <-> ti(X_a,Ba) = ti(X_a,Aa) & hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),X_1),Y_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))) | hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),Aa),Ba)),R_2)))) # label(fact_92_lexord__cons__cons) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 328 (all N_1 all M_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),M_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,M_1))) -> M_1 = N_1))) # label(fact_474_less__antisym) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 329 (all X_a all X_b all F all G ((all X_2 hAPP(X_a,X_b,G,X_2) = hAPP(X_a,X_b,F,X_2)) -> ti(fun(X_a,X_b),G) = ti(fun(X_a,X_b),F))) # label(fact_75_ext) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 330 (all X_a all X_b (ord(X_b) -> (all F all G (-hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),G),F)) & hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) <-> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less(fun(X_a,X_b)),F),G)))))) # label(fact_450_less__fun__def) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 331 (all X_a all Xs (Xs != nil(X_a) -> (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)))))) # label(fact_95_distinct__butlast) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 332 (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),Y),X)) | ti(X_a,X) = ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_399_linorder__less__linear) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 333 (all X_a (order(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> ti(X_a,X_1) != ti(X_a,Y_1) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)))))) # label(fact_437_order__less__le) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 334 (all X_a (linorder(X_a) -> (all Xs (Xs != nil(X_a) -> (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Xs)))))))) # label(fact_101_sorted__butlast) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 335 (all X_a (top(X_a) -> (all A_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),top_top(X_a)))))) # label(fact_346_top__greatest) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 336 (all X_b all X_a all P all Q hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P)) # label(help_COMBK_1_1_U) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 337 (all X_a all X_b all X_c all X_d all X_e all Y -(all A_4 all B_2 all C_2 all D all E hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),A_4),hAPP(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,X_e))),B_2),hAPP(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e)),hAPP(X_c,fun(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e))),product_Pair(X_c,product_prod(X_d,X_e)),C_2),hAPP(X_e,product_prod(X_d,X_e),hAPP(X_d,fun(X_e,product_prod(X_d,X_e)),product_Pair(X_d,X_e),D),E)))) != ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),Y))) # label(fact_68_prod__cases5) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 338 (all X_a (preorder(X_a) -> (all Pa all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) -> hBOOL(Pa)))))) # label(fact_407_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 339 (all X_b all X_c all X_a product_prod_case(X_b,X_c,X_a) = ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),product_prod_case(X_b,X_c,X_a))) # label(tsy_c_Product__Type_Oprod_Oprod__case_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 340 (all P all Q (hBOOL(P) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 341 (all X_a all I_1 all X hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),I_1),X)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a))) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),I_1),X))) # label(fact_243_replicate__append__same) # label(axiom) # label(non_clause). [assumption]. 2.14/2.56 342 (all X_a (order(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2)) -> (ti(X_a,A_2) != ti(X_a,B_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))))))) # label(fact_424_xt1_I11_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 343 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 344 (all X_a all X_b ti(fun(X_a,fun(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a))),list_rec(X_a,X_b)) = list_rec(X_a,X_b)) # label(tsy_c_List_Olist_Olist__rec_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 345 (all X_a all N_1 all Xs hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),hAPP(list(X_a),list(X_a),tl(X_a),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),hAPP(nat,nat,suc,N_1)),Xs)) # label(fact_357_drop__Suc) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 346 (all X_a all X_b all X_c produc1605651328_split(X_a,X_b,X_c) = product_prod_case(X_a,X_b,X_c)) # label(fact_192_internal__split__def) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 347 (all X_a all X all Xs hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs) != Xs) # label(fact_39_not__Cons__self2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 348 (all X_a all Xs_1 (nil(X_a) = hAPP(list(X_a),list(X_a),rev(X_a),Xs_1) <-> Xs_1 = nil(X_a))) # label(fact_259_Nil__is__rev__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 349 (all X_b all X_a all F1 all Aa all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),F1,Aa),Ba)) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),F1),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))))) # label(fact_201_prod__caseI) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 350 (all X_a ti(list(X_a),nil(X_a)) = nil(X_a)) # label(tsy_c_List_Olist_ONil_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 351 (all X_a all Xs (Xs != nil(X_a) -> hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs)) = hAPP(list(X_a),X_a,last(X_a),Xs))) # label(fact_242_hd__rev) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 352 (all X_a all N all Xs_1 ((exists Y_2 exists Ys (N = hAPP(list(X_a),nat,size_size(list(X_a)),Ys) & hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys) = Xs_1)) <-> hAPP(nat,nat,suc,N) = hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1))) # label(fact_364_Suc__length__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 353 (all X_a all Xs_1 all Y_1 all Ys_1 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_1) = hAPP(list(X_a),list(X_a),rev(X_a),Xs_1) <-> Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Ys_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),nil(X_a))))) # label(fact_268_rev__eq__Cons__iff) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 354 (all X_a all N all Xs_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N),Xs_1))),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)))) # label(fact_371_set__take__subset) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 355 (all X_a all Ys_2 all Xs (Xs != nil(X_a) -> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),tl(X_a),Xs)),Ys_2) = hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_2)))) # label(fact_224_tl__append2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 356 (all X_a all X_b all F all Aa all Ba (hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba)))) # label(fact_82_curryI) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 357 (all X_a (ord(X_a) -> (all C_1 all A_2 all B_1 (A_2 = B_1 -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C_1))))))) # label(fact_334_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 358 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)))) # label(fact_469_Suc__lessD) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 359 (all K all I_1 all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),K))))) # label(fact_466_le__trans) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 360 (all X_1 all Y_1 all L_1 (hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_1),arrow_2064824852le_Lin)) -> (ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Y_1) -> (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Y_1),X_1)),L_1)) <-> -hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_1)),L_1)))))) # label(fact_26_notin__Lin__iff) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 361 (all X_a all Xs_1 all Ys_1 all R_2 all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_2,X_1),Y_1)) -> (hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_2),Xs_1),Ys_1)) -> hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_2),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_1)))))) # label(fact_231_listrelp_OCons) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 362 (all X_a all Ys_2 all Us_2 all Xs all Xs1 all Zs_1 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Xs1) = Zs_1 -> (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs1),Us_2) = Ys_2 -> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs_1),Us_2) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_2)))) # label(fact_127_append__eq__appendI) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 363 (all X_a all X hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X),nil(X_a))) # label(fact_73_insert__Nil) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 364 (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_331_order__eq__refl) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 365 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_arg2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 366 (all X_a all X_1 hBOOL(hAPP(X_a,bool,top_top(fun(X_a,bool)),X_1))) # label(fact_98_top1I) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 367 (all X_a all A_6 all List_3 nil(X_a) != hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_6),List_3)) # label(fact_35_list_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 368 (all X_b all X_a all F all B all A_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,fun(X_b,bool),B,X_2))))) -> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))))) # label(fact_58_Pi__I_H) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 369 (all X_a all X_b all Ca all P_1 ((all A_4 all B_2 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_2) = ti(product_prod(X_a,X_b),P_1) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Ca,A_4),B_2)))) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),Ca),P_1)))) # label(fact_205_splitI2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 370 (all X_a all C all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),C)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),C))))) # label(fact_447_psubset__subset__trans) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 371 (all X_a all A_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),A_1))) # label(fact_383_subset__refl) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 372 (all X_a all Xs_1 all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),M),Xs_1))),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs_1)))))) # label(fact_374_set__drop__subset__set__drop) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 373 (all X_a (linorder(X_a) -> (all X_1 all Xs_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),X_2)))) & hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)) <-> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))))))) # label(fact_358_sorted__Cons) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 374 (all X_b all X_a all F1 all F2 hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a)),list_case(X_a,X_b),F1),F2),nil(X_b)) = ti(X_a,F1)) # label(fact_50_list_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 375 (all Q all P (-hBOOL(P) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | -hBOOL(Q))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 376 (all X_a all X_b all Y -(all A_4 all B_2 hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_2) != ti(product_prod(X_a,X_b),Y))) # label(fact_61_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 377 (all X_a all Xs_1 all R_2 -hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),nil(X_a))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lex(X_a),R_2)))) # label(fact_125_Nil2__notin__lex) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 378 (all X_a all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)) | ti(X_a,X) = ti(X_a,Y))) # label(help_fequal_1_1_T) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 379 (all X_a rotate1(X_a) = ti(fun(list(X_a),list(X_a)),rotate1(X_a))) # label(tsy_c_List_Orotate1_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 380 (all X_b all X_a all B all C all A_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_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_a,fun(X_b,bool),B,X_2)),hAPP(X_a,fun(X_b,bool),C,X_2))))) -> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(fun(X_a,X_b),bool),fun(fun(fun(X_a,X_b),bool),bool),ord_less_eq(fun(fun(X_a,X_b),bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),C))))) # label(fact_393_Pi__mono) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 381 (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),fFalse),X),Y) = ti(X_a,Y)) # label(help_If_2_1_T) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 382 (all X_a all Xs_1 (Xs_1 = nil(X_a) <-> hBOOL(hAPP(list(X_a),bool,null(X_a),Xs_1)))) # label(fact_85_eq__Nil__null) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 383 (all L_1 (hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_1),arrow_2064824852le_Lin)) -> hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),combk(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),arrow_660593299e_indi),L_1)),arrow_1111136790e_Prof)))) # label(fact_22_const__Lin__Prof) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 384 (all X_a all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) & ti(fun(X_a,bool),B) != ti(fun(X_a,bool),A_1) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)))) # label(fact_451_psubset__eq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 385 (all X_a all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) <-> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),rotate1(X_a),Xs_1))))) # label(fact_164_distinct1__rotate) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 386 (all X_a (cl_HOL_Oequal(X_a) -> equal_equal(X_a) = ti(fun(X_a,fun(X_a,bool)),equal_equal(X_a)))) # label(tsy_c_HOL_Oequal__class_Oequal_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 387 (all X_a all Ys_1 all Xs_1 (Ys_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1) <-> nil(X_a) = Xs_1)) # label(fact_138_self__append__conv2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 388 (all X_a all X_b all S_2 all Xs_1 all X_1 all F ((all X_2 all Y_2 all S_3 hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,S_3),Y_2)),X_2) = hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,S_3),X_2)),Y_2)) -> hAPP(list(X_a),X_b,hAPP(X_b,fun(list(X_a),X_b),hAPP(fun(X_b,fun(X_a,X_b)),fun(X_b,fun(list(X_a),X_b)),foldl(X_b,X_a),F),hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,S_2),X_1)),Xs_1) = hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F,hAPP(list(X_a),X_b,hAPP(X_b,fun(list(X_a),X_b),hAPP(fun(X_b,fun(X_a,X_b)),fun(X_b,fun(list(X_a),X_b)),foldl(X_b,X_a),F),S_2),Xs_1)),X_1))) # label(fact_314_foldl__fun__comm) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 389 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M))) <-> M = N))) # label(fact_493_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 390 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),N_1))) # label(fact_479_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 391 (all X_a all Q_1 all Pa all L all K_1 (K_1 = L -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),L))) -> (hBOOL(hAPP(X_a,bool,Q_1,X_2)) <-> hBOOL(hAPP(X_a,bool,Pa,X_2))))) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Q_1),K_1) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),L)))) # label(fact_303_dropWhile__cong) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 392 (all X_a hAPP(list(X_a),list(X_a),tl(X_a),nil(X_a)) = nil(X_a)) # label(fact_219_tl_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 393 (all X_a all Xs all X hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs) != Xs) # label(fact_40_not__Cons__self) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 394 (all X_a (linorder(X_a) -> (all Xs (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),tl(X_a),Xs))))))) # label(fact_221_sorted__tl) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 395 (all X_a all Xs (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),tl(X_a),Xs))))) # label(fact_220_distinct__tl) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 396 (all X_a all X_1 all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))) -> ((all Y_2 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Xs_1) = Ys_1 -> -hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_2)),R_2)))) -> -(all Zs_2 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Zs_2) = Ys_1 -> -hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Zs_2)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2)))))))) # label(fact_173_Cons__listrel1E1) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 397 (all X_c all X_b all X_a all Ca all X_1 all P_1 ((all A_4 all B_2 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_2) = ti(product_prod(X_a,X_b),P_1) -> hBOOL(hAPP(X_c,bool,hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),Ca,A_4),B_2),X_1)))) -> hBOOL(hAPP(X_c,bool,hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),Ca),P_1),X_1)))) # label(fact_208_splitI2_H) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 398 (all X_a all R_1 all S_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),R_1),S_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_1)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S_1))))) # label(fact_378_pred__subset__eq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 399 (all X_a all Xs_1 (nil(X_a) != Xs_1 -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(list(X_a),X_a,hd(X_a),Xs_1)),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_290_hd__in__set) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 400 (all X_a all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)))) # label(fact_448_psubset__imp__subset) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 401 (all N_1 hAPP(nat,nat,suc,N_1) != N_1) # label(fact_453_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 402 (all X_a all N_1 nil(X_a) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),nil(X_a))) # label(fact_318_take__Nil) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 403 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M_1)),N_1)))) # label(fact_494_Suc__leI) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 404 (all X_1 all L_1 (hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_1),arrow_2064824852le_Lin)) -> hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,L_1),X_1)),arrow_2064824852le_Lin)))) # label(fact_24_mktop__Lin) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 405 (all X_a all Xs_1 hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1) = hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),rotate1(X_a),Xs_1))) # label(fact_275_set__rotate1) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 406 (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_417_linorder__cases) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 407 (all X_a all A_1 all B (ti(fun(X_a,bool),B) = ti(fun(X_a,bool),A_1) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1)) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)))) # label(fact_384_set__eq__subset) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 408 (all X_a (linorder(X_a) -> (all Pa all Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),Xs_1))))))) # label(fact_187_sorted__dropWhile) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 409 (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]. 2.14/2.57 410 (all X_a all Xs_1 (hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),equal_equal(list(X_a)),Xs_1),nil(X_a))) <-> hBOOL(hAPP(list(X_a),bool,null(X_a),Xs_1)))) # label(fact_90_equal__Nil__null) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 411 (all X_a all Xs_1 all Ys_1 (hAPP(list(X_a),list(X_a),rev(X_a),Ys_1) = Xs_1 <-> hAPP(list(X_a),list(X_a),rev(X_a),Xs_1) = Ys_1)) # label(fact_252_rev__swap) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 412 (all X_a append(X_a) = ti(fun(list(X_a),fun(list(X_a),list(X_a))),append(X_a))) # label(tsy_c_List_Oappend_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 413 (all X_a (order(X_a) -> (all C_1 all A_2 all B_1 (ti(X_a,A_2) = ti(X_a,B_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),A_2))))))) # label(fact_411_xt1_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 414 (all X_a (linorder(X_a) -> (all Pa all Xs_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Xs_1))))))) # label(fact_117_sorted__takeWhile) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 415 (all X_a all Xs_1 all Pa (hBOOL(hAPP(list(X_a),bool,Pa,nil(X_a))) -> ((all X_2 all Xs_2 (hBOOL(hAPP(list(X_a),bool,Pa,Xs_2)) -> hBOOL(hAPP(list(X_a),bool,Pa,hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_2),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),nil(X_a))))))) -> hBOOL(hAPP(list(X_a),bool,Pa,Xs_1))))) # label(fact_158_rev__induct) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 416 (all N_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_1))) # label(fact_456_less__not__refl) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 417 (all X_c all X_a all B_1_1 all B_2_1 hAPP(X_a,X_c,B_1_1,B_2_1) = ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1))) # label(tsy_c_hAPP_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 418 (all X_a all Pa all Xs_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Xs_1))),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)))) # label(fact_354_length__takeWhile__le) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 419 (all X_a all X all Xs ((Xs = nil(X_a) -> ti(X_a,X) = hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))) & (Xs != nil(X_a) -> hAPP(list(X_a),X_a,last(X_a),Xs) = hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))))) # label(fact_106_last_Osimps) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 420 (all X_1 all Y_1 all L_1 all Aa all Ba (ti(arrow_490897120le_alt,Ba) != ti(arrow_490897120le_alt,Aa) -> (hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_1),arrow_2064824852le_Lin)) -> (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,L_1),Aa),Ba))) <-> ti(arrow_490897120le_alt,Y_1) != ti(arrow_490897120le_alt,X_1) & (ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,Y_1) -> (ti(arrow_490897120le_alt,Aa) != ti(arrow_490897120le_alt,X_1) -> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_1)),L_1))) & (ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Aa) -> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Ba),Y_1)),L_1)) | ti(arrow_490897120le_alt,Ba) = ti(arrow_490897120le_alt,Y_1))) & (ti(arrow_490897120le_alt,Aa) = ti(arrow_490897120le_alt,Y_1) -> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Ba)),L_1))))))) # label(fact_12_in__below) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 421 (all X_b all X_c all X_a ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),produc1605651328_split(X_b,X_c,X_a)) = produc1605651328_split(X_b,X_c,X_a)) # label(tsy_c_Product__Type_Ointernal__split_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 422 (all X_a all R_2 hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),nil(X_a)),nil(X_a))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2)))) # label(fact_222_listrel_ONil) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 423 (exists L_2 hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_2),arrow_2064824852le_Lin))) # label(fact_37_linear__alt) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 424 (all X_a all X_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) <-> hBOOL(hAPP(X_a,bool,A_1,X_1)))) # label(fact_76_mem__def) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 425 (all X_b all X_a all Aa all Ba all A_5 all B_3 (ti(X_b,Ba) = ti(X_b,B_3) & ti(X_a,Aa) = ti(X_a,A_5) <-> hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_5),B_3))) # label(fact_14_Pair__eq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 426 (all X_a all Ys_1 all Xs_1 all Zs (Zs = Ys_1 <-> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs),Xs_1))) # label(fact_128_append__same__eq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 427 (all X_a all Ys_2 all Xs ((Xs != nil(X_a) -> hAPP(list(X_a),X_a,hd(X_a),Xs) = hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_2))) & (nil(X_a) = Xs -> hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_2)) = hAPP(list(X_a),X_a,hd(X_a),Ys_2)))) # label(fact_233_hd__append) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 428 (all X_a all X_1 all Xs_1 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X_1),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1))) # label(fact_293_not__in__set__insert) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 429 (all X_a all Xs_1 all Ys_1 all R_2 all N (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(nat,fun(product_prod(list(X_a),list(X_a)),bool),hAPP(fun(product_prod(X_a,X_a),bool),fun(nat,fun(product_prod(list(X_a),list(X_a)),bool)),lexn(X_a),R_2),N))) -> hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1) = N & hAPP(list(X_a),nat,size_size(list(X_a)),Ys_1) = N)) # label(fact_199_lexn__length) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 430 (all X_a all Xs all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),N_1)) -> nil(X_a) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs))) # label(fact_361_drop__all) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 431 (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]. 2.14/2.57 432 (all X_a all Q_1 all Pa all X_1 (hBOOL(hAPP(X_a,bool,Pa,X_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),Pa),Q_1)) -> hBOOL(hAPP(X_a,bool,Q_1,X_1))))) # label(fact_379_rev__predicate1D) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 433 (all A_2 all B_1 (ti(arrow_490897120le_alt,B_1) != ti(arrow_490897120le_alt,A_2) -> (exists C_2 hBOOL(hAPP(list(arrow_490897120le_alt),bool,distinct(arrow_490897120le_alt),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),A_2),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),B_1),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),C_2),nil(arrow_490897120le_alt))))))))) # label(fact_27_third__alt) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 434 (all X_a (linorder(X_a) -> (all Aa (nil(X_a) = Aa | (exists Xs_2 exists X_2 ((all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_2))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Xa)))) & hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_2)) & hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2) = Aa)) <-> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Aa)))))) # label(fact_362_sorted_Osimps) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 435 (all X_a nil(X_a) = hAPP(list(X_a),list(X_a),rev(X_a),nil(X_a))) # label(fact_260_rev_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 436 (all X_b all X_a all F all Aa all X_1 all Xs_1 hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),Aa),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),X_1),Xs_1)) = hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),F,Aa),X_1)),Xs_1)) # label(fact_282_foldl__Cons) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 437 (all X_a ti(fun(fun(X_a,bool),fun(list(X_a),list(X_a))),takeWhile(X_a)) = takeWhile(X_a)) # label(tsy_c_List_OtakeWhile_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 438 (exists A_4 exists B_2 exists C_2 hBOOL(hAPP(list(arrow_490897120le_alt),bool,distinct(arrow_490897120le_alt),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),A_4),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),B_2),hAPP(list(arrow_490897120le_alt),list(arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(list(arrow_490897120le_alt),list(arrow_490897120le_alt)),cons(arrow_490897120le_alt),C_2),nil(arrow_490897120le_alt))))))) # label(fact_36_alt3) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 439 (all X_a all N_1 all X all K hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),K),X)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),K),X))) # label(fact_261_append__replicate__commute) # label(axiom) # label(non_clause). [assumption]. 2.14/2.57 440 (all N all M (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) -> (N = M <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M)))))) # label(fact_475_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 441 (all X_a all X all Xs all Ys_2 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs)),Ys_2) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_2))) # label(fact_132_append__Cons) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 442 (all Fa ((all X_2 (hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof)) -> (all A_4 all B_2 ((all I hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_4),B_2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I)))) -> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),A_4),B_2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2))))))) <-> hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,Fa)))) # label(fact_29_unanimity__def) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 443 (all X_b all X_a all F all X_1 all Xs_1 hAPP(list(X_b),list(X_a),hAPP(fun(X_b,list(X_a)),fun(list(X_b),list(X_a)),maps(X_b,X_a),F),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),X_1),Xs_1)) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(X_b,list(X_a),F,X_1)),hAPP(list(X_b),list(X_a),hAPP(fun(X_b,list(X_a)),fun(list(X_b),list(X_a)),maps(X_b,X_a),F),Xs_1))) # label(fact_152_maps__simps_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 444 (all X_a all X_1 all Pa all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Xs_1)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(X_a,bool,Pa,X_1)))) # label(fact_276_set__takeWhileD) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 445 (all X_a all X_b all R_1 all S_1 (hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(product_prod(X_a,X_b),bool),bool),ord_less_eq(fun(product_prod(X_a,X_b),bool)),R_1),S_1)) <-> hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),R_1)),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),S_1))))) # label(fact_366_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 446 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,N_1)))) # label(fact_444_lessI) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 447 (all X_a all N all Xs_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs_1))),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1)))) # label(fact_372_set__drop__subset) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 448 (all X_a all Ys_1 all Pa all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (-hBOOL(hAPP(X_a,bool,Pa,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),Xs_1)),Ys_1) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1))))) # label(fact_291_dropWhile__append1) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 449 (all X_a all A1 all A2 all R_2 (A2 = nil(X_a) & nil(X_a) = A1 | (exists X_2 exists Y_2 exists Xs_2 exists Ys (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),Y_2)),R_2)) & hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_2),Ys)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2))) & A2 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys) & A1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_2))) <-> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),A1),A2)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2))))) # label(fact_229_listrel_Osimps) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 450 (all X_a all I_1 all Xs (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),I_1),Xs))))) # label(fact_255_distinct__drop) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 451 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),hAPP(nat,nat,suc,N_1))))) # label(fact_495_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 452 (all X_a all A_1 all B (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1)) -> ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)))) # label(fact_377_equalityI) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 453 (all X_a hBOOL(hAPP(list(X_a),bool,distinct(X_a),nil(X_a)))) # label(fact_33_distinct_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 454 (all X_a all Ys_2 all Xs (nil(X_a) != Xs -> hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_2)) = hAPP(list(X_a),X_a,hd(X_a),Xs))) # label(fact_234_hd__append2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 455 (all X_c all X_a all X_b all Ca all P_1 all Z_2 (hBOOL(hAPP(X_c,bool,hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),Ca),P_1),Z_2)) -> -(all X_2 all Y_2 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2) = ti(product_prod(X_a,X_b),P_1) -> -hBOOL(hAPP(X_c,bool,hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),Ca,X_2),Y_2),Z_2)))))) # label(fact_211_splitE_H) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 456 (all X_a all X_1 all N all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs_1)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_273_in__set__dropD) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 457 (all X_a all N_1 all Xs (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(list(X_a),nat,size_size(list(X_a)),Xs))) -> hAPP(list(X_a),X_a,last(X_a),Xs) = hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs)))) # label(fact_443_last__drop) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 458 (all X_a all Pa all Xs_1 ((exists Ys exists X_2 exists Zs_2 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs_2)) = Xs_1 & (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Zs_2))) -> -hBOOL(hAPP(X_a,bool,Pa,Xa)))) & hBOOL(hAPP(X_a,bool,Pa,X_2)))) <-> (exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) & hBOOL(hAPP(X_a,bool,Pa,X_2)))))) # label(fact_308_split__list__last__prop__iff) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 459 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N)))) # label(fact_496_Suc__le__eq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 460 (all X_b all X_c all X_a ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),product_prod_rec(X_b,X_c,X_a)) = product_prod_rec(X_b,X_c,X_a)) # label(tsy_c_Product__Type_Oprod_Oprod__rec_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 461 (all X_a all Xs_1 all Ys_1 hAPP(list(X_a),list(X_a),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),list(X_a)),hAPP(list(X_a),fun(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),list(X_a))),list_case(list(X_a),X_a),hAPP(list(X_a),list(X_a),tl(X_a),Ys_1)),hAPP(fun(list(X_a),list(X_a)),fun(X_a,fun(list(X_a),list(X_a))),combk(fun(list(X_a),list(X_a)),X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),hAPP(fun(list(X_a),fun(list(X_a),list(X_a))),fun(list(X_a),fun(list(X_a),list(X_a))),combc(list(X_a),list(X_a),list(X_a)),append(X_a)),Ys_1))),Xs_1) = hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1))) # label(fact_215_tl__append) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 462 (all X_a (order(X_a) -> (all A_2 all B_1 (ti(X_a,B_1) != ti(X_a,A_2) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))))))) # label(fact_430_xt1_I12_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 463 (all X_a (ord(X_a) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) -> (C_1 = B_1 -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),C_1))))))) # label(fact_336_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 464 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Zs (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Zs))) <-> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Zs)))))))) # label(fact_352_sorted__many__eq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 465 (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,Y) = ti(X_a,X))))) # label(fact_426_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 466 (all X_a all X_b all X_c all F ti(fun(X_a,fun(X_b,X_c)),F) = hAPP(fun(product_prod(X_a,X_b),X_c),fun(X_a,fun(X_b,X_c)),product_curry(X_a,X_b,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),F))) # label(fact_190_curry__split) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 467 (all X_a (top(X_a) -> (all A_2 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),top_top(X_a)),A_2))))) # label(fact_419_not__top__less) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 468 (all X_a all X_b all X_c all X_d all X_1 all Pa ((all A_4 all B_2 all C_2 all D hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,Pa,hAPP(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d)))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,X_d))),A_4),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),B_2),hAPP(X_d,product_prod(X_c,X_d),hAPP(X_c,fun(X_d,product_prod(X_c,X_d)),product_Pair(X_c,X_d),C_2),D)))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,Pa,X_1)))) # label(fact_69_prod__induct4) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 469 (all X_a all Xs_1 all Ys_1 (Ys_1 = nil(X_a) <-> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1) = Xs_1)) # label(fact_137_self__append__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 470 (all X_a all N_1 all X hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),hAPP(nat,nat,suc,N_1)),X) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N_1),X))) # label(fact_350_replicate__Suc) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 471 (all X_a all Aa all List all A_5 all List_2 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Aa),List) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_5),List_2) <-> List_2 = List & ti(X_a,A_5) = ti(X_a,Aa))) # label(fact_38_list_Oinject) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 472 (all X_a lex(X_a) = ti(fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool)),lex(X_a))) # label(tsy_c_List_Olex_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 473 (all X_a (ord(X_a) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> (B_1 = C_1 -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),C_1))))))) # label(fact_412_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 474 (all X_a all Pa all Xs_1 ((exists X_2 (hBOOL(hAPP(X_a,bool,Pa,X_2)) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) <-> (exists Ys exists X_2 (hBOOL(hAPP(X_a,bool,Pa,X_2)) & (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys))) -> -hBOOL(hAPP(X_a,bool,Pa,Xa)))) & (exists Zs_2 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Zs_2)) = Xs_1))))) # label(fact_309_split__list__first__prop__iff) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 475 (all X_a all X_b all X_1 all Y_1 all Pa all Q_1 (hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),Pa),Q_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Pa,X_1),Y_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_1),Y_1))))) # label(fact_381_predicate2D) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 476 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M))) <-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_478_not__less__eq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 477 (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_404_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 478 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 479 (all X_a all A_6 all List_3 hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_6),List_3) != nil(X_a)) # label(fact_34_list_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 480 (all X_a all B all X_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B))))) # label(fact_388_set__rev__mp) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 481 (all X_1 all Y_1 all L_1 all Z_2 (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,L_1),Z_2))) <-> ti(arrow_490897120le_alt,Y_1) != ti(arrow_490897120le_alt,Z_2) & (ti(arrow_490897120le_alt,X_1) != ti(arrow_490897120le_alt,Z_2) -> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_1)),L_1))) & (ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Z_2) -> ti(arrow_490897120le_alt,Y_1) != ti(arrow_490897120le_alt,X_1)))) # label(fact_10_in__mkbot) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 482 (all X_a all Ys_1 all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Ys_1)))) | hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),Xs_1)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1))))))) # label(fact_289_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 483 (all X_a all Xs_1 all Ys_1 (Xs_1 = nil(X_a) <-> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1) = Ys_1)) # label(fact_141_append__self__conv2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 484 (all X_a all Xs_1 hAPP(list(X_a),list(X_a),rotate1(X_a),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),list(X_a)),hAPP(list(X_a),fun(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),list(X_a))),list_case(list(X_a),X_a),nil(X_a)),hAPP(fun(X_a,list(X_a)),fun(X_a,fun(list(X_a),list(X_a))),hAPP(fun(list(X_a),fun(list(X_a),list(X_a))),fun(fun(X_a,list(X_a)),fun(X_a,fun(list(X_a),list(X_a)))),combb(list(X_a),fun(list(X_a),list(X_a)),X_a),hAPP(fun(list(X_a),fun(list(X_a),list(X_a))),fun(list(X_a),fun(list(X_a),list(X_a))),combc(list(X_a),list(X_a),list(X_a)),append(X_a))),hAPP(list(X_a),fun(X_a,list(X_a)),hAPP(fun(X_a,fun(list(X_a),list(X_a))),fun(list(X_a),fun(X_a,list(X_a))),combc(X_a,list(X_a),list(X_a)),cons(X_a)),nil(X_a)))),Xs_1)) # label(fact_161_rotate1__def) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 485 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M_1)),hAPP(nat,nat,suc,N_1))))) # label(fact_445_Suc__mono) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 486 (all X_a all Xs_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),nil(X_a)),Xs_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2))) -> Xs_1 = nil(X_a))) # label(fact_217_listrel__Nil1) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 487 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> Xs_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X_1),Xs_1))) # label(fact_283_in__set__insert) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 488 (all X_a all R_2 hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),R_2),nil(X_a)),nil(X_a)))) # label(fact_232_listrelp_ONil) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 489 (all X_a all X_b all X_c all X_d all Y -(all A_4 all B_2 all C_2 all D hAPP(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d)))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,X_d))),A_4),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),B_2),hAPP(X_d,product_prod(X_c,X_d),hAPP(X_c,fun(X_d,product_prod(X_c,X_d)),product_Pair(X_c,X_d),C_2),D))) != ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),Y))) # label(fact_70_prod__cases4) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 490 (all X_a all X_b all X_c all F hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,X_c)),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,X_c)),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,X_c))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,X_c),X_a),hAPP(fun(product_prod(X_a,X_b),X_c),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,X_c)),combb(product_prod(X_a,X_b),X_c,X_b),F)),product_Pair(X_a,X_b))) = ti(fun(product_prod(X_a,X_b),X_c),F)) # label(fact_188_split__eta) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 491 (all X_c all X_a all X_b all Ca all P_1 all Q_2 (ti(product_prod(X_a,X_b),P_1) = ti(product_prod(X_a,X_b),Q_2) -> hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),Ca),Q_2) = hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),Ca),P_1))) # label(fact_180_split__weak__cong) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 492 (all X_a (order(X_a) -> (all C_1 all A_2 all B_1 (ti(X_a,A_2) = ti(X_a,B_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2))))))) # label(fact_335_xt1_I3_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 493 (all X_a ti(fun(nat,fun(X_a,list(X_a))),replicate(X_a)) = replicate(X_a)) # label(tsy_c_List_Oreplicate_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 494 (all X_a all Xs_1 all R_2 ((all X_2 -hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),X_2)),R_2))) -> -hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Xs_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),lexord(X_a),R_2))))) # label(fact_108_lexord__irreflexive) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 495 (all X_a all X_1 all Xs_1 ((-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X_1),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)) & (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X_1),Xs_1) = Xs_1))) # label(fact_292_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 496 (all X_a splice(X_a) = ti(fun(list(X_a),fun(list(X_a),list(X_a))),splice(X_a))) # label(tsy_c_List_Osplice_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 497 (all X_a hAPP(list(X_a),list(X_a),butlast(X_a),nil(X_a)) = nil(X_a)) # label(fact_103_butlast_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 498 (all X_a all Xs_1 all Ys_1 all Zs all Ts (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs),Ts) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1) <-> (exists Us (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs),Us) = Xs_1 & Ts = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us),Ys_1) | hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Us) = Zs & hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us),Ts) = Ys_1)))) # label(fact_130_append__eq__append__conv2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 499 (all X_b all X_a all F all Pa all Xs_1 all Q_1 all X_1 (hBOOL(hAPP(X_a,bool,Q_1,X_1)) -> ((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(list(X_b),fun(X_b,bool),set(X_b),Xs_1))) -> hBOOL(hAPP(X_b,bool,Pa,X_2)))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,Q_1,Y_2)) & hBOOL(hAPP(X_b,bool,Pa,X_2)) -> hBOOL(hAPP(X_a,bool,Q_1,hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),F,Y_2),X_2))))) -> hBOOL(hAPP(X_a,bool,Q_1,hAPP(list(X_b),X_a,hAPP(X_a,fun(list(X_b),X_a),hAPP(fun(X_a,fun(X_b,X_a)),fun(X_a,fun(list(X_b),X_a)),foldl(X_a,X_b),F),X_1),Xs_1))))))) # label(fact_315_foldl__invariant) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 500 (all X_a ti(fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool)),listrel1(X_a)) = listrel1(X_a)) # label(tsy_c_List_Olistrel1_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 501 (all X_a all Y (Y != nil(X_a) -> -(all A_4 all List_1 Y != hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_4),List_1)))) # label(fact_44_list_Oexhaust) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 502 (all N_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_1))) # label(fact_463_le__refl) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 503 (all X_a (linorder(X_a) -> (all Xs_1 all Ys_1 (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs_1)) & (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),hAPP(list(X_a),fun(X_a,bool),set(X_a),Ys_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Xa)))))) & hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Ys_1)) <-> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1))))))) # label(fact_359_sorted__append) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 504 (all X_a drop(X_a) = ti(fun(nat,fun(list(X_a),list(X_a))),drop(X_a))) # label(tsy_c_List_Odrop_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 505 (all M all N (N != M <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)))) # label(fact_457_nat__neq__iff) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 506 (all X_a all R_2 all X_2 all Xa (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),X_2),Xa)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2))) <-> hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),hAPP(fun(X_a,fun(X_a,bool)),fun(list(X_a),fun(list(X_a),bool)),listrelp(X_a),hAPP(fun(product_prod(X_a,X_a),bool),fun(X_a,fun(X_a,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_a),bool),fun(X_a,bool))),fun(fun(product_prod(X_a,X_a),bool),fun(X_a,fun(X_a,bool))),combc(X_a,fun(product_prod(X_a,X_a),bool),fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,fun(fun(product_prod(X_a,X_a),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_a),bool),fun(X_a,bool))),hAPP(fun(fun(X_a,fun(fun(product_prod(X_a,X_a),bool),bool)),fun(fun(product_prod(X_a,X_a),bool),fun(X_a,bool))),fun(fun(X_a,fun(X_a,fun(fun(product_prod(X_a,X_a),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_a),bool),fun(X_a,bool)))),combb(fun(X_a,fun(fun(product_prod(X_a,X_a),bool),bool)),fun(fun(product_prod(X_a,X_a),bool),fun(X_a,bool)),X_a),combc(X_a,fun(product_prod(X_a,X_a),bool),bool)),hAPP(fun(X_a,fun(X_a,product_prod(X_a,X_a))),fun(X_a,fun(X_a,fun(fun(product_prod(X_a,X_a),bool),bool))),hAPP(fun(fun(X_a,product_prod(X_a,X_a)),fun(X_a,fun(fun(product_prod(X_a,X_a),bool),bool))),fun(fun(X_a,fun(X_a,product_prod(X_a,X_a))),fun(X_a,fun(X_a,fun(fun(product_prod(X_a,X_a),bool),bool)))),combb(fun(X_a,product_prod(X_a,X_a)),fun(X_a,fun(fun(product_prod(X_a,X_a),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool)),fun(fun(X_a,product_prod(X_a,X_a)),fun(X_a,fun(fun(product_prod(X_a,X_a),bool),bool))),combb(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),X_a),member(product_prod(X_a,X_a)))),product_Pair(X_a,X_a)))),R_2)),X_2),Xa)))) # label(fact_227_listrelp__listrel__eq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 507 (all X_a all Xs all Ys_2 ((nil(X_a) = Ys_2 -> hAPP(list(X_a),list(X_a),butlast(X_a),Xs) = hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_2))) & (Ys_2 != nil(X_a) -> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),butlast(X_a),Ys_2)) = hAPP(list(X_a),list(X_a),butlast(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_2))))) # label(fact_147_butlast__append) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 508 (all X_a all Xs_1 (nil(X_a) != Xs_1 <-> (exists Y_2 exists Ys Xs_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys)))) # label(fact_45_neq__Nil__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.58 509 (all Nat all Nat_1 (hAPP(nat,nat,suc,Nat) = hAPP(nat,nat,suc,Nat_1) <-> Nat = Nat_1)) # label(fact_454_nat_Oinject) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 510 (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_441_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 511 (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_415_xt1_I10_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 512 (all X_a all N_1 all Xs hAPP(list(X_a),list(X_a),tl(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),hAPP(nat,nat,suc,N_1)),Xs)) = hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),take(X_a),N_1),hAPP(list(X_a),list(X_a),tl(X_a),Xs))) # label(fact_355_take__tl) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 513 (all X_a all Ys_2 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),nil(X_a)),Ys_2) = Ys_2) # label(fact_53_splice_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 514 (all X_a all X_1 all Xs_1 all Ys_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Ys_1))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))))) # label(fact_165_listrel1I2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 515 (all X_a all X all Xs (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X),Xs))))) # label(fact_74_distinct__insert) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 516 (all X_a all As (nil(X_a) != As -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(list(X_a),X_a,last(X_a),As)),hAPP(list(X_a),fun(X_a,bool),set(X_a),As))))) # label(fact_287_last__in__set) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 517 (all X_a all Xs Xs = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),Xs),nil(X_a))) # label(fact_54_splice__Nil2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 518 (all X_a all Xs_1 all X_1 all Y_1 all R_2 (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),R_2)) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Xs_1))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2))))) # label(fact_170_listrel1I1) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 519 (all X_a ti(fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),nat_case(X_a)) = nat_case(X_a)) # label(tsy_c_Nat_Onat_Onat__case_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 520 (all X_a all Xs_1 all R_2 -hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),nil(X_a))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel1(X_a),R_2)))) # label(fact_166_not__listrel1__Nil) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 521 (all X_b all X_a all B all F all G all A_1 ((all W (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),W),A_1)) -> hAPP(X_a,X_b,F,W) = hAPP(X_a,X_b,G,W))) -> (hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))) <-> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),G),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B)))))) # label(fact_59_Pi__cong) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 522 (all X_a (linorder(X_a) -> (all N_1 all Xs (hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),Xs)) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N_1),Xs))))))) # label(fact_249_sorted__drop) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 523 (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,Y) = ti(X_a,X)))))) # label(fact_340_xt1_I5_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 524 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)))))) # label(fact_440_linorder__not__less) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 525 (all X_a all X_1 all Xs_1 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)) = hAPP(list(X_a),list(X_a),rev(X_a),Xs_1) <-> Xs_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)))) # label(fact_265_singleton__rev__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 526 (all X_a all Y_1 all X_1 all Xs_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)))) -> ti(X_a,Y_1) = ti(X_a,X_1) | hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))))) # label(fact_280_set__ConsD) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 527 (all X_b all X_c all X_a all F all G ((all X_2 all Y_2 hAPP(product_prod(X_a,X_b),X_c,G,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2)) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),F,X_2),Y_2)) -> ti(fun(product_prod(X_a,X_b),X_c),G) = hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),F))) # label(fact_196_cond__split__eta) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 528 (all Fa all I_2 (hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,Fa),I_2)) <-> (all X_2 (hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X_2),arrow_1111136790e_Prof)) -> hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),Fa,X_2) = hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X_2,I_2))))) # label(fact_46_dictator__def) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 529 (all X_a all X all Xs hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a))) = hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs))) # label(fact_267_rev_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 530 (all X_a all X_1 all Xs_1 (hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_1))),Xs_1))) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_1))),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1))))) # label(fact_270_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 531 (all T_1 cl_HOL_Oequal(list(T_1))) # label(arity_List_Olist___HOL_Oequal) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 532 (all X_a all Pa hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),nil(X_a)) = nil(X_a)) # label(fact_185_dropWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 533 (all X_a (preorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)))))) # label(fact_436_less__le__not__le) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 534 (all X_b all X_a all R_1 all X_1 all Y_1 (hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Y_1)),R_1)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),in_rel(X_a,X_b),R_1),X_1),Y_1)))) # label(fact_16_in__rel__def) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 535 (all P (fFalse = ti(bool,P) | ti(bool,P) = fTrue)) # label(help_If_3_1_T) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 536 (all X_a all A_1 all B (ti(fun(X_a,bool),B) = ti(fun(X_a,bool),A_1) -> -(hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1))))) # label(fact_391_equalityE) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 537 (all X_a all Xs_1 all Ys_1 all X_1 all Y_1 all R_2 (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),R_2)) -> (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Xs_1),Ys_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2))) -> hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_1))),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2)))))) # label(fact_214_listrel_OCons) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 538 (all X_a all Xs (nil(X_a) != Xs -> -(all Ys all Y_2 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),nil(X_a))) != Xs))) # label(fact_159_rev__cases) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 539 (all X_a all A_1 all B (ti(fun(X_a,bool),B) = ti(fun(X_a,bool),A_1) | hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_1),B)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)))) # label(fact_449_subset__iff__psubset__eq) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 540 (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_396_order__less__irrefl) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 541 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) -> (ti(X_a,X_1) = ti(X_a,Y_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1))))))) # label(fact_432_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 542 (all M_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N_1)) -> (N_1 != M_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_1),N_1))))) # label(fact_487_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 543 (all X_a all X_b all X_c all F ti(fun(product_prod(X_a,X_b),X_c),F) = hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),hAPP(fun(product_prod(X_a,X_b),X_c),fun(X_a,fun(X_b,X_c)),product_curry(X_a,X_b,X_c),F))) # label(fact_189_split__curry) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 544 (all X_a all Xs_1 all X_1 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)) = hAPP(list(X_a),list(X_a),rev(X_a),Xs_1) <-> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),nil(X_a)) = Xs_1)) # label(fact_264_rev__singleton__conv) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 545 (all X_b all X_a all F all B all A_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,fun(X_b,bool),B,X_2))))) -> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))))) # label(fact_56_Pi__I) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 546 (all X_a all Pa all Xs_1 Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),Xs_1))) # label(fact_193_takeWhile__dropWhile__id) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 547 (all X_a (linorder(X_a) -> (all X hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a))))))) # label(fact_94_sorted__single) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 548 (all X_a all N all Xs_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs_1)),N)) <-> hAPP(list(X_a),list(X_a),hAPP(nat,fun(list(X_a),list(X_a)),drop(X_a),N),Xs_1) = nil(X_a))) # label(fact_360_drop__eq__Nil) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 549 (all X_a all Pa all Xs_1 (hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),Xs_1) != nil(X_a) -> -hBOOL(hAPP(X_a,bool,Pa,hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),Xs_1)))))) # label(fact_235_hd__dropWhile) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 550 (all Aa all Ba (ti(arrow_490897120le_alt,Ba) != ti(arrow_490897120le_alt,Aa) -> (exists X_2 (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Ba)),X_2)) & hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X_2),arrow_2064824852le_Lin)))))) # label(fact_30_complete__Lin) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 551 (all X_a all X all Xs all Ys_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(list(X_a),nat,size_size(list(X_a)),Xs)),hAPP(list(X_a),nat,size_size(list(X_a)),Ys_2))) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Ys_2) != Xs)) # label(fact_347_impossible__Cons) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 552 (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),Y),X)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_438_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 553 (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]. 2.14/2.59 554 (all X_a all Xs all X hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a)))) = ti(X_a,X)) # label(fact_154_last__snoc) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 555 (all X_a all X_1 all Y_1 (hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),equal_equal(list(X_a)),X_1),Y_1)) <-> X_1 = Y_1)) # label(fact_100_equal__list__def) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 556 (all X_a (ord(X_a) -> (all C_1 all A_2 all B_1 (A_2 = B_1 -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),C_1))))))) # label(fact_410_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 557 (all X_a (linorder(X_a) -> hBOOL(hAPP(list(X_a),bool,linorder_sorted(X_a),nil(X_a))))) # label(fact_99_sorted_ONil) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 558 (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_343_linorder__le__cases) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 559 (all T_2 all T_1 cl_HOL_Oequal(product_prod(T_2,T_1))) # label(arity_prod___HOL_Oequal) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 560 (all X_a all Ys_1 all Pa all Xs_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),Xs_1))) -> hBOOL(hAPP(X_a,bool,Pa,X_2)))) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),Ys_1) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),Pa),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys_1)))) # label(fact_296_dropWhile__append2) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 561 (all X_a all B all A_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)))) # label(fact_394_subsetI) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 562 (all X_b all X_a all F1 all F2 all Aa all List hAPP(list(X_b),X_a,hAPP(X_b,fun(list(X_b),X_a),F2,Aa),List) = hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a)),list_case(X_a,X_b),F1),F2),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Aa),List))) # label(fact_51_list_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 563 (all X_a all Q_1 all Pa all L all K_1 (K_1 = L -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(list(X_a),fun(X_a,bool),set(X_a),L))) -> (hBOOL(hAPP(X_a,bool,Q_1,X_2)) <-> hBOOL(hAPP(X_a,bool,Pa,X_2))))) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Q_1),K_1) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),L)))) # label(fact_304_takeWhile__cong) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 564 (all X_a all Pa hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),takeWhile(X_a),Pa),nil(X_a)) = nil(X_a)) # label(fact_115_takeWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 565 (all X_a all Y_1 all Ys_1 all Xs_1 all R_2 (hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys_1)),Xs_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2))) -> -(all Y_2 all Ys (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys) = Xs_1 -> (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),Y_1),Y_2)),R_2)) -> -hBOOL(hAPP(fun(product_prod(list(X_a),list(X_a)),bool),bool,hAPP(product_prod(list(X_a),list(X_a)),fun(fun(product_prod(list(X_a),list(X_a)),bool),bool),member(product_prod(list(X_a),list(X_a))),hAPP(list(X_a),product_prod(list(X_a),list(X_a)),hAPP(list(X_a),fun(list(X_a),product_prod(list(X_a),list(X_a))),product_Pair(list(X_a),list(X_a)),Ys_1),Ys)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(list(X_a),list(X_a)),bool),listrel(X_a),R_2)))))))) # label(fact_226_listrel__Cons1) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 566 (all Pa all M all N ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N),M))) -> ((N = M -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N),M))) -> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N),M))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),Pa,N),M)))))) # label(fact_462_nat__less__cases) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 567 (all X_b all X_a all F1 all F2 all Aa all List hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a)),list_rec(X_a,X_b),F1),F2),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Aa),List)) = hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(X_b,fun(list(X_b),fun(X_a,X_a)),F2,Aa),List),hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a)),list_rec(X_a,X_b),F1),F2),List))) # label(fact_80_list_Orecs_I2_J) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 568 (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_403_order__less__not__sym) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 569 (all X_a insert(X_a) = ti(fun(X_a,fun(list(X_a),list(X_a))),insert(X_a))) # label(tsy_c_List_Oinsert_res) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 570 (all X_a (order(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) <-> ti(X_a,Y_1) = ti(X_a,X_1))))) # label(fact_330_order__eq__iff) # label(axiom) # label(non_clause). [assumption]. 2.14/2.59 571 (all X_1 all Y_1 all L_1 all Aa all Ba (ti(arrow_490897120le_alt,Ba) != ti(arrow_490897120le_alt,Aa) -> (hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),L_1),arrow_2064824852le_Lin)) -> ((ti(arrow_490897120le_alt,Ba) = ti(arrow_490897120le_alt,X_1) -> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),Aa),Y_1)),L_1))) & (ti(arrow_490897120le_alt,Ba) != ti(arrow_490897120le_alt,X_1) -> (ti(arrow_490897120le_alt,Y_1) != ti(arrow_490897120le_alt,Ba) -> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_1)),L_1))) & (ti(arrow_490897120le_alt,Ba) = ti(arrow_490897120le_alt,Y_1) -> ti(arrow_490897120le_alt,X_1) = ti(arrow_490897120le_alt,Aa) | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Aa)),L_1)))) & ti(arrow_490897120le_alt,Y_1) != ti(arrow_490897120le_alt,X_1) <-> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X_1),Y_1)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,L_1),Aa),Ba))))))) # label(fact_31_in__above) # label(axiom) # label(non_clause). [assumption]. 2.14/2.62 572 -(all I (hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),c)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I)),c),b))) <-> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,I))))) # label(conj_0) # label(negated_conjecture) # label(non_clause). [assumption]. 2.14/2.62 2.14/2.62 ============================== end of process non-clausal formulas === 2.14/2.62 2.14/2.62 ============================== PROCESS INITIAL CLAUSES =============== 2.14/2.62 2.14/2.62 ============================== PREDICATE ELIMINATION ================= 2.14/2.62 573 linorder(nat) # label(arity_Nat_Onat___Orderings_Olinorder) # label(axiom). [assumption]. 2.14/2.62 574 -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_433_not__leE) # label(axiom). [clausify(6)]. 2.14/2.62 575 -linorder(A) | ti(A,B) = ti(A,C) | 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_401_linorder__neqE) # label(axiom). [clausify(38)]. 2.14/2.62 576 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,B) != ti(A,C) # label(fact_397_linorder__neq__iff) # label(axiom). [clausify(52)]. 2.14/2.62 577 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_397_linorder__neq__iff) # label(axiom). [clausify(52)]. 2.14/2.62 578 -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,B) = ti(A,C) # label(fact_397_linorder__neq__iff) # label(axiom). [clausify(52)]. 2.14/2.62 579 -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_329_linorder__linear) # label(axiom). [clausify(92)]. 2.14/2.62 580 -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_400_linorder__antisym__conv3) # label(axiom). [clausify(95)]. 2.14/2.62 581 -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_400_linorder__antisym__conv3) # label(axiom). [clausify(95)]. 2.14/2.62 582 -linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f38(A,B,C)),hAPP(list(A),fun(A,bool),set(A),C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C))) # label(fact_363_sorted_OCons) # label(axiom). [clausify(99)]. 2.14/2.62 583 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),f38(A,B,C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C))) # label(fact_363_sorted_OCons) # label(axiom). [clausify(99)]. 2.14/2.62 584 -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_427_linorder__antisym__conv2) # label(axiom). [clausify(115)]. 2.14/2.62 585 -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_427_linorder__antisym__conv2) # label(axiom). [clausify(115)]. 2.14/2.62 586 -linorder(A) | linorder_sorted(A) = ti(fun(list(A),bool),linorder_sorted(A)) # label(tsy_c_List_Olinorder__class_Osorted_res) # label(axiom). [clausify(130)]. 2.14/2.62 587 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(nat,fun(list(A),list(A)),take(A),C),B))) # label(fact_320_sorted__take) # label(axiom). [clausify(155)]. 2.14/2.62 588 -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_439_linorder__not__le) # label(axiom). [clausify(161)]. 2.14/2.62 589 -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_439_linorder__not__le) # label(axiom). [clausify(161)]. 2.14/2.62 590 -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_434_leI) # label(axiom). [clausify(169)]. 2.14/2.62 591 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | -hBOOL(hAPP(list(A),bool,distinct(A),B)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | -hBOOL(hAPP(list(A),bool,distinct(A),C)) | hAPP(list(A),fun(A,bool),set(A),C) != hAPP(list(A),fun(A,bool),set(A),B) | C = B # label(fact_285_sorted__distinct__set__unique) # label(axiom). [clausify(196)]. 2.14/2.62 592 -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_398_not__less__iff__gr__or__eq) # label(axiom). [clausify(198)]. 2.14/2.62 593 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_398_not__less__iff__gr__or__eq) # label(axiom). [clausify(198)]. 2.14/2.62 594 -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_398_not__less__iff__gr__or__eq) # label(axiom). [clausify(198)]. 2.14/2.62 595 -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_429_leD) # label(axiom). [clausify(214)]. 2.14/2.62 596 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D)))) # label(fact_351_sorted__many) # label(axiom). [clausify(292)]. 2.14/2.62 597 -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_399_linorder__less__linear) # label(axiom). [clausify(332)]. 2.14/2.62 598 -linorder(A) | nil(A) = B | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),butlast(A),B))) # label(fact_101_sorted__butlast) # label(axiom). [clausify(334)]. 2.14/2.62 599 -linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f140(A,B,C)),hAPP(list(A),fun(A,bool),set(A),C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C))) # label(fact_358_sorted__Cons) # label(axiom). [clausify(373)]. 2.14/2.62 600 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),f140(A,B,C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C))) # label(fact_358_sorted__Cons) # label(axiom). [clausify(373)]. 2.14/2.62 601 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(list(A),fun(A,bool),set(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),C))) # label(fact_358_sorted__Cons) # label(axiom). [clausify(373)]. 2.14/2.62 602 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),B))) # label(fact_358_sorted__Cons) # label(axiom). [clausify(373)]. 2.14/2.62 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),B),A)). [resolve(573,a,574,a)]. 2.14/2.62 Derived: ti(nat,A) = ti(nat,B) | 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(573,a,575,a)]. 2.14/2.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,A) != ti(nat,B). [resolve(573,a,576,a)]. 2.14/2.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) != ti(nat,A). [resolve(573,a,577,a)]. 2.14/2.62 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(573,a,579,a)]. 2.14/2.62 Derived: hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f38(nat,A,B)),hAPP(list(nat),fun(nat,bool),set(nat),B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),B))). [resolve(573,a,582,a)]. 2.14/2.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f38(nat,A,B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),B))). [resolve(573,a,583,a)]. 2.14/2.62 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(573,a,584,a)]. 2.14/2.62 Derived: linorder_sorted(nat) = ti(fun(list(nat),bool),linorder_sorted(nat)). [resolve(573,a,586,a)]. 2.14/2.62 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),take(nat),B),A))). [resolve(573,a,587,a)]. 2.14/2.62 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(573,a,588,a)]. 2.14/2.62 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | -hBOOL(hAPP(list(nat),bool,distinct(nat),A)) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | -hBOOL(hAPP(list(nat),bool,distinct(nat),B)) | hAPP(list(nat),fun(nat,bool),set(nat),B) != hAPP(list(nat),fun(nat,bool),set(nat),A) | B = A. [resolve(573,a,591,a)]. 2.14/2.62 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(573,a,594,a)]. 2.14/2.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),B),C))) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),B),C)))). [resolve(573,a,596,a)]. 2.14/2.62 Derived: nil(nat) = A | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),butlast(nat),A))). [resolve(573,a,598,a)]. 2.14/2.62 Derived: hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f140(nat,A,B)),hAPP(list(nat),fun(nat,bool),set(nat),B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),B))). [resolve(573,a,599,a)]. 2.14/2.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f140(nat,A,B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),B))). [resolve(573,a,600,a)]. 2.14/2.62 Derived: -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),A),hAPP(list(nat),fun(nat,bool),set(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),A)) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),C),B))). [resolve(573,a,601,a)]. 2.14/2.62 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),B),A))). [resolve(573,a,602,a)]. 2.14/2.62 603 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),tl(A),B))) # label(fact_221_sorted__tl) # label(axiom). [clausify(394)]. 2.14/2.62 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),tl(nat),A))). [resolve(603,a,573,a)]. 2.14/2.62 604 -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_417_linorder__cases) # label(axiom). [clausify(406)]. 2.14/2.62 605 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),dropWhile(A),C),B))) # label(fact_187_sorted__dropWhile) # label(axiom). [clausify(408)]. 2.14/2.63 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(fun(nat,bool),fun(list(nat),list(nat)),dropWhile(nat),B),A))). [resolve(605,a,573,a)]. 2.14/2.63 606 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(fun(A,bool),fun(list(A),list(A)),takeWhile(A),C),B))) # label(fact_117_sorted__takeWhile) # label(axiom). [clausify(414)]. 2.14/2.63 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(fun(nat,bool),fun(list(nat),list(nat)),takeWhile(nat),B),A))). [resolve(606,a,573,a)]. 2.14/2.63 607 -linorder(A) | nil(A) != B | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) # label(fact_362_sorted_Osimps) # label(axiom). [clausify(434)]. 2.14/2.63 Derived: nil(nat) != A | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)). [resolve(607,a,573,a)]. 2.14/2.63 608 -linorder(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f155(A,B,C,D)),hAPP(list(A),fun(A,bool),set(A),C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),C) != B | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) # label(fact_362_sorted_Osimps) # label(axiom). [clausify(434)]. 2.14/2.63 Derived: hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f155(nat,A,B,C)),hAPP(list(nat),fun(nat,bool),set(nat),B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),C),B) != A | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)). [resolve(608,a,573,a)]. 2.14/2.63 609 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),f155(A,C,D,B))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),D)) | hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),D) != C | hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) # label(fact_362_sorted_Osimps) # label(axiom). [clausify(434)]. 2.14/2.63 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f155(nat,B,C,A))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),C)) | hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),C) != B | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)). [resolve(609,a,573,a)]. 2.14/2.63 610 -linorder(A) | nil(A) = B | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),hAPP(list(A),fun(A,bool),set(A),f156(A,B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f157(A,B)),C)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) # label(fact_362_sorted_Osimps) # label(axiom). [clausify(434)]. 2.14/2.63 Derived: nil(nat) = A | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),B),hAPP(list(nat),fun(nat,bool),set(nat),f156(nat,A)))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f157(nat,A)),B)) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)). [resolve(610,a,573,a)]. 2.14/2.63 611 -linorder(A) | nil(A) = B | hBOOL(hAPP(list(A),bool,linorder_sorted(A),f156(A,B))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) # label(fact_362_sorted_Osimps) # label(axiom). [clausify(434)]. 2.14/2.63 Derived: nil(nat) = A | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),f156(nat,A))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)). [resolve(611,a,573,a)]. 2.14/2.63 612 -linorder(A) | nil(A) = B | hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),f157(A,B)),f156(A,B)) = B | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) # label(fact_362_sorted_Osimps) # label(axiom). [clausify(434)]. 2.14/2.63 Derived: nil(nat) = A | hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),f157(nat,A)),f156(nat,A)) = A | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)). [resolve(612,a,573,a)]. 2.14/2.63 613 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D))) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D)))) # label(fact_352_sorted__many__eq) # label(axiom). [clausify(464)]. 2.14/2.64 614 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),C),D)))) # label(fact_352_sorted__many__eq) # label(axiom). [clausify(464)]. 2.14/2.64 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),B),C)))). [resolve(614,a,573,a)]. 2.14/2.64 615 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),D),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),C)))) # label(fact_352_sorted__many__eq) # label(axiom). [clausify(464)]. 2.14/2.64 616 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f193(A,B,C)),hAPP(list(A),fun(A,bool),set(A),B))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C))) # label(fact_359_sorted__append) # label(axiom). [clausify(503)]. 2.14/2.64 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f193(nat,A,B)),hAPP(list(nat),fun(nat,bool),set(nat),A))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(list(nat),fun(list(nat),list(nat)),append(nat),A),B))). [resolve(616,a,573,a)]. 2.14/2.64 617 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f194(A,B,C)),hAPP(list(A),fun(A,bool),set(A),C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C))) # label(fact_359_sorted__append) # label(axiom). [clausify(503)]. 2.14/2.64 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),f194(nat,A,B)),hAPP(list(nat),fun(nat,bool),set(nat),B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(list(nat),fun(list(nat),list(nat)),append(nat),A),B))). [resolve(617,a,573,a)]. 2.14/2.64 618 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),f193(A,B,C)),f194(A,B,C))) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),C)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C))) # label(fact_359_sorted__append) # label(axiom). [clausify(503)]. 2.14/2.64 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),f193(nat,A,B)),f194(nat,A,B))) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),B)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(list(nat),fun(list(nat),list(nat)),append(nat),A),B))). [resolve(618,a,573,a)]. 2.14/2.64 619 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),B),C))) # label(fact_359_sorted__append) # label(axiom). [clausify(503)]. 2.14/2.64 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(list(nat),fun(list(nat),list(nat)),append(nat),A),B))). [resolve(619,a,573,a)]. 2.98/3.25 620 -linorder(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),hAPP(list(A),fun(A,bool),set(A),C))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),hAPP(list(A),fun(A,bool),set(A),E))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),C),E))) # label(fact_359_sorted__append) # label(axiom). [clausify(503)]. 2.98/3.25 Derived: -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),A),hAPP(list(nat),fun(nat,bool),set(nat),B))) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),C),hAPP(list(nat),fun(nat,bool),set(nat),D))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(list(nat),fun(list(nat),list(nat)),append(nat),B),D))). [resolve(620,a,573,a)]. 2.98/3.25 621 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(list(A),fun(list(A),list(A)),append(A),C),B))) # label(fact_359_sorted__append) # label(axiom). [clausify(503)]. 2.98/3.25 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(list(nat),fun(list(nat),list(nat)),append(nat),B),A))). [resolve(621,a,573,a)]. 2.98/3.25 622 -linorder(A) | -hBOOL(hAPP(list(A),bool,linorder_sorted(A),B)) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(nat,fun(list(A),list(A)),drop(A),C),B))) # label(fact_249_sorted__drop) # label(axiom). [clausify(522)]. 2.98/3.25 Derived: -hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),A)) | hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),drop(nat),B),A))). [resolve(622,a,573,a)]. 2.98/3.25 623 -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_440_linorder__not__less) # label(axiom). [clausify(524)]. 2.98/3.25 624 -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_440_linorder__not__less) # label(axiom). [clausify(524)]. 2.98/3.25 625 -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_432_linorder__antisym__conv1) # label(axiom). [clausify(541)]. 2.98/3.25 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(625,a,573,a)]. 2.98/3.25 626 -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_432_linorder__antisym__conv1) # label(axiom). [clausify(541)]. 2.98/3.25 627 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),hAPP(list(A),list(A),hAPP(A,fun(list(A),list(A)),cons(A),B),nil(A)))) # label(fact_94_sorted__single) # label(axiom). [clausify(547)]. 2.98/3.25 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),hAPP(list(nat),list(nat),hAPP(nat,fun(list(nat),list(nat)),cons(nat),A),nil(nat)))). [resolve(627,a,573,a)]. 2.98/3.25 628 -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_438_linorder__le__less__linear) # label(axiom). [clausify(552)]. 2.98/3.25 629 -linorder(A) | hBOOL(hAPP(list(A),bool,linorder_sorted(A),nil(A))) # label(fact_99_sorted_ONil) # label(axiom). [clausify(557)]. 2.98/3.25 Derived: hBOOL(hAPP(list(nat),bool,linorder_sorted(nat),nil(nat))). [resolve(629,a,573,a)]. 2.98/3.25 630 -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_343_linorder__le__cases) # label(axiom). [clausify(558)]. 2.98/3.25 2.98/3.25 ============================== end predicate elimination ============= 2.98/3.25 2.98/3.25 Auto_denials: (non-Horn, no changes). 6.77/7.03 6.77/7.03 Term ordering decisions: 6.77/7.03 Function symbol KB weights: bool=1. arrow_490897120le_alt=1. nat=1. arrow_660593299e_indi=1. suc=1. arrow_2064824852le_Lin=1. arrow_1111136790e_Prof=1. arrow_1322701812_below=1. arrow_14103264_above=1. f=1. b=1. a=1. arrow_2037941124le_IIA=1. p=1. arrow_218898985ctator=1. c=1. fNot=1. fconj=1. arrow_1278947948_mkbot=1. arrow_1427655034_mktop=1. arrow_831799591nimity=1. fTrue=1. fFalse=1. p_1=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. fun=1. product_prod=1. ti=1. product_Pair=1. pi=1. foldl=1. combk=1. list_case=1. list_rec=1. maps=1. in_rel=1. f5=1. f6=1. f7=1. f8=1. f35=1. f36=1. f37=1. f44=1. f128=1. f154=1. f156=1. f157=1. f191=1. f192=1. f195=1. f196=1. f200=1. f201=1. f202=1. f204=1. list=1. member=1. cons=1. append=1. nil=1. ord_less_eq=1. ord_less=1. set=1. size_size=1. linorder_sorted=1. listrel1=1. rev=1. distinct=1. drop=1. lexord=1. takeWhile=1. take=1. listrel=1. dropWhile=1. butlast=1. last=1. top_top=1. listrelp=1. tl=1. hd=1. replicate=1. lex=1. rotate1=1. equal_equal=1. fequal=1. null=1. insert=1. splice=1. partition=1. collect=1. if=1. nat_case=1. combi=1. lexn=1. order_215145569der_on=1. undefined=1. f17=1. f18=1. f19=1. f20=1. f65=1. f158=1. f159=1. f160=1. combb=1. product_prod_case=1. combc=1. product_curry=1. combs=1. produc1605651328_split=1. product_prod_rec=1. f3=1. f4=1. f9=1. f10=1. f11=1. f23=1. f32=1. f33=1. f34=1. f38=1. f50=1. f51=1. f54=1. f55=1. f66=1. f67=1. f68=1. f69=1. f70=1. f81=1. f82=1. f83=1. f84=1. f85=1. f86=1. f87=1. f88=1. f89=1. f90=1. f91=1. f92=1. f93=1. f101=1. f102=1. f108=1. f109=1. f110=1. f116=1. f117=1. f127=1. f135=1. f136=1. f140=1. f141=1. f142=1. f152=1. f153=1. f169=1. f170=1. f171=1. f172=1. f177=1. f178=1. f179=1. f180=1. f186=1. f193=1. f194=1. f206=1. hAPP=1. f12=1. f13=1. f14=1. f15=1. f39=1. f40=1. f41=1. f42=1. f45=1. f46=1. f48=1. f49=1. f78=1. f94=1. f95=1. f96=1. f99=1. f100=1. f103=1. f106=1. f107=1. f129=1. f138=1. f139=1. f155=1. f161=1. f162=1. f163=1. f164=1. f165=1. f205=1. f16=1. f24=1. f25=1. f26=1. f43=1. f47=1. f52=1. f53=1. f58=1. f71=1. f72=1. f73=1. f74=1. f75=1. f76=1. f77=1. f104=1. f105=1. f113=1. f118=1. f119=1. f120=1. f137=1. f143=1. f147=1. f148=1. f149=1. f181=1. f182=1. f183=1. f184=1. f185=1. f187=1. f198=1. f199=1. f203=1. f207=1. f208=1. f209=1. f1=1. f2=1. f56=1. f57=1. f79=1. f80=1. f111=1. f112=1. f114=1. f115=1. f130=1. f131=1. f132=1. f133=1. f134=1. f144=1. f145=1. f146=1. f150=1. f151=1. f166=1. f167=1. f168=1. f173=1. f174=1. f175=1. f176=1. f197=1. f27=1. f28=1. f29=1. f30=1. f31=1. f59=1. f60=1. f61=1. f62=1. f63=1. f64=1. f97=1. f98=1. f188=1. f189=1. f190=1. f21=1. f22=1. f121=1. f122=1. f123=1. f124=1. f125=1. f126=1. 6.77/7.03 6.77/7.03 ============================== end of process initial clauses ======== 6.77/7.03 6.77/7.03 ============================== CLAUSES FOR SEARCH ==================== 6.77/7.03 6.77/7.03 ============================== end of clauses for search ============= 6.77/7.03 6.77/7.03 ============================== SEARCH ================================ 6.77/7.03 6.77/7.03 % Starting search at 0.86 seconds. 6.77/7.03 6.77/7.03 Low Water (keep): wt=189.000, iters=3452 6.77/7.03 6.77/7.03 Low Water (keep): wt=182.000, iters=3388 6.77/7.03 6.77/7.03 Low Water (keep): wt=178.000, iters=3404 6.77/7.03 6.77/7.03 Low Water (keep): wt=168.000, iters=3337 6.77/7.03 6.77/7.03 Low Water (keep): wt=164.000, iters=3378 6.77/7.03 6.77/7.03 Low Water (keep): wt=161.000, iters=3381 6.77/7.03 6.77/7.03 Low Water (keep): wt=160.000, iters=3364 6.77/7.03 6.77/7.03 Low Water (keep): wt=159.000, iters=3337 6.77/7.03 6.77/7.03 Low Water (keep): wt=158.000, iters=3370 6.77/7.03 6.77/7.03 Low Water (keep): wt=156.000, iters=3368 6.77/7.03 6.77/7.03 Low Water (keep): wt=151.000, iters=3365 6.77/7.03 6.77/7.03 Low Water (keep): wt=147.000, iters=3365 6.77/7.03 6.77/7.03 Low Water (keep): wt=146.000, iters=3348 6.77/7.03 6.77/7.03 Low Water (keep): wt=144.000, iters=3345 6.77/7.03 6.77/7.03 Low Water (keep): wt=137.000, iters=3333 6.77/7.03 6.77/7.03 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 38 (0.00 of 4.04 sec). 6.77/7.03 6.77/7.03 Low Water (keep): wt=134.000, iters=3363 6.77/7.03 6.77/7.03 Low Water (keep): wt=132.000, iters=3488 6.77/7.03 6.77/7.03 Low Water (keep): wt=129.000, iters=3432 6.77/7.03 6.77/7.03 Low Water (keep): wt=123.000, iters=3342 6.77/7.03 6.77/7.03 Low Water (keep): wt=119.000, iters=3383 6.77/7.03 6.77/7.03 Low Water (keep): wt=116.000, iters=3397 6.77/7.03 6.77/7.03 Low Water (keep): wt=114.000, iters=3363 6.77/7.03 6.77/7.03 Low Water (keep): wt=113.000, iters=3336 6.77/7.03 6.77/7.03 Low WaterAlarm clock 119.61/120.05 Prover9 interrupted 119.61/120.05 EOF