0.06/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.33 % Computer : n003.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 1200 0.12/0.33 % DateTime : Wed Jul 14 16:49:40 EDT 2021 0.12/0.33 % CPUTime : 0.95/1.25 ============================== Prover9 =============================== 0.95/1.25 Prover9 (32) version 2009-11A, November 2009. 0.95/1.25 Process 16016 was started by sandbox on n003.cluster.edu, 0.95/1.25 Wed Jul 14 16:49:41 2021 0.95/1.25 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_15863_n003.cluster.edu". 0.95/1.25 ============================== end of head =========================== 0.95/1.25 0.95/1.25 ============================== INPUT ================================= 0.95/1.25 0.95/1.25 % Reading from file /tmp/Prover9_15863_n003.cluster.edu 0.95/1.25 0.95/1.25 set(prolog_style_variables). 0.95/1.25 set(auto2). 0.95/1.25 % set(auto2) -> set(auto). 0.95/1.25 % set(auto) -> set(auto_inference). 0.95/1.25 % set(auto) -> set(auto_setup). 0.95/1.25 % set(auto_setup) -> set(predicate_elim). 0.95/1.25 % set(auto_setup) -> assign(eq_defs, unfold). 0.95/1.25 % set(auto) -> set(auto_limits). 0.95/1.25 % set(auto_limits) -> assign(max_weight, "100.000"). 0.95/1.25 % set(auto_limits) -> assign(sos_limit, 20000). 0.95/1.25 % set(auto) -> set(auto_denials). 0.95/1.25 % set(auto) -> set(auto_process). 0.95/1.25 % set(auto2) -> assign(new_constants, 1). 0.95/1.25 % set(auto2) -> assign(fold_denial_max, 3). 0.95/1.25 % set(auto2) -> assign(max_weight, "200.000"). 0.95/1.25 % set(auto2) -> assign(max_hours, 1). 0.95/1.25 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.95/1.25 % set(auto2) -> assign(max_seconds, 0). 0.95/1.25 % set(auto2) -> assign(max_minutes, 5). 0.95/1.25 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.95/1.25 % set(auto2) -> set(sort_initial_sos). 0.95/1.25 % set(auto2) -> assign(sos_limit, -1). 0.95/1.25 % set(auto2) -> assign(lrs_ticks, 3000). 0.95/1.25 % set(auto2) -> assign(max_megs, 400). 0.95/1.25 % set(auto2) -> assign(stats, some). 0.95/1.25 % set(auto2) -> clear(echo_input). 0.95/1.25 % set(auto2) -> set(quiet). 0.95/1.25 % set(auto2) -> clear(print_initial_clauses). 0.95/1.25 % set(auto2) -> clear(print_given). 0.95/1.25 assign(lrs_ticks,-1). 0.95/1.25 assign(sos_limit,10000). 0.95/1.25 assign(order,kbo). 0.95/1.25 set(lex_order_vars). 0.95/1.25 clear(print_given). 0.95/1.25 0.95/1.25 % formulas(sos). % not echoed (163 formulas) 0.95/1.25 0.95/1.25 ============================== end of input ========================== 0.95/1.25 0.95/1.25 % From the command line: assign(max_seconds, 1200). 0.95/1.25 0.95/1.25 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.95/1.25 0.95/1.25 % Formulas that are not ordinary clauses: 0.95/1.25 1 (all X_b all A_4 all Pa hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fimplies),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),fNot),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_4)))),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) # label(fact_31_insert__Collect) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 2 (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]. 0.95/1.25 3 (all X_b the_elem(X_b) = ti(fun(fun(X_b,bool),X_b),the_elem(X_b))) # label(tsy_c_Set_Othe__elem_res) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 4 (all X_b all Pa hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = ti(fun(X_b,bool),Pa)) # label(fact_77_Collect__def) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 5 (all X_b hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse)) = bot_bot(fun(X_b,bool))) # label(fact_23_empty__def) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 6 (all X_b ti(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),insert(X_b)) = insert(X_b)) # label(tsy_c_Set_Oinsert_res) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 7 (all X_b all Pa all A_4 ((-hBOOL(hAPP(X_b,bool,Pa,A_4)) -> bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_4))),Pa))) & (hBOOL(hAPP(X_b,bool,Pa,A_4)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_4))),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),bot_bot(fun(X_b,bool)))))) # label(fact_15_Collect__conv__if) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 8 (all X_b all F_1 all X_1 -hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F_1),bot_bot(fun(X_b,bool))),X_1))) # label(fact_67_empty__fold1SetE) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 9 (all X_c all X_b all F_1 all Z all A1 all A2 (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F_1),Z),A1),A2)) <-> ti(X_c,Z) = ti(X_c,A2) & ti(fun(X_b,bool),A1) = bot_bot(fun(X_b,bool)) | (exists X_2 exists A_2 exists Y_1 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),A_2) = ti(fun(X_b,bool),A1) & hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F_1,X_2),Y_1) = ti(X_c,A2) & hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F_1),Z),A_2),Y_1)) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_2)))))) # label(fact_95_fold__graph_Osimps) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 10 (all X_b all Y_2 -(all Fun1 all Com all Fun2 hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Fun1),Com),Fun2) != Y_2)) # label(fact_47_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 11 (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_1_1_T) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 12 (all X_c all X_b hoare_728318379le_rec(X_c,X_b) = ti(fun(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_509422987triple(X_c),X_b)),hoare_728318379le_rec(X_c,X_b))) # label(tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__rec_res) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 13 (all X_b all A_4 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),A_1)) -> ti(fun(X_b,bool),A_1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),A_1))) # label(fact_24_insert__absorb) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 14 (all X_b all Ga all Ca all Q_1 all Pa ((all Z_1 all S (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S)) -> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),hAPP(fun(state,bool),fun(X_b,fun(state,bool)),combk(fun(state,bool),X_b),hAPP(state,fun(state,bool),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),S))),Ca),hAPP(fun(state,bool),fun(X_b,fun(state,bool)),combk(fun(state,bool),X_b),hAPP(X_b,fun(state,bool),Q_1,Z_1)))),bot_bot(fun(hoare_509422987triple(X_b),bool))))))) -> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool))))))) # label(fact_5_escape) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 15 (all X_b all X_a all P all Q ti(X_a,P) = hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q)) # label(help_COMBK_1_1_U) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 16 (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]. 0.95/1.25 17 (all X_b all A_4 all A_1 bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),A_1)) # label(fact_39_insert__not__empty) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 18 (all X_b all A_1 all F_1 all F (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F_1),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F_1),A_1) = hAPP(fun(X_b,bool),X_b,F,A_1)))) # label(fact_78_folding__one_Oeq__fold) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 19 (all X_b all A_4 all A_1 (bot_bot(fun(X_b,bool)) = ti(fun(X_b,bool),A_1) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),A_1)))) # label(fact_17_equals0D) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 20 (all X_a all X_c all B_1_1 all B_2 hAPP(X_a,X_c,B_1_1,B_2) = hAPP(X_a,X_c,B_1_1,ti(X_a,B_2))) # label(tsy_c_hAPP_arg2) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 21 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | hBOOL(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 22 (all X_b all X_c all F_1 all G ((all X_2 hAPP(X_b,X_c,F_1,X_2) = hAPP(X_b,X_c,G,X_2)) -> ti(fun(X_b,X_c),F_1) = ti(fun(X_b,X_c),G))) # label(fact_75_ext) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 23 (all P all Q (hBOOL(Q) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 24 (all X_b all Pa all A_4 ((-hBOOL(hAPP(X_b,bool,Pa,A_4)) -> bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_4))),Pa))) & (hBOOL(hAPP(X_b,bool,Pa,A_4)) -> hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_4))),Pa)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),bot_bot(fun(X_b,bool)))))) # label(fact_14_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 25 (all X_b (finite_finite(X_b) -> (all A_1 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))))) # label(fact_83_finite__code) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 26 (all X_b all F_1 all A_4 all X_3 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),X_3)),X_1)) -> -(all A_3 all A_2 (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),X_3) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),A_2) -> (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),F_1),A_3),A_2),X_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),A_2))))))) # label(fact_89_insert__fold1SetE) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 27 (all X_b all A_1 (ti(fun(X_b,bool),A_1) = bot_bot(fun(X_b,bool)) <-> (all X_2 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))))) # label(fact_22_all__not__in__conv) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 28 (all P all Q (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | -hBOOL(Q))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 29 (all X_b all X_1 all A_1 (hBOOL(hAPP(X_b,bool,A_1,X_1)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)))) # label(fact_76_mem__def) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 30 (all X_b all A_4 all Ba all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),A_1))) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),A_1)) | ti(X_b,Ba) = ti(X_b,A_4))) # label(fact_28_insert__iff) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 31 (all T all A ti(T,A) = ti(T,ti(T,A))) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 32 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),finite2073411215e_idem(X_b)) = finite2073411215e_idem(X_b)) # label(tsy_c_Finite__Set_Ofolding__one__idem_res) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 33 (all X_b all Ca -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ca),bot_bot(fun(X_b,bool))))) # label(fact_19_empty__iff) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 34 (all X_b all Pa all F (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,bot_bot(fun(X_b,bool)))) -> ((all X_2 all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),F_2))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,F)))))) # label(fact_91_finite__induct) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 35 (all X_b all A_4 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),A_1))))) # label(fact_85_finite__insert) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 36 (all X_b hoare_1008221573triple(X_b) = ti(fun(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)))),hoare_1008221573triple(X_b))) # label(tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple_res) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 37 (all X_c all X_a all B_1_1 all B_2 ti(X_c,hAPP(X_a,X_c,B_1_1,B_2)) = hAPP(X_a,X_c,B_1_1,B_2)) # label(tsy_c_hAPP_res) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 38 (all P all Q (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)) | -hBOOL(Q))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 39 (all X_c all X_b hoare_885240885e_case(X_c,X_b) = ti(fun(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_509422987triple(X_c),X_b)),hoare_885240885e_case(X_c,X_b))) # label(tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__case_res) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 40 (all X_b all X_1 hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),X_1)) = ti(X_b,X_1)) # label(fact_54_the__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 41 (all X_b all X_1 all Y_2 all A_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),A_1))) # label(fact_29_insert__commute) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 42 (all X_b all X_1 all A_1 all F_1 all F (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F_1),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F_1,X_1),hAPP(fun(X_b,bool),X_b,F,A_1)) = hAPP(fun(X_b,bool),X_b,F,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)))))) # label(fact_96_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption]. 0.95/1.25 43 (all X_b all Ga all Pa all Ca all Q_1 all C ((hBOOL(C) -> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))) -> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),hAPP(bool,fun(X_b,fun(state,bool)),hAPP(fun(X_b,fun(bool,fun(state,bool))),fun(bool,fun(X_b,fun(state,bool))),combc(X_b,bool,fun(state,bool)),hAPP(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(bool,fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(bool,fun(state,bool))),fun(fun(X_b,fun(state,fun(bool,bool))),fun(X_b,fun(bool,fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(bool,fun(state,bool)),X_b),combc(state,bool,bool)),hAPP(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(X_b,fun(state,bool)),fun(X_b,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),Pa))),C)),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool))))))) # label(fact_4_constant) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 44 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool))),finite_fold1Set(X_b)) = finite_fold1Set(X_b)) # label(tsy_c_Finite__Set_Ofold1Set_res) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 45 (all X_b hoare_122391849derivs(X_b) = ti(fun(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool)),hoare_122391849derivs(X_b))) # label(tsy_c_Hoare__Mirabelle__pjuwniqynr_Ohoare__derivs_res) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 46 (all X_b all Q_1 all Ga all Ca all Pa ((all Z_1 all S (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S)) -> (exists P_1 exists Q_2 ((all S_1 ((all Z_2 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1)))) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1)))) & hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool))))))))) -> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool))))))) # label(fact_62_conseq) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 47 (all X_a all X_b all X_c ti(fun(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c))),combc(X_a,X_b,X_c)) = combc(X_a,X_b,X_c)) # label(tsy_c_COMBC_res) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 48 (all X_b all A_4 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),A_1)) -> (exists B (ti(fun(X_b,bool),A_1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),B) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),B)))))) # label(fact_52_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 49 (all X_b all D all R_1 all Ga all Pa all Ca all Q_1 (hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool))))) -> (hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Q_1),D),R_1)),bot_bot(fun(hoare_509422987triple(X_b),bool))))) -> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),hAPP(com,com,hAPP(com,fun(com,com),semi,Ca),D)),R_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))))) # label(fact_46_Comp) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 50 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool)),finite_folding_one(X_b)) = finite_folding_one(X_b)) # label(tsy_c_Finite__Set_Ofolding__one_res) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 51 (all X_b all Pa all A_4 (hBOOL(hAPP(X_b,bool,Pa,A_4)) -> ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> ti(X_b,X_2) = ti(X_b,A_4))) -> hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa)))))) # label(fact_59_theI) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 52 (all X_b all X_1 all A_1 all F_1 all F (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F_1),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) -> hAPP(fun(X_b,bool),X_b,F,A_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F_1,X_1),hAPP(fun(X_b,bool),X_b,F,A_1)))))) # label(fact_99_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 53 (all X_c all X_b all F_1 all Z all Y_2 all X_1 all A_1 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) -> (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F_1),Z),A_1),Y_2)) -> hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F_1),Z),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)),hAPP(X_c,X_c,hAPP(X_b,fun(X_c,X_c),F_1,X_1),Y_2)))))) # label(fact_81_fold__graph_OinsertI) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 54 (all X_c all X_b all F1 all Fun1_1 all Com_1 all Fun2_1 hAPP(hoare_509422987triple(X_c),X_b,hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_509422987triple(X_c),X_b),hoare_885240885e_case(X_c,X_b),F1),hAPP(fun(X_c,fun(state,bool)),hoare_509422987triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_509422987triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_509422987triple(X_c))),hoare_1008221573triple(X_c),Fun1_1),Com_1),Fun2_1)) = hAPP(fun(X_c,fun(state,bool)),X_b,hAPP(com,fun(fun(X_c,fun(state,bool)),X_b),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b)),F1,Fun1_1),Com_1),Fun2_1)) # label(fact_42_triple_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 55 (all X_b all X_1 all F_1 all F (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F_1),F)) -> ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,F,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool)))))) # label(fact_65_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 56 (all X_b all Fun1_1 all Com_1 all Fun2_1 all Fun1_2 all Com_2 all Fun2_2 (hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Fun1_2),Com_2),Fun2_2) = hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Fun1_1),Com_1),Fun2_1) <-> Com_2 = Com_1 & Fun2_1 = Fun2_2 & Fun1_2 = Fun1_1)) # label(fact_1_triple_Oinject) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 57 (all X_b all A_4 all Pa ((exists X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) & (all Y_1 (hBOOL(hAPP(X_b,bool,Pa,Y_1)) -> ti(X_b,Y_1) = ti(X_b,X_2))))) -> (hBOOL(hAPP(X_b,bool,Pa,A_4)) -> ti(X_b,A_4) = hAPP(fun(X_b,bool),X_b,the(X_b),Pa)))) # label(fact_60_the1__equality) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 58 (all B_1_1 (hBOOL(B_1_1) <-> hBOOL(ti(bool,B_1_1)))) # label(tsy_c_hBOOL_arg1) # label(hypothesis) # label(non_clause). [assumption]. 0.95/1.26 59 (all X_c all X_b (bot(X_b) -> (all X_1 hAPP(X_c,X_b,bot_bot(fun(X_c,X_b)),X_1) = bot_bot(X_b)))) # label(fact_43_bot__apply) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 60 (all X_b all Q_1 all Pa all Ga all P_2 all Ca all Q_3 (hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_2),Ca),Q_3)),bot_bot(fun(hoare_509422987triple(X_b),bool))))) -> ((all Z_1 all S (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S)) -> (all S_1 ((all Z_2 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_2,Z_2),S)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_3,Z_2),S_1)))) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1)))))) -> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))))) # label(fact_8_conseq12) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 61 (all X_b all Ga all G_1 all Ts (hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),G_1),Ts)) -> (hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),G_1)) -> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),Ts))))) # label(fact_2_cut) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 62 (all X_b (finite_finite(X_b) -> (all A_1 hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1))))) # label(fact_82_finite) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 63 (all X_b all A_4 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_4)) <-> ti(fun(X_b,bool),A_4) = bot_bot(fun(X_b,bool)) | (exists A_2 exists A_3 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_2)) & hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),A_2) = ti(fun(X_b,bool),A_4))))) # label(fact_92_finite_Osimps) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 64 (all X_b all X_2 (hBOOL(hAPP(X_b,bool,bot_bot(fun(X_b,bool)),X_2)) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),bot_bot(fun(X_b,bool)))))) # label(fact_66_bot__empty__eq) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 65 (all X_b all A_4 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),bot_bot(fun(X_b,bool))))) # label(fact_11_emptyE) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 66 (all X_b all X_c all X_a ti(fun(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c))),combb(X_b,X_c,X_a)) = combb(X_b,X_c,X_a)) # label(tsy_c_COMBB_res) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 67 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R) = hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R))) # label(help_COMBB_1_1_U) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 68 (all X_b all Pa all A_4 (hBOOL(hAPP(X_b,bool,Pa,A_4)) -> ((all X_2 (hBOOL(hAPP(X_b,bool,Pa,X_2)) -> ti(X_b,X_2) = ti(X_b,A_4))) -> hAPP(fun(X_b,bool),X_b,the(X_b),Pa) = ti(X_b,A_4)))) # label(fact_58_the__equality) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 69 (all X_a ti(fun(X_a,fun(X_a,bool)),fequal(X_a)) = fequal(X_a)) # label(tsy_c_fequal_res) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 70 (all X_b all X_1 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) -> -(all B (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B) = ti(fun(X_b,bool),A_1) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B)))))) # label(fact_48_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 71 (all Com1_2 all Com2_2 skip != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2)) # label(fact_49_com_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 72 (all T_2 all T_1 (bot(T_1) -> bot(fun(T_2,T_1)))) # label(arity_fun___Orderings_Obot) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 73 (all X_b all F_1 all A_1 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F_1),A_1),X_1)) -> ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)))) # label(fact_68_fold1Set__nonempty) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 74 (all X_b all A_4 all B_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),B_1) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_4))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_1)))) # label(fact_32_insert__compr) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 75 (all X_b all F_1 all A_4 all A_1 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),F_1),A_4),A_1),X_1)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),A_1)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),A_1)),X_1))))) # label(fact_69_fold1Set_Ointros) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 76 (all X_b all X_1 all A_1 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1))) # label(fact_30_insert__absorb2) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 77 (all X_b all A_1 ((all Y_1 -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_1))) -> ti(fun(X_b,bool),A_1) = bot_bot(fun(X_b,bool)))) # label(fact_57_equals0I) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 78 (all X_b all Ts all Ga all T_3 (hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),T_3),bot_bot(fun(hoare_509422987triple(X_b),bool))))) -> (hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),Ts)) -> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),T_3),Ts)))))) # label(fact_3_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 79 (all X_b ti(fun(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b)),finite_fold1(X_b)) = finite_fold1(X_b)) # label(tsy_c_Finite__Set_Ofold1_res) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 80 (all X_b the(X_b) = ti(fun(fun(X_b,bool),X_b),the(X_b))) # label(tsy_c_HOL_OThe_res) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 81 (all X_b all B_1 all X_1 all A_1 (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),B_1)) -> (ti(fun(X_b,bool),A_1) = ti(fun(X_b,bool),B_1) <-> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),B_1))))) # label(fact_26_insert__ident) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 82 (all X_b all A_4 all Ba (hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),bot_bot(fun(X_b,bool))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),bot_bot(fun(X_b,bool))) -> ti(X_b,A_4) = ti(X_b,Ba))) # label(fact_35_singleton__inject) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 83 (all X_b hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),bot_bot(fun(X_b,bool))))) # label(fact_73_finite_OemptyI) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 84 (all X_b all A_4 all B_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),B_1)))) # label(fact_33_insertI1) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 85 (all X_b all Pa ((exists X_2 ((all Y_1 (hBOOL(hAPP(X_b,bool,Pa,Y_1)) -> ti(X_b,X_2) = ti(X_b,Y_1))) & hBOOL(hAPP(X_b,bool,Pa,X_2)))) -> hBOOL(hAPP(X_b,bool,Pa,hAPP(fun(X_b,bool),X_b,the(X_b),Pa))))) # label(fact_61_theI_H) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 86 (all X_c all X_b all F_1 all Z all X_1 (hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F_1),Z),bot_bot(fun(X_b,bool))),X_1)) -> ti(X_c,X_1) = ti(X_c,Z))) # label(fact_80_empty__fold__graphE) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 87 (all Q all P (-hBOOL(P) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 88 (all X_b all X_2 all Xa hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_2))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),Xa))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),Xa)) # label(fact_34_insert__compr__raw) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 89 (all X_c all X_b all F_1 all Z hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F_1),Z),bot_bot(fun(X_b,bool))),Z))) # label(fact_79_fold__graph_OemptyI) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 90 (all X_b all Pa ((all X_2 -hBOOL(hAPP(X_b,bool,Pa,X_2))) <-> bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) # label(fact_18_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 91 (all Q all P (-hBOOL(P) | -hBOOL(Q) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 92 (all X_a all X_b all X_c combs(X_a,X_b,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))) # label(tsy_c_COMBS_res) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 93 (all Com1_1 all Com2_1 all Com1 all Com2 (hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_1),Com2_1) = hAPP(com,com,hAPP(com,fun(com,com),semi,Com1),Com2) <-> Com1_1 = Com1 & Com2_1 = Com2)) # label(fact_53_com_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 94 (all X_c all X_b all F1 all Fun1_1 all Com_1 all Fun2_1 hAPP(hoare_509422987triple(X_c),X_b,hAPP(fun(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b))),fun(hoare_509422987triple(X_c),X_b),hoare_728318379le_rec(X_c,X_b),F1),hAPP(fun(X_c,fun(state,bool)),hoare_509422987triple(X_c),hAPP(com,fun(fun(X_c,fun(state,bool)),hoare_509422987triple(X_c)),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),hoare_509422987triple(X_c))),hoare_1008221573triple(X_c),Fun1_1),Com_1),Fun2_1)) = hAPP(fun(X_c,fun(state,bool)),X_b,hAPP(com,fun(fun(X_c,fun(state,bool)),X_b),hAPP(fun(X_c,fun(state,bool)),fun(com,fun(fun(X_c,fun(state,bool)),X_b)),F1,Fun1_1),Com_1),Fun2_1)) # label(fact_16_triple_Orecs) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 95 (all P all Q (hBOOL(Q) | hBOOL(P) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)))) # label(help_fdisj_3_1_U) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 96 (all X_b all X_c finite_fold_graph(X_b,X_c) = ti(fun(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool)))),finite_fold_graph(X_b,X_c))) # label(tsy_c_Finite__Set_Ofold__graph_res) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 97 (all T_2 all T_1 (finite_finite(T_1) & finite_finite(T_2) -> finite_finite(fun(T_2,T_1)))) # label(arity_fun___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 98 (all X_b all F_1 all A_4 all Ba (ti(X_b,Ba) = ti(X_b,A_4) <-> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),bot_bot(fun(X_b,bool)))),Ba)))) # label(fact_64_fold1Set__sing) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 99 (all X_b all A_4 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),bot_bot(fun(X_b,bool))) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_4))) # label(fact_12_singleton__conv2) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 100 (all X_b all Ga hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),bot_bot(fun(hoare_509422987triple(X_b),bool))))) # label(fact_0_empty) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 101 (all X_b all X_c (bot(X_c) -> (all X_2 hAPP(X_b,X_c,bot_bot(fun(X_b,X_c)),X_2) = bot_bot(X_c)))) # label(fact_44_bot__fun__def) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 102 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 103 (all X_b all F_1 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) -> (exists X1 hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F_1),A_1),X1)))))) # label(fact_90_finite__nonempty__imp__fold1Set) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 104 (all X_b all Q_1 all Ga all Pa all Ca all Q_3 (hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_3)),bot_bot(fun(hoare_509422987triple(X_b),bool))))) -> ((all Z_1 all S (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_3,Z_1),S)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S)))) -> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))))) # label(fact_6_conseq2) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 105 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c)),combs(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R))) # label(help_COMBS_1_1_U) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 106 (all X_b all X_1 all Y_2 all Pa ((hBOOL(Pa) -> hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,Pa)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_1)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,Pa))),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),Y_2)))) = ti(X_b,X_1)) & (-hBOOL(Pa) -> ti(X_b,Y_2) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,Pa)),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),X_1)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,Pa))),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),Y_2))))))) # label(fact_56_If__def) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 107 (all P (hBOOL(P) | hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 108 (all X_b all X_1 ti(X_b,X_1) = hAPP(fun(X_b,bool),X_b,the_elem(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),bot_bot(fun(X_b,bool))))) # label(fact_41_the__elem__eq) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 109 (all X_b all F_1 all A_1 hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F_1),A_1)) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F_1),A_1)) # label(fact_71_fold1__def) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 110 (all X_b all F_1 all A_4 ti(X_b,A_4) = hAPP(fun(X_b,bool),X_b,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F_1),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),bot_bot(fun(X_b,bool))))) # label(fact_87_fold1__singleton) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 111 (all X_b all X_3 hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,bool),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_b,fun(X_b,bool)),fun(X_b,bool)),combb(fun(X_b,bool),bool,X_b),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),fequal(fun(X_b,bool)),X_3)),hAPP(fun(X_b,bool),fun(X_b,fun(X_b,bool)),hAPP(fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_b,fun(X_b,bool))),combc(X_b,fun(X_b,bool),fun(X_b,bool)),insert(X_b)),bot_bot(fun(X_b,bool))))) = hAPP(fun(X_b,bool),X_b,the_elem(X_b),X_3)) # label(fact_51_the__elem__def) # label(axiom) # label(non_clause). [assumption]. 0.95/1.26 112 (all X_b all Pa all Q_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fdisj),Pa)),Q_1)))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_1))))) # label(fact_84_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 113 (all Q all P (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)) | hBOOL(P))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 114 (all X_b all Ba all A_4 (ti(X_b,A_4) = ti(X_b,Ba) <-> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),bot_bot(fun(X_b,bool))))))) # label(fact_38_singleton__iff) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 115 (all X_b all A_4 all Ba all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),A_1))) -> (ti(X_b,A_4) != ti(X_b,Ba) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),A_1))))) # label(fact_9_insertE) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 116 (all X_b finite_finite_1(X_b) = ti(fun(fun(X_b,bool),bool),finite_finite_1(X_b))) # label(tsy_c_Finite__Set_Ofinite_res) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 117 (all X_a all X_b ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b)) = combk(X_a,X_b)) # label(tsy_c_COMBK_res) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 118 (all X_b all Ga all Pa hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),skip),Pa)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))) # label(fact_45_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 119 (all X_b all Q_1 all Pa (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Q_1))) | hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),Pa)),Q_1)))))) # label(fact_72_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 120 (all X_b all Y_2 all A_1 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_2),A_1),X_1)) <-> ti(X_b,X_1) = ti(X_b,Y_2) | hBOOL(hAPP(X_b,bool,A_1,X_1)))) # label(fact_27_insert__code) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 121 (all Com1_2 all Com2_2 skip != hAPP(com,com,hAPP(com,fun(com,com),semi,Com1_2),Com2_2)) # label(fact_50_com_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 122 (all X_b all Pa (bot_bot(fun(X_b,bool)) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) <-> (all X_2 -hBOOL(hAPP(X_b,bool,Pa,X_2))))) # label(fact_20_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 123 (all P (-hBOOL(P) | -hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 124 (all X_b all Ba all A_4 all B_1 ((-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),B_1)) -> ti(X_b,Ba) = ti(X_b,A_4)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),B_1))))) # label(fact_10_insertCI) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 125 (all X_c all X_b all F_1 all Z all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (exists X1 hBOOL(hAPP(X_c,bool,hAPP(fun(X_b,bool),fun(X_c,bool),hAPP(X_c,fun(fun(X_b,bool),fun(X_c,bool)),hAPP(fun(X_b,fun(X_c,X_c)),fun(X_c,fun(fun(X_b,bool),fun(X_c,bool))),finite_fold_graph(X_b,X_c),F_1),Z),A_1),X1))))) # label(fact_93_finite__imp__fold__graph) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 126 (all X_b all A_4 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),bot_bot(fun(X_b,bool))) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_4))) # label(fact_13_singleton__conv) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 127 (all X_b all X_1 all F_1 all F (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite2073411215e_idem(X_b),F_1),F)) -> ti(X_b,X_1) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F_1,X_1),X_1))) # label(fact_98_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 128 (all X_b ti(fun(fun(X_b,bool),fun(X_b,bool)),collect(X_b)) = collect(X_b)) # label(tsy_c_Set_OCollect_res) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 129 (all X_b all A_4 all Ba all Ca all D (ti(X_b,Ba) = ti(X_b,D) & ti(X_b,A_4) = ti(X_b,Ca) | ti(X_b,A_4) = ti(X_b,D) & ti(X_b,Ca) = ti(X_b,Ba) <-> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ca),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),D),bot_bot(fun(X_b,bool)))) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),bot_bot(fun(X_b,bool)))))) # label(fact_37_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 130 (all X_b all Pa all Ga all P_2 all Ca all Q_1 (hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_2),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool))))) -> ((all Z_1 all S (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_2,Z_1),S)))) -> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool)))))))) # label(fact_7_conseq1) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 131 (all X_a all X_c all B_1_1 all B_2 hAPP(X_a,X_c,B_1_1,B_2) = hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2)) # label(tsy_c_hAPP_arg1) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 132 (all X_b all A_1 ((exists X_2 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))) <-> bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),A_1))) # label(fact_21_ex__in__conv) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 133 (all X_b all Ba all A_4 all B_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),B_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_4),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Ba),B_1))))) # label(fact_25_insertI2) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 134 (all X_b all Pa all F (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F)) -> (bot_bot(fun(X_b,bool)) != ti(fun(X_b,bool),F) -> ((all X_2 hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),bot_bot(fun(X_b,bool)))))) -> ((all X_2 all F_2 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),F_2)) -> (ti(fun(X_b,bool),F_2) != bot_bot(fun(X_b,bool)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),F_2)) -> (hBOOL(hAPP(fun(X_b,bool),bool,Pa,F_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),F_2)))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,Pa,F))))))) # label(fact_97_finite__ne__induct) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 135 (all X_b all A_4 ti(X_b,A_4) = hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(X_b,bool)),combc(X_b,X_b,bool),fequal(X_b)),A_4))) # label(fact_55_the__eq__trivial) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 136 (all X_b all X_1 all A_1 all F_1 all F (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F_1),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) -> (ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) -> hAPP(fun(X_b,bool),X_b,F,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_1),A_1)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F_1,X_1),hAPP(fun(X_b,bool),X_b,F,A_1))))))) # label(fact_70_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 137 (all X_b all A_1 ((exists X_2 exists B (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),B)) & ti(fun(X_b,bool),A_1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),B))) <-> ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)))) # label(fact_63_nonempty__iff) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 138 (all X_b all F_1 all A1 all A2 ((exists A_3 exists A_2 exists X_2 (ti(fun(X_b,bool),A1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),A_2) & ti(X_b,A2) = ti(X_b,X_2) & hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,X_b)),fun(X_b,fun(fun(X_b,bool),fun(X_b,bool))),finite_fold_graph(X_b,X_b),F_1),A_3),A_2),X_2)) & -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),A_2)))) <-> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),fun(X_b,bool)),finite_fold1Set(X_b),F_1),A1),A2)))) # label(fact_94_fold1Set_Osimps) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 139 (all X_b all Ba all A_4 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Ba),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),bot_bot(fun(X_b,bool))))) -> ti(X_b,A_4) = ti(X_b,Ba))) # label(fact_36_singletonE) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 140 (all X_b all A_4 all A_1 (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),A_1))))) # label(fact_74_finite_OinsertI) # label(axiom) # label(non_clause). [assumption]. 0.95/1.27 141 (all X_b all A_4 all G all F_1 (G = hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_b,bool),X_b),finite_fold1(X_b),F_1) -> hAPP(fun(X_b,bool),X_b,G,hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),bot_bot(fun(X_b,bool)))) = ti(X_b,A_4))) # label(fact_86_fold1__singleton__def) # label(axiom) # label(non_clause). [assumption]. 1.69/1.97 142 (all X_b all A_1 all F_1 all F (hBOOL(hAPP(fun(fun(X_b,bool),X_b),bool,hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(fun(X_b,bool),X_b),bool),finite_folding_one(X_b),F_1),F)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_1)) -> (ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) -> ((all X_2 all Y_1 hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),F_1,X_2),Y_1)),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),Y_1),bot_bot(fun(X_b,bool))))))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(fun(X_b,bool),X_b,F,A_1)),A_1))))))) # label(fact_88_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption]. 1.69/1.97 143 (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]. 1.69/1.97 144 (all X_b all A_4 all A_1 bot_bot(fun(X_b,bool)) != hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),A_1)) # label(fact_40_empty__not__insert) # label(axiom) # label(non_clause). [assumption]. 1.69/1.97 145 (all P (fTrue = ti(bool,P) | ti(bool,P) = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption]. 1.69/1.97 146 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)) | hBOOL(Q) | -hBOOL(P))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption]. 1.69/1.97 147 (all X_b (bot(X_b) -> bot_bot(X_b) = ti(X_b,bot_bot(X_b)))) # label(tsy_c_Orderings_Obot__class_Obot_res) # label(axiom) # label(non_clause). [assumption]. 1.69/1.97 1.69/1.97 ============================== end of process non-clausal formulas === 1.69/1.97 1.69/1.97 ============================== PROCESS INITIAL CLAUSES =============== 1.69/1.97 1.69/1.97 ============================== PREDICATE ELIMINATION ================= 1.69/1.97 1.69/1.97 ============================== end predicate elimination ============= 1.69/1.97 1.69/1.97 Auto_denials: (non-Horn, no changes). 1.69/1.97 1.69/1.97 Term ordering decisions: 1.69/1.97 Function symbol KB weights: bool=1. state=1. com=1. fconj=1. fdisj=1. fimplies=1. semi=1. fNot=1. fFalse=1. fTrue=1. skip=1. b=1. c=1. g=1. p=1. x_a=1. fun=1. ti=1. finite_fold_graph=1. combk=1. hoare_728318379le_rec=1. hoare_885240885e_case=1. f4=1. f5=1. f6=1. f12=1. f24=1. f25=1. f28=1. f30=1. f34=1. f38=1. f42=1. f43=1. hoare_509422987triple=1. insert=1. bot_bot=1. member=1. finite_finite_1=1. hoare_1008221573triple=1. hoare_122391849derivs=1. collect=1. fequal=1. the=1. finite_fold1Set=1. finite_fold1=1. finite_folding_one=1. finite2073411215e_idem=1. the_elem=1. undefined=1. combb=1. combc=1. combs=1. f13=1. f14=1. f18=1. f19=1. f26=1. f27=1. f29=1. f31=1. f39=1. f40=1. f41=1. hAPP=1. f9=1. f20=1. f44=1. f45=1. f46=1. f47=1. f48=1. f7=1. f8=1. f10=1. f11=1. f15=1. f16=1. f35=1. f1=1. f2=1. f3=1. f32=1. f33=1. f36=1. f37=1. f17=1. f21=1. f22=1. f23=1. 1.69/1.97 1.69/1.97 ============================== end of process initial clauses ======== 1.69/1.97 1.69/1.97 ============================== CLAUSES FOR SEARCH ==================== 1.69/1.97 1.69/1.97 ============================== end of clauses for search ============= 1.69/1.97 1.69/1.97 ============================== SEARCH ================================ 1.69/1.97 1.69/1.97 % Starting search at 0.18 seconds. 1.69/1.97 1.69/1.97 ============================== PROOF ================================= 1.69/1.97 % SZS status Theorem 1.69/1.97 % SZS output start Refutation 1.69/1.97 1.69/1.97 % Proof 1 at 0.76 (+ 0.01) seconds. 1.69/1.97 % Length of proof is 40. 1.69/1.97 % Level of proof is 8. 1.69/1.97 % Maximum clause weight is 305.000. 1.69/1.97 % Given clauses 217. 1.69/1.97 1.69/1.97 4 (all X_b all Pa hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),Pa) = ti(fun(X_b,bool),Pa)) # label(fact_77_Collect__def) # label(axiom) # label(non_clause). [assumption]. 1.69/1.97 5 (all X_b hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(bool,fun(X_b,bool),combk(bool,X_b),fFalse)) = bot_bot(fun(X_b,bool))) # label(fact_23_empty__def) # label(axiom) # label(non_clause). [assumption]. 1.69/1.97 15 (all X_b all X_a all P all Q ti(X_a,P) = hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q)) # label(help_COMBK_1_1_U) # label(axiom) # label(non_clause). [assumption]. 1.69/1.97 37 (all X_c all X_a all B_1_1 all B_2 ti(X_c,hAPP(X_a,X_c,B_1_1,B_2)) = hAPP(X_a,X_c,B_1_1,B_2)) # label(tsy_c_hAPP_res) # label(axiom) # label(non_clause). [assumption]. 1.69/1.97 40 (all X_b all X_1 hAPP(fun(X_b,bool),X_b,the(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),X_1)) = ti(X_b,X_1)) # label(fact_54_the__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption]. 1.69/1.97 46 (all X_b all Q_1 all Ga all Ca all Pa ((all Z_1 all S (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Pa,Z_1),S)) -> (exists P_1 exists Q_2 ((all S_1 ((all Z_2 (hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),P_1,Z_2),S)) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_2,Z_2),S_1)))) -> hBOOL(hAPP(state,bool,hAPP(X_b,fun(state,bool),Q_1,Z_1),S_1)))) & hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),P_1),Ca),Q_2)),bot_bot(fun(hoare_509422987triple(X_b),bool))))))))) -> hBOOL(hAPP(fun(hoare_509422987triple(X_b),bool),bool,hAPP(fun(hoare_509422987triple(X_b),bool),fun(fun(hoare_509422987triple(X_b),bool),bool),hoare_122391849derivs(X_b),Ga),hAPP(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool),hAPP(hoare_509422987triple(X_b),fun(fun(hoare_509422987triple(X_b),bool),fun(hoare_509422987triple(X_b),bool)),insert(hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b),hAPP(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b)),hAPP(fun(X_b,fun(state,bool)),fun(com,fun(fun(X_b,fun(state,bool)),hoare_509422987triple(X_b))),hoare_1008221573triple(X_b),Pa),Ca),Q_1)),bot_bot(fun(hoare_509422987triple(X_b),bool))))))) # label(fact_62_conseq) # label(axiom) # label(non_clause). [assumption]. 1.69/1.97 59 (all X_c all X_b (bot(X_b) -> (all X_1 hAPP(X_c,X_b,bot_bot(fun(X_c,X_b)),X_1) = bot_bot(X_b)))) # label(fact_43_bot__apply) # label(axiom) # label(non_clause). [assumption]. 1.69/1.97 99 (all X_b all A_4 hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_4),bot_bot(fun(X_b,bool))) = hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_b,fun(X_b,bool),fequal(X_b),A_4))) # label(fact_12_singleton__conv2) # label(axiom) # label(non_clause). [assumption]. 1.69/1.97 152 ti(fun(A,bool),B) = hAPP(fun(A,bool),fun(A,bool),collect(A),B) # label(fact_77_Collect__def) # label(axiom). [clausify(4)]. 1.69/1.97 153 hAPP(fun(A,bool),fun(A,bool),collect(A),B) = ti(fun(A,bool),B). [copy(152),flip(a)]. 1.69/1.97 154 bot_bot(fun(A,bool)) = hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(bool,fun(A,bool),combk(bool,A),fFalse)) # label(fact_23_empty__def) # label(axiom). [clausify(5)]. 1.69/1.97 155 ti(fun(A,bool),hAPP(bool,fun(A,bool),combk(bool,A),fFalse)) = bot_bot(fun(A,bool)). [copy(154),rewrite([153(16)]),flip(a)]. 1.69/1.97 187 ti(A,B) = hAPP(C,A,hAPP(A,fun(C,A),combk(A,C),B),D) # label(help_COMBK_1_1_U) # label(axiom). [clausify(15)]. 1.69/1.97 188 hAPP(A,B,hAPP(B,fun(A,B),combk(B,A),C),D) = ti(B,C). [copy(187),flip(a)]. 1.69/1.97 208 -hBOOL(fFalse) # label(help_fFalse_1_1_U) # label(axiom). [assumption]. 1.69/1.97 230 ti(A,hAPP(B,A,C,D)) = hAPP(B,A,C,D) # label(tsy_c_hAPP_res) # label(axiom). [clausify(37)]. 1.69/1.97 234 ti(A,B) = hAPP(fun(A,bool),A,the(A),hAPP(A,fun(A,bool),fequal(A),B)) # label(fact_54_the__sym__eq__trivial) # label(axiom). [clausify(40)]. 1.69/1.97 244 hBOOL(hAPP(state,bool,hAPP(A,fun(state,bool),B,f15(A,C,D,E,B)),f16(A,C,D,E,B))) | hBOOL(hAPP(fun(hoare_509422987triple(A),bool),bool,hAPP(fun(hoare_509422987triple(A),bool),fun(fun(hoare_509422987triple(A),bool),bool),hoare_122391849derivs(A),D),hAPP(fun(hoare_509422987triple(A),bool),fun(hoare_509422987triple(A),bool),hAPP(hoare_509422987triple(A),fun(fun(hoare_509422987triple(A),bool),fun(hoare_509422987triple(A),bool)),insert(hoare_509422987triple(A)),hAPP(fun(A,fun(state,bool)),hoare_509422987triple(A),hAPP(com,fun(fun(A,fun(state,bool)),hoare_509422987triple(A)),hAPP(fun(A,fun(state,bool)),fun(com,fun(fun(A,fun(state,bool)),hoare_509422987triple(A))),hoare_1008221573triple(A),B),E),C)),bot_bot(fun(hoare_509422987triple(A),bool))))) # label(fact_62_conseq) # label(axiom). [clausify(46)]. 1.69/1.97 268 bot(bool) # label(arity_HOL_Obool___Orderings_Obot) # label(axiom). [assumption]. 1.69/1.97 277 -bot(A) | bot_bot(A) = hAPP(B,A,bot_bot(fun(B,A)),C) # label(fact_43_bot__apply) # label(axiom). [clausify(59)]. 1.69/1.97 278 -bot(A) | hAPP(B,A,bot_bot(fun(B,A)),C) = bot_bot(A). [copy(277),flip(b)]. 1.69/1.97 360 hAPP(fun(A,bool),fun(A,bool),collect(A),hAPP(A,fun(A,bool),fequal(A),B)) = hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),bot_bot(fun(A,bool))) # label(fact_12_singleton__conv2) # label(axiom). [clausify(99)]. 1.69/1.97 361 hAPP(fun(fun(A,bool),bool),fun(A,bool),the(fun(A,bool)),hAPP(fun(A,bool),fun(fun(A,bool),bool),fequal(fun(A,bool)),hAPP(A,fun(A,bool),fequal(A),B))) = hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),bot_bot(fun(A,bool))). [copy(360),rewrite([153(10),234(7)])]. 1.69/1.97 471 fFalse = ti(bool,fFalse) # label(tsy_c_fFalse_res) # label(hypothesis). [assumption]. 1.69/1.97 472 hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),fFalse)) = fFalse. [copy(471),rewrite([234(4)]),flip(a)]. 1.69/1.97 501 -hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool))))) # label(conj_0) # label(negated_conjecture). [assumption]. 1.69/1.97 508 hAPP(fun(fun(A,bool),bool),fun(A,bool),the(fun(A,bool)),hAPP(fun(A,bool),fun(fun(A,bool),bool),fequal(fun(A,bool)),hAPP(bool,fun(A,bool),combk(bool,A),fFalse))) = bot_bot(fun(A,bool)). [back_rewrite(155),rewrite([234(10)])]. 1.69/1.97 510 hAPP(fun(A,bool),A,the(A),hAPP(A,fun(A,bool),fequal(A),hAPP(B,A,C,D))) = hAPP(B,A,C,D). [back_rewrite(230),rewrite([234(2)])]. 1.69/1.97 518 hAPP(fun(A,bool),A,the(A),hAPP(A,fun(A,bool),fequal(A),B)) = hAPP(C,A,hAPP(A,fun(C,A),combk(A,C),B),D). [back_rewrite(188),rewrite([234(5)]),flip(a)]. 1.69/1.97 533 hAPP(fun(fun(A,bool),bool),fun(A,bool),the(fun(A,bool)),hAPP(fun(A,bool),fun(fun(A,bool),bool),fequal(fun(A,bool)),B)) = hAPP(fun(A,bool),fun(A,bool),collect(A),B). [back_rewrite(153),rewrite([234(9)]),flip(a)]. 1.69/1.97 550 hAPP(bool,fun(A,bool),combk(bool,A),fFalse) = bot_bot(fun(A,bool)). [back_rewrite(508),rewrite([510(27)])]. 1.69/1.97 562 hAPP(fun(A,bool),fun(A,bool),hAPP(A,fun(fun(A,bool),fun(A,bool)),insert(A),B),bot_bot(fun(A,bool))) = hAPP(A,fun(A,bool),fequal(A),B). [back_rewrite(361),rewrite([510(24)]),flip(a)]. 1.69/1.97 608 -hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool)))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))). [back_rewrite(501),rewrite([550(96),562(298)])]. 1.69/1.97 642 hBOOL(hAPP(state,bool,hAPP(A,fun(state,bool),B,f15(A,C,D,E,B)),f16(A,C,D,E,B))) | hBOOL(hAPP(fun(hoare_509422987triple(A),bool),bool,hAPP(fun(hoare_509422987triple(A),bool),fun(fun(hoare_509422987triple(A),bool),bool),hoare_122391849derivs(A),D),hAPP(hoare_509422987triple(A),fun(hoare_509422987triple(A),bool),fequal(hoare_509422987triple(A)),hAPP(fun(A,fun(state,bool)),hoare_509422987triple(A),hAPP(com,fun(fun(A,fun(state,bool)),hoare_509422987triple(A)),hAPP(fun(A,fun(state,bool)),fun(com,fun(fun(A,fun(state,bool)),hoare_509422987triple(A))),hoare_1008221573triple(A),B),E),C)))). [back_rewrite(244),rewrite([562(74)])]. 1.69/1.97 718 hAPP(A,bool,bot_bot(fun(A,bool)),B) = bot_bot(bool). [resolve(278,a,268,a)]. 1.69/1.97 1476 bot_bot(bool) = fFalse. [para(518(a,1),472(a,1)),rewrite([550(8),718(5)])]. 1.69/1.97 1492 hAPP(A,bool,bot_bot(fun(A,bool)),B) = fFalse. [back_rewrite(718),rewrite([1476(7)])]. 1.69/1.97 1531 hAPP(A,fun(B,bool),hAPP(fun(B,bool),fun(A,fun(B,bool)),combk(fun(B,bool),A),C),D) = hAPP(fun(B,bool),fun(B,bool),collect(B),C). [para(533(a,1),518(a,1)),flip(a)]. 1.69/1.97 1708 hAPP(fun(A,bool),fun(A,bool),collect(A),bot_bot(fun(A,bool))) = bot_bot(fun(A,bool)). [para(550(a,1),510(a,1,4,4)),rewrite([533(23),550(16)])]. 1.69/1.97 2634 $F. [resolve(642,b,608,a),rewrite([1531(242),1708(15),1492(224)]),unit_del(a,208)]. 1.69/1.97 1.69/1.97 % SZS output end Refutation 1.69/1.97 ============================== end of proof ========================== 1.69/1.97 1.69/1.97 ============================== STATISTICS ============================ 1.69/1.97 1.69/1.97 Given=217. Generated=5389. Kept=2355. proofs=1. 1.69/1.97 Usable=211. Sos=1663. Demods=139. Limbo=39, Disabled=678. Hints=0. 1.69/1.97 Megabytes=16.21. 1.69/1.97 User_CPU=0.76, System_CPU=0.01, Wall_clock=1. 1.69/1.97 1.69/1.97 ============================== end of statistics ===================== 1.69/1.97 1.69/1.97 ============================== end of search ========================= 1.69/1.97 1.69/1.97 THEOREM PROVED 1.69/1.97 % SZS status Theorem 1.69/1.97 1.69/1.97 Exiting with 1 proof. 1.69/1.97 1.69/1.97 Process 16016 exit (max_proofs) Wed Jul 14 16:49:42 2021 1.69/1.97 Prover9 interrupted 1.69/1.97 EOF