TSTP Solution File: SCT171+5 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT171+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 22:04:28 EDT 2022
% Result : Theorem 0.99s 1.41s
% Output : Refutation 0.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT171+5 : TPTP v8.1.0. Released v5.3.0.
% 0.12/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 2 01:31:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.99/1.33 ============================== Prover9 ===============================
% 0.99/1.33 Prover9 (32) version 2009-11A, November 2009.
% 0.99/1.33 Process 9305 was started by sandbox on n008.cluster.edu,
% 0.99/1.33 Sat Jul 2 01:31:09 2022
% 0.99/1.33 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_9152_n008.cluster.edu".
% 0.99/1.33 ============================== end of head ===========================
% 0.99/1.33
% 0.99/1.33 ============================== INPUT =================================
% 0.99/1.33
% 0.99/1.33 % Reading from file /tmp/Prover9_9152_n008.cluster.edu
% 0.99/1.33
% 0.99/1.33 set(prolog_style_variables).
% 0.99/1.33 set(auto2).
% 0.99/1.33 % set(auto2) -> set(auto).
% 0.99/1.33 % set(auto) -> set(auto_inference).
% 0.99/1.33 % set(auto) -> set(auto_setup).
% 0.99/1.33 % set(auto_setup) -> set(predicate_elim).
% 0.99/1.33 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.99/1.33 % set(auto) -> set(auto_limits).
% 0.99/1.33 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.99/1.33 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.99/1.33 % set(auto) -> set(auto_denials).
% 0.99/1.33 % set(auto) -> set(auto_process).
% 0.99/1.33 % set(auto2) -> assign(new_constants, 1).
% 0.99/1.33 % set(auto2) -> assign(fold_denial_max, 3).
% 0.99/1.33 % set(auto2) -> assign(max_weight, "200.000").
% 0.99/1.33 % set(auto2) -> assign(max_hours, 1).
% 0.99/1.33 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.99/1.33 % set(auto2) -> assign(max_seconds, 0).
% 0.99/1.33 % set(auto2) -> assign(max_minutes, 5).
% 0.99/1.33 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.99/1.33 % set(auto2) -> set(sort_initial_sos).
% 0.99/1.33 % set(auto2) -> assign(sos_limit, -1).
% 0.99/1.33 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.99/1.33 % set(auto2) -> assign(max_megs, 400).
% 0.99/1.33 % set(auto2) -> assign(stats, some).
% 0.99/1.33 % set(auto2) -> clear(echo_input).
% 0.99/1.33 % set(auto2) -> set(quiet).
% 0.99/1.33 % set(auto2) -> clear(print_initial_clauses).
% 0.99/1.33 % set(auto2) -> clear(print_given).
% 0.99/1.33 assign(lrs_ticks,-1).
% 0.99/1.33 assign(sos_limit,10000).
% 0.99/1.33 assign(order,kbo).
% 0.99/1.33 set(lex_order_vars).
% 0.99/1.33 clear(print_given).
% 0.99/1.33
% 0.99/1.33 % formulas(sos). % not echoed (169 formulas)
% 0.99/1.33
% 0.99/1.33 ============================== end of input ==========================
% 0.99/1.33
% 0.99/1.33 % From the command line: assign(max_seconds, 300).
% 0.99/1.33
% 0.99/1.33 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.99/1.33
% 0.99/1.33 % Formulas that are not ordinary clauses:
% 0.99/1.33 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].
% 0.99/1.33 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].
% 0.99/1.33 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].
% 0.99/1.33 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].
% 0.99/1.33 5 (all X_a all X_b all X_c ti(fun(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c))),combs(X_a,X_b,X_c)) = combs(X_a,X_b,X_c)) # label(tsy_c_COMBS_res) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.33 6 (all X_a all X_b ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),bool)),inj_on(X_a,X_b)) = inj_on(X_a,X_b)) # label(tsy_c_Fun_Oinj__on_res) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.33 7 (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].
% 0.99/1.33 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].
% 0.99/1.33 9 (all X_a all X_b ti(fun(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a))),hilbert_inv_into(X_a,X_b)) = hilbert_inv_into(X_a,X_b)) # label(tsy_c_Hilbert__Choice_Oinv__into_res) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.33 10 (all X_a ti(fun(bool,fun(X_a,fun(X_a,X_a))),if(X_a)) = if(X_a)) # label(tsy_c_If_res) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.33 11 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,bool)),ord_less(X_a)) = ord_less(X_a))) # label(tsy_c_Orderings_Oord__class_Oless_res) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.33 12 (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].
% 0.99/1.33 13 (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].
% 0.99/1.33 14 (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].
% 0.99/1.33 15 (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].
% 0.99/1.33 16 (all X_a ti(fun(X_a,fun(X_a,bool)),fequal(X_a)) = fequal(X_a)) # label(tsy_c_fequal_res) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.33 17 (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].
% 0.99/1.33 18 (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].
% 0.99/1.33 19 (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].
% 0.99/1.33 20 (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].
% 0.99/1.33 21 (all X_a ti(fun(X_a,fun(fun(X_a,bool),bool)),member(X_a)) = member(X_a)) # label(tsy_c_member_res) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.33 22 (all X_2 all Y_1 all L all Z_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),X_2),Y_1)),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),Z_1))) <-> ti(arrow_1212486748le_alt,Y_1) != ti(arrow_1212486748le_alt,Z_1) & (ti(arrow_1212486748le_alt,X_2) = ti(arrow_1212486748le_alt,Z_1) -> ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Y_1)) & (ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Z_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),X_2),Y_1)),L))))) # label(fact_4_in__mkbot) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.33 23 (all X_2 all Y_1 all L all Z_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),X_2),Y_1)),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),Z_1))) <-> ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Z_1) & (ti(arrow_1212486748le_alt,Y_1) = ti(arrow_1212486748le_alt,Z_1) -> ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Y_1)) & (ti(arrow_1212486748le_alt,Y_1) != ti(arrow_1212486748le_alt,Z_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),X_2),Y_1)),L))))) # label(fact_5_in__mktop) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.33 24 (all P_1 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_1),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_1,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_1)))))))))))) # label(fact_6__C2_C) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.33 25 (all P_1 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_1),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_1,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_1)))))))))))) # label(fact_7__C1_C) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.34 26 (all P_1 all Pa all Ca all Aa all Ba (ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,Ba) -> (ti(arrow_1212486748le_alt,Ba) != ti(arrow_1212486748le_alt,Ca) -> (ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,Ca) -> (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_1),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),Ba),Ca)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),P_1,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),Ba),Ca)),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_1))))))))))) # label(fact_8__C4_C) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.34 27 (all P_1 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) -> (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_1),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_1,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_1)))))))))) # label(fact_9_pairwise__neutrality) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.34 28 (all P_1 all Pa all Aa all Ba (ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,Ba) -> (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_1),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),Ba),Aa)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),P_1,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),Ba),Aa)),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_1))))))))) # label(fact_10__C3_C) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.34 29 (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),c),d)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I))) <-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n)) -> 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),c),d)),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,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),e)))) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n)) -> (hAPP(arrow_1384031255e_indi,nat,h,I) = n -> 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),c),d)),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,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),c),e)))) & (hAPP(arrow_1384031255e_indi,nat,h,I) != n -> 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),c),d)),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,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),e))))))) # label(fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.34 30 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),c),d)),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))) <-> 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),c),d)),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,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(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_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(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)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(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_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(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_1384031255e_indi),arrow_844286440_mkbot),p)),e)))))) # label(fact_14_PW) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.34 31 (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_1 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_1)))))) # label(fact_15_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.34 32 (all X_b all X_a all A_3 all B_2 all A_5 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_3),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_5),B_4) -> -(ti(X_a,A_3) = ti(X_a,A_5) -> ti(X_b,B_2) != ti(X_b,B_4)))) # label(fact_21_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.34 33 (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_22_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.34 34 (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_1 (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_1),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_1 ((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_1)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X_1,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_1)),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_1)),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_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_1)),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_23_IIA__def) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.34 35 (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_1 (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_1),arrow_1834574746e_Prof)) -> (all A_2 all B_1 ((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_1)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X_1,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_1)),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_1))))))))) # label(fact_24_unanimity__def) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 36 (all X_a all X_2 hBOOL(hAPP(X_a,bool,top_top(fun(X_a,bool)),X_2))) # label(fact_25_top1I) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 37 (all X_a all X_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),top_top(fun(X_a,bool))))) # label(fact_26_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 38 (all X_a all X_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),top_top(fun(X_a,bool))))) # label(fact_27_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 39 (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_28_prod_Orecs) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 40 (all X_b all X_a (top(X_a) -> (all X_2 hAPP(X_b,X_a,top_top(fun(X_b,X_a)),X_2) = top_top(X_a)))) # label(fact_29_top__apply) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 41 (all X_a (top(X_a) -> (all A_3 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),top_top(X_a)),A_3))))) # label(fact_30_not__top__less) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 42 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (ti(X_a,X) != ti(X_a,Y) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_31_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 43 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_32_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 44 (all X_a (order(X_a) -> (all Z all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X))))))) # label(fact_33_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 45 (all X_a (preorder(X_a) -> (all Z all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z))))))) # label(fact_34_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 46 (all X_a (order(X_a) -> (all C all B_2 all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)) -> (B_2 = C -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_3))))))) # label(fact_35_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 47 (all X_a (ord(X_a) -> (all C all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)) -> (B_2 = C -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),C))))))) # label(fact_36_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 48 (all X_a (order(X_a) -> (all C all A_3 all B_2 (A_3 = B_2 -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_3))))))) # label(fact_37_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 49 (all X_a (ord(X_a) -> (all C all A_3 all B_2 (A_3 = B_2 -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),C))))))) # label(fact_38_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 50 (all X_a (order(X_a) -> (all B_2 all A_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)))))) # label(fact_39_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 51 (all X_a (preorder(X_a) -> (all A_3 all B_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_3),B_2)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_2),A_3)))))) # label(fact_40_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 52 (all X_a (preorder(X_a) -> (all Pa all X_2 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2)) -> hBOOL(Pa)))))) # label(fact_41_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 53 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> Y != X)))) # label(fact_42_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 54 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> X != Y)))) # label(fact_43_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 55 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_44_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 56 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_45_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 57 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> X != Y)))) # label(fact_46_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 58 (all X_a (linorder(X_a) -> (all X all Y (ti(X_a,X) != ti(X_a,Y) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_47_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 59 (all X_a (linorder(X_a) -> (all Y_1 all X_2 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1)) <-> ti(X_a,X_2) = ti(X_a,Y_1)))))) # label(fact_48_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 60 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) | ti(X_a,X) = ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_49_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 61 (all X_a (linorder(X_a) -> (all X_2 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2)) | ti(X_a,X_2) = ti(X_a,Y_1))))) # label(fact_50_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 62 (all X_a (linorder(X_a) -> (all X_2 all Y_1 (ti(X_a,X_2) != ti(X_a,Y_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_2)))))) # label(fact_51_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 63 (all X_a (preorder(X_a) -> (all X -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),X))))) # label(fact_52_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 64 (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_53_UNIV__def) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 65 (all X_a all X_b all S all R_1 ((all X_1 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_1),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_1),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_54_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 66 (all X_a (top(X_a) -> (all Aa (ti(X_a,Aa) != top_top(X_a) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Aa),top_top(X_a))))))) # label(fact_55_less__top) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 67 (all X_a all X_b all X_2 all Y_1 all F (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) -> (hAPP(X_a,X_b,F,X_2) = ti(X_b,Y_1) -> hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F),Y_1) = ti(X_a,X_2)))) # label(fact_56_inv__f__eq) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 68 (all X_a all X_b all X_2 all F (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) -> hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F),hAPP(X_a,X_b,F,X_2)) = ti(X_a,X_2))) # label(fact_57_inv__f__f) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 69 (all X_c all X_a all X_b all F (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,fun(X_c,X_b)),fun(fun(X_a,bool),bool),inj_on(X_a,fun(X_c,X_b)),hAPP(fun(X_a,X_b),fun(X_a,fun(X_c,X_b)),hAPP(fun(X_b,fun(X_c,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_c,X_b))),combb(X_b,fun(X_c,X_b),X_a),combk(X_b,X_c)),F)),top_top(fun(X_a,bool)))))) # label(fact_58_inj__fun) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 70 (all X_a all X_b all X_2 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),A_1),F),hAPP(X_a,X_b,F,X_2)) = ti(X_a,X_2)))) # label(fact_59_inv__into__f__f) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 71 (all X_a all X_b all Y_1 all X_2 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (hAPP(X_a,X_b,F,X_2) = ti(X_b,Y_1) -> hAPP(X_b,X_a,hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),A_1),F),Y_1) = ti(X_a,X_2))))) # label(fact_60_inv__into__f__eq) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 72 (all X_a all X_b all X_2 all Y_1 all F (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) -> (hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_1) <-> ti(X_a,X_2) = ti(X_a,Y_1)))) # label(fact_61_inj__eq) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 73 (all X_a all X_b all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) <-> (all 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)) -> (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_1)) -> (hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,F,Xa) -> ti(X_a,X_1) = ti(X_a,Xa)))))))) # label(fact_62_inj__on__def) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 74 (all X_a all X_b all X_2 all Y_1 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> (ti(X_a,X_2) != ti(X_a,Y_1) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_1)) -> hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,Y_1)))))) # label(fact_63_inj__on__contraD) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 75 (all X_a all X_b all Y_1 all X_2 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_1)) -> (hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_1) <-> ti(X_a,X_2) = ti(X_a,Y_1)))))) # label(fact_64_inj__on__iff) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 76 (all X_a all X_b all X_2 all Y_1 all F all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),A_1)) -> (hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_1) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Y_1),A_1)) -> ti(X_a,X_2) = ti(X_a,Y_1)))))) # label(fact_65_inj__onD) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 77 (all X_a all A_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_a),fun(fun(X_a,bool),bool),inj_on(X_a,X_a),combi(X_a)),A_1))) # label(fact_66_inj__on__id2) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 78 (all X_a all X_b all X_2 all Y_1 all F (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) -> (hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,F,Y_1) -> ti(X_a,X_2) = ti(X_a,Y_1)))) # label(fact_67_injD) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 79 (all X_a all X_b all G all F (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))) -> ((all X_1 hAPP(X_a,X_b,F,hAPP(X_b,X_a,G,X_1)) = ti(X_b,X_1)) -> hAPP(fun(X_a,X_b),fun(X_b,X_a),hAPP(fun(X_a,bool),fun(fun(X_a,X_b),fun(X_b,X_a)),hilbert_inv_into(X_a,X_b),top_top(fun(X_a,bool))),F) = ti(fun(X_b,X_a),G)))) # label(fact_68_inj__imp__inv__eq) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 80 (all X_a all X_b all F ((all X_1 all Y_2 (hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,F,Y_2) -> ti(X_a,X_1) = ti(X_a,Y_2))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),inj_on(X_a,X_b),F),top_top(fun(X_a,bool)))))) # label(fact_69_injI) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 81 (all Aa all Ba all 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)) -> (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)) -> -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))))) # label(fact_73_Lin__irrefl) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 82 (all X_2 all Y_1 all 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)) -> (ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Y_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),X_2),Y_1)),L)) <-> 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_1),X_2)),L)))))) # label(fact_74_notin__Lin__iff) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 83 (all X_a all X_b all F all G ((all X_1 hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,G,X_1)) -> ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G))) # label(fact_75_ext) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 84 (all X_a all X_2 all A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) <-> hBOOL(hAPP(X_a,bool,A_1,X_2)))) # label(fact_76_mem__def) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 85 (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].
% 0.99/1.35 86 (all X_2 all 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)) -> 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),X_2)),arrow_638930832le_Lin)))) # label(fact_78_mktop__Lin) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 87 (all X_2 all 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)) -> 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),X_2)),arrow_638930832le_Lin)))) # label(fact_79_mkbot__Lin) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 88 (all L all X_2 all Y_1 (ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Y_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),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),X_2),Y_1)),arrow_638930832le_Lin))))) # label(fact_80_above__Lin) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 89 (all 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)) -> 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)),arrow_1834574746e_Prof)))) # label(fact_81_const__Lin__Prof) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 90 (all X_2 all Y_1 all L 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),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_2),Y_1)),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),Aa),Ba))) <-> ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Y_1) & (ti(arrow_1212486748le_alt,X_2) = 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_1)),L))) & (ti(arrow_1212486748le_alt,X_2) != ti(arrow_1212486748le_alt,Ba) -> (ti(arrow_1212486748le_alt,Y_1) = ti(arrow_1212486748le_alt,Ba) -> ti(arrow_1212486748le_alt,X_2) = 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_2),Aa)),L))) & (ti(arrow_1212486748le_alt,Y_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),X_2),Y_1)),L)))))))) # label(fact_82_in__above) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 91 (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_1 (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_1),arrow_1834574746e_Prof)) -> (all A_2 all B_1 (ti(arrow_1212486748le_alt,A_2) != ti(arrow_1212486748le_alt,B_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_1)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X_1,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_1)),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_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))))) # label(fact_83_dictatorI) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 92 (all X_a all X_b all X_2 all F all A_1 all B (hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))) -> (-hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,fun(X_b,bool),B,X_2))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))))) # label(fact_84_PiE) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 93 (all Aa all Ba (ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,Ba) -> (exists X_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)),X_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)),X_1)))))) # label(fact_85_complete__Lin) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 94 (all Na 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)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),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(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),Na))),lab)),lba)),arrow_1834574746e_Prof))) # label(fact_86_PiProf) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 95 (all X_a all X_b all X_2 all F all A_1 all B (hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,fun(X_b,bool),B,X_2)))))) # label(fact_87_Pi__mem) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 96 (all X_a all X_b all X_2 all F all A_1 all B (hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B)))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),B))))) # label(fact_89_funcset__mem) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.35 97 (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_90_funcset__id) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.36 98 (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_1 (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_1),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_1) = hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X_1,I_1))))) # label(fact_91_dictator__def) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.36 99 (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_92_Pi__UNIV) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.36 100 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),e),d)),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,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(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_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(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)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(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_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(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_1384031255e_indi),arrow_844286440_mkbot),p)),e)))))) <-> 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(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,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)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),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(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),lab)),lba)))) # label(fact_93__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.36 101 (all I ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n)) -> 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),e),d)),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,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),e)))) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n)) -> (hAPP(arrow_1384031255e_indi,nat,h,I) = n -> 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),e),d)),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,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),c),e)))) & (hAPP(arrow_1384031255e_indi,nat,h,I) != n -> 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),e),d)),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,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),e))))) <-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n)) -> 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)),lab))) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_1384031255e_indi,nat,h,I)),n)) -> 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)),lba))))) # label(fact_94__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.36 102 (all T_2 all T_1 (preorder(T_1) -> preorder(fun(T_2,T_1)))) # label(arity_fun___Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.36 103 (all T_2 all T_1 (order(T_1) -> order(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oorder) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.36 104 (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].
% 0.99/1.36 105 (all T_2 all T_1 (ord(T_1) -> ord(fun(T_2,T_1)))) # label(arity_fun___Orderings_Oord) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.36 106 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.36 107 (all X_a all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fTrue),X),Y) = ti(X_a,X)) # label(help_If_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.36 108 (all X_a all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),fFalse),X),Y) = ti(X_a,Y)) # label(help_If_2_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.36 109 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_If_3_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.36 110 (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].
% 0.99/1.36 111 (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].
% 0.99/1.36 112 (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].
% 0.99/1.36 113 (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].
% 0.99/1.36 114 (all X_a all X_c all X_b all P all Q all R hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c)),combs(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),hAPP(X_a,X_b,Q,R))) # label(help_COMBS_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.36 115 (all P (ti(bool,P) = fTrue | ti(bool,P) = fFalse)) # label(help_fTrue_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.36 116 (all X_a all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)) | ti(X_a,X) = ti(X_a,Y))) # label(help_fequal_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.36 117 (all X_a all X all Y (ti(X_a,X) != ti(X_a,Y) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)))) # label(help_fequal_2_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.36
% 0.99/1.36 ============================== end of process non-clausal formulas ===
% 0.99/1.36
% 0.99/1.36 ============================== PROCESS INITIAL CLAUSES ===============
% 0.99/1.36
% 0.99/1.36 ============================== PREDICATE ELIMINATION =================
% 0.99/1.36 118 linorder(nat) # label(arity_Nat_Onat___Orderings_Olinorder) # label(axiom). [assumption].
% 0.99/1.36 119 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_31_linorder__cases) # label(axiom). [clausify(42)].
% 0.99/1.36 120 -linorder(A) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_47_linorder__neqE) # label(axiom). [clausify(58)].
% 0.99/1.36 121 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | ti(A,B) = ti(A,C) # label(fact_48_linorder__antisym__conv3) # label(axiom). [clausify(59)].
% 0.99/1.36 122 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | ti(A,B) != ti(A,C) # label(fact_48_linorder__antisym__conv3) # label(axiom). [clausify(59)].
% 0.99/1.36 123 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_49_linorder__less__linear) # label(axiom). [clausify(60)].
% 0.99/1.36 124 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | ti(A,C) = ti(A,B) # label(fact_50_not__less__iff__gr__or__eq) # label(axiom). [clausify(61)].
% 0.99/1.36 125 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_50_not__less__iff__gr__or__eq) # label(axiom). [clausify(61)].
% 0.99/1.36 126 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_50_not__less__iff__gr__or__eq) # label(axiom). [clausify(61)].
% 0.99/1.36 127 -linorder(A) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_51_linorder__neq__iff) # label(axiom). [clausify(62)].
% 0.99/1.36 128 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_51_linorder__neq__iff) # label(axiom). [clausify(62)].
% 0.99/1.36 129 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_51_linorder__neq__iff) # label(axiom). [clausify(62)].
% 0.99/1.41 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) = ti(nat,A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). [resolve(118,a,119,a)].
% 0.99/1.41 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)) | ti(nat,A) != ti(nat,B). [resolve(118,a,122,a)].
% 0.99/1.41 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). [resolve(118,a,125,a)].
% 0.99/1.41 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) != ti(nat,A). [resolve(118,a,126,a)].
% 0.99/1.41 Derived: ti(nat,A) != ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(118,a,129,a)].
% 0.99/1.41
% 0.99/1.41 ============================== end predicate elimination =============
% 0.99/1.41
% 0.99/1.41 Auto_denials: (non-Horn, no changes).
% 0.99/1.41
% 0.99/1.41 Term ordering decisions:
% 0.99/1.41 Function symbol KB weights: arrow_1212486748le_alt=1. bool=1. arrow_1384031255e_indi=1. nat=1. arrow_1834574746e_Prof=1. p=1. e=1. f=1. c=1. h=1. n=1. d=1. arrow_638930832le_Lin=1. arrow_1726925404_above=1. arrow_844286440_mkbot=1. arrow_992993526_mktop=1. a=1. arrow_612047104le_IIA=1. b=1. lba=1. arrow_1990387629ctator=1. lab=1. arrow_1932713123nimity=1. fTrue=1. fFalse=1. fun=1. product_prod=1. ti=1. product_Pair=1. inj_on=1. combk=1. pi=1. hilbert_inv_into=1. f26=1. f27=1. f28=1. f29=1. f30=1. member=1. ord_less=1. top_top=1. if=1. fequal=1. combi=1. collect=1. finite_card=1. undefined=1. f10=1. f11=1. f12=1. f13=1. f15=1. f16=1. f17=1. combb=1. combc=1. combs=1. product_prod_rec=1. f6=1. f7=1. f8=1. f23=1. f24=1. hAPP=1. f5=1. f14=1. f18=1. f19=1. f20=1. f21=1. f22=1. f25=1. f3=1. f9=1. f1=1. f2=1. f4=1.
% 0.99/1.41
% 0.99/1.41 ============================== PROOF =================================
% 0.99/1.41 % SZS status Theorem
% 0.99/1.41 % SZS output start Refutation
% 0.99/1.41
% 0.99/1.41 % Proof 1 at 0.19 (+ 0.00) seconds.
% 0.99/1.41 % Length of proof is 6.
% 0.99/1.41 % Level of proof is 3.
% 0.99/1.41 % Maximum clause weight is 974.000.
% 0.99/1.41 % Given clauses 0.
% 0.99/1.41
% 0.99/1.41 30 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),c),d)),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))) <-> 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),c),d)),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,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(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_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(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)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(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_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(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_1384031255e_indi),arrow_844286440_mkbot),p)),e)))))) # label(fact_14_PW) # label(axiom) # label(non_clause). [assumption].
% 0.99/1.41 238 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),c),d)),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,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(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_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(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)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(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_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(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_1384031255e_indi),arrow_844286440_mkbot),p)),e)))))) # label(fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) # label(axiom). [assumption].
% 0.99/1.42 239 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),c),d)),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))) | -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),c),d)),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,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),ord_less(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(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_1384031255e_indi),arrow_992993526_mktop),p)),e))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combs(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),if(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(nat,fun(arrow_1384031255e_indi,bool),hAPP(fun(arrow_1384031255e_indi,fun(nat,bool)),fun(nat,fun(arrow_1384031255e_indi,bool)),combc(arrow_1384031255e_indi,nat,bool),hAPP(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_1384031255e_indi,nat),fun(arrow_1384031255e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_1384031255e_indi),fequal(nat)),h)),n))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(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)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(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_1384031255e_indi),arrow_1726925404_above),p)),c)),e))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combb(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_1384031255e_indi),arrow_844286440_mkbot),p)),e)))))) # label(fact_14_PW) # label(axiom). [clausify(30)].
% 0.99/1.42 240 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),c),d)),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))). [copy(239),unit_del(b,238)].
% 0.99/1.42 395 -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),c),d)),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))) # label(conj_0) # label(negated_conjecture). [assumption].
% 0.99/1.42 396 $F. [copy(395),unit_del(a,240)].
% 0.99/1.42
% 0.99/1.42 % SZS output end Refutation
% 0.99/1.42 ============================== end of proof ==========================
% 0.99/1.42
% 0.99/1.42 ============================== STATISTICS ============================
% 0.99/1.42
% 0.99/1.42 Given=0. Generated=252. Kept=234. proofs=1.
% 0.99/1.42 Usable=0. Sos=0. Demods=52. Limbo=234, Disabled=264. Hints=0.
% 0.99/1.42 Megabytes=2.93.
% 0.99/1.42 User_CPU=0.20, System_CPU=0.00, Wall_clock=0.
% 0.99/1.42
% 0.99/1.42 ============================== end of statistics =====================
% 0.99/1.42
% 0.99/1.42 ============================== end of search =========================
% 0.99/1.42
% 0.99/1.42 THEOREM PROVED
% 0.99/1.42 % SZS status Theorem
% 0.99/1.42
% 0.99/1.42 Exiting with 1 proof.
% 0.99/1.42
% 0.99/1.42 Process 9305 exit (max_proofs) Sat Jul 2 01:31:09 2022
% 0.99/1.42 Prover9 interrupted
%------------------------------------------------------------------------------