TSTP Solution File: SCT170+5 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT170+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n003.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 22:04:24 EDT 2022
% Result : Unknown 201.21s 201.52s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SCT170+5 : TPTP v8.1.0. Released v5.3.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 2 03:47:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.95/1.25 ============================== Prover9 ===============================
% 0.95/1.25 Prover9 (32) version 2009-11A, November 2009.
% 0.95/1.25 Process 27109 was started by sandbox on n003.cluster.edu,
% 0.95/1.25 Sat Jul 2 03:47:54 2022
% 0.95/1.25 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26955_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_26955_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 (154 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, 300).
% 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 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].
% 0.95/1.25 2 (all X_a all X_b all X_c ti(fun(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c))),combc(X_a,X_b,X_c)) = combc(X_a,X_b,X_c)) # label(tsy_c_COMBC_res) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 3 (all X_a ti(fun(X_a,X_a),combi(X_a)) = combi(X_a)) # label(tsy_c_COMBI_res) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 4 (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].
% 0.95/1.25 5 (all X_a all X_b ti(fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),in_rel(X_a,X_b)) = in_rel(X_a,X_b)) # label(tsy_c_FunDef_Oin__rel_res) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 6 (all X_a all X_b ti(fun(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool))),pi(X_a,X_b)) = pi(X_a,X_b)) # label(tsy_c_FuncSet_OPi_res) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 7 (all X_a ti(fun(list(X_a),fun(list(X_a),bool)),equal_equal(list(X_a))) = equal_equal(list(X_a))) # label(tsy_c_HOL_Oequal__class_Oequal_res) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 8 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 9 (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].
% 0.95/1.25 10 (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].
% 0.95/1.25 11 (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].
% 0.95/1.25 12 (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].
% 0.95/1.25 13 (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].
% 0.95/1.25 14 (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].
% 0.95/1.25 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].
% 0.95/1.25 16 (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].
% 0.95/1.25 17 (all X_a (top(X_a) -> ti(X_a,top_top(X_a)) = top_top(X_a))) # label(tsy_c_Orderings_Otop__class_Otop_res) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 18 (all X_a all X_b ti(fun(X_a,fun(X_b,product_prod(X_a,X_b))),product_Pair(X_a,X_b)) = product_Pair(X_a,X_b)) # label(tsy_c_Product__Type_OPair_res) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 19 (all X_a all X_b all X_c ti(fun(fun(product_prod(X_a,X_b),X_c),fun(X_a,fun(X_b,X_c))),product_curry(X_a,X_b,X_c)) = product_curry(X_a,X_b,X_c)) # label(tsy_c_Product__Type_Ocurry_res) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 20 (all X_b all X_c all X_a ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),produc1605651328_split(X_b,X_c,X_a)) = produc1605651328_split(X_b,X_c,X_a)) # label(tsy_c_Product__Type_Ointernal__split_res) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 21 (all X_b all X_c all X_a ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),product_prod_rec(X_b,X_c,X_a)) = product_prod_rec(X_b,X_c,X_a)) # label(tsy_c_Product__Type_Oprod_Oprod__rec_res) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 22 (all X_a ti(fun(fun(X_a,bool),fun(X_a,bool)),collect(X_a)) = collect(X_a)) # label(tsy_c_Set_OCollect_res) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 23 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_arg1) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 24 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_arg2) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 25 (all X_c all X_a all B_1_1 all B_2_1 ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_res) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 26 (all B_1_1 (hBOOL(ti(bool,B_1_1)) <-> hBOOL(B_1_1))) # label(tsy_c_hBOOL_arg1) # label(hypothesis) # label(non_clause). [assumption].
% 0.95/1.25 27 (all X_b ti(fun(X_b,fun(fun(X_b,bool),bool)),member(X_b)) = member(X_b)) # label(tsy_c_member_res) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 28 (all I (hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),a),b)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I))) <-> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p_1,I))))) # label(fact_5_iff) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 29 -(all 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(fact_6__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 30 (all X_1 all Y all L_1 all Z (hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_1),Y)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,L_1),Z))) <-> ti(arrow_1212486748le_alt,Y) != ti(arrow_1212486748le_alt,Z) & (ti(arrow_1212486748le_alt,X_1) = ti(arrow_1212486748le_alt,Z) -> ti(arrow_1212486748le_alt,X_1) != ti(arrow_1212486748le_alt,Y)) & (ti(arrow_1212486748le_alt,X_1) != ti(arrow_1212486748le_alt,Z) -> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_1),Y)),L_1))))) # label(fact_10_in__mkbot) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 31 (all X_1 all Y all L_1 all Z (hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_1),Y)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,L_1),Z))) <-> ti(arrow_1212486748le_alt,X_1) != ti(arrow_1212486748le_alt,Z) & (ti(arrow_1212486748le_alt,Y) = ti(arrow_1212486748le_alt,Z) -> ti(arrow_1212486748le_alt,X_1) != ti(arrow_1212486748le_alt,Y)) & (ti(arrow_1212486748le_alt,Y) != ti(arrow_1212486748le_alt,Z) -> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_1),Y)),L_1))))) # label(fact_11_in__mktop) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 32 (all X_1 all Y all L_1 all Aa all Ba (ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,Ba) -> (hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L_1),arrow_638930832le_Lin)) -> (hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_1),Y)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_888040304_below,L_1),Aa),Ba))) <-> ti(arrow_1212486748le_alt,X_1) != ti(arrow_1212486748le_alt,Y) & (ti(arrow_1212486748le_alt,Y) = ti(arrow_1212486748le_alt,Aa) -> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_1),Ba)),L_1))) & (ti(arrow_1212486748le_alt,Y) != ti(arrow_1212486748le_alt,Aa) -> (ti(arrow_1212486748le_alt,X_1) = ti(arrow_1212486748le_alt,Aa) -> ti(arrow_1212486748le_alt,Y) = ti(arrow_1212486748le_alt,Ba) | hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Ba),Y)),L_1))) & (ti(arrow_1212486748le_alt,X_1) != ti(arrow_1212486748le_alt,Aa) -> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_1),Y)),L_1)))))))) # label(fact_12_in__below) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 33 (all X_a all X_b all Pa ((all X1 hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,X1))) <-> (all A_2 all B hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B)))))) # label(fact_13_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 34 (all X_b all X_a all Aa all Ba all A_4 all B_3 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_3) <-> ti(X_a,Aa) = ti(X_a,A_4) & ti(X_b,Ba) = ti(X_b,B_3))) # label(fact_14_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 35 (all X_b all X_a all A_5 all B_2 all A_3 all B_4 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_5),B_2) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_3),B_4) -> -(ti(X_a,A_5) = ti(X_a,A_3) -> ti(X_b,B_2) != ti(X_b,B_4)))) # label(fact_15_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 36 (all X_b all X_a all R_1 all X_1 all Y (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),in_rel(X_a,X_b),R_1),X_1),Y)) <-> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Y)),R_1)))) # label(fact_16_in__rel__def) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 37 (all L_1 all X_1 all Y (ti(arrow_1212486748le_alt,X_1) != ti(arrow_1212486748le_alt,Y) -> (hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L_1),arrow_638930832le_Lin)) -> hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_888040304_below,L_1),X_1),Y)),arrow_638930832le_Lin))))) # label(fact_17_below__Lin) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 38 (all P_a all Pa all A_4 all B_3 all Aa all Ba (ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,Ba) -> (ti(arrow_1212486748le_alt,A_4) != ti(arrow_1212486748le_alt,B_3) -> (ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,B_3) -> (ti(arrow_1212486748le_alt,Ba) != ti(arrow_1212486748le_alt,A_4) -> (hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Pa),arrow_1834574746e_Prof)) -> (hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),P_a),arrow_1834574746e_Prof)) -> ((all I (hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Pa,I))) <-> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),P_a,I))))) -> (hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,Pa))) -> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,P_a)))))))))))) # label(fact_19__C1_C) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 39 (all P_a all Pa all A_4 all B_3 all Aa all Ba (ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,Ba) -> (ti(arrow_1212486748le_alt,A_4) != ti(arrow_1212486748le_alt,B_3) -> (ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,B_3) -> (ti(arrow_1212486748le_alt,Ba) != ti(arrow_1212486748le_alt,A_4) -> (hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Pa),arrow_1834574746e_Prof)) -> (hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),P_a),arrow_1834574746e_Prof)) -> ((all I (hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Pa,I))) <-> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),P_a,I))))) -> (hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,Pa))) <-> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,P_a)))))))))))) # label(fact_20__C2_C) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 40 (all L_1 (hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L_1),arrow_638930832le_Lin)) -> hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),combk(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),arrow_1384031255e_indi),L_1)),arrow_1834574746e_Prof)))) # label(fact_22_const__Lin__Prof) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 41 (all X_1 all L_1 (hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L_1),arrow_638930832le_Lin)) -> hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,L_1),X_1)),arrow_638930832le_Lin)))) # label(fact_23_mkbot__Lin) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 42 (all X_1 all L_1 (hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L_1),arrow_638930832le_Lin)) -> hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,L_1),X_1)),arrow_638930832le_Lin)))) # label(fact_24_mktop__Lin) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 43 (all Aa all Ba all L_1 (hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L_1),arrow_638930832le_Lin)) -> (hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),L_1)) -> -hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Ba),Aa)),L_1))))) # label(fact_25_Lin__irrefl) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 44 (all X_1 all Y all L_1 (hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L_1),arrow_638930832le_Lin)) -> (ti(arrow_1212486748le_alt,X_1) != ti(arrow_1212486748le_alt,Y) -> (-hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_1),Y)),L_1)) <-> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Y),X_1)),L_1)))))) # label(fact_26_notin__Lin__iff) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 45 (all A_5 all B_2 (ti(arrow_1212486748le_alt,A_5) != ti(arrow_1212486748le_alt,B_2) -> (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_5),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_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),C),nil(arrow_1212486748le_alt))))))))) # label(fact_27_third__alt) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.25 46 (all Fa (hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,Fa)) <-> (all X (hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),X),arrow_1834574746e_Prof)) -> (all Xa (hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Xa),arrow_1834574746e_Prof)) -> (all A_2 all B ((all I (hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X,I))) <-> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Xa,I))))) -> (hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,X))) <-> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,Xa)))))))))))) # label(fact_28_IIA__def) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 47 (all Fa (hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,Fa)) <-> (all X (hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),X),arrow_1834574746e_Prof)) -> (all A_2 all B ((all I hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X,I)))) -> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,X))))))))) # label(fact_29_unanimity__def) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 48 (all Aa all Ba (ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,Ba) -> (exists X (hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),X),arrow_638930832le_Lin)) & hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),X)))))) # label(fact_30_complete__Lin) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 49 (all X_1 all Y all L_1 all Aa all Ba (ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,Ba) -> (hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L_1),arrow_638930832le_Lin)) -> (hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_1),Y)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,L_1),Aa),Ba))) <-> ti(arrow_1212486748le_alt,X_1) != ti(arrow_1212486748le_alt,Y) & (ti(arrow_1212486748le_alt,X_1) = ti(arrow_1212486748le_alt,Ba) -> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Y)),L_1))) & (ti(arrow_1212486748le_alt,X_1) != ti(arrow_1212486748le_alt,Ba) -> (ti(arrow_1212486748le_alt,Y) = ti(arrow_1212486748le_alt,Ba) -> ti(arrow_1212486748le_alt,X_1) = ti(arrow_1212486748le_alt,Aa) | hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_1),Aa)),L_1))) & (ti(arrow_1212486748le_alt,Y) != ti(arrow_1212486748le_alt,Ba) -> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_1),Y)),L_1)))))))) # label(fact_31_in__above) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 50 (all X_b all X_c all X_a all F1 all Aa all Ba hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_rec(X_b,X_c,X_a),F1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,Aa),Ba)) # label(fact_32_prod_Orecs) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 51 (all X_a hBOOL(hAPP(list(X_a),bool,distinct(X_a),nil(X_a)))) # label(fact_33_distinct_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 52 (all X_a all A_3 all List_2 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_2)) # label(fact_34_list_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 53 (all X_a all Aa all List all A_4 all List_3 (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_4),List_3) <-> ti(X_a,Aa) = ti(X_a,A_4) & List = List_3)) # label(fact_35_list_Oinject) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 54 (all X_a all X_2 all Xs_1 hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_1) != Xs_1) # label(fact_36_not__Cons__self2) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 55 (all X_a all Xs_1 all X_2 Xs_1 != hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_1)) # label(fact_37_not__Cons__self) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 56 (all L_1 all X_1 all Y (ti(arrow_1212486748le_alt,X_1) != ti(arrow_1212486748le_alt,Y) -> (hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L_1),arrow_638930832le_Lin)) -> hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,L_1),X_1),Y)),arrow_638930832le_Lin))))) # label(fact_38_above__Lin) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 57 (all X_a all A_3 all List_2 hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_3),List_2) != nil(X_a)) # label(fact_39_list_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 58 (all I_1 all Fa (hBOOL(hAPP(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Fa),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool)),pi(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1834574746e_Prof),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_638930832le_Lin)))) -> ((all X (hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),X),arrow_1834574746e_Prof)) -> (all A_2 all B (ti(arrow_1212486748le_alt,A_2) != ti(arrow_1212486748le_alt,B) -> (hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X,I_1))) -> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,X)))))))) -> hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,Fa),I_1))))) # label(fact_40_dictatorI) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 59 (all X_a all X_b all X_1 all F all A_1 all B_1 (hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B_1))) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,fun(X_b,bool),B_1,X_1))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))))) # label(fact_41_PiE) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 60 (all X_a all Y_1 (Y_1 != nil(X_a) -> -(all A_2 all List_1 Y_1 != hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_2),List_1)))) # label(fact_42_list_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 61 (all X_a all Xs (Xs != nil(X_a) <-> (exists Y_2 exists Ys_1 Xs = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_1)))) # label(fact_43_neq__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 62 (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_44_alt3) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 63 (all X_a all X_b all X_1 all F all A_1 all B_1 (hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B_1))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,fun(X_b,bool),B_1,X_1)))))) # label(fact_45_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 64 (all X_a all X_b all X_1 all F all A_1 all B_1 (hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B_1)))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),B_1))))) # label(fact_46_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 65 (all X_a all A_1 hBOOL(hAPP(fun(fun(X_a,X_a),bool),bool,hAPP(fun(X_a,X_a),fun(fun(fun(X_a,X_a),bool),bool),member(fun(X_a,X_a)),combi(X_a)),hAPP(fun(X_a,fun(X_a,bool)),fun(fun(X_a,X_a),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_a,bool)),fun(fun(X_a,X_a),bool)),pi(X_a,X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,fun(X_a,bool)),combk(fun(X_a,bool),X_a),A_1))))) # label(fact_47_funcset__id) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 66 (all Fa all I_1 (hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,Fa),I_1)) <-> (all X (hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),X),arrow_1834574746e_Prof)) -> hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,X) = hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X,I_1))))) # label(fact_48_dictator__def) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 67 (all X_b all X_a all F all B_1 all A_1 ((all X (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X)),hAPP(X_a,fun(X_b,bool),B_1,X))))) -> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B_1))))) # label(fact_49_Pi__I) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 68 (all X_b all X_a all F all B_1 all A_1 ((all X (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X)),B_1)))) -> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B_1)))))) # label(fact_50_funcsetI) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 69 (exists L hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L),arrow_638930832le_Lin))) # label(fact_51_linear__alt) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 70 (all X_b all X_a all F all B_1 all A_1 ((all X (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X)),hAPP(X_a,fun(X_b,bool),B_1,X))))) -> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B_1))))) # label(fact_52_Pi__I_H) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 71 (all X_b all X_a all B_1 all F all G all A_1 ((all W (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),W),A_1)) -> hAPP(X_a,X_b,F,W) = hAPP(X_a,X_b,G,W))) -> (hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B_1))) <-> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),G),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B_1)))))) # label(fact_53_Pi__cong) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 72 (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_54_splice_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 73 (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_55_list_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 74 (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_56_list_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 75 (all X_a all X_2 all Xs_1 all Y_1 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_2),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),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_57_splice_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 76 (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_58_splice_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 77 (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_59_splice__Nil2) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 78 (all X_a all X_b all S all R_1 ((all X all Xa (hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X),Xa)),R_1)) <-> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X),Xa)),S)))) <-> ti(fun(product_prod(X_a,X_b),bool),R_1) = ti(fun(product_prod(X_a,X_b),bool),S))) # label(fact_60_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 79 (all X_a all X_b all Y_1 -(all A_2 all B ti(product_prod(X_a,X_b),Y_1) != hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B))) # label(fact_61_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 80 (all X_a all X_b all P_1 -(all X all Y_2 ti(product_prod(X_a,X_b),P_1) != hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X),Y_2))) # label(fact_62_PairE) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 81 (all X_a all X_b all Pa ((exists X1 hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,X1))) <-> (exists A_2 exists B hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B)))))) # label(fact_63_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 82 (all X_a all X_b all X_c all X_d all X_e all X_f all X_1 all Pa ((all A_2 all B all C all D all E all F_1 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),bool,Pa,hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),A_2),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),B),hAPP(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),hAPP(X_c,fun(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_Pair(X_c,product_prod(X_d,product_prod(X_e,X_f))),C),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),D),hAPP(X_f,product_prod(X_e,X_f),hAPP(X_e,fun(X_f,product_prod(X_e,X_f)),product_Pair(X_e,X_f),E),F_1)))))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),bool,Pa,X_1)))) # label(fact_64_prod__induct6) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 83 (all X_a all X_b all X_c all X_d all X_e all X_f all Y_1 -(all A_2 all B all C all D all E all F_1 ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),Y_1) != hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),A_2),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),B),hAPP(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),hAPP(X_c,fun(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_Pair(X_c,product_prod(X_d,product_prod(X_e,X_f))),C),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),D),hAPP(X_f,product_prod(X_e,X_f),hAPP(X_e,fun(X_f,product_prod(X_e,X_f)),product_Pair(X_e,X_f),E),F_1))))))) # label(fact_65_prod__cases6) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 84 (all X_a all X_b all X_c all X_d all X_e all Y_1 -(all A_2 all B all C all D all E ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),Y_1) != hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),A_2),hAPP(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,X_e))),B),hAPP(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e)),hAPP(X_c,fun(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e))),product_Pair(X_c,product_prod(X_d,X_e)),C),hAPP(X_e,product_prod(X_d,X_e),hAPP(X_d,fun(X_e,product_prod(X_d,X_e)),product_Pair(X_d,X_e),D),E)))))) # label(fact_66_prod__cases5) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 85 (all X_a all X_b all X_c all X_d all X_e all X_1 all Pa ((all A_2 all B all C all D all E hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,Pa,hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),A_2),hAPP(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,X_e))),B),hAPP(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e)),hAPP(X_c,fun(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e))),product_Pair(X_c,product_prod(X_d,X_e)),C),hAPP(X_e,product_prod(X_d,X_e),hAPP(X_d,fun(X_e,product_prod(X_d,X_e)),product_Pair(X_d,X_e),D),E))))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,Pa,X_1)))) # label(fact_67_prod__induct5) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 86 (all X_a all X_b all X_c all X_d all Y_1 -(all A_2 all B all C all D ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),Y_1) != hAPP(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d)))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,X_d))),A_2),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),B),hAPP(X_d,product_prod(X_c,X_d),hAPP(X_c,fun(X_d,product_prod(X_c,X_d)),product_Pair(X_c,X_d),C),D))))) # label(fact_68_prod__cases4) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.26 87 (all X_a all X_b all X_c all X_d all X_1 all Pa ((all A_2 all B all C all D hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,Pa,hAPP(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d)))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,X_d))),A_2),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),B),hAPP(X_d,product_prod(X_c,X_d),hAPP(X_c,fun(X_d,product_prod(X_c,X_d)),product_Pair(X_c,X_d),C),D)))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,Pa,X_1)))) # label(fact_69_prod__induct4) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 88 (all X_a all X_b all X_c all X_1 all Pa ((all A_2 all B all C hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,Pa,hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),A_2),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),B),C))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,Pa,X_1)))) # label(fact_70_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 89 (all X_a all X_b all X_c all Y_1 -(all A_2 all B all C ti(product_prod(X_a,product_prod(X_b,X_c)),Y_1) != hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),A_2),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),B),C)))) # label(fact_71_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 90 (all X_b all X_c all X_a all Ca all Aa all Ba hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),produc1605651328_split(X_b,X_c,X_a),Ca),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),Ca,Aa),Ba)) # label(fact_72_internal__split__conv) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 91 (all X_a all X_2 hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X_2),nil(X_a)) = 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))) # label(fact_73_insert__Nil) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 92 (all X_a all X_2 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_2),Xs_1))))) # label(fact_74_distinct__insert) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 93 (all X_a all X_b all F all G ((all X hAPP(X_a,X_b,F,X) = hAPP(X_a,X_b,G,X)) -> ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G))) # label(fact_75_ext) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 94 (all X_a all X_1 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) <-> hBOOL(hAPP(X_a,bool,A_1,X_1)))) # label(fact_76_mem__def) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 95 (all X_a all Pa hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa) = ti(fun(X_a,bool),Pa)) # label(fact_77_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 96 (all X_a all Pa all Xs (Xs != nil(X_a) -> ((all X hBOOL(hAPP(list(X_a),bool,Pa,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a))))) -> ((all X all Xs_2 (Xs_2 != nil(X_a) -> (hBOOL(hAPP(list(X_a),bool,Pa,Xs_2)) -> hBOOL(hAPP(list(X_a),bool,Pa,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs_2)))))) -> hBOOL(hAPP(list(X_a),bool,Pa,Xs)))))) # label(fact_78_list__nonempty__induct) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 97 (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_79_list_Orecs_I1_J) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 98 (all X_b all X_a all F1 all F2 all Aa all List hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a)),list_rec(X_a,X_b),F1),F2),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Aa),List)) = hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(X_b,fun(list(X_b),fun(X_a,X_a)),F2,Aa),List),hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a)),list_rec(X_a,X_b),F1),F2),List))) # label(fact_80_list_Orecs_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 99 (all X_b all X_c all X_a all X all Xa all Xb hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),hAPP(fun(product_prod(X_a,X_b),X_c),fun(X_a,fun(X_b,X_c)),product_curry(X_a,X_b,X_c),X),Xa),Xb) = hAPP(product_prod(X_a,X_b),X_c,X,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Xa),Xb))) # label(fact_81_curry__def) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 100 (all X_a all X_b all F all Aa all Ba (hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba)))) # label(fact_82_curryI) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 101 (all X_b all X_a all F all Aa all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba)) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))))) # label(fact_83_curryE) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 102 (all X_b all X_a all F all Aa all Ba (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba)) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))))) # label(fact_84_curryD) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 103 (all X_c all X_a all X_b all F all Aa all Ba hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),hAPP(fun(product_prod(X_b,X_c),X_a),fun(X_b,fun(X_c,X_a)),product_curry(X_b,X_c,X_a),F),Aa),Ba) = hAPP(product_prod(X_b,X_c),X_a,F,hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba))) # label(fact_85_curry__conv) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 104 (all X_a all Xs (Xs = nil(X_a) <-> hBOOL(hAPP(list(X_a),bool,null(X_a),Xs)))) # label(fact_86_eq__Nil__null) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 105 (all X_a all Xs (hBOOL(hAPP(list(X_a),bool,null(X_a),Xs)) <-> Xs = nil(X_a))) # label(fact_87_List_Onull__def) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 106 (all X_a all X_2 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_2),Xs_1)))) # label(fact_88_null__rec_I1_J) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 107 (all X_b hBOOL(hAPP(list(X_b),bool,null(X_b),nil(X_b)))) # label(fact_89_null__rec_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 108 (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_90_equal__Nil__null) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 109 (all X_a all X_1 hBOOL(hAPP(X_a,bool,top_top(fun(X_a,bool)),X_1))) # label(fact_92_top1I) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 110 (all X_a all X_b all A_1 hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),top_top(fun(X_b,bool)))) = top_top(fun(fun(X_a,X_b),bool))) # label(fact_93_Pi__UNIV) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 111 (all X_a all X_1 all Y (hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),equal_equal(list(X_a)),X_1),Y)) <-> X_1 = Y)) # label(fact_94_equal__list__def) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 112 (all X_a all X_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),top_top(fun(X_a,bool))))) # label(fact_95_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 113 (all X_a all X_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),top_top(fun(X_a,bool))))) # label(fact_96_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 114 (all X_a top_top(fun(X_a,bool)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(bool,fun(X_a,bool),combk(bool,X_a),fTrue))) # label(fact_97_UNIV__def) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 115 (all X_b all X_a (top(X_a) -> (all X_1 hAPP(X_b,X_a,top_top(fun(X_b,X_a)),X_1) = top_top(X_a)))) # label(fact_98_top__apply) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 116 (all X_a all A_1 ((all X hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X),A_1))) -> top_top(fun(X_a,bool)) = ti(fun(X_a,bool),A_1))) # label(fact_99_UNIV__eq__I) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 117 (all T_2 all T_1 (top(T_1) -> top(fun(T_2,T_1)))) # label(arity_fun___Orderings_Otop) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 118 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 119 (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].
% 0.95/1.27 120 (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].
% 0.95/1.27 121 (all X_a all P hAPP(X_a,X_a,combi(X_a),P) = ti(X_a,P)) # label(help_COMBI_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 122 (all X_b all X_a all P all Q hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P)) # label(help_COMBK_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 123 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fTrue_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.27 124 -(all I (hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),a),b)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I))) <-> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),a),c)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_888040304_below,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),c),b))))) # label(conj_0) # label(negated_conjecture) # label(non_clause). [assumption].
% 7.74/8.06
% 7.74/8.06 ============================== end of process non-clausal formulas ===
% 7.74/8.06
% 7.74/8.06 ============================== PROCESS INITIAL CLAUSES ===============
% 7.74/8.06
% 7.74/8.06 ============================== PREDICATE ELIMINATION =================
% 7.74/8.06
% 7.74/8.06 ============================== end predicate elimination =============
% 7.74/8.06
% 7.74/8.06 Auto_denials: (non-Horn, no changes).
% 7.74/8.06
% 7.74/8.06 Term ordering decisions:
% 7.74/8.06 Function symbol KB weights: arrow_1212486748le_alt=1. bool=1. arrow_1384031255e_indi=1. arrow_638930832le_Lin=1. arrow_1834574746e_Prof=1. arrow_888040304_below=1. arrow_1726925404_above=1. f=1. b=1. a=1. arrow_612047104le_IIA=1. p=1. arrow_1990387629ctator=1. c=1. arrow_1932713123nimity=1. arrow_844286440_mkbot=1. arrow_992993526_mktop=1. fTrue=1. p_1=1. fFalse=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. fun=1. product_prod=1. ti=1. product_Pair=1. pi=1. combk=1. list_rec=1. in_rel=1. list_case=1. f6=1. f16=1. f17=1. f18=1. f19=1. f20=1. f21=1. f22=1. f23=1. f24=1. f78=1. member=1. list=1. cons=1. nil=1. top_top=1. distinct=1. null=1. splice=1. equal_equal=1. collect=1. combi=1. insert=1. undefined=1. f8=1. f9=1. f10=1. f11=1. f13=1. f14=1. f15=1. combc=1. combb=1. product_curry=1. produc1605651328_split=1. product_prod_rec=1. f1=1. f2=1. f3=1. f31=1. f32=1. f33=1. f34=1. f35=1. f36=1. f37=1. f75=1. f76=1. f77=1. hAPP=1. f12=1. f29=1. f30=1. f71=1. f72=1. f73=1. f74=1. f7=1. f25=1. f26=1. f27=1. f60=1. f61=1. f62=1. f63=1. f68=1. f69=1. f70=1. f4=1. f5=1. f28=1. f50=1. f51=1. f52=1. f53=1. f54=1. f64=1. f65=1. f66=1. f67=1. f44=1. f45=1. f46=1. f47=1. f48=1. f49=1. f55=1. f56=1. f57=1. f58=1. f59=1. f38=1. f39=1. f40=1. f41=1. f42=1. f43=1.
% 7.74/8.06
% 7.74/8.06 ============================== end of process initial clauses ========
% 7.74/8.06
% 7.74/8.06 ============================== CLAUSES FOR SEARCH ====================
% 7.74/8.06
% 7.74/8.06 ============================== end of clauses for search =============
% 7.74/8.06
% 7.74/8.06 ============================== SEARCH ================================
% 7.74/8.06
% 7.74/8.06 % Starting search at 0.28 seconds.
% 7.74/8.06
% 7.74/8.06 Low Water (keep): wt=200.000, iters=3387
% 7.74/8.06
% 7.74/8.06 Low Water (keep): wt=199.000, iters=3363
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% 7.74/8.06 Low Water (keep): wt=197.000, iters=3392
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% 7.74/8.06 Low Water (keep): wt=196.000, iters=3373
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% 7.74/8.06 Low Water (keep): wt=192.000, iters=3341
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% 7.74/8.06 Low Water (keep): wt=164.000, iters=3351
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% 7.74/8.06 Low Water (keep): wt=162.000, iters=3336
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% 7.74/8.06 Low Water (keep): wt=155.000, iters=3409
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% 7.74/8.06 Low Water (keep): wt=150.000, iters=3347
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% 7.74/8.06 Low Water (keep): wt=149.000, iters=3338
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% 7.74/8.06 Low Water (keep): wt=145.000, iters=3380
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% 7.74/8.06 Low Water (keep): wt=140.000, iters=3340
% 7.74/8.06
% 7.74/8.06 Low Water (keep): wt=139.000, iters=3420
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% 7.74/8.06 Low Water (keep): wt=138.000, iters=3395
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% 7.74/8.06 Low Water (keep): wt=134.000, iters=3400
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% 7.74/8.06 Low Water (keep): wt=131.000, iters=3361
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% 7.74/8.06 Low Water (keep): wt=130.000, iters=3345
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% 7.74/8.06 Low Water (keep): wt=128.000, iters=3368
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% 7.74/8.06 Low Water (keep): wt=127.000, iters=3380
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% 7.74/8.06 Low Water (keep): wt=125.000, iters=3368
% 7.74/8.06
% 7.74/8.06 Low Water (keep): wt=124.000, iters=3400
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% 7.74/8.06 Low Water (keep): wt=123.000, iters=3365
% 7.74/8.06
% 7.74/8.06 Low Water (keep): wt=122.000, iters=3338
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% 7.74/8.06 Low Water (keep): wt=120.000, iters=3366
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% 7.74/8.06 Low Water (keep): wt=119.000, iters=3336
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% 7.74/8.06 Low Water (keep): wt=117.000, iters=3393
% 7.74/8.06
% 7.74/8.06 Low Water (keep): wt=113.000, iters=3361
% 7.74/8.06
% 7.74/8.06 Low Water (keep): wt=112.000, iters=3346
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% 7.74/8.06 Low Water (keep): wt=109.000, iters=3425
% 7.74/8.06
% 7.74/8.06 Low Water (keep): wt=108.000, iters=3413
% 7.74/8.06
% 7.74/8.06 Low Water (keep): wt=104.000, iters=3395
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% 7.74/8.06 Low Water (keep): wt=103.000, iters=3365
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% 7.74/8.06 Low Water (keep): wt=101.000, iters=3381
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% 7.74/8.06 Low Water (keep): wt=100.000, iters=3357
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% 7.74/8.06 Low Water (keep): wt=99.000, iters=3360
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% 7.74/8.06 Low Water (keep): wt=91.000, iters=3396
% 7.74/8.06
% 7.74/8.06 Low Water (keep): wt=89.000, iters=3340
% 7.74/8.06
% 7.74/8.06 Low Water (keep): wt=88.000, iters=3359
% 7.74/8.06
% 7.74/8.06 Low Water (keep): wt=85.000, iters=3396
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% 7.74/8.06 Low Water (keep): wt=80.000, iters=3352
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% 7.74/8.06 Low Water (keep): wt=77.000, iters=3379
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% 7.74/8.06 Low Water (keep): wt=75.000, iters=3414
% 7.74/8.06
% 7.74/8.06 Low Water (keep): wt=74.000, iters=3378
% 7.74/8.06
% 7.74/8.06 Low Water (keep): wt=70.000, iters=3341
% 7.74/8.06
% 7.74/8.06 Low Water (keep): wt=68.000, iters=3363
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=66.000, iters=3352
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=65.000, iters=3393
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=64.000, iters=3368
% 201.21/201.52
% 201.21/201.52 Low Water (displace): id=7089, wt=200.000
% 201.21/201.52
% 201.21/201.52 Low Water (displace): id=12564, wt=41.000
% 201.21/201.52
% 201.21/201.52 Low Water (displace): id=12567, wt=37.000
% 201.21/201.52
% 201.21/201.52 Low Water (displace): id=12571, wt=36.000
% 201.21/201.52
% 201.21/201.52 Low Water (displace): id=12577, wt=35.000
% 201.21/201.52
% 201.21/201.52 Low Water (displace): id=12583, wt=32.000
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=63.000, iters=3378
% 201.21/201.52
% 201.21/201.52 Low Water (displace): id=12717, wt=29.000
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=62.000, iters=3348
% 201.21/201.52
% 201.21/201.52 Low Water (displace): id=12843, wt=28.000
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=61.000, iters=3340
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=60.000, iters=3363
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=59.000, iters=3346
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=58.000, iters=3380
% 201.21/201.52
% 201.21/201.52 Low Water (displace): id=14616, wt=27.000
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=57.000, iters=3406
% 201.21/201.52
% 201.21/201.52 Low Water (displace): id=14965, wt=26.000
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=56.000, iters=3356
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=54.000, iters=3337
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=53.000, iters=3358
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=52.000, iters=3444
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=51.000, iters=3380
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=50.000, iters=3412
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=49.000, iters=3370
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=48.000, iters=3465
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=45.000, iters=3341
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=44.000, iters=3346
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=43.000, iters=3336
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=42.000, iters=3335
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=41.000, iters=3362
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=40.000, iters=5942
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=35.000, iters=3677
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=34.000, iters=3335
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=33.000, iters=3335
% 201.21/201.52
% 201.21/201.52 Low Water (keep): wt=32.000, iters=3340
% 201.21/201.52
% 201.21/201.52 ============================== STATISTICS ============================
% 201.21/201.52
% 201.21/201.52 Given=7631. Generated=4152844. Kept=134397. proofs=0.
% 201.21/201.52 Usable=6959. Sos=10000. Demods=189. Limbo=17, Disabled=117664. Hints=0.
% 201.21/201.52 Kept_by_rule=0, Deleted_by_rule=113699.
% 201.21/201.52 Forward_subsumed=766187. Back_subsumed=3872.
% 201.21/201.52 Sos_limit_deleted=3138561. Sos_displaced=112612. Sos_removed=0.
% 201.21/201.52 New_demodulators=328 (0 lex), Back_demodulated=880. Back_unit_deleted=57.
% 201.21/201.52 Demod_attempts=237078750. Demod_rewrites=1464807.
% 201.21/201.52 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
% 201.21/201.52 Nonunit_fsub_feature_tests=1926658. Nonunit_bsub_feature_tests=167348.
% 201.21/201.52 Megabytes=419.43.
% 201.21/201.52 User_CPU=197.90, System_CPU=2.40, Wall_clock=200.
% 201.21/201.52
% 201.21/201.52 Megs malloced by palloc(): 400.
% 201.21/201.52 type (bytes each) gets frees in use bytes
% 201.21/201.52 chunk ( 104) 13670 13670 0 0.0 K
% 201.21/201.52 string_buf ( 8) 11868 11868 0 0.0 K
% 201.21/201.52 token ( 20) 30040 30040 0 0.0 K
% 201.21/201.52 pterm ( 16) 21478 21478 0 0.0 K
% 201.21/201.52 hashtab ( 8) 124 124 0 0.0 K
% 201.21/201.52 hashnode ( 8) 412 412 0 0.0 K
% 201.21/201.52 term ( 20) 426892737 419004021 7888716 154076.5 K
% 201.21/201.52 term arg arrays: 59768.3 K
% 201.21/201.52 attribute ( 12) 1280 22 1258 14.7 K
% 201.21/201.52 ilist ( 8) 828095247 827412221 683026 5336.1 K
% 201.21/201.52 plist ( 8) 15054348 14898761 155587 1215.5 K
% 201.21/201.52 i2list ( 12) 82219342 82219342 0 0.0 K
% 201.21/201.52 just ( 12) 6670541 6477776 192765 2259.0 K
% 201.21/201.52 parajust ( 16) 3760854 3641395 119459 1866.5 K
% 201.21/201.52 instancejust ( 8) 0 0 0 0.0 K
% 201.21/201.52 ivyjust ( 24) 0 0 0 0.0 K
% 201.21/201.52 formula ( 28) 5547 3689 1858 50.8 K
% 201.21/201.52 formula arg arrays: 6.3 K
% 201.21/201.52 topform ( 52) 4153211 4018447 134764 6843.5 K
% 201.21/201.52 clist_pos ( 20) 394643 259814 134829 2633.4 K
% 201.21/201.52 clist ( 16) 8 1 7 0.1 K
% 201.21/201.52 context ( 808) 38445623 38445623 0 0.0 K
% 201.21/201.52 trail ( 12) 58558420 58558420 0 0.0 K
% 201.21/201.52 ac_match_pos (70044) 0 0 0 0.0 K
% 201.21/201.52 ac_match_free_vars_pos (20020)
% 201.21/201.52 0 0 0 0.0 K
% 201.21/201.52 btm_state ( 60) 0 0 0 0.0 K
% 201.21/201.52 btu_state ( 60) 0 0 0 0.0 K
% 201.21/201.52 ac_position (285432) 0 0 0 0.0 K
% 201.21/201.52 fpa_trie ( 20) 6615779 5892792 722987 14120.8 K
% 201.21/201.52 fpa_state ( 28) 34554370 34554370 0 0.0 K
% 201.21/201.52 fpa_index ( 12) 10 0 10 0.1 K
% 201.21/201.52 fpa_chunk ( 20) 8482290 8354880 127410 2488.5 K
% 201.21/201.52 fpa_list ( 16) 5962585 0 5962585 93165.4 K
% 201.21/201.52 fpa_list chunks: 10684.8 K
% 201.21/201.52 discrim ( 12) 9139090 9026229 112861 1322.6 K
% 201.21/201.52 discrim_pos ( 16) 1798817 1798817 0 0.0 K
% 201.21/201.52 flat2 ( 32) 224642637 224642637 0 0.0 K
% 201.21/201.52 flat ( 48) 0 0 0 0.0 K
% 201.21/201.52 flatterm ( 32) 365539137 365539137 0 0.0 K
% 201.21/201.52 mindex ( 28) 13 0 13 0.4 K
% 201.21/201.52 mindex_pos ( 56) 29097313 29097313 0 0.0 K
% 201.21/201.52 lindex ( 12) 5 0 5 0.1 K
% 201.21/201.52 clash ( 40) 0 0 0 0.0 K
% 201.21/201.52 di_tree ( 12) 13022269 8724504 4297765 50364.4 K
% 201.21/201.52 avl_node ( 20) 268343 248343 20000 390.6 K
% 201.21/201.52
% 201.21/201.52 Memory report, 20 @ 20 = 400 megs (400.00 megs used).
% 201.21/201.52 List 1, length 7, 0.0 K
% 201.21/201.52 List 2, length 567, 4.4 K
% 201.21/201.52 List 3, length 6926, 81.2 K
% 201.21/201.52 List 5, length 955, 18.7 K
% 201.21/201.52 List 6, length 49, 1.1 K
% 201.21/201.52 List 7, length 171, 4.7 K
% 201.21/201.52 List 8, length 242, 7.6 K
% 201.21/201.52 List 9, length 31, 1.1 K
% 201.21/201.52 List 10, length 5, 0.2 K
% 201.21/201.52 List 11, length 3, 0.1 K
% 201.21/201.52 List 12, length 4, 0.2 K
% 201.21/201.52 List 13, length 1, 0.1 K
% 201.21/201.52 List 14, length 2, 0.1 K
% 201.21/201.52 List 15, length 2, 0.1 K
% 201.21/201.52 List 16, length 100, 6.2 K
% 201.21/201.52 List 26, length 575, 58.4 K
% 201.21/201.52 List 32, length 193, 24.1 K
% 201.21/201.52 List 64, length 145, 36.2 K
% 201.21/201.52 List 128, length 400, 200.0 K
% 201.21/201.52 List 202, length 4, 3.2 K
% 201.21/201.52 List 256, length 1, 1.0 K
% 201.21/201.52
% 201.21/201.52 ============================== SELECTOR REPORT =======================
% 201.21/201.52 Sos_deleted=3138561, Sos_displaced=112612, Sos_size=10000
% 201.21/201.52 SELECTOR PART PRIORITY ORDER SIZE SELECTED
% 201.21/201.52 I 2147483647 high age 0 289
% 201.21/201.52 H 1 high weight 0 0
% 201.21/201.52 A 1 low age 10000 908
% 201.21/201.52 F 4 low weight 824 2806
% 201.21/201.52 T 4 low weight 9176 3628
% 201.21/201.52 ============================== end of selector report ================
% 201.21/201.52
% 201.21/201.52 ============================== end of statistics =====================
% 201.21/201.52
% 201.21/201.52 Exiting with failure.
% 201.21/201.52
% 201.21/201.52 Process 27109 exit (max_megs) Sat Jul 2 03:51:14 2022
% 201.21/201.52 Prover9 interrupted
%------------------------------------------------------------------------------