%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWW474+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 09:08:04 AM UTC 2026
% Result : Theorem 150.44s 155.71s
% Output : Proof 152.09s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(tsy_c_COMBB_res,axiom,
! [X_b,X_c,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),
file('theBenchmark.p',tsy_c_COMBB_res) ).
fof(tsy_c_COMBC_res,axiom,
! [X_a,X_b,X_c] : ti(fun(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c))),combc(X_a,X_b,X_c)) = combc(X_a,X_b,X_c),
file('theBenchmark.p',tsy_c_COMBC_res) ).
fof(tsy_c_COMBI_res,axiom,
! [X_a] : ti(fun(X_a,X_a),combi(X_a)) = combi(X_a),
file('theBenchmark.p',tsy_c_COMBI_res) ).
fof(tsy_c_COMBK_res,axiom,
! [X_a,X_b] : ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b)) = combk(X_a,X_b),
file('theBenchmark.p',tsy_c_COMBK_res) ).
fof(tsy_c_COMBS_res,axiom,
! [X_a,X_b,X_c] : ti(fun(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c))),combs(X_a,X_b,X_c)) = combs(X_a,X_b,X_c),
file('theBenchmark.p',tsy_c_COMBS_res) ).
fof(tsy_c_Com_OWT_res,axiom,
ti(fun(com,bool),wt) = wt,
file('theBenchmark.p',tsy_c_Com_OWT_res) ).
fof(tsy_c_Com_OWT__bodies_res,hypothesis,
ti(bool,wT_bodies) = wT_bodies,
file('theBenchmark.p',tsy_c_Com_OWT__bodies_res) ).
fof(tsy_c_Com_Obody_res,hypothesis,
ti(fun(pname,option(com)),body) = body,
file('theBenchmark.p',tsy_c_Com_Obody_res) ).
fof(tsy_c_Com_Ocom_OBODY_res,hypothesis,
ti(fun(pname,com),body_1) = body_1,
file('theBenchmark.p',tsy_c_Com_Ocom_OBODY_res) ).
fof(tsy_c_Finite__Set_Ofinite_res,axiom,
! [X_a] : ti(fun(fun(X_a,bool),bool),finite_finite(X_a)) = finite_finite(X_a),
file('theBenchmark.p',tsy_c_Finite__Set_Ofinite_res) ).
fof(tsy_c_HOL_Oundefined_res,axiom,
! [X_a] : ti(X_a,undefined(X_a)) = undefined(X_a),
file('theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
fof(tsy_c_Hoare__Mirabelle__pjuwniqynr_OMGT_res,hypothesis,
ti(fun(com,hoare_509422987triple(state)),hoare_Mirabelle_MGT) = hoare_Mirabelle_MGT,
file('theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_OMGT_res) ).
fof(tsy_c_Hoare__Mirabelle__pjuwniqynr_Ohoare__derivs_res,axiom,
! [X_a] : ti(fun(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool)),hoare_122391849derivs(X_a)) = hoare_122391849derivs(X_a),
file('theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_Ohoare__derivs_res) ).
fof(tsy_c_Hoare__Mirabelle__pjuwniqynr_Ostate__not__singleton_res,hypothesis,
ti(bool,hoare_1883395792gleton) = hoare_1883395792gleton,
file('theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_Ostate__not__singleton_res) ).
fof(tsy_c_Map_Odom_res,axiom,
! [X_b,X_a] : ti(fun(fun(X_b,option(X_a)),fun(X_b,bool)),dom(X_b,X_a)) = dom(X_b,X_a),
file('theBenchmark.p',tsy_c_Map_Odom_res) ).
fof(tsy_c_Option_Ooption_OSome_res,axiom,
! [X_a] : ti(fun(X_a,option(X_a)),some(X_a)) = some(X_a),
file('theBenchmark.p',tsy_c_Option_Ooption_OSome_res) ).
fof(tsy_c_Option_Othe_res,hypothesis,
ti(fun(option(com),com),the(com)) = the(com),
file('theBenchmark.p',tsy_c_Option_Othe_res) ).
fof(tsy_c_Orderings_Obot__class_Obot_res,axiom,
! [X_a] : ti(fun(X_a,bool),bot_bot(fun(X_a,bool))) = bot_bot(fun(X_a,bool)),
file('theBenchmark.p',tsy_c_Orderings_Obot__class_Obot_res) ).
fof(tsy_c_Orderings_Oord__class_Oless__eq_res,axiom,
! [X_a] : ti(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),ord_less_eq(fun(X_a,bool))) = ord_less_eq(fun(X_a,bool)),
file('theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_res) ).
fof(tsy_c_Set_OCollect_res,axiom,
! [X_a] : ti(fun(fun(X_a,bool),fun(X_a,bool)),collect(X_a)) = collect(X_a),
file('theBenchmark.p',tsy_c_Set_OCollect_res) ).
fof(tsy_c_Set_Oimage_res,axiom,
! [X_a,X_b] : ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool))),image(X_a,X_b)) = image(X_a,X_b),
file('theBenchmark.p',tsy_c_Set_Oimage_res) ).
fof(tsy_c_Set_Oinsert_res,axiom,
! [X_a] : ti(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),insert(X_a)) = insert(X_a),
file('theBenchmark.p',tsy_c_Set_Oinsert_res) ).
fof(tsy_c_fFalse_res,axiom,
ti(bool,fFalse) = fFalse,
file('theBenchmark.p',tsy_c_fFalse_res) ).
fof(tsy_c_fNot_res,axiom,
ti(fun(bool,bool),fNot) = fNot,
file('theBenchmark.p',tsy_c_fNot_res) ).
fof(tsy_c_fTrue_res,axiom,
ti(bool,fTrue) = fTrue,
file('theBenchmark.p',tsy_c_fTrue_res) ).
fof(tsy_c_fconj_res,axiom,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
file('theBenchmark.p',tsy_c_fconj_res) ).
fof(tsy_c_fdisj_res,axiom,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
file('theBenchmark.p',tsy_c_fdisj_res) ).
fof(tsy_c_fequal_res,axiom,
! [X_a] : ti(fun(X_a,fun(X_a,bool)),fequal(X_a)) = fequal(X_a),
file('theBenchmark.p',tsy_c_fequal_res) ).
fof(tsy_c_fimplies_res,axiom,
ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
file('theBenchmark.p',tsy_c_fimplies_res) ).
fof(tsy_c_hAPP_arg1,axiom,
! [X_a,X_c,B_1_1,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),
file('theBenchmark.p',tsy_c_hAPP_arg1) ).
fof(tsy_c_hAPP_arg2,axiom,
! [X_a,X_c,B_1_1,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),
file('theBenchmark.p',tsy_c_hAPP_arg2) ).
fof(tsy_c_hAPP_res,axiom,
! [X_c,X_a,B_1_1,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),
file('theBenchmark.p',tsy_c_hAPP_res) ).
fof(tsy_c_hBOOL_arg1,hypothesis,
! [B_1_1] :
( hBOOL(ti(bool,B_1_1))
<=> hBOOL(B_1_1) ),
file('theBenchmark.p',tsy_c_hBOOL_arg1) ).
fof(tsy_c_member_res,axiom,
! [X_a] : ti(fun(X_a,fun(fun(X_a,bool),bool)),member(X_a)) = member(X_a),
file('theBenchmark.p',tsy_c_member_res) ).
fof(tsy_v_Fa_res,hypothesis,
ti(fun(hoare_509422987triple(state),bool),fa) = fa,
file('theBenchmark.p',tsy_v_Fa_res) ).
fof(tsy_v_pn_res,hypothesis,
ti(pname,pn) = pn,
file('theBenchmark.p',tsy_v_pn_res) ).
fof(tsy_v_y_res,hypothesis,
ti(com,y) = y,
file('theBenchmark.p',tsy_v_y_res) ).
fof(fact_0_empty,axiom,
! [X_a,G] : hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),bot_bot(fun(hoare_509422987triple(X_a),bool)))),
file('theBenchmark.p',fact_0_empty) ).
fof(fact_1_asm,axiom,
! [X_a,Ts,G] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),ord_less_eq(fun(hoare_509422987triple(X_a),bool)),Ts),G))
=> hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),Ts)) ),
file('theBenchmark.p',fact_1_asm) ).
fof(fact_2_weaken,axiom,
! [X_a,Ts,G,Ts_1] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),Ts_1))
=> ( hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),ord_less_eq(fun(hoare_509422987triple(X_a),bool)),Ts),Ts_1))
=> hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),Ts)) ) ),
file('theBenchmark.p',fact_2_weaken) ).
fof(fact_3_thin,axiom,
! [X_a,G,G_2,Ts] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_2),Ts))
=> ( hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),ord_less_eq(fun(hoare_509422987triple(X_a),bool)),G_2),G))
=> hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),Ts)) ) ),
file('theBenchmark.p',fact_3_thin) ).
fof(fact_4_cut,axiom,
! [X_a,G,G_2,Ts] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_2),Ts))
=> ( hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),G_2))
=> hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),Ts)) ) ),
file('theBenchmark.p',fact_4_cut) ).
fof(fact_5_hoare__derivs_Oinsert,axiom,
! [X_a,Ts,G,T_3] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),T_3),bot_bot(fun(hoare_509422987triple(X_a),bool)))))
=> ( hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),Ts))
=> hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),T_3),Ts))) ) ),
file('theBenchmark.p',fact_5_hoare__derivs_Oinsert) ).
fof(fact_6_derivs__insertD,axiom,
! [X_a,G,T_3,Ts] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),T_3),Ts)))
=> ( hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),Ts))
& hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),T_3),bot_bot(fun(hoare_509422987triple(X_a),bool))))) ) ),
file('theBenchmark.p',fact_6_derivs__insertD) ).
fof(fact_7_MGT__BodyN,axiom,
! [Pn_1,G] :
( hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,Pn_1))),G)),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,hAPP(option(com),com,the(com),hAPP(pname,option(com),body,Pn_1)))),bot_bot(fun(hoare_509422987triple(state),bool)))))
=> hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),G),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,Pn_1))),bot_bot(fun(hoare_509422987triple(state),bool))))) ),
file('theBenchmark.p',fact_7_MGT__BodyN) ).
fof(fact_8_finite__Collect__subsets,axiom,
! [X_a,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1))
=> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),collect(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),combc(fun(X_a,bool),fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool))),A_1)))) ),
file('theBenchmark.p',fact_8_finite__Collect__subsets) ).
fof(fact_9_finite__imageI,axiom,
! [X_b,X_a,H,Fa] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),Fa))
=> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),H),Fa))) ),
file('theBenchmark.p',fact_9_finite__imageI) ).
fof(fact_10_empty__subsetI,axiom,
! [X_a,A_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),bot_bot(fun(X_a,bool))),A_1)),
file('theBenchmark.p',fact_10_empty__subsetI) ).
fof(fact_11_finite_OinsertI,axiom,
! [X_a,A_3,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1))
=> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),A_1))) ),
file('theBenchmark.p',fact_11_finite_OinsertI) ).
fof(fact_12_finite_OemptyI,axiom,
! [X_a] : hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),bot_bot(fun(X_a,bool)))),
file('theBenchmark.p',fact_12_finite_OemptyI) ).
fof(fact_13_finite__Collect__conjI,axiom,
! [X_a,Q_1,P_1] :
( ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1)))
| hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) )
=> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),P_1)),Q_1)))) ),
file('theBenchmark.p',fact_13_finite__Collect__conjI) ).
fof(fact_14_image__constant__conv,axiom,
! [X_b,X_a,C_1,A_1] :
( ( ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool))
=> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),C_1)),A_1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),C_1),bot_bot(fun(X_b,bool))) )
& ( ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool))
=> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),C_1)),A_1) = bot_bot(fun(X_b,bool)) ) ),
file('theBenchmark.p',fact_14_image__constant__conv) ).
fof(fact_15_image__constant,axiom,
! [X_b,X_a,C_1,X_2,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),C_1)),A_1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),C_1),bot_bot(fun(X_b,bool))) ),
file('theBenchmark.p',fact_15_image__constant) ).
fof(fact_16_insert__dom,axiom,
! [X_b,X_a,F,X_2,Y_3] :
( hAPP(X_b,option(X_a),F,X_2) = hAPP(X_a,option(X_a),some(X_a),Y_3)
=> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,option(X_a)),fun(X_b,bool),dom(X_b,X_a),F)) = hAPP(fun(X_b,option(X_a)),fun(X_b,bool),dom(X_b,X_a),F) ),
file('theBenchmark.p',fact_16_insert__dom) ).
fof(fact_17_finite__surj,axiom,
! [X_b,X_a,B,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1))
=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
=> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B)) ) ),
file('theBenchmark.p',fact_17_finite__surj) ).
fof(fact_18_subset__singletonD,axiom,
! [X_a,A_1,X_2] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))))
=> ( ti(fun(X_a,bool),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))
| ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)) ) ),
file('theBenchmark.p',fact_18_subset__singletonD) ).
fof(fact_19_MGF,axiom,
! [C_1] :
( hBOOL(hoare_1883395792gleton)
=> ( hBOOL(wT_bodies)
=> ( hBOOL(hAPP(com,bool,wt,C_1))
=> hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),bot_bot(fun(hoare_509422987triple(state),bool))),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,C_1)),bot_bot(fun(hoare_509422987triple(state),bool))))) ) ) ),
file('theBenchmark.p',fact_19_MGF) ).
fof(fact_20_emptyE,axiom,
! [X_a,A_3] : ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),bot_bot(fun(X_a,bool)))),
file('theBenchmark.p',fact_20_emptyE) ).
fof(fact_21_insertCI,axiom,
! [X_a,B_1,A_3,B] :
( ( ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),B))
=> ti(X_a,A_3) = ti(X_a,B_1) )
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),B))) ),
file('theBenchmark.p',fact_21_insertCI) ).
fof(fact_22_insertE,axiom,
! [X_a,A_3,B_1,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),A_1)))
=> ( ti(X_a,A_3) != ti(X_a,B_1)
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1)) ) ),
file('theBenchmark.p',fact_22_insertE) ).
fof(fact_23_equalityI,axiom,
! [X_a,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1))
=> ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B) ) ),
file('theBenchmark.p',fact_23_equalityI) ).
fof(fact_24_subsetD,axiom,
! [X_a,C_1,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B)) ) ),
file('theBenchmark.p',fact_24_subsetD) ).
fof(fact_25_image__eqI,axiom,
! [X_a,X_b,A_1,B_1,F,X_2] :
( ti(X_a,B_1) = hAPP(X_b,X_a,F,X_2)
=> ( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))) ) ),
file('theBenchmark.p',fact_25_image__eqI) ).
fof(fact_26_equals0D,axiom,
! [X_a,A_3,A_1] :
( ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool))
=> ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1)) ),
file('theBenchmark.p',fact_26_equals0D) ).
fof(fact_27_Collect__empty__eq,axiom,
! [X_a,P_1] :
( hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1) = bot_bot(fun(X_a,bool))
<=> ! [X_1] : ~ hBOOL(hAPP(X_a,bool,P_1,X_1)) ),
file('theBenchmark.p',fact_27_Collect__empty__eq) ).
fof(fact_28_empty__iff,axiom,
! [X_a,C_1] : ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),bot_bot(fun(X_a,bool)))),
file('theBenchmark.p',fact_28_empty__iff) ).
fof(fact_29_empty__Collect__eq,axiom,
! [X_a,P_1] :
( bot_bot(fun(X_a,bool)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)
<=> ! [X_1] : ~ hBOOL(hAPP(X_a,bool,P_1,X_1)) ),
file('theBenchmark.p',fact_29_empty__Collect__eq) ).
fof(fact_30_ex__in__conv,axiom,
! [X_a,A_1] :
( ? [X_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
<=> ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) ),
file('theBenchmark.p',fact_30_ex__in__conv) ).
fof(fact_31_all__not__in__conv,axiom,
! [X_a,A_1] :
( ! [X_1] : ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
<=> ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)) ),
file('theBenchmark.p',fact_31_all__not__in__conv) ).
fof(fact_32_empty__def,axiom,
! [X_a] : bot_bot(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),fFalse)),
file('theBenchmark.p',fact_32_empty__def) ).
fof(fact_33_finite__code,axiom,
! [X_a] :
( finite_finite_1(X_a)
=> ! [A_1] : hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) ),
file('theBenchmark.p',fact_33_finite__code) ).
fof(fact_34_finite,axiom,
! [X_a] :
( finite_finite_1(X_a)
=> ! [A_1] : hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) ),
file('theBenchmark.p',fact_34_finite) ).
fof(fact_35_insert__absorb,axiom,
! [X_a,A_3,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1))
=> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),A_1) = ti(fun(X_a,bool),A_1) ),
file('theBenchmark.p',fact_35_insert__absorb) ).
fof(fact_36_insertI2,axiom,
! [X_a,B_1,A_3,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),B))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),B))) ),
file('theBenchmark.p',fact_36_insertI2) ).
fof(fact_37_insert__ident,axiom,
! [X_a,B,X_2,A_1] :
( ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> ( ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B))
=> ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),B)
<=> ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B) ) ) ),
file('theBenchmark.p',fact_37_insert__ident) ).
fof(fact_38_insert__code,axiom,
! [X_a,Y_3,A_1,X_2] :
( hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_3),A_1),X_2))
<=> ( hBOOL(hAPP(X_a,bool,A_1,X_2))
| ti(X_a,Y_3) = ti(X_a,X_2) ) ),
file('theBenchmark.p',fact_38_insert__code) ).
fof(fact_39_insert__iff,axiom,
! [X_a,A_3,B_1,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),A_1)))
<=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1))
| ti(X_a,A_3) = ti(X_a,B_1) ) ),
file('theBenchmark.p',fact_39_insert__iff) ).
fof(fact_40_insert__commute,axiom,
! [X_a,X_2,Y_3,A_1] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_3),A_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)),
file('theBenchmark.p',fact_40_insert__commute) ).
fof(fact_41_insert__absorb2,axiom,
! [X_a,X_2,A_1] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1),
file('theBenchmark.p',fact_41_insert__absorb2) ).
fof(fact_42_insert__Collect,axiom,
! [X_a,A_3,P_1] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fimplies),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_3)))),P_1)),
file('theBenchmark.p',fact_42_insert__Collect) ).
fof(fact_43_insert__compr,axiom,
! [X_a,A_3,B] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),B) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_3))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B))),
file('theBenchmark.p',fact_43_insert__compr) ).
fof(fact_44_insertI1,axiom,
! [X_a,A_3,B] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),B))),
file('theBenchmark.p',fact_44_insertI1) ).
fof(fact_45_equalityE,axiom,
! [X_a,A_1,B] :
( ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
=> ~ ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1)) ) ),
file('theBenchmark.p',fact_45_equalityE) ).
fof(fact_46_subset__trans,axiom,
! [X_a,C_2,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),C_2))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C_2)) ) ),
file('theBenchmark.p',fact_46_subset__trans) ).
fof(fact_47_set__mp,axiom,
! [X_a,X_2,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B)) ) ),
file('theBenchmark.p',fact_47_set__mp) ).
fof(fact_48_set__rev__mp,axiom,
! [X_a,B,X_2,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B)) ) ),
file('theBenchmark.p',fact_48_set__rev__mp) ).
fof(fact_49_in__mono,axiom,
! [X_a,X_2,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B)) ) ),
file('theBenchmark.p',fact_49_in__mono) ).
fof(fact_50_equalityD2,axiom,
! [X_a,A_1,B] :
( ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1)) ),
file('theBenchmark.p',fact_50_equalityD2) ).
fof(fact_51_equalityD1,axiom,
! [X_a,A_1,B] :
( ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
file('theBenchmark.p',fact_51_equalityD1) ).
fof(fact_52_set__eq__subset,axiom,
! [X_a,A_1,B] :
( ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
<=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1))
& hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ) ),
file('theBenchmark.p',fact_52_set__eq__subset) ).
fof(fact_53_subset__refl,axiom,
! [X_a,A_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),A_1)),
file('theBenchmark.p',fact_53_subset__refl) ).
fof(fact_54_rev__image__eqI,axiom,
! [X_b,X_a,B_1,F,X_2,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> ( ti(X_b,B_1) = hAPP(X_a,X_b,F,X_2)
=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_1),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))) ) ),
file('theBenchmark.p',fact_54_rev__image__eqI) ).
fof(fact_55_imageI,axiom,
! [X_b,X_a,F,X_2,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),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(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1))) ),
file('theBenchmark.p',fact_55_imageI) ).
fof(fact_56_image__iff,axiom,
! [X_a,X_b,Z,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
<=> ? [X_1] :
( ti(X_a,Z) = hAPP(X_b,X_a,F,X_1)
& hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) ) ),
file('theBenchmark.p',fact_56_image__iff) ).
fof(fact_57_finite__Collect__disjI,axiom,
! [X_a,P_1,Q_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),P_1)),Q_1))))
<=> ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1)))
& hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) ) ),
file('theBenchmark.p',fact_57_finite__Collect__disjI) ).
fof(fact_58_insert__compr__raw,axiom,
! [X_a,X_1,Xa] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),Xa) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),Xa))),
file('theBenchmark.p',fact_58_insert__compr__raw) ).
fof(fact_59_image__ident,axiom,
! [X_a,Y_2] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),combi(X_a)),Y_2) = ti(fun(X_a,bool),Y_2),
file('theBenchmark.p',fact_59_image__ident) ).
fof(fact_60_image__image,axiom,
! [X_b,X_a,X_c,F,G_1,A_1] : hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),G_1),A_1)) = hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),hAPP(fun(X_c,X_b),fun(X_c,X_a),hAPP(fun(X_b,X_a),fun(fun(X_c,X_b),fun(X_c,X_a)),combb(X_b,X_a,X_c),F),G_1)),A_1),
file('theBenchmark.p',fact_60_image__image) ).
fof(fact_61_singleton__inject,axiom,
! [X_a,A_3,B_1] :
( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),bot_bot(fun(X_a,bool))) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),bot_bot(fun(X_a,bool)))
=> ti(X_a,A_3) = ti(X_a,B_1) ),
file('theBenchmark.p',fact_61_singleton__inject) ).
fof(fact_62_singletonE,axiom,
! [X_a,B_1,A_3] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),bot_bot(fun(X_a,bool)))))
=> ti(X_a,B_1) = ti(X_a,A_3) ),
file('theBenchmark.p',fact_62_singletonE) ).
fof(fact_63_doubleton__eq__iff,axiom,
! [X_a,A_3,B_1,C_1,D_1] :
( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),bot_bot(fun(X_a,bool)))) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),D_1),bot_bot(fun(X_a,bool))))
<=> ( ( ti(X_a,B_1) = ti(X_a,C_1)
& ti(X_a,A_3) = ti(X_a,D_1) )
| ( ti(X_a,B_1) = ti(X_a,D_1)
& ti(X_a,A_3) = ti(X_a,C_1) ) ) ),
file('theBenchmark.p',fact_63_doubleton__eq__iff) ).
fof(fact_64_singleton__iff,axiom,
! [X_a,B_1,A_3] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),bot_bot(fun(X_a,bool)))))
<=> ti(X_a,B_1) = ti(X_a,A_3) ),
file('theBenchmark.p',fact_64_singleton__iff) ).
fof(fact_65_insert__not__empty,axiom,
! [X_a,A_3,A_1] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),A_1) != bot_bot(fun(X_a,bool)),
file('theBenchmark.p',fact_65_insert__not__empty) ).
fof(fact_66_empty__not__insert,axiom,
! [X_a,A_3,A_1] : bot_bot(fun(X_a,bool)) != hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),A_1),
file('theBenchmark.p',fact_66_empty__not__insert) ).
fof(fact_67_finite__insert,axiom,
! [X_a,A_3,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),A_1)))
<=> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) ),
file('theBenchmark.p',fact_67_finite__insert) ).
fof(fact_68_subset__empty,axiom,
! [X_a,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),bot_bot(fun(X_a,bool))))
<=> ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)) ),
file('theBenchmark.p',fact_68_subset__empty) ).
fof(fact_69_image__is__empty,axiom,
! [X_b,X_a,F,A_1] :
( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1) = bot_bot(fun(X_a,bool))
<=> ti(fun(X_b,bool),A_1) = bot_bot(fun(X_b,bool)) ),
file('theBenchmark.p',fact_69_image__is__empty) ).
fof(fact_70_image__empty,axiom,
! [X_b,X_a,F] : hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),bot_bot(fun(X_b,bool))) = bot_bot(fun(X_a,bool)),
file('theBenchmark.p',fact_70_image__empty) ).
fof(fact_71_empty__is__image,axiom,
! [X_a,X_b,F,A_1] :
( bot_bot(fun(X_a,bool)) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)
<=> ti(fun(X_b,bool),A_1) = bot_bot(fun(X_b,bool)) ),
file('theBenchmark.p',fact_71_empty__is__image) ).
fof(fact_72_finite__subset,axiom,
! [X_a,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B))
=> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) ) ),
file('theBenchmark.p',fact_72_finite__subset) ).
fof(fact_73_rev__finite__subset,axiom,
! [X_a,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) ) ),
file('theBenchmark.p',fact_73_rev__finite__subset) ).
fof(fact_74_insert__mono,axiom,
! [X_a,A_3,C_2,D] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),C_2),D))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),C_2)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),D))) ),
file('theBenchmark.p',fact_74_insert__mono) ).
fof(fact_75_ext,axiom,
! [X_a,X_b,F,G_1] :
( ! [X_1] : hAPP(X_a,X_b,F,X_1) = hAPP(X_a,X_b,G_1,X_1)
=> ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G_1) ),
file('theBenchmark.p',fact_75_ext) ).
fof(fact_76_mem__def,axiom,
! [X_a,X_2,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
<=> hBOOL(hAPP(X_a,bool,A_1,X_2)) ),
file('theBenchmark.p',fact_76_mem__def) ).
fof(fact_77_Collect__def,axiom,
! [X_a,P_1] : hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1) = ti(fun(X_a,bool),P_1),
file('theBenchmark.p',fact_77_Collect__def) ).
fof(fact_78_subset__insertI2,axiom,
! [X_a,B_1,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),B))) ),
file('theBenchmark.p',fact_78_subset__insertI2) ).
fof(fact_79_subset__insert,axiom,
! [X_a,B,X_2,A_1] :
( ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),B)))
<=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ) ),
file('theBenchmark.p',fact_79_subset__insert) ).
fof(fact_80_insert__subset,axiom,
! [X_a,X_2,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)),B))
<=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
& hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B)) ) ),
file('theBenchmark.p',fact_80_insert__subset) ).
fof(fact_81_subset__insertI,axiom,
! [X_a,B,A_3] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),B))),
file('theBenchmark.p',fact_81_subset__insertI) ).
fof(fact_82_insert__image,axiom,
! [X_b,X_a,F,X_2,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
=> hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)) = hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1) ),
file('theBenchmark.p',fact_82_insert__image) ).
fof(fact_83_image__insert,axiom,
! [X_b,X_a,F,A_3,B] : hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),B)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),hAPP(X_b,X_a,F,A_3)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),B)),
file('theBenchmark.p',fact_83_image__insert) ).
fof(fact_84_image__mono,axiom,
! [X_b,X_a,F,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B))) ),
file('theBenchmark.p',fact_84_image__mono) ).
fof(fact_85_subset__image__iff,axiom,
! [X_a,X_b,B,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
<=> ? [AA] :
( ti(fun(X_a,bool),B) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),AA)
& hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),AA),A_1)) ) ),
file('theBenchmark.p',fact_85_subset__image__iff) ).
fof(fact_86_domI,axiom,
! [X_b,X_a,M,A_3,B_1] :
( hAPP(X_b,option(X_a),M,A_3) = hAPP(X_a,option(X_a),some(X_a),B_1)
=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),hAPP(fun(X_b,option(X_a)),fun(X_b,bool),dom(X_b,X_a),M))) ),
file('theBenchmark.p',fact_86_domI) ).
fof(fact_87_Collect__conv__if,axiom,
! [X_a,P_1,A_3] :
( ( ~ hBOOL(hAPP(X_a,bool,P_1,A_3))
=> hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_3))),P_1)) = bot_bot(fun(X_a,bool)) )
& ( hBOOL(hAPP(X_a,bool,P_1,A_3))
=> hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_3))),P_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),bot_bot(fun(X_a,bool))) ) ),
file('theBenchmark.p',fact_87_Collect__conv__if) ).
fof(fact_88_Collect__conv__if2,axiom,
! [X_a,P_1,A_3] :
( ( ~ hBOOL(hAPP(X_a,bool,P_1,A_3))
=> hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_3))),P_1)) = bot_bot(fun(X_a,bool)) )
& ( hBOOL(hAPP(X_a,bool,P_1,A_3))
=> hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_3))),P_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),bot_bot(fun(X_a,bool))) ) ),
file('theBenchmark.p',fact_88_Collect__conv__if2) ).
fof(fact_89_singleton__conv,axiom,
! [X_a,A_3] : hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_3)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),bot_bot(fun(X_a,bool))),
file('theBenchmark.p',fact_89_singleton__conv) ).
fof(fact_90_singleton__conv2,axiom,
! [X_a,A_3] : hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_3)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),bot_bot(fun(X_a,bool))),
file('theBenchmark.p',fact_90_singleton__conv2) ).
fof(fact_91_MGF__lemma1,axiom,
! [C_1,G] :
( hBOOL(hoare_1883395792gleton)
=> ( ! [X_1] :
( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X_1),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body)))
=> hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),G),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,X_1))),bot_bot(fun(hoare_509422987triple(state),bool))))) )
=> ( hBOOL(hAPP(com,bool,wt,C_1))
=> hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),G),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,C_1)),bot_bot(fun(hoare_509422987triple(state),bool))))) ) ) ),
file('theBenchmark.p',fact_91_MGF__lemma1) ).
fof(fact_92_WT__bodiesD,axiom,
! [Pn,B_2] :
( hBOOL(wT_bodies)
=> ( hAPP(pname,option(com),body,Pn) = hAPP(com,option(com),some(com),B_2)
=> hBOOL(hAPP(com,bool,wt,B_2)) ) ),
file('theBenchmark.p',fact_92_WT__bodiesD) ).
fof(fact_93_imageE,axiom,
! [X_a,X_b,B_1,F,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
=> ~ ! [X_1] :
( ti(X_a,B_1) = hAPP(X_b,X_a,F,X_1)
=> ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) ) ),
file('theBenchmark.p',fact_93_imageE) ).
fof(fact_94_finite__subset__induct,axiom,
! [X_a,P_1,A_1,Fa] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),Fa))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),Fa),A_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,P_1,bot_bot(fun(X_a,bool))))
=> ( ! [A_2,F_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),F_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1))
=> ( ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),F_1))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,P_1,F_1))
=> hBOOL(hAPP(fun(X_a,bool),bool,P_1,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),F_1))) ) ) ) )
=> hBOOL(hAPP(fun(X_a,bool),bool,P_1,Fa)) ) ) ) ),
file('theBenchmark.p',fact_94_finite__subset__induct) ).
fof(fact_95_WTs__elim__cases_I7_J,axiom,
! [P] :
( hBOOL(hAPP(com,bool,wt,hAPP(pname,com,body_1,P)))
=> ~ ! [Y_1] : hAPP(pname,option(com),body,P) != hAPP(com,option(com),some(com),Y_1) ),
file('theBenchmark.p',fact_95_WTs__elim__cases_I7_J) ).
fof(fact_96_subsetI,axiom,
! [X_a,B,A_1] :
( ! [X_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B)) )
=> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
file('theBenchmark.p',fact_96_subsetI) ).
fof(fact_97_finite__subset__image,axiom,
! [X_b,X_a,F,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
=> ? [C] :
( ti(fun(X_a,bool),B) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),C)
& hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),C))
& hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),C),A_1)) ) ) ),
file('theBenchmark.p',fact_97_finite__subset__image) ).
fof(fact_98_finite__dom__body,axiom,
hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body))),
file('theBenchmark.p',fact_98_finite__dom__body) ).
fof(fact_99_com_Osimps_I6_J,axiom,
! [Pname_1,Pname] :
( hAPP(pname,com,body_1,Pname_1) = hAPP(pname,com,body_1,Pname)
<=> ti(pname,Pname_1) = ti(pname,Pname) ),
file('theBenchmark.p',fact_99_com_Osimps_I6_J) ).
fof(arity_fun___Finite__Set_Ofinite,axiom,
! [T_2,T_1] :
( ( finite_finite_1(T_2)
& finite_finite_1(T_1) )
=> finite_finite_1(fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).
fof(arity_HOL_Obool___Finite__Set_Ofinite,axiom,
finite_finite_1(bool),
file('theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).
fof(arity_Option_Ooption___Finite__Set_Ofinite,axiom,
! [T_1] :
( finite_finite_1(T_1)
=> finite_finite_1(option(T_1)) ),
file('theBenchmark.p',arity_Option_Ooption___Finite__Set_Ofinite) ).
fof(help_ti_idem,axiom,
! [T,A] : ti(T,ti(T,A)) = ti(T,A),
file('theBenchmark.p',help_ti_idem) ).
fof(help_fNot_1_1_U,axiom,
! [P] :
( ~ hBOOL(P)
| ~ hBOOL(hAPP(bool,bool,fNot,P)) ),
file('theBenchmark.p',help_fNot_1_1_U) ).
fof(help_fNot_2_1_U,axiom,
! [P] :
( hBOOL(hAPP(bool,bool,fNot,P))
| hBOOL(P) ),
file('theBenchmark.p',help_fNot_2_1_U) ).
fof(help_COMBB_1_1_U,axiom,
! [X_a,X_c,X_b,P,Q,R] : hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R) = hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R)),
file('theBenchmark.p',help_COMBB_1_1_U) ).
fof(help_COMBC_1_1_U,axiom,
! [X_a,X_c,X_b,P,Q,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),
file('theBenchmark.p',help_COMBC_1_1_U) ).
fof(help_COMBI_1_1_U,axiom,
! [X_a,P] : hAPP(X_a,X_a,combi(X_a),P) = ti(X_a,P),
file('theBenchmark.p',help_COMBI_1_1_U) ).
fof(help_COMBK_1_1_U,axiom,
! [X_b,X_a,P,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),
file('theBenchmark.p',help_COMBK_1_1_U) ).
fof(help_COMBS_1_1_U,axiom,
! [X_a,X_c,X_b,P,Q,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)),
file('theBenchmark.p',help_COMBS_1_1_U) ).
fof(help_fconj_1_1_U,axiom,
! [Q,P] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))
| ~ hBOOL(Q)
| ~ hBOOL(P) ),
file('theBenchmark.p',help_fconj_1_1_U) ).
fof(help_fconj_2_1_U,axiom,
! [P,Q] :
( hBOOL(P)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) ),
file('theBenchmark.p',help_fconj_2_1_U) ).
fof(help_fconj_3_1_U,axiom,
! [P,Q] :
( hBOOL(Q)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) ),
file('theBenchmark.p',help_fconj_3_1_U) ).
fof(help_fdisj_1_1_U,axiom,
! [Q,P] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q))
| ~ hBOOL(P) ),
file('theBenchmark.p',help_fdisj_1_1_U) ).
fof(help_fdisj_2_1_U,axiom,
! [P,Q] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q))
| ~ hBOOL(Q) ),
file('theBenchmark.p',help_fdisj_2_1_U) ).
fof(help_fdisj_3_1_U,axiom,
! [P,Q] :
( hBOOL(Q)
| hBOOL(P)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) ),
file('theBenchmark.p',help_fdisj_3_1_U) ).
fof(help_fFalse_1_1_U,axiom,
~ hBOOL(fFalse),
file('theBenchmark.p',help_fFalse_1_1_U) ).
fof(help_fFalse_1_1_T,axiom,
! [P] :
( ti(bool,P) = fFalse
| ti(bool,P) = fTrue ),
file('theBenchmark.p',help_fFalse_1_1_T) ).
fof(help_fequal_1_1_T,axiom,
! [X_a,X,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)) ),
file('theBenchmark.p',help_fequal_1_1_T) ).
fof(help_fequal_2_1_T,axiom,
! [X_a,X,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) ),
file('theBenchmark.p',help_fequal_2_1_T) ).
fof(help_fimplies_1_1_U,axiom,
! [Q,P] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q))
| hBOOL(P) ),
file('theBenchmark.p',help_fimplies_1_1_U) ).
fof(help_fimplies_2_1_U,axiom,
! [P,Q] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q))
| ~ hBOOL(Q) ),
file('theBenchmark.p',help_fimplies_2_1_U) ).
fof(help_fimplies_3_1_U,axiom,
! [P,Q] :
( hBOOL(Q)
| ~ hBOOL(P)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)) ),
file('theBenchmark.p',help_fimplies_3_1_U) ).
fof(conj_0,hypothesis,
hBOOL(hoare_1883395792gleton),
file('theBenchmark.p',conj_0) ).
fof(conj_1,hypothesis,
hBOOL(wT_bodies),
file('theBenchmark.p',conj_1) ).
fof(conj_2,hypothesis,
hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,finite_finite(hoare_509422987triple(state)),fa)),
file('theBenchmark.p',conj_2) ).
fof(conj_3,hypothesis,
~ hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),bool),member(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,y)),fa)),
file('theBenchmark.p',conj_3) ).
fof(conj_4,hypothesis,
hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),ord_less_eq(fun(hoare_509422987triple(state),bool)),fa),hAPP(fun(pname,bool),fun(hoare_509422987triple(state),bool),hAPP(fun(pname,hoare_509422987triple(state)),fun(fun(pname,bool),fun(hoare_509422987triple(state),bool)),image(pname,hoare_509422987triple(state)),hAPP(fun(pname,com),fun(pname,hoare_509422987triple(state)),hAPP(fun(com,hoare_509422987triple(state)),fun(fun(pname,com),fun(pname,hoare_509422987triple(state))),combb(com,hoare_509422987triple(state),pname),hoare_Mirabelle_MGT),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body))),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body)))),
file('theBenchmark.p',conj_4) ).
fof(conj_5,hypothesis,
hAPP(pname,option(com),body,pn) = hAPP(com,option(com),some(com),y),
file('theBenchmark.p',conj_5) ).
fof(conj_6,hypothesis,
hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),hAPP(fun(pname,bool),fun(hoare_509422987triple(state),bool),hAPP(fun(pname,hoare_509422987triple(state)),fun(fun(pname,bool),fun(hoare_509422987triple(state),bool)),image(pname,hoare_509422987triple(state)),hAPP(fun(pname,com),fun(pname,hoare_509422987triple(state)),hAPP(fun(com,hoare_509422987triple(state)),fun(fun(pname,com),fun(pname,hoare_509422987triple(state))),combb(com,hoare_509422987triple(state),pname),hoare_Mirabelle_MGT),body_1)),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body))),fa)),
file('theBenchmark.p',conj_6) ).
fof(conj_7,conjecture,
hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),hAPP(fun(pname,bool),fun(hoare_509422987triple(state),bool),hAPP(fun(pname,hoare_509422987triple(state)),fun(fun(pname,bool),fun(hoare_509422987triple(state),bool)),image(pname,hoare_509422987triple(state)),hAPP(fun(pname,com),fun(pname,hoare_509422987triple(state)),hAPP(fun(com,hoare_509422987triple(state)),fun(fun(pname,com),fun(pname,hoare_509422987triple(state))),combb(com,hoare_509422987triple(state),pname),hoare_Mirabelle_MGT),body_1)),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body))),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,y)),bot_bot(fun(hoare_509422987triple(state),bool))))),
file('theBenchmark.p',conj_7) ).
fof(f_1_1,plain,
! [X_b,X_c,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),
inference(fof_nnf,[status(thm)],[tsy_c_COMBB_res]) ).
fof(f_1_2,plain,
! [U_2,U_1,U_0] : ti(fun(fun(U_2,U_1),fun(fun(U_0,U_2),fun(U_0,U_1))),combb(U_2,U_1,U_0)) = combb(U_2,U_1,U_0),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_1,U_2,U_0] : ti(fun(fun(U_2,U_1),fun(fun(U_0,U_2),fun(U_0,U_1))),combb(U_2,U_1,U_0)) = combb(U_2,U_1,U_0),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
ti(fun(fun(U_2,U_1),fun(fun(U_0,U_2),fun(U_0,U_1))),combb(U_2,U_1,U_0)) = combb(U_2,U_1,U_0),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [X_a,X_b,X_c] : ti(fun(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c))),combc(X_a,X_b,X_c)) = combc(X_a,X_b,X_c),
inference(fof_nnf,[status(thm)],[tsy_c_COMBC_res]) ).
fof(f_2_2,plain,
! [U_5,U_4,U_3] : ti(fun(fun(U_5,fun(U_4,U_3)),fun(U_4,fun(U_5,U_3))),combc(U_5,U_4,U_3)) = combc(U_5,U_4,U_3),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_3,U_5,U_4] : ti(fun(fun(U_5,fun(U_4,U_3)),fun(U_4,fun(U_5,U_3))),combc(U_5,U_4,U_3)) = combc(U_5,U_4,U_3),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
ti(fun(fun(U_5,fun(U_4,U_3)),fun(U_4,fun(U_5,U_3))),combc(U_5,U_4,U_3)) = combc(U_5,U_4,U_3),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [X_a] : ti(fun(X_a,X_a),combi(X_a)) = combi(X_a),
inference(fof_nnf,[status(thm)],[tsy_c_COMBI_res]) ).
fof(f_3_2,plain,
! [U_6] : ti(fun(U_6,U_6),combi(U_6)) = combi(U_6),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_6] : ti(fun(U_6,U_6),combi(U_6)) = combi(U_6),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
ti(fun(U_6,U_6),combi(U_6)) = combi(U_6),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [X_a,X_b] : ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b)) = combk(X_a,X_b),
inference(fof_nnf,[status(thm)],[tsy_c_COMBK_res]) ).
fof(f_4_2,plain,
! [U_8,U_7] : ti(fun(U_8,fun(U_7,U_8)),combk(U_8,U_7)) = combk(U_8,U_7),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_8,U_7] : ti(fun(U_8,fun(U_7,U_8)),combk(U_8,U_7)) = combk(U_8,U_7),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
ti(fun(U_8,fun(U_7,U_8)),combk(U_8,U_7)) = combk(U_8,U_7),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [X_a,X_b,X_c] : ti(fun(fun(X_a,fun(X_b,X_c)),fun(fun(X_a,X_b),fun(X_a,X_c))),combs(X_a,X_b,X_c)) = combs(X_a,X_b,X_c),
inference(fof_nnf,[status(thm)],[tsy_c_COMBS_res]) ).
fof(f_5_2,plain,
! [U_11,U_10,U_9] : ti(fun(fun(U_11,fun(U_10,U_9)),fun(fun(U_11,U_10),fun(U_11,U_9))),combs(U_11,U_10,U_9)) = combs(U_11,U_10,U_9),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_9,U_11,U_10] : ti(fun(fun(U_11,fun(U_10,U_9)),fun(fun(U_11,U_10),fun(U_11,U_9))),combs(U_11,U_10,U_9)) = combs(U_11,U_10,U_9),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
ti(fun(fun(U_11,fun(U_10,U_9)),fun(fun(U_11,U_10),fun(U_11,U_9))),combs(U_11,U_10,U_9)) = combs(U_11,U_10,U_9),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
ti(fun(com,bool),wt) = wt,
inference(fof_nnf,[status(thm)],[tsy_c_Com_OWT_res]) ).
fof(f_6_2,plain,
ti(fun(com,bool),wt) = wt,
inference(definitional_conversion,[status(esa)],[f_6_1]) ).
cnf(f_6_3,plain,
ti(fun(com,bool),wt) = wt,
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
ti(bool,wT_bodies) = wT_bodies,
inference(fof_nnf,[status(thm)],[tsy_c_Com_OWT__bodies_res]) ).
fof(f_7_2,plain,
ti(bool,wT_bodies) = wT_bodies,
inference(definitional_conversion,[status(esa)],[f_7_1]) ).
cnf(f_7_3,plain,
ti(bool,wT_bodies) = wT_bodies,
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
ti(fun(pname,option(com)),body) = body,
inference(fof_nnf,[status(thm)],[tsy_c_Com_Obody_res]) ).
fof(f_8_2,plain,
ti(fun(pname,option(com)),body) = body,
inference(definitional_conversion,[status(esa)],[f_8_1]) ).
cnf(f_8_3,plain,
ti(fun(pname,option(com)),body) = body,
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
ti(fun(pname,com),body_1) = body_1,
inference(fof_nnf,[status(thm)],[tsy_c_Com_Ocom_OBODY_res]) ).
fof(f_9_2,plain,
ti(fun(pname,com),body_1) = body_1,
inference(definitional_conversion,[status(esa)],[f_9_1]) ).
cnf(f_9_3,plain,
ti(fun(pname,com),body_1) = body_1,
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [X_a] : ti(fun(fun(X_a,bool),bool),finite_finite(X_a)) = finite_finite(X_a),
inference(fof_nnf,[status(thm)],[tsy_c_Finite__Set_Ofinite_res]) ).
fof(f_10_2,plain,
! [U_12] : ti(fun(fun(U_12,bool),bool),finite_finite(U_12)) = finite_finite(U_12),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_12] : ti(fun(fun(U_12,bool),bool),finite_finite(U_12)) = finite_finite(U_12),
inference(definitional_conversion,[status(esa)],[f_10_2]) ).
cnf(f_10_4,plain,
ti(fun(fun(U_12,bool),bool),finite_finite(U_12)) = finite_finite(U_12),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [X_a] : ti(X_a,undefined(X_a)) = undefined(X_a),
inference(fof_nnf,[status(thm)],[tsy_c_HOL_Oundefined_res]) ).
fof(f_11_2,plain,
! [U_13] : ti(U_13,undefined(U_13)) = undefined(U_13),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_13] : ti(U_13,undefined(U_13)) = undefined(U_13),
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
ti(U_13,undefined(U_13)) = undefined(U_13),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
ti(fun(com,hoare_509422987triple(state)),hoare_Mirabelle_MGT) = hoare_Mirabelle_MGT,
inference(fof_nnf,[status(thm)],[tsy_c_Hoare__Mirabelle__pjuwniqynr_OMGT_res]) ).
fof(f_12_2,plain,
ti(fun(com,hoare_509422987triple(state)),hoare_Mirabelle_MGT) = hoare_Mirabelle_MGT,
inference(definitional_conversion,[status(esa)],[f_12_1]) ).
cnf(f_12_3,plain,
ti(fun(com,hoare_509422987triple(state)),hoare_Mirabelle_MGT) = hoare_Mirabelle_MGT,
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [X_a] : ti(fun(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool)),hoare_122391849derivs(X_a)) = hoare_122391849derivs(X_a),
inference(fof_nnf,[status(thm)],[tsy_c_Hoare__Mirabelle__pjuwniqynr_Ohoare__derivs_res]) ).
fof(f_13_2,plain,
! [U_14] : ti(fun(fun(hoare_509422987triple(U_14),bool),fun(fun(hoare_509422987triple(U_14),bool),bool)),hoare_122391849derivs(U_14)) = hoare_122391849derivs(U_14),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_14] : ti(fun(fun(hoare_509422987triple(U_14),bool),fun(fun(hoare_509422987triple(U_14),bool),bool)),hoare_122391849derivs(U_14)) = hoare_122391849derivs(U_14),
inference(definitional_conversion,[status(esa)],[f_13_2]) ).
cnf(f_13_4,plain,
ti(fun(fun(hoare_509422987triple(U_14),bool),fun(fun(hoare_509422987triple(U_14),bool),bool)),hoare_122391849derivs(U_14)) = hoare_122391849derivs(U_14),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
ti(bool,hoare_1883395792gleton) = hoare_1883395792gleton,
inference(fof_nnf,[status(thm)],[tsy_c_Hoare__Mirabelle__pjuwniqynr_Ostate__not__singleton_res]) ).
fof(f_14_2,plain,
ti(bool,hoare_1883395792gleton) = hoare_1883395792gleton,
inference(definitional_conversion,[status(esa)],[f_14_1]) ).
cnf(f_14_3,plain,
ti(bool,hoare_1883395792gleton) = hoare_1883395792gleton,
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [X_b,X_a] : ti(fun(fun(X_b,option(X_a)),fun(X_b,bool)),dom(X_b,X_a)) = dom(X_b,X_a),
inference(fof_nnf,[status(thm)],[tsy_c_Map_Odom_res]) ).
fof(f_15_2,plain,
! [U_16,U_15] : ti(fun(fun(U_16,option(U_15)),fun(U_16,bool)),dom(U_16,U_15)) = dom(U_16,U_15),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_16,U_15] : ti(fun(fun(U_16,option(U_15)),fun(U_16,bool)),dom(U_16,U_15)) = dom(U_16,U_15),
inference(definitional_conversion,[status(esa)],[f_15_2]) ).
cnf(f_15_4,plain,
ti(fun(fun(U_16,option(U_15)),fun(U_16,bool)),dom(U_16,U_15)) = dom(U_16,U_15),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [X_a] : ti(fun(X_a,option(X_a)),some(X_a)) = some(X_a),
inference(fof_nnf,[status(thm)],[tsy_c_Option_Ooption_OSome_res]) ).
fof(f_16_2,plain,
! [U_17] : ti(fun(U_17,option(U_17)),some(U_17)) = some(U_17),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_17] : ti(fun(U_17,option(U_17)),some(U_17)) = some(U_17),
inference(definitional_conversion,[status(esa)],[f_16_2]) ).
cnf(f_16_4,plain,
ti(fun(U_17,option(U_17)),some(U_17)) = some(U_17),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
ti(fun(option(com),com),the(com)) = the(com),
inference(fof_nnf,[status(thm)],[tsy_c_Option_Othe_res]) ).
fof(f_17_2,plain,
ti(fun(option(com),com),the(com)) = the(com),
inference(definitional_conversion,[status(esa)],[f_17_1]) ).
cnf(f_17_3,plain,
ti(fun(option(com),com),the(com)) = the(com),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [X_a] : ti(fun(X_a,bool),bot_bot(fun(X_a,bool))) = bot_bot(fun(X_a,bool)),
inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Obot__class_Obot_res]) ).
fof(f_18_2,plain,
! [U_18] : ti(fun(U_18,bool),bot_bot(fun(U_18,bool))) = bot_bot(fun(U_18,bool)),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_18] : ti(fun(U_18,bool),bot_bot(fun(U_18,bool))) = bot_bot(fun(U_18,bool)),
inference(definitional_conversion,[status(esa)],[f_18_2]) ).
cnf(f_18_4,plain,
ti(fun(U_18,bool),bot_bot(fun(U_18,bool))) = bot_bot(fun(U_18,bool)),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [X_a] : ti(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),ord_less_eq(fun(X_a,bool))) = ord_less_eq(fun(X_a,bool)),
inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Oord__class_Oless__eq_res]) ).
fof(f_19_2,plain,
! [U_19] : ti(fun(fun(U_19,bool),fun(fun(U_19,bool),bool)),ord_less_eq(fun(U_19,bool))) = ord_less_eq(fun(U_19,bool)),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_19] : ti(fun(fun(U_19,bool),fun(fun(U_19,bool),bool)),ord_less_eq(fun(U_19,bool))) = ord_less_eq(fun(U_19,bool)),
inference(definitional_conversion,[status(esa)],[f_19_2]) ).
cnf(f_19_4,plain,
ti(fun(fun(U_19,bool),fun(fun(U_19,bool),bool)),ord_less_eq(fun(U_19,bool))) = ord_less_eq(fun(U_19,bool)),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [X_a] : ti(fun(fun(X_a,bool),fun(X_a,bool)),collect(X_a)) = collect(X_a),
inference(fof_nnf,[status(thm)],[tsy_c_Set_OCollect_res]) ).
fof(f_20_2,plain,
! [U_20] : ti(fun(fun(U_20,bool),fun(U_20,bool)),collect(U_20)) = collect(U_20),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_20] : ti(fun(fun(U_20,bool),fun(U_20,bool)),collect(U_20)) = collect(U_20),
inference(definitional_conversion,[status(esa)],[f_20_2]) ).
cnf(f_20_4,plain,
ti(fun(fun(U_20,bool),fun(U_20,bool)),collect(U_20)) = collect(U_20),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [X_a,X_b] : ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool))),image(X_a,X_b)) = image(X_a,X_b),
inference(fof_nnf,[status(thm)],[tsy_c_Set_Oimage_res]) ).
fof(f_21_2,plain,
! [U_22,U_21] : ti(fun(fun(U_22,U_21),fun(fun(U_22,bool),fun(U_21,bool))),image(U_22,U_21)) = image(U_22,U_21),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_21,U_22] : ti(fun(fun(U_22,U_21),fun(fun(U_22,bool),fun(U_21,bool))),image(U_22,U_21)) = image(U_22,U_21),
inference(definitional_conversion,[status(esa)],[f_21_2]) ).
cnf(f_21_4,plain,
ti(fun(fun(U_22,U_21),fun(fun(U_22,bool),fun(U_21,bool))),image(U_22,U_21)) = image(U_22,U_21),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [X_a] : ti(fun(X_a,fun(fun(X_a,bool),fun(X_a,bool))),insert(X_a)) = insert(X_a),
inference(fof_nnf,[status(thm)],[tsy_c_Set_Oinsert_res]) ).
fof(f_22_2,plain,
! [U_23] : ti(fun(U_23,fun(fun(U_23,bool),fun(U_23,bool))),insert(U_23)) = insert(U_23),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_23] : ti(fun(U_23,fun(fun(U_23,bool),fun(U_23,bool))),insert(U_23)) = insert(U_23),
inference(definitional_conversion,[status(esa)],[f_22_2]) ).
cnf(f_22_4,plain,
ti(fun(U_23,fun(fun(U_23,bool),fun(U_23,bool))),insert(U_23)) = insert(U_23),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
ti(bool,fFalse) = fFalse,
inference(fof_nnf,[status(thm)],[tsy_c_fFalse_res]) ).
fof(f_23_2,plain,
ti(bool,fFalse) = fFalse,
inference(definitional_conversion,[status(esa)],[f_23_1]) ).
cnf(f_23_3,plain,
ti(bool,fFalse) = fFalse,
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
ti(fun(bool,bool),fNot) = fNot,
inference(fof_nnf,[status(thm)],[tsy_c_fNot_res]) ).
fof(f_24_2,plain,
ti(fun(bool,bool),fNot) = fNot,
inference(definitional_conversion,[status(esa)],[f_24_1]) ).
cnf(f_24_3,plain,
ti(fun(bool,bool),fNot) = fNot,
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
ti(bool,fTrue) = fTrue,
inference(fof_nnf,[status(thm)],[tsy_c_fTrue_res]) ).
fof(f_25_2,plain,
ti(bool,fTrue) = fTrue,
inference(definitional_conversion,[status(esa)],[f_25_1]) ).
cnf(f_25_3,plain,
ti(bool,fTrue) = fTrue,
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
inference(fof_nnf,[status(thm)],[tsy_c_fconj_res]) ).
fof(f_26_2,plain,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
inference(definitional_conversion,[status(esa)],[f_26_1]) ).
cnf(f_26_3,plain,
ti(fun(bool,fun(bool,bool)),fconj) = fconj,
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
inference(fof_nnf,[status(thm)],[tsy_c_fdisj_res]) ).
fof(f_27_2,plain,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
inference(definitional_conversion,[status(esa)],[f_27_1]) ).
cnf(f_27_3,plain,
ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [X_a] : ti(fun(X_a,fun(X_a,bool)),fequal(X_a)) = fequal(X_a),
inference(fof_nnf,[status(thm)],[tsy_c_fequal_res]) ).
fof(f_28_2,plain,
! [U_24] : ti(fun(U_24,fun(U_24,bool)),fequal(U_24)) = fequal(U_24),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_24] : ti(fun(U_24,fun(U_24,bool)),fequal(U_24)) = fequal(U_24),
inference(definitional_conversion,[status(esa)],[f_28_2]) ).
cnf(f_28_4,plain,
ti(fun(U_24,fun(U_24,bool)),fequal(U_24)) = fequal(U_24),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
inference(fof_nnf,[status(thm)],[tsy_c_fimplies_res]) ).
fof(f_29_2,plain,
ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
inference(definitional_conversion,[status(esa)],[f_29_1]) ).
cnf(f_29_3,plain,
ti(fun(bool,fun(bool,bool)),fimplies) = fimplies,
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [X_a,X_c,B_1_1,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),
inference(fof_nnf,[status(thm)],[tsy_c_hAPP_arg1]) ).
fof(f_30_2,plain,
! [U_28,U_27,U_26,U_25] : hAPP(U_28,U_27,ti(fun(U_28,U_27),U_26),U_25) = hAPP(U_28,U_27,U_26,U_25),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_27,U_28,U_26,U_25] : hAPP(U_28,U_27,ti(fun(U_28,U_27),U_26),U_25) = hAPP(U_28,U_27,U_26,U_25),
inference(definitional_conversion,[status(esa)],[f_30_2]) ).
cnf(f_30_4,plain,
hAPP(U_28,U_27,ti(fun(U_28,U_27),U_26),U_25) = hAPP(U_28,U_27,U_26,U_25),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [X_a,X_c,B_1_1,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),
inference(fof_nnf,[status(thm)],[tsy_c_hAPP_arg2]) ).
fof(f_31_2,plain,
! [U_32,U_31,U_30,U_29] : hAPP(U_32,U_31,U_30,ti(U_32,U_29)) = hAPP(U_32,U_31,U_30,U_29),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_31,U_29,U_30,U_32] : hAPP(U_32,U_31,U_30,ti(U_32,U_29)) = hAPP(U_32,U_31,U_30,U_29),
inference(definitional_conversion,[status(esa)],[f_31_2]) ).
cnf(f_31_4,plain,
hAPP(U_32,U_31,U_30,ti(U_32,U_29)) = hAPP(U_32,U_31,U_30,U_29),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [X_c,X_a,B_1_1,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),
inference(fof_nnf,[status(thm)],[tsy_c_hAPP_res]) ).
fof(f_32_2,plain,
! [U_36,U_35,U_34,U_33] : ti(U_36,hAPP(U_35,U_36,U_34,U_33)) = hAPP(U_35,U_36,U_34,U_33),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_34,U_33,U_35,U_36] : ti(U_36,hAPP(U_35,U_36,U_34,U_33)) = hAPP(U_35,U_36,U_34,U_33),
inference(definitional_conversion,[status(esa)],[f_32_2]) ).
cnf(f_32_4,plain,
ti(U_36,hAPP(U_35,U_36,U_34,U_33)) = hAPP(U_35,U_36,U_34,U_33),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
! [B_1_1] :
( ( hBOOL(ti(bool,B_1_1))
| ~ hBOOL(B_1_1) )
& ( hBOOL(B_1_1)
| ~ hBOOL(ti(bool,B_1_1)) ) ),
inference(fof_nnf,[status(thm)],[tsy_c_hBOOL_arg1]) ).
fof(f_33_2,plain,
! [U_37] :
( ( hBOOL(ti(bool,U_37))
| ~ hBOOL(U_37) )
& ( hBOOL(U_37)
| ~ hBOOL(ti(bool,U_37)) ) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ! [U_39] :
( hBOOL(ti(bool,U_39))
| ~ hBOOL(U_39) )
& ! [U_38] :
( hBOOL(U_38)
| ~ hBOOL(ti(bool,U_38)) ) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
( ! [U_39] :
( hBOOL(ti(bool,U_39))
| ~ hBOOL(U_39) )
& ! [U_38] :
( hBOOL(U_38)
| ~ hBOOL(ti(bool,U_38)) ) ),
inference(definitional_conversion,[status(esa)],[f_33_3]) ).
cnf(f_33_5,plain,
( hBOOL(U_38)
| ~ hBOOL(ti(bool,U_38)) ),
inference(clausify,[status(thm)],[f_33_4]) ).
cnf(f_33_6,plain,
( hBOOL(ti(bool,U_39))
| ~ hBOOL(U_39) ),
inference(clausify,[status(thm)],[f_33_4]) ).
fof(f_34_1,plain,
! [X_a] : ti(fun(X_a,fun(fun(X_a,bool),bool)),member(X_a)) = member(X_a),
inference(fof_nnf,[status(thm)],[tsy_c_member_res]) ).
fof(f_34_2,plain,
! [U_40] : ti(fun(U_40,fun(fun(U_40,bool),bool)),member(U_40)) = member(U_40),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_40] : ti(fun(U_40,fun(fun(U_40,bool),bool)),member(U_40)) = member(U_40),
inference(definitional_conversion,[status(esa)],[f_34_2]) ).
cnf(f_34_4,plain,
ti(fun(U_40,fun(fun(U_40,bool),bool)),member(U_40)) = member(U_40),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
ti(fun(hoare_509422987triple(state),bool),fa) = fa,
inference(fof_nnf,[status(thm)],[tsy_v_Fa_res]) ).
fof(f_35_2,plain,
ti(fun(hoare_509422987triple(state),bool),fa) = fa,
inference(definitional_conversion,[status(esa)],[f_35_1]) ).
cnf(f_35_3,plain,
ti(fun(hoare_509422987triple(state),bool),fa) = fa,
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
ti(pname,pn) = pn,
inference(fof_nnf,[status(thm)],[tsy_v_pn_res]) ).
fof(f_36_2,plain,
ti(pname,pn) = pn,
inference(definitional_conversion,[status(esa)],[f_36_1]) ).
cnf(f_36_3,plain,
ti(pname,pn) = pn,
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
ti(com,y) = y,
inference(fof_nnf,[status(thm)],[tsy_v_y_res]) ).
fof(f_37_2,plain,
ti(com,y) = y,
inference(definitional_conversion,[status(esa)],[f_37_1]) ).
cnf(f_37_3,plain,
ti(com,y) = y,
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
! [X_a,G] : hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),bot_bot(fun(hoare_509422987triple(X_a),bool)))),
inference(fof_nnf,[status(thm)],[fact_0_empty]) ).
fof(f_38_2,plain,
! [U_42,U_41] : hBOOL(hAPP(fun(hoare_509422987triple(U_42),bool),bool,hAPP(fun(hoare_509422987triple(U_42),bool),fun(fun(hoare_509422987triple(U_42),bool),bool),hoare_122391849derivs(U_42),U_41),bot_bot(fun(hoare_509422987triple(U_42),bool)))),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_41,U_42] : hBOOL(hAPP(fun(hoare_509422987triple(U_42),bool),bool,hAPP(fun(hoare_509422987triple(U_42),bool),fun(fun(hoare_509422987triple(U_42),bool),bool),hoare_122391849derivs(U_42),U_41),bot_bot(fun(hoare_509422987triple(U_42),bool)))),
inference(definitional_conversion,[status(esa)],[f_38_2]) ).
cnf(f_38_4,plain,
hBOOL(hAPP(fun(hoare_509422987triple(U_42),bool),bool,hAPP(fun(hoare_509422987triple(U_42),bool),fun(fun(hoare_509422987triple(U_42),bool),bool),hoare_122391849derivs(U_42),U_41),bot_bot(fun(hoare_509422987triple(U_42),bool)))),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [X_a,Ts,G] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),Ts))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),ord_less_eq(fun(hoare_509422987triple(X_a),bool)),Ts),G)) ),
inference(fof_nnf,[status(thm)],[fact_1_asm]) ).
fof(f_39_2,plain,
! [U_45,U_44,U_43] :
( hBOOL(hAPP(fun(hoare_509422987triple(U_45),bool),bool,hAPP(fun(hoare_509422987triple(U_45),bool),fun(fun(hoare_509422987triple(U_45),bool),bool),hoare_122391849derivs(U_45),U_43),U_44))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_45),bool),bool,hAPP(fun(hoare_509422987triple(U_45),bool),fun(fun(hoare_509422987triple(U_45),bool),bool),ord_less_eq(fun(hoare_509422987triple(U_45),bool)),U_44),U_43)) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_45,U_43,U_44] :
( hBOOL(hAPP(fun(hoare_509422987triple(U_45),bool),bool,hAPP(fun(hoare_509422987triple(U_45),bool),fun(fun(hoare_509422987triple(U_45),bool),bool),hoare_122391849derivs(U_45),U_43),U_44))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_45),bool),bool,hAPP(fun(hoare_509422987triple(U_45),bool),fun(fun(hoare_509422987triple(U_45),bool),bool),ord_less_eq(fun(hoare_509422987triple(U_45),bool)),U_44),U_43)) ),
inference(definitional_conversion,[status(esa)],[f_39_2]) ).
cnf(f_39_4,plain,
( hBOOL(hAPP(fun(hoare_509422987triple(U_45),bool),bool,hAPP(fun(hoare_509422987triple(U_45),bool),fun(fun(hoare_509422987triple(U_45),bool),bool),hoare_122391849derivs(U_45),U_43),U_44))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_45),bool),bool,hAPP(fun(hoare_509422987triple(U_45),bool),fun(fun(hoare_509422987triple(U_45),bool),bool),ord_less_eq(fun(hoare_509422987triple(U_45),bool)),U_44),U_43)) ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [X_a,Ts,G,Ts_1] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),Ts))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),ord_less_eq(fun(hoare_509422987triple(X_a),bool)),Ts),Ts_1))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),Ts_1)) ),
inference(fof_nnf,[status(thm)],[fact_2_weaken]) ).
fof(f_40_2,plain,
! [U_49,U_48,U_47,U_46] :
( hBOOL(hAPP(fun(hoare_509422987triple(U_49),bool),bool,hAPP(fun(hoare_509422987triple(U_49),bool),fun(fun(hoare_509422987triple(U_49),bool),bool),hoare_122391849derivs(U_49),U_47),U_48))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_49),bool),bool,hAPP(fun(hoare_509422987triple(U_49),bool),fun(fun(hoare_509422987triple(U_49),bool),bool),ord_less_eq(fun(hoare_509422987triple(U_49),bool)),U_48),U_46))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_49),bool),bool,hAPP(fun(hoare_509422987triple(U_49),bool),fun(fun(hoare_509422987triple(U_49),bool),bool),hoare_122391849derivs(U_49),U_47),U_46)) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_46,U_49,U_47,U_48] :
( hBOOL(hAPP(fun(hoare_509422987triple(U_49),bool),bool,hAPP(fun(hoare_509422987triple(U_49),bool),fun(fun(hoare_509422987triple(U_49),bool),bool),hoare_122391849derivs(U_49),U_47),U_48))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_49),bool),bool,hAPP(fun(hoare_509422987triple(U_49),bool),fun(fun(hoare_509422987triple(U_49),bool),bool),ord_less_eq(fun(hoare_509422987triple(U_49),bool)),U_48),U_46))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_49),bool),bool,hAPP(fun(hoare_509422987triple(U_49),bool),fun(fun(hoare_509422987triple(U_49),bool),bool),hoare_122391849derivs(U_49),U_47),U_46)) ),
inference(definitional_conversion,[status(esa)],[f_40_2]) ).
cnf(f_40_4,plain,
( hBOOL(hAPP(fun(hoare_509422987triple(U_49),bool),bool,hAPP(fun(hoare_509422987triple(U_49),bool),fun(fun(hoare_509422987triple(U_49),bool),bool),hoare_122391849derivs(U_49),U_47),U_48))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_49),bool),bool,hAPP(fun(hoare_509422987triple(U_49),bool),fun(fun(hoare_509422987triple(U_49),bool),bool),ord_less_eq(fun(hoare_509422987triple(U_49),bool)),U_48),U_46))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_49),bool),bool,hAPP(fun(hoare_509422987triple(U_49),bool),fun(fun(hoare_509422987triple(U_49),bool),bool),hoare_122391849derivs(U_49),U_47),U_46)) ),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
! [X_a,G,G_2,Ts] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),Ts))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),ord_less_eq(fun(hoare_509422987triple(X_a),bool)),G_2),G))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_2),Ts)) ),
inference(fof_nnf,[status(thm)],[fact_3_thin]) ).
fof(f_41_2,plain,
! [U_53,U_52,U_51,U_50] :
( hBOOL(hAPP(fun(hoare_509422987triple(U_53),bool),bool,hAPP(fun(hoare_509422987triple(U_53),bool),fun(fun(hoare_509422987triple(U_53),bool),bool),hoare_122391849derivs(U_53),U_52),U_50))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_53),bool),bool,hAPP(fun(hoare_509422987triple(U_53),bool),fun(fun(hoare_509422987triple(U_53),bool),bool),ord_less_eq(fun(hoare_509422987triple(U_53),bool)),U_51),U_52))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_53),bool),bool,hAPP(fun(hoare_509422987triple(U_53),bool),fun(fun(hoare_509422987triple(U_53),bool),bool),hoare_122391849derivs(U_53),U_51),U_50)) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_51,U_50,U_53,U_52] :
( hBOOL(hAPP(fun(hoare_509422987triple(U_53),bool),bool,hAPP(fun(hoare_509422987triple(U_53),bool),fun(fun(hoare_509422987triple(U_53),bool),bool),hoare_122391849derivs(U_53),U_52),U_50))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_53),bool),bool,hAPP(fun(hoare_509422987triple(U_53),bool),fun(fun(hoare_509422987triple(U_53),bool),bool),ord_less_eq(fun(hoare_509422987triple(U_53),bool)),U_51),U_52))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_53),bool),bool,hAPP(fun(hoare_509422987triple(U_53),bool),fun(fun(hoare_509422987triple(U_53),bool),bool),hoare_122391849derivs(U_53),U_51),U_50)) ),
inference(definitional_conversion,[status(esa)],[f_41_2]) ).
cnf(f_41_4,plain,
( hBOOL(hAPP(fun(hoare_509422987triple(U_53),bool),bool,hAPP(fun(hoare_509422987triple(U_53),bool),fun(fun(hoare_509422987triple(U_53),bool),bool),hoare_122391849derivs(U_53),U_52),U_50))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_53),bool),bool,hAPP(fun(hoare_509422987triple(U_53),bool),fun(fun(hoare_509422987triple(U_53),bool),bool),ord_less_eq(fun(hoare_509422987triple(U_53),bool)),U_51),U_52))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_53),bool),bool,hAPP(fun(hoare_509422987triple(U_53),bool),fun(fun(hoare_509422987triple(U_53),bool),bool),hoare_122391849derivs(U_53),U_51),U_50)) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
! [X_a,G,G_2,Ts] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),Ts))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),G_2))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G_2),Ts)) ),
inference(fof_nnf,[status(thm)],[fact_4_cut]) ).
fof(f_42_2,plain,
! [U_57,U_56,U_55,U_54] :
( hBOOL(hAPP(fun(hoare_509422987triple(U_57),bool),bool,hAPP(fun(hoare_509422987triple(U_57),bool),fun(fun(hoare_509422987triple(U_57),bool),bool),hoare_122391849derivs(U_57),U_56),U_54))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_57),bool),bool,hAPP(fun(hoare_509422987triple(U_57),bool),fun(fun(hoare_509422987triple(U_57),bool),bool),hoare_122391849derivs(U_57),U_56),U_55))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_57),bool),bool,hAPP(fun(hoare_509422987triple(U_57),bool),fun(fun(hoare_509422987triple(U_57),bool),bool),hoare_122391849derivs(U_57),U_55),U_54)) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_55,U_54,U_57,U_56] :
( hBOOL(hAPP(fun(hoare_509422987triple(U_57),bool),bool,hAPP(fun(hoare_509422987triple(U_57),bool),fun(fun(hoare_509422987triple(U_57),bool),bool),hoare_122391849derivs(U_57),U_56),U_54))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_57),bool),bool,hAPP(fun(hoare_509422987triple(U_57),bool),fun(fun(hoare_509422987triple(U_57),bool),bool),hoare_122391849derivs(U_57),U_56),U_55))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_57),bool),bool,hAPP(fun(hoare_509422987triple(U_57),bool),fun(fun(hoare_509422987triple(U_57),bool),bool),hoare_122391849derivs(U_57),U_55),U_54)) ),
inference(definitional_conversion,[status(esa)],[f_42_2]) ).
cnf(f_42_4,plain,
( hBOOL(hAPP(fun(hoare_509422987triple(U_57),bool),bool,hAPP(fun(hoare_509422987triple(U_57),bool),fun(fun(hoare_509422987triple(U_57),bool),bool),hoare_122391849derivs(U_57),U_56),U_54))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_57),bool),bool,hAPP(fun(hoare_509422987triple(U_57),bool),fun(fun(hoare_509422987triple(U_57),bool),bool),hoare_122391849derivs(U_57),U_56),U_55))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_57),bool),bool,hAPP(fun(hoare_509422987triple(U_57),bool),fun(fun(hoare_509422987triple(U_57),bool),bool),hoare_122391849derivs(U_57),U_55),U_54)) ),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,plain,
! [X_a,Ts,G,T_3] :
( hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),T_3),Ts)))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),Ts))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),T_3),bot_bot(fun(hoare_509422987triple(X_a),bool))))) ),
inference(fof_nnf,[status(thm)],[fact_5_hoare__derivs_Oinsert]) ).
fof(f_43_2,plain,
! [U_61,U_60,U_59,U_58] :
( hBOOL(hAPP(fun(hoare_509422987triple(U_61),bool),bool,hAPP(fun(hoare_509422987triple(U_61),bool),fun(fun(hoare_509422987triple(U_61),bool),bool),hoare_122391849derivs(U_61),U_59),hAPP(fun(hoare_509422987triple(U_61),bool),fun(hoare_509422987triple(U_61),bool),hAPP(hoare_509422987triple(U_61),fun(fun(hoare_509422987triple(U_61),bool),fun(hoare_509422987triple(U_61),bool)),insert(hoare_509422987triple(U_61)),U_58),U_60)))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_61),bool),bool,hAPP(fun(hoare_509422987triple(U_61),bool),fun(fun(hoare_509422987triple(U_61),bool),bool),hoare_122391849derivs(U_61),U_59),U_60))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_61),bool),bool,hAPP(fun(hoare_509422987triple(U_61),bool),fun(fun(hoare_509422987triple(U_61),bool),bool),hoare_122391849derivs(U_61),U_59),hAPP(fun(hoare_509422987triple(U_61),bool),fun(hoare_509422987triple(U_61),bool),hAPP(hoare_509422987triple(U_61),fun(fun(hoare_509422987triple(U_61),bool),fun(hoare_509422987triple(U_61),bool)),insert(hoare_509422987triple(U_61)),U_58),bot_bot(fun(hoare_509422987triple(U_61),bool))))) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_59,U_58,U_61,U_60] :
( hBOOL(hAPP(fun(hoare_509422987triple(U_61),bool),bool,hAPP(fun(hoare_509422987triple(U_61),bool),fun(fun(hoare_509422987triple(U_61),bool),bool),hoare_122391849derivs(U_61),U_59),hAPP(fun(hoare_509422987triple(U_61),bool),fun(hoare_509422987triple(U_61),bool),hAPP(hoare_509422987triple(U_61),fun(fun(hoare_509422987triple(U_61),bool),fun(hoare_509422987triple(U_61),bool)),insert(hoare_509422987triple(U_61)),U_58),U_60)))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_61),bool),bool,hAPP(fun(hoare_509422987triple(U_61),bool),fun(fun(hoare_509422987triple(U_61),bool),bool),hoare_122391849derivs(U_61),U_59),U_60))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_61),bool),bool,hAPP(fun(hoare_509422987triple(U_61),bool),fun(fun(hoare_509422987triple(U_61),bool),bool),hoare_122391849derivs(U_61),U_59),hAPP(fun(hoare_509422987triple(U_61),bool),fun(hoare_509422987triple(U_61),bool),hAPP(hoare_509422987triple(U_61),fun(fun(hoare_509422987triple(U_61),bool),fun(hoare_509422987triple(U_61),bool)),insert(hoare_509422987triple(U_61)),U_58),bot_bot(fun(hoare_509422987triple(U_61),bool))))) ),
inference(definitional_conversion,[status(esa)],[f_43_2]) ).
cnf(f_43_4,plain,
( hBOOL(hAPP(fun(hoare_509422987triple(U_61),bool),bool,hAPP(fun(hoare_509422987triple(U_61),bool),fun(fun(hoare_509422987triple(U_61),bool),bool),hoare_122391849derivs(U_61),U_59),hAPP(fun(hoare_509422987triple(U_61),bool),fun(hoare_509422987triple(U_61),bool),hAPP(hoare_509422987triple(U_61),fun(fun(hoare_509422987triple(U_61),bool),fun(hoare_509422987triple(U_61),bool)),insert(hoare_509422987triple(U_61)),U_58),U_60)))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_61),bool),bool,hAPP(fun(hoare_509422987triple(U_61),bool),fun(fun(hoare_509422987triple(U_61),bool),bool),hoare_122391849derivs(U_61),U_59),U_60))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_61),bool),bool,hAPP(fun(hoare_509422987triple(U_61),bool),fun(fun(hoare_509422987triple(U_61),bool),bool),hoare_122391849derivs(U_61),U_59),hAPP(fun(hoare_509422987triple(U_61),bool),fun(hoare_509422987triple(U_61),bool),hAPP(hoare_509422987triple(U_61),fun(fun(hoare_509422987triple(U_61),bool),fun(hoare_509422987triple(U_61),bool)),insert(hoare_509422987triple(U_61)),U_58),bot_bot(fun(hoare_509422987triple(U_61),bool))))) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [X_a,G,T_3,Ts] :
( ( hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),Ts))
& hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),T_3),bot_bot(fun(hoare_509422987triple(X_a),bool))))) )
| ~ hBOOL(hAPP(fun(hoare_509422987triple(X_a),bool),bool,hAPP(fun(hoare_509422987triple(X_a),bool),fun(fun(hoare_509422987triple(X_a),bool),bool),hoare_122391849derivs(X_a),G),hAPP(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool),hAPP(hoare_509422987triple(X_a),fun(fun(hoare_509422987triple(X_a),bool),fun(hoare_509422987triple(X_a),bool)),insert(hoare_509422987triple(X_a)),T_3),Ts))) ),
inference(fof_nnf,[status(thm)],[fact_6_derivs__insertD]) ).
fof(f_44_2,plain,
! [U_65,U_64,U_63,U_62] :
( ( hBOOL(hAPP(fun(hoare_509422987triple(U_65),bool),bool,hAPP(fun(hoare_509422987triple(U_65),bool),fun(fun(hoare_509422987triple(U_65),bool),bool),hoare_122391849derivs(U_65),U_64),U_62))
& hBOOL(hAPP(fun(hoare_509422987triple(U_65),bool),bool,hAPP(fun(hoare_509422987triple(U_65),bool),fun(fun(hoare_509422987triple(U_65),bool),bool),hoare_122391849derivs(U_65),U_64),hAPP(fun(hoare_509422987triple(U_65),bool),fun(hoare_509422987triple(U_65),bool),hAPP(hoare_509422987triple(U_65),fun(fun(hoare_509422987triple(U_65),bool),fun(hoare_509422987triple(U_65),bool)),insert(hoare_509422987triple(U_65)),U_63),bot_bot(fun(hoare_509422987triple(U_65),bool))))) )
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_65),bool),bool,hAPP(fun(hoare_509422987triple(U_65),bool),fun(fun(hoare_509422987triple(U_65),bool),bool),hoare_122391849derivs(U_65),U_64),hAPP(fun(hoare_509422987triple(U_65),bool),fun(hoare_509422987triple(U_65),bool),hAPP(hoare_509422987triple(U_65),fun(fun(hoare_509422987triple(U_65),bool),fun(hoare_509422987triple(U_65),bool)),insert(hoare_509422987triple(U_65)),U_63),U_62))) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
( ! [U_63,U_62,U_64,U_65] :
( hBOOL(hAPP(fun(hoare_509422987triple(U_65),bool),bool,hAPP(fun(hoare_509422987triple(U_65),bool),fun(fun(hoare_509422987triple(U_65),bool),bool),hoare_122391849derivs(U_65),U_64),U_62))
| ~ sP0(U_63,U_62,U_64,U_65) )
& ! [U_63,U_62,U_64,U_65] :
( hBOOL(hAPP(fun(hoare_509422987triple(U_65),bool),bool,hAPP(fun(hoare_509422987triple(U_65),bool),fun(fun(hoare_509422987triple(U_65),bool),bool),hoare_122391849derivs(U_65),U_64),hAPP(fun(hoare_509422987triple(U_65),bool),fun(hoare_509422987triple(U_65),bool),hAPP(hoare_509422987triple(U_65),fun(fun(hoare_509422987triple(U_65),bool),fun(hoare_509422987triple(U_65),bool)),insert(hoare_509422987triple(U_65)),U_63),bot_bot(fun(hoare_509422987triple(U_65),bool)))))
| ~ sP0(U_63,U_62,U_64,U_65) )
& ! [U_63,U_62,U_64,U_65] :
( sP0(U_63,U_62,U_64,U_65)
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_65),bool),bool,hAPP(fun(hoare_509422987triple(U_65),bool),fun(fun(hoare_509422987triple(U_65),bool),bool),hoare_122391849derivs(U_65),U_64),hAPP(fun(hoare_509422987triple(U_65),bool),fun(hoare_509422987triple(U_65),bool),hAPP(hoare_509422987triple(U_65),fun(fun(hoare_509422987triple(U_65),bool),fun(hoare_509422987triple(U_65),bool)),insert(hoare_509422987triple(U_65)),U_63),U_62))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_44_2]) ).
cnf(f_44_4,plain,
( sP0(U_63,U_62,U_64,U_65)
| ~ hBOOL(hAPP(fun(hoare_509422987triple(U_65),bool),bool,hAPP(fun(hoare_509422987triple(U_65),bool),fun(fun(hoare_509422987triple(U_65),bool),bool),hoare_122391849derivs(U_65),U_64),hAPP(fun(hoare_509422987triple(U_65),bool),fun(hoare_509422987triple(U_65),bool),hAPP(hoare_509422987triple(U_65),fun(fun(hoare_509422987triple(U_65),bool),fun(hoare_509422987triple(U_65),bool)),insert(hoare_509422987triple(U_65)),U_63),U_62))) ),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(f_44_5,plain,
( hBOOL(hAPP(fun(hoare_509422987triple(U_65),bool),bool,hAPP(fun(hoare_509422987triple(U_65),bool),fun(fun(hoare_509422987triple(U_65),bool),bool),hoare_122391849derivs(U_65),U_64),hAPP(fun(hoare_509422987triple(U_65),bool),fun(hoare_509422987triple(U_65),bool),hAPP(hoare_509422987triple(U_65),fun(fun(hoare_509422987triple(U_65),bool),fun(hoare_509422987triple(U_65),bool)),insert(hoare_509422987triple(U_65)),U_63),bot_bot(fun(hoare_509422987triple(U_65),bool)))))
| ~ sP0(U_63,U_62,U_64,U_65) ),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(f_44_6,plain,
( hBOOL(hAPP(fun(hoare_509422987triple(U_65),bool),bool,hAPP(fun(hoare_509422987triple(U_65),bool),fun(fun(hoare_509422987triple(U_65),bool),bool),hoare_122391849derivs(U_65),U_64),U_62))
| ~ sP0(U_63,U_62,U_64,U_65) ),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [Pn_1,G] :
( hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),G),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,Pn_1))),bot_bot(fun(hoare_509422987triple(state),bool)))))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,Pn_1))),G)),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,hAPP(option(com),com,the(com),hAPP(pname,option(com),body,Pn_1)))),bot_bot(fun(hoare_509422987triple(state),bool))))) ),
inference(fof_nnf,[status(thm)],[fact_7_MGT__BodyN]) ).
fof(f_45_2,plain,
! [U_67,U_66] :
( hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),U_66),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,U_67))),bot_bot(fun(hoare_509422987triple(state),bool)))))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,U_67))),U_66)),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,hAPP(option(com),com,the(com),hAPP(pname,option(com),body,U_67)))),bot_bot(fun(hoare_509422987triple(state),bool))))) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_66,U_67] :
( hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),U_66),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,U_67))),bot_bot(fun(hoare_509422987triple(state),bool)))))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,U_67))),U_66)),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,hAPP(option(com),com,the(com),hAPP(pname,option(com),body,U_67)))),bot_bot(fun(hoare_509422987triple(state),bool))))) ),
inference(definitional_conversion,[status(esa)],[f_45_2]) ).
cnf(f_45_4,plain,
( hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),U_66),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,U_67))),bot_bot(fun(hoare_509422987triple(state),bool)))))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,U_67))),U_66)),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,hAPP(option(com),com,the(com),hAPP(pname,option(com),body,U_67)))),bot_bot(fun(hoare_509422987triple(state),bool))))) ),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_1,plain,
! [X_a,A_1] :
( hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),collect(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),combc(fun(X_a,bool),fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool))),A_1))))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) ),
inference(fof_nnf,[status(thm)],[fact_8_finite__Collect__subsets]) ).
fof(f_46_2,plain,
! [U_69,U_68] :
( hBOOL(hAPP(fun(fun(U_69,bool),bool),bool,finite_finite(fun(U_69,bool)),hAPP(fun(fun(U_69,bool),bool),fun(fun(U_69,bool),bool),collect(fun(U_69,bool)),hAPP(fun(U_69,bool),fun(fun(U_69,bool),bool),hAPP(fun(fun(U_69,bool),fun(fun(U_69,bool),bool)),fun(fun(U_69,bool),fun(fun(U_69,bool),bool)),combc(fun(U_69,bool),fun(U_69,bool),bool),ord_less_eq(fun(U_69,bool))),U_68))))
| ~ hBOOL(hAPP(fun(U_69,bool),bool,finite_finite(U_69),U_68)) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_69,U_68] :
( hBOOL(hAPP(fun(fun(U_69,bool),bool),bool,finite_finite(fun(U_69,bool)),hAPP(fun(fun(U_69,bool),bool),fun(fun(U_69,bool),bool),collect(fun(U_69,bool)),hAPP(fun(U_69,bool),fun(fun(U_69,bool),bool),hAPP(fun(fun(U_69,bool),fun(fun(U_69,bool),bool)),fun(fun(U_69,bool),fun(fun(U_69,bool),bool)),combc(fun(U_69,bool),fun(U_69,bool),bool),ord_less_eq(fun(U_69,bool))),U_68))))
| ~ hBOOL(hAPP(fun(U_69,bool),bool,finite_finite(U_69),U_68)) ),
inference(definitional_conversion,[status(esa)],[f_46_2]) ).
cnf(f_46_4,plain,
( hBOOL(hAPP(fun(fun(U_69,bool),bool),bool,finite_finite(fun(U_69,bool)),hAPP(fun(fun(U_69,bool),bool),fun(fun(U_69,bool),bool),collect(fun(U_69,bool)),hAPP(fun(U_69,bool),fun(fun(U_69,bool),bool),hAPP(fun(fun(U_69,bool),fun(fun(U_69,bool),bool)),fun(fun(U_69,bool),fun(fun(U_69,bool),bool)),combc(fun(U_69,bool),fun(U_69,bool),bool),ord_less_eq(fun(U_69,bool))),U_68))))
| ~ hBOOL(hAPP(fun(U_69,bool),bool,finite_finite(U_69),U_68)) ),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_1,plain,
! [X_b,X_a,H,Fa] :
( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),H),Fa)))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),Fa)) ),
inference(fof_nnf,[status(thm)],[fact_9_finite__imageI]) ).
fof(f_47_2,plain,
! [U_73,U_72,U_71,U_70] :
( hBOOL(hAPP(fun(U_73,bool),bool,finite_finite(U_73),hAPP(fun(U_72,bool),fun(U_73,bool),hAPP(fun(U_72,U_73),fun(fun(U_72,bool),fun(U_73,bool)),image(U_72,U_73),U_71),U_70)))
| ~ hBOOL(hAPP(fun(U_72,bool),bool,finite_finite(U_72),U_70)) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_70,U_72,U_71,U_73] :
( hBOOL(hAPP(fun(U_73,bool),bool,finite_finite(U_73),hAPP(fun(U_72,bool),fun(U_73,bool),hAPP(fun(U_72,U_73),fun(fun(U_72,bool),fun(U_73,bool)),image(U_72,U_73),U_71),U_70)))
| ~ hBOOL(hAPP(fun(U_72,bool),bool,finite_finite(U_72),U_70)) ),
inference(definitional_conversion,[status(esa)],[f_47_2]) ).
cnf(f_47_4,plain,
( hBOOL(hAPP(fun(U_73,bool),bool,finite_finite(U_73),hAPP(fun(U_72,bool),fun(U_73,bool),hAPP(fun(U_72,U_73),fun(fun(U_72,bool),fun(U_73,bool)),image(U_72,U_73),U_71),U_70)))
| ~ hBOOL(hAPP(fun(U_72,bool),bool,finite_finite(U_72),U_70)) ),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
! [X_a,A_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),bot_bot(fun(X_a,bool))),A_1)),
inference(fof_nnf,[status(thm)],[fact_10_empty__subsetI]) ).
fof(f_48_2,plain,
! [U_75,U_74] : hBOOL(hAPP(fun(U_75,bool),bool,hAPP(fun(U_75,bool),fun(fun(U_75,bool),bool),ord_less_eq(fun(U_75,bool)),bot_bot(fun(U_75,bool))),U_74)),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_75,U_74] : hBOOL(hAPP(fun(U_75,bool),bool,hAPP(fun(U_75,bool),fun(fun(U_75,bool),bool),ord_less_eq(fun(U_75,bool)),bot_bot(fun(U_75,bool))),U_74)),
inference(definitional_conversion,[status(esa)],[f_48_2]) ).
cnf(f_48_4,plain,
hBOOL(hAPP(fun(U_75,bool),bool,hAPP(fun(U_75,bool),fun(fun(U_75,bool),bool),ord_less_eq(fun(U_75,bool)),bot_bot(fun(U_75,bool))),U_74)),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,plain,
! [X_a,A_3,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),A_1)))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) ),
inference(fof_nnf,[status(thm)],[fact_11_finite_OinsertI]) ).
fof(f_49_2,plain,
! [U_78,U_77,U_76] :
( hBOOL(hAPP(fun(U_78,bool),bool,finite_finite(U_78),hAPP(fun(U_78,bool),fun(U_78,bool),hAPP(U_78,fun(fun(U_78,bool),fun(U_78,bool)),insert(U_78),U_77),U_76)))
| ~ hBOOL(hAPP(fun(U_78,bool),bool,finite_finite(U_78),U_76)) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_77,U_76,U_78] :
( hBOOL(hAPP(fun(U_78,bool),bool,finite_finite(U_78),hAPP(fun(U_78,bool),fun(U_78,bool),hAPP(U_78,fun(fun(U_78,bool),fun(U_78,bool)),insert(U_78),U_77),U_76)))
| ~ hBOOL(hAPP(fun(U_78,bool),bool,finite_finite(U_78),U_76)) ),
inference(definitional_conversion,[status(esa)],[f_49_2]) ).
cnf(f_49_4,plain,
( hBOOL(hAPP(fun(U_78,bool),bool,finite_finite(U_78),hAPP(fun(U_78,bool),fun(U_78,bool),hAPP(U_78,fun(fun(U_78,bool),fun(U_78,bool)),insert(U_78),U_77),U_76)))
| ~ hBOOL(hAPP(fun(U_78,bool),bool,finite_finite(U_78),U_76)) ),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_1,plain,
! [X_a] : hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),bot_bot(fun(X_a,bool)))),
inference(fof_nnf,[status(thm)],[fact_12_finite_OemptyI]) ).
fof(f_50_2,plain,
! [U_79] : hBOOL(hAPP(fun(U_79,bool),bool,finite_finite(U_79),bot_bot(fun(U_79,bool)))),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_79] : hBOOL(hAPP(fun(U_79,bool),bool,finite_finite(U_79),bot_bot(fun(U_79,bool)))),
inference(definitional_conversion,[status(esa)],[f_50_2]) ).
cnf(f_50_4,plain,
hBOOL(hAPP(fun(U_79,bool),bool,finite_finite(U_79),bot_bot(fun(U_79,bool)))),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_1,plain,
! [X_a,Q_1,P_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),P_1)),Q_1))))
| ( ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1)))
& ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_13_finite__Collect__conjI]) ).
fof(f_51_2,plain,
! [U_82,U_81,U_80] :
( hBOOL(hAPP(fun(U_82,bool),bool,finite_finite(U_82),hAPP(fun(U_82,bool),fun(U_82,bool),collect(U_82),hAPP(fun(U_82,bool),fun(U_82,bool),hAPP(fun(U_82,fun(bool,bool)),fun(fun(U_82,bool),fun(U_82,bool)),combs(U_82,bool,bool),hAPP(fun(U_82,bool),fun(U_82,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_82,bool),fun(U_82,fun(bool,bool))),combb(bool,fun(bool,bool),U_82),fconj),U_80)),U_81))))
| ( ~ hBOOL(hAPP(fun(U_82,bool),bool,finite_finite(U_82),hAPP(fun(U_82,bool),fun(U_82,bool),collect(U_82),U_81)))
& ~ hBOOL(hAPP(fun(U_82,bool),bool,finite_finite(U_82),hAPP(fun(U_82,bool),fun(U_82,bool),collect(U_82),U_80))) ) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
( ! [U_82,U_81,U_80] :
( ~ hBOOL(hAPP(fun(U_82,bool),bool,finite_finite(U_82),hAPP(fun(U_82,bool),fun(U_82,bool),collect(U_82),U_81)))
| ~ sP1(U_82,U_81,U_80) )
& ! [U_82,U_81,U_80] :
( ~ hBOOL(hAPP(fun(U_82,bool),bool,finite_finite(U_82),hAPP(fun(U_82,bool),fun(U_82,bool),collect(U_82),U_80)))
| ~ sP1(U_82,U_81,U_80) )
& ! [U_82,U_81,U_80] :
( hBOOL(hAPP(fun(U_82,bool),bool,finite_finite(U_82),hAPP(fun(U_82,bool),fun(U_82,bool),collect(U_82),hAPP(fun(U_82,bool),fun(U_82,bool),hAPP(fun(U_82,fun(bool,bool)),fun(fun(U_82,bool),fun(U_82,bool)),combs(U_82,bool,bool),hAPP(fun(U_82,bool),fun(U_82,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_82,bool),fun(U_82,fun(bool,bool))),combb(bool,fun(bool,bool),U_82),fconj),U_80)),U_81))))
| sP1(U_82,U_81,U_80) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_51_2]) ).
cnf(f_51_4,plain,
( hBOOL(hAPP(fun(U_82,bool),bool,finite_finite(U_82),hAPP(fun(U_82,bool),fun(U_82,bool),collect(U_82),hAPP(fun(U_82,bool),fun(U_82,bool),hAPP(fun(U_82,fun(bool,bool)),fun(fun(U_82,bool),fun(U_82,bool)),combs(U_82,bool,bool),hAPP(fun(U_82,bool),fun(U_82,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_82,bool),fun(U_82,fun(bool,bool))),combb(bool,fun(bool,bool),U_82),fconj),U_80)),U_81))))
| sP1(U_82,U_81,U_80) ),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_5,plain,
( ~ hBOOL(hAPP(fun(U_82,bool),bool,finite_finite(U_82),hAPP(fun(U_82,bool),fun(U_82,bool),collect(U_82),U_80)))
| ~ sP1(U_82,U_81,U_80) ),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_6,plain,
( ~ hBOOL(hAPP(fun(U_82,bool),bool,finite_finite(U_82),hAPP(fun(U_82,bool),fun(U_82,bool),collect(U_82),U_81)))
| ~ sP1(U_82,U_81,U_80) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_1,plain,
! [X_b,X_a,C_1,A_1] :
( ( hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),C_1)),A_1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),C_1),bot_bot(fun(X_b,bool)))
| ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)) )
& ( hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),C_1)),A_1) = bot_bot(fun(X_b,bool))
| ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) ) ),
inference(fof_nnf,[status(thm)],[fact_14_image__constant__conv]) ).
fof(f_52_2,plain,
! [U_86,U_85,U_84,U_83] :
( ( hAPP(fun(U_85,bool),fun(U_86,bool),hAPP(fun(U_85,U_86),fun(fun(U_85,bool),fun(U_86,bool)),image(U_85,U_86),hAPP(U_86,fun(U_85,U_86),combk(U_86,U_85),U_84)),U_83) = hAPP(fun(U_86,bool),fun(U_86,bool),hAPP(U_86,fun(fun(U_86,bool),fun(U_86,bool)),insert(U_86),U_84),bot_bot(fun(U_86,bool)))
| ti(fun(U_85,bool),U_83) = bot_bot(fun(U_85,bool)) )
& ( hAPP(fun(U_85,bool),fun(U_86,bool),hAPP(fun(U_85,U_86),fun(fun(U_85,bool),fun(U_86,bool)),image(U_85,U_86),hAPP(U_86,fun(U_85,U_86),combk(U_86,U_85),U_84)),U_83) = bot_bot(fun(U_86,bool))
| ti(fun(U_85,bool),U_83) != bot_bot(fun(U_85,bool)) ) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
( ! [U_94,U_92,U_90,U_88] :
( hAPP(fun(U_92,bool),fun(U_94,bool),hAPP(fun(U_92,U_94),fun(fun(U_92,bool),fun(U_94,bool)),image(U_92,U_94),hAPP(U_94,fun(U_92,U_94),combk(U_94,U_92),U_90)),U_88) = hAPP(fun(U_94,bool),fun(U_94,bool),hAPP(U_94,fun(fun(U_94,bool),fun(U_94,bool)),insert(U_94),U_90),bot_bot(fun(U_94,bool)))
| ti(fun(U_92,bool),U_88) = bot_bot(fun(U_92,bool)) )
& ! [U_93,U_91,U_89,U_87] :
( hAPP(fun(U_91,bool),fun(U_93,bool),hAPP(fun(U_91,U_93),fun(fun(U_91,bool),fun(U_93,bool)),image(U_91,U_93),hAPP(U_93,fun(U_91,U_93),combk(U_93,U_91),U_89)),U_87) = bot_bot(fun(U_93,bool))
| ti(fun(U_91,bool),U_87) != bot_bot(fun(U_91,bool)) ) ),
inference(miniscope,[status(thm)],[f_52_2]) ).
fof(f_52_4,plain,
( ! [U_92,U_94,U_88,U_90] :
( hAPP(fun(U_92,bool),fun(U_94,bool),hAPP(fun(U_92,U_94),fun(fun(U_92,bool),fun(U_94,bool)),image(U_92,U_94),hAPP(U_94,fun(U_92,U_94),combk(U_94,U_92),U_90)),U_88) = hAPP(fun(U_94,bool),fun(U_94,bool),hAPP(U_94,fun(fun(U_94,bool),fun(U_94,bool)),insert(U_94),U_90),bot_bot(fun(U_94,bool)))
| ti(fun(U_92,bool),U_88) = bot_bot(fun(U_92,bool)) )
& ! [U_91,U_93,U_87,U_89] :
( hAPP(fun(U_91,bool),fun(U_93,bool),hAPP(fun(U_91,U_93),fun(fun(U_91,bool),fun(U_93,bool)),image(U_91,U_93),hAPP(U_93,fun(U_91,U_93),combk(U_93,U_91),U_89)),U_87) = bot_bot(fun(U_93,bool))
| ti(fun(U_91,bool),U_87) != bot_bot(fun(U_91,bool)) ) ),
inference(definitional_conversion,[status(esa)],[f_52_3]) ).
cnf(f_52_5,plain,
( hAPP(fun(U_91,bool),fun(U_93,bool),hAPP(fun(U_91,U_93),fun(fun(U_91,bool),fun(U_93,bool)),image(U_91,U_93),hAPP(U_93,fun(U_91,U_93),combk(U_93,U_91),U_89)),U_87) = bot_bot(fun(U_93,bool))
| ti(fun(U_91,bool),U_87) != bot_bot(fun(U_91,bool)) ),
inference(clausify,[status(thm)],[f_52_4]) ).
cnf(f_52_6,plain,
( hAPP(fun(U_92,bool),fun(U_94,bool),hAPP(fun(U_92,U_94),fun(fun(U_92,bool),fun(U_94,bool)),image(U_92,U_94),hAPP(U_94,fun(U_92,U_94),combk(U_94,U_92),U_90)),U_88) = hAPP(fun(U_94,bool),fun(U_94,bool),hAPP(U_94,fun(fun(U_94,bool),fun(U_94,bool)),insert(U_94),U_90),bot_bot(fun(U_94,bool)))
| ti(fun(U_92,bool),U_88) = bot_bot(fun(U_92,bool)) ),
inference(clausify,[status(thm)],[f_52_4]) ).
fof(f_53_1,plain,
! [X_b,X_a,C_1,X_2,A_1] :
( hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),C_1)),A_1) = hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),C_1),bot_bot(fun(X_b,bool)))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) ),
inference(fof_nnf,[status(thm)],[fact_15_image__constant]) ).
fof(f_53_2,plain,
! [U_99,U_98,U_97,U_96,U_95] :
( hAPP(fun(U_98,bool),fun(U_99,bool),hAPP(fun(U_98,U_99),fun(fun(U_98,bool),fun(U_99,bool)),image(U_98,U_99),hAPP(U_99,fun(U_98,U_99),combk(U_99,U_98),U_97)),U_95) = hAPP(fun(U_99,bool),fun(U_99,bool),hAPP(U_99,fun(fun(U_99,bool),fun(U_99,bool)),insert(U_99),U_97),bot_bot(fun(U_99,bool)))
| ~ hBOOL(hAPP(fun(U_98,bool),bool,hAPP(U_98,fun(fun(U_98,bool),bool),member(U_98),U_96),U_95)) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_95,U_97,U_98,U_96,U_99] :
( hAPP(fun(U_98,bool),fun(U_99,bool),hAPP(fun(U_98,U_99),fun(fun(U_98,bool),fun(U_99,bool)),image(U_98,U_99),hAPP(U_99,fun(U_98,U_99),combk(U_99,U_98),U_97)),U_95) = hAPP(fun(U_99,bool),fun(U_99,bool),hAPP(U_99,fun(fun(U_99,bool),fun(U_99,bool)),insert(U_99),U_97),bot_bot(fun(U_99,bool)))
| ~ hBOOL(hAPP(fun(U_98,bool),bool,hAPP(U_98,fun(fun(U_98,bool),bool),member(U_98),U_96),U_95)) ),
inference(definitional_conversion,[status(esa)],[f_53_2]) ).
cnf(f_53_4,plain,
( hAPP(fun(U_98,bool),fun(U_99,bool),hAPP(fun(U_98,U_99),fun(fun(U_98,bool),fun(U_99,bool)),image(U_98,U_99),hAPP(U_99,fun(U_98,U_99),combk(U_99,U_98),U_97)),U_95) = hAPP(fun(U_99,bool),fun(U_99,bool),hAPP(U_99,fun(fun(U_99,bool),fun(U_99,bool)),insert(U_99),U_97),bot_bot(fun(U_99,bool)))
| ~ hBOOL(hAPP(fun(U_98,bool),bool,hAPP(U_98,fun(fun(U_98,bool),bool),member(U_98),U_96),U_95)) ),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_1,plain,
! [X_b,X_a,F,X_2,Y_3] :
( hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),X_2),hAPP(fun(X_b,option(X_a)),fun(X_b,bool),dom(X_b,X_a),F)) = hAPP(fun(X_b,option(X_a)),fun(X_b,bool),dom(X_b,X_a),F)
| hAPP(X_b,option(X_a),F,X_2) != hAPP(X_a,option(X_a),some(X_a),Y_3) ),
inference(fof_nnf,[status(thm)],[fact_16_insert__dom]) ).
fof(f_54_2,plain,
! [U_104,U_103,U_102,U_101,U_100] :
( hAPP(fun(U_104,bool),fun(U_104,bool),hAPP(U_104,fun(fun(U_104,bool),fun(U_104,bool)),insert(U_104),U_101),hAPP(fun(U_104,option(U_103)),fun(U_104,bool),dom(U_104,U_103),U_102)) = hAPP(fun(U_104,option(U_103)),fun(U_104,bool),dom(U_104,U_103),U_102)
| hAPP(U_104,option(U_103),U_102,U_101) != hAPP(U_103,option(U_103),some(U_103),U_100) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_104,U_103,U_102,U_101] :
( ! [U_100] : hAPP(U_104,option(U_103),U_102,U_101) != hAPP(U_103,option(U_103),some(U_103),U_100)
| hAPP(fun(U_104,bool),fun(U_104,bool),hAPP(U_104,fun(fun(U_104,bool),fun(U_104,bool)),insert(U_104),U_101),hAPP(fun(U_104,option(U_103)),fun(U_104,bool),dom(U_104,U_103),U_102)) = hAPP(fun(U_104,option(U_103)),fun(U_104,bool),dom(U_104,U_103),U_102) ),
inference(miniscope,[status(thm)],[f_54_2]) ).
fof(f_54_4,plain,
! [U_101,U_102,U_100,U_103,U_104] :
( hAPP(U_104,option(U_103),U_102,U_101) != hAPP(U_103,option(U_103),some(U_103),U_100)
| hAPP(fun(U_104,bool),fun(U_104,bool),hAPP(U_104,fun(fun(U_104,bool),fun(U_104,bool)),insert(U_104),U_101),hAPP(fun(U_104,option(U_103)),fun(U_104,bool),dom(U_104,U_103),U_102)) = hAPP(fun(U_104,option(U_103)),fun(U_104,bool),dom(U_104,U_103),U_102) ),
inference(definitional_conversion,[status(esa)],[f_54_3]) ).
cnf(f_54_5,plain,
( hAPP(U_104,option(U_103),U_102,U_101) != hAPP(U_103,option(U_103),some(U_103),U_100)
| hAPP(fun(U_104,bool),fun(U_104,bool),hAPP(U_104,fun(fun(U_104,bool),fun(U_104,bool)),insert(U_104),U_101),hAPP(fun(U_104,option(U_103)),fun(U_104,bool),dom(U_104,U_103),U_102)) = hAPP(fun(U_104,option(U_103)),fun(U_104,bool),dom(U_104,U_103),U_102) ),
inference(clausify,[status(thm)],[f_54_4]) ).
fof(f_55_1,plain,
! [X_b,X_a,B,F,A_1] :
( hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),B))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) ),
inference(fof_nnf,[status(thm)],[fact_17_finite__surj]) ).
fof(f_55_2,plain,
! [U_109,U_108,U_107,U_106,U_105] :
( hBOOL(hAPP(fun(U_109,bool),bool,finite_finite(U_109),U_107))
| ~ hBOOL(hAPP(fun(U_109,bool),bool,hAPP(fun(U_109,bool),fun(fun(U_109,bool),bool),ord_less_eq(fun(U_109,bool)),U_107),hAPP(fun(U_108,bool),fun(U_109,bool),hAPP(fun(U_108,U_109),fun(fun(U_108,bool),fun(U_109,bool)),image(U_108,U_109),U_106),U_105)))
| ~ hBOOL(hAPP(fun(U_108,bool),bool,finite_finite(U_108),U_105)) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_107,U_108,U_105,U_106,U_109] :
( hBOOL(hAPP(fun(U_109,bool),bool,finite_finite(U_109),U_107))
| ~ hBOOL(hAPP(fun(U_109,bool),bool,hAPP(fun(U_109,bool),fun(fun(U_109,bool),bool),ord_less_eq(fun(U_109,bool)),U_107),hAPP(fun(U_108,bool),fun(U_109,bool),hAPP(fun(U_108,U_109),fun(fun(U_108,bool),fun(U_109,bool)),image(U_108,U_109),U_106),U_105)))
| ~ hBOOL(hAPP(fun(U_108,bool),bool,finite_finite(U_108),U_105)) ),
inference(definitional_conversion,[status(esa)],[f_55_2]) ).
cnf(f_55_4,plain,
( hBOOL(hAPP(fun(U_109,bool),bool,finite_finite(U_109),U_107))
| ~ hBOOL(hAPP(fun(U_109,bool),bool,hAPP(fun(U_109,bool),fun(fun(U_109,bool),bool),ord_less_eq(fun(U_109,bool)),U_107),hAPP(fun(U_108,bool),fun(U_109,bool),hAPP(fun(U_108,U_109),fun(fun(U_108,bool),fun(U_109,bool)),image(U_108,U_109),U_106),U_105)))
| ~ hBOOL(hAPP(fun(U_108,bool),bool,finite_finite(U_108),U_105)) ),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_1,plain,
! [X_a,A_1,X_2] :
( ti(fun(X_a,bool),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool)))
| ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),bot_bot(fun(X_a,bool))))) ),
inference(fof_nnf,[status(thm)],[fact_18_subset__singletonD]) ).
fof(f_56_2,plain,
! [U_112,U_111,U_110] :
( ti(fun(U_112,bool),U_111) = hAPP(fun(U_112,bool),fun(U_112,bool),hAPP(U_112,fun(fun(U_112,bool),fun(U_112,bool)),insert(U_112),U_110),bot_bot(fun(U_112,bool)))
| ti(fun(U_112,bool),U_111) = bot_bot(fun(U_112,bool))
| ~ hBOOL(hAPP(fun(U_112,bool),bool,hAPP(fun(U_112,bool),fun(fun(U_112,bool),bool),ord_less_eq(fun(U_112,bool)),U_111),hAPP(fun(U_112,bool),fun(U_112,bool),hAPP(U_112,fun(fun(U_112,bool),fun(U_112,bool)),insert(U_112),U_110),bot_bot(fun(U_112,bool))))) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
! [U_112,U_110,U_111] :
( ti(fun(U_112,bool),U_111) = hAPP(fun(U_112,bool),fun(U_112,bool),hAPP(U_112,fun(fun(U_112,bool),fun(U_112,bool)),insert(U_112),U_110),bot_bot(fun(U_112,bool)))
| ti(fun(U_112,bool),U_111) = bot_bot(fun(U_112,bool))
| ~ hBOOL(hAPP(fun(U_112,bool),bool,hAPP(fun(U_112,bool),fun(fun(U_112,bool),bool),ord_less_eq(fun(U_112,bool)),U_111),hAPP(fun(U_112,bool),fun(U_112,bool),hAPP(U_112,fun(fun(U_112,bool),fun(U_112,bool)),insert(U_112),U_110),bot_bot(fun(U_112,bool))))) ),
inference(definitional_conversion,[status(esa)],[f_56_2]) ).
cnf(f_56_4,plain,
( ti(fun(U_112,bool),U_111) = hAPP(fun(U_112,bool),fun(U_112,bool),hAPP(U_112,fun(fun(U_112,bool),fun(U_112,bool)),insert(U_112),U_110),bot_bot(fun(U_112,bool)))
| ti(fun(U_112,bool),U_111) = bot_bot(fun(U_112,bool))
| ~ hBOOL(hAPP(fun(U_112,bool),bool,hAPP(fun(U_112,bool),fun(fun(U_112,bool),bool),ord_less_eq(fun(U_112,bool)),U_111),hAPP(fun(U_112,bool),fun(U_112,bool),hAPP(U_112,fun(fun(U_112,bool),fun(U_112,bool)),insert(U_112),U_110),bot_bot(fun(U_112,bool))))) ),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_1,plain,
! [C_1] :
( hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),bot_bot(fun(hoare_509422987triple(state),bool))),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,C_1)),bot_bot(fun(hoare_509422987triple(state),bool)))))
| ~ hBOOL(hAPP(com,bool,wt,C_1))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1883395792gleton) ),
inference(fof_nnf,[status(thm)],[fact_19_MGF]) ).
fof(f_57_2,plain,
! [U_113] :
( hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),bot_bot(fun(hoare_509422987triple(state),bool))),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,U_113)),bot_bot(fun(hoare_509422987triple(state),bool)))))
| ~ hBOOL(hAPP(com,bool,wt,U_113))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1883395792gleton) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
( ! [U_113] :
( hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),bot_bot(fun(hoare_509422987triple(state),bool))),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,U_113)),bot_bot(fun(hoare_509422987triple(state),bool)))))
| ~ hBOOL(hAPP(com,bool,wt,U_113)) )
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1883395792gleton) ),
inference(miniscope,[status(thm)],[f_57_2]) ).
fof(f_57_4,plain,
! [U_113] :
( hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),bot_bot(fun(hoare_509422987triple(state),bool))),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,U_113)),bot_bot(fun(hoare_509422987triple(state),bool)))))
| ~ hBOOL(hAPP(com,bool,wt,U_113))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1883395792gleton) ),
inference(definitional_conversion,[status(esa)],[f_57_3]) ).
cnf(f_57_5,plain,
( hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),bot_bot(fun(hoare_509422987triple(state),bool))),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,U_113)),bot_bot(fun(hoare_509422987triple(state),bool)))))
| ~ hBOOL(hAPP(com,bool,wt,U_113))
| ~ hBOOL(wT_bodies)
| ~ hBOOL(hoare_1883395792gleton) ),
inference(clausify,[status(thm)],[f_57_4]) ).
fof(f_58_1,plain,
! [X_a,A_3] : ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),bot_bot(fun(X_a,bool)))),
inference(fof_nnf,[status(thm)],[fact_20_emptyE]) ).
fof(f_58_2,plain,
! [U_115,U_114] : ~ hBOOL(hAPP(fun(U_115,bool),bool,hAPP(U_115,fun(fun(U_115,bool),bool),member(U_115),U_114),bot_bot(fun(U_115,bool)))),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
! [U_115,U_114] : ~ hBOOL(hAPP(fun(U_115,bool),bool,hAPP(U_115,fun(fun(U_115,bool),bool),member(U_115),U_114),bot_bot(fun(U_115,bool)))),
inference(definitional_conversion,[status(esa)],[f_58_2]) ).
cnf(f_58_4,plain,
~ hBOOL(hAPP(fun(U_115,bool),bool,hAPP(U_115,fun(fun(U_115,bool),bool),member(U_115),U_114),bot_bot(fun(U_115,bool)))),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_1,plain,
! [X_a,B_1,A_3,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),B)))
| ( ti(X_a,A_3) != ti(X_a,B_1)
& ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),B)) ) ),
inference(fof_nnf,[status(thm)],[fact_21_insertCI]) ).
fof(f_59_2,plain,
! [U_119,U_118,U_117,U_116] :
( hBOOL(hAPP(fun(U_119,bool),bool,hAPP(U_119,fun(fun(U_119,bool),bool),member(U_119),U_117),hAPP(fun(U_119,bool),fun(U_119,bool),hAPP(U_119,fun(fun(U_119,bool),fun(U_119,bool)),insert(U_119),U_118),U_116)))
| ( ti(U_119,U_117) != ti(U_119,U_118)
& ~ hBOOL(hAPP(fun(U_119,bool),bool,hAPP(U_119,fun(fun(U_119,bool),bool),member(U_119),U_117),U_116)) ) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
( ! [U_118,U_116,U_117,U_119] :
( ti(U_119,U_117) != ti(U_119,U_118)
| ~ sP2(U_118,U_116,U_117,U_119) )
& ! [U_118,U_116,U_117,U_119] :
( ~ hBOOL(hAPP(fun(U_119,bool),bool,hAPP(U_119,fun(fun(U_119,bool),bool),member(U_119),U_117),U_116))
| ~ sP2(U_118,U_116,U_117,U_119) )
& ! [U_118,U_116,U_117,U_119] :
( hBOOL(hAPP(fun(U_119,bool),bool,hAPP(U_119,fun(fun(U_119,bool),bool),member(U_119),U_117),hAPP(fun(U_119,bool),fun(U_119,bool),hAPP(U_119,fun(fun(U_119,bool),fun(U_119,bool)),insert(U_119),U_118),U_116)))
| sP2(U_118,U_116,U_117,U_119) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_59_2]) ).
cnf(f_59_4,plain,
( hBOOL(hAPP(fun(U_119,bool),bool,hAPP(U_119,fun(fun(U_119,bool),bool),member(U_119),U_117),hAPP(fun(U_119,bool),fun(U_119,bool),hAPP(U_119,fun(fun(U_119,bool),fun(U_119,bool)),insert(U_119),U_118),U_116)))
| sP2(U_118,U_116,U_117,U_119) ),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_5,plain,
( ~ hBOOL(hAPP(fun(U_119,bool),bool,hAPP(U_119,fun(fun(U_119,bool),bool),member(U_119),U_117),U_116))
| ~ sP2(U_118,U_116,U_117,U_119) ),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_6,plain,
( ti(U_119,U_117) != ti(U_119,U_118)
| ~ sP2(U_118,U_116,U_117,U_119) ),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_1,plain,
! [X_a,A_3,B_1,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1))
| ti(X_a,A_3) = ti(X_a,B_1)
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),A_1))) ),
inference(fof_nnf,[status(thm)],[fact_22_insertE]) ).
fof(f_60_2,plain,
! [U_123,U_122,U_121,U_120] :
( hBOOL(hAPP(fun(U_123,bool),bool,hAPP(U_123,fun(fun(U_123,bool),bool),member(U_123),U_122),U_120))
| ti(U_123,U_122) = ti(U_123,U_121)
| ~ hBOOL(hAPP(fun(U_123,bool),bool,hAPP(U_123,fun(fun(U_123,bool),bool),member(U_123),U_122),hAPP(fun(U_123,bool),fun(U_123,bool),hAPP(U_123,fun(fun(U_123,bool),fun(U_123,bool)),insert(U_123),U_121),U_120))) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_121,U_120,U_122,U_123] :
( hBOOL(hAPP(fun(U_123,bool),bool,hAPP(U_123,fun(fun(U_123,bool),bool),member(U_123),U_122),U_120))
| ti(U_123,U_122) = ti(U_123,U_121)
| ~ hBOOL(hAPP(fun(U_123,bool),bool,hAPP(U_123,fun(fun(U_123,bool),bool),member(U_123),U_122),hAPP(fun(U_123,bool),fun(U_123,bool),hAPP(U_123,fun(fun(U_123,bool),fun(U_123,bool)),insert(U_123),U_121),U_120))) ),
inference(definitional_conversion,[status(esa)],[f_60_2]) ).
cnf(f_60_4,plain,
( hBOOL(hAPP(fun(U_123,bool),bool,hAPP(U_123,fun(fun(U_123,bool),bool),member(U_123),U_122),U_120))
| ti(U_123,U_122) = ti(U_123,U_121)
| ~ hBOOL(hAPP(fun(U_123,bool),bool,hAPP(U_123,fun(fun(U_123,bool),bool),member(U_123),U_122),hAPP(fun(U_123,bool),fun(U_123,bool),hAPP(U_123,fun(fun(U_123,bool),fun(U_123,bool)),insert(U_123),U_121),U_120))) ),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_1,plain,
! [X_a,A_1,B] :
( ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
inference(fof_nnf,[status(thm)],[fact_23_equalityI]) ).
fof(f_61_2,plain,
! [U_126,U_125,U_124] :
( ti(fun(U_126,bool),U_125) = ti(fun(U_126,bool),U_124)
| ~ hBOOL(hAPP(fun(U_126,bool),bool,hAPP(fun(U_126,bool),fun(fun(U_126,bool),bool),ord_less_eq(fun(U_126,bool)),U_124),U_125))
| ~ hBOOL(hAPP(fun(U_126,bool),bool,hAPP(fun(U_126,bool),fun(fun(U_126,bool),bool),ord_less_eq(fun(U_126,bool)),U_125),U_124)) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
! [U_124,U_125,U_126] :
( ti(fun(U_126,bool),U_125) = ti(fun(U_126,bool),U_124)
| ~ hBOOL(hAPP(fun(U_126,bool),bool,hAPP(fun(U_126,bool),fun(fun(U_126,bool),bool),ord_less_eq(fun(U_126,bool)),U_124),U_125))
| ~ hBOOL(hAPP(fun(U_126,bool),bool,hAPP(fun(U_126,bool),fun(fun(U_126,bool),bool),ord_less_eq(fun(U_126,bool)),U_125),U_124)) ),
inference(definitional_conversion,[status(esa)],[f_61_2]) ).
cnf(f_61_4,plain,
( ti(fun(U_126,bool),U_125) = ti(fun(U_126,bool),U_124)
| ~ hBOOL(hAPP(fun(U_126,bool),bool,hAPP(fun(U_126,bool),fun(fun(U_126,bool),bool),ord_less_eq(fun(U_126,bool)),U_124),U_125))
| ~ hBOOL(hAPP(fun(U_126,bool),bool,hAPP(fun(U_126,bool),fun(fun(U_126,bool),bool),ord_less_eq(fun(U_126,bool)),U_125),U_124)) ),
inference(clausify,[status(thm)],[f_61_3]) ).
fof(f_62_1,plain,
! [X_a,C_1,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_1))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
inference(fof_nnf,[status(thm)],[fact_24_subsetD]) ).
fof(f_62_2,plain,
! [U_130,U_129,U_128,U_127] :
( hBOOL(hAPP(fun(U_130,bool),bool,hAPP(U_130,fun(fun(U_130,bool),bool),member(U_130),U_129),U_127))
| ~ hBOOL(hAPP(fun(U_130,bool),bool,hAPP(U_130,fun(fun(U_130,bool),bool),member(U_130),U_129),U_128))
| ~ hBOOL(hAPP(fun(U_130,bool),bool,hAPP(fun(U_130,bool),fun(fun(U_130,bool),bool),ord_less_eq(fun(U_130,bool)),U_128),U_127)) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_128,U_127,U_130,U_129] :
( hBOOL(hAPP(fun(U_130,bool),bool,hAPP(U_130,fun(fun(U_130,bool),bool),member(U_130),U_129),U_127))
| ~ hBOOL(hAPP(fun(U_130,bool),bool,hAPP(U_130,fun(fun(U_130,bool),bool),member(U_130),U_129),U_128))
| ~ hBOOL(hAPP(fun(U_130,bool),bool,hAPP(fun(U_130,bool),fun(fun(U_130,bool),bool),ord_less_eq(fun(U_130,bool)),U_128),U_127)) ),
inference(definitional_conversion,[status(esa)],[f_62_2]) ).
cnf(f_62_4,plain,
( hBOOL(hAPP(fun(U_130,bool),bool,hAPP(U_130,fun(fun(U_130,bool),bool),member(U_130),U_129),U_127))
| ~ hBOOL(hAPP(fun(U_130,bool),bool,hAPP(U_130,fun(fun(U_130,bool),bool),member(U_130),U_129),U_128))
| ~ hBOOL(hAPP(fun(U_130,bool),bool,hAPP(fun(U_130,bool),fun(fun(U_130,bool),bool),ord_less_eq(fun(U_130,bool)),U_128),U_127)) ),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_1,plain,
! [X_a,X_b,A_1,B_1,F,X_2] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_1))
| ti(X_a,B_1) != hAPP(X_b,X_a,F,X_2) ),
inference(fof_nnf,[status(thm)],[fact_25_image__eqI]) ).
fof(f_63_2,plain,
! [U_136,U_135,U_134,U_133,U_132,U_131] :
( hBOOL(hAPP(fun(U_136,bool),bool,hAPP(U_136,fun(fun(U_136,bool),bool),member(U_136),U_133),hAPP(fun(U_135,bool),fun(U_136,bool),hAPP(fun(U_135,U_136),fun(fun(U_135,bool),fun(U_136,bool)),image(U_135,U_136),U_132),U_134)))
| ~ hBOOL(hAPP(fun(U_135,bool),bool,hAPP(U_135,fun(fun(U_135,bool),bool),member(U_135),U_131),U_134))
| ti(U_136,U_133) != hAPP(U_135,U_136,U_132,U_131) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
! [U_133,U_131,U_132,U_135,U_134,U_136] :
( hBOOL(hAPP(fun(U_136,bool),bool,hAPP(U_136,fun(fun(U_136,bool),bool),member(U_136),U_133),hAPP(fun(U_135,bool),fun(U_136,bool),hAPP(fun(U_135,U_136),fun(fun(U_135,bool),fun(U_136,bool)),image(U_135,U_136),U_132),U_134)))
| ~ hBOOL(hAPP(fun(U_135,bool),bool,hAPP(U_135,fun(fun(U_135,bool),bool),member(U_135),U_131),U_134))
| ti(U_136,U_133) != hAPP(U_135,U_136,U_132,U_131) ),
inference(definitional_conversion,[status(esa)],[f_63_2]) ).
cnf(f_63_4,plain,
( hBOOL(hAPP(fun(U_136,bool),bool,hAPP(U_136,fun(fun(U_136,bool),bool),member(U_136),U_133),hAPP(fun(U_135,bool),fun(U_136,bool),hAPP(fun(U_135,U_136),fun(fun(U_135,bool),fun(U_136,bool)),image(U_135,U_136),U_132),U_134)))
| ~ hBOOL(hAPP(fun(U_135,bool),bool,hAPP(U_135,fun(fun(U_135,bool),bool),member(U_135),U_131),U_134))
| ti(U_136,U_133) != hAPP(U_135,U_136,U_132,U_131) ),
inference(clausify,[status(thm)],[f_63_3]) ).
fof(f_64_1,plain,
! [X_a,A_3,A_1] :
( ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1))
| ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) ),
inference(fof_nnf,[status(thm)],[fact_26_equals0D]) ).
fof(f_64_2,plain,
! [U_139,U_138,U_137] :
( ~ hBOOL(hAPP(fun(U_139,bool),bool,hAPP(U_139,fun(fun(U_139,bool),bool),member(U_139),U_138),U_137))
| ti(fun(U_139,bool),U_137) != bot_bot(fun(U_139,bool)) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
! [U_137,U_138,U_139] :
( ~ hBOOL(hAPP(fun(U_139,bool),bool,hAPP(U_139,fun(fun(U_139,bool),bool),member(U_139),U_138),U_137))
| ti(fun(U_139,bool),U_137) != bot_bot(fun(U_139,bool)) ),
inference(definitional_conversion,[status(esa)],[f_64_2]) ).
cnf(f_64_4,plain,
( ~ hBOOL(hAPP(fun(U_139,bool),bool,hAPP(U_139,fun(fun(U_139,bool),bool),member(U_139),U_138),U_137))
| ti(fun(U_139,bool),U_137) != bot_bot(fun(U_139,bool)) ),
inference(clausify,[status(thm)],[f_64_3]) ).
fof(f_65_1,plain,
! [X_a,P_1] :
( ( hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1) = bot_bot(fun(X_a,bool))
| ? [X_1] : hBOOL(hAPP(X_a,bool,P_1,X_1)) )
& ( ! [X_1] : ~ hBOOL(hAPP(X_a,bool,P_1,X_1))
| hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1) != bot_bot(fun(X_a,bool)) ) ),
inference(fof_nnf,[status(thm)],[fact_27_Collect__empty__eq]) ).
fof(f_65_2,plain,
! [U_143,U_142] :
( ( hAPP(fun(U_143,bool),fun(U_143,bool),collect(U_143),U_142) = bot_bot(fun(U_143,bool))
| ? [U_141] : hBOOL(hAPP(U_143,bool,U_142,U_141)) )
& ( ! [U_140] : ~ hBOOL(hAPP(U_143,bool,U_142,U_140))
| hAPP(fun(U_143,bool),fun(U_143,bool),collect(U_143),U_142) != bot_bot(fun(U_143,bool)) ) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
( ! [U_147,U_145] :
( hAPP(fun(U_147,bool),fun(U_147,bool),collect(U_147),U_145) = bot_bot(fun(U_147,bool))
| ? [U_141] : hBOOL(hAPP(U_147,bool,U_145,U_141)) )
& ! [U_146,U_144] :
( ! [U_140] : ~ hBOOL(hAPP(U_146,bool,U_144,U_140))
| hAPP(fun(U_146,bool),fun(U_146,bool),collect(U_146),U_144) != bot_bot(fun(U_146,bool)) ) ),
inference(miniscope,[status(thm)],[f_65_2]) ).
fof(f_65_4,plain,
( ! [U_147,U_145] :
( hAPP(fun(U_147,bool),fun(U_147,bool),collect(U_147),U_145) = bot_bot(fun(U_147,bool))
| hBOOL(hAPP(U_147,bool,U_145,sK1(U_147,U_145))) )
& ! [U_146,U_144] :
( ! [U_140] : ~ hBOOL(hAPP(U_146,bool,U_144,U_140))
| hAPP(fun(U_146,bool),fun(U_146,bool),collect(U_146),U_144) != bot_bot(fun(U_146,bool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_141,sK1(U_147,U_145))],[f_65_3]) ).
fof(f_65_5,plain,
( ! [U_145,U_147] :
( hAPP(fun(U_147,bool),fun(U_147,bool),collect(U_147),U_145) = bot_bot(fun(U_147,bool))
| hBOOL(hAPP(U_147,bool,U_145,sK1(U_147,U_145))) )
& ! [U_140,U_146,U_144] :
( ~ hBOOL(hAPP(U_146,bool,U_144,U_140))
| hAPP(fun(U_146,bool),fun(U_146,bool),collect(U_146),U_144) != bot_bot(fun(U_146,bool)) ) ),
inference(definitional_conversion,[status(esa)],[f_65_4]) ).
cnf(f_65_6,plain,
( ~ hBOOL(hAPP(U_146,bool,U_144,U_140))
| hAPP(fun(U_146,bool),fun(U_146,bool),collect(U_146),U_144) != bot_bot(fun(U_146,bool)) ),
inference(clausify,[status(thm)],[f_65_5]) ).
cnf(f_65_7,plain,
( hAPP(fun(U_147,bool),fun(U_147,bool),collect(U_147),U_145) = bot_bot(fun(U_147,bool))
| hBOOL(hAPP(U_147,bool,U_145,sK1(U_147,U_145))) ),
inference(clausify,[status(thm)],[f_65_5]) ).
fof(f_66_1,plain,
! [X_a,C_1] : ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),bot_bot(fun(X_a,bool)))),
inference(fof_nnf,[status(thm)],[fact_28_empty__iff]) ).
fof(f_66_2,plain,
! [U_149,U_148] : ~ hBOOL(hAPP(fun(U_149,bool),bool,hAPP(U_149,fun(fun(U_149,bool),bool),member(U_149),U_148),bot_bot(fun(U_149,bool)))),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
! [U_149,U_148] : ~ hBOOL(hAPP(fun(U_149,bool),bool,hAPP(U_149,fun(fun(U_149,bool),bool),member(U_149),U_148),bot_bot(fun(U_149,bool)))),
inference(definitional_conversion,[status(esa)],[f_66_2]) ).
cnf(f_66_4,plain,
~ hBOOL(hAPP(fun(U_149,bool),bool,hAPP(U_149,fun(fun(U_149,bool),bool),member(U_149),U_148),bot_bot(fun(U_149,bool)))),
inference(clausify,[status(thm)],[f_66_3]) ).
fof(f_67_1,plain,
! [X_a,P_1] :
( ( bot_bot(fun(X_a,bool)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)
| ? [X_1] : hBOOL(hAPP(X_a,bool,P_1,X_1)) )
& ( ! [X_1] : ~ hBOOL(hAPP(X_a,bool,P_1,X_1))
| bot_bot(fun(X_a,bool)) != hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1) ) ),
inference(fof_nnf,[status(thm)],[fact_29_empty__Collect__eq]) ).
fof(f_67_2,plain,
! [U_153,U_152] :
( ( bot_bot(fun(U_153,bool)) = hAPP(fun(U_153,bool),fun(U_153,bool),collect(U_153),U_152)
| ? [U_151] : hBOOL(hAPP(U_153,bool,U_152,U_151)) )
& ( ! [U_150] : ~ hBOOL(hAPP(U_153,bool,U_152,U_150))
| bot_bot(fun(U_153,bool)) != hAPP(fun(U_153,bool),fun(U_153,bool),collect(U_153),U_152) ) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
( ! [U_157,U_155] :
( bot_bot(fun(U_157,bool)) = hAPP(fun(U_157,bool),fun(U_157,bool),collect(U_157),U_155)
| ? [U_151] : hBOOL(hAPP(U_157,bool,U_155,U_151)) )
& ! [U_156,U_154] :
( ! [U_150] : ~ hBOOL(hAPP(U_156,bool,U_154,U_150))
| bot_bot(fun(U_156,bool)) != hAPP(fun(U_156,bool),fun(U_156,bool),collect(U_156),U_154) ) ),
inference(miniscope,[status(thm)],[f_67_2]) ).
fof(f_67_4,plain,
( ! [U_157,U_155] :
( bot_bot(fun(U_157,bool)) = hAPP(fun(U_157,bool),fun(U_157,bool),collect(U_157),U_155)
| hBOOL(hAPP(U_157,bool,U_155,sK2(U_157,U_155))) )
& ! [U_156,U_154] :
( ! [U_150] : ~ hBOOL(hAPP(U_156,bool,U_154,U_150))
| bot_bot(fun(U_156,bool)) != hAPP(fun(U_156,bool),fun(U_156,bool),collect(U_156),U_154) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_151,sK2(U_157,U_155))],[f_67_3]) ).
fof(f_67_5,plain,
( ! [U_157,U_155] :
( bot_bot(fun(U_157,bool)) = hAPP(fun(U_157,bool),fun(U_157,bool),collect(U_157),U_155)
| hBOOL(hAPP(U_157,bool,U_155,sK2(U_157,U_155))) )
& ! [U_150,U_156,U_154] :
( ~ hBOOL(hAPP(U_156,bool,U_154,U_150))
| bot_bot(fun(U_156,bool)) != hAPP(fun(U_156,bool),fun(U_156,bool),collect(U_156),U_154) ) ),
inference(definitional_conversion,[status(esa)],[f_67_4]) ).
cnf(f_67_6,plain,
( ~ hBOOL(hAPP(U_156,bool,U_154,U_150))
| bot_bot(fun(U_156,bool)) != hAPP(fun(U_156,bool),fun(U_156,bool),collect(U_156),U_154) ),
inference(clausify,[status(thm)],[f_67_5]) ).
cnf(f_67_7,plain,
( bot_bot(fun(U_157,bool)) = hAPP(fun(U_157,bool),fun(U_157,bool),collect(U_157),U_155)
| hBOOL(hAPP(U_157,bool,U_155,sK2(U_157,U_155))) ),
inference(clausify,[status(thm)],[f_67_5]) ).
fof(f_68_1,plain,
! [X_a,A_1] :
( ( ? [X_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
| ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool)) )
& ( ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool))
| ! [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)) ) ),
inference(fof_nnf,[status(thm)],[fact_30_ex__in__conv]) ).
fof(f_68_2,plain,
! [U_161,U_160] :
( ( ? [U_159] : hBOOL(hAPP(fun(U_161,bool),bool,hAPP(U_161,fun(fun(U_161,bool),bool),member(U_161),U_159),U_160))
| ti(fun(U_161,bool),U_160) = bot_bot(fun(U_161,bool)) )
& ( ti(fun(U_161,bool),U_160) != bot_bot(fun(U_161,bool))
| ! [U_158] : ~ hBOOL(hAPP(fun(U_161,bool),bool,hAPP(U_161,fun(fun(U_161,bool),bool),member(U_161),U_158),U_160)) ) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
( ! [U_165,U_163] :
( ? [U_159] : hBOOL(hAPP(fun(U_165,bool),bool,hAPP(U_165,fun(fun(U_165,bool),bool),member(U_165),U_159),U_163))
| ti(fun(U_165,bool),U_163) = bot_bot(fun(U_165,bool)) )
& ! [U_164,U_162] :
( ti(fun(U_164,bool),U_162) != bot_bot(fun(U_164,bool))
| ! [U_158] : ~ hBOOL(hAPP(fun(U_164,bool),bool,hAPP(U_164,fun(fun(U_164,bool),bool),member(U_164),U_158),U_162)) ) ),
inference(miniscope,[status(thm)],[f_68_2]) ).
fof(f_68_4,plain,
( ! [U_165,U_163] :
( hBOOL(hAPP(fun(U_165,bool),bool,hAPP(U_165,fun(fun(U_165,bool),bool),member(U_165),sK3(U_165,U_163)),U_163))
| ti(fun(U_165,bool),U_163) = bot_bot(fun(U_165,bool)) )
& ! [U_164,U_162] :
( ti(fun(U_164,bool),U_162) != bot_bot(fun(U_164,bool))
| ! [U_158] : ~ hBOOL(hAPP(fun(U_164,bool),bool,hAPP(U_164,fun(fun(U_164,bool),bool),member(U_164),U_158),U_162)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_159,sK3(U_165,U_163))],[f_68_3]) ).
fof(f_68_5,plain,
( ! [U_163,U_165] :
( hBOOL(hAPP(fun(U_165,bool),bool,hAPP(U_165,fun(fun(U_165,bool),bool),member(U_165),sK3(U_165,U_163)),U_163))
| ti(fun(U_165,bool),U_163) = bot_bot(fun(U_165,bool)) )
& ! [U_158,U_162,U_164] :
( ti(fun(U_164,bool),U_162) != bot_bot(fun(U_164,bool))
| ~ hBOOL(hAPP(fun(U_164,bool),bool,hAPP(U_164,fun(fun(U_164,bool),bool),member(U_164),U_158),U_162)) ) ),
inference(definitional_conversion,[status(esa)],[f_68_4]) ).
cnf(f_68_6,plain,
( ti(fun(U_164,bool),U_162) != bot_bot(fun(U_164,bool))
| ~ hBOOL(hAPP(fun(U_164,bool),bool,hAPP(U_164,fun(fun(U_164,bool),bool),member(U_164),U_158),U_162)) ),
inference(clausify,[status(thm)],[f_68_5]) ).
cnf(f_68_7,plain,
( hBOOL(hAPP(fun(U_165,bool),bool,hAPP(U_165,fun(fun(U_165,bool),bool),member(U_165),sK3(U_165,U_163)),U_163))
| ti(fun(U_165,bool),U_163) = bot_bot(fun(U_165,bool)) ),
inference(clausify,[status(thm)],[f_68_5]) ).
fof(f_69_1,plain,
! [X_a,A_1] :
( ( ! [X_1] : ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
| ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) )
& ( ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool))
| ? [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)) ) ),
inference(fof_nnf,[status(thm)],[fact_31_all__not__in__conv]) ).
fof(f_69_2,plain,
! [U_169,U_168] :
( ( ! [U_167] : ~ hBOOL(hAPP(fun(U_169,bool),bool,hAPP(U_169,fun(fun(U_169,bool),bool),member(U_169),U_167),U_168))
| ti(fun(U_169,bool),U_168) != bot_bot(fun(U_169,bool)) )
& ( ti(fun(U_169,bool),U_168) = bot_bot(fun(U_169,bool))
| ? [U_166] : hBOOL(hAPP(fun(U_169,bool),bool,hAPP(U_169,fun(fun(U_169,bool),bool),member(U_169),U_166),U_168)) ) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
( ! [U_173,U_171] :
( ! [U_167] : ~ hBOOL(hAPP(fun(U_173,bool),bool,hAPP(U_173,fun(fun(U_173,bool),bool),member(U_173),U_167),U_171))
| ti(fun(U_173,bool),U_171) != bot_bot(fun(U_173,bool)) )
& ! [U_172,U_170] :
( ti(fun(U_172,bool),U_170) = bot_bot(fun(U_172,bool))
| ? [U_166] : hBOOL(hAPP(fun(U_172,bool),bool,hAPP(U_172,fun(fun(U_172,bool),bool),member(U_172),U_166),U_170)) ) ),
inference(miniscope,[status(thm)],[f_69_2]) ).
fof(f_69_4,plain,
( ! [U_173,U_171] :
( ! [U_167] : ~ hBOOL(hAPP(fun(U_173,bool),bool,hAPP(U_173,fun(fun(U_173,bool),bool),member(U_173),U_167),U_171))
| ti(fun(U_173,bool),U_171) != bot_bot(fun(U_173,bool)) )
& ! [U_172,U_170] :
( ti(fun(U_172,bool),U_170) = bot_bot(fun(U_172,bool))
| hBOOL(hAPP(fun(U_172,bool),bool,hAPP(U_172,fun(fun(U_172,bool),bool),member(U_172),sK4(U_172,U_170)),U_170)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_166,sK4(U_172,U_170))],[f_69_3]) ).
fof(f_69_5,plain,
( ! [U_167,U_171,U_173] :
( ~ hBOOL(hAPP(fun(U_173,bool),bool,hAPP(U_173,fun(fun(U_173,bool),bool),member(U_173),U_167),U_171))
| ti(fun(U_173,bool),U_171) != bot_bot(fun(U_173,bool)) )
& ! [U_170,U_172] :
( ti(fun(U_172,bool),U_170) = bot_bot(fun(U_172,bool))
| hBOOL(hAPP(fun(U_172,bool),bool,hAPP(U_172,fun(fun(U_172,bool),bool),member(U_172),sK4(U_172,U_170)),U_170)) ) ),
inference(definitional_conversion,[status(esa)],[f_69_4]) ).
cnf(f_69_6,plain,
( ti(fun(U_172,bool),U_170) = bot_bot(fun(U_172,bool))
| hBOOL(hAPP(fun(U_172,bool),bool,hAPP(U_172,fun(fun(U_172,bool),bool),member(U_172),sK4(U_172,U_170)),U_170)) ),
inference(clausify,[status(thm)],[f_69_5]) ).
cnf(f_69_7,plain,
( ~ hBOOL(hAPP(fun(U_173,bool),bool,hAPP(U_173,fun(fun(U_173,bool),bool),member(U_173),U_167),U_171))
| ti(fun(U_173,bool),U_171) != bot_bot(fun(U_173,bool)) ),
inference(clausify,[status(thm)],[f_69_5]) ).
fof(f_70_1,plain,
! [X_a] : bot_bot(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),fFalse)),
inference(fof_nnf,[status(thm)],[fact_32_empty__def]) ).
fof(f_70_2,plain,
! [U_174] : bot_bot(fun(U_174,bool)) = hAPP(fun(U_174,bool),fun(U_174,bool),collect(U_174),hAPP(bool,fun(U_174,bool),combk(bool,U_174),fFalse)),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
! [U_174] : bot_bot(fun(U_174,bool)) = hAPP(fun(U_174,bool),fun(U_174,bool),collect(U_174),hAPP(bool,fun(U_174,bool),combk(bool,U_174),fFalse)),
inference(definitional_conversion,[status(esa)],[f_70_2]) ).
cnf(f_70_4,plain,
bot_bot(fun(U_174,bool)) = hAPP(fun(U_174,bool),fun(U_174,bool),collect(U_174),hAPP(bool,fun(U_174,bool),combk(bool,U_174),fFalse)),
inference(clausify,[status(thm)],[f_70_3]) ).
fof(f_71_1,plain,
! [X_a] :
( ! [A_1] : hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1))
| ~ finite_finite_1(X_a) ),
inference(fof_nnf,[status(thm)],[fact_33_finite__code]) ).
fof(f_71_2,plain,
! [U_176] :
( ! [U_175] : hBOOL(hAPP(fun(U_176,bool),bool,finite_finite(U_176),U_175))
| ~ finite_finite_1(U_176) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
! [U_175,U_176] :
( hBOOL(hAPP(fun(U_176,bool),bool,finite_finite(U_176),U_175))
| ~ finite_finite_1(U_176) ),
inference(definitional_conversion,[status(esa)],[f_71_2]) ).
cnf(f_71_4,plain,
( hBOOL(hAPP(fun(U_176,bool),bool,finite_finite(U_176),U_175))
| ~ finite_finite_1(U_176) ),
inference(clausify,[status(thm)],[f_71_3]) ).
fof(f_72_1,plain,
! [X_a] :
( ! [A_1] : hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1))
| ~ finite_finite_1(X_a) ),
inference(fof_nnf,[status(thm)],[fact_34_finite]) ).
fof(f_72_2,plain,
! [U_178] :
( ! [U_177] : hBOOL(hAPP(fun(U_178,bool),bool,finite_finite(U_178),U_177))
| ~ finite_finite_1(U_178) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
! [U_177,U_178] :
( hBOOL(hAPP(fun(U_178,bool),bool,finite_finite(U_178),U_177))
| ~ finite_finite_1(U_178) ),
inference(definitional_conversion,[status(esa)],[f_72_2]) ).
cnf(f_72_4,plain,
( hBOOL(hAPP(fun(U_178,bool),bool,finite_finite(U_178),U_177))
| ~ finite_finite_1(U_178) ),
inference(clausify,[status(thm)],[f_72_3]) ).
fof(f_73_1,plain,
! [X_a,A_3,A_1] :
( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),A_1) = ti(fun(X_a,bool),A_1)
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1)) ),
inference(fof_nnf,[status(thm)],[fact_35_insert__absorb]) ).
fof(f_73_2,plain,
! [U_181,U_180,U_179] :
( hAPP(fun(U_181,bool),fun(U_181,bool),hAPP(U_181,fun(fun(U_181,bool),fun(U_181,bool)),insert(U_181),U_180),U_179) = ti(fun(U_181,bool),U_179)
| ~ hBOOL(hAPP(fun(U_181,bool),bool,hAPP(U_181,fun(fun(U_181,bool),bool),member(U_181),U_180),U_179)) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
! [U_179,U_181,U_180] :
( hAPP(fun(U_181,bool),fun(U_181,bool),hAPP(U_181,fun(fun(U_181,bool),fun(U_181,bool)),insert(U_181),U_180),U_179) = ti(fun(U_181,bool),U_179)
| ~ hBOOL(hAPP(fun(U_181,bool),bool,hAPP(U_181,fun(fun(U_181,bool),bool),member(U_181),U_180),U_179)) ),
inference(definitional_conversion,[status(esa)],[f_73_2]) ).
cnf(f_73_4,plain,
( hAPP(fun(U_181,bool),fun(U_181,bool),hAPP(U_181,fun(fun(U_181,bool),fun(U_181,bool)),insert(U_181),U_180),U_179) = ti(fun(U_181,bool),U_179)
| ~ hBOOL(hAPP(fun(U_181,bool),bool,hAPP(U_181,fun(fun(U_181,bool),bool),member(U_181),U_180),U_179)) ),
inference(clausify,[status(thm)],[f_73_3]) ).
fof(f_74_1,plain,
! [X_a,B_1,A_3,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),B)))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),B)) ),
inference(fof_nnf,[status(thm)],[fact_36_insertI2]) ).
fof(f_74_2,plain,
! [U_185,U_184,U_183,U_182] :
( hBOOL(hAPP(fun(U_185,bool),bool,hAPP(U_185,fun(fun(U_185,bool),bool),member(U_185),U_183),hAPP(fun(U_185,bool),fun(U_185,bool),hAPP(U_185,fun(fun(U_185,bool),fun(U_185,bool)),insert(U_185),U_184),U_182)))
| ~ hBOOL(hAPP(fun(U_185,bool),bool,hAPP(U_185,fun(fun(U_185,bool),bool),member(U_185),U_183),U_182)) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
fof(f_74_3,plain,
! [U_183,U_185,U_182,U_184] :
( hBOOL(hAPP(fun(U_185,bool),bool,hAPP(U_185,fun(fun(U_185,bool),bool),member(U_185),U_183),hAPP(fun(U_185,bool),fun(U_185,bool),hAPP(U_185,fun(fun(U_185,bool),fun(U_185,bool)),insert(U_185),U_184),U_182)))
| ~ hBOOL(hAPP(fun(U_185,bool),bool,hAPP(U_185,fun(fun(U_185,bool),bool),member(U_185),U_183),U_182)) ),
inference(definitional_conversion,[status(esa)],[f_74_2]) ).
cnf(f_74_4,plain,
( hBOOL(hAPP(fun(U_185,bool),bool,hAPP(U_185,fun(fun(U_185,bool),bool),member(U_185),U_183),hAPP(fun(U_185,bool),fun(U_185,bool),hAPP(U_185,fun(fun(U_185,bool),fun(U_185,bool)),insert(U_185),U_184),U_182)))
| ~ hBOOL(hAPP(fun(U_185,bool),bool,hAPP(U_185,fun(fun(U_185,bool),bool),member(U_185),U_183),U_182)) ),
inference(clausify,[status(thm)],[f_74_3]) ).
fof(f_75_1,plain,
! [X_a,B,X_2,A_1] :
( ( ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),B)
| ti(fun(X_a,bool),A_1) != ti(fun(X_a,bool),B) )
& ( ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
| hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1) != hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),B) ) )
| hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B))
| hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) ),
inference(fof_nnf,[status(thm)],[fact_37_insert__ident]) ).
fof(f_75_2,plain,
! [U_189,U_188,U_187,U_186] :
( ( ( hAPP(fun(U_189,bool),fun(U_189,bool),hAPP(U_189,fun(fun(U_189,bool),fun(U_189,bool)),insert(U_189),U_187),U_186) = hAPP(fun(U_189,bool),fun(U_189,bool),hAPP(U_189,fun(fun(U_189,bool),fun(U_189,bool)),insert(U_189),U_187),U_188)
| ti(fun(U_189,bool),U_186) != ti(fun(U_189,bool),U_188) )
& ( ti(fun(U_189,bool),U_186) = ti(fun(U_189,bool),U_188)
| hAPP(fun(U_189,bool),fun(U_189,bool),hAPP(U_189,fun(fun(U_189,bool),fun(U_189,bool)),insert(U_189),U_187),U_186) != hAPP(fun(U_189,bool),fun(U_189,bool),hAPP(U_189,fun(fun(U_189,bool),fun(U_189,bool)),insert(U_189),U_187),U_188) ) )
| hBOOL(hAPP(fun(U_189,bool),bool,hAPP(U_189,fun(fun(U_189,bool),bool),member(U_189),U_187),U_188))
| hBOOL(hAPP(fun(U_189,bool),bool,hAPP(U_189,fun(fun(U_189,bool),bool),member(U_189),U_187),U_186)) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
fof(f_75_3,plain,
( ! [U_186,U_187,U_188,U_189] :
( hAPP(fun(U_189,bool),fun(U_189,bool),hAPP(U_189,fun(fun(U_189,bool),fun(U_189,bool)),insert(U_189),U_187),U_186) = hAPP(fun(U_189,bool),fun(U_189,bool),hAPP(U_189,fun(fun(U_189,bool),fun(U_189,bool)),insert(U_189),U_187),U_188)
| ti(fun(U_189,bool),U_186) != ti(fun(U_189,bool),U_188)
| ~ sP3(U_186,U_187,U_188,U_189) )
& ! [U_186,U_187,U_188,U_189] :
( ti(fun(U_189,bool),U_186) = ti(fun(U_189,bool),U_188)
| hAPP(fun(U_189,bool),fun(U_189,bool),hAPP(U_189,fun(fun(U_189,bool),fun(U_189,bool)),insert(U_189),U_187),U_186) != hAPP(fun(U_189,bool),fun(U_189,bool),hAPP(U_189,fun(fun(U_189,bool),fun(U_189,bool)),insert(U_189),U_187),U_188)
| ~ sP3(U_186,U_187,U_188,U_189) )
& ! [U_186,U_187,U_188,U_189] :
( sP3(U_186,U_187,U_188,U_189)
| hBOOL(hAPP(fun(U_189,bool),bool,hAPP(U_189,fun(fun(U_189,bool),bool),member(U_189),U_187),U_188))
| hBOOL(hAPP(fun(U_189,bool),bool,hAPP(U_189,fun(fun(U_189,bool),bool),member(U_189),U_187),U_186)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_75_2]) ).
cnf(f_75_4,plain,
( sP3(U_186,U_187,U_188,U_189)
| hBOOL(hAPP(fun(U_189,bool),bool,hAPP(U_189,fun(fun(U_189,bool),bool),member(U_189),U_187),U_188))
| hBOOL(hAPP(fun(U_189,bool),bool,hAPP(U_189,fun(fun(U_189,bool),bool),member(U_189),U_187),U_186)) ),
inference(clausify,[status(thm)],[f_75_3]) ).
cnf(f_75_5,plain,
( ti(fun(U_189,bool),U_186) = ti(fun(U_189,bool),U_188)
| hAPP(fun(U_189,bool),fun(U_189,bool),hAPP(U_189,fun(fun(U_189,bool),fun(U_189,bool)),insert(U_189),U_187),U_186) != hAPP(fun(U_189,bool),fun(U_189,bool),hAPP(U_189,fun(fun(U_189,bool),fun(U_189,bool)),insert(U_189),U_187),U_188)
| ~ sP3(U_186,U_187,U_188,U_189) ),
inference(clausify,[status(thm)],[f_75_3]) ).
cnf(f_75_6,plain,
( hAPP(fun(U_189,bool),fun(U_189,bool),hAPP(U_189,fun(fun(U_189,bool),fun(U_189,bool)),insert(U_189),U_187),U_186) = hAPP(fun(U_189,bool),fun(U_189,bool),hAPP(U_189,fun(fun(U_189,bool),fun(U_189,bool)),insert(U_189),U_187),U_188)
| ti(fun(U_189,bool),U_186) != ti(fun(U_189,bool),U_188)
| ~ sP3(U_186,U_187,U_188,U_189) ),
inference(clausify,[status(thm)],[f_75_3]) ).
fof(f_76_1,plain,
! [X_a,Y_3,A_1,X_2] :
( ( hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_3),A_1),X_2))
| ( ~ hBOOL(hAPP(X_a,bool,A_1,X_2))
& ti(X_a,Y_3) != ti(X_a,X_2) ) )
& ( hBOOL(hAPP(X_a,bool,A_1,X_2))
| ti(X_a,Y_3) = ti(X_a,X_2)
| ~ hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_3),A_1),X_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_38_insert__code]) ).
fof(f_76_2,plain,
! [U_193,U_192,U_191,U_190] :
( ( hBOOL(hAPP(U_193,bool,hAPP(fun(U_193,bool),fun(U_193,bool),hAPP(U_193,fun(fun(U_193,bool),fun(U_193,bool)),insert(U_193),U_192),U_191),U_190))
| ( ~ hBOOL(hAPP(U_193,bool,U_191,U_190))
& ti(U_193,U_192) != ti(U_193,U_190) ) )
& ( hBOOL(hAPP(U_193,bool,U_191,U_190))
| ti(U_193,U_192) = ti(U_193,U_190)
| ~ hBOOL(hAPP(U_193,bool,hAPP(fun(U_193,bool),fun(U_193,bool),hAPP(U_193,fun(fun(U_193,bool),fun(U_193,bool)),insert(U_193),U_192),U_191),U_190)) ) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
fof(f_76_3,plain,
( ! [U_201,U_199,U_197,U_195] :
( hBOOL(hAPP(U_201,bool,hAPP(fun(U_201,bool),fun(U_201,bool),hAPP(U_201,fun(fun(U_201,bool),fun(U_201,bool)),insert(U_201),U_199),U_197),U_195))
| ( ~ hBOOL(hAPP(U_201,bool,U_197,U_195))
& ti(U_201,U_199) != ti(U_201,U_195) ) )
& ! [U_200,U_198,U_196,U_194] :
( hBOOL(hAPP(U_200,bool,U_196,U_194))
| ti(U_200,U_198) = ti(U_200,U_194)
| ~ hBOOL(hAPP(U_200,bool,hAPP(fun(U_200,bool),fun(U_200,bool),hAPP(U_200,fun(fun(U_200,bool),fun(U_200,bool)),insert(U_200),U_198),U_196),U_194)) ) ),
inference(miniscope,[status(thm)],[f_76_2]) ).
fof(f_76_4,plain,
( ! [U_195,U_199,U_197,U_201] :
( ~ hBOOL(hAPP(U_201,bool,U_197,U_195))
| ~ sP4(U_195,U_199,U_197,U_201) )
& ! [U_195,U_199,U_197,U_201] :
( ti(U_201,U_199) != ti(U_201,U_195)
| ~ sP4(U_195,U_199,U_197,U_201) )
& ! [U_195,U_199,U_197,U_201] :
( hBOOL(hAPP(U_201,bool,hAPP(fun(U_201,bool),fun(U_201,bool),hAPP(U_201,fun(fun(U_201,bool),fun(U_201,bool)),insert(U_201),U_199),U_197),U_195))
| sP4(U_195,U_199,U_197,U_201) )
& ! [U_194,U_196,U_198,U_200] :
( hBOOL(hAPP(U_200,bool,U_196,U_194))
| ti(U_200,U_198) = ti(U_200,U_194)
| ~ hBOOL(hAPP(U_200,bool,hAPP(fun(U_200,bool),fun(U_200,bool),hAPP(U_200,fun(fun(U_200,bool),fun(U_200,bool)),insert(U_200),U_198),U_196),U_194)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_76_3]) ).
cnf(f_76_5,plain,
( hBOOL(hAPP(U_200,bool,U_196,U_194))
| ti(U_200,U_198) = ti(U_200,U_194)
| ~ hBOOL(hAPP(U_200,bool,hAPP(fun(U_200,bool),fun(U_200,bool),hAPP(U_200,fun(fun(U_200,bool),fun(U_200,bool)),insert(U_200),U_198),U_196),U_194)) ),
inference(clausify,[status(thm)],[f_76_4]) ).
cnf(f_76_6,plain,
( hBOOL(hAPP(U_201,bool,hAPP(fun(U_201,bool),fun(U_201,bool),hAPP(U_201,fun(fun(U_201,bool),fun(U_201,bool)),insert(U_201),U_199),U_197),U_195))
| sP4(U_195,U_199,U_197,U_201) ),
inference(clausify,[status(thm)],[f_76_4]) ).
cnf(f_76_7,plain,
( ti(U_201,U_199) != ti(U_201,U_195)
| ~ sP4(U_195,U_199,U_197,U_201) ),
inference(clausify,[status(thm)],[f_76_4]) ).
cnf(f_76_8,plain,
( ~ hBOOL(hAPP(U_201,bool,U_197,U_195))
| ~ sP4(U_195,U_199,U_197,U_201) ),
inference(clausify,[status(thm)],[f_76_4]) ).
fof(f_77_1,plain,
! [X_a,A_3,B_1,A_1] :
( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),A_1)))
| ( ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1))
& ti(X_a,A_3) != ti(X_a,B_1) ) )
& ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),A_1))
| ti(X_a,A_3) = ti(X_a,B_1)
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),A_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_39_insert__iff]) ).
fof(f_77_2,plain,
! [U_205,U_204,U_203,U_202] :
( ( hBOOL(hAPP(fun(U_205,bool),bool,hAPP(U_205,fun(fun(U_205,bool),bool),member(U_205),U_204),hAPP(fun(U_205,bool),fun(U_205,bool),hAPP(U_205,fun(fun(U_205,bool),fun(U_205,bool)),insert(U_205),U_203),U_202)))
| ( ~ hBOOL(hAPP(fun(U_205,bool),bool,hAPP(U_205,fun(fun(U_205,bool),bool),member(U_205),U_204),U_202))
& ti(U_205,U_204) != ti(U_205,U_203) ) )
& ( hBOOL(hAPP(fun(U_205,bool),bool,hAPP(U_205,fun(fun(U_205,bool),bool),member(U_205),U_204),U_202))
| ti(U_205,U_204) = ti(U_205,U_203)
| ~ hBOOL(hAPP(fun(U_205,bool),bool,hAPP(U_205,fun(fun(U_205,bool),bool),member(U_205),U_204),hAPP(fun(U_205,bool),fun(U_205,bool),hAPP(U_205,fun(fun(U_205,bool),fun(U_205,bool)),insert(U_205),U_203),U_202))) ) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
( ! [U_213,U_211,U_209,U_207] :
( hBOOL(hAPP(fun(U_213,bool),bool,hAPP(U_213,fun(fun(U_213,bool),bool),member(U_213),U_211),hAPP(fun(U_213,bool),fun(U_213,bool),hAPP(U_213,fun(fun(U_213,bool),fun(U_213,bool)),insert(U_213),U_209),U_207)))
| ( ~ hBOOL(hAPP(fun(U_213,bool),bool,hAPP(U_213,fun(fun(U_213,bool),bool),member(U_213),U_211),U_207))
& ti(U_213,U_211) != ti(U_213,U_209) ) )
& ! [U_212,U_210,U_208,U_206] :
( hBOOL(hAPP(fun(U_212,bool),bool,hAPP(U_212,fun(fun(U_212,bool),bool),member(U_212),U_210),U_206))
| ti(U_212,U_210) = ti(U_212,U_208)
| ~ hBOOL(hAPP(fun(U_212,bool),bool,hAPP(U_212,fun(fun(U_212,bool),bool),member(U_212),U_210),hAPP(fun(U_212,bool),fun(U_212,bool),hAPP(U_212,fun(fun(U_212,bool),fun(U_212,bool)),insert(U_212),U_208),U_206))) ) ),
inference(miniscope,[status(thm)],[f_77_2]) ).
fof(f_77_4,plain,
( ! [U_209,U_207,U_211,U_213] :
( ~ hBOOL(hAPP(fun(U_213,bool),bool,hAPP(U_213,fun(fun(U_213,bool),bool),member(U_213),U_211),U_207))
| ~ sP5(U_209,U_207,U_211,U_213) )
& ! [U_209,U_207,U_211,U_213] :
( ti(U_213,U_211) != ti(U_213,U_209)
| ~ sP5(U_209,U_207,U_211,U_213) )
& ! [U_209,U_207,U_211,U_213] :
( hBOOL(hAPP(fun(U_213,bool),bool,hAPP(U_213,fun(fun(U_213,bool),bool),member(U_213),U_211),hAPP(fun(U_213,bool),fun(U_213,bool),hAPP(U_213,fun(fun(U_213,bool),fun(U_213,bool)),insert(U_213),U_209),U_207)))
| sP5(U_209,U_207,U_211,U_213) )
& ! [U_212,U_208,U_206,U_210] :
( hBOOL(hAPP(fun(U_212,bool),bool,hAPP(U_212,fun(fun(U_212,bool),bool),member(U_212),U_210),U_206))
| ti(U_212,U_210) = ti(U_212,U_208)
| ~ hBOOL(hAPP(fun(U_212,bool),bool,hAPP(U_212,fun(fun(U_212,bool),bool),member(U_212),U_210),hAPP(fun(U_212,bool),fun(U_212,bool),hAPP(U_212,fun(fun(U_212,bool),fun(U_212,bool)),insert(U_212),U_208),U_206))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_77_3]) ).
cnf(f_77_5,plain,
( hBOOL(hAPP(fun(U_212,bool),bool,hAPP(U_212,fun(fun(U_212,bool),bool),member(U_212),U_210),U_206))
| ti(U_212,U_210) = ti(U_212,U_208)
| ~ hBOOL(hAPP(fun(U_212,bool),bool,hAPP(U_212,fun(fun(U_212,bool),bool),member(U_212),U_210),hAPP(fun(U_212,bool),fun(U_212,bool),hAPP(U_212,fun(fun(U_212,bool),fun(U_212,bool)),insert(U_212),U_208),U_206))) ),
inference(clausify,[status(thm)],[f_77_4]) ).
cnf(f_77_6,plain,
( hBOOL(hAPP(fun(U_213,bool),bool,hAPP(U_213,fun(fun(U_213,bool),bool),member(U_213),U_211),hAPP(fun(U_213,bool),fun(U_213,bool),hAPP(U_213,fun(fun(U_213,bool),fun(U_213,bool)),insert(U_213),U_209),U_207)))
| sP5(U_209,U_207,U_211,U_213) ),
inference(clausify,[status(thm)],[f_77_4]) ).
cnf(f_77_7,plain,
( ti(U_213,U_211) != ti(U_213,U_209)
| ~ sP5(U_209,U_207,U_211,U_213) ),
inference(clausify,[status(thm)],[f_77_4]) ).
cnf(f_77_8,plain,
( ~ hBOOL(hAPP(fun(U_213,bool),bool,hAPP(U_213,fun(fun(U_213,bool),bool),member(U_213),U_211),U_207))
| ~ sP5(U_209,U_207,U_211,U_213) ),
inference(clausify,[status(thm)],[f_77_4]) ).
fof(f_78_1,plain,
! [X_a,X_2,Y_3,A_1] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_3),A_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),Y_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)),
inference(fof_nnf,[status(thm)],[fact_40_insert__commute]) ).
fof(f_78_2,plain,
! [U_217,U_216,U_215,U_214] : hAPP(fun(U_217,bool),fun(U_217,bool),hAPP(U_217,fun(fun(U_217,bool),fun(U_217,bool)),insert(U_217),U_216),hAPP(fun(U_217,bool),fun(U_217,bool),hAPP(U_217,fun(fun(U_217,bool),fun(U_217,bool)),insert(U_217),U_215),U_214)) = hAPP(fun(U_217,bool),fun(U_217,bool),hAPP(U_217,fun(fun(U_217,bool),fun(U_217,bool)),insert(U_217),U_215),hAPP(fun(U_217,bool),fun(U_217,bool),hAPP(U_217,fun(fun(U_217,bool),fun(U_217,bool)),insert(U_217),U_216),U_214)),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
! [U_214,U_215,U_216,U_217] : hAPP(fun(U_217,bool),fun(U_217,bool),hAPP(U_217,fun(fun(U_217,bool),fun(U_217,bool)),insert(U_217),U_216),hAPP(fun(U_217,bool),fun(U_217,bool),hAPP(U_217,fun(fun(U_217,bool),fun(U_217,bool)),insert(U_217),U_215),U_214)) = hAPP(fun(U_217,bool),fun(U_217,bool),hAPP(U_217,fun(fun(U_217,bool),fun(U_217,bool)),insert(U_217),U_215),hAPP(fun(U_217,bool),fun(U_217,bool),hAPP(U_217,fun(fun(U_217,bool),fun(U_217,bool)),insert(U_217),U_216),U_214)),
inference(definitional_conversion,[status(esa)],[f_78_2]) ).
cnf(f_78_4,plain,
hAPP(fun(U_217,bool),fun(U_217,bool),hAPP(U_217,fun(fun(U_217,bool),fun(U_217,bool)),insert(U_217),U_216),hAPP(fun(U_217,bool),fun(U_217,bool),hAPP(U_217,fun(fun(U_217,bool),fun(U_217,bool)),insert(U_217),U_215),U_214)) = hAPP(fun(U_217,bool),fun(U_217,bool),hAPP(U_217,fun(fun(U_217,bool),fun(U_217,bool)),insert(U_217),U_215),hAPP(fun(U_217,bool),fun(U_217,bool),hAPP(U_217,fun(fun(U_217,bool),fun(U_217,bool)),insert(U_217),U_216),U_214)),
inference(clausify,[status(thm)],[f_78_3]) ).
fof(f_79_1,plain,
! [X_a,X_2,A_1] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1),
inference(fof_nnf,[status(thm)],[fact_41_insert__absorb2]) ).
fof(f_79_2,plain,
! [U_220,U_219,U_218] : hAPP(fun(U_220,bool),fun(U_220,bool),hAPP(U_220,fun(fun(U_220,bool),fun(U_220,bool)),insert(U_220),U_219),hAPP(fun(U_220,bool),fun(U_220,bool),hAPP(U_220,fun(fun(U_220,bool),fun(U_220,bool)),insert(U_220),U_219),U_218)) = hAPP(fun(U_220,bool),fun(U_220,bool),hAPP(U_220,fun(fun(U_220,bool),fun(U_220,bool)),insert(U_220),U_219),U_218),
inference(variable_rename,[status(thm)],[f_79_1]) ).
fof(f_79_3,plain,
! [U_219,U_218,U_220] : hAPP(fun(U_220,bool),fun(U_220,bool),hAPP(U_220,fun(fun(U_220,bool),fun(U_220,bool)),insert(U_220),U_219),hAPP(fun(U_220,bool),fun(U_220,bool),hAPP(U_220,fun(fun(U_220,bool),fun(U_220,bool)),insert(U_220),U_219),U_218)) = hAPP(fun(U_220,bool),fun(U_220,bool),hAPP(U_220,fun(fun(U_220,bool),fun(U_220,bool)),insert(U_220),U_219),U_218),
inference(definitional_conversion,[status(esa)],[f_79_2]) ).
cnf(f_79_4,plain,
hAPP(fun(U_220,bool),fun(U_220,bool),hAPP(U_220,fun(fun(U_220,bool),fun(U_220,bool)),insert(U_220),U_219),hAPP(fun(U_220,bool),fun(U_220,bool),hAPP(U_220,fun(fun(U_220,bool),fun(U_220,bool)),insert(U_220),U_219),U_218)) = hAPP(fun(U_220,bool),fun(U_220,bool),hAPP(U_220,fun(fun(U_220,bool),fun(U_220,bool)),insert(U_220),U_219),U_218),
inference(clausify,[status(thm)],[f_79_3]) ).
fof(f_80_1,plain,
! [X_a,A_3,P_1] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fimplies),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_3)))),P_1)),
inference(fof_nnf,[status(thm)],[fact_42_insert__Collect]) ).
fof(f_80_2,plain,
! [U_223,U_222,U_221] : hAPP(fun(U_223,bool),fun(U_223,bool),hAPP(U_223,fun(fun(U_223,bool),fun(U_223,bool)),insert(U_223),U_222),hAPP(fun(U_223,bool),fun(U_223,bool),collect(U_223),U_221)) = hAPP(fun(U_223,bool),fun(U_223,bool),collect(U_223),hAPP(fun(U_223,bool),fun(U_223,bool),hAPP(fun(U_223,fun(bool,bool)),fun(fun(U_223,bool),fun(U_223,bool)),combs(U_223,bool,bool),hAPP(fun(U_223,bool),fun(U_223,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_223,bool),fun(U_223,fun(bool,bool))),combb(bool,fun(bool,bool),U_223),fimplies),hAPP(fun(U_223,bool),fun(U_223,bool),hAPP(fun(bool,bool),fun(fun(U_223,bool),fun(U_223,bool)),combb(bool,bool,U_223),fNot),hAPP(U_223,fun(U_223,bool),hAPP(fun(U_223,fun(U_223,bool)),fun(U_223,fun(U_223,bool)),combc(U_223,U_223,bool),fequal(U_223)),U_222)))),U_221)),
inference(variable_rename,[status(thm)],[f_80_1]) ).
fof(f_80_3,plain,
! [U_222,U_223,U_221] : hAPP(fun(U_223,bool),fun(U_223,bool),hAPP(U_223,fun(fun(U_223,bool),fun(U_223,bool)),insert(U_223),U_222),hAPP(fun(U_223,bool),fun(U_223,bool),collect(U_223),U_221)) = hAPP(fun(U_223,bool),fun(U_223,bool),collect(U_223),hAPP(fun(U_223,bool),fun(U_223,bool),hAPP(fun(U_223,fun(bool,bool)),fun(fun(U_223,bool),fun(U_223,bool)),combs(U_223,bool,bool),hAPP(fun(U_223,bool),fun(U_223,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_223,bool),fun(U_223,fun(bool,bool))),combb(bool,fun(bool,bool),U_223),fimplies),hAPP(fun(U_223,bool),fun(U_223,bool),hAPP(fun(bool,bool),fun(fun(U_223,bool),fun(U_223,bool)),combb(bool,bool,U_223),fNot),hAPP(U_223,fun(U_223,bool),hAPP(fun(U_223,fun(U_223,bool)),fun(U_223,fun(U_223,bool)),combc(U_223,U_223,bool),fequal(U_223)),U_222)))),U_221)),
inference(definitional_conversion,[status(esa)],[f_80_2]) ).
cnf(f_80_4,plain,
hAPP(fun(U_223,bool),fun(U_223,bool),hAPP(U_223,fun(fun(U_223,bool),fun(U_223,bool)),insert(U_223),U_222),hAPP(fun(U_223,bool),fun(U_223,bool),collect(U_223),U_221)) = hAPP(fun(U_223,bool),fun(U_223,bool),collect(U_223),hAPP(fun(U_223,bool),fun(U_223,bool),hAPP(fun(U_223,fun(bool,bool)),fun(fun(U_223,bool),fun(U_223,bool)),combs(U_223,bool,bool),hAPP(fun(U_223,bool),fun(U_223,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_223,bool),fun(U_223,fun(bool,bool))),combb(bool,fun(bool,bool),U_223),fimplies),hAPP(fun(U_223,bool),fun(U_223,bool),hAPP(fun(bool,bool),fun(fun(U_223,bool),fun(U_223,bool)),combb(bool,bool,U_223),fNot),hAPP(U_223,fun(U_223,bool),hAPP(fun(U_223,fun(U_223,bool)),fun(U_223,fun(U_223,bool)),combc(U_223,U_223,bool),fequal(U_223)),U_222)))),U_221)),
inference(clausify,[status(thm)],[f_80_3]) ).
fof(f_81_1,plain,
! [X_a,A_3,B] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),B) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_3))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B))),
inference(fof_nnf,[status(thm)],[fact_43_insert__compr]) ).
fof(f_81_2,plain,
! [U_226,U_225,U_224] : hAPP(fun(U_226,bool),fun(U_226,bool),hAPP(U_226,fun(fun(U_226,bool),fun(U_226,bool)),insert(U_226),U_225),U_224) = hAPP(fun(U_226,bool),fun(U_226,bool),collect(U_226),hAPP(fun(U_226,bool),fun(U_226,bool),hAPP(fun(U_226,fun(bool,bool)),fun(fun(U_226,bool),fun(U_226,bool)),combs(U_226,bool,bool),hAPP(fun(U_226,bool),fun(U_226,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_226,bool),fun(U_226,fun(bool,bool))),combb(bool,fun(bool,bool),U_226),fdisj),hAPP(U_226,fun(U_226,bool),hAPP(fun(U_226,fun(U_226,bool)),fun(U_226,fun(U_226,bool)),combc(U_226,U_226,bool),fequal(U_226)),U_225))),hAPP(fun(U_226,bool),fun(U_226,bool),hAPP(fun(U_226,fun(fun(U_226,bool),bool)),fun(fun(U_226,bool),fun(U_226,bool)),combc(U_226,fun(U_226,bool),bool),member(U_226)),U_224))),
inference(variable_rename,[status(thm)],[f_81_1]) ).
fof(f_81_3,plain,
! [U_224,U_226,U_225] : hAPP(fun(U_226,bool),fun(U_226,bool),hAPP(U_226,fun(fun(U_226,bool),fun(U_226,bool)),insert(U_226),U_225),U_224) = hAPP(fun(U_226,bool),fun(U_226,bool),collect(U_226),hAPP(fun(U_226,bool),fun(U_226,bool),hAPP(fun(U_226,fun(bool,bool)),fun(fun(U_226,bool),fun(U_226,bool)),combs(U_226,bool,bool),hAPP(fun(U_226,bool),fun(U_226,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_226,bool),fun(U_226,fun(bool,bool))),combb(bool,fun(bool,bool),U_226),fdisj),hAPP(U_226,fun(U_226,bool),hAPP(fun(U_226,fun(U_226,bool)),fun(U_226,fun(U_226,bool)),combc(U_226,U_226,bool),fequal(U_226)),U_225))),hAPP(fun(U_226,bool),fun(U_226,bool),hAPP(fun(U_226,fun(fun(U_226,bool),bool)),fun(fun(U_226,bool),fun(U_226,bool)),combc(U_226,fun(U_226,bool),bool),member(U_226)),U_224))),
inference(definitional_conversion,[status(esa)],[f_81_2]) ).
cnf(f_81_4,plain,
hAPP(fun(U_226,bool),fun(U_226,bool),hAPP(U_226,fun(fun(U_226,bool),fun(U_226,bool)),insert(U_226),U_225),U_224) = hAPP(fun(U_226,bool),fun(U_226,bool),collect(U_226),hAPP(fun(U_226,bool),fun(U_226,bool),hAPP(fun(U_226,fun(bool,bool)),fun(fun(U_226,bool),fun(U_226,bool)),combs(U_226,bool,bool),hAPP(fun(U_226,bool),fun(U_226,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_226,bool),fun(U_226,fun(bool,bool))),combb(bool,fun(bool,bool),U_226),fdisj),hAPP(U_226,fun(U_226,bool),hAPP(fun(U_226,fun(U_226,bool)),fun(U_226,fun(U_226,bool)),combc(U_226,U_226,bool),fequal(U_226)),U_225))),hAPP(fun(U_226,bool),fun(U_226,bool),hAPP(fun(U_226,fun(fun(U_226,bool),bool)),fun(fun(U_226,bool),fun(U_226,bool)),combc(U_226,fun(U_226,bool),bool),member(U_226)),U_224))),
inference(clausify,[status(thm)],[f_81_3]) ).
fof(f_82_1,plain,
! [X_a,A_3,B] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),B))),
inference(fof_nnf,[status(thm)],[fact_44_insertI1]) ).
fof(f_82_2,plain,
! [U_229,U_228,U_227] : hBOOL(hAPP(fun(U_229,bool),bool,hAPP(U_229,fun(fun(U_229,bool),bool),member(U_229),U_228),hAPP(fun(U_229,bool),fun(U_229,bool),hAPP(U_229,fun(fun(U_229,bool),fun(U_229,bool)),insert(U_229),U_228),U_227))),
inference(variable_rename,[status(thm)],[f_82_1]) ).
fof(f_82_3,plain,
! [U_229,U_228,U_227] : hBOOL(hAPP(fun(U_229,bool),bool,hAPP(U_229,fun(fun(U_229,bool),bool),member(U_229),U_228),hAPP(fun(U_229,bool),fun(U_229,bool),hAPP(U_229,fun(fun(U_229,bool),fun(U_229,bool)),insert(U_229),U_228),U_227))),
inference(definitional_conversion,[status(esa)],[f_82_2]) ).
cnf(f_82_4,plain,
hBOOL(hAPP(fun(U_229,bool),bool,hAPP(U_229,fun(fun(U_229,bool),bool),member(U_229),U_228),hAPP(fun(U_229,bool),fun(U_229,bool),hAPP(U_229,fun(fun(U_229,bool),fun(U_229,bool)),insert(U_229),U_228),U_227))),
inference(clausify,[status(thm)],[f_82_3]) ).
fof(f_83_1,plain,
! [X_a,A_1,B] :
( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1))
& hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) )
| ti(fun(X_a,bool),A_1) != ti(fun(X_a,bool),B) ),
inference(fof_nnf,[status(thm)],[fact_45_equalityE]) ).
fof(f_83_2,plain,
! [U_232,U_231,U_230] :
( ( hBOOL(hAPP(fun(U_232,bool),bool,hAPP(fun(U_232,bool),fun(fun(U_232,bool),bool),ord_less_eq(fun(U_232,bool)),U_230),U_231))
& hBOOL(hAPP(fun(U_232,bool),bool,hAPP(fun(U_232,bool),fun(fun(U_232,bool),bool),ord_less_eq(fun(U_232,bool)),U_231),U_230)) )
| ti(fun(U_232,bool),U_231) != ti(fun(U_232,bool),U_230) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
( ! [U_230,U_231,U_232] :
( hBOOL(hAPP(fun(U_232,bool),bool,hAPP(fun(U_232,bool),fun(fun(U_232,bool),bool),ord_less_eq(fun(U_232,bool)),U_230),U_231))
| ~ sP6(U_230,U_231,U_232) )
& ! [U_230,U_231,U_232] :
( hBOOL(hAPP(fun(U_232,bool),bool,hAPP(fun(U_232,bool),fun(fun(U_232,bool),bool),ord_less_eq(fun(U_232,bool)),U_231),U_230))
| ~ sP6(U_230,U_231,U_232) )
& ! [U_230,U_231,U_232] :
( sP6(U_230,U_231,U_232)
| ti(fun(U_232,bool),U_231) != ti(fun(U_232,bool),U_230) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_83_2]) ).
cnf(f_83_4,plain,
( sP6(U_230,U_231,U_232)
| ti(fun(U_232,bool),U_231) != ti(fun(U_232,bool),U_230) ),
inference(clausify,[status(thm)],[f_83_3]) ).
cnf(f_83_5,plain,
( hBOOL(hAPP(fun(U_232,bool),bool,hAPP(fun(U_232,bool),fun(fun(U_232,bool),bool),ord_less_eq(fun(U_232,bool)),U_231),U_230))
| ~ sP6(U_230,U_231,U_232) ),
inference(clausify,[status(thm)],[f_83_3]) ).
cnf(f_83_6,plain,
( hBOOL(hAPP(fun(U_232,bool),bool,hAPP(fun(U_232,bool),fun(fun(U_232,bool),bool),ord_less_eq(fun(U_232,bool)),U_230),U_231))
| ~ sP6(U_230,U_231,U_232) ),
inference(clausify,[status(thm)],[f_83_3]) ).
fof(f_84_1,plain,
! [X_a,C_2,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),C_2))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),C_2))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
inference(fof_nnf,[status(thm)],[fact_46_subset__trans]) ).
fof(f_84_2,plain,
! [U_236,U_235,U_234,U_233] :
( hBOOL(hAPP(fun(U_236,bool),bool,hAPP(fun(U_236,bool),fun(fun(U_236,bool),bool),ord_less_eq(fun(U_236,bool)),U_234),U_235))
| ~ hBOOL(hAPP(fun(U_236,bool),bool,hAPP(fun(U_236,bool),fun(fun(U_236,bool),bool),ord_less_eq(fun(U_236,bool)),U_233),U_235))
| ~ hBOOL(hAPP(fun(U_236,bool),bool,hAPP(fun(U_236,bool),fun(fun(U_236,bool),bool),ord_less_eq(fun(U_236,bool)),U_234),U_233)) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
fof(f_84_3,plain,
! [U_233,U_234,U_236,U_235] :
( hBOOL(hAPP(fun(U_236,bool),bool,hAPP(fun(U_236,bool),fun(fun(U_236,bool),bool),ord_less_eq(fun(U_236,bool)),U_234),U_235))
| ~ hBOOL(hAPP(fun(U_236,bool),bool,hAPP(fun(U_236,bool),fun(fun(U_236,bool),bool),ord_less_eq(fun(U_236,bool)),U_233),U_235))
| ~ hBOOL(hAPP(fun(U_236,bool),bool,hAPP(fun(U_236,bool),fun(fun(U_236,bool),bool),ord_less_eq(fun(U_236,bool)),U_234),U_233)) ),
inference(definitional_conversion,[status(esa)],[f_84_2]) ).
cnf(f_84_4,plain,
( hBOOL(hAPP(fun(U_236,bool),bool,hAPP(fun(U_236,bool),fun(fun(U_236,bool),bool),ord_less_eq(fun(U_236,bool)),U_234),U_235))
| ~ hBOOL(hAPP(fun(U_236,bool),bool,hAPP(fun(U_236,bool),fun(fun(U_236,bool),bool),ord_less_eq(fun(U_236,bool)),U_233),U_235))
| ~ hBOOL(hAPP(fun(U_236,bool),bool,hAPP(fun(U_236,bool),fun(fun(U_236,bool),bool),ord_less_eq(fun(U_236,bool)),U_234),U_233)) ),
inference(clausify,[status(thm)],[f_84_3]) ).
fof(f_85_1,plain,
! [X_a,X_2,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
inference(fof_nnf,[status(thm)],[fact_47_set__mp]) ).
fof(f_85_2,plain,
! [U_240,U_239,U_238,U_237] :
( hBOOL(hAPP(fun(U_240,bool),bool,hAPP(U_240,fun(fun(U_240,bool),bool),member(U_240),U_239),U_237))
| ~ hBOOL(hAPP(fun(U_240,bool),bool,hAPP(U_240,fun(fun(U_240,bool),bool),member(U_240),U_239),U_238))
| ~ hBOOL(hAPP(fun(U_240,bool),bool,hAPP(fun(U_240,bool),fun(fun(U_240,bool),bool),ord_less_eq(fun(U_240,bool)),U_238),U_237)) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
fof(f_85_3,plain,
! [U_238,U_237,U_240,U_239] :
( hBOOL(hAPP(fun(U_240,bool),bool,hAPP(U_240,fun(fun(U_240,bool),bool),member(U_240),U_239),U_237))
| ~ hBOOL(hAPP(fun(U_240,bool),bool,hAPP(U_240,fun(fun(U_240,bool),bool),member(U_240),U_239),U_238))
| ~ hBOOL(hAPP(fun(U_240,bool),bool,hAPP(fun(U_240,bool),fun(fun(U_240,bool),bool),ord_less_eq(fun(U_240,bool)),U_238),U_237)) ),
inference(definitional_conversion,[status(esa)],[f_85_2]) ).
cnf(f_85_4,plain,
( hBOOL(hAPP(fun(U_240,bool),bool,hAPP(U_240,fun(fun(U_240,bool),bool),member(U_240),U_239),U_237))
| ~ hBOOL(hAPP(fun(U_240,bool),bool,hAPP(U_240,fun(fun(U_240,bool),bool),member(U_240),U_239),U_238))
| ~ hBOOL(hAPP(fun(U_240,bool),bool,hAPP(fun(U_240,bool),fun(fun(U_240,bool),bool),ord_less_eq(fun(U_240,bool)),U_238),U_237)) ),
inference(clausify,[status(thm)],[f_85_3]) ).
fof(f_86_1,plain,
! [X_a,B,X_2,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) ),
inference(fof_nnf,[status(thm)],[fact_48_set__rev__mp]) ).
fof(f_86_2,plain,
! [U_244,U_243,U_242,U_241] :
( hBOOL(hAPP(fun(U_244,bool),bool,hAPP(U_244,fun(fun(U_244,bool),bool),member(U_244),U_242),U_243))
| ~ hBOOL(hAPP(fun(U_244,bool),bool,hAPP(fun(U_244,bool),fun(fun(U_244,bool),bool),ord_less_eq(fun(U_244,bool)),U_241),U_243))
| ~ hBOOL(hAPP(fun(U_244,bool),bool,hAPP(U_244,fun(fun(U_244,bool),bool),member(U_244),U_242),U_241)) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
fof(f_86_3,plain,
! [U_242,U_241,U_244,U_243] :
( hBOOL(hAPP(fun(U_244,bool),bool,hAPP(U_244,fun(fun(U_244,bool),bool),member(U_244),U_242),U_243))
| ~ hBOOL(hAPP(fun(U_244,bool),bool,hAPP(fun(U_244,bool),fun(fun(U_244,bool),bool),ord_less_eq(fun(U_244,bool)),U_241),U_243))
| ~ hBOOL(hAPP(fun(U_244,bool),bool,hAPP(U_244,fun(fun(U_244,bool),bool),member(U_244),U_242),U_241)) ),
inference(definitional_conversion,[status(esa)],[f_86_2]) ).
cnf(f_86_4,plain,
( hBOOL(hAPP(fun(U_244,bool),bool,hAPP(U_244,fun(fun(U_244,bool),bool),member(U_244),U_242),U_243))
| ~ hBOOL(hAPP(fun(U_244,bool),bool,hAPP(fun(U_244,bool),fun(fun(U_244,bool),bool),ord_less_eq(fun(U_244,bool)),U_241),U_243))
| ~ hBOOL(hAPP(fun(U_244,bool),bool,hAPP(U_244,fun(fun(U_244,bool),bool),member(U_244),U_242),U_241)) ),
inference(clausify,[status(thm)],[f_86_3]) ).
fof(f_87_1,plain,
! [X_a,X_2,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
inference(fof_nnf,[status(thm)],[fact_49_in__mono]) ).
fof(f_87_2,plain,
! [U_248,U_247,U_246,U_245] :
( hBOOL(hAPP(fun(U_248,bool),bool,hAPP(U_248,fun(fun(U_248,bool),bool),member(U_248),U_247),U_245))
| ~ hBOOL(hAPP(fun(U_248,bool),bool,hAPP(U_248,fun(fun(U_248,bool),bool),member(U_248),U_247),U_246))
| ~ hBOOL(hAPP(fun(U_248,bool),bool,hAPP(fun(U_248,bool),fun(fun(U_248,bool),bool),ord_less_eq(fun(U_248,bool)),U_246),U_245)) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
fof(f_87_3,plain,
! [U_246,U_248,U_245,U_247] :
( hBOOL(hAPP(fun(U_248,bool),bool,hAPP(U_248,fun(fun(U_248,bool),bool),member(U_248),U_247),U_245))
| ~ hBOOL(hAPP(fun(U_248,bool),bool,hAPP(U_248,fun(fun(U_248,bool),bool),member(U_248),U_247),U_246))
| ~ hBOOL(hAPP(fun(U_248,bool),bool,hAPP(fun(U_248,bool),fun(fun(U_248,bool),bool),ord_less_eq(fun(U_248,bool)),U_246),U_245)) ),
inference(definitional_conversion,[status(esa)],[f_87_2]) ).
cnf(f_87_4,plain,
( hBOOL(hAPP(fun(U_248,bool),bool,hAPP(U_248,fun(fun(U_248,bool),bool),member(U_248),U_247),U_245))
| ~ hBOOL(hAPP(fun(U_248,bool),bool,hAPP(U_248,fun(fun(U_248,bool),bool),member(U_248),U_247),U_246))
| ~ hBOOL(hAPP(fun(U_248,bool),bool,hAPP(fun(U_248,bool),fun(fun(U_248,bool),bool),ord_less_eq(fun(U_248,bool)),U_246),U_245)) ),
inference(clausify,[status(thm)],[f_87_3]) ).
fof(f_88_1,plain,
! [X_a,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1))
| ti(fun(X_a,bool),A_1) != ti(fun(X_a,bool),B) ),
inference(fof_nnf,[status(thm)],[fact_50_equalityD2]) ).
fof(f_88_2,plain,
! [U_251,U_250,U_249] :
( hBOOL(hAPP(fun(U_251,bool),bool,hAPP(fun(U_251,bool),fun(fun(U_251,bool),bool),ord_less_eq(fun(U_251,bool)),U_249),U_250))
| ti(fun(U_251,bool),U_250) != ti(fun(U_251,bool),U_249) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
fof(f_88_3,plain,
! [U_251,U_250,U_249] :
( hBOOL(hAPP(fun(U_251,bool),bool,hAPP(fun(U_251,bool),fun(fun(U_251,bool),bool),ord_less_eq(fun(U_251,bool)),U_249),U_250))
| ti(fun(U_251,bool),U_250) != ti(fun(U_251,bool),U_249) ),
inference(definitional_conversion,[status(esa)],[f_88_2]) ).
cnf(f_88_4,plain,
( hBOOL(hAPP(fun(U_251,bool),bool,hAPP(fun(U_251,bool),fun(fun(U_251,bool),bool),ord_less_eq(fun(U_251,bool)),U_249),U_250))
| ti(fun(U_251,bool),U_250) != ti(fun(U_251,bool),U_249) ),
inference(clausify,[status(thm)],[f_88_3]) ).
fof(f_89_1,plain,
! [X_a,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
| ti(fun(X_a,bool),A_1) != ti(fun(X_a,bool),B) ),
inference(fof_nnf,[status(thm)],[fact_51_equalityD1]) ).
fof(f_89_2,plain,
! [U_254,U_253,U_252] :
( hBOOL(hAPP(fun(U_254,bool),bool,hAPP(fun(U_254,bool),fun(fun(U_254,bool),bool),ord_less_eq(fun(U_254,bool)),U_253),U_252))
| ti(fun(U_254,bool),U_253) != ti(fun(U_254,bool),U_252) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
fof(f_89_3,plain,
! [U_252,U_253,U_254] :
( hBOOL(hAPP(fun(U_254,bool),bool,hAPP(fun(U_254,bool),fun(fun(U_254,bool),bool),ord_less_eq(fun(U_254,bool)),U_253),U_252))
| ti(fun(U_254,bool),U_253) != ti(fun(U_254,bool),U_252) ),
inference(definitional_conversion,[status(esa)],[f_89_2]) ).
cnf(f_89_4,plain,
( hBOOL(hAPP(fun(U_254,bool),bool,hAPP(fun(U_254,bool),fun(fun(U_254,bool),bool),ord_less_eq(fun(U_254,bool)),U_253),U_252))
| ti(fun(U_254,bool),U_253) != ti(fun(U_254,bool),U_252) ),
inference(clausify,[status(thm)],[f_89_3]) ).
fof(f_90_1,plain,
! [X_a,A_1,B] :
( ( ti(fun(X_a,bool),A_1) = ti(fun(X_a,bool),B)
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) )
& ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),A_1))
& hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) )
| ti(fun(X_a,bool),A_1) != ti(fun(X_a,bool),B) ) ),
inference(fof_nnf,[status(thm)],[fact_52_set__eq__subset]) ).
fof(f_90_2,plain,
! [U_257,U_256,U_255] :
( ( ti(fun(U_257,bool),U_256) = ti(fun(U_257,bool),U_255)
| ~ hBOOL(hAPP(fun(U_257,bool),bool,hAPP(fun(U_257,bool),fun(fun(U_257,bool),bool),ord_less_eq(fun(U_257,bool)),U_255),U_256))
| ~ hBOOL(hAPP(fun(U_257,bool),bool,hAPP(fun(U_257,bool),fun(fun(U_257,bool),bool),ord_less_eq(fun(U_257,bool)),U_256),U_255)) )
& ( ( hBOOL(hAPP(fun(U_257,bool),bool,hAPP(fun(U_257,bool),fun(fun(U_257,bool),bool),ord_less_eq(fun(U_257,bool)),U_255),U_256))
& hBOOL(hAPP(fun(U_257,bool),bool,hAPP(fun(U_257,bool),fun(fun(U_257,bool),bool),ord_less_eq(fun(U_257,bool)),U_256),U_255)) )
| ti(fun(U_257,bool),U_256) != ti(fun(U_257,bool),U_255) ) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
fof(f_90_3,plain,
( ! [U_263,U_261,U_259] :
( ti(fun(U_263,bool),U_261) = ti(fun(U_263,bool),U_259)
| ~ hBOOL(hAPP(fun(U_263,bool),bool,hAPP(fun(U_263,bool),fun(fun(U_263,bool),bool),ord_less_eq(fun(U_263,bool)),U_259),U_261))
| ~ hBOOL(hAPP(fun(U_263,bool),bool,hAPP(fun(U_263,bool),fun(fun(U_263,bool),bool),ord_less_eq(fun(U_263,bool)),U_261),U_259)) )
& ! [U_262,U_260,U_258] :
( ( hBOOL(hAPP(fun(U_262,bool),bool,hAPP(fun(U_262,bool),fun(fun(U_262,bool),bool),ord_less_eq(fun(U_262,bool)),U_258),U_260))
& hBOOL(hAPP(fun(U_262,bool),bool,hAPP(fun(U_262,bool),fun(fun(U_262,bool),bool),ord_less_eq(fun(U_262,bool)),U_260),U_258)) )
| ti(fun(U_262,bool),U_260) != ti(fun(U_262,bool),U_258) ) ),
inference(miniscope,[status(thm)],[f_90_2]) ).
fof(f_90_4,plain,
( ! [U_258,U_262,U_260] :
( hBOOL(hAPP(fun(U_262,bool),bool,hAPP(fun(U_262,bool),fun(fun(U_262,bool),bool),ord_less_eq(fun(U_262,bool)),U_258),U_260))
| ~ sP7(U_258,U_262,U_260) )
& ! [U_258,U_262,U_260] :
( hBOOL(hAPP(fun(U_262,bool),bool,hAPP(fun(U_262,bool),fun(fun(U_262,bool),bool),ord_less_eq(fun(U_262,bool)),U_260),U_258))
| ~ sP7(U_258,U_262,U_260) )
& ! [U_263,U_259,U_261] :
( ti(fun(U_263,bool),U_261) = ti(fun(U_263,bool),U_259)
| ~ hBOOL(hAPP(fun(U_263,bool),bool,hAPP(fun(U_263,bool),fun(fun(U_263,bool),bool),ord_less_eq(fun(U_263,bool)),U_259),U_261))
| ~ hBOOL(hAPP(fun(U_263,bool),bool,hAPP(fun(U_263,bool),fun(fun(U_263,bool),bool),ord_less_eq(fun(U_263,bool)),U_261),U_259)) )
& ! [U_258,U_262,U_260] :
( sP7(U_258,U_262,U_260)
| ti(fun(U_262,bool),U_260) != ti(fun(U_262,bool),U_258) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_90_3]) ).
cnf(f_90_5,plain,
( sP7(U_258,U_262,U_260)
| ti(fun(U_262,bool),U_260) != ti(fun(U_262,bool),U_258) ),
inference(clausify,[status(thm)],[f_90_4]) ).
cnf(f_90_6,plain,
( ti(fun(U_263,bool),U_261) = ti(fun(U_263,bool),U_259)
| ~ hBOOL(hAPP(fun(U_263,bool),bool,hAPP(fun(U_263,bool),fun(fun(U_263,bool),bool),ord_less_eq(fun(U_263,bool)),U_259),U_261))
| ~ hBOOL(hAPP(fun(U_263,bool),bool,hAPP(fun(U_263,bool),fun(fun(U_263,bool),bool),ord_less_eq(fun(U_263,bool)),U_261),U_259)) ),
inference(clausify,[status(thm)],[f_90_4]) ).
cnf(f_90_7,plain,
( hBOOL(hAPP(fun(U_262,bool),bool,hAPP(fun(U_262,bool),fun(fun(U_262,bool),bool),ord_less_eq(fun(U_262,bool)),U_260),U_258))
| ~ sP7(U_258,U_262,U_260) ),
inference(clausify,[status(thm)],[f_90_4]) ).
cnf(f_90_8,plain,
( hBOOL(hAPP(fun(U_262,bool),bool,hAPP(fun(U_262,bool),fun(fun(U_262,bool),bool),ord_less_eq(fun(U_262,bool)),U_258),U_260))
| ~ sP7(U_258,U_262,U_260) ),
inference(clausify,[status(thm)],[f_90_4]) ).
fof(f_91_1,plain,
! [X_a,A_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),A_1)),
inference(fof_nnf,[status(thm)],[fact_53_subset__refl]) ).
fof(f_91_2,plain,
! [U_265,U_264] : hBOOL(hAPP(fun(U_265,bool),bool,hAPP(fun(U_265,bool),fun(fun(U_265,bool),bool),ord_less_eq(fun(U_265,bool)),U_264),U_264)),
inference(variable_rename,[status(thm)],[f_91_1]) ).
fof(f_91_3,plain,
! [U_265,U_264] : hBOOL(hAPP(fun(U_265,bool),bool,hAPP(fun(U_265,bool),fun(fun(U_265,bool),bool),ord_less_eq(fun(U_265,bool)),U_264),U_264)),
inference(definitional_conversion,[status(esa)],[f_91_2]) ).
cnf(f_91_4,plain,
hBOOL(hAPP(fun(U_265,bool),bool,hAPP(fun(U_265,bool),fun(fun(U_265,bool),bool),ord_less_eq(fun(U_265,bool)),U_264),U_264)),
inference(clausify,[status(thm)],[f_91_3]) ).
fof(f_92_1,plain,
! [X_b,X_a,B_1,F,X_2,A_1] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_1),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)))
| ti(X_b,B_1) != hAPP(X_a,X_b,F,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)) ),
inference(fof_nnf,[status(thm)],[fact_54_rev__image__eqI]) ).
fof(f_92_2,plain,
! [U_271,U_270,U_269,U_268,U_267,U_266] :
( hBOOL(hAPP(fun(U_271,bool),bool,hAPP(U_271,fun(fun(U_271,bool),bool),member(U_271),U_269),hAPP(fun(U_270,bool),fun(U_271,bool),hAPP(fun(U_270,U_271),fun(fun(U_270,bool),fun(U_271,bool)),image(U_270,U_271),U_268),U_266)))
| ti(U_271,U_269) != hAPP(U_270,U_271,U_268,U_267)
| ~ hBOOL(hAPP(fun(U_270,bool),bool,hAPP(U_270,fun(fun(U_270,bool),bool),member(U_270),U_267),U_266)) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
fof(f_92_3,plain,
! [U_268,U_266,U_269,U_267,U_270,U_271] :
( hBOOL(hAPP(fun(U_271,bool),bool,hAPP(U_271,fun(fun(U_271,bool),bool),member(U_271),U_269),hAPP(fun(U_270,bool),fun(U_271,bool),hAPP(fun(U_270,U_271),fun(fun(U_270,bool),fun(U_271,bool)),image(U_270,U_271),U_268),U_266)))
| ti(U_271,U_269) != hAPP(U_270,U_271,U_268,U_267)
| ~ hBOOL(hAPP(fun(U_270,bool),bool,hAPP(U_270,fun(fun(U_270,bool),bool),member(U_270),U_267),U_266)) ),
inference(definitional_conversion,[status(esa)],[f_92_2]) ).
cnf(f_92_4,plain,
( hBOOL(hAPP(fun(U_271,bool),bool,hAPP(U_271,fun(fun(U_271,bool),bool),member(U_271),U_269),hAPP(fun(U_270,bool),fun(U_271,bool),hAPP(fun(U_270,U_271),fun(fun(U_270,bool),fun(U_271,bool)),image(U_270,U_271),U_268),U_266)))
| ti(U_271,U_269) != hAPP(U_270,U_271,U_268,U_267)
| ~ hBOOL(hAPP(fun(U_270,bool),bool,hAPP(U_270,fun(fun(U_270,bool),bool),member(U_270),U_267),U_266)) ),
inference(clausify,[status(thm)],[f_92_3]) ).
fof(f_93_1,plain,
! [X_b,X_a,F,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(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(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)) ),
inference(fof_nnf,[status(thm)],[fact_55_imageI]) ).
fof(f_93_2,plain,
! [U_276,U_275,U_274,U_273,U_272] :
( hBOOL(hAPP(fun(U_276,bool),bool,hAPP(U_276,fun(fun(U_276,bool),bool),member(U_276),hAPP(U_275,U_276,U_274,U_273)),hAPP(fun(U_275,bool),fun(U_276,bool),hAPP(fun(U_275,U_276),fun(fun(U_275,bool),fun(U_276,bool)),image(U_275,U_276),U_274),U_272)))
| ~ hBOOL(hAPP(fun(U_275,bool),bool,hAPP(U_275,fun(fun(U_275,bool),bool),member(U_275),U_273),U_272)) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
fof(f_93_3,plain,
! [U_273,U_275,U_272,U_274,U_276] :
( hBOOL(hAPP(fun(U_276,bool),bool,hAPP(U_276,fun(fun(U_276,bool),bool),member(U_276),hAPP(U_275,U_276,U_274,U_273)),hAPP(fun(U_275,bool),fun(U_276,bool),hAPP(fun(U_275,U_276),fun(fun(U_275,bool),fun(U_276,bool)),image(U_275,U_276),U_274),U_272)))
| ~ hBOOL(hAPP(fun(U_275,bool),bool,hAPP(U_275,fun(fun(U_275,bool),bool),member(U_275),U_273),U_272)) ),
inference(definitional_conversion,[status(esa)],[f_93_2]) ).
cnf(f_93_4,plain,
( hBOOL(hAPP(fun(U_276,bool),bool,hAPP(U_276,fun(fun(U_276,bool),bool),member(U_276),hAPP(U_275,U_276,U_274,U_273)),hAPP(fun(U_275,bool),fun(U_276,bool),hAPP(fun(U_275,U_276),fun(fun(U_275,bool),fun(U_276,bool)),image(U_275,U_276),U_274),U_272)))
| ~ hBOOL(hAPP(fun(U_275,bool),bool,hAPP(U_275,fun(fun(U_275,bool),bool),member(U_275),U_273),U_272)) ),
inference(clausify,[status(thm)],[f_93_3]) ).
fof(f_94_1,plain,
! [X_a,X_b,Z,F,A_1] :
( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
| ! [X_1] :
( ti(X_a,Z) != hAPP(X_b,X_a,F,X_1)
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) ) )
& ( ? [X_1] :
( ti(X_a,Z) = hAPP(X_b,X_a,F,X_1)
& hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1)) )
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_56_image__iff]) ).
fof(f_94_2,plain,
! [U_283,U_282,U_281,U_280,U_279] :
( ( hBOOL(hAPP(fun(U_283,bool),bool,hAPP(U_283,fun(fun(U_283,bool),bool),member(U_283),U_281),hAPP(fun(U_282,bool),fun(U_283,bool),hAPP(fun(U_282,U_283),fun(fun(U_282,bool),fun(U_283,bool)),image(U_282,U_283),U_280),U_279)))
| ! [U_278] :
( ti(U_283,U_281) != hAPP(U_282,U_283,U_280,U_278)
| ~ hBOOL(hAPP(fun(U_282,bool),bool,hAPP(U_282,fun(fun(U_282,bool),bool),member(U_282),U_278),U_279)) ) )
& ( ? [U_277] :
( ti(U_283,U_281) = hAPP(U_282,U_283,U_280,U_277)
& hBOOL(hAPP(fun(U_282,bool),bool,hAPP(U_282,fun(fun(U_282,bool),bool),member(U_282),U_277),U_279)) )
| ~ hBOOL(hAPP(fun(U_283,bool),bool,hAPP(U_283,fun(fun(U_283,bool),bool),member(U_283),U_281),hAPP(fun(U_282,bool),fun(U_283,bool),hAPP(fun(U_282,U_283),fun(fun(U_282,bool),fun(U_283,bool)),image(U_282,U_283),U_280),U_279))) ) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
fof(f_94_3,plain,
( ! [U_293,U_291,U_289,U_287,U_285] :
( hBOOL(hAPP(fun(U_293,bool),bool,hAPP(U_293,fun(fun(U_293,bool),bool),member(U_293),U_289),hAPP(fun(U_291,bool),fun(U_293,bool),hAPP(fun(U_291,U_293),fun(fun(U_291,bool),fun(U_293,bool)),image(U_291,U_293),U_287),U_285)))
| ! [U_278] :
( ti(U_293,U_289) != hAPP(U_291,U_293,U_287,U_278)
| ~ hBOOL(hAPP(fun(U_291,bool),bool,hAPP(U_291,fun(fun(U_291,bool),bool),member(U_291),U_278),U_285)) ) )
& ! [U_292,U_290,U_288,U_286,U_284] :
( ? [U_277] :
( ti(U_292,U_288) = hAPP(U_290,U_292,U_286,U_277)
& hBOOL(hAPP(fun(U_290,bool),bool,hAPP(U_290,fun(fun(U_290,bool),bool),member(U_290),U_277),U_284)) )
| ~ hBOOL(hAPP(fun(U_292,bool),bool,hAPP(U_292,fun(fun(U_292,bool),bool),member(U_292),U_288),hAPP(fun(U_290,bool),fun(U_292,bool),hAPP(fun(U_290,U_292),fun(fun(U_290,bool),fun(U_292,bool)),image(U_290,U_292),U_286),U_284))) ) ),
inference(miniscope,[status(thm)],[f_94_2]) ).
fof(f_94_4,plain,
( ! [U_293,U_291,U_289,U_287,U_285] :
( hBOOL(hAPP(fun(U_293,bool),bool,hAPP(U_293,fun(fun(U_293,bool),bool),member(U_293),U_289),hAPP(fun(U_291,bool),fun(U_293,bool),hAPP(fun(U_291,U_293),fun(fun(U_291,bool),fun(U_293,bool)),image(U_291,U_293),U_287),U_285)))
| ! [U_278] :
( ti(U_293,U_289) != hAPP(U_291,U_293,U_287,U_278)
| ~ hBOOL(hAPP(fun(U_291,bool),bool,hAPP(U_291,fun(fun(U_291,bool),bool),member(U_291),U_278),U_285)) ) )
& ! [U_292,U_290,U_288,U_286,U_284] :
( ( ti(U_292,U_288) = hAPP(U_290,U_292,U_286,sK5(U_292,U_290,U_288,U_286,U_284))
& hBOOL(hAPP(fun(U_290,bool),bool,hAPP(U_290,fun(fun(U_290,bool),bool),member(U_290),sK5(U_292,U_290,U_288,U_286,U_284)),U_284)) )
| ~ hBOOL(hAPP(fun(U_292,bool),bool,hAPP(U_292,fun(fun(U_292,bool),bool),member(U_292),U_288),hAPP(fun(U_290,bool),fun(U_292,bool),hAPP(fun(U_290,U_292),fun(fun(U_290,bool),fun(U_292,bool)),image(U_290,U_292),U_286),U_284))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_277,sK5(U_292,U_290,U_288,U_286,U_284))],[f_94_3]) ).
fof(f_94_5,plain,
( ! [U_286,U_290,U_284,U_288,U_292] :
( ti(U_292,U_288) = hAPP(U_290,U_292,U_286,sK5(U_292,U_290,U_288,U_286,U_284))
| ~ sP8(U_286,U_290,U_284,U_288,U_292) )
& ! [U_286,U_290,U_284,U_288,U_292] :
( hBOOL(hAPP(fun(U_290,bool),bool,hAPP(U_290,fun(fun(U_290,bool),bool),member(U_290),sK5(U_292,U_290,U_288,U_286,U_284)),U_284))
| ~ sP8(U_286,U_290,U_284,U_288,U_292) )
& ! [U_278,U_287,U_285,U_289,U_291,U_293] :
( hBOOL(hAPP(fun(U_293,bool),bool,hAPP(U_293,fun(fun(U_293,bool),bool),member(U_293),U_289),hAPP(fun(U_291,bool),fun(U_293,bool),hAPP(fun(U_291,U_293),fun(fun(U_291,bool),fun(U_293,bool)),image(U_291,U_293),U_287),U_285)))
| ti(U_293,U_289) != hAPP(U_291,U_293,U_287,U_278)
| ~ hBOOL(hAPP(fun(U_291,bool),bool,hAPP(U_291,fun(fun(U_291,bool),bool),member(U_291),U_278),U_285)) )
& ! [U_286,U_290,U_284,U_288,U_292] :
( sP8(U_286,U_290,U_284,U_288,U_292)
| ~ hBOOL(hAPP(fun(U_292,bool),bool,hAPP(U_292,fun(fun(U_292,bool),bool),member(U_292),U_288),hAPP(fun(U_290,bool),fun(U_292,bool),hAPP(fun(U_290,U_292),fun(fun(U_290,bool),fun(U_292,bool)),image(U_290,U_292),U_286),U_284))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_94_4]) ).
cnf(f_94_6,plain,
( sP8(U_286,U_290,U_284,U_288,U_292)
| ~ hBOOL(hAPP(fun(U_292,bool),bool,hAPP(U_292,fun(fun(U_292,bool),bool),member(U_292),U_288),hAPP(fun(U_290,bool),fun(U_292,bool),hAPP(fun(U_290,U_292),fun(fun(U_290,bool),fun(U_292,bool)),image(U_290,U_292),U_286),U_284))) ),
inference(clausify,[status(thm)],[f_94_5]) ).
cnf(f_94_7,plain,
( hBOOL(hAPP(fun(U_293,bool),bool,hAPP(U_293,fun(fun(U_293,bool),bool),member(U_293),U_289),hAPP(fun(U_291,bool),fun(U_293,bool),hAPP(fun(U_291,U_293),fun(fun(U_291,bool),fun(U_293,bool)),image(U_291,U_293),U_287),U_285)))
| ti(U_293,U_289) != hAPP(U_291,U_293,U_287,U_278)
| ~ hBOOL(hAPP(fun(U_291,bool),bool,hAPP(U_291,fun(fun(U_291,bool),bool),member(U_291),U_278),U_285)) ),
inference(clausify,[status(thm)],[f_94_5]) ).
cnf(f_94_8,plain,
( hBOOL(hAPP(fun(U_290,bool),bool,hAPP(U_290,fun(fun(U_290,bool),bool),member(U_290),sK5(U_292,U_290,U_288,U_286,U_284)),U_284))
| ~ sP8(U_286,U_290,U_284,U_288,U_292) ),
inference(clausify,[status(thm)],[f_94_5]) ).
cnf(f_94_9,plain,
( ti(U_292,U_288) = hAPP(U_290,U_292,U_286,sK5(U_292,U_290,U_288,U_286,U_284))
| ~ sP8(U_286,U_290,U_284,U_288,U_292) ),
inference(clausify,[status(thm)],[f_94_5]) ).
fof(f_95_1,plain,
! [X_a,P_1,Q_1] :
( ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),P_1)),Q_1))))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1)))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) )
& ( ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1)))
& hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) )
| ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),P_1)),Q_1)))) ) ),
inference(fof_nnf,[status(thm)],[fact_57_finite__Collect__disjI]) ).
fof(f_95_2,plain,
! [U_296,U_295,U_294] :
( ( hBOOL(hAPP(fun(U_296,bool),bool,finite_finite(U_296),hAPP(fun(U_296,bool),fun(U_296,bool),collect(U_296),hAPP(fun(U_296,bool),fun(U_296,bool),hAPP(fun(U_296,fun(bool,bool)),fun(fun(U_296,bool),fun(U_296,bool)),combs(U_296,bool,bool),hAPP(fun(U_296,bool),fun(U_296,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_296,bool),fun(U_296,fun(bool,bool))),combb(bool,fun(bool,bool),U_296),fdisj),U_295)),U_294))))
| ~ hBOOL(hAPP(fun(U_296,bool),bool,finite_finite(U_296),hAPP(fun(U_296,bool),fun(U_296,bool),collect(U_296),U_294)))
| ~ hBOOL(hAPP(fun(U_296,bool),bool,finite_finite(U_296),hAPP(fun(U_296,bool),fun(U_296,bool),collect(U_296),U_295))) )
& ( ( hBOOL(hAPP(fun(U_296,bool),bool,finite_finite(U_296),hAPP(fun(U_296,bool),fun(U_296,bool),collect(U_296),U_294)))
& hBOOL(hAPP(fun(U_296,bool),bool,finite_finite(U_296),hAPP(fun(U_296,bool),fun(U_296,bool),collect(U_296),U_295))) )
| ~ hBOOL(hAPP(fun(U_296,bool),bool,finite_finite(U_296),hAPP(fun(U_296,bool),fun(U_296,bool),collect(U_296),hAPP(fun(U_296,bool),fun(U_296,bool),hAPP(fun(U_296,fun(bool,bool)),fun(fun(U_296,bool),fun(U_296,bool)),combs(U_296,bool,bool),hAPP(fun(U_296,bool),fun(U_296,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_296,bool),fun(U_296,fun(bool,bool))),combb(bool,fun(bool,bool),U_296),fdisj),U_295)),U_294)))) ) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
( ! [U_302,U_300,U_298] :
( hBOOL(hAPP(fun(U_302,bool),bool,finite_finite(U_302),hAPP(fun(U_302,bool),fun(U_302,bool),collect(U_302),hAPP(fun(U_302,bool),fun(U_302,bool),hAPP(fun(U_302,fun(bool,bool)),fun(fun(U_302,bool),fun(U_302,bool)),combs(U_302,bool,bool),hAPP(fun(U_302,bool),fun(U_302,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_302,bool),fun(U_302,fun(bool,bool))),combb(bool,fun(bool,bool),U_302),fdisj),U_300)),U_298))))
| ~ hBOOL(hAPP(fun(U_302,bool),bool,finite_finite(U_302),hAPP(fun(U_302,bool),fun(U_302,bool),collect(U_302),U_298)))
| ~ hBOOL(hAPP(fun(U_302,bool),bool,finite_finite(U_302),hAPP(fun(U_302,bool),fun(U_302,bool),collect(U_302),U_300))) )
& ! [U_301,U_299,U_297] :
( ( hBOOL(hAPP(fun(U_301,bool),bool,finite_finite(U_301),hAPP(fun(U_301,bool),fun(U_301,bool),collect(U_301),U_297)))
& hBOOL(hAPP(fun(U_301,bool),bool,finite_finite(U_301),hAPP(fun(U_301,bool),fun(U_301,bool),collect(U_301),U_299))) )
| ~ hBOOL(hAPP(fun(U_301,bool),bool,finite_finite(U_301),hAPP(fun(U_301,bool),fun(U_301,bool),collect(U_301),hAPP(fun(U_301,bool),fun(U_301,bool),hAPP(fun(U_301,fun(bool,bool)),fun(fun(U_301,bool),fun(U_301,bool)),combs(U_301,bool,bool),hAPP(fun(U_301,bool),fun(U_301,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_301,bool),fun(U_301,fun(bool,bool))),combb(bool,fun(bool,bool),U_301),fdisj),U_299)),U_297)))) ) ),
inference(miniscope,[status(thm)],[f_95_2]) ).
fof(f_95_4,plain,
( ! [U_299,U_301,U_297] :
( hBOOL(hAPP(fun(U_301,bool),bool,finite_finite(U_301),hAPP(fun(U_301,bool),fun(U_301,bool),collect(U_301),U_297)))
| ~ sP9(U_299,U_301,U_297) )
& ! [U_299,U_301,U_297] :
( hBOOL(hAPP(fun(U_301,bool),bool,finite_finite(U_301),hAPP(fun(U_301,bool),fun(U_301,bool),collect(U_301),U_299)))
| ~ sP9(U_299,U_301,U_297) )
& ! [U_302,U_298,U_300] :
( hBOOL(hAPP(fun(U_302,bool),bool,finite_finite(U_302),hAPP(fun(U_302,bool),fun(U_302,bool),collect(U_302),hAPP(fun(U_302,bool),fun(U_302,bool),hAPP(fun(U_302,fun(bool,bool)),fun(fun(U_302,bool),fun(U_302,bool)),combs(U_302,bool,bool),hAPP(fun(U_302,bool),fun(U_302,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_302,bool),fun(U_302,fun(bool,bool))),combb(bool,fun(bool,bool),U_302),fdisj),U_300)),U_298))))
| ~ hBOOL(hAPP(fun(U_302,bool),bool,finite_finite(U_302),hAPP(fun(U_302,bool),fun(U_302,bool),collect(U_302),U_298)))
| ~ hBOOL(hAPP(fun(U_302,bool),bool,finite_finite(U_302),hAPP(fun(U_302,bool),fun(U_302,bool),collect(U_302),U_300))) )
& ! [U_299,U_301,U_297] :
( sP9(U_299,U_301,U_297)
| ~ hBOOL(hAPP(fun(U_301,bool),bool,finite_finite(U_301),hAPP(fun(U_301,bool),fun(U_301,bool),collect(U_301),hAPP(fun(U_301,bool),fun(U_301,bool),hAPP(fun(U_301,fun(bool,bool)),fun(fun(U_301,bool),fun(U_301,bool)),combs(U_301,bool,bool),hAPP(fun(U_301,bool),fun(U_301,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_301,bool),fun(U_301,fun(bool,bool))),combb(bool,fun(bool,bool),U_301),fdisj),U_299)),U_297)))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_95_3]) ).
cnf(f_95_5,plain,
( sP9(U_299,U_301,U_297)
| ~ hBOOL(hAPP(fun(U_301,bool),bool,finite_finite(U_301),hAPP(fun(U_301,bool),fun(U_301,bool),collect(U_301),hAPP(fun(U_301,bool),fun(U_301,bool),hAPP(fun(U_301,fun(bool,bool)),fun(fun(U_301,bool),fun(U_301,bool)),combs(U_301,bool,bool),hAPP(fun(U_301,bool),fun(U_301,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_301,bool),fun(U_301,fun(bool,bool))),combb(bool,fun(bool,bool),U_301),fdisj),U_299)),U_297)))) ),
inference(clausify,[status(thm)],[f_95_4]) ).
cnf(f_95_6,plain,
( hBOOL(hAPP(fun(U_302,bool),bool,finite_finite(U_302),hAPP(fun(U_302,bool),fun(U_302,bool),collect(U_302),hAPP(fun(U_302,bool),fun(U_302,bool),hAPP(fun(U_302,fun(bool,bool)),fun(fun(U_302,bool),fun(U_302,bool)),combs(U_302,bool,bool),hAPP(fun(U_302,bool),fun(U_302,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_302,bool),fun(U_302,fun(bool,bool))),combb(bool,fun(bool,bool),U_302),fdisj),U_300)),U_298))))
| ~ hBOOL(hAPP(fun(U_302,bool),bool,finite_finite(U_302),hAPP(fun(U_302,bool),fun(U_302,bool),collect(U_302),U_298)))
| ~ hBOOL(hAPP(fun(U_302,bool),bool,finite_finite(U_302),hAPP(fun(U_302,bool),fun(U_302,bool),collect(U_302),U_300))) ),
inference(clausify,[status(thm)],[f_95_4]) ).
cnf(f_95_7,plain,
( hBOOL(hAPP(fun(U_301,bool),bool,finite_finite(U_301),hAPP(fun(U_301,bool),fun(U_301,bool),collect(U_301),U_299)))
| ~ sP9(U_299,U_301,U_297) ),
inference(clausify,[status(thm)],[f_95_4]) ).
cnf(f_95_8,plain,
( hBOOL(hAPP(fun(U_301,bool),bool,finite_finite(U_301),hAPP(fun(U_301,bool),fun(U_301,bool),collect(U_301),U_297)))
| ~ sP9(U_299,U_301,U_297) ),
inference(clausify,[status(thm)],[f_95_4]) ).
fof(f_96_1,plain,
! [X_a,X_1,Xa] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_1),Xa) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_1))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),Xa))),
inference(fof_nnf,[status(thm)],[fact_58_insert__compr__raw]) ).
fof(f_96_2,plain,
! [U_305,U_304,U_303] : hAPP(fun(U_305,bool),fun(U_305,bool),hAPP(U_305,fun(fun(U_305,bool),fun(U_305,bool)),insert(U_305),U_304),U_303) = hAPP(fun(U_305,bool),fun(U_305,bool),collect(U_305),hAPP(fun(U_305,bool),fun(U_305,bool),hAPP(fun(U_305,fun(bool,bool)),fun(fun(U_305,bool),fun(U_305,bool)),combs(U_305,bool,bool),hAPP(fun(U_305,bool),fun(U_305,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_305,bool),fun(U_305,fun(bool,bool))),combb(bool,fun(bool,bool),U_305),fdisj),hAPP(U_305,fun(U_305,bool),hAPP(fun(U_305,fun(U_305,bool)),fun(U_305,fun(U_305,bool)),combc(U_305,U_305,bool),fequal(U_305)),U_304))),hAPP(fun(U_305,bool),fun(U_305,bool),hAPP(fun(U_305,fun(fun(U_305,bool),bool)),fun(fun(U_305,bool),fun(U_305,bool)),combc(U_305,fun(U_305,bool),bool),member(U_305)),U_303))),
inference(variable_rename,[status(thm)],[f_96_1]) ).
fof(f_96_3,plain,
! [U_303,U_305,U_304] : hAPP(fun(U_305,bool),fun(U_305,bool),hAPP(U_305,fun(fun(U_305,bool),fun(U_305,bool)),insert(U_305),U_304),U_303) = hAPP(fun(U_305,bool),fun(U_305,bool),collect(U_305),hAPP(fun(U_305,bool),fun(U_305,bool),hAPP(fun(U_305,fun(bool,bool)),fun(fun(U_305,bool),fun(U_305,bool)),combs(U_305,bool,bool),hAPP(fun(U_305,bool),fun(U_305,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_305,bool),fun(U_305,fun(bool,bool))),combb(bool,fun(bool,bool),U_305),fdisj),hAPP(U_305,fun(U_305,bool),hAPP(fun(U_305,fun(U_305,bool)),fun(U_305,fun(U_305,bool)),combc(U_305,U_305,bool),fequal(U_305)),U_304))),hAPP(fun(U_305,bool),fun(U_305,bool),hAPP(fun(U_305,fun(fun(U_305,bool),bool)),fun(fun(U_305,bool),fun(U_305,bool)),combc(U_305,fun(U_305,bool),bool),member(U_305)),U_303))),
inference(definitional_conversion,[status(esa)],[f_96_2]) ).
cnf(f_96_4,plain,
hAPP(fun(U_305,bool),fun(U_305,bool),hAPP(U_305,fun(fun(U_305,bool),fun(U_305,bool)),insert(U_305),U_304),U_303) = hAPP(fun(U_305,bool),fun(U_305,bool),collect(U_305),hAPP(fun(U_305,bool),fun(U_305,bool),hAPP(fun(U_305,fun(bool,bool)),fun(fun(U_305,bool),fun(U_305,bool)),combs(U_305,bool,bool),hAPP(fun(U_305,bool),fun(U_305,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_305,bool),fun(U_305,fun(bool,bool))),combb(bool,fun(bool,bool),U_305),fdisj),hAPP(U_305,fun(U_305,bool),hAPP(fun(U_305,fun(U_305,bool)),fun(U_305,fun(U_305,bool)),combc(U_305,U_305,bool),fequal(U_305)),U_304))),hAPP(fun(U_305,bool),fun(U_305,bool),hAPP(fun(U_305,fun(fun(U_305,bool),bool)),fun(fun(U_305,bool),fun(U_305,bool)),combc(U_305,fun(U_305,bool),bool),member(U_305)),U_303))),
inference(clausify,[status(thm)],[f_96_3]) ).
fof(f_97_1,plain,
! [X_a,Y_2] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),combi(X_a)),Y_2) = ti(fun(X_a,bool),Y_2),
inference(fof_nnf,[status(thm)],[fact_59_image__ident]) ).
fof(f_97_2,plain,
! [U_307,U_306] : hAPP(fun(U_307,bool),fun(U_307,bool),hAPP(fun(U_307,U_307),fun(fun(U_307,bool),fun(U_307,bool)),image(U_307,U_307),combi(U_307)),U_306) = ti(fun(U_307,bool),U_306),
inference(variable_rename,[status(thm)],[f_97_1]) ).
fof(f_97_3,plain,
! [U_306,U_307] : hAPP(fun(U_307,bool),fun(U_307,bool),hAPP(fun(U_307,U_307),fun(fun(U_307,bool),fun(U_307,bool)),image(U_307,U_307),combi(U_307)),U_306) = ti(fun(U_307,bool),U_306),
inference(definitional_conversion,[status(esa)],[f_97_2]) ).
cnf(f_97_4,plain,
hAPP(fun(U_307,bool),fun(U_307,bool),hAPP(fun(U_307,U_307),fun(fun(U_307,bool),fun(U_307,bool)),image(U_307,U_307),combi(U_307)),U_306) = ti(fun(U_307,bool),U_306),
inference(clausify,[status(thm)],[f_97_3]) ).
fof(f_98_1,plain,
! [X_b,X_a,X_c,F,G_1,A_1] : hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),G_1),A_1)) = hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),hAPP(fun(X_c,X_b),fun(X_c,X_a),hAPP(fun(X_b,X_a),fun(fun(X_c,X_b),fun(X_c,X_a)),combb(X_b,X_a,X_c),F),G_1)),A_1),
inference(fof_nnf,[status(thm)],[fact_60_image__image]) ).
fof(f_98_2,plain,
! [U_313,U_312,U_311,U_310,U_309,U_308] : hAPP(fun(U_313,bool),fun(U_312,bool),hAPP(fun(U_313,U_312),fun(fun(U_313,bool),fun(U_312,bool)),image(U_313,U_312),U_310),hAPP(fun(U_311,bool),fun(U_313,bool),hAPP(fun(U_311,U_313),fun(fun(U_311,bool),fun(U_313,bool)),image(U_311,U_313),U_309),U_308)) = hAPP(fun(U_311,bool),fun(U_312,bool),hAPP(fun(U_311,U_312),fun(fun(U_311,bool),fun(U_312,bool)),image(U_311,U_312),hAPP(fun(U_311,U_313),fun(U_311,U_312),hAPP(fun(U_313,U_312),fun(fun(U_311,U_313),fun(U_311,U_312)),combb(U_313,U_312,U_311),U_310),U_309)),U_308),
inference(variable_rename,[status(thm)],[f_98_1]) ).
fof(f_98_3,plain,
! [U_310,U_308,U_309,U_311,U_312,U_313] : hAPP(fun(U_313,bool),fun(U_312,bool),hAPP(fun(U_313,U_312),fun(fun(U_313,bool),fun(U_312,bool)),image(U_313,U_312),U_310),hAPP(fun(U_311,bool),fun(U_313,bool),hAPP(fun(U_311,U_313),fun(fun(U_311,bool),fun(U_313,bool)),image(U_311,U_313),U_309),U_308)) = hAPP(fun(U_311,bool),fun(U_312,bool),hAPP(fun(U_311,U_312),fun(fun(U_311,bool),fun(U_312,bool)),image(U_311,U_312),hAPP(fun(U_311,U_313),fun(U_311,U_312),hAPP(fun(U_313,U_312),fun(fun(U_311,U_313),fun(U_311,U_312)),combb(U_313,U_312,U_311),U_310),U_309)),U_308),
inference(definitional_conversion,[status(esa)],[f_98_2]) ).
cnf(f_98_4,plain,
hAPP(fun(U_313,bool),fun(U_312,bool),hAPP(fun(U_313,U_312),fun(fun(U_313,bool),fun(U_312,bool)),image(U_313,U_312),U_310),hAPP(fun(U_311,bool),fun(U_313,bool),hAPP(fun(U_311,U_313),fun(fun(U_311,bool),fun(U_313,bool)),image(U_311,U_313),U_309),U_308)) = hAPP(fun(U_311,bool),fun(U_312,bool),hAPP(fun(U_311,U_312),fun(fun(U_311,bool),fun(U_312,bool)),image(U_311,U_312),hAPP(fun(U_311,U_313),fun(U_311,U_312),hAPP(fun(U_313,U_312),fun(fun(U_311,U_313),fun(U_311,U_312)),combb(U_313,U_312,U_311),U_310),U_309)),U_308),
inference(clausify,[status(thm)],[f_98_3]) ).
fof(f_99_1,plain,
! [X_a,A_3,B_1] :
( ti(X_a,A_3) = ti(X_a,B_1)
| hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),bot_bot(fun(X_a,bool))) != hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),bot_bot(fun(X_a,bool))) ),
inference(fof_nnf,[status(thm)],[fact_61_singleton__inject]) ).
fof(f_99_2,plain,
! [U_316,U_315,U_314] :
( ti(U_316,U_315) = ti(U_316,U_314)
| hAPP(fun(U_316,bool),fun(U_316,bool),hAPP(U_316,fun(fun(U_316,bool),fun(U_316,bool)),insert(U_316),U_315),bot_bot(fun(U_316,bool))) != hAPP(fun(U_316,bool),fun(U_316,bool),hAPP(U_316,fun(fun(U_316,bool),fun(U_316,bool)),insert(U_316),U_314),bot_bot(fun(U_316,bool))) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
fof(f_99_3,plain,
! [U_314,U_315,U_316] :
( ti(U_316,U_315) = ti(U_316,U_314)
| hAPP(fun(U_316,bool),fun(U_316,bool),hAPP(U_316,fun(fun(U_316,bool),fun(U_316,bool)),insert(U_316),U_315),bot_bot(fun(U_316,bool))) != hAPP(fun(U_316,bool),fun(U_316,bool),hAPP(U_316,fun(fun(U_316,bool),fun(U_316,bool)),insert(U_316),U_314),bot_bot(fun(U_316,bool))) ),
inference(definitional_conversion,[status(esa)],[f_99_2]) ).
cnf(f_99_4,plain,
( ti(U_316,U_315) = ti(U_316,U_314)
| hAPP(fun(U_316,bool),fun(U_316,bool),hAPP(U_316,fun(fun(U_316,bool),fun(U_316,bool)),insert(U_316),U_315),bot_bot(fun(U_316,bool))) != hAPP(fun(U_316,bool),fun(U_316,bool),hAPP(U_316,fun(fun(U_316,bool),fun(U_316,bool)),insert(U_316),U_314),bot_bot(fun(U_316,bool))) ),
inference(clausify,[status(thm)],[f_99_3]) ).
fof(f_100_1,plain,
! [X_a,B_1,A_3] :
( ti(X_a,B_1) = ti(X_a,A_3)
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),bot_bot(fun(X_a,bool))))) ),
inference(fof_nnf,[status(thm)],[fact_62_singletonE]) ).
fof(f_100_2,plain,
! [U_319,U_318,U_317] :
( ti(U_319,U_318) = ti(U_319,U_317)
| ~ hBOOL(hAPP(fun(U_319,bool),bool,hAPP(U_319,fun(fun(U_319,bool),bool),member(U_319),U_318),hAPP(fun(U_319,bool),fun(U_319,bool),hAPP(U_319,fun(fun(U_319,bool),fun(U_319,bool)),insert(U_319),U_317),bot_bot(fun(U_319,bool))))) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
! [U_317,U_318,U_319] :
( ti(U_319,U_318) = ti(U_319,U_317)
| ~ hBOOL(hAPP(fun(U_319,bool),bool,hAPP(U_319,fun(fun(U_319,bool),bool),member(U_319),U_318),hAPP(fun(U_319,bool),fun(U_319,bool),hAPP(U_319,fun(fun(U_319,bool),fun(U_319,bool)),insert(U_319),U_317),bot_bot(fun(U_319,bool))))) ),
inference(definitional_conversion,[status(esa)],[f_100_2]) ).
cnf(f_100_4,plain,
( ti(U_319,U_318) = ti(U_319,U_317)
| ~ hBOOL(hAPP(fun(U_319,bool),bool,hAPP(U_319,fun(fun(U_319,bool),bool),member(U_319),U_318),hAPP(fun(U_319,bool),fun(U_319,bool),hAPP(U_319,fun(fun(U_319,bool),fun(U_319,bool)),insert(U_319),U_317),bot_bot(fun(U_319,bool))))) ),
inference(clausify,[status(thm)],[f_100_3]) ).
fof(f_101_1,plain,
! [X_a,A_3,B_1,C_1,D_1] :
( ( hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),bot_bot(fun(X_a,bool)))) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),D_1),bot_bot(fun(X_a,bool))))
| ( ( ti(X_a,B_1) != ti(X_a,C_1)
| ti(X_a,A_3) != ti(X_a,D_1) )
& ( ti(X_a,B_1) != ti(X_a,D_1)
| ti(X_a,A_3) != ti(X_a,C_1) ) ) )
& ( ( ti(X_a,B_1) = ti(X_a,C_1)
& ti(X_a,A_3) = ti(X_a,D_1) )
| ( ti(X_a,B_1) = ti(X_a,D_1)
& ti(X_a,A_3) = ti(X_a,C_1) )
| hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),bot_bot(fun(X_a,bool)))) != hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),D_1),bot_bot(fun(X_a,bool)))) ) ),
inference(fof_nnf,[status(thm)],[fact_63_doubleton__eq__iff]) ).
fof(f_101_2,plain,
! [U_324,U_323,U_322,U_321,U_320] :
( ( hAPP(fun(U_324,bool),fun(U_324,bool),hAPP(U_324,fun(fun(U_324,bool),fun(U_324,bool)),insert(U_324),U_323),hAPP(fun(U_324,bool),fun(U_324,bool),hAPP(U_324,fun(fun(U_324,bool),fun(U_324,bool)),insert(U_324),U_322),bot_bot(fun(U_324,bool)))) = hAPP(fun(U_324,bool),fun(U_324,bool),hAPP(U_324,fun(fun(U_324,bool),fun(U_324,bool)),insert(U_324),U_321),hAPP(fun(U_324,bool),fun(U_324,bool),hAPP(U_324,fun(fun(U_324,bool),fun(U_324,bool)),insert(U_324),U_320),bot_bot(fun(U_324,bool))))
| ( ( ti(U_324,U_322) != ti(U_324,U_321)
| ti(U_324,U_323) != ti(U_324,U_320) )
& ( ti(U_324,U_322) != ti(U_324,U_320)
| ti(U_324,U_323) != ti(U_324,U_321) ) ) )
& ( ( ti(U_324,U_322) = ti(U_324,U_321)
& ti(U_324,U_323) = ti(U_324,U_320) )
| ( ti(U_324,U_322) = ti(U_324,U_320)
& ti(U_324,U_323) = ti(U_324,U_321) )
| hAPP(fun(U_324,bool),fun(U_324,bool),hAPP(U_324,fun(fun(U_324,bool),fun(U_324,bool)),insert(U_324),U_323),hAPP(fun(U_324,bool),fun(U_324,bool),hAPP(U_324,fun(fun(U_324,bool),fun(U_324,bool)),insert(U_324),U_322),bot_bot(fun(U_324,bool)))) != hAPP(fun(U_324,bool),fun(U_324,bool),hAPP(U_324,fun(fun(U_324,bool),fun(U_324,bool)),insert(U_324),U_321),hAPP(fun(U_324,bool),fun(U_324,bool),hAPP(U_324,fun(fun(U_324,bool),fun(U_324,bool)),insert(U_324),U_320),bot_bot(fun(U_324,bool)))) ) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
fof(f_101_3,plain,
( ! [U_334,U_332,U_330,U_328,U_326] :
( hAPP(fun(U_334,bool),fun(U_334,bool),hAPP(U_334,fun(fun(U_334,bool),fun(U_334,bool)),insert(U_334),U_332),hAPP(fun(U_334,bool),fun(U_334,bool),hAPP(U_334,fun(fun(U_334,bool),fun(U_334,bool)),insert(U_334),U_330),bot_bot(fun(U_334,bool)))) = hAPP(fun(U_334,bool),fun(U_334,bool),hAPP(U_334,fun(fun(U_334,bool),fun(U_334,bool)),insert(U_334),U_328),hAPP(fun(U_334,bool),fun(U_334,bool),hAPP(U_334,fun(fun(U_334,bool),fun(U_334,bool)),insert(U_334),U_326),bot_bot(fun(U_334,bool))))
| ( ( ti(U_334,U_330) != ti(U_334,U_328)
| ti(U_334,U_332) != ti(U_334,U_326) )
& ( ti(U_334,U_330) != ti(U_334,U_326)
| ti(U_334,U_332) != ti(U_334,U_328) ) ) )
& ! [U_333,U_331,U_329,U_327,U_325] :
( ( ti(U_333,U_329) = ti(U_333,U_327)
& ti(U_333,U_331) = ti(U_333,U_325) )
| ( ti(U_333,U_329) = ti(U_333,U_325)
& ti(U_333,U_331) = ti(U_333,U_327) )
| hAPP(fun(U_333,bool),fun(U_333,bool),hAPP(U_333,fun(fun(U_333,bool),fun(U_333,bool)),insert(U_333),U_331),hAPP(fun(U_333,bool),fun(U_333,bool),hAPP(U_333,fun(fun(U_333,bool),fun(U_333,bool)),insert(U_333),U_329),bot_bot(fun(U_333,bool)))) != hAPP(fun(U_333,bool),fun(U_333,bool),hAPP(U_333,fun(fun(U_333,bool),fun(U_333,bool)),insert(U_333),U_327),hAPP(fun(U_333,bool),fun(U_333,bool),hAPP(U_333,fun(fun(U_333,bool),fun(U_333,bool)),insert(U_333),U_325),bot_bot(fun(U_333,bool)))) ) ),
inference(miniscope,[status(thm)],[f_101_2]) ).
fof(f_101_4,plain,
( ! [U_334,U_326,U_328,U_330,U_332] :
( ti(U_334,U_330) != ti(U_334,U_328)
| ti(U_334,U_332) != ti(U_334,U_326)
| ~ sP12(U_334,U_326,U_328,U_330,U_332) )
& ! [U_334,U_326,U_328,U_330,U_332] :
( ti(U_334,U_330) != ti(U_334,U_326)
| ti(U_334,U_332) != ti(U_334,U_328)
| ~ sP12(U_334,U_326,U_328,U_330,U_332) )
& ! [U_329,U_325,U_331,U_327,U_333] :
( ti(U_333,U_329) = ti(U_333,U_327)
| ~ sP11(U_329,U_325,U_331,U_327,U_333) )
& ! [U_329,U_325,U_331,U_327,U_333] :
( ti(U_333,U_331) = ti(U_333,U_325)
| ~ sP11(U_329,U_325,U_331,U_327,U_333) )
& ! [U_329,U_325,U_331,U_327,U_333] :
( ti(U_333,U_329) = ti(U_333,U_325)
| ~ sP10(U_329,U_325,U_331,U_327,U_333) )
& ! [U_329,U_325,U_331,U_327,U_333] :
( ti(U_333,U_331) = ti(U_333,U_327)
| ~ sP10(U_329,U_325,U_331,U_327,U_333) )
& ! [U_334,U_326,U_328,U_330,U_332] :
( hAPP(fun(U_334,bool),fun(U_334,bool),hAPP(U_334,fun(fun(U_334,bool),fun(U_334,bool)),insert(U_334),U_332),hAPP(fun(U_334,bool),fun(U_334,bool),hAPP(U_334,fun(fun(U_334,bool),fun(U_334,bool)),insert(U_334),U_330),bot_bot(fun(U_334,bool)))) = hAPP(fun(U_334,bool),fun(U_334,bool),hAPP(U_334,fun(fun(U_334,bool),fun(U_334,bool)),insert(U_334),U_328),hAPP(fun(U_334,bool),fun(U_334,bool),hAPP(U_334,fun(fun(U_334,bool),fun(U_334,bool)),insert(U_334),U_326),bot_bot(fun(U_334,bool))))
| sP12(U_334,U_326,U_328,U_330,U_332) )
& ! [U_329,U_325,U_331,U_327,U_333] :
( sP11(U_329,U_325,U_331,U_327,U_333)
| sP10(U_329,U_325,U_331,U_327,U_333)
| hAPP(fun(U_333,bool),fun(U_333,bool),hAPP(U_333,fun(fun(U_333,bool),fun(U_333,bool)),insert(U_333),U_331),hAPP(fun(U_333,bool),fun(U_333,bool),hAPP(U_333,fun(fun(U_333,bool),fun(U_333,bool)),insert(U_333),U_329),bot_bot(fun(U_333,bool)))) != hAPP(fun(U_333,bool),fun(U_333,bool),hAPP(U_333,fun(fun(U_333,bool),fun(U_333,bool)),insert(U_333),U_327),hAPP(fun(U_333,bool),fun(U_333,bool),hAPP(U_333,fun(fun(U_333,bool),fun(U_333,bool)),insert(U_333),U_325),bot_bot(fun(U_333,bool)))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10,sP11,sP12])],[f_101_3]) ).
cnf(f_101_5,plain,
( sP11(U_329,U_325,U_331,U_327,U_333)
| sP10(U_329,U_325,U_331,U_327,U_333)
| hAPP(fun(U_333,bool),fun(U_333,bool),hAPP(U_333,fun(fun(U_333,bool),fun(U_333,bool)),insert(U_333),U_331),hAPP(fun(U_333,bool),fun(U_333,bool),hAPP(U_333,fun(fun(U_333,bool),fun(U_333,bool)),insert(U_333),U_329),bot_bot(fun(U_333,bool)))) != hAPP(fun(U_333,bool),fun(U_333,bool),hAPP(U_333,fun(fun(U_333,bool),fun(U_333,bool)),insert(U_333),U_327),hAPP(fun(U_333,bool),fun(U_333,bool),hAPP(U_333,fun(fun(U_333,bool),fun(U_333,bool)),insert(U_333),U_325),bot_bot(fun(U_333,bool)))) ),
inference(clausify,[status(thm)],[f_101_4]) ).
cnf(f_101_6,plain,
( hAPP(fun(U_334,bool),fun(U_334,bool),hAPP(U_334,fun(fun(U_334,bool),fun(U_334,bool)),insert(U_334),U_332),hAPP(fun(U_334,bool),fun(U_334,bool),hAPP(U_334,fun(fun(U_334,bool),fun(U_334,bool)),insert(U_334),U_330),bot_bot(fun(U_334,bool)))) = hAPP(fun(U_334,bool),fun(U_334,bool),hAPP(U_334,fun(fun(U_334,bool),fun(U_334,bool)),insert(U_334),U_328),hAPP(fun(U_334,bool),fun(U_334,bool),hAPP(U_334,fun(fun(U_334,bool),fun(U_334,bool)),insert(U_334),U_326),bot_bot(fun(U_334,bool))))
| sP12(U_334,U_326,U_328,U_330,U_332) ),
inference(clausify,[status(thm)],[f_101_4]) ).
cnf(f_101_7,plain,
( ti(U_333,U_331) = ti(U_333,U_327)
| ~ sP10(U_329,U_325,U_331,U_327,U_333) ),
inference(clausify,[status(thm)],[f_101_4]) ).
cnf(f_101_8,plain,
( ti(U_333,U_329) = ti(U_333,U_325)
| ~ sP10(U_329,U_325,U_331,U_327,U_333) ),
inference(clausify,[status(thm)],[f_101_4]) ).
cnf(f_101_9,plain,
( ti(U_333,U_331) = ti(U_333,U_325)
| ~ sP11(U_329,U_325,U_331,U_327,U_333) ),
inference(clausify,[status(thm)],[f_101_4]) ).
cnf(f_101_10,plain,
( ti(U_333,U_329) = ti(U_333,U_327)
| ~ sP11(U_329,U_325,U_331,U_327,U_333) ),
inference(clausify,[status(thm)],[f_101_4]) ).
cnf(f_101_11,plain,
( ti(U_334,U_330) != ti(U_334,U_326)
| ti(U_334,U_332) != ti(U_334,U_328)
| ~ sP12(U_334,U_326,U_328,U_330,U_332) ),
inference(clausify,[status(thm)],[f_101_4]) ).
cnf(f_101_12,plain,
( ti(U_334,U_330) != ti(U_334,U_328)
| ti(U_334,U_332) != ti(U_334,U_326)
| ~ sP12(U_334,U_326,U_328,U_330,U_332) ),
inference(clausify,[status(thm)],[f_101_4]) ).
fof(f_102_1,plain,
! [X_a,B_1,A_3] :
( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),bot_bot(fun(X_a,bool)))))
| ti(X_a,B_1) != ti(X_a,A_3) )
& ( ti(X_a,B_1) = ti(X_a,A_3)
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),bot_bot(fun(X_a,bool))))) ) ),
inference(fof_nnf,[status(thm)],[fact_64_singleton__iff]) ).
fof(f_102_2,plain,
! [U_337,U_336,U_335] :
( ( hBOOL(hAPP(fun(U_337,bool),bool,hAPP(U_337,fun(fun(U_337,bool),bool),member(U_337),U_336),hAPP(fun(U_337,bool),fun(U_337,bool),hAPP(U_337,fun(fun(U_337,bool),fun(U_337,bool)),insert(U_337),U_335),bot_bot(fun(U_337,bool)))))
| ti(U_337,U_336) != ti(U_337,U_335) )
& ( ti(U_337,U_336) = ti(U_337,U_335)
| ~ hBOOL(hAPP(fun(U_337,bool),bool,hAPP(U_337,fun(fun(U_337,bool),bool),member(U_337),U_336),hAPP(fun(U_337,bool),fun(U_337,bool),hAPP(U_337,fun(fun(U_337,bool),fun(U_337,bool)),insert(U_337),U_335),bot_bot(fun(U_337,bool))))) ) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
fof(f_102_3,plain,
( ! [U_343,U_341,U_339] :
( hBOOL(hAPP(fun(U_343,bool),bool,hAPP(U_343,fun(fun(U_343,bool),bool),member(U_343),U_341),hAPP(fun(U_343,bool),fun(U_343,bool),hAPP(U_343,fun(fun(U_343,bool),fun(U_343,bool)),insert(U_343),U_339),bot_bot(fun(U_343,bool)))))
| ti(U_343,U_341) != ti(U_343,U_339) )
& ! [U_342,U_340,U_338] :
( ti(U_342,U_340) = ti(U_342,U_338)
| ~ hBOOL(hAPP(fun(U_342,bool),bool,hAPP(U_342,fun(fun(U_342,bool),bool),member(U_342),U_340),hAPP(fun(U_342,bool),fun(U_342,bool),hAPP(U_342,fun(fun(U_342,bool),fun(U_342,bool)),insert(U_342),U_338),bot_bot(fun(U_342,bool))))) ) ),
inference(miniscope,[status(thm)],[f_102_2]) ).
fof(f_102_4,plain,
( ! [U_339,U_341,U_343] :
( hBOOL(hAPP(fun(U_343,bool),bool,hAPP(U_343,fun(fun(U_343,bool),bool),member(U_343),U_341),hAPP(fun(U_343,bool),fun(U_343,bool),hAPP(U_343,fun(fun(U_343,bool),fun(U_343,bool)),insert(U_343),U_339),bot_bot(fun(U_343,bool)))))
| ti(U_343,U_341) != ti(U_343,U_339) )
& ! [U_340,U_338,U_342] :
( ti(U_342,U_340) = ti(U_342,U_338)
| ~ hBOOL(hAPP(fun(U_342,bool),bool,hAPP(U_342,fun(fun(U_342,bool),bool),member(U_342),U_340),hAPP(fun(U_342,bool),fun(U_342,bool),hAPP(U_342,fun(fun(U_342,bool),fun(U_342,bool)),insert(U_342),U_338),bot_bot(fun(U_342,bool))))) ) ),
inference(definitional_conversion,[status(esa)],[f_102_3]) ).
cnf(f_102_5,plain,
( ti(U_342,U_340) = ti(U_342,U_338)
| ~ hBOOL(hAPP(fun(U_342,bool),bool,hAPP(U_342,fun(fun(U_342,bool),bool),member(U_342),U_340),hAPP(fun(U_342,bool),fun(U_342,bool),hAPP(U_342,fun(fun(U_342,bool),fun(U_342,bool)),insert(U_342),U_338),bot_bot(fun(U_342,bool))))) ),
inference(clausify,[status(thm)],[f_102_4]) ).
cnf(f_102_6,plain,
( hBOOL(hAPP(fun(U_343,bool),bool,hAPP(U_343,fun(fun(U_343,bool),bool),member(U_343),U_341),hAPP(fun(U_343,bool),fun(U_343,bool),hAPP(U_343,fun(fun(U_343,bool),fun(U_343,bool)),insert(U_343),U_339),bot_bot(fun(U_343,bool)))))
| ti(U_343,U_341) != ti(U_343,U_339) ),
inference(clausify,[status(thm)],[f_102_4]) ).
fof(f_103_1,plain,
! [X_a,A_3,A_1] : hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),A_1) != bot_bot(fun(X_a,bool)),
inference(fof_nnf,[status(thm)],[fact_65_insert__not__empty]) ).
fof(f_103_2,plain,
! [U_346,U_345,U_344] : hAPP(fun(U_346,bool),fun(U_346,bool),hAPP(U_346,fun(fun(U_346,bool),fun(U_346,bool)),insert(U_346),U_345),U_344) != bot_bot(fun(U_346,bool)),
inference(variable_rename,[status(thm)],[f_103_1]) ).
fof(f_103_3,plain,
! [U_345,U_344,U_346] : hAPP(fun(U_346,bool),fun(U_346,bool),hAPP(U_346,fun(fun(U_346,bool),fun(U_346,bool)),insert(U_346),U_345),U_344) != bot_bot(fun(U_346,bool)),
inference(definitional_conversion,[status(esa)],[f_103_2]) ).
cnf(f_103_4,plain,
hAPP(fun(U_346,bool),fun(U_346,bool),hAPP(U_346,fun(fun(U_346,bool),fun(U_346,bool)),insert(U_346),U_345),U_344) != bot_bot(fun(U_346,bool)),
inference(clausify,[status(thm)],[f_103_3]) ).
fof(f_104_1,plain,
! [X_a,A_3,A_1] : bot_bot(fun(X_a,bool)) != hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),A_1),
inference(fof_nnf,[status(thm)],[fact_66_empty__not__insert]) ).
fof(f_104_2,plain,
! [U_349,U_348,U_347] : bot_bot(fun(U_349,bool)) != hAPP(fun(U_349,bool),fun(U_349,bool),hAPP(U_349,fun(fun(U_349,bool),fun(U_349,bool)),insert(U_349),U_348),U_347),
inference(variable_rename,[status(thm)],[f_104_1]) ).
fof(f_104_3,plain,
! [U_349,U_348,U_347] : bot_bot(fun(U_349,bool)) != hAPP(fun(U_349,bool),fun(U_349,bool),hAPP(U_349,fun(fun(U_349,bool),fun(U_349,bool)),insert(U_349),U_348),U_347),
inference(definitional_conversion,[status(esa)],[f_104_2]) ).
cnf(f_104_4,plain,
bot_bot(fun(U_349,bool)) != hAPP(fun(U_349,bool),fun(U_349,bool),hAPP(U_349,fun(fun(U_349,bool),fun(U_349,bool)),insert(U_349),U_348),U_347),
inference(clausify,[status(thm)],[f_104_3]) ).
fof(f_105_1,plain,
! [X_a,A_3,A_1] :
( ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),A_1)))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1)) )
& ( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),A_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_67_finite__insert]) ).
fof(f_105_2,plain,
! [U_352,U_351,U_350] :
( ( hBOOL(hAPP(fun(U_352,bool),bool,finite_finite(U_352),hAPP(fun(U_352,bool),fun(U_352,bool),hAPP(U_352,fun(fun(U_352,bool),fun(U_352,bool)),insert(U_352),U_351),U_350)))
| ~ hBOOL(hAPP(fun(U_352,bool),bool,finite_finite(U_352),U_350)) )
& ( hBOOL(hAPP(fun(U_352,bool),bool,finite_finite(U_352),U_350))
| ~ hBOOL(hAPP(fun(U_352,bool),bool,finite_finite(U_352),hAPP(fun(U_352,bool),fun(U_352,bool),hAPP(U_352,fun(fun(U_352,bool),fun(U_352,bool)),insert(U_352),U_351),U_350))) ) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
( ! [U_358,U_356,U_354] :
( hBOOL(hAPP(fun(U_358,bool),bool,finite_finite(U_358),hAPP(fun(U_358,bool),fun(U_358,bool),hAPP(U_358,fun(fun(U_358,bool),fun(U_358,bool)),insert(U_358),U_356),U_354)))
| ~ hBOOL(hAPP(fun(U_358,bool),bool,finite_finite(U_358),U_354)) )
& ! [U_357,U_355,U_353] :
( hBOOL(hAPP(fun(U_357,bool),bool,finite_finite(U_357),U_353))
| ~ hBOOL(hAPP(fun(U_357,bool),bool,finite_finite(U_357),hAPP(fun(U_357,bool),fun(U_357,bool),hAPP(U_357,fun(fun(U_357,bool),fun(U_357,bool)),insert(U_357),U_355),U_353))) ) ),
inference(miniscope,[status(thm)],[f_105_2]) ).
fof(f_105_4,plain,
( ! [U_354,U_358,U_356] :
( hBOOL(hAPP(fun(U_358,bool),bool,finite_finite(U_358),hAPP(fun(U_358,bool),fun(U_358,bool),hAPP(U_358,fun(fun(U_358,bool),fun(U_358,bool)),insert(U_358),U_356),U_354)))
| ~ hBOOL(hAPP(fun(U_358,bool),bool,finite_finite(U_358),U_354)) )
& ! [U_355,U_357,U_353] :
( hBOOL(hAPP(fun(U_357,bool),bool,finite_finite(U_357),U_353))
| ~ hBOOL(hAPP(fun(U_357,bool),bool,finite_finite(U_357),hAPP(fun(U_357,bool),fun(U_357,bool),hAPP(U_357,fun(fun(U_357,bool),fun(U_357,bool)),insert(U_357),U_355),U_353))) ) ),
inference(definitional_conversion,[status(esa)],[f_105_3]) ).
cnf(f_105_5,plain,
( hBOOL(hAPP(fun(U_357,bool),bool,finite_finite(U_357),U_353))
| ~ hBOOL(hAPP(fun(U_357,bool),bool,finite_finite(U_357),hAPP(fun(U_357,bool),fun(U_357,bool),hAPP(U_357,fun(fun(U_357,bool),fun(U_357,bool)),insert(U_357),U_355),U_353))) ),
inference(clausify,[status(thm)],[f_105_4]) ).
cnf(f_105_6,plain,
( hBOOL(hAPP(fun(U_358,bool),bool,finite_finite(U_358),hAPP(fun(U_358,bool),fun(U_358,bool),hAPP(U_358,fun(fun(U_358,bool),fun(U_358,bool)),insert(U_358),U_356),U_354)))
| ~ hBOOL(hAPP(fun(U_358,bool),bool,finite_finite(U_358),U_354)) ),
inference(clausify,[status(thm)],[f_105_4]) ).
fof(f_106_1,plain,
! [X_a,A_1] :
( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),bot_bot(fun(X_a,bool))))
| ti(fun(X_a,bool),A_1) != bot_bot(fun(X_a,bool)) )
& ( ti(fun(X_a,bool),A_1) = bot_bot(fun(X_a,bool))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),bot_bot(fun(X_a,bool)))) ) ),
inference(fof_nnf,[status(thm)],[fact_68_subset__empty]) ).
fof(f_106_2,plain,
! [U_360,U_359] :
( ( hBOOL(hAPP(fun(U_360,bool),bool,hAPP(fun(U_360,bool),fun(fun(U_360,bool),bool),ord_less_eq(fun(U_360,bool)),U_359),bot_bot(fun(U_360,bool))))
| ti(fun(U_360,bool),U_359) != bot_bot(fun(U_360,bool)) )
& ( ti(fun(U_360,bool),U_359) = bot_bot(fun(U_360,bool))
| ~ hBOOL(hAPP(fun(U_360,bool),bool,hAPP(fun(U_360,bool),fun(fun(U_360,bool),bool),ord_less_eq(fun(U_360,bool)),U_359),bot_bot(fun(U_360,bool)))) ) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
( ! [U_364,U_362] :
( hBOOL(hAPP(fun(U_364,bool),bool,hAPP(fun(U_364,bool),fun(fun(U_364,bool),bool),ord_less_eq(fun(U_364,bool)),U_362),bot_bot(fun(U_364,bool))))
| ti(fun(U_364,bool),U_362) != bot_bot(fun(U_364,bool)) )
& ! [U_363,U_361] :
( ti(fun(U_363,bool),U_361) = bot_bot(fun(U_363,bool))
| ~ hBOOL(hAPP(fun(U_363,bool),bool,hAPP(fun(U_363,bool),fun(fun(U_363,bool),bool),ord_less_eq(fun(U_363,bool)),U_361),bot_bot(fun(U_363,bool)))) ) ),
inference(miniscope,[status(thm)],[f_106_2]) ).
fof(f_106_4,plain,
( ! [U_362,U_364] :
( hBOOL(hAPP(fun(U_364,bool),bool,hAPP(fun(U_364,bool),fun(fun(U_364,bool),bool),ord_less_eq(fun(U_364,bool)),U_362),bot_bot(fun(U_364,bool))))
| ti(fun(U_364,bool),U_362) != bot_bot(fun(U_364,bool)) )
& ! [U_361,U_363] :
( ti(fun(U_363,bool),U_361) = bot_bot(fun(U_363,bool))
| ~ hBOOL(hAPP(fun(U_363,bool),bool,hAPP(fun(U_363,bool),fun(fun(U_363,bool),bool),ord_less_eq(fun(U_363,bool)),U_361),bot_bot(fun(U_363,bool)))) ) ),
inference(definitional_conversion,[status(esa)],[f_106_3]) ).
cnf(f_106_5,plain,
( ti(fun(U_363,bool),U_361) = bot_bot(fun(U_363,bool))
| ~ hBOOL(hAPP(fun(U_363,bool),bool,hAPP(fun(U_363,bool),fun(fun(U_363,bool),bool),ord_less_eq(fun(U_363,bool)),U_361),bot_bot(fun(U_363,bool)))) ),
inference(clausify,[status(thm)],[f_106_4]) ).
cnf(f_106_6,plain,
( hBOOL(hAPP(fun(U_364,bool),bool,hAPP(fun(U_364,bool),fun(fun(U_364,bool),bool),ord_less_eq(fun(U_364,bool)),U_362),bot_bot(fun(U_364,bool))))
| ti(fun(U_364,bool),U_362) != bot_bot(fun(U_364,bool)) ),
inference(clausify,[status(thm)],[f_106_4]) ).
fof(f_107_1,plain,
! [X_b,X_a,F,A_1] :
( ( hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1) = bot_bot(fun(X_a,bool))
| ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) )
& ( ti(fun(X_b,bool),A_1) = bot_bot(fun(X_b,bool))
| hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1) != bot_bot(fun(X_a,bool)) ) ),
inference(fof_nnf,[status(thm)],[fact_69_image__is__empty]) ).
fof(f_107_2,plain,
! [U_368,U_367,U_366,U_365] :
( ( hAPP(fun(U_368,bool),fun(U_367,bool),hAPP(fun(U_368,U_367),fun(fun(U_368,bool),fun(U_367,bool)),image(U_368,U_367),U_366),U_365) = bot_bot(fun(U_367,bool))
| ti(fun(U_368,bool),U_365) != bot_bot(fun(U_368,bool)) )
& ( ti(fun(U_368,bool),U_365) = bot_bot(fun(U_368,bool))
| hAPP(fun(U_368,bool),fun(U_367,bool),hAPP(fun(U_368,U_367),fun(fun(U_368,bool),fun(U_367,bool)),image(U_368,U_367),U_366),U_365) != bot_bot(fun(U_367,bool)) ) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
( ! [U_376,U_374,U_372,U_370] :
( hAPP(fun(U_376,bool),fun(U_374,bool),hAPP(fun(U_376,U_374),fun(fun(U_376,bool),fun(U_374,bool)),image(U_376,U_374),U_372),U_370) = bot_bot(fun(U_374,bool))
| ti(fun(U_376,bool),U_370) != bot_bot(fun(U_376,bool)) )
& ! [U_375,U_373,U_371,U_369] :
( ti(fun(U_375,bool),U_369) = bot_bot(fun(U_375,bool))
| hAPP(fun(U_375,bool),fun(U_373,bool),hAPP(fun(U_375,U_373),fun(fun(U_375,bool),fun(U_373,bool)),image(U_375,U_373),U_371),U_369) != bot_bot(fun(U_373,bool)) ) ),
inference(miniscope,[status(thm)],[f_107_2]) ).
fof(f_107_4,plain,
( ! [U_372,U_370,U_374,U_376] :
( hAPP(fun(U_376,bool),fun(U_374,bool),hAPP(fun(U_376,U_374),fun(fun(U_376,bool),fun(U_374,bool)),image(U_376,U_374),U_372),U_370) = bot_bot(fun(U_374,bool))
| ti(fun(U_376,bool),U_370) != bot_bot(fun(U_376,bool)) )
& ! [U_369,U_373,U_371,U_375] :
( ti(fun(U_375,bool),U_369) = bot_bot(fun(U_375,bool))
| hAPP(fun(U_375,bool),fun(U_373,bool),hAPP(fun(U_375,U_373),fun(fun(U_375,bool),fun(U_373,bool)),image(U_375,U_373),U_371),U_369) != bot_bot(fun(U_373,bool)) ) ),
inference(definitional_conversion,[status(esa)],[f_107_3]) ).
cnf(f_107_5,plain,
( ti(fun(U_375,bool),U_369) = bot_bot(fun(U_375,bool))
| hAPP(fun(U_375,bool),fun(U_373,bool),hAPP(fun(U_375,U_373),fun(fun(U_375,bool),fun(U_373,bool)),image(U_375,U_373),U_371),U_369) != bot_bot(fun(U_373,bool)) ),
inference(clausify,[status(thm)],[f_107_4]) ).
cnf(f_107_6,plain,
( hAPP(fun(U_376,bool),fun(U_374,bool),hAPP(fun(U_376,U_374),fun(fun(U_376,bool),fun(U_374,bool)),image(U_376,U_374),U_372),U_370) = bot_bot(fun(U_374,bool))
| ti(fun(U_376,bool),U_370) != bot_bot(fun(U_376,bool)) ),
inference(clausify,[status(thm)],[f_107_4]) ).
fof(f_108_1,plain,
! [X_b,X_a,F] : hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),bot_bot(fun(X_b,bool))) = bot_bot(fun(X_a,bool)),
inference(fof_nnf,[status(thm)],[fact_70_image__empty]) ).
fof(f_108_2,plain,
! [U_379,U_378,U_377] : hAPP(fun(U_379,bool),fun(U_378,bool),hAPP(fun(U_379,U_378),fun(fun(U_379,bool),fun(U_378,bool)),image(U_379,U_378),U_377),bot_bot(fun(U_379,bool))) = bot_bot(fun(U_378,bool)),
inference(variable_rename,[status(thm)],[f_108_1]) ).
fof(f_108_3,plain,
! [U_377,U_378,U_379] : hAPP(fun(U_379,bool),fun(U_378,bool),hAPP(fun(U_379,U_378),fun(fun(U_379,bool),fun(U_378,bool)),image(U_379,U_378),U_377),bot_bot(fun(U_379,bool))) = bot_bot(fun(U_378,bool)),
inference(definitional_conversion,[status(esa)],[f_108_2]) ).
cnf(f_108_4,plain,
hAPP(fun(U_379,bool),fun(U_378,bool),hAPP(fun(U_379,U_378),fun(fun(U_379,bool),fun(U_378,bool)),image(U_379,U_378),U_377),bot_bot(fun(U_379,bool))) = bot_bot(fun(U_378,bool)),
inference(clausify,[status(thm)],[f_108_3]) ).
fof(f_109_1,plain,
! [X_a,X_b,F,A_1] :
( ( bot_bot(fun(X_a,bool)) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)
| ti(fun(X_b,bool),A_1) != bot_bot(fun(X_b,bool)) )
& ( ti(fun(X_b,bool),A_1) = bot_bot(fun(X_b,bool))
| bot_bot(fun(X_a,bool)) != hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1) ) ),
inference(fof_nnf,[status(thm)],[fact_71_empty__is__image]) ).
fof(f_109_2,plain,
! [U_383,U_382,U_381,U_380] :
( ( bot_bot(fun(U_383,bool)) = hAPP(fun(U_382,bool),fun(U_383,bool),hAPP(fun(U_382,U_383),fun(fun(U_382,bool),fun(U_383,bool)),image(U_382,U_383),U_381),U_380)
| ti(fun(U_382,bool),U_380) != bot_bot(fun(U_382,bool)) )
& ( ti(fun(U_382,bool),U_380) = bot_bot(fun(U_382,bool))
| bot_bot(fun(U_383,bool)) != hAPP(fun(U_382,bool),fun(U_383,bool),hAPP(fun(U_382,U_383),fun(fun(U_382,bool),fun(U_383,bool)),image(U_382,U_383),U_381),U_380) ) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
( ! [U_391,U_389,U_387,U_385] :
( bot_bot(fun(U_391,bool)) = hAPP(fun(U_389,bool),fun(U_391,bool),hAPP(fun(U_389,U_391),fun(fun(U_389,bool),fun(U_391,bool)),image(U_389,U_391),U_387),U_385)
| ti(fun(U_389,bool),U_385) != bot_bot(fun(U_389,bool)) )
& ! [U_390,U_388,U_386,U_384] :
( ti(fun(U_388,bool),U_384) = bot_bot(fun(U_388,bool))
| bot_bot(fun(U_390,bool)) != hAPP(fun(U_388,bool),fun(U_390,bool),hAPP(fun(U_388,U_390),fun(fun(U_388,bool),fun(U_390,bool)),image(U_388,U_390),U_386),U_384) ) ),
inference(miniscope,[status(thm)],[f_109_2]) ).
fof(f_109_4,plain,
( ! [U_387,U_385,U_389,U_391] :
( bot_bot(fun(U_391,bool)) = hAPP(fun(U_389,bool),fun(U_391,bool),hAPP(fun(U_389,U_391),fun(fun(U_389,bool),fun(U_391,bool)),image(U_389,U_391),U_387),U_385)
| ti(fun(U_389,bool),U_385) != bot_bot(fun(U_389,bool)) )
& ! [U_384,U_388,U_386,U_390] :
( ti(fun(U_388,bool),U_384) = bot_bot(fun(U_388,bool))
| bot_bot(fun(U_390,bool)) != hAPP(fun(U_388,bool),fun(U_390,bool),hAPP(fun(U_388,U_390),fun(fun(U_388,bool),fun(U_390,bool)),image(U_388,U_390),U_386),U_384) ) ),
inference(definitional_conversion,[status(esa)],[f_109_3]) ).
cnf(f_109_5,plain,
( ti(fun(U_388,bool),U_384) = bot_bot(fun(U_388,bool))
| bot_bot(fun(U_390,bool)) != hAPP(fun(U_388,bool),fun(U_390,bool),hAPP(fun(U_388,U_390),fun(fun(U_388,bool),fun(U_390,bool)),image(U_388,U_390),U_386),U_384) ),
inference(clausify,[status(thm)],[f_109_4]) ).
cnf(f_109_6,plain,
( bot_bot(fun(U_391,bool)) = hAPP(fun(U_389,bool),fun(U_391,bool),hAPP(fun(U_389,U_391),fun(fun(U_389,bool),fun(U_391,bool)),image(U_389,U_391),U_387),U_385)
| ti(fun(U_389,bool),U_385) != bot_bot(fun(U_389,bool)) ),
inference(clausify,[status(thm)],[f_109_4]) ).
fof(f_110_1,plain,
! [X_a,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
inference(fof_nnf,[status(thm)],[fact_72_finite__subset]) ).
fof(f_110_2,plain,
! [U_394,U_393,U_392] :
( hBOOL(hAPP(fun(U_394,bool),bool,finite_finite(U_394),U_393))
| ~ hBOOL(hAPP(fun(U_394,bool),bool,finite_finite(U_394),U_392))
| ~ hBOOL(hAPP(fun(U_394,bool),bool,hAPP(fun(U_394,bool),fun(fun(U_394,bool),bool),ord_less_eq(fun(U_394,bool)),U_393),U_392)) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
fof(f_110_3,plain,
! [U_394,U_393,U_392] :
( hBOOL(hAPP(fun(U_394,bool),bool,finite_finite(U_394),U_393))
| ~ hBOOL(hAPP(fun(U_394,bool),bool,finite_finite(U_394),U_392))
| ~ hBOOL(hAPP(fun(U_394,bool),bool,hAPP(fun(U_394,bool),fun(fun(U_394,bool),bool),ord_less_eq(fun(U_394,bool)),U_393),U_392)) ),
inference(definitional_conversion,[status(esa)],[f_110_2]) ).
cnf(f_110_4,plain,
( hBOOL(hAPP(fun(U_394,bool),bool,finite_finite(U_394),U_393))
| ~ hBOOL(hAPP(fun(U_394,bool),bool,finite_finite(U_394),U_392))
| ~ hBOOL(hAPP(fun(U_394,bool),bool,hAPP(fun(U_394,bool),fun(fun(U_394,bool),bool),ord_less_eq(fun(U_394,bool)),U_393),U_392)) ),
inference(clausify,[status(thm)],[f_110_3]) ).
fof(f_111_1,plain,
! [X_a,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),A_1))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B)) ),
inference(fof_nnf,[status(thm)],[fact_73_rev__finite__subset]) ).
fof(f_111_2,plain,
! [U_397,U_396,U_395] :
( hBOOL(hAPP(fun(U_397,bool),bool,finite_finite(U_397),U_396))
| ~ hBOOL(hAPP(fun(U_397,bool),bool,hAPP(fun(U_397,bool),fun(fun(U_397,bool),bool),ord_less_eq(fun(U_397,bool)),U_396),U_395))
| ~ hBOOL(hAPP(fun(U_397,bool),bool,finite_finite(U_397),U_395)) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
fof(f_111_3,plain,
! [U_397,U_395,U_396] :
( hBOOL(hAPP(fun(U_397,bool),bool,finite_finite(U_397),U_396))
| ~ hBOOL(hAPP(fun(U_397,bool),bool,hAPP(fun(U_397,bool),fun(fun(U_397,bool),bool),ord_less_eq(fun(U_397,bool)),U_396),U_395))
| ~ hBOOL(hAPP(fun(U_397,bool),bool,finite_finite(U_397),U_395)) ),
inference(definitional_conversion,[status(esa)],[f_111_2]) ).
cnf(f_111_4,plain,
( hBOOL(hAPP(fun(U_397,bool),bool,finite_finite(U_397),U_396))
| ~ hBOOL(hAPP(fun(U_397,bool),bool,hAPP(fun(U_397,bool),fun(fun(U_397,bool),bool),ord_less_eq(fun(U_397,bool)),U_396),U_395))
| ~ hBOOL(hAPP(fun(U_397,bool),bool,finite_finite(U_397),U_395)) ),
inference(clausify,[status(thm)],[f_111_3]) ).
fof(f_112_1,plain,
! [X_a,A_3,C_2,D] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),C_2)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),D)))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),C_2),D)) ),
inference(fof_nnf,[status(thm)],[fact_74_insert__mono]) ).
fof(f_112_2,plain,
! [U_401,U_400,U_399,U_398] :
( hBOOL(hAPP(fun(U_401,bool),bool,hAPP(fun(U_401,bool),fun(fun(U_401,bool),bool),ord_less_eq(fun(U_401,bool)),hAPP(fun(U_401,bool),fun(U_401,bool),hAPP(U_401,fun(fun(U_401,bool),fun(U_401,bool)),insert(U_401),U_400),U_399)),hAPP(fun(U_401,bool),fun(U_401,bool),hAPP(U_401,fun(fun(U_401,bool),fun(U_401,bool)),insert(U_401),U_400),U_398)))
| ~ hBOOL(hAPP(fun(U_401,bool),bool,hAPP(fun(U_401,bool),fun(fun(U_401,bool),bool),ord_less_eq(fun(U_401,bool)),U_399),U_398)) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
! [U_399,U_398,U_401,U_400] :
( hBOOL(hAPP(fun(U_401,bool),bool,hAPP(fun(U_401,bool),fun(fun(U_401,bool),bool),ord_less_eq(fun(U_401,bool)),hAPP(fun(U_401,bool),fun(U_401,bool),hAPP(U_401,fun(fun(U_401,bool),fun(U_401,bool)),insert(U_401),U_400),U_399)),hAPP(fun(U_401,bool),fun(U_401,bool),hAPP(U_401,fun(fun(U_401,bool),fun(U_401,bool)),insert(U_401),U_400),U_398)))
| ~ hBOOL(hAPP(fun(U_401,bool),bool,hAPP(fun(U_401,bool),fun(fun(U_401,bool),bool),ord_less_eq(fun(U_401,bool)),U_399),U_398)) ),
inference(definitional_conversion,[status(esa)],[f_112_2]) ).
cnf(f_112_4,plain,
( hBOOL(hAPP(fun(U_401,bool),bool,hAPP(fun(U_401,bool),fun(fun(U_401,bool),bool),ord_less_eq(fun(U_401,bool)),hAPP(fun(U_401,bool),fun(U_401,bool),hAPP(U_401,fun(fun(U_401,bool),fun(U_401,bool)),insert(U_401),U_400),U_399)),hAPP(fun(U_401,bool),fun(U_401,bool),hAPP(U_401,fun(fun(U_401,bool),fun(U_401,bool)),insert(U_401),U_400),U_398)))
| ~ hBOOL(hAPP(fun(U_401,bool),bool,hAPP(fun(U_401,bool),fun(fun(U_401,bool),bool),ord_less_eq(fun(U_401,bool)),U_399),U_398)) ),
inference(clausify,[status(thm)],[f_112_3]) ).
fof(f_113_1,plain,
! [X_a,X_b,F,G_1] :
( ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G_1)
| ? [X_1] : hAPP(X_a,X_b,F,X_1) != hAPP(X_a,X_b,G_1,X_1) ),
inference(fof_nnf,[status(thm)],[fact_75_ext]) ).
fof(f_113_2,plain,
! [U_406,U_405,U_404,U_403] :
( ti(fun(U_406,U_405),U_404) = ti(fun(U_406,U_405),U_403)
| ? [U_402] : hAPP(U_406,U_405,U_404,U_402) != hAPP(U_406,U_405,U_403,U_402) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
! [U_406,U_405,U_404,U_403] :
( ti(fun(U_406,U_405),U_404) = ti(fun(U_406,U_405),U_403)
| hAPP(U_406,U_405,U_404,sK6(U_406,U_405,U_404,U_403)) != hAPP(U_406,U_405,U_403,sK6(U_406,U_405,U_404,U_403)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_402,sK6(U_406,U_405,U_404,U_403))],[f_113_2]) ).
fof(f_113_4,plain,
! [U_404,U_403,U_405,U_406] :
( ti(fun(U_406,U_405),U_404) = ti(fun(U_406,U_405),U_403)
| hAPP(U_406,U_405,U_404,sK6(U_406,U_405,U_404,U_403)) != hAPP(U_406,U_405,U_403,sK6(U_406,U_405,U_404,U_403)) ),
inference(definitional_conversion,[status(esa)],[f_113_3]) ).
cnf(f_113_5,plain,
( ti(fun(U_406,U_405),U_404) = ti(fun(U_406,U_405),U_403)
| hAPP(U_406,U_405,U_404,sK6(U_406,U_405,U_404,U_403)) != hAPP(U_406,U_405,U_403,sK6(U_406,U_405,U_404,U_403)) ),
inference(clausify,[status(thm)],[f_113_4]) ).
fof(f_114_1,plain,
! [X_a,X_2,A_1] :
( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1))
| ~ hBOOL(hAPP(X_a,bool,A_1,X_2)) )
& ( hBOOL(hAPP(X_a,bool,A_1,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)) ) ),
inference(fof_nnf,[status(thm)],[fact_76_mem__def]) ).
fof(f_114_2,plain,
! [U_409,U_408,U_407] :
( ( hBOOL(hAPP(fun(U_409,bool),bool,hAPP(U_409,fun(fun(U_409,bool),bool),member(U_409),U_408),U_407))
| ~ hBOOL(hAPP(U_409,bool,U_407,U_408)) )
& ( hBOOL(hAPP(U_409,bool,U_407,U_408))
| ~ hBOOL(hAPP(fun(U_409,bool),bool,hAPP(U_409,fun(fun(U_409,bool),bool),member(U_409),U_408),U_407)) ) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
fof(f_114_3,plain,
( ! [U_415,U_413,U_411] :
( hBOOL(hAPP(fun(U_415,bool),bool,hAPP(U_415,fun(fun(U_415,bool),bool),member(U_415),U_413),U_411))
| ~ hBOOL(hAPP(U_415,bool,U_411,U_413)) )
& ! [U_414,U_412,U_410] :
( hBOOL(hAPP(U_414,bool,U_410,U_412))
| ~ hBOOL(hAPP(fun(U_414,bool),bool,hAPP(U_414,fun(fun(U_414,bool),bool),member(U_414),U_412),U_410)) ) ),
inference(miniscope,[status(thm)],[f_114_2]) ).
fof(f_114_4,plain,
( ! [U_413,U_411,U_415] :
( hBOOL(hAPP(fun(U_415,bool),bool,hAPP(U_415,fun(fun(U_415,bool),bool),member(U_415),U_413),U_411))
| ~ hBOOL(hAPP(U_415,bool,U_411,U_413)) )
& ! [U_414,U_410,U_412] :
( hBOOL(hAPP(U_414,bool,U_410,U_412))
| ~ hBOOL(hAPP(fun(U_414,bool),bool,hAPP(U_414,fun(fun(U_414,bool),bool),member(U_414),U_412),U_410)) ) ),
inference(definitional_conversion,[status(esa)],[f_114_3]) ).
cnf(f_114_5,plain,
( hBOOL(hAPP(U_414,bool,U_410,U_412))
| ~ hBOOL(hAPP(fun(U_414,bool),bool,hAPP(U_414,fun(fun(U_414,bool),bool),member(U_414),U_412),U_410)) ),
inference(clausify,[status(thm)],[f_114_4]) ).
cnf(f_114_6,plain,
( hBOOL(hAPP(fun(U_415,bool),bool,hAPP(U_415,fun(fun(U_415,bool),bool),member(U_415),U_413),U_411))
| ~ hBOOL(hAPP(U_415,bool,U_411,U_413)) ),
inference(clausify,[status(thm)],[f_114_4]) ).
fof(f_115_1,plain,
! [X_a,P_1] : hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1) = ti(fun(X_a,bool),P_1),
inference(fof_nnf,[status(thm)],[fact_77_Collect__def]) ).
fof(f_115_2,plain,
! [U_417,U_416] : hAPP(fun(U_417,bool),fun(U_417,bool),collect(U_417),U_416) = ti(fun(U_417,bool),U_416),
inference(variable_rename,[status(thm)],[f_115_1]) ).
fof(f_115_3,plain,
! [U_417,U_416] : hAPP(fun(U_417,bool),fun(U_417,bool),collect(U_417),U_416) = ti(fun(U_417,bool),U_416),
inference(definitional_conversion,[status(esa)],[f_115_2]) ).
cnf(f_115_4,plain,
hAPP(fun(U_417,bool),fun(U_417,bool),collect(U_417),U_416) = ti(fun(U_417,bool),U_416),
inference(clausify,[status(thm)],[f_115_3]) ).
fof(f_116_1,plain,
! [X_a,B_1,A_1,B] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),B_1),B)))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
inference(fof_nnf,[status(thm)],[fact_78_subset__insertI2]) ).
fof(f_116_2,plain,
! [U_421,U_420,U_419,U_418] :
( hBOOL(hAPP(fun(U_421,bool),bool,hAPP(fun(U_421,bool),fun(fun(U_421,bool),bool),ord_less_eq(fun(U_421,bool)),U_419),hAPP(fun(U_421,bool),fun(U_421,bool),hAPP(U_421,fun(fun(U_421,bool),fun(U_421,bool)),insert(U_421),U_420),U_418)))
| ~ hBOOL(hAPP(fun(U_421,bool),bool,hAPP(fun(U_421,bool),fun(fun(U_421,bool),bool),ord_less_eq(fun(U_421,bool)),U_419),U_418)) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
fof(f_116_3,plain,
! [U_421,U_419,U_418,U_420] :
( hBOOL(hAPP(fun(U_421,bool),bool,hAPP(fun(U_421,bool),fun(fun(U_421,bool),bool),ord_less_eq(fun(U_421,bool)),U_419),hAPP(fun(U_421,bool),fun(U_421,bool),hAPP(U_421,fun(fun(U_421,bool),fun(U_421,bool)),insert(U_421),U_420),U_418)))
| ~ hBOOL(hAPP(fun(U_421,bool),bool,hAPP(fun(U_421,bool),fun(fun(U_421,bool),bool),ord_less_eq(fun(U_421,bool)),U_419),U_418)) ),
inference(definitional_conversion,[status(esa)],[f_116_2]) ).
cnf(f_116_4,plain,
( hBOOL(hAPP(fun(U_421,bool),bool,hAPP(fun(U_421,bool),fun(fun(U_421,bool),bool),ord_less_eq(fun(U_421,bool)),U_419),hAPP(fun(U_421,bool),fun(U_421,bool),hAPP(U_421,fun(fun(U_421,bool),fun(U_421,bool)),insert(U_421),U_420),U_418)))
| ~ hBOOL(hAPP(fun(U_421,bool),bool,hAPP(fun(U_421,bool),fun(fun(U_421,bool),bool),ord_less_eq(fun(U_421,bool)),U_419),U_418)) ),
inference(clausify,[status(thm)],[f_116_3]) ).
fof(f_117_1,plain,
! [X_a,B,X_2,A_1] :
( ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),B)))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) )
& ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),B))) ) )
| hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_1)) ),
inference(fof_nnf,[status(thm)],[fact_79_subset__insert]) ).
fof(f_117_2,plain,
! [U_425,U_424,U_423,U_422] :
( ( ( hBOOL(hAPP(fun(U_425,bool),bool,hAPP(fun(U_425,bool),fun(fun(U_425,bool),bool),ord_less_eq(fun(U_425,bool)),U_422),hAPP(fun(U_425,bool),fun(U_425,bool),hAPP(U_425,fun(fun(U_425,bool),fun(U_425,bool)),insert(U_425),U_423),U_424)))
| ~ hBOOL(hAPP(fun(U_425,bool),bool,hAPP(fun(U_425,bool),fun(fun(U_425,bool),bool),ord_less_eq(fun(U_425,bool)),U_422),U_424)) )
& ( hBOOL(hAPP(fun(U_425,bool),bool,hAPP(fun(U_425,bool),fun(fun(U_425,bool),bool),ord_less_eq(fun(U_425,bool)),U_422),U_424))
| ~ hBOOL(hAPP(fun(U_425,bool),bool,hAPP(fun(U_425,bool),fun(fun(U_425,bool),bool),ord_less_eq(fun(U_425,bool)),U_422),hAPP(fun(U_425,bool),fun(U_425,bool),hAPP(U_425,fun(fun(U_425,bool),fun(U_425,bool)),insert(U_425),U_423),U_424))) ) )
| hBOOL(hAPP(fun(U_425,bool),bool,hAPP(U_425,fun(fun(U_425,bool),bool),member(U_425),U_423),U_422)) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
( ! [U_423,U_422,U_425,U_424] :
( hBOOL(hAPP(fun(U_425,bool),bool,hAPP(fun(U_425,bool),fun(fun(U_425,bool),bool),ord_less_eq(fun(U_425,bool)),U_422),hAPP(fun(U_425,bool),fun(U_425,bool),hAPP(U_425,fun(fun(U_425,bool),fun(U_425,bool)),insert(U_425),U_423),U_424)))
| ~ hBOOL(hAPP(fun(U_425,bool),bool,hAPP(fun(U_425,bool),fun(fun(U_425,bool),bool),ord_less_eq(fun(U_425,bool)),U_422),U_424))
| ~ sP13(U_423,U_422,U_425,U_424) )
& ! [U_423,U_422,U_425,U_424] :
( hBOOL(hAPP(fun(U_425,bool),bool,hAPP(fun(U_425,bool),fun(fun(U_425,bool),bool),ord_less_eq(fun(U_425,bool)),U_422),U_424))
| ~ hBOOL(hAPP(fun(U_425,bool),bool,hAPP(fun(U_425,bool),fun(fun(U_425,bool),bool),ord_less_eq(fun(U_425,bool)),U_422),hAPP(fun(U_425,bool),fun(U_425,bool),hAPP(U_425,fun(fun(U_425,bool),fun(U_425,bool)),insert(U_425),U_423),U_424)))
| ~ sP13(U_423,U_422,U_425,U_424) )
& ! [U_423,U_422,U_425,U_424] :
( sP13(U_423,U_422,U_425,U_424)
| hBOOL(hAPP(fun(U_425,bool),bool,hAPP(U_425,fun(fun(U_425,bool),bool),member(U_425),U_423),U_422)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13])],[f_117_2]) ).
cnf(f_117_4,plain,
( sP13(U_423,U_422,U_425,U_424)
| hBOOL(hAPP(fun(U_425,bool),bool,hAPP(U_425,fun(fun(U_425,bool),bool),member(U_425),U_423),U_422)) ),
inference(clausify,[status(thm)],[f_117_3]) ).
cnf(f_117_5,plain,
( hBOOL(hAPP(fun(U_425,bool),bool,hAPP(fun(U_425,bool),fun(fun(U_425,bool),bool),ord_less_eq(fun(U_425,bool)),U_422),U_424))
| ~ hBOOL(hAPP(fun(U_425,bool),bool,hAPP(fun(U_425,bool),fun(fun(U_425,bool),bool),ord_less_eq(fun(U_425,bool)),U_422),hAPP(fun(U_425,bool),fun(U_425,bool),hAPP(U_425,fun(fun(U_425,bool),fun(U_425,bool)),insert(U_425),U_423),U_424)))
| ~ sP13(U_423,U_422,U_425,U_424) ),
inference(clausify,[status(thm)],[f_117_3]) ).
cnf(f_117_6,plain,
( hBOOL(hAPP(fun(U_425,bool),bool,hAPP(fun(U_425,bool),fun(fun(U_425,bool),bool),ord_less_eq(fun(U_425,bool)),U_422),hAPP(fun(U_425,bool),fun(U_425,bool),hAPP(U_425,fun(fun(U_425,bool),fun(U_425,bool)),insert(U_425),U_423),U_424)))
| ~ hBOOL(hAPP(fun(U_425,bool),bool,hAPP(fun(U_425,bool),fun(fun(U_425,bool),bool),ord_less_eq(fun(U_425,bool)),U_422),U_424))
| ~ sP13(U_423,U_422,U_425,U_424) ),
inference(clausify,[status(thm)],[f_117_3]) ).
fof(f_118_1,plain,
! [X_a,X_2,A_1,B] :
( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)),B))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B)) )
& ( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
& hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B)) )
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),X_2),A_1)),B)) ) ),
inference(fof_nnf,[status(thm)],[fact_80_insert__subset]) ).
fof(f_118_2,plain,
! [U_429,U_428,U_427,U_426] :
( ( hBOOL(hAPP(fun(U_429,bool),bool,hAPP(fun(U_429,bool),fun(fun(U_429,bool),bool),ord_less_eq(fun(U_429,bool)),hAPP(fun(U_429,bool),fun(U_429,bool),hAPP(U_429,fun(fun(U_429,bool),fun(U_429,bool)),insert(U_429),U_428),U_427)),U_426))
| ~ hBOOL(hAPP(fun(U_429,bool),bool,hAPP(fun(U_429,bool),fun(fun(U_429,bool),bool),ord_less_eq(fun(U_429,bool)),U_427),U_426))
| ~ hBOOL(hAPP(fun(U_429,bool),bool,hAPP(U_429,fun(fun(U_429,bool),bool),member(U_429),U_428),U_426)) )
& ( ( hBOOL(hAPP(fun(U_429,bool),bool,hAPP(fun(U_429,bool),fun(fun(U_429,bool),bool),ord_less_eq(fun(U_429,bool)),U_427),U_426))
& hBOOL(hAPP(fun(U_429,bool),bool,hAPP(U_429,fun(fun(U_429,bool),bool),member(U_429),U_428),U_426)) )
| ~ hBOOL(hAPP(fun(U_429,bool),bool,hAPP(fun(U_429,bool),fun(fun(U_429,bool),bool),ord_less_eq(fun(U_429,bool)),hAPP(fun(U_429,bool),fun(U_429,bool),hAPP(U_429,fun(fun(U_429,bool),fun(U_429,bool)),insert(U_429),U_428),U_427)),U_426)) ) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
fof(f_118_3,plain,
( ! [U_437,U_435,U_433,U_431] :
( hBOOL(hAPP(fun(U_437,bool),bool,hAPP(fun(U_437,bool),fun(fun(U_437,bool),bool),ord_less_eq(fun(U_437,bool)),hAPP(fun(U_437,bool),fun(U_437,bool),hAPP(U_437,fun(fun(U_437,bool),fun(U_437,bool)),insert(U_437),U_435),U_433)),U_431))
| ~ hBOOL(hAPP(fun(U_437,bool),bool,hAPP(fun(U_437,bool),fun(fun(U_437,bool),bool),ord_less_eq(fun(U_437,bool)),U_433),U_431))
| ~ hBOOL(hAPP(fun(U_437,bool),bool,hAPP(U_437,fun(fun(U_437,bool),bool),member(U_437),U_435),U_431)) )
& ! [U_436,U_434,U_432,U_430] :
( ( hBOOL(hAPP(fun(U_436,bool),bool,hAPP(fun(U_436,bool),fun(fun(U_436,bool),bool),ord_less_eq(fun(U_436,bool)),U_432),U_430))
& hBOOL(hAPP(fun(U_436,bool),bool,hAPP(U_436,fun(fun(U_436,bool),bool),member(U_436),U_434),U_430)) )
| ~ hBOOL(hAPP(fun(U_436,bool),bool,hAPP(fun(U_436,bool),fun(fun(U_436,bool),bool),ord_less_eq(fun(U_436,bool)),hAPP(fun(U_436,bool),fun(U_436,bool),hAPP(U_436,fun(fun(U_436,bool),fun(U_436,bool)),insert(U_436),U_434),U_432)),U_430)) ) ),
inference(miniscope,[status(thm)],[f_118_2]) ).
fof(f_118_4,plain,
( ! [U_436,U_432,U_430,U_434] :
( hBOOL(hAPP(fun(U_436,bool),bool,hAPP(fun(U_436,bool),fun(fun(U_436,bool),bool),ord_less_eq(fun(U_436,bool)),U_432),U_430))
| ~ sP14(U_436,U_432,U_430,U_434) )
& ! [U_436,U_432,U_430,U_434] :
( hBOOL(hAPP(fun(U_436,bool),bool,hAPP(U_436,fun(fun(U_436,bool),bool),member(U_436),U_434),U_430))
| ~ sP14(U_436,U_432,U_430,U_434) )
& ! [U_431,U_433,U_435,U_437] :
( hBOOL(hAPP(fun(U_437,bool),bool,hAPP(fun(U_437,bool),fun(fun(U_437,bool),bool),ord_less_eq(fun(U_437,bool)),hAPP(fun(U_437,bool),fun(U_437,bool),hAPP(U_437,fun(fun(U_437,bool),fun(U_437,bool)),insert(U_437),U_435),U_433)),U_431))
| ~ hBOOL(hAPP(fun(U_437,bool),bool,hAPP(fun(U_437,bool),fun(fun(U_437,bool),bool),ord_less_eq(fun(U_437,bool)),U_433),U_431))
| ~ hBOOL(hAPP(fun(U_437,bool),bool,hAPP(U_437,fun(fun(U_437,bool),bool),member(U_437),U_435),U_431)) )
& ! [U_436,U_432,U_430,U_434] :
( sP14(U_436,U_432,U_430,U_434)
| ~ hBOOL(hAPP(fun(U_436,bool),bool,hAPP(fun(U_436,bool),fun(fun(U_436,bool),bool),ord_less_eq(fun(U_436,bool)),hAPP(fun(U_436,bool),fun(U_436,bool),hAPP(U_436,fun(fun(U_436,bool),fun(U_436,bool)),insert(U_436),U_434),U_432)),U_430)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14])],[f_118_3]) ).
cnf(f_118_5,plain,
( sP14(U_436,U_432,U_430,U_434)
| ~ hBOOL(hAPP(fun(U_436,bool),bool,hAPP(fun(U_436,bool),fun(fun(U_436,bool),bool),ord_less_eq(fun(U_436,bool)),hAPP(fun(U_436,bool),fun(U_436,bool),hAPP(U_436,fun(fun(U_436,bool),fun(U_436,bool)),insert(U_436),U_434),U_432)),U_430)) ),
inference(clausify,[status(thm)],[f_118_4]) ).
cnf(f_118_6,plain,
( hBOOL(hAPP(fun(U_437,bool),bool,hAPP(fun(U_437,bool),fun(fun(U_437,bool),bool),ord_less_eq(fun(U_437,bool)),hAPP(fun(U_437,bool),fun(U_437,bool),hAPP(U_437,fun(fun(U_437,bool),fun(U_437,bool)),insert(U_437),U_435),U_433)),U_431))
| ~ hBOOL(hAPP(fun(U_437,bool),bool,hAPP(fun(U_437,bool),fun(fun(U_437,bool),bool),ord_less_eq(fun(U_437,bool)),U_433),U_431))
| ~ hBOOL(hAPP(fun(U_437,bool),bool,hAPP(U_437,fun(fun(U_437,bool),bool),member(U_437),U_435),U_431)) ),
inference(clausify,[status(thm)],[f_118_4]) ).
cnf(f_118_7,plain,
( hBOOL(hAPP(fun(U_436,bool),bool,hAPP(U_436,fun(fun(U_436,bool),bool),member(U_436),U_434),U_430))
| ~ sP14(U_436,U_432,U_430,U_434) ),
inference(clausify,[status(thm)],[f_118_4]) ).
cnf(f_118_8,plain,
( hBOOL(hAPP(fun(U_436,bool),bool,hAPP(fun(U_436,bool),fun(fun(U_436,bool),bool),ord_less_eq(fun(U_436,bool)),U_432),U_430))
| ~ sP14(U_436,U_432,U_430,U_434) ),
inference(clausify,[status(thm)],[f_118_4]) ).
fof(f_119_1,plain,
! [X_a,B,A_3] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),B))),
inference(fof_nnf,[status(thm)],[fact_81_subset__insertI]) ).
fof(f_119_2,plain,
! [U_440,U_439,U_438] : hBOOL(hAPP(fun(U_440,bool),bool,hAPP(fun(U_440,bool),fun(fun(U_440,bool),bool),ord_less_eq(fun(U_440,bool)),U_439),hAPP(fun(U_440,bool),fun(U_440,bool),hAPP(U_440,fun(fun(U_440,bool),fun(U_440,bool)),insert(U_440),U_438),U_439))),
inference(variable_rename,[status(thm)],[f_119_1]) ).
fof(f_119_3,plain,
! [U_439,U_438,U_440] : hBOOL(hAPP(fun(U_440,bool),bool,hAPP(fun(U_440,bool),fun(fun(U_440,bool),bool),ord_less_eq(fun(U_440,bool)),U_439),hAPP(fun(U_440,bool),fun(U_440,bool),hAPP(U_440,fun(fun(U_440,bool),fun(U_440,bool)),insert(U_440),U_438),U_439))),
inference(definitional_conversion,[status(esa)],[f_119_2]) ).
cnf(f_119_4,plain,
hBOOL(hAPP(fun(U_440,bool),bool,hAPP(fun(U_440,bool),fun(fun(U_440,bool),bool),ord_less_eq(fun(U_440,bool)),U_439),hAPP(fun(U_440,bool),fun(U_440,bool),hAPP(U_440,fun(fun(U_440,bool),fun(U_440,bool)),insert(U_440),U_438),U_439))),
inference(clausify,[status(thm)],[f_119_3]) ).
fof(f_120_1,plain,
! [X_b,X_a,F,X_2,A_1] :
( hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)) = hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(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)) ),
inference(fof_nnf,[status(thm)],[fact_82_insert__image]) ).
fof(f_120_2,plain,
! [U_445,U_444,U_443,U_442,U_441] :
( hAPP(fun(U_445,bool),fun(U_445,bool),hAPP(U_445,fun(fun(U_445,bool),fun(U_445,bool)),insert(U_445),hAPP(U_444,U_445,U_443,U_442)),hAPP(fun(U_444,bool),fun(U_445,bool),hAPP(fun(U_444,U_445),fun(fun(U_444,bool),fun(U_445,bool)),image(U_444,U_445),U_443),U_441)) = hAPP(fun(U_444,bool),fun(U_445,bool),hAPP(fun(U_444,U_445),fun(fun(U_444,bool),fun(U_445,bool)),image(U_444,U_445),U_443),U_441)
| ~ hBOOL(hAPP(fun(U_444,bool),bool,hAPP(U_444,fun(fun(U_444,bool),bool),member(U_444),U_442),U_441)) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
! [U_444,U_441,U_442,U_443,U_445] :
( hAPP(fun(U_445,bool),fun(U_445,bool),hAPP(U_445,fun(fun(U_445,bool),fun(U_445,bool)),insert(U_445),hAPP(U_444,U_445,U_443,U_442)),hAPP(fun(U_444,bool),fun(U_445,bool),hAPP(fun(U_444,U_445),fun(fun(U_444,bool),fun(U_445,bool)),image(U_444,U_445),U_443),U_441)) = hAPP(fun(U_444,bool),fun(U_445,bool),hAPP(fun(U_444,U_445),fun(fun(U_444,bool),fun(U_445,bool)),image(U_444,U_445),U_443),U_441)
| ~ hBOOL(hAPP(fun(U_444,bool),bool,hAPP(U_444,fun(fun(U_444,bool),bool),member(U_444),U_442),U_441)) ),
inference(definitional_conversion,[status(esa)],[f_120_2]) ).
cnf(f_120_4,plain,
( hAPP(fun(U_445,bool),fun(U_445,bool),hAPP(U_445,fun(fun(U_445,bool),fun(U_445,bool)),insert(U_445),hAPP(U_444,U_445,U_443,U_442)),hAPP(fun(U_444,bool),fun(U_445,bool),hAPP(fun(U_444,U_445),fun(fun(U_444,bool),fun(U_445,bool)),image(U_444,U_445),U_443),U_441)) = hAPP(fun(U_444,bool),fun(U_445,bool),hAPP(fun(U_444,U_445),fun(fun(U_444,bool),fun(U_445,bool)),image(U_444,U_445),U_443),U_441)
| ~ hBOOL(hAPP(fun(U_444,bool),bool,hAPP(U_444,fun(fun(U_444,bool),bool),member(U_444),U_442),U_441)) ),
inference(clausify,[status(thm)],[f_120_3]) ).
fof(f_121_1,plain,
! [X_b,X_a,F,A_3,B] : hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(X_b,fun(fun(X_b,bool),fun(X_b,bool)),insert(X_b),A_3),B)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),hAPP(X_b,X_a,F,A_3)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),B)),
inference(fof_nnf,[status(thm)],[fact_83_image__insert]) ).
fof(f_121_2,plain,
! [U_450,U_449,U_448,U_447,U_446] : hAPP(fun(U_450,bool),fun(U_449,bool),hAPP(fun(U_450,U_449),fun(fun(U_450,bool),fun(U_449,bool)),image(U_450,U_449),U_448),hAPP(fun(U_450,bool),fun(U_450,bool),hAPP(U_450,fun(fun(U_450,bool),fun(U_450,bool)),insert(U_450),U_447),U_446)) = hAPP(fun(U_449,bool),fun(U_449,bool),hAPP(U_449,fun(fun(U_449,bool),fun(U_449,bool)),insert(U_449),hAPP(U_450,U_449,U_448,U_447)),hAPP(fun(U_450,bool),fun(U_449,bool),hAPP(fun(U_450,U_449),fun(fun(U_450,bool),fun(U_449,bool)),image(U_450,U_449),U_448),U_446)),
inference(variable_rename,[status(thm)],[f_121_1]) ).
fof(f_121_3,plain,
! [U_448,U_446,U_449,U_447,U_450] : hAPP(fun(U_450,bool),fun(U_449,bool),hAPP(fun(U_450,U_449),fun(fun(U_450,bool),fun(U_449,bool)),image(U_450,U_449),U_448),hAPP(fun(U_450,bool),fun(U_450,bool),hAPP(U_450,fun(fun(U_450,bool),fun(U_450,bool)),insert(U_450),U_447),U_446)) = hAPP(fun(U_449,bool),fun(U_449,bool),hAPP(U_449,fun(fun(U_449,bool),fun(U_449,bool)),insert(U_449),hAPP(U_450,U_449,U_448,U_447)),hAPP(fun(U_450,bool),fun(U_449,bool),hAPP(fun(U_450,U_449),fun(fun(U_450,bool),fun(U_449,bool)),image(U_450,U_449),U_448),U_446)),
inference(definitional_conversion,[status(esa)],[f_121_2]) ).
cnf(f_121_4,plain,
hAPP(fun(U_450,bool),fun(U_449,bool),hAPP(fun(U_450,U_449),fun(fun(U_450,bool),fun(U_449,bool)),image(U_450,U_449),U_448),hAPP(fun(U_450,bool),fun(U_450,bool),hAPP(U_450,fun(fun(U_450,bool),fun(U_450,bool)),insert(U_450),U_447),U_446)) = hAPP(fun(U_449,bool),fun(U_449,bool),hAPP(U_449,fun(fun(U_449,bool),fun(U_449,bool)),insert(U_449),hAPP(U_450,U_449,U_448,U_447)),hAPP(fun(U_450,bool),fun(U_449,bool),hAPP(fun(U_450,U_449),fun(fun(U_450,bool),fun(U_449,bool)),image(U_450,U_449),U_448),U_446)),
inference(clausify,[status(thm)],[f_121_3]) ).
fof(f_122_1,plain,
! [X_b,X_a,F,A_1,B] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B)))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B)) ),
inference(fof_nnf,[status(thm)],[fact_84_image__mono]) ).
fof(f_122_2,plain,
! [U_455,U_454,U_453,U_452,U_451] :
( hBOOL(hAPP(fun(U_455,bool),bool,hAPP(fun(U_455,bool),fun(fun(U_455,bool),bool),ord_less_eq(fun(U_455,bool)),hAPP(fun(U_454,bool),fun(U_455,bool),hAPP(fun(U_454,U_455),fun(fun(U_454,bool),fun(U_455,bool)),image(U_454,U_455),U_453),U_452)),hAPP(fun(U_454,bool),fun(U_455,bool),hAPP(fun(U_454,U_455),fun(fun(U_454,bool),fun(U_455,bool)),image(U_454,U_455),U_453),U_451)))
| ~ hBOOL(hAPP(fun(U_454,bool),bool,hAPP(fun(U_454,bool),fun(fun(U_454,bool),bool),ord_less_eq(fun(U_454,bool)),U_452),U_451)) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
fof(f_122_3,plain,
! [U_452,U_451,U_454,U_453,U_455] :
( hBOOL(hAPP(fun(U_455,bool),bool,hAPP(fun(U_455,bool),fun(fun(U_455,bool),bool),ord_less_eq(fun(U_455,bool)),hAPP(fun(U_454,bool),fun(U_455,bool),hAPP(fun(U_454,U_455),fun(fun(U_454,bool),fun(U_455,bool)),image(U_454,U_455),U_453),U_452)),hAPP(fun(U_454,bool),fun(U_455,bool),hAPP(fun(U_454,U_455),fun(fun(U_454,bool),fun(U_455,bool)),image(U_454,U_455),U_453),U_451)))
| ~ hBOOL(hAPP(fun(U_454,bool),bool,hAPP(fun(U_454,bool),fun(fun(U_454,bool),bool),ord_less_eq(fun(U_454,bool)),U_452),U_451)) ),
inference(definitional_conversion,[status(esa)],[f_122_2]) ).
cnf(f_122_4,plain,
( hBOOL(hAPP(fun(U_455,bool),bool,hAPP(fun(U_455,bool),fun(fun(U_455,bool),bool),ord_less_eq(fun(U_455,bool)),hAPP(fun(U_454,bool),fun(U_455,bool),hAPP(fun(U_454,U_455),fun(fun(U_454,bool),fun(U_455,bool)),image(U_454,U_455),U_453),U_452)),hAPP(fun(U_454,bool),fun(U_455,bool),hAPP(fun(U_454,U_455),fun(fun(U_454,bool),fun(U_455,bool)),image(U_454,U_455),U_453),U_451)))
| ~ hBOOL(hAPP(fun(U_454,bool),bool,hAPP(fun(U_454,bool),fun(fun(U_454,bool),bool),ord_less_eq(fun(U_454,bool)),U_452),U_451)) ),
inference(clausify,[status(thm)],[f_122_3]) ).
fof(f_123_1,plain,
! [X_a,X_b,B,F,A_1] :
( ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
| ! [AA] :
( ti(fun(X_a,bool),B) != hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),AA)
| ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),AA),A_1)) ) )
& ( ? [AA] :
( ti(fun(X_a,bool),B) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),AA)
& hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),AA),A_1)) )
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))) ) ),
inference(fof_nnf,[status(thm)],[fact_85_subset__image__iff]) ).
fof(f_123_2,plain,
! [U_462,U_461,U_460,U_459,U_458] :
( ( hBOOL(hAPP(fun(U_462,bool),bool,hAPP(fun(U_462,bool),fun(fun(U_462,bool),bool),ord_less_eq(fun(U_462,bool)),U_460),hAPP(fun(U_461,bool),fun(U_462,bool),hAPP(fun(U_461,U_462),fun(fun(U_461,bool),fun(U_462,bool)),image(U_461,U_462),U_459),U_458)))
| ! [U_457] :
( ti(fun(U_462,bool),U_460) != hAPP(fun(U_461,bool),fun(U_462,bool),hAPP(fun(U_461,U_462),fun(fun(U_461,bool),fun(U_462,bool)),image(U_461,U_462),U_459),U_457)
| ~ hBOOL(hAPP(fun(U_461,bool),bool,hAPP(fun(U_461,bool),fun(fun(U_461,bool),bool),ord_less_eq(fun(U_461,bool)),U_457),U_458)) ) )
& ( ? [U_456] :
( ti(fun(U_462,bool),U_460) = hAPP(fun(U_461,bool),fun(U_462,bool),hAPP(fun(U_461,U_462),fun(fun(U_461,bool),fun(U_462,bool)),image(U_461,U_462),U_459),U_456)
& hBOOL(hAPP(fun(U_461,bool),bool,hAPP(fun(U_461,bool),fun(fun(U_461,bool),bool),ord_less_eq(fun(U_461,bool)),U_456),U_458)) )
| ~ hBOOL(hAPP(fun(U_462,bool),bool,hAPP(fun(U_462,bool),fun(fun(U_462,bool),bool),ord_less_eq(fun(U_462,bool)),U_460),hAPP(fun(U_461,bool),fun(U_462,bool),hAPP(fun(U_461,U_462),fun(fun(U_461,bool),fun(U_462,bool)),image(U_461,U_462),U_459),U_458))) ) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
fof(f_123_3,plain,
( ! [U_472,U_470,U_468,U_466,U_464] :
( hBOOL(hAPP(fun(U_472,bool),bool,hAPP(fun(U_472,bool),fun(fun(U_472,bool),bool),ord_less_eq(fun(U_472,bool)),U_468),hAPP(fun(U_470,bool),fun(U_472,bool),hAPP(fun(U_470,U_472),fun(fun(U_470,bool),fun(U_472,bool)),image(U_470,U_472),U_466),U_464)))
| ! [U_457] :
( ti(fun(U_472,bool),U_468) != hAPP(fun(U_470,bool),fun(U_472,bool),hAPP(fun(U_470,U_472),fun(fun(U_470,bool),fun(U_472,bool)),image(U_470,U_472),U_466),U_457)
| ~ hBOOL(hAPP(fun(U_470,bool),bool,hAPP(fun(U_470,bool),fun(fun(U_470,bool),bool),ord_less_eq(fun(U_470,bool)),U_457),U_464)) ) )
& ! [U_471,U_469,U_467,U_465,U_463] :
( ? [U_456] :
( ti(fun(U_471,bool),U_467) = hAPP(fun(U_469,bool),fun(U_471,bool),hAPP(fun(U_469,U_471),fun(fun(U_469,bool),fun(U_471,bool)),image(U_469,U_471),U_465),U_456)
& hBOOL(hAPP(fun(U_469,bool),bool,hAPP(fun(U_469,bool),fun(fun(U_469,bool),bool),ord_less_eq(fun(U_469,bool)),U_456),U_463)) )
| ~ hBOOL(hAPP(fun(U_471,bool),bool,hAPP(fun(U_471,bool),fun(fun(U_471,bool),bool),ord_less_eq(fun(U_471,bool)),U_467),hAPP(fun(U_469,bool),fun(U_471,bool),hAPP(fun(U_469,U_471),fun(fun(U_469,bool),fun(U_471,bool)),image(U_469,U_471),U_465),U_463))) ) ),
inference(miniscope,[status(thm)],[f_123_2]) ).
fof(f_123_4,plain,
( ! [U_472,U_470,U_468,U_466,U_464] :
( hBOOL(hAPP(fun(U_472,bool),bool,hAPP(fun(U_472,bool),fun(fun(U_472,bool),bool),ord_less_eq(fun(U_472,bool)),U_468),hAPP(fun(U_470,bool),fun(U_472,bool),hAPP(fun(U_470,U_472),fun(fun(U_470,bool),fun(U_472,bool)),image(U_470,U_472),U_466),U_464)))
| ! [U_457] :
( ti(fun(U_472,bool),U_468) != hAPP(fun(U_470,bool),fun(U_472,bool),hAPP(fun(U_470,U_472),fun(fun(U_470,bool),fun(U_472,bool)),image(U_470,U_472),U_466),U_457)
| ~ hBOOL(hAPP(fun(U_470,bool),bool,hAPP(fun(U_470,bool),fun(fun(U_470,bool),bool),ord_less_eq(fun(U_470,bool)),U_457),U_464)) ) )
& ! [U_471,U_469,U_467,U_465,U_463] :
( ( ti(fun(U_471,bool),U_467) = hAPP(fun(U_469,bool),fun(U_471,bool),hAPP(fun(U_469,U_471),fun(fun(U_469,bool),fun(U_471,bool)),image(U_469,U_471),U_465),sK7(U_471,U_469,U_467,U_465,U_463))
& hBOOL(hAPP(fun(U_469,bool),bool,hAPP(fun(U_469,bool),fun(fun(U_469,bool),bool),ord_less_eq(fun(U_469,bool)),sK7(U_471,U_469,U_467,U_465,U_463)),U_463)) )
| ~ hBOOL(hAPP(fun(U_471,bool),bool,hAPP(fun(U_471,bool),fun(fun(U_471,bool),bool),ord_less_eq(fun(U_471,bool)),U_467),hAPP(fun(U_469,bool),fun(U_471,bool),hAPP(fun(U_469,U_471),fun(fun(U_469,bool),fun(U_471,bool)),image(U_469,U_471),U_465),U_463))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_456,sK7(U_471,U_469,U_467,U_465,U_463))],[f_123_3]) ).
fof(f_123_5,plain,
( ! [U_463,U_465,U_467,U_469,U_471] :
( ti(fun(U_471,bool),U_467) = hAPP(fun(U_469,bool),fun(U_471,bool),hAPP(fun(U_469,U_471),fun(fun(U_469,bool),fun(U_471,bool)),image(U_469,U_471),U_465),sK7(U_471,U_469,U_467,U_465,U_463))
| ~ sP15(U_463,U_465,U_467,U_469,U_471) )
& ! [U_463,U_465,U_467,U_469,U_471] :
( hBOOL(hAPP(fun(U_469,bool),bool,hAPP(fun(U_469,bool),fun(fun(U_469,bool),bool),ord_less_eq(fun(U_469,bool)),sK7(U_471,U_469,U_467,U_465,U_463)),U_463))
| ~ sP15(U_463,U_465,U_467,U_469,U_471) )
& ! [U_464,U_468,U_457,U_466,U_470,U_472] :
( hBOOL(hAPP(fun(U_472,bool),bool,hAPP(fun(U_472,bool),fun(fun(U_472,bool),bool),ord_less_eq(fun(U_472,bool)),U_468),hAPP(fun(U_470,bool),fun(U_472,bool),hAPP(fun(U_470,U_472),fun(fun(U_470,bool),fun(U_472,bool)),image(U_470,U_472),U_466),U_464)))
| ti(fun(U_472,bool),U_468) != hAPP(fun(U_470,bool),fun(U_472,bool),hAPP(fun(U_470,U_472),fun(fun(U_470,bool),fun(U_472,bool)),image(U_470,U_472),U_466),U_457)
| ~ hBOOL(hAPP(fun(U_470,bool),bool,hAPP(fun(U_470,bool),fun(fun(U_470,bool),bool),ord_less_eq(fun(U_470,bool)),U_457),U_464)) )
& ! [U_463,U_465,U_467,U_469,U_471] :
( sP15(U_463,U_465,U_467,U_469,U_471)
| ~ hBOOL(hAPP(fun(U_471,bool),bool,hAPP(fun(U_471,bool),fun(fun(U_471,bool),bool),ord_less_eq(fun(U_471,bool)),U_467),hAPP(fun(U_469,bool),fun(U_471,bool),hAPP(fun(U_469,U_471),fun(fun(U_469,bool),fun(U_471,bool)),image(U_469,U_471),U_465),U_463))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP15])],[f_123_4]) ).
cnf(f_123_6,plain,
( sP15(U_463,U_465,U_467,U_469,U_471)
| ~ hBOOL(hAPP(fun(U_471,bool),bool,hAPP(fun(U_471,bool),fun(fun(U_471,bool),bool),ord_less_eq(fun(U_471,bool)),U_467),hAPP(fun(U_469,bool),fun(U_471,bool),hAPP(fun(U_469,U_471),fun(fun(U_469,bool),fun(U_471,bool)),image(U_469,U_471),U_465),U_463))) ),
inference(clausify,[status(thm)],[f_123_5]) ).
cnf(f_123_7,plain,
( hBOOL(hAPP(fun(U_472,bool),bool,hAPP(fun(U_472,bool),fun(fun(U_472,bool),bool),ord_less_eq(fun(U_472,bool)),U_468),hAPP(fun(U_470,bool),fun(U_472,bool),hAPP(fun(U_470,U_472),fun(fun(U_470,bool),fun(U_472,bool)),image(U_470,U_472),U_466),U_464)))
| ti(fun(U_472,bool),U_468) != hAPP(fun(U_470,bool),fun(U_472,bool),hAPP(fun(U_470,U_472),fun(fun(U_470,bool),fun(U_472,bool)),image(U_470,U_472),U_466),U_457)
| ~ hBOOL(hAPP(fun(U_470,bool),bool,hAPP(fun(U_470,bool),fun(fun(U_470,bool),bool),ord_less_eq(fun(U_470,bool)),U_457),U_464)) ),
inference(clausify,[status(thm)],[f_123_5]) ).
cnf(f_123_8,plain,
( hBOOL(hAPP(fun(U_469,bool),bool,hAPP(fun(U_469,bool),fun(fun(U_469,bool),bool),ord_less_eq(fun(U_469,bool)),sK7(U_471,U_469,U_467,U_465,U_463)),U_463))
| ~ sP15(U_463,U_465,U_467,U_469,U_471) ),
inference(clausify,[status(thm)],[f_123_5]) ).
cnf(f_123_9,plain,
( ti(fun(U_471,bool),U_467) = hAPP(fun(U_469,bool),fun(U_471,bool),hAPP(fun(U_469,U_471),fun(fun(U_469,bool),fun(U_471,bool)),image(U_469,U_471),U_465),sK7(U_471,U_469,U_467,U_465,U_463))
| ~ sP15(U_463,U_465,U_467,U_469,U_471) ),
inference(clausify,[status(thm)],[f_123_5]) ).
fof(f_124_1,plain,
! [X_b,X_a,M,A_3,B_1] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),A_3),hAPP(fun(X_b,option(X_a)),fun(X_b,bool),dom(X_b,X_a),M)))
| hAPP(X_b,option(X_a),M,A_3) != hAPP(X_a,option(X_a),some(X_a),B_1) ),
inference(fof_nnf,[status(thm)],[fact_86_domI]) ).
fof(f_124_2,plain,
! [U_477,U_476,U_475,U_474,U_473] :
( hBOOL(hAPP(fun(U_477,bool),bool,hAPP(U_477,fun(fun(U_477,bool),bool),member(U_477),U_474),hAPP(fun(U_477,option(U_476)),fun(U_477,bool),dom(U_477,U_476),U_475)))
| hAPP(U_477,option(U_476),U_475,U_474) != hAPP(U_476,option(U_476),some(U_476),U_473) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
fof(f_124_3,plain,
! [U_477,U_476,U_475,U_474] :
( ! [U_473] : hAPP(U_477,option(U_476),U_475,U_474) != hAPP(U_476,option(U_476),some(U_476),U_473)
| hBOOL(hAPP(fun(U_477,bool),bool,hAPP(U_477,fun(fun(U_477,bool),bool),member(U_477),U_474),hAPP(fun(U_477,option(U_476)),fun(U_477,bool),dom(U_477,U_476),U_475))) ),
inference(miniscope,[status(thm)],[f_124_2]) ).
fof(f_124_4,plain,
! [U_476,U_475,U_473,U_474,U_477] :
( hAPP(U_477,option(U_476),U_475,U_474) != hAPP(U_476,option(U_476),some(U_476),U_473)
| hBOOL(hAPP(fun(U_477,bool),bool,hAPP(U_477,fun(fun(U_477,bool),bool),member(U_477),U_474),hAPP(fun(U_477,option(U_476)),fun(U_477,bool),dom(U_477,U_476),U_475))) ),
inference(definitional_conversion,[status(esa)],[f_124_3]) ).
cnf(f_124_5,plain,
( hAPP(U_477,option(U_476),U_475,U_474) != hAPP(U_476,option(U_476),some(U_476),U_473)
| hBOOL(hAPP(fun(U_477,bool),bool,hAPP(U_477,fun(fun(U_477,bool),bool),member(U_477),U_474),hAPP(fun(U_477,option(U_476)),fun(U_477,bool),dom(U_477,U_476),U_475))) ),
inference(clausify,[status(thm)],[f_124_4]) ).
fof(f_125_1,plain,
! [X_a,P_1,A_3] :
( ( hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_3))),P_1)) = bot_bot(fun(X_a,bool))
| hBOOL(hAPP(X_a,bool,P_1,A_3)) )
& ( hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_3))),P_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),bot_bot(fun(X_a,bool)))
| ~ hBOOL(hAPP(X_a,bool,P_1,A_3)) ) ),
inference(fof_nnf,[status(thm)],[fact_87_Collect__conv__if]) ).
fof(f_125_2,plain,
! [U_480,U_479,U_478] :
( ( hAPP(fun(U_480,bool),fun(U_480,bool),collect(U_480),hAPP(fun(U_480,bool),fun(U_480,bool),hAPP(fun(U_480,fun(bool,bool)),fun(fun(U_480,bool),fun(U_480,bool)),combs(U_480,bool,bool),hAPP(fun(U_480,bool),fun(U_480,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_480,bool),fun(U_480,fun(bool,bool))),combb(bool,fun(bool,bool),U_480),fconj),hAPP(U_480,fun(U_480,bool),hAPP(fun(U_480,fun(U_480,bool)),fun(U_480,fun(U_480,bool)),combc(U_480,U_480,bool),fequal(U_480)),U_478))),U_479)) = bot_bot(fun(U_480,bool))
| hBOOL(hAPP(U_480,bool,U_479,U_478)) )
& ( hAPP(fun(U_480,bool),fun(U_480,bool),collect(U_480),hAPP(fun(U_480,bool),fun(U_480,bool),hAPP(fun(U_480,fun(bool,bool)),fun(fun(U_480,bool),fun(U_480,bool)),combs(U_480,bool,bool),hAPP(fun(U_480,bool),fun(U_480,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_480,bool),fun(U_480,fun(bool,bool))),combb(bool,fun(bool,bool),U_480),fconj),hAPP(U_480,fun(U_480,bool),hAPP(fun(U_480,fun(U_480,bool)),fun(U_480,fun(U_480,bool)),combc(U_480,U_480,bool),fequal(U_480)),U_478))),U_479)) = hAPP(fun(U_480,bool),fun(U_480,bool),hAPP(U_480,fun(fun(U_480,bool),fun(U_480,bool)),insert(U_480),U_478),bot_bot(fun(U_480,bool)))
| ~ hBOOL(hAPP(U_480,bool,U_479,U_478)) ) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
fof(f_125_3,plain,
( ! [U_486,U_484,U_482] :
( hAPP(fun(U_486,bool),fun(U_486,bool),collect(U_486),hAPP(fun(U_486,bool),fun(U_486,bool),hAPP(fun(U_486,fun(bool,bool)),fun(fun(U_486,bool),fun(U_486,bool)),combs(U_486,bool,bool),hAPP(fun(U_486,bool),fun(U_486,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_486,bool),fun(U_486,fun(bool,bool))),combb(bool,fun(bool,bool),U_486),fconj),hAPP(U_486,fun(U_486,bool),hAPP(fun(U_486,fun(U_486,bool)),fun(U_486,fun(U_486,bool)),combc(U_486,U_486,bool),fequal(U_486)),U_482))),U_484)) = bot_bot(fun(U_486,bool))
| hBOOL(hAPP(U_486,bool,U_484,U_482)) )
& ! [U_485,U_483,U_481] :
( hAPP(fun(U_485,bool),fun(U_485,bool),collect(U_485),hAPP(fun(U_485,bool),fun(U_485,bool),hAPP(fun(U_485,fun(bool,bool)),fun(fun(U_485,bool),fun(U_485,bool)),combs(U_485,bool,bool),hAPP(fun(U_485,bool),fun(U_485,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_485,bool),fun(U_485,fun(bool,bool))),combb(bool,fun(bool,bool),U_485),fconj),hAPP(U_485,fun(U_485,bool),hAPP(fun(U_485,fun(U_485,bool)),fun(U_485,fun(U_485,bool)),combc(U_485,U_485,bool),fequal(U_485)),U_481))),U_483)) = hAPP(fun(U_485,bool),fun(U_485,bool),hAPP(U_485,fun(fun(U_485,bool),fun(U_485,bool)),insert(U_485),U_481),bot_bot(fun(U_485,bool)))
| ~ hBOOL(hAPP(U_485,bool,U_483,U_481)) ) ),
inference(miniscope,[status(thm)],[f_125_2]) ).
fof(f_125_4,plain,
( ! [U_482,U_484,U_486] :
( hAPP(fun(U_486,bool),fun(U_486,bool),collect(U_486),hAPP(fun(U_486,bool),fun(U_486,bool),hAPP(fun(U_486,fun(bool,bool)),fun(fun(U_486,bool),fun(U_486,bool)),combs(U_486,bool,bool),hAPP(fun(U_486,bool),fun(U_486,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_486,bool),fun(U_486,fun(bool,bool))),combb(bool,fun(bool,bool),U_486),fconj),hAPP(U_486,fun(U_486,bool),hAPP(fun(U_486,fun(U_486,bool)),fun(U_486,fun(U_486,bool)),combc(U_486,U_486,bool),fequal(U_486)),U_482))),U_484)) = bot_bot(fun(U_486,bool))
| hBOOL(hAPP(U_486,bool,U_484,U_482)) )
& ! [U_485,U_483,U_481] :
( hAPP(fun(U_485,bool),fun(U_485,bool),collect(U_485),hAPP(fun(U_485,bool),fun(U_485,bool),hAPP(fun(U_485,fun(bool,bool)),fun(fun(U_485,bool),fun(U_485,bool)),combs(U_485,bool,bool),hAPP(fun(U_485,bool),fun(U_485,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_485,bool),fun(U_485,fun(bool,bool))),combb(bool,fun(bool,bool),U_485),fconj),hAPP(U_485,fun(U_485,bool),hAPP(fun(U_485,fun(U_485,bool)),fun(U_485,fun(U_485,bool)),combc(U_485,U_485,bool),fequal(U_485)),U_481))),U_483)) = hAPP(fun(U_485,bool),fun(U_485,bool),hAPP(U_485,fun(fun(U_485,bool),fun(U_485,bool)),insert(U_485),U_481),bot_bot(fun(U_485,bool)))
| ~ hBOOL(hAPP(U_485,bool,U_483,U_481)) ) ),
inference(definitional_conversion,[status(esa)],[f_125_3]) ).
cnf(f_125_5,plain,
( hAPP(fun(U_485,bool),fun(U_485,bool),collect(U_485),hAPP(fun(U_485,bool),fun(U_485,bool),hAPP(fun(U_485,fun(bool,bool)),fun(fun(U_485,bool),fun(U_485,bool)),combs(U_485,bool,bool),hAPP(fun(U_485,bool),fun(U_485,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_485,bool),fun(U_485,fun(bool,bool))),combb(bool,fun(bool,bool),U_485),fconj),hAPP(U_485,fun(U_485,bool),hAPP(fun(U_485,fun(U_485,bool)),fun(U_485,fun(U_485,bool)),combc(U_485,U_485,bool),fequal(U_485)),U_481))),U_483)) = hAPP(fun(U_485,bool),fun(U_485,bool),hAPP(U_485,fun(fun(U_485,bool),fun(U_485,bool)),insert(U_485),U_481),bot_bot(fun(U_485,bool)))
| ~ hBOOL(hAPP(U_485,bool,U_483,U_481)) ),
inference(clausify,[status(thm)],[f_125_4]) ).
cnf(f_125_6,plain,
( hAPP(fun(U_486,bool),fun(U_486,bool),collect(U_486),hAPP(fun(U_486,bool),fun(U_486,bool),hAPP(fun(U_486,fun(bool,bool)),fun(fun(U_486,bool),fun(U_486,bool)),combs(U_486,bool,bool),hAPP(fun(U_486,bool),fun(U_486,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_486,bool),fun(U_486,fun(bool,bool))),combb(bool,fun(bool,bool),U_486),fconj),hAPP(U_486,fun(U_486,bool),hAPP(fun(U_486,fun(U_486,bool)),fun(U_486,fun(U_486,bool)),combc(U_486,U_486,bool),fequal(U_486)),U_482))),U_484)) = bot_bot(fun(U_486,bool))
| hBOOL(hAPP(U_486,bool,U_484,U_482)) ),
inference(clausify,[status(thm)],[f_125_4]) ).
fof(f_126_1,plain,
! [X_a,P_1,A_3] :
( ( hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_3))),P_1)) = bot_bot(fun(X_a,bool))
| hBOOL(hAPP(X_a,bool,P_1,A_3)) )
& ( hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_3))),P_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),bot_bot(fun(X_a,bool)))
| ~ hBOOL(hAPP(X_a,bool,P_1,A_3)) ) ),
inference(fof_nnf,[status(thm)],[fact_88_Collect__conv__if2]) ).
fof(f_126_2,plain,
! [U_489,U_488,U_487] :
( ( hAPP(fun(U_489,bool),fun(U_489,bool),collect(U_489),hAPP(fun(U_489,bool),fun(U_489,bool),hAPP(fun(U_489,fun(bool,bool)),fun(fun(U_489,bool),fun(U_489,bool)),combs(U_489,bool,bool),hAPP(fun(U_489,bool),fun(U_489,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_489,bool),fun(U_489,fun(bool,bool))),combb(bool,fun(bool,bool),U_489),fconj),hAPP(U_489,fun(U_489,bool),fequal(U_489),U_487))),U_488)) = bot_bot(fun(U_489,bool))
| hBOOL(hAPP(U_489,bool,U_488,U_487)) )
& ( hAPP(fun(U_489,bool),fun(U_489,bool),collect(U_489),hAPP(fun(U_489,bool),fun(U_489,bool),hAPP(fun(U_489,fun(bool,bool)),fun(fun(U_489,bool),fun(U_489,bool)),combs(U_489,bool,bool),hAPP(fun(U_489,bool),fun(U_489,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_489,bool),fun(U_489,fun(bool,bool))),combb(bool,fun(bool,bool),U_489),fconj),hAPP(U_489,fun(U_489,bool),fequal(U_489),U_487))),U_488)) = hAPP(fun(U_489,bool),fun(U_489,bool),hAPP(U_489,fun(fun(U_489,bool),fun(U_489,bool)),insert(U_489),U_487),bot_bot(fun(U_489,bool)))
| ~ hBOOL(hAPP(U_489,bool,U_488,U_487)) ) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
fof(f_126_3,plain,
( ! [U_495,U_493,U_491] :
( hAPP(fun(U_495,bool),fun(U_495,bool),collect(U_495),hAPP(fun(U_495,bool),fun(U_495,bool),hAPP(fun(U_495,fun(bool,bool)),fun(fun(U_495,bool),fun(U_495,bool)),combs(U_495,bool,bool),hAPP(fun(U_495,bool),fun(U_495,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_495,bool),fun(U_495,fun(bool,bool))),combb(bool,fun(bool,bool),U_495),fconj),hAPP(U_495,fun(U_495,bool),fequal(U_495),U_491))),U_493)) = bot_bot(fun(U_495,bool))
| hBOOL(hAPP(U_495,bool,U_493,U_491)) )
& ! [U_494,U_492,U_490] :
( hAPP(fun(U_494,bool),fun(U_494,bool),collect(U_494),hAPP(fun(U_494,bool),fun(U_494,bool),hAPP(fun(U_494,fun(bool,bool)),fun(fun(U_494,bool),fun(U_494,bool)),combs(U_494,bool,bool),hAPP(fun(U_494,bool),fun(U_494,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_494,bool),fun(U_494,fun(bool,bool))),combb(bool,fun(bool,bool),U_494),fconj),hAPP(U_494,fun(U_494,bool),fequal(U_494),U_490))),U_492)) = hAPP(fun(U_494,bool),fun(U_494,bool),hAPP(U_494,fun(fun(U_494,bool),fun(U_494,bool)),insert(U_494),U_490),bot_bot(fun(U_494,bool)))
| ~ hBOOL(hAPP(U_494,bool,U_492,U_490)) ) ),
inference(miniscope,[status(thm)],[f_126_2]) ).
fof(f_126_4,plain,
( ! [U_493,U_491,U_495] :
( hAPP(fun(U_495,bool),fun(U_495,bool),collect(U_495),hAPP(fun(U_495,bool),fun(U_495,bool),hAPP(fun(U_495,fun(bool,bool)),fun(fun(U_495,bool),fun(U_495,bool)),combs(U_495,bool,bool),hAPP(fun(U_495,bool),fun(U_495,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_495,bool),fun(U_495,fun(bool,bool))),combb(bool,fun(bool,bool),U_495),fconj),hAPP(U_495,fun(U_495,bool),fequal(U_495),U_491))),U_493)) = bot_bot(fun(U_495,bool))
| hBOOL(hAPP(U_495,bool,U_493,U_491)) )
& ! [U_494,U_492,U_490] :
( hAPP(fun(U_494,bool),fun(U_494,bool),collect(U_494),hAPP(fun(U_494,bool),fun(U_494,bool),hAPP(fun(U_494,fun(bool,bool)),fun(fun(U_494,bool),fun(U_494,bool)),combs(U_494,bool,bool),hAPP(fun(U_494,bool),fun(U_494,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_494,bool),fun(U_494,fun(bool,bool))),combb(bool,fun(bool,bool),U_494),fconj),hAPP(U_494,fun(U_494,bool),fequal(U_494),U_490))),U_492)) = hAPP(fun(U_494,bool),fun(U_494,bool),hAPP(U_494,fun(fun(U_494,bool),fun(U_494,bool)),insert(U_494),U_490),bot_bot(fun(U_494,bool)))
| ~ hBOOL(hAPP(U_494,bool,U_492,U_490)) ) ),
inference(definitional_conversion,[status(esa)],[f_126_3]) ).
cnf(f_126_5,plain,
( hAPP(fun(U_494,bool),fun(U_494,bool),collect(U_494),hAPP(fun(U_494,bool),fun(U_494,bool),hAPP(fun(U_494,fun(bool,bool)),fun(fun(U_494,bool),fun(U_494,bool)),combs(U_494,bool,bool),hAPP(fun(U_494,bool),fun(U_494,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_494,bool),fun(U_494,fun(bool,bool))),combb(bool,fun(bool,bool),U_494),fconj),hAPP(U_494,fun(U_494,bool),fequal(U_494),U_490))),U_492)) = hAPP(fun(U_494,bool),fun(U_494,bool),hAPP(U_494,fun(fun(U_494,bool),fun(U_494,bool)),insert(U_494),U_490),bot_bot(fun(U_494,bool)))
| ~ hBOOL(hAPP(U_494,bool,U_492,U_490)) ),
inference(clausify,[status(thm)],[f_126_4]) ).
cnf(f_126_6,plain,
( hAPP(fun(U_495,bool),fun(U_495,bool),collect(U_495),hAPP(fun(U_495,bool),fun(U_495,bool),hAPP(fun(U_495,fun(bool,bool)),fun(fun(U_495,bool),fun(U_495,bool)),combs(U_495,bool,bool),hAPP(fun(U_495,bool),fun(U_495,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(U_495,bool),fun(U_495,fun(bool,bool))),combb(bool,fun(bool,bool),U_495),fconj),hAPP(U_495,fun(U_495,bool),fequal(U_495),U_491))),U_493)) = bot_bot(fun(U_495,bool))
| hBOOL(hAPP(U_495,bool,U_493,U_491)) ),
inference(clausify,[status(thm)],[f_126_4]) ).
fof(f_127_1,plain,
! [X_a,A_3] : hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_3)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),bot_bot(fun(X_a,bool))),
inference(fof_nnf,[status(thm)],[fact_89_singleton__conv]) ).
fof(f_127_2,plain,
! [U_497,U_496] : hAPP(fun(U_497,bool),fun(U_497,bool),collect(U_497),hAPP(U_497,fun(U_497,bool),hAPP(fun(U_497,fun(U_497,bool)),fun(U_497,fun(U_497,bool)),combc(U_497,U_497,bool),fequal(U_497)),U_496)) = hAPP(fun(U_497,bool),fun(U_497,bool),hAPP(U_497,fun(fun(U_497,bool),fun(U_497,bool)),insert(U_497),U_496),bot_bot(fun(U_497,bool))),
inference(variable_rename,[status(thm)],[f_127_1]) ).
fof(f_127_3,plain,
! [U_496,U_497] : hAPP(fun(U_497,bool),fun(U_497,bool),collect(U_497),hAPP(U_497,fun(U_497,bool),hAPP(fun(U_497,fun(U_497,bool)),fun(U_497,fun(U_497,bool)),combc(U_497,U_497,bool),fequal(U_497)),U_496)) = hAPP(fun(U_497,bool),fun(U_497,bool),hAPP(U_497,fun(fun(U_497,bool),fun(U_497,bool)),insert(U_497),U_496),bot_bot(fun(U_497,bool))),
inference(definitional_conversion,[status(esa)],[f_127_2]) ).
cnf(f_127_4,plain,
hAPP(fun(U_497,bool),fun(U_497,bool),collect(U_497),hAPP(U_497,fun(U_497,bool),hAPP(fun(U_497,fun(U_497,bool)),fun(U_497,fun(U_497,bool)),combc(U_497,U_497,bool),fequal(U_497)),U_496)) = hAPP(fun(U_497,bool),fun(U_497,bool),hAPP(U_497,fun(fun(U_497,bool),fun(U_497,bool)),insert(U_497),U_496),bot_bot(fun(U_497,bool))),
inference(clausify,[status(thm)],[f_127_3]) ).
fof(f_128_1,plain,
! [X_a,A_3] : hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_3)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_3),bot_bot(fun(X_a,bool))),
inference(fof_nnf,[status(thm)],[fact_90_singleton__conv2]) ).
fof(f_128_2,plain,
! [U_499,U_498] : hAPP(fun(U_499,bool),fun(U_499,bool),collect(U_499),hAPP(U_499,fun(U_499,bool),fequal(U_499),U_498)) = hAPP(fun(U_499,bool),fun(U_499,bool),hAPP(U_499,fun(fun(U_499,bool),fun(U_499,bool)),insert(U_499),U_498),bot_bot(fun(U_499,bool))),
inference(variable_rename,[status(thm)],[f_128_1]) ).
fof(f_128_3,plain,
! [U_499,U_498] : hAPP(fun(U_499,bool),fun(U_499,bool),collect(U_499),hAPP(U_499,fun(U_499,bool),fequal(U_499),U_498)) = hAPP(fun(U_499,bool),fun(U_499,bool),hAPP(U_499,fun(fun(U_499,bool),fun(U_499,bool)),insert(U_499),U_498),bot_bot(fun(U_499,bool))),
inference(definitional_conversion,[status(esa)],[f_128_2]) ).
cnf(f_128_4,plain,
hAPP(fun(U_499,bool),fun(U_499,bool),collect(U_499),hAPP(U_499,fun(U_499,bool),fequal(U_499),U_498)) = hAPP(fun(U_499,bool),fun(U_499,bool),hAPP(U_499,fun(fun(U_499,bool),fun(U_499,bool)),insert(U_499),U_498),bot_bot(fun(U_499,bool))),
inference(clausify,[status(thm)],[f_128_3]) ).
fof(f_129_1,plain,
! [C_1,G] :
( hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),G),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,C_1)),bot_bot(fun(hoare_509422987triple(state),bool)))))
| ~ hBOOL(hAPP(com,bool,wt,C_1))
| ? [X_1] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),G),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,X_1))),bot_bot(fun(hoare_509422987triple(state),bool)))))
& hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X_1),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body))) )
| ~ hBOOL(hoare_1883395792gleton) ),
inference(fof_nnf,[status(thm)],[fact_91_MGF__lemma1]) ).
fof(f_129_2,plain,
! [U_502,U_501] :
( hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),U_501),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,U_502)),bot_bot(fun(hoare_509422987triple(state),bool)))))
| ~ hBOOL(hAPP(com,bool,wt,U_502))
| ? [U_500] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),U_501),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,U_500))),bot_bot(fun(hoare_509422987triple(state),bool)))))
& hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),U_500),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body))) )
| ~ hBOOL(hoare_1883395792gleton) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
fof(f_129_3,plain,
( ! [U_502,U_501] :
( hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),U_501),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,U_502)),bot_bot(fun(hoare_509422987triple(state),bool)))))
| ~ hBOOL(hAPP(com,bool,wt,U_502))
| ? [U_500] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),U_501),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,U_500))),bot_bot(fun(hoare_509422987triple(state),bool)))))
& hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),U_500),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body))) ) )
| ~ hBOOL(hoare_1883395792gleton) ),
inference(miniscope,[status(thm)],[f_129_2]) ).
fof(f_129_4,plain,
( ! [U_502,U_501] :
( hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),U_501),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,U_502)),bot_bot(fun(hoare_509422987triple(state),bool)))))
| ~ hBOOL(hAPP(com,bool,wt,U_502))
| ( ~ hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),U_501),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,sK8(U_502,U_501)))),bot_bot(fun(hoare_509422987triple(state),bool)))))
& hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),sK8(U_502,U_501)),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body))) ) )
| ~ hBOOL(hoare_1883395792gleton) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_500,sK8(U_502,U_501))],[f_129_3]) ).
fof(f_129_5,plain,
( ! [U_501,U_502] :
( ~ hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),U_501),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,sK8(U_502,U_501)))),bot_bot(fun(hoare_509422987triple(state),bool)))))
| ~ sP16(U_501,U_502) )
& ! [U_501,U_502] :
( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),sK8(U_502,U_501)),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body)))
| ~ sP16(U_501,U_502) )
& ! [U_501,U_502] :
( hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),U_501),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,U_502)),bot_bot(fun(hoare_509422987triple(state),bool)))))
| ~ hBOOL(hAPP(com,bool,wt,U_502))
| sP16(U_501,U_502)
| ~ hBOOL(hoare_1883395792gleton) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16])],[f_129_4]) ).
cnf(f_129_6,plain,
( hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),U_501),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,U_502)),bot_bot(fun(hoare_509422987triple(state),bool)))))
| ~ hBOOL(hAPP(com,bool,wt,U_502))
| sP16(U_501,U_502)
| ~ hBOOL(hoare_1883395792gleton) ),
inference(clausify,[status(thm)],[f_129_5]) ).
cnf(f_129_7,plain,
( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),sK8(U_502,U_501)),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body)))
| ~ sP16(U_501,U_502) ),
inference(clausify,[status(thm)],[f_129_5]) ).
cnf(f_129_8,plain,
( ~ hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),U_501),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,hAPP(pname,com,body_1,sK8(U_502,U_501)))),bot_bot(fun(hoare_509422987triple(state),bool)))))
| ~ sP16(U_501,U_502) ),
inference(clausify,[status(thm)],[f_129_5]) ).
fof(f_130_1,plain,
! [Pn,B_2] :
( hBOOL(hAPP(com,bool,wt,B_2))
| hAPP(pname,option(com),body,Pn) != hAPP(com,option(com),some(com),B_2)
| ~ hBOOL(wT_bodies) ),
inference(fof_nnf,[status(thm)],[fact_92_WT__bodiesD]) ).
fof(f_130_2,plain,
! [U_504,U_503] :
( hBOOL(hAPP(com,bool,wt,U_503))
| hAPP(pname,option(com),body,U_504) != hAPP(com,option(com),some(com),U_503)
| ~ hBOOL(wT_bodies) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
fof(f_130_3,plain,
( ! [U_504,U_503] :
( hBOOL(hAPP(com,bool,wt,U_503))
| hAPP(pname,option(com),body,U_504) != hAPP(com,option(com),some(com),U_503) )
| ~ hBOOL(wT_bodies) ),
inference(miniscope,[status(thm)],[f_130_2]) ).
fof(f_130_4,plain,
! [U_504,U_503] :
( hBOOL(hAPP(com,bool,wt,U_503))
| hAPP(pname,option(com),body,U_504) != hAPP(com,option(com),some(com),U_503)
| ~ hBOOL(wT_bodies) ),
inference(definitional_conversion,[status(esa)],[f_130_3]) ).
cnf(f_130_5,plain,
( hBOOL(hAPP(com,bool,wt,U_503))
| hAPP(pname,option(com),body,U_504) != hAPP(com,option(com),some(com),U_503)
| ~ hBOOL(wT_bodies) ),
inference(clausify,[status(thm)],[f_130_4]) ).
fof(f_131_1,plain,
! [X_a,X_b,B_1,F,A_1] :
( ? [X_1] :
( hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1))
& ti(X_a,B_1) = hAPP(X_b,X_a,F,X_1) )
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1))) ),
inference(fof_nnf,[status(thm)],[fact_93_imageE]) ).
fof(f_131_2,plain,
! [U_510,U_509,U_508,U_507,U_506] :
( ? [U_505] :
( hBOOL(hAPP(fun(U_509,bool),bool,hAPP(U_509,fun(fun(U_509,bool),bool),member(U_509),U_505),U_506))
& ti(U_510,U_508) = hAPP(U_509,U_510,U_507,U_505) )
| ~ hBOOL(hAPP(fun(U_510,bool),bool,hAPP(U_510,fun(fun(U_510,bool),bool),member(U_510),U_508),hAPP(fun(U_509,bool),fun(U_510,bool),hAPP(fun(U_509,U_510),fun(fun(U_509,bool),fun(U_510,bool)),image(U_509,U_510),U_507),U_506))) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
fof(f_131_3,plain,
! [U_510,U_509,U_508,U_507,U_506] :
( ( hBOOL(hAPP(fun(U_509,bool),bool,hAPP(U_509,fun(fun(U_509,bool),bool),member(U_509),sK9(U_510,U_509,U_508,U_507,U_506)),U_506))
& ti(U_510,U_508) = hAPP(U_509,U_510,U_507,sK9(U_510,U_509,U_508,U_507,U_506)) )
| ~ hBOOL(hAPP(fun(U_510,bool),bool,hAPP(U_510,fun(fun(U_510,bool),bool),member(U_510),U_508),hAPP(fun(U_509,bool),fun(U_510,bool),hAPP(fun(U_509,U_510),fun(fun(U_509,bool),fun(U_510,bool)),image(U_509,U_510),U_507),U_506))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_505,sK9(U_510,U_509,U_508,U_507,U_506))],[f_131_2]) ).
fof(f_131_4,plain,
( ! [U_507,U_509,U_508,U_506,U_510] :
( hBOOL(hAPP(fun(U_509,bool),bool,hAPP(U_509,fun(fun(U_509,bool),bool),member(U_509),sK9(U_510,U_509,U_508,U_507,U_506)),U_506))
| ~ sP17(U_507,U_509,U_508,U_506,U_510) )
& ! [U_507,U_509,U_508,U_506,U_510] :
( ti(U_510,U_508) = hAPP(U_509,U_510,U_507,sK9(U_510,U_509,U_508,U_507,U_506))
| ~ sP17(U_507,U_509,U_508,U_506,U_510) )
& ! [U_507,U_509,U_508,U_506,U_510] :
( sP17(U_507,U_509,U_508,U_506,U_510)
| ~ hBOOL(hAPP(fun(U_510,bool),bool,hAPP(U_510,fun(fun(U_510,bool),bool),member(U_510),U_508),hAPP(fun(U_509,bool),fun(U_510,bool),hAPP(fun(U_509,U_510),fun(fun(U_509,bool),fun(U_510,bool)),image(U_509,U_510),U_507),U_506))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17])],[f_131_3]) ).
cnf(f_131_5,plain,
( sP17(U_507,U_509,U_508,U_506,U_510)
| ~ hBOOL(hAPP(fun(U_510,bool),bool,hAPP(U_510,fun(fun(U_510,bool),bool),member(U_510),U_508),hAPP(fun(U_509,bool),fun(U_510,bool),hAPP(fun(U_509,U_510),fun(fun(U_509,bool),fun(U_510,bool)),image(U_509,U_510),U_507),U_506))) ),
inference(clausify,[status(thm)],[f_131_4]) ).
cnf(f_131_6,plain,
( ti(U_510,U_508) = hAPP(U_509,U_510,U_507,sK9(U_510,U_509,U_508,U_507,U_506))
| ~ sP17(U_507,U_509,U_508,U_506,U_510) ),
inference(clausify,[status(thm)],[f_131_4]) ).
cnf(f_131_7,plain,
( hBOOL(hAPP(fun(U_509,bool),bool,hAPP(U_509,fun(fun(U_509,bool),bool),member(U_509),sK9(U_510,U_509,U_508,U_507,U_506)),U_506))
| ~ sP17(U_507,U_509,U_508,U_506,U_510) ),
inference(clausify,[status(thm)],[f_131_4]) ).
fof(f_132_1,plain,
! [X_a,P_1,A_1,Fa] :
( hBOOL(hAPP(fun(X_a,bool),bool,P_1,Fa))
| ? [A_2,F_1] :
( ~ hBOOL(hAPP(fun(X_a,bool),bool,P_1,hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(X_a,fun(fun(X_a,bool),fun(X_a,bool)),insert(X_a),A_2),F_1)))
& hBOOL(hAPP(fun(X_a,bool),bool,P_1,F_1))
& ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),F_1))
& hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),A_1))
& hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),F_1)) )
| ~ hBOOL(hAPP(fun(X_a,bool),bool,P_1,bot_bot(fun(X_a,bool))))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),Fa),A_1))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),Fa)) ),
inference(fof_nnf,[status(thm)],[fact_94_finite__subset__induct]) ).
fof(f_132_2,plain,
! [U_516,U_515,U_514,U_513] :
( hBOOL(hAPP(fun(U_516,bool),bool,U_515,U_513))
| ? [U_512,U_511] :
( ~ hBOOL(hAPP(fun(U_516,bool),bool,U_515,hAPP(fun(U_516,bool),fun(U_516,bool),hAPP(U_516,fun(fun(U_516,bool),fun(U_516,bool)),insert(U_516),U_512),U_511)))
& hBOOL(hAPP(fun(U_516,bool),bool,U_515,U_511))
& ~ hBOOL(hAPP(fun(U_516,bool),bool,hAPP(U_516,fun(fun(U_516,bool),bool),member(U_516),U_512),U_511))
& hBOOL(hAPP(fun(U_516,bool),bool,hAPP(U_516,fun(fun(U_516,bool),bool),member(U_516),U_512),U_514))
& hBOOL(hAPP(fun(U_516,bool),bool,finite_finite(U_516),U_511)) )
| ~ hBOOL(hAPP(fun(U_516,bool),bool,U_515,bot_bot(fun(U_516,bool))))
| ~ hBOOL(hAPP(fun(U_516,bool),bool,hAPP(fun(U_516,bool),fun(fun(U_516,bool),bool),ord_less_eq(fun(U_516,bool)),U_513),U_514))
| ~ hBOOL(hAPP(fun(U_516,bool),bool,finite_finite(U_516),U_513)) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
fof(f_132_3,plain,
! [U_516,U_515,U_514,U_513] :
( hBOOL(hAPP(fun(U_516,bool),bool,U_515,U_513))
| ? [U_511] :
( ~ hBOOL(hAPP(fun(U_516,bool),bool,U_515,hAPP(fun(U_516,bool),fun(U_516,bool),hAPP(U_516,fun(fun(U_516,bool),fun(U_516,bool)),insert(U_516),sK10(U_516,U_515,U_514,U_513)),U_511)))
& hBOOL(hAPP(fun(U_516,bool),bool,U_515,U_511))
& ~ hBOOL(hAPP(fun(U_516,bool),bool,hAPP(U_516,fun(fun(U_516,bool),bool),member(U_516),sK10(U_516,U_515,U_514,U_513)),U_511))
& hBOOL(hAPP(fun(U_516,bool),bool,hAPP(U_516,fun(fun(U_516,bool),bool),member(U_516),sK10(U_516,U_515,U_514,U_513)),U_514))
& hBOOL(hAPP(fun(U_516,bool),bool,finite_finite(U_516),U_511)) )
| ~ hBOOL(hAPP(fun(U_516,bool),bool,U_515,bot_bot(fun(U_516,bool))))
| ~ hBOOL(hAPP(fun(U_516,bool),bool,hAPP(fun(U_516,bool),fun(fun(U_516,bool),bool),ord_less_eq(fun(U_516,bool)),U_513),U_514))
| ~ hBOOL(hAPP(fun(U_516,bool),bool,finite_finite(U_516),U_513)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_512,sK10(U_516,U_515,U_514,U_513))],[f_132_2]) ).
fof(f_132_4,plain,
! [U_516,U_515,U_514,U_513] :
( hBOOL(hAPP(fun(U_516,bool),bool,U_515,U_513))
| ( ~ hBOOL(hAPP(fun(U_516,bool),bool,U_515,hAPP(fun(U_516,bool),fun(U_516,bool),hAPP(U_516,fun(fun(U_516,bool),fun(U_516,bool)),insert(U_516),sK10(U_516,U_515,U_514,U_513)),sK11(U_516,U_515,U_514,U_513))))
& hBOOL(hAPP(fun(U_516,bool),bool,U_515,sK11(U_516,U_515,U_514,U_513)))
& ~ hBOOL(hAPP(fun(U_516,bool),bool,hAPP(U_516,fun(fun(U_516,bool),bool),member(U_516),sK10(U_516,U_515,U_514,U_513)),sK11(U_516,U_515,U_514,U_513)))
& hBOOL(hAPP(fun(U_516,bool),bool,hAPP(U_516,fun(fun(U_516,bool),bool),member(U_516),sK10(U_516,U_515,U_514,U_513)),U_514))
& hBOOL(hAPP(fun(U_516,bool),bool,finite_finite(U_516),sK11(U_516,U_515,U_514,U_513))) )
| ~ hBOOL(hAPP(fun(U_516,bool),bool,U_515,bot_bot(fun(U_516,bool))))
| ~ hBOOL(hAPP(fun(U_516,bool),bool,hAPP(fun(U_516,bool),fun(fun(U_516,bool),bool),ord_less_eq(fun(U_516,bool)),U_513),U_514))
| ~ hBOOL(hAPP(fun(U_516,bool),bool,finite_finite(U_516),U_513)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_511,sK11(U_516,U_515,U_514,U_513))],[f_132_3]) ).
fof(f_132_5,plain,
( ! [U_515,U_513,U_514,U_516] :
( ~ hBOOL(hAPP(fun(U_516,bool),bool,U_515,hAPP(fun(U_516,bool),fun(U_516,bool),hAPP(U_516,fun(fun(U_516,bool),fun(U_516,bool)),insert(U_516),sK10(U_516,U_515,U_514,U_513)),sK11(U_516,U_515,U_514,U_513))))
| ~ sP18(U_515,U_513,U_514,U_516) )
& ! [U_515,U_513,U_514,U_516] :
( hBOOL(hAPP(fun(U_516,bool),bool,U_515,sK11(U_516,U_515,U_514,U_513)))
| ~ sP18(U_515,U_513,U_514,U_516) )
& ! [U_515,U_513,U_514,U_516] :
( ~ hBOOL(hAPP(fun(U_516,bool),bool,hAPP(U_516,fun(fun(U_516,bool),bool),member(U_516),sK10(U_516,U_515,U_514,U_513)),sK11(U_516,U_515,U_514,U_513)))
| ~ sP18(U_515,U_513,U_514,U_516) )
& ! [U_515,U_513,U_514,U_516] :
( hBOOL(hAPP(fun(U_516,bool),bool,hAPP(U_516,fun(fun(U_516,bool),bool),member(U_516),sK10(U_516,U_515,U_514,U_513)),U_514))
| ~ sP18(U_515,U_513,U_514,U_516) )
& ! [U_515,U_513,U_514,U_516] :
( hBOOL(hAPP(fun(U_516,bool),bool,finite_finite(U_516),sK11(U_516,U_515,U_514,U_513)))
| ~ sP18(U_515,U_513,U_514,U_516) )
& ! [U_515,U_513,U_514,U_516] :
( hBOOL(hAPP(fun(U_516,bool),bool,U_515,U_513))
| sP18(U_515,U_513,U_514,U_516)
| ~ hBOOL(hAPP(fun(U_516,bool),bool,U_515,bot_bot(fun(U_516,bool))))
| ~ hBOOL(hAPP(fun(U_516,bool),bool,hAPP(fun(U_516,bool),fun(fun(U_516,bool),bool),ord_less_eq(fun(U_516,bool)),U_513),U_514))
| ~ hBOOL(hAPP(fun(U_516,bool),bool,finite_finite(U_516),U_513)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18])],[f_132_4]) ).
cnf(f_132_6,plain,
( hBOOL(hAPP(fun(U_516,bool),bool,U_515,U_513))
| sP18(U_515,U_513,U_514,U_516)
| ~ hBOOL(hAPP(fun(U_516,bool),bool,U_515,bot_bot(fun(U_516,bool))))
| ~ hBOOL(hAPP(fun(U_516,bool),bool,hAPP(fun(U_516,bool),fun(fun(U_516,bool),bool),ord_less_eq(fun(U_516,bool)),U_513),U_514))
| ~ hBOOL(hAPP(fun(U_516,bool),bool,finite_finite(U_516),U_513)) ),
inference(clausify,[status(thm)],[f_132_5]) ).
cnf(f_132_7,plain,
( hBOOL(hAPP(fun(U_516,bool),bool,finite_finite(U_516),sK11(U_516,U_515,U_514,U_513)))
| ~ sP18(U_515,U_513,U_514,U_516) ),
inference(clausify,[status(thm)],[f_132_5]) ).
cnf(f_132_8,plain,
( hBOOL(hAPP(fun(U_516,bool),bool,hAPP(U_516,fun(fun(U_516,bool),bool),member(U_516),sK10(U_516,U_515,U_514,U_513)),U_514))
| ~ sP18(U_515,U_513,U_514,U_516) ),
inference(clausify,[status(thm)],[f_132_5]) ).
cnf(f_132_9,plain,
( ~ hBOOL(hAPP(fun(U_516,bool),bool,hAPP(U_516,fun(fun(U_516,bool),bool),member(U_516),sK10(U_516,U_515,U_514,U_513)),sK11(U_516,U_515,U_514,U_513)))
| ~ sP18(U_515,U_513,U_514,U_516) ),
inference(clausify,[status(thm)],[f_132_5]) ).
cnf(f_132_10,plain,
( hBOOL(hAPP(fun(U_516,bool),bool,U_515,sK11(U_516,U_515,U_514,U_513)))
| ~ sP18(U_515,U_513,U_514,U_516) ),
inference(clausify,[status(thm)],[f_132_5]) ).
cnf(f_132_11,plain,
( ~ hBOOL(hAPP(fun(U_516,bool),bool,U_515,hAPP(fun(U_516,bool),fun(U_516,bool),hAPP(U_516,fun(fun(U_516,bool),fun(U_516,bool)),insert(U_516),sK10(U_516,U_515,U_514,U_513)),sK11(U_516,U_515,U_514,U_513))))
| ~ sP18(U_515,U_513,U_514,U_516) ),
inference(clausify,[status(thm)],[f_132_5]) ).
fof(f_133_1,plain,
! [P] :
( ? [Y_1] : hAPP(pname,option(com),body,P) = hAPP(com,option(com),some(com),Y_1)
| ~ hBOOL(hAPP(com,bool,wt,hAPP(pname,com,body_1,P))) ),
inference(fof_nnf,[status(thm)],[fact_95_WTs__elim__cases_I7_J]) ).
fof(f_133_2,plain,
! [U_518] :
( ? [U_517] : hAPP(pname,option(com),body,U_518) = hAPP(com,option(com),some(com),U_517)
| ~ hBOOL(hAPP(com,bool,wt,hAPP(pname,com,body_1,U_518))) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
fof(f_133_3,plain,
! [U_518] :
( hAPP(pname,option(com),body,U_518) = hAPP(com,option(com),some(com),sK12(U_518))
| ~ hBOOL(hAPP(com,bool,wt,hAPP(pname,com,body_1,U_518))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_517,sK12(U_518))],[f_133_2]) ).
fof(f_133_4,plain,
! [U_518] :
( hAPP(pname,option(com),body,U_518) = hAPP(com,option(com),some(com),sK12(U_518))
| ~ hBOOL(hAPP(com,bool,wt,hAPP(pname,com,body_1,U_518))) ),
inference(definitional_conversion,[status(esa)],[f_133_3]) ).
cnf(f_133_5,plain,
( hAPP(pname,option(com),body,U_518) = hAPP(com,option(com),some(com),sK12(U_518))
| ~ hBOOL(hAPP(com,bool,wt,hAPP(pname,com,body_1,U_518))) ),
inference(clausify,[status(thm)],[f_133_4]) ).
fof(f_134_1,plain,
! [X_a,B,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_1),B))
| ? [X_1] :
( ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B))
& hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) ),
inference(fof_nnf,[status(thm)],[fact_96_subsetI]) ).
fof(f_134_2,plain,
! [U_522,U_521,U_520] :
( hBOOL(hAPP(fun(U_522,bool),bool,hAPP(fun(U_522,bool),fun(fun(U_522,bool),bool),ord_less_eq(fun(U_522,bool)),U_520),U_521))
| ? [U_519] :
( ~ hBOOL(hAPP(fun(U_522,bool),bool,hAPP(U_522,fun(fun(U_522,bool),bool),member(U_522),U_519),U_521))
& hBOOL(hAPP(fun(U_522,bool),bool,hAPP(U_522,fun(fun(U_522,bool),bool),member(U_522),U_519),U_520)) ) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
fof(f_134_3,plain,
! [U_522,U_521,U_520] :
( hBOOL(hAPP(fun(U_522,bool),bool,hAPP(fun(U_522,bool),fun(fun(U_522,bool),bool),ord_less_eq(fun(U_522,bool)),U_520),U_521))
| ( ~ hBOOL(hAPP(fun(U_522,bool),bool,hAPP(U_522,fun(fun(U_522,bool),bool),member(U_522),sK13(U_522,U_521,U_520)),U_521))
& hBOOL(hAPP(fun(U_522,bool),bool,hAPP(U_522,fun(fun(U_522,bool),bool),member(U_522),sK13(U_522,U_521,U_520)),U_520)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_519,sK13(U_522,U_521,U_520))],[f_134_2]) ).
fof(f_134_4,plain,
( ! [U_520,U_522,U_521] :
( ~ hBOOL(hAPP(fun(U_522,bool),bool,hAPP(U_522,fun(fun(U_522,bool),bool),member(U_522),sK13(U_522,U_521,U_520)),U_521))
| ~ sP19(U_520,U_522,U_521) )
& ! [U_520,U_522,U_521] :
( hBOOL(hAPP(fun(U_522,bool),bool,hAPP(U_522,fun(fun(U_522,bool),bool),member(U_522),sK13(U_522,U_521,U_520)),U_520))
| ~ sP19(U_520,U_522,U_521) )
& ! [U_520,U_522,U_521] :
( hBOOL(hAPP(fun(U_522,bool),bool,hAPP(fun(U_522,bool),fun(fun(U_522,bool),bool),ord_less_eq(fun(U_522,bool)),U_520),U_521))
| sP19(U_520,U_522,U_521) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19])],[f_134_3]) ).
cnf(f_134_5,plain,
( hBOOL(hAPP(fun(U_522,bool),bool,hAPP(fun(U_522,bool),fun(fun(U_522,bool),bool),ord_less_eq(fun(U_522,bool)),U_520),U_521))
| sP19(U_520,U_522,U_521) ),
inference(clausify,[status(thm)],[f_134_4]) ).
cnf(f_134_6,plain,
( hBOOL(hAPP(fun(U_522,bool),bool,hAPP(U_522,fun(fun(U_522,bool),bool),member(U_522),sK13(U_522,U_521,U_520)),U_520))
| ~ sP19(U_520,U_522,U_521) ),
inference(clausify,[status(thm)],[f_134_4]) ).
cnf(f_134_7,plain,
( ~ hBOOL(hAPP(fun(U_522,bool),bool,hAPP(U_522,fun(fun(U_522,bool),bool),member(U_522),sK13(U_522,U_521,U_520)),U_521))
| ~ sP19(U_520,U_522,U_521) ),
inference(clausify,[status(thm)],[f_134_4]) ).
fof(f_135_1,plain,
! [X_b,X_a,F,A_1,B] :
( ? [C] :
( ti(fun(X_a,bool),B) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),C)
& hBOOL(hAPP(fun(X_b,bool),bool,finite_finite(X_b),C))
& hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),C),A_1)) )
| ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_1)))
| ~ hBOOL(hAPP(fun(X_a,bool),bool,finite_finite(X_a),B)) ),
inference(fof_nnf,[status(thm)],[fact_97_finite__subset__image]) ).
fof(f_135_2,plain,
! [U_528,U_527,U_526,U_525,U_524] :
( ? [U_523] :
( ti(fun(U_527,bool),U_524) = hAPP(fun(U_528,bool),fun(U_527,bool),hAPP(fun(U_528,U_527),fun(fun(U_528,bool),fun(U_527,bool)),image(U_528,U_527),U_526),U_523)
& hBOOL(hAPP(fun(U_528,bool),bool,finite_finite(U_528),U_523))
& hBOOL(hAPP(fun(U_528,bool),bool,hAPP(fun(U_528,bool),fun(fun(U_528,bool),bool),ord_less_eq(fun(U_528,bool)),U_523),U_525)) )
| ~ hBOOL(hAPP(fun(U_527,bool),bool,hAPP(fun(U_527,bool),fun(fun(U_527,bool),bool),ord_less_eq(fun(U_527,bool)),U_524),hAPP(fun(U_528,bool),fun(U_527,bool),hAPP(fun(U_528,U_527),fun(fun(U_528,bool),fun(U_527,bool)),image(U_528,U_527),U_526),U_525)))
| ~ hBOOL(hAPP(fun(U_527,bool),bool,finite_finite(U_527),U_524)) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
fof(f_135_3,plain,
! [U_528,U_527,U_526,U_525,U_524] :
( ( ti(fun(U_527,bool),U_524) = hAPP(fun(U_528,bool),fun(U_527,bool),hAPP(fun(U_528,U_527),fun(fun(U_528,bool),fun(U_527,bool)),image(U_528,U_527),U_526),sK14(U_528,U_527,U_526,U_525,U_524))
& hBOOL(hAPP(fun(U_528,bool),bool,finite_finite(U_528),sK14(U_528,U_527,U_526,U_525,U_524)))
& hBOOL(hAPP(fun(U_528,bool),bool,hAPP(fun(U_528,bool),fun(fun(U_528,bool),bool),ord_less_eq(fun(U_528,bool)),sK14(U_528,U_527,U_526,U_525,U_524)),U_525)) )
| ~ hBOOL(hAPP(fun(U_527,bool),bool,hAPP(fun(U_527,bool),fun(fun(U_527,bool),bool),ord_less_eq(fun(U_527,bool)),U_524),hAPP(fun(U_528,bool),fun(U_527,bool),hAPP(fun(U_528,U_527),fun(fun(U_528,bool),fun(U_527,bool)),image(U_528,U_527),U_526),U_525)))
| ~ hBOOL(hAPP(fun(U_527,bool),bool,finite_finite(U_527),U_524)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_523,sK14(U_528,U_527,U_526,U_525,U_524))],[f_135_2]) ).
fof(f_135_4,plain,
( ! [U_528,U_524,U_526,U_527,U_525] :
( ti(fun(U_527,bool),U_524) = hAPP(fun(U_528,bool),fun(U_527,bool),hAPP(fun(U_528,U_527),fun(fun(U_528,bool),fun(U_527,bool)),image(U_528,U_527),U_526),sK14(U_528,U_527,U_526,U_525,U_524))
| ~ sP20(U_528,U_524,U_526,U_527,U_525) )
& ! [U_528,U_524,U_526,U_527,U_525] :
( hBOOL(hAPP(fun(U_528,bool),bool,finite_finite(U_528),sK14(U_528,U_527,U_526,U_525,U_524)))
| ~ sP20(U_528,U_524,U_526,U_527,U_525) )
& ! [U_528,U_524,U_526,U_527,U_525] :
( hBOOL(hAPP(fun(U_528,bool),bool,hAPP(fun(U_528,bool),fun(fun(U_528,bool),bool),ord_less_eq(fun(U_528,bool)),sK14(U_528,U_527,U_526,U_525,U_524)),U_525))
| ~ sP20(U_528,U_524,U_526,U_527,U_525) )
& ! [U_528,U_524,U_526,U_527,U_525] :
( sP20(U_528,U_524,U_526,U_527,U_525)
| ~ hBOOL(hAPP(fun(U_527,bool),bool,hAPP(fun(U_527,bool),fun(fun(U_527,bool),bool),ord_less_eq(fun(U_527,bool)),U_524),hAPP(fun(U_528,bool),fun(U_527,bool),hAPP(fun(U_528,U_527),fun(fun(U_528,bool),fun(U_527,bool)),image(U_528,U_527),U_526),U_525)))
| ~ hBOOL(hAPP(fun(U_527,bool),bool,finite_finite(U_527),U_524)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP20])],[f_135_3]) ).
cnf(f_135_5,plain,
( sP20(U_528,U_524,U_526,U_527,U_525)
| ~ hBOOL(hAPP(fun(U_527,bool),bool,hAPP(fun(U_527,bool),fun(fun(U_527,bool),bool),ord_less_eq(fun(U_527,bool)),U_524),hAPP(fun(U_528,bool),fun(U_527,bool),hAPP(fun(U_528,U_527),fun(fun(U_528,bool),fun(U_527,bool)),image(U_528,U_527),U_526),U_525)))
| ~ hBOOL(hAPP(fun(U_527,bool),bool,finite_finite(U_527),U_524)) ),
inference(clausify,[status(thm)],[f_135_4]) ).
cnf(f_135_6,plain,
( hBOOL(hAPP(fun(U_528,bool),bool,hAPP(fun(U_528,bool),fun(fun(U_528,bool),bool),ord_less_eq(fun(U_528,bool)),sK14(U_528,U_527,U_526,U_525,U_524)),U_525))
| ~ sP20(U_528,U_524,U_526,U_527,U_525) ),
inference(clausify,[status(thm)],[f_135_4]) ).
cnf(f_135_7,plain,
( hBOOL(hAPP(fun(U_528,bool),bool,finite_finite(U_528),sK14(U_528,U_527,U_526,U_525,U_524)))
| ~ sP20(U_528,U_524,U_526,U_527,U_525) ),
inference(clausify,[status(thm)],[f_135_4]) ).
cnf(f_135_8,plain,
( ti(fun(U_527,bool),U_524) = hAPP(fun(U_528,bool),fun(U_527,bool),hAPP(fun(U_528,U_527),fun(fun(U_528,bool),fun(U_527,bool)),image(U_528,U_527),U_526),sK14(U_528,U_527,U_526,U_525,U_524))
| ~ sP20(U_528,U_524,U_526,U_527,U_525) ),
inference(clausify,[status(thm)],[f_135_4]) ).
fof(f_136_1,plain,
hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body))),
inference(fof_nnf,[status(thm)],[fact_98_finite__dom__body]) ).
fof(f_136_2,plain,
hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body))),
inference(definitional_conversion,[status(esa)],[f_136_1]) ).
cnf(f_136_3,plain,
hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body))),
inference(clausify,[status(thm)],[f_136_2]) ).
fof(f_137_1,plain,
! [Pname_1,Pname] :
( ( hAPP(pname,com,body_1,Pname_1) = hAPP(pname,com,body_1,Pname)
| ti(pname,Pname_1) != ti(pname,Pname) )
& ( ti(pname,Pname_1) = ti(pname,Pname)
| hAPP(pname,com,body_1,Pname_1) != hAPP(pname,com,body_1,Pname) ) ),
inference(fof_nnf,[status(thm)],[fact_99_com_Osimps_I6_J]) ).
fof(f_137_2,plain,
! [U_530,U_529] :
( ( hAPP(pname,com,body_1,U_530) = hAPP(pname,com,body_1,U_529)
| ti(pname,U_530) != ti(pname,U_529) )
& ( ti(pname,U_530) = ti(pname,U_529)
| hAPP(pname,com,body_1,U_530) != hAPP(pname,com,body_1,U_529) ) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
fof(f_137_3,plain,
( ! [U_534,U_532] :
( hAPP(pname,com,body_1,U_534) = hAPP(pname,com,body_1,U_532)
| ti(pname,U_534) != ti(pname,U_532) )
& ! [U_533,U_531] :
( ti(pname,U_533) = ti(pname,U_531)
| hAPP(pname,com,body_1,U_533) != hAPP(pname,com,body_1,U_531) ) ),
inference(miniscope,[status(thm)],[f_137_2]) ).
fof(f_137_4,plain,
( ! [U_534,U_532] :
( hAPP(pname,com,body_1,U_534) = hAPP(pname,com,body_1,U_532)
| ti(pname,U_534) != ti(pname,U_532) )
& ! [U_531,U_533] :
( ti(pname,U_533) = ti(pname,U_531)
| hAPP(pname,com,body_1,U_533) != hAPP(pname,com,body_1,U_531) ) ),
inference(definitional_conversion,[status(esa)],[f_137_3]) ).
cnf(f_137_5,plain,
( ti(pname,U_533) = ti(pname,U_531)
| hAPP(pname,com,body_1,U_533) != hAPP(pname,com,body_1,U_531) ),
inference(clausify,[status(thm)],[f_137_4]) ).
cnf(f_137_6,plain,
( hAPP(pname,com,body_1,U_534) = hAPP(pname,com,body_1,U_532)
| ti(pname,U_534) != ti(pname,U_532) ),
inference(clausify,[status(thm)],[f_137_4]) ).
fof(f_138_1,plain,
! [T_2,T_1] :
( finite_finite_1(fun(T_2,T_1))
| ~ finite_finite_1(T_2)
| ~ finite_finite_1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun___Finite__Set_Ofinite]) ).
fof(f_138_2,plain,
! [U_536,U_535] :
( finite_finite_1(fun(U_536,U_535))
| ~ finite_finite_1(U_536)
| ~ finite_finite_1(U_535) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
fof(f_138_3,plain,
! [U_536,U_535] :
( finite_finite_1(fun(U_536,U_535))
| ~ finite_finite_1(U_536)
| ~ finite_finite_1(U_535) ),
inference(definitional_conversion,[status(esa)],[f_138_2]) ).
cnf(f_138_4,plain,
( finite_finite_1(fun(U_536,U_535))
| ~ finite_finite_1(U_536)
| ~ finite_finite_1(U_535) ),
inference(clausify,[status(thm)],[f_138_3]) ).
fof(f_139_1,plain,
finite_finite_1(bool),
inference(fof_nnf,[status(thm)],[arity_HOL_Obool___Finite__Set_Ofinite]) ).
fof(f_139_2,plain,
finite_finite_1(bool),
inference(definitional_conversion,[status(esa)],[f_139_1]) ).
cnf(f_139_3,plain,
finite_finite_1(bool),
inference(clausify,[status(thm)],[f_139_2]) ).
fof(f_140_1,plain,
! [T_1] :
( finite_finite_1(option(T_1))
| ~ finite_finite_1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Option_Ooption___Finite__Set_Ofinite]) ).
fof(f_140_2,plain,
! [U_537] :
( finite_finite_1(option(U_537))
| ~ finite_finite_1(U_537) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
fof(f_140_3,plain,
! [U_537] :
( finite_finite_1(option(U_537))
| ~ finite_finite_1(U_537) ),
inference(definitional_conversion,[status(esa)],[f_140_2]) ).
cnf(f_140_4,plain,
( finite_finite_1(option(U_537))
| ~ finite_finite_1(U_537) ),
inference(clausify,[status(thm)],[f_140_3]) ).
fof(f_141_1,plain,
! [T,A] : ti(T,ti(T,A)) = ti(T,A),
inference(fof_nnf,[status(thm)],[help_ti_idem]) ).
fof(f_141_2,plain,
! [U_539,U_538] : ti(U_539,ti(U_539,U_538)) = ti(U_539,U_538),
inference(variable_rename,[status(thm)],[f_141_1]) ).
fof(f_141_3,plain,
! [U_538,U_539] : ti(U_539,ti(U_539,U_538)) = ti(U_539,U_538),
inference(definitional_conversion,[status(esa)],[f_141_2]) ).
cnf(f_141_4,plain,
ti(U_539,ti(U_539,U_538)) = ti(U_539,U_538),
inference(clausify,[status(thm)],[f_141_3]) ).
fof(f_142_1,plain,
! [P] :
( ~ hBOOL(P)
| ~ hBOOL(hAPP(bool,bool,fNot,P)) ),
inference(fof_nnf,[status(thm)],[help_fNot_1_1_U]) ).
fof(f_142_2,plain,
! [U_540] :
( ~ hBOOL(U_540)
| ~ hBOOL(hAPP(bool,bool,fNot,U_540)) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
fof(f_142_3,plain,
! [U_540] :
( ~ hBOOL(U_540)
| ~ hBOOL(hAPP(bool,bool,fNot,U_540)) ),
inference(definitional_conversion,[status(esa)],[f_142_2]) ).
cnf(f_142_4,plain,
( ~ hBOOL(U_540)
| ~ hBOOL(hAPP(bool,bool,fNot,U_540)) ),
inference(clausify,[status(thm)],[f_142_3]) ).
fof(f_143_1,plain,
! [P] :
( hBOOL(hAPP(bool,bool,fNot,P))
| hBOOL(P) ),
inference(fof_nnf,[status(thm)],[help_fNot_2_1_U]) ).
fof(f_143_2,plain,
! [U_541] :
( hBOOL(hAPP(bool,bool,fNot,U_541))
| hBOOL(U_541) ),
inference(variable_rename,[status(thm)],[f_143_1]) ).
fof(f_143_3,plain,
! [U_541] :
( hBOOL(hAPP(bool,bool,fNot,U_541))
| hBOOL(U_541) ),
inference(definitional_conversion,[status(esa)],[f_143_2]) ).
cnf(f_143_4,plain,
( hBOOL(hAPP(bool,bool,fNot,U_541))
| hBOOL(U_541) ),
inference(clausify,[status(thm)],[f_143_3]) ).
fof(f_144_1,plain,
! [X_a,X_c,X_b,P,Q,R] : hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R) = hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R)),
inference(fof_nnf,[status(thm)],[help_COMBB_1_1_U]) ).
fof(f_144_2,plain,
! [U_547,U_546,U_545,U_544,U_543,U_542] : hAPP(U_547,U_546,hAPP(fun(U_547,U_545),fun(U_547,U_546),hAPP(fun(U_545,U_546),fun(fun(U_547,U_545),fun(U_547,U_546)),combb(U_545,U_546,U_547),U_544),U_543),U_542) = hAPP(U_545,U_546,U_544,hAPP(U_547,U_545,U_543,U_542)),
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
! [U_545,U_542,U_543,U_544,U_546,U_547] : hAPP(U_547,U_546,hAPP(fun(U_547,U_545),fun(U_547,U_546),hAPP(fun(U_545,U_546),fun(fun(U_547,U_545),fun(U_547,U_546)),combb(U_545,U_546,U_547),U_544),U_543),U_542) = hAPP(U_545,U_546,U_544,hAPP(U_547,U_545,U_543,U_542)),
inference(definitional_conversion,[status(esa)],[f_144_2]) ).
cnf(f_144_4,plain,
hAPP(U_547,U_546,hAPP(fun(U_547,U_545),fun(U_547,U_546),hAPP(fun(U_545,U_546),fun(fun(U_547,U_545),fun(U_547,U_546)),combb(U_545,U_546,U_547),U_544),U_543),U_542) = hAPP(U_545,U_546,U_544,hAPP(U_547,U_545,U_543,U_542)),
inference(clausify,[status(thm)],[f_144_3]) ).
fof(f_145_1,plain,
! [X_a,X_c,X_b,P,Q,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),
inference(fof_nnf,[status(thm)],[help_COMBC_1_1_U]) ).
fof(f_145_2,plain,
! [U_553,U_552,U_551,U_550,U_549,U_548] : hAPP(U_553,U_552,hAPP(U_551,fun(U_553,U_552),hAPP(fun(U_553,fun(U_551,U_552)),fun(U_551,fun(U_553,U_552)),combc(U_553,U_551,U_552),U_550),U_549),U_548) = hAPP(U_551,U_552,hAPP(U_553,fun(U_551,U_552),U_550,U_548),U_549),
inference(variable_rename,[status(thm)],[f_145_1]) ).
fof(f_145_3,plain,
! [U_548,U_549,U_551,U_550,U_552,U_553] : hAPP(U_553,U_552,hAPP(U_551,fun(U_553,U_552),hAPP(fun(U_553,fun(U_551,U_552)),fun(U_551,fun(U_553,U_552)),combc(U_553,U_551,U_552),U_550),U_549),U_548) = hAPP(U_551,U_552,hAPP(U_553,fun(U_551,U_552),U_550,U_548),U_549),
inference(definitional_conversion,[status(esa)],[f_145_2]) ).
cnf(f_145_4,plain,
hAPP(U_553,U_552,hAPP(U_551,fun(U_553,U_552),hAPP(fun(U_553,fun(U_551,U_552)),fun(U_551,fun(U_553,U_552)),combc(U_553,U_551,U_552),U_550),U_549),U_548) = hAPP(U_551,U_552,hAPP(U_553,fun(U_551,U_552),U_550,U_548),U_549),
inference(clausify,[status(thm)],[f_145_3]) ).
fof(f_146_1,plain,
! [X_a,P] : hAPP(X_a,X_a,combi(X_a),P) = ti(X_a,P),
inference(fof_nnf,[status(thm)],[help_COMBI_1_1_U]) ).
fof(f_146_2,plain,
! [U_555,U_554] : hAPP(U_555,U_555,combi(U_555),U_554) = ti(U_555,U_554),
inference(variable_rename,[status(thm)],[f_146_1]) ).
fof(f_146_3,plain,
! [U_554,U_555] : hAPP(U_555,U_555,combi(U_555),U_554) = ti(U_555,U_554),
inference(definitional_conversion,[status(esa)],[f_146_2]) ).
cnf(f_146_4,plain,
hAPP(U_555,U_555,combi(U_555),U_554) = ti(U_555,U_554),
inference(clausify,[status(thm)],[f_146_3]) ).
fof(f_147_1,plain,
! [X_b,X_a,P,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),
inference(fof_nnf,[status(thm)],[help_COMBK_1_1_U]) ).
fof(f_147_2,plain,
! [U_559,U_558,U_557,U_556] : hAPP(U_559,U_558,hAPP(U_558,fun(U_559,U_558),combk(U_558,U_559),U_557),U_556) = ti(U_558,U_557),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
! [U_556,U_557,U_558,U_559] : hAPP(U_559,U_558,hAPP(U_558,fun(U_559,U_558),combk(U_558,U_559),U_557),U_556) = ti(U_558,U_557),
inference(definitional_conversion,[status(esa)],[f_147_2]) ).
cnf(f_147_4,plain,
hAPP(U_559,U_558,hAPP(U_558,fun(U_559,U_558),combk(U_558,U_559),U_557),U_556) = ti(U_558,U_557),
inference(clausify,[status(thm)],[f_147_3]) ).
fof(f_148_1,plain,
! [X_a,X_c,X_b,P,Q,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)),
inference(fof_nnf,[status(thm)],[help_COMBS_1_1_U]) ).
fof(f_148_2,plain,
! [U_565,U_564,U_563,U_562,U_561,U_560] : hAPP(U_565,U_564,hAPP(fun(U_565,U_563),fun(U_565,U_564),hAPP(fun(U_565,fun(U_563,U_564)),fun(fun(U_565,U_563),fun(U_565,U_564)),combs(U_565,U_563,U_564),U_562),U_561),U_560) = hAPP(U_563,U_564,hAPP(U_565,fun(U_563,U_564),U_562,U_560),hAPP(U_565,U_563,U_561,U_560)),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
! [U_563,U_560,U_561,U_562,U_564,U_565] : hAPP(U_565,U_564,hAPP(fun(U_565,U_563),fun(U_565,U_564),hAPP(fun(U_565,fun(U_563,U_564)),fun(fun(U_565,U_563),fun(U_565,U_564)),combs(U_565,U_563,U_564),U_562),U_561),U_560) = hAPP(U_563,U_564,hAPP(U_565,fun(U_563,U_564),U_562,U_560),hAPP(U_565,U_563,U_561,U_560)),
inference(definitional_conversion,[status(esa)],[f_148_2]) ).
cnf(f_148_4,plain,
hAPP(U_565,U_564,hAPP(fun(U_565,U_563),fun(U_565,U_564),hAPP(fun(U_565,fun(U_563,U_564)),fun(fun(U_565,U_563),fun(U_565,U_564)),combs(U_565,U_563,U_564),U_562),U_561),U_560) = hAPP(U_563,U_564,hAPP(U_565,fun(U_563,U_564),U_562,U_560),hAPP(U_565,U_563,U_561,U_560)),
inference(clausify,[status(thm)],[f_148_3]) ).
fof(f_149_1,plain,
! [Q,P] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q))
| ~ hBOOL(Q)
| ~ hBOOL(P) ),
inference(fof_nnf,[status(thm)],[help_fconj_1_1_U]) ).
fof(f_149_2,plain,
! [U_567,U_566] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_566),U_567))
| ~ hBOOL(U_567)
| ~ hBOOL(U_566) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
fof(f_149_3,plain,
! [U_567] :
( ! [U_566] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_566),U_567))
| ~ hBOOL(U_566) )
| ~ hBOOL(U_567) ),
inference(miniscope,[status(thm)],[f_149_2]) ).
fof(f_149_4,plain,
! [U_567,U_566] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_566),U_567))
| ~ hBOOL(U_566)
| ~ hBOOL(U_567) ),
inference(definitional_conversion,[status(esa)],[f_149_3]) ).
cnf(f_149_5,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_566),U_567))
| ~ hBOOL(U_566)
| ~ hBOOL(U_567) ),
inference(clausify,[status(thm)],[f_149_4]) ).
fof(f_150_1,plain,
! [P,Q] :
( hBOOL(P)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) ),
inference(fof_nnf,[status(thm)],[help_fconj_2_1_U]) ).
fof(f_150_2,plain,
! [U_569,U_568] :
( hBOOL(U_569)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_569),U_568)) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
fof(f_150_3,plain,
! [U_569] :
( ! [U_568] : ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_569),U_568))
| hBOOL(U_569) ),
inference(miniscope,[status(thm)],[f_150_2]) ).
fof(f_150_4,plain,
! [U_569,U_568] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_569),U_568))
| hBOOL(U_569) ),
inference(definitional_conversion,[status(esa)],[f_150_3]) ).
cnf(f_150_5,plain,
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_569),U_568))
| hBOOL(U_569) ),
inference(clausify,[status(thm)],[f_150_4]) ).
fof(f_151_1,plain,
! [P,Q] :
( hBOOL(Q)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) ),
inference(fof_nnf,[status(thm)],[help_fconj_3_1_U]) ).
fof(f_151_2,plain,
! [U_571,U_570] :
( hBOOL(U_570)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_571),U_570)) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
fof(f_151_3,plain,
! [U_570,U_571] :
( hBOOL(U_570)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_571),U_570)) ),
inference(definitional_conversion,[status(esa)],[f_151_2]) ).
cnf(f_151_4,plain,
( hBOOL(U_570)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,U_571),U_570)) ),
inference(clausify,[status(thm)],[f_151_3]) ).
fof(f_152_1,plain,
! [Q,P] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q))
| ~ hBOOL(P) ),
inference(fof_nnf,[status(thm)],[help_fdisj_1_1_U]) ).
fof(f_152_2,plain,
! [U_573,U_572] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_572),U_573))
| ~ hBOOL(U_572) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
fof(f_152_3,plain,
! [U_572,U_573] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_572),U_573))
| ~ hBOOL(U_572) ),
inference(definitional_conversion,[status(esa)],[f_152_2]) ).
cnf(f_152_4,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_572),U_573))
| ~ hBOOL(U_572) ),
inference(clausify,[status(thm)],[f_152_3]) ).
fof(f_153_1,plain,
! [P,Q] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q))
| ~ hBOOL(Q) ),
inference(fof_nnf,[status(thm)],[help_fdisj_2_1_U]) ).
fof(f_153_2,plain,
! [U_575,U_574] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_575),U_574))
| ~ hBOOL(U_574) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
! [U_574,U_575] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_575),U_574))
| ~ hBOOL(U_574) ),
inference(definitional_conversion,[status(esa)],[f_153_2]) ).
cnf(f_153_4,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_575),U_574))
| ~ hBOOL(U_574) ),
inference(clausify,[status(thm)],[f_153_3]) ).
fof(f_154_1,plain,
! [P,Q] :
( hBOOL(Q)
| hBOOL(P)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) ),
inference(fof_nnf,[status(thm)],[help_fdisj_3_1_U]) ).
fof(f_154_2,plain,
! [U_577,U_576] :
( hBOOL(U_576)
| hBOOL(U_577)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_577),U_576)) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
fof(f_154_3,plain,
! [U_577] :
( ! [U_576] :
( hBOOL(U_576)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_577),U_576)) )
| hBOOL(U_577) ),
inference(miniscope,[status(thm)],[f_154_2]) ).
fof(f_154_4,plain,
! [U_576,U_577] :
( hBOOL(U_576)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_577),U_576))
| hBOOL(U_577) ),
inference(definitional_conversion,[status(esa)],[f_154_3]) ).
cnf(f_154_5,plain,
( hBOOL(U_576)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,U_577),U_576))
| hBOOL(U_577) ),
inference(clausify,[status(thm)],[f_154_4]) ).
fof(f_155_1,plain,
~ hBOOL(fFalse),
inference(fof_nnf,[status(thm)],[help_fFalse_1_1_U]) ).
fof(f_155_2,plain,
~ hBOOL(fFalse),
inference(definitional_conversion,[status(esa)],[f_155_1]) ).
cnf(f_155_3,plain,
~ hBOOL(fFalse),
inference(clausify,[status(thm)],[f_155_2]) ).
fof(f_156_1,plain,
! [P] :
( ti(bool,P) = fFalse
| ti(bool,P) = fTrue ),
inference(fof_nnf,[status(thm)],[help_fFalse_1_1_T]) ).
fof(f_156_2,plain,
! [U_578] :
( ti(bool,U_578) = fFalse
| ti(bool,U_578) = fTrue ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
fof(f_156_3,plain,
! [U_578] :
( ti(bool,U_578) = fFalse
| ti(bool,U_578) = fTrue ),
inference(definitional_conversion,[status(esa)],[f_156_2]) ).
cnf(f_156_4,plain,
( ti(bool,U_578) = fFalse
| ti(bool,U_578) = fTrue ),
inference(clausify,[status(thm)],[f_156_3]) ).
fof(f_157_1,plain,
! [X_a,X,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)) ),
inference(fof_nnf,[status(thm)],[help_fequal_1_1_T]) ).
fof(f_157_2,plain,
! [U_581,U_580,U_579] :
( ti(U_581,U_580) = ti(U_581,U_579)
| ~ hBOOL(hAPP(U_581,bool,hAPP(U_581,fun(U_581,bool),fequal(U_581),U_580),U_579)) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
fof(f_157_3,plain,
! [U_579,U_580,U_581] :
( ti(U_581,U_580) = ti(U_581,U_579)
| ~ hBOOL(hAPP(U_581,bool,hAPP(U_581,fun(U_581,bool),fequal(U_581),U_580),U_579)) ),
inference(definitional_conversion,[status(esa)],[f_157_2]) ).
cnf(f_157_4,plain,
( ti(U_581,U_580) = ti(U_581,U_579)
| ~ hBOOL(hAPP(U_581,bool,hAPP(U_581,fun(U_581,bool),fequal(U_581),U_580),U_579)) ),
inference(clausify,[status(thm)],[f_157_3]) ).
fof(f_158_1,plain,
! [X_a,X,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) ),
inference(fof_nnf,[status(thm)],[help_fequal_2_1_T]) ).
fof(f_158_2,plain,
! [U_584,U_583,U_582] :
( hBOOL(hAPP(U_584,bool,hAPP(U_584,fun(U_584,bool),fequal(U_584),U_583),U_582))
| ti(U_584,U_583) != ti(U_584,U_582) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
fof(f_158_3,plain,
! [U_582,U_583,U_584] :
( hBOOL(hAPP(U_584,bool,hAPP(U_584,fun(U_584,bool),fequal(U_584),U_583),U_582))
| ti(U_584,U_583) != ti(U_584,U_582) ),
inference(definitional_conversion,[status(esa)],[f_158_2]) ).
cnf(f_158_4,plain,
( hBOOL(hAPP(U_584,bool,hAPP(U_584,fun(U_584,bool),fequal(U_584),U_583),U_582))
| ti(U_584,U_583) != ti(U_584,U_582) ),
inference(clausify,[status(thm)],[f_158_3]) ).
fof(f_159_1,plain,
! [Q,P] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q))
| hBOOL(P) ),
inference(fof_nnf,[status(thm)],[help_fimplies_1_1_U]) ).
fof(f_159_2,plain,
! [U_586,U_585] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_585),U_586))
| hBOOL(U_585) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
fof(f_159_3,plain,
! [U_585,U_586] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_585),U_586))
| hBOOL(U_585) ),
inference(definitional_conversion,[status(esa)],[f_159_2]) ).
cnf(f_159_4,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_585),U_586))
| hBOOL(U_585) ),
inference(clausify,[status(thm)],[f_159_3]) ).
fof(f_160_1,plain,
! [P,Q] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q))
| ~ hBOOL(Q) ),
inference(fof_nnf,[status(thm)],[help_fimplies_2_1_U]) ).
fof(f_160_2,plain,
! [U_588,U_587] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_588),U_587))
| ~ hBOOL(U_587) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
fof(f_160_3,plain,
! [U_587,U_588] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_588),U_587))
| ~ hBOOL(U_587) ),
inference(definitional_conversion,[status(esa)],[f_160_2]) ).
cnf(f_160_4,plain,
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_588),U_587))
| ~ hBOOL(U_587) ),
inference(clausify,[status(thm)],[f_160_3]) ).
fof(f_161_1,plain,
! [P,Q] :
( hBOOL(Q)
| ~ hBOOL(P)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)) ),
inference(fof_nnf,[status(thm)],[help_fimplies_3_1_U]) ).
fof(f_161_2,plain,
! [U_590,U_589] :
( hBOOL(U_589)
| ~ hBOOL(U_590)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_590),U_589)) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
fof(f_161_3,plain,
! [U_590] :
( ! [U_589] :
( hBOOL(U_589)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_590),U_589)) )
| ~ hBOOL(U_590) ),
inference(miniscope,[status(thm)],[f_161_2]) ).
fof(f_161_4,plain,
! [U_589,U_590] :
( hBOOL(U_589)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_590),U_589))
| ~ hBOOL(U_590) ),
inference(definitional_conversion,[status(esa)],[f_161_3]) ).
cnf(f_161_5,plain,
( hBOOL(U_589)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,U_590),U_589))
| ~ hBOOL(U_590) ),
inference(clausify,[status(thm)],[f_161_4]) ).
fof(f_162_1,plain,
hBOOL(hoare_1883395792gleton),
inference(fof_nnf,[status(thm)],[conj_0]) ).
fof(f_162_2,plain,
hBOOL(hoare_1883395792gleton),
inference(definitional_conversion,[status(esa)],[f_162_1]) ).
cnf(f_162_3,plain,
hBOOL(hoare_1883395792gleton),
inference(clausify,[status(thm)],[f_162_2]) ).
fof(f_163_1,plain,
hBOOL(wT_bodies),
inference(fof_nnf,[status(thm)],[conj_1]) ).
fof(f_163_2,plain,
hBOOL(wT_bodies),
inference(definitional_conversion,[status(esa)],[f_163_1]) ).
cnf(f_163_3,plain,
hBOOL(wT_bodies),
inference(clausify,[status(thm)],[f_163_2]) ).
fof(f_164_1,plain,
hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,finite_finite(hoare_509422987triple(state)),fa)),
inference(fof_nnf,[status(thm)],[conj_2]) ).
fof(f_164_2,plain,
hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,finite_finite(hoare_509422987triple(state)),fa)),
inference(definitional_conversion,[status(esa)],[f_164_1]) ).
cnf(f_164_3,plain,
hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,finite_finite(hoare_509422987triple(state)),fa)),
inference(clausify,[status(thm)],[f_164_2]) ).
fof(f_165_1,plain,
~ hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),bool),member(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,y)),fa)),
inference(fof_nnf,[status(thm)],[conj_3]) ).
fof(f_165_2,plain,
~ hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),bool),member(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,y)),fa)),
inference(definitional_conversion,[status(esa)],[f_165_1]) ).
cnf(f_165_3,plain,
~ hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),bool),member(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,y)),fa)),
inference(clausify,[status(thm)],[f_165_2]) ).
fof(f_166_1,plain,
hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),ord_less_eq(fun(hoare_509422987triple(state),bool)),fa),hAPP(fun(pname,bool),fun(hoare_509422987triple(state),bool),hAPP(fun(pname,hoare_509422987triple(state)),fun(fun(pname,bool),fun(hoare_509422987triple(state),bool)),image(pname,hoare_509422987triple(state)),hAPP(fun(pname,com),fun(pname,hoare_509422987triple(state)),hAPP(fun(com,hoare_509422987triple(state)),fun(fun(pname,com),fun(pname,hoare_509422987triple(state))),combb(com,hoare_509422987triple(state),pname),hoare_Mirabelle_MGT),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body))),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body)))),
inference(fof_nnf,[status(thm)],[conj_4]) ).
fof(f_166_2,plain,
hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),ord_less_eq(fun(hoare_509422987triple(state),bool)),fa),hAPP(fun(pname,bool),fun(hoare_509422987triple(state),bool),hAPP(fun(pname,hoare_509422987triple(state)),fun(fun(pname,bool),fun(hoare_509422987triple(state),bool)),image(pname,hoare_509422987triple(state)),hAPP(fun(pname,com),fun(pname,hoare_509422987triple(state)),hAPP(fun(com,hoare_509422987triple(state)),fun(fun(pname,com),fun(pname,hoare_509422987triple(state))),combb(com,hoare_509422987triple(state),pname),hoare_Mirabelle_MGT),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body))),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body)))),
inference(definitional_conversion,[status(esa)],[f_166_1]) ).
cnf(f_166_3,plain,
hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),ord_less_eq(fun(hoare_509422987triple(state),bool)),fa),hAPP(fun(pname,bool),fun(hoare_509422987triple(state),bool),hAPP(fun(pname,hoare_509422987triple(state)),fun(fun(pname,bool),fun(hoare_509422987triple(state),bool)),image(pname,hoare_509422987triple(state)),hAPP(fun(pname,com),fun(pname,hoare_509422987triple(state)),hAPP(fun(com,hoare_509422987triple(state)),fun(fun(pname,com),fun(pname,hoare_509422987triple(state))),combb(com,hoare_509422987triple(state),pname),hoare_Mirabelle_MGT),hAPP(fun(pname,option(com)),fun(pname,com),hAPP(fun(option(com),com),fun(fun(pname,option(com)),fun(pname,com)),combb(option(com),com,pname),the(com)),body))),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body)))),
inference(clausify,[status(thm)],[f_166_2]) ).
fof(f_167_1,plain,
hAPP(pname,option(com),body,pn) = hAPP(com,option(com),some(com),y),
inference(fof_nnf,[status(thm)],[conj_5]) ).
fof(f_167_2,plain,
hAPP(pname,option(com),body,pn) = hAPP(com,option(com),some(com),y),
inference(definitional_conversion,[status(esa)],[f_167_1]) ).
cnf(f_167_3,plain,
hAPP(pname,option(com),body,pn) = hAPP(com,option(com),some(com),y),
inference(clausify,[status(thm)],[f_167_2]) ).
fof(f_168_1,plain,
hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),hAPP(fun(pname,bool),fun(hoare_509422987triple(state),bool),hAPP(fun(pname,hoare_509422987triple(state)),fun(fun(pname,bool),fun(hoare_509422987triple(state),bool)),image(pname,hoare_509422987triple(state)),hAPP(fun(pname,com),fun(pname,hoare_509422987triple(state)),hAPP(fun(com,hoare_509422987triple(state)),fun(fun(pname,com),fun(pname,hoare_509422987triple(state))),combb(com,hoare_509422987triple(state),pname),hoare_Mirabelle_MGT),body_1)),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body))),fa)),
inference(fof_nnf,[status(thm)],[conj_6]) ).
fof(f_168_2,plain,
hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),hAPP(fun(pname,bool),fun(hoare_509422987triple(state),bool),hAPP(fun(pname,hoare_509422987triple(state)),fun(fun(pname,bool),fun(hoare_509422987triple(state),bool)),image(pname,hoare_509422987triple(state)),hAPP(fun(pname,com),fun(pname,hoare_509422987triple(state)),hAPP(fun(com,hoare_509422987triple(state)),fun(fun(pname,com),fun(pname,hoare_509422987triple(state))),combb(com,hoare_509422987triple(state),pname),hoare_Mirabelle_MGT),body_1)),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body))),fa)),
inference(definitional_conversion,[status(esa)],[f_168_1]) ).
cnf(f_168_3,plain,
hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),hAPP(fun(pname,bool),fun(hoare_509422987triple(state),bool),hAPP(fun(pname,hoare_509422987triple(state)),fun(fun(pname,bool),fun(hoare_509422987triple(state),bool)),image(pname,hoare_509422987triple(state)),hAPP(fun(pname,com),fun(pname,hoare_509422987triple(state)),hAPP(fun(com,hoare_509422987triple(state)),fun(fun(pname,com),fun(pname,hoare_509422987triple(state))),combb(com,hoare_509422987triple(state),pname),hoare_Mirabelle_MGT),body_1)),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body))),fa)),
inference(clausify,[status(thm)],[f_168_2]) ).
fof(f_169_1,negated_conjecture,
~ hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),hAPP(fun(pname,bool),fun(hoare_509422987triple(state),bool),hAPP(fun(pname,hoare_509422987triple(state)),fun(fun(pname,bool),fun(hoare_509422987triple(state),bool)),image(pname,hoare_509422987triple(state)),hAPP(fun(pname,com),fun(pname,hoare_509422987triple(state)),hAPP(fun(com,hoare_509422987triple(state)),fun(fun(pname,com),fun(pname,hoare_509422987triple(state))),combb(com,hoare_509422987triple(state),pname),hoare_Mirabelle_MGT),body_1)),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body))),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,y)),bot_bot(fun(hoare_509422987triple(state),bool))))),
inference(negate,[status(cth)],[conj_7]) ).
fof(f_169_2,negated_conjecture,
~ hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),hAPP(fun(pname,bool),fun(hoare_509422987triple(state),bool),hAPP(fun(pname,hoare_509422987triple(state)),fun(fun(pname,bool),fun(hoare_509422987triple(state),bool)),image(pname,hoare_509422987triple(state)),hAPP(fun(pname,com),fun(pname,hoare_509422987triple(state)),hAPP(fun(com,hoare_509422987triple(state)),fun(fun(pname,com),fun(pname,hoare_509422987triple(state))),combb(com,hoare_509422987triple(state),pname),hoare_Mirabelle_MGT),body_1)),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body))),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,y)),bot_bot(fun(hoare_509422987triple(state),bool))))),
inference(definitional_conversion,[status(esa)],[f_169_1]) ).
cnf(f_169_3,negated_conjecture,
~ hBOOL(hAPP(fun(hoare_509422987triple(state),bool),bool,hAPP(fun(hoare_509422987triple(state),bool),fun(fun(hoare_509422987triple(state),bool),bool),hoare_122391849derivs(state),hAPP(fun(pname,bool),fun(hoare_509422987triple(state),bool),hAPP(fun(pname,hoare_509422987triple(state)),fun(fun(pname,bool),fun(hoare_509422987triple(state),bool)),image(pname,hoare_509422987triple(state)),hAPP(fun(pname,com),fun(pname,hoare_509422987triple(state)),hAPP(fun(com,hoare_509422987triple(state)),fun(fun(pname,com),fun(pname,hoare_509422987triple(state))),combb(com,hoare_509422987triple(state),pname),hoare_Mirabelle_MGT),body_1)),hAPP(fun(pname,option(com)),fun(pname,bool),dom(pname,com),body))),hAPP(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool),hAPP(hoare_509422987triple(state),fun(fun(hoare_509422987triple(state),bool),fun(hoare_509422987triple(state),bool)),insert(hoare_509422987triple(state)),hAPP(com,hoare_509422987triple(state),hoare_Mirabelle_MGT,y)),bot_bot(fun(hoare_509422987triple(state),bool))))),
inference(clausify,[status(thm)],[f_169_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( fun(Eq_x_0,Eq_x_1) = fun(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( combb(Eq_x_0,Eq_x_1,Eq_x_2) = combb(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( ti(Eq_x_0,Eq_x_1) = ti(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( combc(Eq_x_0,Eq_x_1,Eq_x_2) = combc(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( combi(Eq_x_0) = combi(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( combk(Eq_x_0,Eq_x_1) = combk(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( combs(Eq_x_0,Eq_x_1,Eq_x_2) = combs(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( option(Eq_x_0) = option(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( finite_finite(Eq_x_0) = finite_finite(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( undefined(Eq_x_0) = undefined(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( hoare_509422987triple(Eq_x_0) = hoare_509422987triple(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( hoare_122391849derivs(Eq_x_0) = hoare_122391849derivs(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( dom(Eq_x_0,Eq_x_1) = dom(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( some(Eq_x_0) = some(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( the(Eq_x_0) = the(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( bot_bot(Eq_x_0) = bot_bot(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( ord_less_eq(Eq_x_0) = ord_less_eq(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( collect(Eq_x_0) = collect(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( image(Eq_x_0,Eq_x_1) = image(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( insert(Eq_x_0) = insert(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( fequal(Eq_x_0) = fequal(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( hAPP(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = hAPP(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( member(Eq_x_0) = member(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( sK4(Eq_x_0,Eq_x_1) = sK4(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,axiom,
( sK5(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK5(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,axiom,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK6(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( sK7(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK7(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_34,axiom,
( sK8(Eq_x_0,Eq_x_1) = sK8(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_35,axiom,
( sK9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,axiom,
( sK10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK10(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,axiom,
( sK11(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK11(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_38,axiom,
( sK12(Eq_x_0) = sK12(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( sK13(Eq_x_0,Eq_x_1,Eq_x_2) = sK13(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,axiom,
( sK14(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK14(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_41,axiom,
( hBOOL(Eq_y_0)
| ~ hBOOL(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_42,axiom,
( finite_finite_1(Eq_y_0)
| ~ finite_finite_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_43,axiom,
( sP0(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP0(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_44,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_45,axiom,
( sP2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_46,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_47,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_48,axiom,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP5(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_49,axiom,
( sP6(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP6(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_50,axiom,
( sP7(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP7(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_51,axiom,
( sP8(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP8(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_52,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP9(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_53,axiom,
( sP10(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_54,axiom,
( sP11(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP11(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_55,axiom,
( sP12(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP12(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_56,axiom,
( sP13(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP13(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_57,axiom,
( sP14(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP14(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_58,axiom,
( sP15(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP15(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_59,axiom,
( sP16(Eq_y_0,Eq_y_1)
| ~ sP16(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_60,axiom,
( sP17(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP17(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_61,axiom,
( sP18(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP18(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_62,axiom,
( sP19(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP19(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_63,axiom,
( sP20(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP20(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW474+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.37 % Computer : n009.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Sun Sep 20 05:42:33 UTC 2026
% 0.08/5.38 % CPUTime :
% 150.44/155.71 % SZS status Theorem for theBenchmark
% 150.44/155.71 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------