TSTP Solution File: SCT169+5 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT169+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 22:04:21 EDT 2022
% Result : Timeout 300.02s 300.33s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SCT169+5 : TPTP v8.1.0. Released v5.3.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jul 2 03:51:49 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.89/1.18 ============================== Prover9 ===============================
% 0.89/1.18 Prover9 (32) version 2009-11A, November 2009.
% 0.89/1.18 Process 16716 was started by sandbox2 on n011.cluster.edu,
% 0.89/1.18 Sat Jul 2 03:51:50 2022
% 0.89/1.18 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_16563_n011.cluster.edu".
% 0.89/1.18 ============================== end of head ===========================
% 0.89/1.18
% 0.89/1.18 ============================== INPUT =================================
% 0.89/1.18
% 0.89/1.18 % Reading from file /tmp/Prover9_16563_n011.cluster.edu
% 0.89/1.18
% 0.89/1.18 set(prolog_style_variables).
% 0.89/1.18 set(auto2).
% 0.89/1.18 % set(auto2) -> set(auto).
% 0.89/1.18 % set(auto) -> set(auto_inference).
% 0.89/1.18 % set(auto) -> set(auto_setup).
% 0.89/1.18 % set(auto_setup) -> set(predicate_elim).
% 0.89/1.18 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.89/1.18 % set(auto) -> set(auto_limits).
% 0.89/1.18 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.89/1.18 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.89/1.18 % set(auto) -> set(auto_denials).
% 0.89/1.18 % set(auto) -> set(auto_process).
% 0.89/1.18 % set(auto2) -> assign(new_constants, 1).
% 0.89/1.18 % set(auto2) -> assign(fold_denial_max, 3).
% 0.89/1.18 % set(auto2) -> assign(max_weight, "200.000").
% 0.89/1.18 % set(auto2) -> assign(max_hours, 1).
% 0.89/1.18 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.89/1.18 % set(auto2) -> assign(max_seconds, 0).
% 0.89/1.18 % set(auto2) -> assign(max_minutes, 5).
% 0.89/1.18 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.89/1.18 % set(auto2) -> set(sort_initial_sos).
% 0.89/1.18 % set(auto2) -> assign(sos_limit, -1).
% 0.89/1.18 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.89/1.18 % set(auto2) -> assign(max_megs, 400).
% 0.89/1.18 % set(auto2) -> assign(stats, some).
% 0.89/1.18 % set(auto2) -> clear(echo_input).
% 0.89/1.18 % set(auto2) -> set(quiet).
% 0.89/1.18 % set(auto2) -> clear(print_initial_clauses).
% 0.89/1.18 % set(auto2) -> clear(print_given).
% 0.89/1.18 assign(lrs_ticks,-1).
% 0.89/1.18 assign(sos_limit,10000).
% 0.89/1.18 assign(order,kbo).
% 0.89/1.18 set(lex_order_vars).
% 0.89/1.18 clear(print_given).
% 0.89/1.18
% 0.89/1.18 % formulas(sos). % not echoed (137 formulas)
% 0.89/1.18
% 0.89/1.18 ============================== end of input ==========================
% 0.89/1.18
% 0.89/1.18 % From the command line: assign(max_seconds, 300).
% 0.89/1.18
% 0.89/1.18 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.89/1.18
% 0.89/1.18 % Formulas that are not ordinary clauses:
% 0.89/1.18 1 (all X_a (cl_HOL_Oequal(X_a) -> ti(fun(X_a,fun(X_a,bool)),equal_equal(X_a)) = equal_equal(X_a))) # label(tsy_c_HOL_Oequal__class_Oequal_res) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 2 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 3 (all X_a ti(fun(list(X_a),fun(list(X_a),list(X_a))),append(X_a)) = append(X_a)) # label(tsy_c_List_Oappend_res) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 4 (all X_a ti(fun(list(X_a),list(X_a)),butlast(X_a)) = butlast(X_a)) # label(tsy_c_List_Obutlast_res) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 5 (all X_a ti(fun(list(X_a),bool),distinct(X_a)) = distinct(X_a)) # label(tsy_c_List_Odistinct_res) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 6 (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].
% 0.89/1.18 7 (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].
% 0.89/1.18 8 (all X_a ti(fun(X_a,fun(list(X_a),list(X_a))),insert(X_a)) = insert(X_a)) # label(tsy_c_List_Oinsert_res) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 9 (all X_a ti(fun(list(X_a),X_a),last(X_a)) = last(X_a)) # label(tsy_c_List_Olast_res) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 10 (all X_a ti(fun(X_a,fun(list(X_a),list(X_a))),cons(X_a)) = cons(X_a)) # label(tsy_c_List_Olist_OCons_res) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 11 (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].
% 0.89/1.18 12 (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].
% 0.89/1.18 13 (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].
% 0.89/1.18 14 (all X_b all X_a ti(fun(fun(X_b,list(X_a)),fun(list(X_b),list(X_a))),maps(X_b,X_a)) = maps(X_b,X_a)) # label(tsy_c_List_Omaps_res) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 15 (all X_a ti(fun(list(X_a),bool),null(X_a)) = null(X_a)) # label(tsy_c_List_Onull_res) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 16 (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].
% 0.89/1.18 17 (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].
% 0.89/1.18 18 (all X_a ti(fun(list(X_a),list(X_a)),rotate1(X_a)) = rotate1(X_a)) # label(tsy_c_List_Orotate1_res) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 19 (all X_a ti(fun(list(X_a),fun(list(X_a),list(X_a))),splice(X_a)) = splice(X_a)) # label(tsy_c_List_Osplice_res) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 20 (all X_a ti(fun(list(X_a),list(X_a)),tl(X_a)) = tl(X_a)) # label(tsy_c_List_Otl_res) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 21 (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].
% 0.89/1.18 22 (all X_a all X_b all B_1 all B_2 hAPP(X_a,X_b,ti(fun(X_a,X_b),B_1),B_2) = hAPP(X_a,X_b,B_1,B_2)) # label(tsy_c_hAPP_arg1) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 23 (all X_a all X_b all B_1 all B_2 hAPP(X_a,X_b,B_1,ti(X_a,B_2)) = hAPP(X_a,X_b,B_1,B_2)) # label(tsy_c_hAPP_arg2) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 24 (all X_b all X_a all B_1 all B_2 ti(X_b,hAPP(X_a,X_b,B_1,B_2)) = hAPP(X_a,X_b,B_1,B_2)) # label(tsy_c_hAPP_res) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 25 (all B_1 (hBOOL(ti(bool,B_1)) <-> hBOOL(B_1))) # label(tsy_c_hBOOL_arg1) # label(hypothesis) # label(non_clause). [assumption].
% 0.89/1.18 26 (exists A_2 exists B exists C hBOOL(hAPP(list(arrow_1212486748le_alt),bool,distinct(arrow_1212486748le_alt),hAPP(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt)),cons(arrow_1212486748le_alt),A_2),hAPP(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt)),cons(arrow_1212486748le_alt),B),hAPP(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt)),cons(arrow_1212486748le_alt),C),nil(arrow_1212486748le_alt))))))) # label(fact_0_alt3) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 27 (all X_a hBOOL(hAPP(list(X_a),bool,distinct(X_a),nil(X_a)))) # label(fact_1_distinct_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 28 (all X_a all A_3 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_3),List_3)) # label(fact_2_list_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 29 (all X_a all A_3 all List_3 hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_3),List_3) != nil(X_a)) # label(fact_3_list_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 30 (all X_a all Xs (Xs != nil(X_a) <-> (exists Y_2 exists Ys_2 Xs = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_2)))) # label(fact_4_neq__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 31 (all X_a all Y (Y != nil(X_a) -> -(all A_2 all List_2 Y != hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_2),List_2)))) # label(fact_5_list_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 32 (all X_a all Xs_1 all X Xs_1 != hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs_1)) # label(fact_6_not__Cons__self) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 33 (all X_a all X all Xs_1 hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs_1) != Xs_1) # label(fact_7_not__Cons__self2) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 34 (all X_a all Aa all List all A_1 all List_1 (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_1),List_1) <-> ti(X_a,Aa) = ti(X_a,A_1) & List = List_1)) # label(fact_8_list_Oinject) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 35 (all X_a all V 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),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),Va)) # label(fact_9_splice_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 36 (all X_a all X hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(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),nil(X_a))) # label(fact_10_insert__Nil) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 37 (all X_a all P all Xs (Xs != nil(X_a) -> ((all X_2 hBOOL(hAPP(list(X_a),bool,P,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 (Xs_2 != nil(X_a) -> (hBOOL(hAPP(list(X_a),bool,P,Xs_2)) -> hBOOL(hAPP(list(X_a),bool,P,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,P,Xs)))))) # label(fact_11_list__nonempty__induct) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 38 (all X_a all Xs_1 (Xs_1 != nil(X_a) -> (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),butlast(X_a),Xs_1)))))) # label(fact_12_distinct__butlast) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 39 (all X_a hAPP(list(X_a),list(X_a),butlast(X_a),nil(X_a)) = nil(X_a)) # label(fact_13_butlast_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 40 (all X_a all X 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(X_a,fun(list(X_a),list(X_a)),insert(X_a),X),Xs_1))))) # label(fact_14_distinct__insert) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 41 (all X_a all X all Xs_1 all Y all Ys 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_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y),Ys)) = 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_1),Ys)))) # label(fact_15_splice_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 42 (all X_a all Xs_1 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),Xs_1),nil(X_a)) = Xs_1) # label(fact_16_splice__Nil2) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 43 (all X_a all Ys 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) = Ys) # label(fact_17_splice_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 44 (all X_a all X all Xs_1 ((Xs_1 = 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_1)) = nil(X_a)) & (Xs_1 != 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_1)) = 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_1))))) # label(fact_18_butlast_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 45 (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_19_list_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 46 (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),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)) = hAPP(list(X_b),X_a,hAPP(X_b,fun(list(X_b),X_a),F2,Aa),List)) # label(fact_20_list_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 47 (all X_b all X_a all F1 all F2 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)) = ti(X_a,F1)) # label(fact_21_list_Orecs_I1_J) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 48 (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_22_list_Orecs_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 49 (all X_a all Xs (Xs = nil(X_a) <-> hBOOL(hAPP(list(X_a),bool,null(X_a),Xs)))) # label(fact_23_eq__Nil__null) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 50 (all X_a all Xs (hBOOL(hAPP(list(X_a),bool,null(X_a),Xs)) <-> Xs = nil(X_a))) # label(fact_24_List_Onull__def) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 51 (all X_b hBOOL(hAPP(list(X_b),bool,null(X_b),nil(X_b)))) # label(fact_25_null__rec_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 52 (all X_a all X all Xs_1 -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_1)))) # label(fact_26_null__rec_I1_J) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 53 (all X_a all Xs_1 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_1),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_1) # label(fact_27_butlast__snoc) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 54 (all X_a all Xs_1 all Ys all Zs_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(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys)),Zs_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(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),Zs_2))) # label(fact_28_append__assoc) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 55 (all X_a all Xs all Ys_1 all Zs_1 all Ts (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs_1),Ts) <-> (exists Us_1 (Xs = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs_1),Us_1) & hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us_1),Ys_1) = Ts | hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Us_1) = Zs_1 & Ys_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Us_1),Ts))))) # label(fact_29_append__eq__append__conv2) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 56 (all X_a all Xs all Ys_1 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),Ys_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Zs_1) <-> Ys_1 = Zs_1)) # label(fact_30_same__append__eq) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.18 57 (all X_a all Ys_1 all Xs all Zs_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) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs_1),Xs) <-> Ys_1 = Zs_1)) # label(fact_31_append__same__eq) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 58 (all X_a all Ys all Us all Xs_1 all Xs1 all Zs_2 (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Xs1) = Zs_2 -> (Ys = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs1),Us) -> hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),Ys) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Zs_2),Us)))) # label(fact_32_append__eq__appendI) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 59 (all X_a all X all Xs_1 all 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),X),Xs_1)),Ys) = 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_1),Ys))) # label(fact_33_append__Cons) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 60 (all X_a all Xs_1 all Zs_2 all X all Xs1 all Ys (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs1) = Ys -> (Xs_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs1),Zs_2) -> hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs_1) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys),Zs_2)))) # label(fact_34_Cons__eq__appendI) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 61 (all X_a all Ys 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) = Ys) # label(fact_35_append__Nil) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 62 (all X_a all Xs 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),Ys_1) <-> Xs = nil(X_a) & Ys_1 = nil(X_a))) # label(fact_36_Nil__is__append__conv) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 63 (all X_a all Xs_1 hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs_1),nil(X_a)) = Xs_1) # label(fact_37_append__Nil2) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 64 (all X_a all Xs all Ys_1 (Xs = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1) <-> Ys_1 = nil(X_a))) # label(fact_38_self__append__conv) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 65 (all X_a all Ys_1 all Xs (Ys_1 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Xs),Ys_1) <-> Xs = nil(X_a))) # label(fact_39_self__append__conv2) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 66 (all X_a all Xs 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),Ys_1) = nil(X_a) <-> Xs = nil(X_a) & Ys_1 = nil(X_a))) # label(fact_40_append__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 67 (all X_a all Xs 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),Ys_1) = Xs <-> Ys_1 = nil(X_a))) # label(fact_41_append__self__conv) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 68 (all X_a all Xs 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),Ys_1) = Ys_1 <-> Xs = nil(X_a))) # label(fact_42_append__self__conv2) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 69 (all X_a all Xs_1 all Ys (Xs_1 = Ys -> Xs_1 = 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))) # label(fact_43_eq__Nil__appendI) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 70 (all X_a all Ys_1 all Zs_1 all X_1 all Xs (hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Zs_1) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs) <-> Ys_1 = nil(X_a) & Zs_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs) | (exists Ys_3 (Ys_1 = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Ys_3) & hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),Zs_1) = Xs)))) # label(fact_44_append__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 71 (all X_a all X_1 all Xs all Ys_1 all Zs_1 (hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs) = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_1),Zs_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) = Zs_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 = hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),append(X_a),Ys_3),Zs_1))))) # label(fact_45_Cons__eq__append__conv) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 72 (all X_a all Xs 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),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))) <-> Xs = Ys_1 & ti(X_a,X_1) = ti(X_a,Y_1))) # label(fact_46_append1__eq__conv) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 73 (all X_a all Xs_1 all Ys ((Ys = nil(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)) = hAPP(list(X_a),list(X_a),butlast(X_a),Xs_1)) & (Ys != nil(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)) = 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),butlast(X_a),Ys))))) # label(fact_47_butlast__append) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 74 (all X_a all Xs all P (hBOOL(hAPP(list(X_a),bool,P,nil(X_a))) -> ((all X_2 all Xs_2 (hBOOL(hAPP(list(X_a),bool,P,Xs_2)) -> hBOOL(hAPP(list(X_a),bool,P,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,P,Xs))))) # label(fact_48_rev__induct) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 75 (all X_a all Xs_1 (Xs_1 != nil(X_a) -> -(all Ys_2 all Y_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_2),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)))))) # label(fact_49_rev__cases) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 76 (all X_a all Xs (hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),equal_equal(list(X_a)),Xs),nil(X_a))) <-> hBOOL(hAPP(list(X_a),bool,null(X_a),Xs)))) # label(fact_50_equal__Nil__null) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 77 (all X_a all Xs all X_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),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 <-> Ys_1 != nil(X_a) & hAPP(list(X_a),list(X_a),butlast(X_a),Ys_1) = Xs & hAPP(list(X_a),X_a,last(X_a),Ys_1) = ti(X_a,X_1))) # label(fact_51_snoc__eq__iff__butlast) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 78 (all X_a all Xs_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),hAPP(list(X_a),list(X_a),butlast(X_a),Xs_1)),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_1)),nil(X_a))) = Xs_1)) # label(fact_52_append__butlast__last__id) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 79 (all X_b all X_a all X all Xs_1 (hAPP(list(X_a),list(X_a),rotate1(X_a),nil(X_a)) = nil(X_a) & 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_1)) = hAPP(list(X_b),list(X_b),hAPP(list(X_b),fun(list(X_b),list(X_b)),append(X_b),Xs_1),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),X),nil(X_b))))) # label(fact_53_rotate__simps) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 80 (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_54_equal__list__def) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 81 (all X_a all Xs (hAPP(list(X_a),list(X_a),rotate1(X_a),Xs) = nil(X_a) <-> Xs = nil(X_a))) # label(fact_55_rotate1__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 82 (all X_a all Xs (hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),rotate1(X_a),Xs))) <-> hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs)))) # label(fact_56_distinct1__rotate) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 83 (all X_a all X all Xs_1 (Xs_1 = 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_1)) = ti(X_a,X))) # label(fact_57_last__ConsL) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 84 (all X_a all X all Xs_1 (Xs_1 != 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_1)) = hAPP(list(X_a),X_a,last(X_a),Xs_1))) # label(fact_58_last__ConsR) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 85 (all X_a all X all Xs_1 ((Xs_1 = 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_1)) = ti(X_a,X)) & (Xs_1 != 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_1)) = hAPP(list(X_a),X_a,last(X_a),Xs_1)))) # label(fact_59_last_Osimps) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 86 (all X_a all Xs_1 all Ys (Ys = 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_1),Ys)) = hAPP(list(X_a),X_a,last(X_a),Xs_1))) # label(fact_60_last__appendL) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 87 (all X_a all Xs_1 all Ys (Ys != 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_1),Ys)) = hAPP(list(X_a),X_a,last(X_a),Ys))) # label(fact_61_last__appendR) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 88 (all X_a all Xs_1 all Ys ((Ys = 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_1),Ys)) = hAPP(list(X_a),X_a,last(X_a),Xs_1)) & (Ys != 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_1),Ys)) = hAPP(list(X_a),X_a,last(X_a),Ys)))) # label(fact_62_last__append) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 89 (all X_a all Xs_1 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_1),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_63_last__snoc) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 90 (all X_b all X_a all F all X_1 all Xs 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)) = 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))) # label(fact_64_maps__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 91 (all X_a all Ws (-hBOOL(hAPP(list(X_a),bool,distinct(X_a),Ws)) -> (exists Xs_2 exists Ys_2 exists Zs 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_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))),Zs))))))) # label(fact_65_not__distinct__decomp) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 92 (all X_a (cl_HOL_Oequal(X_a) -> equal_equal(X_a) = fequal(X_a))) # label(fact_66_equal) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 93 (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_67_equal__refl) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 94 (all X_b all X_a all F 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)) = nil(X_a)) # label(fact_68_maps__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 95 (all X_a (cl_HOL_Oequal(X_a) -> fequal(X_a) = equal_equal(X_a))) # label(fact_69_eq__equal) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 96 (all X_a (cl_HOL_Oequal(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),equal_equal(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_70_equal__eq) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 97 (all X_a all I 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),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),X))) # label(fact_71_replicate__append__same) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 98 (all X_a all X all Xs_1 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_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),Xs_1)),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_72_rev_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 99 (all X_a all Xs all Y_1 all Ys_1 (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),Y_1),Ys_1) <-> 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),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_73_rev__eq__Cons__iff) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 100 (all X_a all Xs all Ys_1 (hAPP(list(X_a),list(X_a),rev(X_a),Xs) = hAPP(list(X_a),list(X_a),rev(X_a),Ys_1) <-> Xs = Ys_1)) # label(fact_74_rev__is__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 101 (all X_a all X_b all F all G ((all X_2 hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2)) -> ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G))) # label(fact_75_ext) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 102 (all X_a all Xs all Ys_1 (hAPP(list(X_a),list(X_a),rev(X_a),Xs) = Ys_1 <-> Xs = hAPP(list(X_a),list(X_a),rev(X_a),Ys_1))) # label(fact_76_rev__swap) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 103 (all X_a all N 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),X)) = hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)) # label(fact_77_rev__replicate) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 104 (all X_a all Xs_1 hAPP(list(X_a),list(X_a),rev(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)) = Xs_1) # label(fact_78_rev__rev__ident) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 105 (all X_a all N 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),N),X)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),K),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),K),X)),hAPP(X_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X))) # label(fact_79_append__replicate__commute) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 106 (all X_a all Xs (hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs))) <-> hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs)))) # label(fact_80_distinct__rev) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 107 (all X_a all Xs_1 all Ys 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_1),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),rev(X_a),Ys)),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1))) # label(fact_81_rev__append) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 108 (all X_a hAPP(list(X_a),list(X_a),rev(X_a),nil(X_a)) = nil(X_a)) # label(fact_82_rev_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 109 (all X_a all Xs (nil(X_a) = hAPP(list(X_a),list(X_a),rev(X_a),Xs) <-> Xs = nil(X_a))) # label(fact_83_Nil__is__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 110 (all X_a all Xs (hAPP(list(X_a),list(X_a),rev(X_a),Xs) = nil(X_a) <-> Xs = nil(X_a))) # label(fact_84_rev__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 111 (all X_a all X_1 all Xs (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) <-> Xs = 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_85_singleton__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 112 (all X_a all Xs all X_1 (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_1),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_1),nil(X_a)))) # label(fact_86_rev__singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 113 (all X_a all N all X all 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_a,list(X_a),hAPP(nat,fun(X_a,list(X_a)),replicate(X_a),N),X)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs_1)) = 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),X)),Xs_1))) # label(fact_87_replicate__app__Cons__same) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 114 (all X_a all Xs_1 (Xs_1 != nil(X_a) -> hAPP(list(X_a),X_a,hd(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)) = hAPP(list(X_a),X_a,last(X_a),Xs_1))) # label(fact_88_hd__rev) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 115 (all X_a all Xs_1 (Xs_1 != nil(X_a) -> hAPP(list(X_a),X_a,last(X_a),hAPP(list(X_a),list(X_a),rev(X_a),Xs_1)) = hAPP(list(X_a),X_a,hd(X_a),Xs_1))) # label(fact_89_last__rev) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 116 (all X_a all X all Xs_1 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_1)) = ti(X_a,X)) # label(fact_90_hd_Osimps) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 117 (all X_a all Ys all Xs_1 ((Xs_1 = nil(X_a) -> 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_1),Ys)) = hAPP(list(X_a),X_a,hd(X_a),Ys)) & (Xs_1 != nil(X_a) -> 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_1),Ys)) = hAPP(list(X_a),X_a,hd(X_a),Xs_1)))) # label(fact_91_hd__append) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 118 (all X_a all Ys all Xs_1 (Xs_1 != nil(X_a) -> 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_1),Ys)) = hAPP(list(X_a),X_a,hd(X_a),Xs_1))) # label(fact_92_hd__append2) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 119 (all X_a all Xs_1 (Xs_1 != nil(X_a) -> hAPP(list(X_a),list(X_a),rotate1(X_a),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),tl(X_a),Xs_1)),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_1)),nil(X_a))))) # label(fact_93_rotate1__hd__tl) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 120 (all X_a all P all Xs (hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P),Xs) != nil(X_a) -> -hBOOL(hAPP(X_a,bool,P,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),P),Xs)))))) # label(fact_94_hd__dropWhile) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 121 (all X_a all Ys all Xs_1 (Xs_1 != nil(X_a) -> 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)) = 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_1)),Ys))) # label(fact_95_tl__append2) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 122 (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),tl(X_a),Xs_1))))) # label(fact_96_distinct__tl) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 123 (all X_a all P 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(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P),Xs))))) # label(fact_97_distinct__dropWhile) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 124 (all X_a all P hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P),nil(X_a)) = nil(X_a)) # label(fact_98_dropWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 125 (all X_a all Xs all P all X_1 ((hBOOL(hAPP(X_a,bool,P,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs)) = hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P),Xs)) & (-hBOOL(hAPP(X_a,bool,P,X_1)) -> hAPP(list(X_a),list(X_a),hAPP(fun(X_a,bool),fun(list(X_a),list(X_a)),dropWhile(X_a),P),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_1),Xs)))) # label(fact_99_dropWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 126 (all T_2 all T_1 (enum(T_1) & enum(T_2) -> enum(fun(T_2,T_1)))) # label(arity_fun___Enum_Oenum) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 127 (all T_2 all T_1 (cl_HOL_Oequal(T_1) & enum(T_2) -> cl_HOL_Oequal(fun(T_2,T_1)))) # label(arity_fun___HOL_Oequal) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 128 (all T_1 cl_HOL_Oequal(list(T_1))) # label(arity_List_Olist___HOL_Oequal) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 129 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 130 (all X_a all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)) | ti(X_a,X) = ti(X_a,Y))) # label(help_fequal_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 131 (all X_a all X all Y (ti(X_a,X) != ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)))) # label(help_fequal_2_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.89/1.19 132 -(exists C hBOOL(hAPP(list(arrow_1212486748le_alt),bool,distinct(arrow_1212486748le_alt),hAPP(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt)),cons(arrow_1212486748le_alt),a),hAPP(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt)),cons(arrow_1212486748le_alt),b),hAPP(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt)),cons(arrow_1212486748le_alt),C),nil(arrow_1212486748le_alt))))))) # label(conj_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.89/1.19
% 300.02/300.33 Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------