%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : ITP001+5 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 23:08:46 EDT 2022
% Result : Theorem 0.21s 0.46s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named input)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
% Orienting axioms whose shape is orientable
fof(ax_thm_2Ebool_2EDATATYPE__TAG__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ebool_2EDATATYPE(A_27a) = k(A_27a,c_2Ebool_2ET) ),
input ).
fof(ax_thm_2Ebool_2EDATATYPE__TAG__DEF_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| c_2Ebool_2EDATATYPE(A_27a) = k(A_27a,c_2Ebool_2ET) ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2EDATATYPE__TAG__DEF]) ).
fof(ax_thm_2Ebool_2EBOUNDED__DEF,axiom,
c_2Ebool_2EBOUNDED = k(bool,c_2Ebool_2ET),
input ).
fof(ax_thm_2Ebool_2EBOUNDED__DEF_0,plain,
( c_2Ebool_2EBOUNDED = k(bool,c_2Ebool_2ET)
| $false ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2EBOUNDED__DEF]) ).
fof(ax_thm_2Ebool_2ERES__SELECT__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ebool_2ERES__SELECT(A_27a) = f46(A_27a) ),
input ).
fof(ax_thm_2Ebool_2ERES__SELECT__DEF_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| c_2Ebool_2ERES__SELECT(A_27a) = f46(A_27a) ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2ERES__SELECT__DEF]) ).
fof(lameq_f46,axiom,
! [A_27a,V0p] : ap(f46(A_27a),V0p) = f45(A_27a,V0p),
input ).
fof(lameq_f46_0,plain,
! [A_27a,V0p] :
( ap(f46(A_27a),V0p) = f45(A_27a,V0p)
| $false ),
inference(orientation,[status(thm)],[lameq_f46]) ).
fof(lameq_f45,axiom,
! [A_27a,V0p] :
( mem(V0p,arr(A_27a,bool))
=> ! [V1m] : ap(f45(A_27a,V0p),V1m) = ap(c_2Emin_2E_40(A_27a),f37(A_27a,V0p,V1m)) ),
input ).
fof(lameq_f45_0,plain,
! [A_27a,V0p] :
( ~ mem(V0p,arr(A_27a,bool))
| ! [V1m] : ap(f45(A_27a,V0p),V1m) = ap(c_2Emin_2E_40(A_27a),f37(A_27a,V0p,V1m)) ),
inference(orientation,[status(thm)],[lameq_f45]) ).
fof(ax_thm_2Ebool_2ERES__EXISTS__UNIQUE__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a) = f44(A_27a) ),
input ).
fof(ax_thm_2Ebool_2ERES__EXISTS__UNIQUE__DEF_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a) = f44(A_27a) ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2ERES__EXISTS__UNIQUE__DEF]) ).
fof(lameq_f44,axiom,
! [A_27a,V0p] : ap(f44(A_27a),V0p) = f43(A_27a,V0p),
input ).
fof(lameq_f44_0,plain,
! [A_27a,V0p] :
( ap(f44(A_27a),V0p) = f43(A_27a,V0p)
| $false ),
inference(orientation,[status(thm)],[lameq_f44]) ).
fof(lameq_f43,axiom,
! [A_27a,V0p] :
( mem(V0p,arr(A_27a,bool))
=> ! [V1m] : ap(f43(A_27a,V0p),V1m) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0p),f40(A_27a,V1m))),ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0p),f42(A_27a,V1m,V0p))) ),
input ).
fof(lameq_f43_0,plain,
! [A_27a,V0p] :
( ~ mem(V0p,arr(A_27a,bool))
| ! [V1m] : ap(f43(A_27a,V0p),V1m) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0p),f40(A_27a,V1m))),ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0p),f42(A_27a,V1m,V0p))) ),
inference(orientation,[status(thm)],[lameq_f43]) ).
fof(lameq_f42,axiom,
! [A_27a,V1m] :
( mem(V1m,arr(A_27a,bool))
=> ! [V0p] :
( mem(V0p,arr(A_27a,bool))
=> ! [V3x] : ap(f42(A_27a,V1m,V0p),V3x) = ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0p),f41(A_27a,V1m,V3x)) ) ),
input ).
fof(lameq_f42_0,plain,
! [A_27a,V1m] :
( ~ mem(V1m,arr(A_27a,bool))
| ! [V0p] :
( mem(V0p,arr(A_27a,bool))
=> ! [V3x] : ap(f42(A_27a,V1m,V0p),V3x) = ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0p),f41(A_27a,V1m,V3x)) ) ),
inference(orientation,[status(thm)],[lameq_f42]) ).
fof(lameq_f41,axiom,
! [A_27a,V1m] :
( mem(V1m,arr(A_27a,bool))
=> ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4y] : ap(f41(A_27a,V1m,V3x),V4y) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(V1m,V3x)),ap(V1m,V4y))),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V4y)) ) ),
input ).
fof(lameq_f41_0,plain,
! [A_27a,V1m] :
( ~ mem(V1m,arr(A_27a,bool))
| ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4y] : ap(f41(A_27a,V1m,V3x),V4y) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(V1m,V3x)),ap(V1m,V4y))),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V4y)) ) ),
inference(orientation,[status(thm)],[lameq_f41]) ).
fof(lameq_f40,axiom,
! [A_27a,V1m] :
( mem(V1m,arr(A_27a,bool))
=> ! [V2x] : ap(f40(A_27a,V1m),V2x) = ap(V1m,V2x) ),
input ).
fof(lameq_f40_0,plain,
! [A_27a,V1m] :
( ~ mem(V1m,arr(A_27a,bool))
| ! [V2x] : ap(f40(A_27a,V1m),V2x) = ap(V1m,V2x) ),
inference(orientation,[status(thm)],[lameq_f40]) ).
fof(ax_thm_2Ebool_2ERES__EXISTS__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ebool_2ERES__EXISTS(A_27a) = f39(A_27a) ),
input ).
fof(ax_thm_2Ebool_2ERES__EXISTS__DEF_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| c_2Ebool_2ERES__EXISTS(A_27a) = f39(A_27a) ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2ERES__EXISTS__DEF]) ).
fof(lameq_f39,axiom,
! [A_27a,V0p] : ap(f39(A_27a),V0p) = f38(A_27a,V0p),
input ).
fof(lameq_f39_0,plain,
! [A_27a,V0p] :
( ap(f39(A_27a),V0p) = f38(A_27a,V0p)
| $false ),
inference(orientation,[status(thm)],[lameq_f39]) ).
fof(lameq_f38,axiom,
! [A_27a,V0p] :
( mem(V0p,arr(A_27a,bool))
=> ! [V1m] : ap(f38(A_27a,V0p),V1m) = ap(c_2Ebool_2E_3F(A_27a),f37(A_27a,V0p,V1m)) ),
input ).
fof(lameq_f38_0,plain,
! [A_27a,V0p] :
( ~ mem(V0p,arr(A_27a,bool))
| ! [V1m] : ap(f38(A_27a,V0p),V1m) = ap(c_2Ebool_2E_3F(A_27a),f37(A_27a,V0p,V1m)) ),
inference(orientation,[status(thm)],[lameq_f38]) ).
fof(lameq_f37,axiom,
! [A_27a,V0p] :
( mem(V0p,arr(A_27a,bool))
=> ! [V1m] :
( mem(V1m,arr(A_27a,bool))
=> ! [V2x] : ap(f37(A_27a,V0p,V1m),V2x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0p)),ap(V1m,V2x)) ) ),
input ).
fof(lameq_f37_0,plain,
! [A_27a,V0p] :
( ~ mem(V0p,arr(A_27a,bool))
| ! [V1m] :
( mem(V1m,arr(A_27a,bool))
=> ! [V2x] : ap(f37(A_27a,V0p,V1m),V2x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0p)),ap(V1m,V2x)) ) ),
inference(orientation,[status(thm)],[lameq_f37]) ).
fof(ax_thm_2Ebool_2ERES__FORALL__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ebool_2ERES__FORALL(A_27a) = f36(A_27a) ),
input ).
fof(ax_thm_2Ebool_2ERES__FORALL__DEF_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| c_2Ebool_2ERES__FORALL(A_27a) = f36(A_27a) ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2ERES__FORALL__DEF]) ).
fof(lameq_f36,axiom,
! [A_27a,V0p] : ap(f36(A_27a),V0p) = f35(A_27a,V0p),
input ).
fof(lameq_f36_0,plain,
! [A_27a,V0p] :
( ap(f36(A_27a),V0p) = f35(A_27a,V0p)
| $false ),
inference(orientation,[status(thm)],[lameq_f36]) ).
fof(lameq_f35,axiom,
! [A_27a,V0p] :
( mem(V0p,arr(A_27a,bool))
=> ! [V1m] : ap(f35(A_27a,V0p),V1m) = ap(c_2Ebool_2E_21(A_27a),f34(A_27a,V0p,V1m)) ),
input ).
fof(lameq_f35_0,plain,
! [A_27a,V0p] :
( ~ mem(V0p,arr(A_27a,bool))
| ! [V1m] : ap(f35(A_27a,V0p),V1m) = ap(c_2Ebool_2E_21(A_27a),f34(A_27a,V0p,V1m)) ),
inference(orientation,[status(thm)],[lameq_f35]) ).
fof(lameq_f34,axiom,
! [A_27a,V0p] :
( mem(V0p,arr(A_27a,bool))
=> ! [V1m] :
( mem(V1m,arr(A_27a,bool))
=> ! [V2x] : ap(f34(A_27a,V0p,V1m),V2x) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0p)),ap(V1m,V2x)) ) ),
input ).
fof(lameq_f34_0,plain,
! [A_27a,V0p] :
( ~ mem(V0p,arr(A_27a,bool))
| ! [V1m] :
( mem(V1m,arr(A_27a,bool))
=> ! [V2x] : ap(f34(A_27a,V0p,V1m),V2x) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0p)),ap(V1m,V2x)) ) ),
inference(orientation,[status(thm)],[lameq_f34]) ).
fof(ax_thm_2Ebool_2EIN__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ebool_2EIN(A_27a) = f33(A_27a) ),
input ).
fof(ax_thm_2Ebool_2EIN__DEF_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| c_2Ebool_2EIN(A_27a) = f33(A_27a) ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2EIN__DEF]) ).
fof(lameq_f33,axiom,
! [A_27a,V0x] : ap(f33(A_27a),V0x) = f32(A_27a,V0x),
input ).
fof(lameq_f33_0,plain,
! [A_27a,V0x] :
( ap(f33(A_27a),V0x) = f32(A_27a,V0x)
| $false ),
inference(orientation,[status(thm)],[lameq_f33]) ).
fof(lameq_f32,axiom,
! [A_27a,V0x] :
( mem(V0x,A_27a)
=> ! [V1f] : ap(f32(A_27a,V0x),V1f) = ap(V1f,V0x) ),
input ).
fof(lameq_f32_0,plain,
! [A_27a,V0x] :
( ~ mem(V0x,A_27a)
| ! [V1f] : ap(f32(A_27a,V0x),V1f) = ap(V1f,V0x) ),
inference(orientation,[status(thm)],[lameq_f32]) ).
fof(ax_thm_2Ebool_2Eliteral__case__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> c_2Ebool_2Eliteral__case(A_27a,A_27b) = f14(A_27b,A_27a) ) ),
input ).
fof(ax_thm_2Ebool_2Eliteral__case__DEF_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> c_2Ebool_2Eliteral__case(A_27a,A_27b) = f14(A_27b,A_27a) ) ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2Eliteral__case__DEF]) ).
fof(ax_thm_2Ebool_2ESELECT__AX,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ( p(ap(V0P,V1x))
=> p(ap(V0P,ap(c_2Emin_2E_40(A_27a),V0P))) ) ) ) ),
input ).
fof(ax_thm_2Ebool_2ESELECT__AX_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ( p(ap(V0P,V1x))
=> p(ap(V0P,ap(c_2Emin_2E_40(A_27a),V0P))) ) ) ) ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2ESELECT__AX]) ).
fof(ax_thm_2Ebool_2EETA__AX,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0t] :
( mem(V0t,arr(A_27a,A_27b))
=> f31(A_27b,A_27a,V0t) = V0t ) ) ),
input ).
fof(ax_thm_2Ebool_2EETA__AX_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> ! [V0t] :
( mem(V0t,arr(A_27a,A_27b))
=> f31(A_27b,A_27a,V0t) = V0t ) ) ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2EETA__AX]) ).
fof(lameq_f31,axiom,
! [A_27b,A_27a,V0t] :
( mem(V0t,arr(A_27a,A_27b))
=> ! [V1x] : ap(f31(A_27b,A_27a,V0t),V1x) = ap(V0t,V1x) ),
input ).
fof(lameq_f31_0,plain,
! [A_27a,A_27b,V0t] :
( ~ mem(V0t,arr(A_27a,A_27b))
| ! [V1x] : ap(f31(A_27b,A_27a,V0t),V1x) = ap(V0t,V1x) ),
inference(orientation,[status(thm)],[lameq_f31]) ).
fof(ax_thm_2Ebool_2EBOOL__CASES__AX,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( ( p(V0t)
<=> $true )
| ( p(V0t)
<=> $false ) ) ),
input ).
fof(ax_thm_2Ebool_2EBOOL__CASES__AX_0,plain,
! [V0t] :
( ~ mem(V0t,bool)
| ( p(V0t)
<=> $true )
| ( p(V0t)
<=> $false ) ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2EBOOL__CASES__AX]) ).
fof(ax_thm_2Ebool_2ETYPE__DEFINITION,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> c_2Ebool_2ETYPE__DEFINITION(A_27a,A_27b) = f30(A_27b,A_27a) ) ),
input ).
fof(ax_thm_2Ebool_2ETYPE__DEFINITION_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> c_2Ebool_2ETYPE__DEFINITION(A_27a,A_27b) = f30(A_27b,A_27a) ) ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2ETYPE__DEFINITION]) ).
fof(lameq_f30,axiom,
! [A_27b,A_27a,V0P] : ap(f30(A_27b,A_27a),V0P) = f29(A_27b,A_27a,V0P),
input ).
fof(lameq_f30_0,plain,
! [A_27a,A_27b,V0P] :
( ap(f30(A_27b,A_27a),V0P) = f29(A_27b,A_27a,V0P)
| $false ),
inference(orientation,[status(thm)],[lameq_f30]) ).
fof(lameq_f29,axiom,
! [A_27b,A_27a,V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1rep] : ap(f29(A_27b,A_27a,V0P),V1rep) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_21(A_27b),f26(A_27a,A_27b,V1rep))),ap(c_2Ebool_2E_21(A_27a),f28(A_27b,A_27a,V0P,V1rep))) ),
input ).
fof(lameq_f29_0,plain,
! [A_27a,A_27b,V0P] :
( ~ mem(V0P,arr(A_27a,bool))
| ! [V1rep] : ap(f29(A_27b,A_27a,V0P),V1rep) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_21(A_27b),f26(A_27a,A_27b,V1rep))),ap(c_2Ebool_2E_21(A_27a),f28(A_27b,A_27a,V0P,V1rep))) ),
inference(orientation,[status(thm)],[lameq_f29]) ).
fof(lameq_f28,axiom,
! [A_27b,A_27a,V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1rep] :
( mem(V1rep,arr(A_27b,A_27a))
=> ! [V4x] : ap(f28(A_27b,A_27a,V0P,V1rep),V4x) = ap(ap(c_2Emin_2E_3D(bool),ap(V0P,V4x)),ap(c_2Ebool_2E_3F(A_27b),f27(A_27a,A_27b,V1rep,V4x))) ) ),
input ).
fof(lameq_f28_0,plain,
! [A_27a,A_27b,V0P] :
( ~ mem(V0P,arr(A_27a,bool))
| ! [V1rep] :
( mem(V1rep,arr(A_27b,A_27a))
=> ! [V4x] : ap(f28(A_27b,A_27a,V0P,V1rep),V4x) = ap(ap(c_2Emin_2E_3D(bool),ap(V0P,V4x)),ap(c_2Ebool_2E_3F(A_27b),f27(A_27a,A_27b,V1rep,V4x))) ) ),
inference(orientation,[status(thm)],[lameq_f28]) ).
fof(lameq_f27,axiom,
! [A_27a,A_27b,V1rep] :
( mem(V1rep,arr(A_27b,A_27a))
=> ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5x_27] : ap(f27(A_27a,A_27b,V1rep,V4x),V5x_27) = ap(ap(c_2Emin_2E_3D(A_27a),V4x),ap(V1rep,V5x_27)) ) ),
input ).
fof(lameq_f27_0,plain,
! [A_27a,A_27b,V1rep] :
( ~ mem(V1rep,arr(A_27b,A_27a))
| ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5x_27] : ap(f27(A_27a,A_27b,V1rep,V4x),V5x_27) = ap(ap(c_2Emin_2E_3D(A_27a),V4x),ap(V1rep,V5x_27)) ) ),
inference(orientation,[status(thm)],[lameq_f27]) ).
fof(lameq_f26,axiom,
! [A_27a,A_27b,V1rep] :
( mem(V1rep,arr(A_27b,A_27a))
=> ! [V2x_27] : ap(f26(A_27a,A_27b,V1rep),V2x_27) = ap(c_2Ebool_2E_21(A_27b),f25(A_27a,A_27b,V1rep,V2x_27)) ),
input ).
fof(lameq_f26_0,plain,
! [A_27a,A_27b,V1rep] :
( ~ mem(V1rep,arr(A_27b,A_27a))
| ! [V2x_27] : ap(f26(A_27a,A_27b,V1rep),V2x_27) = ap(c_2Ebool_2E_21(A_27b),f25(A_27a,A_27b,V1rep,V2x_27)) ),
inference(orientation,[status(thm)],[lameq_f26]) ).
fof(lameq_f25,axiom,
! [A_27a,A_27b,V1rep] :
( mem(V1rep,arr(A_27b,A_27a))
=> ! [V2x_27] :
( mem(V2x_27,A_27b)
=> ! [V3x_27_27] : ap(f25(A_27a,A_27b,V1rep,V2x_27),V3x_27_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(A_27a),ap(V1rep,V2x_27)),ap(V1rep,V3x_27_27))),ap(ap(c_2Emin_2E_3D(A_27b),V2x_27),V3x_27_27)) ) ),
input ).
fof(lameq_f25_0,plain,
! [A_27a,A_27b,V1rep] :
( ~ mem(V1rep,arr(A_27b,A_27a))
| ! [V2x_27] :
( mem(V2x_27,A_27b)
=> ! [V3x_27_27] : ap(f25(A_27a,A_27b,V1rep,V2x_27),V3x_27_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(A_27a),ap(V1rep,V2x_27)),ap(V1rep,V3x_27_27))),ap(ap(c_2Emin_2E_3D(A_27b),V2x_27),V3x_27_27)) ) ),
inference(orientation,[status(thm)],[lameq_f25]) ).
fof(ax_thm_2Ebool_2EONTO__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> c_2Ebool_2EONTO(A_27a,A_27b) = f24(A_27a,A_27b) ) ),
input ).
fof(ax_thm_2Ebool_2EONTO__DEF_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> c_2Ebool_2EONTO(A_27a,A_27b) = f24(A_27a,A_27b) ) ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2EONTO__DEF]) ).
fof(lameq_f24,axiom,
! [A_27a,A_27b,V0f] : ap(f24(A_27a,A_27b),V0f) = ap(c_2Ebool_2E_21(A_27b),f23(A_27a,A_27b,V0f)),
input ).
fof(lameq_f24_0,plain,
! [A_27a,A_27b,V0f] :
( ap(f24(A_27a,A_27b),V0f) = ap(c_2Ebool_2E_21(A_27b),f23(A_27a,A_27b,V0f))
| $false ),
inference(orientation,[status(thm)],[lameq_f24]) ).
fof(lameq_f23,axiom,
! [A_27a,A_27b,V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1y] : ap(f23(A_27a,A_27b,V0f),V1y) = ap(c_2Ebool_2E_3F(A_27a),f22(A_27b,A_27a,V0f,V1y)) ),
input ).
fof(lameq_f23_0,plain,
! [A_27a,A_27b,V0f] :
( ~ mem(V0f,arr(A_27a,A_27b))
| ! [V1y] : ap(f23(A_27a,A_27b,V0f),V1y) = ap(c_2Ebool_2E_3F(A_27a),f22(A_27b,A_27a,V0f,V1y)) ),
inference(orientation,[status(thm)],[lameq_f23]) ).
fof(lameq_f22,axiom,
! [A_27b,A_27a,V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1y] :
( mem(V1y,A_27b)
=> ! [V2x] : ap(f22(A_27b,A_27a,V0f,V1y),V2x) = ap(ap(c_2Emin_2E_3D(A_27b),V1y),ap(V0f,V2x)) ) ),
input ).
fof(lameq_f22_0,plain,
! [A_27a,A_27b,V0f] :
( ~ mem(V0f,arr(A_27a,A_27b))
| ! [V1y] :
( mem(V1y,A_27b)
=> ! [V2x] : ap(f22(A_27b,A_27a,V0f,V1y),V2x) = ap(ap(c_2Emin_2E_3D(A_27b),V1y),ap(V0f,V2x)) ) ),
inference(orientation,[status(thm)],[lameq_f22]) ).
fof(ax_thm_2Ebool_2EONE__ONE__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> c_2Ebool_2EONE__ONE(A_27a,A_27b) = f21(A_27b,A_27a) ) ),
input ).
fof(ax_thm_2Ebool_2EONE__ONE__DEF_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> c_2Ebool_2EONE__ONE(A_27a,A_27b) = f21(A_27b,A_27a) ) ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2EONE__ONE__DEF]) ).
fof(lameq_f21,axiom,
! [A_27b,A_27a,V0f] : ap(f21(A_27b,A_27a),V0f) = ap(c_2Ebool_2E_21(A_27a),f20(A_27b,A_27a,V0f)),
input ).
fof(lameq_f21_0,plain,
! [A_27a,A_27b,V0f] :
( ap(f21(A_27b,A_27a),V0f) = ap(c_2Ebool_2E_21(A_27a),f20(A_27b,A_27a,V0f))
| $false ),
inference(orientation,[status(thm)],[lameq_f21]) ).
fof(lameq_f20,axiom,
! [A_27b,A_27a,V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1x1] : ap(f20(A_27b,A_27a,V0f),V1x1) = ap(c_2Ebool_2E_21(A_27a),f19(A_27b,A_27a,V0f,V1x1)) ),
input ).
fof(lameq_f20_0,plain,
! [A_27a,A_27b,V0f] :
( ~ mem(V0f,arr(A_27a,A_27b))
| ! [V1x1] : ap(f20(A_27b,A_27a,V0f),V1x1) = ap(c_2Ebool_2E_21(A_27a),f19(A_27b,A_27a,V0f,V1x1)) ),
inference(orientation,[status(thm)],[lameq_f20]) ).
fof(lameq_f19,axiom,
! [A_27b,A_27a,V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1x1] :
( mem(V1x1,A_27a)
=> ! [V2x2] : ap(f19(A_27b,A_27a,V0f,V1x1),V2x2) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(A_27b),ap(V0f,V1x1)),ap(V0f,V2x2))),ap(ap(c_2Emin_2E_3D(A_27a),V1x1),V2x2)) ) ),
input ).
fof(lameq_f19_0,plain,
! [A_27a,A_27b,V0f] :
( ~ mem(V0f,arr(A_27a,A_27b))
| ! [V1x1] :
( mem(V1x1,A_27a)
=> ! [V2x2] : ap(f19(A_27b,A_27a,V0f,V1x1),V2x2) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(A_27b),ap(V0f,V1x1)),ap(V0f,V2x2))),ap(ap(c_2Emin_2E_3D(A_27a),V1x1),V2x2)) ) ),
inference(orientation,[status(thm)],[lameq_f19]) ).
fof(ax_thm_2Ebool_2ECOND__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ebool_2ECOND(A_27a) = f18(A_27a) ),
input ).
fof(ax_thm_2Ebool_2ECOND__DEF_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| c_2Ebool_2ECOND(A_27a) = f18(A_27a) ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2ECOND__DEF]) ).
fof(lameq_f18,axiom,
! [A_27a,V0t] : ap(f18(A_27a),V0t) = f17(A_27a,V0t),
input ).
fof(lameq_f18_0,plain,
! [A_27a,V0t] :
( ap(f18(A_27a),V0t) = f17(A_27a,V0t)
| $false ),
inference(orientation,[status(thm)],[lameq_f18]) ).
fof(lameq_f17,axiom,
! [A_27a,V0t] :
( mem(V0t,bool)
=> ! [V1t1] : ap(f17(A_27a,V0t),V1t1) = f16(A_27a,V0t,V1t1) ),
input ).
fof(lameq_f17_0,plain,
! [A_27a,V0t] :
( ~ mem(V0t,bool)
| ! [V1t1] : ap(f17(A_27a,V0t),V1t1) = f16(A_27a,V0t,V1t1) ),
inference(orientation,[status(thm)],[lameq_f17]) ).
fof(lameq_f16,axiom,
! [A_27a,V0t] :
( mem(V0t,bool)
=> ! [V1t1] :
( mem(V1t1,A_27a)
=> ! [V2t2] : ap(f16(A_27a,V0t,V1t1),V2t2) = ap(c_2Emin_2E_40(A_27a),f15(A_27a,V1t1,V2t2,V0t)) ) ),
input ).
fof(lameq_f16_0,plain,
! [A_27a,V0t] :
( ~ mem(V0t,bool)
| ! [V1t1] :
( mem(V1t1,A_27a)
=> ! [V2t2] : ap(f16(A_27a,V0t,V1t1),V2t2) = ap(c_2Emin_2E_40(A_27a),f15(A_27a,V1t1,V2t2,V0t)) ) ),
inference(orientation,[status(thm)],[lameq_f16]) ).
fof(lameq_f15,axiom,
! [A_27a,V1t1] :
( mem(V1t1,A_27a)
=> ! [V2t2] :
( mem(V2t2,A_27a)
=> ! [V0t] :
( mem(V0t,bool)
=> ! [V3x] : ap(f15(A_27a,V1t1,V2t2,V0t),V3x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),V0t),c_2Ebool_2ET)),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V1t1))),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),V0t),c_2Ebool_2EF)),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V2t2))) ) ) ),
input ).
fof(lameq_f15_0,plain,
! [A_27a,V1t1] :
( ~ mem(V1t1,A_27a)
| ! [V2t2] :
( mem(V2t2,A_27a)
=> ! [V0t] :
( mem(V0t,bool)
=> ! [V3x] : ap(f15(A_27a,V1t1,V2t2,V0t),V3x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),V0t),c_2Ebool_2ET)),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V1t1))),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),V0t),c_2Ebool_2EF)),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V2t2))) ) ) ),
inference(orientation,[status(thm)],[lameq_f15]) ).
fof(ax_thm_2Ebool_2ELET__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> c_2Ebool_2ELET(A_27a,A_27b) = f14(A_27b,A_27a) ) ),
input ).
fof(ax_thm_2Ebool_2ELET__DEF_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> c_2Ebool_2ELET(A_27a,A_27b) = f14(A_27b,A_27a) ) ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2ELET__DEF]) ).
fof(lameq_f14,axiom,
! [A_27b,A_27a,V0f] : ap(f14(A_27b,A_27a),V0f) = f13(A_27b,A_27a,V0f),
input ).
fof(lameq_f14_0,plain,
! [A_27a,A_27b,V0f] :
( ap(f14(A_27b,A_27a),V0f) = f13(A_27b,A_27a,V0f)
| $false ),
inference(orientation,[status(thm)],[lameq_f14]) ).
fof(lameq_f13,axiom,
! [A_27b,A_27a,V0f] :
( mem(V0f,arr(A_27a,A_27b))
=> ! [V1x] : ap(f13(A_27b,A_27a,V0f),V1x) = ap(V0f,V1x) ),
input ).
fof(lameq_f13_0,plain,
! [A_27a,A_27b,V0f] :
( ~ mem(V0f,arr(A_27a,A_27b))
| ! [V1x] : ap(f13(A_27b,A_27a,V0f),V1x) = ap(V0f,V1x) ),
inference(orientation,[status(thm)],[lameq_f13]) ).
fof(ax_thm_2Ebool_2EEXISTS__UNIQUE__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ebool_2E_3F_21(A_27a) = f12(A_27a) ),
input ).
fof(ax_thm_2Ebool_2EEXISTS__UNIQUE__DEF_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| c_2Ebool_2E_3F_21(A_27a) = f12(A_27a) ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2EEXISTS__UNIQUE__DEF]) ).
fof(lameq_f12,axiom,
! [A_27a,V0P] : ap(f12(A_27a),V0P) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_3F(A_27a),V0P)),ap(c_2Ebool_2E_21(A_27a),f11(A_27a,V0P))),
input ).
fof(lameq_f12_0,plain,
! [A_27a,V0P] :
( ap(f12(A_27a),V0P) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_3F(A_27a),V0P)),ap(c_2Ebool_2E_21(A_27a),f11(A_27a,V0P)))
| $false ),
inference(orientation,[status(thm)],[lameq_f12]) ).
fof(lameq_f11,axiom,
! [A_27a,V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1x] : ap(f11(A_27a,V0P),V1x) = ap(c_2Ebool_2E_21(A_27a),f10(A_27a,V0P,V1x)) ),
input ).
fof(lameq_f11_0,plain,
! [A_27a,V0P] :
( ~ mem(V0P,arr(A_27a,bool))
| ! [V1x] : ap(f11(A_27a,V0P),V1x) = ap(c_2Ebool_2E_21(A_27a),f10(A_27a,V0P,V1x)) ),
inference(orientation,[status(thm)],[lameq_f11]) ).
fof(lameq_f10,axiom,
! [A_27a,V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] : ap(f10(A_27a,V0P,V1x),V2y) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(V0P,V1x)),ap(V0P,V2y))),ap(ap(c_2Emin_2E_3D(A_27a),V1x),V2y)) ) ),
input ).
fof(lameq_f10_0,plain,
! [A_27a,V0P] :
( ~ mem(V0P,arr(A_27a,bool))
| ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] : ap(f10(A_27a,V0P,V1x),V2y) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(V0P,V1x)),ap(V0P,V2y))),ap(ap(c_2Emin_2E_3D(A_27a),V1x),V2y)) ) ),
inference(orientation,[status(thm)],[lameq_f10]) ).
fof(ax_thm_2Ebool_2ENOT__DEF,axiom,
c_2Ebool_2E_7E = f9,
input ).
fof(ax_thm_2Ebool_2ENOT__DEF_0,plain,
( c_2Ebool_2E_7E = f9
| $false ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2ENOT__DEF]) ).
fof(lameq_f9,axiom,
! [V0t] : ap(f9,V0t) = ap(ap(c_2Emin_2E_3D_3D_3E,V0t),c_2Ebool_2EF),
input ).
fof(lameq_f9_0,plain,
! [V0t] :
( ap(f9,V0t) = ap(ap(c_2Emin_2E_3D_3D_3E,V0t),c_2Ebool_2EF)
| $false ),
inference(orientation,[status(thm)],[lameq_f9]) ).
fof(ax_thm_2Ebool_2EF__DEF,axiom,
( $false
<=> ! [V0t] :
( mem(V0t,bool)
=> p(V0t) ) ),
input ).
fof(ax_thm_2Ebool_2EF__DEF_0,plain,
( $false
| ~ ! [V0t] :
( mem(V0t,bool)
=> p(V0t) ) ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2EF__DEF]) ).
fof(ax_thm_2Ebool_2EF__DEF_1,plain,
( ~ $false
| ! [V0t] :
( mem(V0t,bool)
=> p(V0t) ) ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2EF__DEF]) ).
fof(ax_thm_2Ebool_2EOR__DEF,axiom,
c_2Ebool_2E_5C_2F = f8,
input ).
fof(ax_thm_2Ebool_2EOR__DEF_0,plain,
( c_2Ebool_2E_5C_2F = f8
| $false ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2EOR__DEF]) ).
fof(lameq_f8,axiom,
! [V0t1] : ap(f8,V0t1) = f7(V0t1),
input ).
fof(lameq_f8_0,plain,
! [V0t1] :
( ap(f8,V0t1) = f7(V0t1)
| $false ),
inference(orientation,[status(thm)],[lameq_f8]) ).
fof(lameq_f7,axiom,
! [V0t1] :
( mem(V0t1,bool)
=> ! [V1t2] : ap(f7(V0t1),V1t2) = ap(c_2Ebool_2E_21(bool),f6(V0t1,V1t2)) ),
input ).
fof(lameq_f7_0,plain,
! [V0t1] :
( ~ mem(V0t1,bool)
| ! [V1t2] : ap(f7(V0t1),V1t2) = ap(c_2Ebool_2E_21(bool),f6(V0t1,V1t2)) ),
inference(orientation,[status(thm)],[lameq_f7]) ).
fof(lameq_f6,axiom,
! [V0t1] :
( mem(V0t1,bool)
=> ! [V1t2] :
( mem(V1t2,bool)
=> ! [V2t] : ap(f6(V0t1,V1t2),V2t) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,V0t1),V2t)),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,V1t2),V2t)),V2t)) ) ),
input ).
fof(lameq_f6_0,plain,
! [V0t1] :
( ~ mem(V0t1,bool)
| ! [V1t2] :
( mem(V1t2,bool)
=> ! [V2t] : ap(f6(V0t1,V1t2),V2t) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,V0t1),V2t)),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,V1t2),V2t)),V2t)) ) ),
inference(orientation,[status(thm)],[lameq_f6]) ).
fof(ax_thm_2Ebool_2EAND__DEF,axiom,
c_2Ebool_2E_2F_5C = f5,
input ).
fof(ax_thm_2Ebool_2EAND__DEF_0,plain,
( c_2Ebool_2E_2F_5C = f5
| $false ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2EAND__DEF]) ).
fof(lameq_f5,axiom,
! [V0t1] : ap(f5,V0t1) = f4(V0t1),
input ).
fof(lameq_f5_0,plain,
! [V0t1] :
( ap(f5,V0t1) = f4(V0t1)
| $false ),
inference(orientation,[status(thm)],[lameq_f5]) ).
fof(lameq_f4,axiom,
! [V0t1] :
( mem(V0t1,bool)
=> ! [V1t2] : ap(f4(V0t1),V1t2) = ap(c_2Ebool_2E_21(bool),f3(V1t2,V0t1)) ),
input ).
fof(lameq_f4_0,plain,
! [V0t1] :
( ~ mem(V0t1,bool)
| ! [V1t2] : ap(f4(V0t1),V1t2) = ap(c_2Ebool_2E_21(bool),f3(V1t2,V0t1)) ),
inference(orientation,[status(thm)],[lameq_f4]) ).
fof(lameq_f3,axiom,
! [V1t2] :
( mem(V1t2,bool)
=> ! [V0t1] :
( mem(V0t1,bool)
=> ! [V2t] : ap(f3(V1t2,V0t1),V2t) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,V0t1),ap(ap(c_2Emin_2E_3D_3D_3E,V1t2),V2t))),V2t) ) ),
input ).
fof(lameq_f3_0,plain,
! [V1t2] :
( ~ mem(V1t2,bool)
| ! [V0t1] :
( mem(V0t1,bool)
=> ! [V2t] : ap(f3(V1t2,V0t1),V2t) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,V0t1),ap(ap(c_2Emin_2E_3D_3D_3E,V1t2),V2t))),V2t) ) ),
inference(orientation,[status(thm)],[lameq_f3]) ).
fof(ax_thm_2Ebool_2EEXISTS__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ebool_2E_3F(A_27a) = f2(A_27a) ),
input ).
fof(ax_thm_2Ebool_2EEXISTS__DEF_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| c_2Ebool_2E_3F(A_27a) = f2(A_27a) ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2EEXISTS__DEF]) ).
fof(lameq_f2,axiom,
! [A_27a,V0P] : ap(f2(A_27a),V0P) = ap(V0P,ap(c_2Emin_2E_40(A_27a),V0P)),
input ).
fof(lameq_f2_0,plain,
! [A_27a,V0P] :
( ap(f2(A_27a),V0P) = ap(V0P,ap(c_2Emin_2E_40(A_27a),V0P))
| $false ),
inference(orientation,[status(thm)],[lameq_f2]) ).
fof(ax_thm_2Ebool_2EFORALL__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> c_2Ebool_2E_21(A_27a) = f1(A_27a) ),
input ).
fof(ax_thm_2Ebool_2EFORALL__DEF_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| c_2Ebool_2E_21(A_27a) = f1(A_27a) ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2EFORALL__DEF]) ).
fof(lameq_f1,axiom,
! [A_27a,V0P] : ap(f1(A_27a),V0P) = ap(ap(c_2Emin_2E_3D(arr(A_27a,bool)),V0P),k(A_27a,c_2Ebool_2ET)),
input ).
fof(lameq_f1_0,plain,
! [A_27a,V0P] :
( ap(f1(A_27a),V0P) = ap(ap(c_2Emin_2E_3D(arr(A_27a,bool)),V0P),k(A_27a,c_2Ebool_2ET))
| $false ),
inference(orientation,[status(thm)],[lameq_f1]) ).
fof(ax_thm_2Ebool_2ET__DEF,axiom,
( $true
<=> i(bool) = i(bool) ),
input ).
fof(ax_thm_2Ebool_2ET__DEF_0,plain,
( $true
| i(bool) != i(bool) ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2ET__DEF]) ).
fof(ax_thm_2Ebool_2ET__DEF_1,plain,
( ~ $true
| i(bool) = i(bool) ),
inference(orientation,[status(thm)],[ax_thm_2Ebool_2ET__DEF]) ).
fof(ax_neg_p,axiom,
! [Q] :
( mem(Q,bool)
=> ( p(ap(c_2Ebool_2E_7E,Q))
<=> ~ p(Q) ) ),
input ).
fof(ax_neg_p_0,plain,
! [Q] :
( ~ mem(Q,bool)
| ( p(ap(c_2Ebool_2E_7E,Q))
<=> ~ p(Q) ) ),
inference(orientation,[status(thm)],[ax_neg_p]) ).
fof(mem_c_2Ebool_2E_7E,axiom,
mem(c_2Ebool_2E_7E,arr(bool,bool)),
input ).
fof(mem_c_2Ebool_2E_7E_0,plain,
( mem(c_2Ebool_2E_7E,arr(bool,bool))
| $false ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2E_7E]) ).
fof(mem_c_2Ebool_2Ethe__value,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2Ethe__value(A_27a),ty_2Ebool_2Eitself(A_27a)) ),
input ).
fof(mem_c_2Ebool_2Ethe__value_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| mem(c_2Ebool_2Ethe__value(A_27a),ty_2Ebool_2Eitself(A_27a)) ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2Ethe__value]) ).
fof(mem_c_2Ebool_2Eliteral__case,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ebool_2Eliteral__case(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) ) ),
input ).
fof(mem_c_2Ebool_2Eliteral__case_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ebool_2Eliteral__case(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) ) ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2Eliteral__case]) ).
fof(mem_c_2Ebool_2Eitself__case,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ebool_2Eitself__case(A_27a,A_27b),arr(ty_2Ebool_2Eitself(A_27a),arr(A_27b,A_27b))) ) ),
input ).
fof(mem_c_2Ebool_2Eitself__case_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ebool_2Eitself__case(A_27a,A_27b),arr(ty_2Ebool_2Eitself(A_27a),arr(A_27b,A_27b))) ) ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2Eitself__case]) ).
fof(ax_or_p,axiom,
! [Q] :
( mem(Q,bool)
=> ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Ebool_2E_5C_2F,Q),R))
<=> ( p(Q)
| p(R) ) ) ) ),
input ).
fof(ax_or_p_0,plain,
! [Q] :
( ~ mem(Q,bool)
| ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Ebool_2E_5C_2F,Q),R))
<=> ( p(Q)
| p(R) ) ) ) ),
inference(orientation,[status(thm)],[ax_or_p]) ).
fof(mem_c_2Ebool_2E_5C_2F,axiom,
mem(c_2Ebool_2E_5C_2F,arr(bool,arr(bool,bool))),
input ).
fof(mem_c_2Ebool_2E_5C_2F_0,plain,
( mem(c_2Ebool_2E_5C_2F,arr(bool,arr(bool,bool)))
| $false ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2E_5C_2F]) ).
fof(mem_c_2Ebool_2ETYPE__DEFINITION,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ebool_2ETYPE__DEFINITION(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,A_27a),bool))) ) ),
input ).
fof(mem_c_2Ebool_2ETYPE__DEFINITION_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ebool_2ETYPE__DEFINITION(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,A_27a),bool))) ) ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2ETYPE__DEFINITION]) ).
fof(ax_true_p,axiom,
p(c_2Ebool_2ET),
input ).
fof(ax_true_p_0,plain,
( p(c_2Ebool_2ET)
| $false ),
inference(orientation,[status(thm)],[ax_true_p]) ).
fof(mem_c_2Ebool_2ET,axiom,
mem(c_2Ebool_2ET,bool),
input ).
fof(mem_c_2Ebool_2ET_0,plain,
( mem(c_2Ebool_2ET,bool)
| $false ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2ET]) ).
fof(mem_c_2Ebool_2ERES__SELECT,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2ERES__SELECT(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),A_27a))) ),
input ).
fof(mem_c_2Ebool_2ERES__SELECT_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| mem(c_2Ebool_2ERES__SELECT(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),A_27a))) ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2ERES__SELECT]) ).
fof(mem_c_2Ebool_2ERES__FORALL,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2ERES__FORALL(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))) ),
input ).
fof(mem_c_2Ebool_2ERES__FORALL_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| mem(c_2Ebool_2ERES__FORALL(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))) ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2ERES__FORALL]) ).
fof(mem_c_2Ebool_2ERES__EXISTS__UNIQUE,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))) ),
input ).
fof(mem_c_2Ebool_2ERES__EXISTS__UNIQUE_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| mem(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))) ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2ERES__EXISTS__UNIQUE]) ).
fof(mem_c_2Ebool_2ERES__EXISTS,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2ERES__EXISTS(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))) ),
input ).
fof(mem_c_2Ebool_2ERES__EXISTS_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| mem(c_2Ebool_2ERES__EXISTS(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))) ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2ERES__EXISTS]) ).
fof(mem_c_2Ebool_2ERES__ABSTRACT,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27a,A_27b),arr(A_27a,A_27b)))) ) ),
input ).
fof(mem_c_2Ebool_2ERES__ABSTRACT_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27a,A_27b),arr(A_27a,A_27b)))) ) ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2ERES__ABSTRACT]) ).
fof(mem_c_2Ebool_2EONTO,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ebool_2EONTO(A_27a,A_27b),arr(arr(A_27a,A_27b),bool)) ) ),
input ).
fof(mem_c_2Ebool_2EONTO_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ebool_2EONTO(A_27a,A_27b),arr(arr(A_27a,A_27b),bool)) ) ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2EONTO]) ).
fof(mem_c_2Ebool_2EONE__ONE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ebool_2EONE__ONE(A_27a,A_27b),arr(arr(A_27a,A_27b),bool)) ) ),
input ).
fof(mem_c_2Ebool_2EONE__ONE_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ebool_2EONE__ONE(A_27a,A_27b),arr(arr(A_27a,A_27b),bool)) ) ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2EONE__ONE]) ).
fof(mem_c_2Ebool_2ELET,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ebool_2ELET(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) ) ),
input ).
fof(mem_c_2Ebool_2ELET_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ebool_2ELET(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) ) ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2ELET]) ).
fof(mem_c_2Ebool_2EIN,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2EIN(A_27a),arr(A_27a,arr(arr(A_27a,bool),bool))) ),
input ).
fof(mem_c_2Ebool_2EIN_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| mem(c_2Ebool_2EIN(A_27a),arr(A_27a,arr(arr(A_27a,bool),bool))) ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2EIN]) ).
fof(ax_false_p,axiom,
~ p(c_2Ebool_2EF),
input ).
fof(ax_false_p_0,plain,
( ~ p(c_2Ebool_2EF)
| $false ),
inference(orientation,[status(thm)],[ax_false_p]) ).
fof(mem_c_2Ebool_2EF,axiom,
mem(c_2Ebool_2EF,bool),
input ).
fof(mem_c_2Ebool_2EF_0,plain,
( mem(c_2Ebool_2EF,bool)
| $false ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2EF]) ).
fof(mem_c_2Ebool_2EDATATYPE,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2EDATATYPE(A_27a),arr(A_27a,bool)) ),
input ).
fof(mem_c_2Ebool_2EDATATYPE_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| mem(c_2Ebool_2EDATATYPE(A_27a),arr(A_27a,bool)) ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2EDATATYPE]) ).
fof(mem_c_2Ebool_2ECOND,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2ECOND(A_27a),arr(bool,arr(A_27a,arr(A_27a,A_27a)))) ),
input ).
fof(mem_c_2Ebool_2ECOND_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| mem(c_2Ebool_2ECOND(A_27a),arr(bool,arr(A_27a,arr(A_27a,A_27a)))) ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2ECOND]) ).
fof(mem_c_2Ebool_2EBOUNDED,axiom,
mem(c_2Ebool_2EBOUNDED,arr(bool,bool)),
input ).
fof(mem_c_2Ebool_2EBOUNDED_0,plain,
( mem(c_2Ebool_2EBOUNDED,arr(bool,bool))
| $false ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2EBOUNDED]) ).
fof(mem_c_2Ebool_2EARB,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2EARB(A_27a),A_27a) ),
input ).
fof(mem_c_2Ebool_2EARB_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| mem(c_2Ebool_2EARB(A_27a),A_27a) ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2EARB]) ).
fof(mem_c_2Ebool_2E_3F_21,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2E_3F_21(A_27a),arr(arr(A_27a,bool),bool)) ),
input ).
fof(mem_c_2Ebool_2E_3F_21_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| mem(c_2Ebool_2E_3F_21(A_27a),arr(arr(A_27a,bool),bool)) ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2E_3F_21]) ).
fof(ax_ex_p,axiom,
! [A] :
( ne(A)
=> ! [Q] :
( mem(Q,arr(A,bool))
=> ( p(ap(c_2Ebool_2E_3F(A),Q))
<=> ? [X] :
( mem(X,A)
& p(ap(Q,X)) ) ) ) ),
input ).
fof(ax_ex_p_0,plain,
! [A] :
( ~ ne(A)
| ! [Q] :
( mem(Q,arr(A,bool))
=> ( p(ap(c_2Ebool_2E_3F(A),Q))
<=> ? [X] :
( mem(X,A)
& p(ap(Q,X)) ) ) ) ),
inference(orientation,[status(thm)],[ax_ex_p]) ).
fof(mem_c_2Ebool_2E_3F,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2E_3F(A_27a),arr(arr(A_27a,bool),bool)) ),
input ).
fof(mem_c_2Ebool_2E_3F_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| mem(c_2Ebool_2E_3F(A_27a),arr(arr(A_27a,bool),bool)) ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2E_3F]) ).
fof(ax_and_p,axiom,
! [Q] :
( mem(Q,bool)
=> ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Ebool_2E_2F_5C,Q),R))
<=> ( p(Q)
& p(R) ) ) ) ),
input ).
fof(ax_and_p_0,plain,
! [Q] :
( ~ mem(Q,bool)
| ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Ebool_2E_2F_5C,Q),R))
<=> ( p(Q)
& p(R) ) ) ) ),
inference(orientation,[status(thm)],[ax_and_p]) ).
fof(mem_c_2Ebool_2E_2F_5C,axiom,
mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))),
input ).
fof(mem_c_2Ebool_2E_2F_5C_0,plain,
( mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool)))
| $false ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2E_2F_5C]) ).
fof(ax_all_p,axiom,
! [A] :
( ne(A)
=> ! [Q] :
( mem(Q,arr(A,bool))
=> ( p(ap(c_2Ebool_2E_21(A),Q))
<=> ! [X] :
( mem(X,A)
=> p(ap(Q,X)) ) ) ) ),
input ).
fof(ax_all_p_0,plain,
! [A] :
( ~ ne(A)
| ! [Q] :
( mem(Q,arr(A,bool))
=> ( p(ap(c_2Ebool_2E_21(A),Q))
<=> ! [X] :
( mem(X,A)
=> p(ap(Q,X)) ) ) ) ),
inference(orientation,[status(thm)],[ax_all_p]) ).
fof(mem_c_2Ebool_2E_21,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)) ),
input ).
fof(mem_c_2Ebool_2E_21_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)) ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2E_21]) ).
fof(ne_ty_2Ebool_2Eitself,axiom,
! [A0] :
( ne(A0)
=> ne(ty_2Ebool_2Eitself(A0)) ),
input ).
fof(ne_ty_2Ebool_2Eitself_0,plain,
! [A0] :
( ~ ne(A0)
| ne(ty_2Ebool_2Eitself(A0)) ),
inference(orientation,[status(thm)],[ne_ty_2Ebool_2Eitself]) ).
fof(mem_c_2Emin_2E_40,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Emin_2E_40(A_27a),arr(arr(A_27a,bool),A_27a)) ),
input ).
fof(mem_c_2Emin_2E_40_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| mem(c_2Emin_2E_40(A_27a),arr(arr(A_27a,bool),A_27a)) ),
inference(orientation,[status(thm)],[mem_c_2Emin_2E_40]) ).
fof(ax_imp_p,axiom,
! [Q] :
( mem(Q,bool)
=> ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R))
<=> ( p(Q)
=> p(R) ) ) ) ),
input ).
fof(ax_imp_p_0,plain,
! [Q] :
( ~ mem(Q,bool)
| ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R))
<=> ( p(Q)
=> p(R) ) ) ) ),
inference(orientation,[status(thm)],[ax_imp_p]) ).
fof(mem_c_2Emin_2E_3D_3D_3E,axiom,
mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))),
input ).
fof(mem_c_2Emin_2E_3D_3D_3E_0,plain,
( mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool)))
| $false ),
inference(orientation,[status(thm)],[mem_c_2Emin_2E_3D_3D_3E]) ).
fof(ax_eq_p,axiom,
! [A] :
( ne(A)
=> ! [X] :
( mem(X,A)
=> ! [Y] :
( mem(Y,A)
=> ( p(ap(ap(c_2Emin_2E_3D(A),X),Y))
<=> X = Y ) ) ) ),
input ).
fof(ax_eq_p_0,plain,
! [A] :
( ~ ne(A)
| ! [X] :
( mem(X,A)
=> ! [Y] :
( mem(Y,A)
=> ( p(ap(ap(c_2Emin_2E_3D(A),X),Y))
<=> X = Y ) ) ) ),
inference(orientation,[status(thm)],[ax_eq_p]) ).
fof(mem_c_2Emin_2E_3D,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))) ),
input ).
fof(mem_c_2Emin_2E_3D_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))) ),
inference(orientation,[status(thm)],[mem_c_2Emin_2E_3D]) ).
fof(ibeta,axiom,
! [A,X] :
( mem(X,A)
=> ap(i(A),X) = X ),
input ).
fof(ibeta_0,plain,
! [A,X] :
( ~ mem(X,A)
| ap(i(A),X) = X ),
inference(orientation,[status(thm)],[ibeta]) ).
fof(kbeta,axiom,
! [A,Y,X] :
( mem(X,A)
=> ap(k(A,Y),X) = Y ),
input ).
fof(kbeta_0,plain,
! [A,X,Y] :
( ~ mem(X,A)
| ap(k(A,Y),X) = Y ),
inference(orientation,[status(thm)],[kbeta]) ).
fof(funcext,axiom,
! [A,B,F] :
( mem(F,arr(A,B))
=> ! [G] :
( mem(G,arr(A,B))
=> ( ! [X] :
( mem(X,A)
=> ap(F,X) = ap(G,X) )
=> F = G ) ) ),
input ).
fof(funcext_0,plain,
! [A,B,F] :
( ~ mem(F,arr(A,B))
| ! [G] :
( mem(G,arr(A,B))
=> ( ! [X] :
( mem(X,A)
=> ap(F,X) = ap(G,X) )
=> F = G ) ) ),
inference(orientation,[status(thm)],[funcext]) ).
fof(boolext,axiom,
! [Q] :
( mem(Q,bool)
=> ! [R] :
( mem(R,bool)
=> ( ( p(Q)
<=> p(R) )
=> Q = R ) ) ),
input ).
fof(boolext_0,plain,
! [Q] :
( ~ mem(Q,bool)
| ! [R] :
( mem(R,bool)
=> ( ( p(Q)
<=> p(R) )
=> Q = R ) ) ),
inference(orientation,[status(thm)],[boolext]) ).
fof(ap_tp,axiom,
! [A,B,F] :
( mem(F,arr(A,B))
=> ! [X] :
( mem(X,A)
=> mem(ap(F,X),B) ) ),
input ).
fof(ap_tp_0,plain,
! [A,B,F] :
( ~ mem(F,arr(A,B))
| ! [X] :
( mem(X,A)
=> mem(ap(F,X),B) ) ),
inference(orientation,[status(thm)],[ap_tp]) ).
fof(arr_ne,axiom,
! [A] :
( ne(A)
=> ! [B] :
( ne(B)
=> ne(arr(A,B)) ) ),
input ).
fof(arr_ne_0,plain,
! [A] :
( ~ ne(A)
| ! [B] :
( ne(B)
=> ne(arr(A,B)) ) ),
inference(orientation,[status(thm)],[arr_ne]) ).
fof(ind_ne,axiom,
ne(ind),
input ).
fof(ind_ne_0,plain,
( ne(ind)
| $false ),
inference(orientation,[status(thm)],[ind_ne]) ).
fof(bool_ne,axiom,
ne(bool),
input ).
fof(bool_ne_0,plain,
( ne(bool)
| $false ),
inference(orientation,[status(thm)],[bool_ne]) ).
fof(def_lhs_atom1,axiom,
( lhs_atom1
<=> ne(bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_0,plain,
( lhs_atom1
| $false ),
inference(fold_definition,[status(thm)],[bool_ne_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
( lhs_atom2
<=> ne(ind) ),
inference(definition,[],[]) ).
fof(to_be_clausified_1,plain,
( lhs_atom2
| $false ),
inference(fold_definition,[status(thm)],[ind_ne_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [A] :
( lhs_atom3(A)
<=> ~ ne(A) ),
inference(definition,[],[]) ).
fof(to_be_clausified_2,plain,
! [A] :
( lhs_atom3(A)
| ! [B] :
( ne(B)
=> ne(arr(A,B)) ) ),
inference(fold_definition,[status(thm)],[arr_ne_0,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
! [F,B,A] :
( lhs_atom4(F,B,A)
<=> ~ mem(F,arr(A,B)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_3,plain,
! [A,B,F] :
( lhs_atom4(F,B,A)
| ! [X] :
( mem(X,A)
=> mem(ap(F,X),B) ) ),
inference(fold_definition,[status(thm)],[ap_tp_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
! [Q] :
( lhs_atom5(Q)
<=> ~ mem(Q,bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_4,plain,
! [Q] :
( lhs_atom5(Q)
| ! [R] :
( mem(R,bool)
=> ( ( p(Q)
<=> p(R) )
=> Q = R ) ) ),
inference(fold_definition,[status(thm)],[boolext_0,def_lhs_atom5]) ).
fof(to_be_clausified_5,plain,
! [A,B,F] :
( lhs_atom4(F,B,A)
| ! [G] :
( mem(G,arr(A,B))
=> ( ! [X] :
( mem(X,A)
=> ap(F,X) = ap(G,X) )
=> F = G ) ) ),
inference(fold_definition,[status(thm)],[funcext_0,def_lhs_atom4]) ).
fof(def_lhs_atom6,axiom,
! [X,A] :
( lhs_atom6(X,A)
<=> ~ mem(X,A) ),
inference(definition,[],[]) ).
fof(to_be_clausified_6,plain,
! [A,X,Y] :
( lhs_atom6(X,A)
| ap(k(A,Y),X) = Y ),
inference(fold_definition,[status(thm)],[kbeta_0,def_lhs_atom6]) ).
fof(to_be_clausified_7,plain,
! [A,X] :
( lhs_atom6(X,A)
| ap(i(A),X) = X ),
inference(fold_definition,[status(thm)],[ibeta_0,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
! [A_27a] :
( lhs_atom7(A_27a)
<=> ~ ne(A_27a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_8,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))) ),
inference(fold_definition,[status(thm)],[mem_c_2Emin_2E_3D_0,def_lhs_atom7]) ).
fof(to_be_clausified_9,plain,
! [A] :
( lhs_atom3(A)
| ! [X] :
( mem(X,A)
=> ! [Y] :
( mem(Y,A)
=> ( p(ap(ap(c_2Emin_2E_3D(A),X),Y))
<=> X = Y ) ) ) ),
inference(fold_definition,[status(thm)],[ax_eq_p_0,def_lhs_atom3]) ).
fof(def_lhs_atom8,axiom,
( lhs_atom8
<=> mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))) ),
inference(definition,[],[]) ).
fof(to_be_clausified_10,plain,
( lhs_atom8
| $false ),
inference(fold_definition,[status(thm)],[mem_c_2Emin_2E_3D_3D_3E_0,def_lhs_atom8]) ).
fof(to_be_clausified_11,plain,
! [Q] :
( lhs_atom5(Q)
| ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R))
<=> ( p(Q)
=> p(R) ) ) ) ),
inference(fold_definition,[status(thm)],[ax_imp_p_0,def_lhs_atom5]) ).
fof(to_be_clausified_12,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| mem(c_2Emin_2E_40(A_27a),arr(arr(A_27a,bool),A_27a)) ),
inference(fold_definition,[status(thm)],[mem_c_2Emin_2E_40_0,def_lhs_atom7]) ).
fof(def_lhs_atom9,axiom,
! [A0] :
( lhs_atom9(A0)
<=> ~ ne(A0) ),
inference(definition,[],[]) ).
fof(to_be_clausified_13,plain,
! [A0] :
( lhs_atom9(A0)
| ne(ty_2Ebool_2Eitself(A0)) ),
inference(fold_definition,[status(thm)],[ne_ty_2Ebool_2Eitself_0,def_lhs_atom9]) ).
fof(to_be_clausified_14,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)) ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2E_21_0,def_lhs_atom7]) ).
fof(to_be_clausified_15,plain,
! [A] :
( lhs_atom3(A)
| ! [Q] :
( mem(Q,arr(A,bool))
=> ( p(ap(c_2Ebool_2E_21(A),Q))
<=> ! [X] :
( mem(X,A)
=> p(ap(Q,X)) ) ) ) ),
inference(fold_definition,[status(thm)],[ax_all_p_0,def_lhs_atom3]) ).
fof(def_lhs_atom10,axiom,
( lhs_atom10
<=> mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))) ),
inference(definition,[],[]) ).
fof(to_be_clausified_16,plain,
( lhs_atom10
| $false ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2E_2F_5C_0,def_lhs_atom10]) ).
fof(to_be_clausified_17,plain,
! [Q] :
( lhs_atom5(Q)
| ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Ebool_2E_2F_5C,Q),R))
<=> ( p(Q)
& p(R) ) ) ) ),
inference(fold_definition,[status(thm)],[ax_and_p_0,def_lhs_atom5]) ).
fof(to_be_clausified_18,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| mem(c_2Ebool_2E_3F(A_27a),arr(arr(A_27a,bool),bool)) ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2E_3F_0,def_lhs_atom7]) ).
fof(to_be_clausified_19,plain,
! [A] :
( lhs_atom3(A)
| ! [Q] :
( mem(Q,arr(A,bool))
=> ( p(ap(c_2Ebool_2E_3F(A),Q))
<=> ? [X] :
( mem(X,A)
& p(ap(Q,X)) ) ) ) ),
inference(fold_definition,[status(thm)],[ax_ex_p_0,def_lhs_atom3]) ).
fof(to_be_clausified_20,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| mem(c_2Ebool_2E_3F_21(A_27a),arr(arr(A_27a,bool),bool)) ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2E_3F_21_0,def_lhs_atom7]) ).
fof(to_be_clausified_21,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| mem(c_2Ebool_2EARB(A_27a),A_27a) ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2EARB_0,def_lhs_atom7]) ).
fof(def_lhs_atom11,axiom,
( lhs_atom11
<=> mem(c_2Ebool_2EBOUNDED,arr(bool,bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_22,plain,
( lhs_atom11
| $false ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2EBOUNDED_0,def_lhs_atom11]) ).
fof(to_be_clausified_23,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| mem(c_2Ebool_2ECOND(A_27a),arr(bool,arr(A_27a,arr(A_27a,A_27a)))) ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2ECOND_0,def_lhs_atom7]) ).
fof(to_be_clausified_24,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| mem(c_2Ebool_2EDATATYPE(A_27a),arr(A_27a,bool)) ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2EDATATYPE_0,def_lhs_atom7]) ).
fof(def_lhs_atom12,axiom,
( lhs_atom12
<=> mem(c_2Ebool_2EF,bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_25,plain,
( lhs_atom12
| $false ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2EF_0,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
( lhs_atom13
<=> ~ p(c_2Ebool_2EF) ),
inference(definition,[],[]) ).
fof(to_be_clausified_26,plain,
( lhs_atom13
| $false ),
inference(fold_definition,[status(thm)],[ax_false_p_0,def_lhs_atom13]) ).
fof(to_be_clausified_27,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| mem(c_2Ebool_2EIN(A_27a),arr(A_27a,arr(arr(A_27a,bool),bool))) ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2EIN_0,def_lhs_atom7]) ).
fof(to_be_clausified_28,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ebool_2ELET(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) ) ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2ELET_0,def_lhs_atom7]) ).
fof(to_be_clausified_29,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ebool_2EONE__ONE(A_27a,A_27b),arr(arr(A_27a,A_27b),bool)) ) ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2EONE__ONE_0,def_lhs_atom7]) ).
fof(to_be_clausified_30,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ebool_2EONTO(A_27a,A_27b),arr(arr(A_27a,A_27b),bool)) ) ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2EONTO_0,def_lhs_atom7]) ).
fof(to_be_clausified_31,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27a,A_27b),arr(A_27a,A_27b)))) ) ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2ERES__ABSTRACT_0,def_lhs_atom7]) ).
fof(to_be_clausified_32,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| mem(c_2Ebool_2ERES__EXISTS(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))) ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2ERES__EXISTS_0,def_lhs_atom7]) ).
fof(to_be_clausified_33,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| mem(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))) ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2ERES__EXISTS__UNIQUE_0,def_lhs_atom7]) ).
fof(to_be_clausified_34,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| mem(c_2Ebool_2ERES__FORALL(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))) ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2ERES__FORALL_0,def_lhs_atom7]) ).
fof(to_be_clausified_35,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| mem(c_2Ebool_2ERES__SELECT(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),A_27a))) ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2ERES__SELECT_0,def_lhs_atom7]) ).
fof(def_lhs_atom14,axiom,
( lhs_atom14
<=> mem(c_2Ebool_2ET,bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_36,plain,
( lhs_atom14
| $false ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2ET_0,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
( lhs_atom15
<=> p(c_2Ebool_2ET) ),
inference(definition,[],[]) ).
fof(to_be_clausified_37,plain,
( lhs_atom15
| $false ),
inference(fold_definition,[status(thm)],[ax_true_p_0,def_lhs_atom15]) ).
fof(to_be_clausified_38,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ebool_2ETYPE__DEFINITION(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,A_27a),bool))) ) ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2ETYPE__DEFINITION_0,def_lhs_atom7]) ).
fof(def_lhs_atom16,axiom,
( lhs_atom16
<=> mem(c_2Ebool_2E_5C_2F,arr(bool,arr(bool,bool))) ),
inference(definition,[],[]) ).
fof(to_be_clausified_39,plain,
( lhs_atom16
| $false ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2E_5C_2F_0,def_lhs_atom16]) ).
fof(to_be_clausified_40,plain,
! [Q] :
( lhs_atom5(Q)
| ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Ebool_2E_5C_2F,Q),R))
<=> ( p(Q)
| p(R) ) ) ) ),
inference(fold_definition,[status(thm)],[ax_or_p_0,def_lhs_atom5]) ).
fof(to_be_clausified_41,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ebool_2Eitself__case(A_27a,A_27b),arr(ty_2Ebool_2Eitself(A_27a),arr(A_27b,A_27b))) ) ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2Eitself__case_0,def_lhs_atom7]) ).
fof(to_be_clausified_42,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ebool_2Eliteral__case(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) ) ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2Eliteral__case_0,def_lhs_atom7]) ).
fof(to_be_clausified_43,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| mem(c_2Ebool_2Ethe__value(A_27a),ty_2Ebool_2Eitself(A_27a)) ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2Ethe__value_0,def_lhs_atom7]) ).
fof(def_lhs_atom17,axiom,
( lhs_atom17
<=> mem(c_2Ebool_2E_7E,arr(bool,bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_44,plain,
( lhs_atom17
| $false ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2E_7E_0,def_lhs_atom17]) ).
fof(to_be_clausified_45,plain,
! [Q] :
( lhs_atom5(Q)
| ( p(ap(c_2Ebool_2E_7E,Q))
<=> ~ p(Q) ) ),
inference(fold_definition,[status(thm)],[ax_neg_p_0,def_lhs_atom5]) ).
fof(def_lhs_atom18,axiom,
( lhs_atom18
<=> ~ $true ),
inference(definition,[],[]) ).
fof(to_be_clausified_46,plain,
( lhs_atom18
| i(bool) = i(bool) ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2ET__DEF_1,def_lhs_atom18]) ).
fof(def_lhs_atom19,axiom,
( lhs_atom19
<=> $true ),
inference(definition,[],[]) ).
fof(to_be_clausified_47,plain,
( lhs_atom19
| i(bool) != i(bool) ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2ET__DEF_0,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
! [V0P,A_27a] :
( lhs_atom20(V0P,A_27a)
<=> ap(f1(A_27a),V0P) = ap(ap(c_2Emin_2E_3D(arr(A_27a,bool)),V0P),k(A_27a,c_2Ebool_2ET)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_48,plain,
! [A_27a,V0P] :
( lhs_atom20(V0P,A_27a)
| $false ),
inference(fold_definition,[status(thm)],[lameq_f1_0,def_lhs_atom20]) ).
fof(to_be_clausified_49,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| c_2Ebool_2E_21(A_27a) = f1(A_27a) ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2EFORALL__DEF_0,def_lhs_atom7]) ).
fof(def_lhs_atom21,axiom,
! [V0P,A_27a] :
( lhs_atom21(V0P,A_27a)
<=> ap(f2(A_27a),V0P) = ap(V0P,ap(c_2Emin_2E_40(A_27a),V0P)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_50,plain,
! [A_27a,V0P] :
( lhs_atom21(V0P,A_27a)
| $false ),
inference(fold_definition,[status(thm)],[lameq_f2_0,def_lhs_atom21]) ).
fof(to_be_clausified_51,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| c_2Ebool_2E_3F(A_27a) = f2(A_27a) ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2EEXISTS__DEF_0,def_lhs_atom7]) ).
fof(def_lhs_atom22,axiom,
! [V1t2] :
( lhs_atom22(V1t2)
<=> ~ mem(V1t2,bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_52,plain,
! [V1t2] :
( lhs_atom22(V1t2)
| ! [V0t1] :
( mem(V0t1,bool)
=> ! [V2t] : ap(f3(V1t2,V0t1),V2t) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,V0t1),ap(ap(c_2Emin_2E_3D_3D_3E,V1t2),V2t))),V2t) ) ),
inference(fold_definition,[status(thm)],[lameq_f3_0,def_lhs_atom22]) ).
fof(def_lhs_atom23,axiom,
! [V0t1] :
( lhs_atom23(V0t1)
<=> ~ mem(V0t1,bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_53,plain,
! [V0t1] :
( lhs_atom23(V0t1)
| ! [V1t2] : ap(f4(V0t1),V1t2) = ap(c_2Ebool_2E_21(bool),f3(V1t2,V0t1)) ),
inference(fold_definition,[status(thm)],[lameq_f4_0,def_lhs_atom23]) ).
fof(def_lhs_atom24,axiom,
! [V0t1] :
( lhs_atom24(V0t1)
<=> ap(f5,V0t1) = f4(V0t1) ),
inference(definition,[],[]) ).
fof(to_be_clausified_54,plain,
! [V0t1] :
( lhs_atom24(V0t1)
| $false ),
inference(fold_definition,[status(thm)],[lameq_f5_0,def_lhs_atom24]) ).
fof(def_lhs_atom25,axiom,
( lhs_atom25
<=> c_2Ebool_2E_2F_5C = f5 ),
inference(definition,[],[]) ).
fof(to_be_clausified_55,plain,
( lhs_atom25
| $false ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2EAND__DEF_0,def_lhs_atom25]) ).
fof(to_be_clausified_56,plain,
! [V0t1] :
( lhs_atom23(V0t1)
| ! [V1t2] :
( mem(V1t2,bool)
=> ! [V2t] : ap(f6(V0t1,V1t2),V2t) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,V0t1),V2t)),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,V1t2),V2t)),V2t)) ) ),
inference(fold_definition,[status(thm)],[lameq_f6_0,def_lhs_atom23]) ).
fof(to_be_clausified_57,plain,
! [V0t1] :
( lhs_atom23(V0t1)
| ! [V1t2] : ap(f7(V0t1),V1t2) = ap(c_2Ebool_2E_21(bool),f6(V0t1,V1t2)) ),
inference(fold_definition,[status(thm)],[lameq_f7_0,def_lhs_atom23]) ).
fof(def_lhs_atom26,axiom,
! [V0t1] :
( lhs_atom26(V0t1)
<=> ap(f8,V0t1) = f7(V0t1) ),
inference(definition,[],[]) ).
fof(to_be_clausified_58,plain,
! [V0t1] :
( lhs_atom26(V0t1)
| $false ),
inference(fold_definition,[status(thm)],[lameq_f8_0,def_lhs_atom26]) ).
fof(def_lhs_atom27,axiom,
( lhs_atom27
<=> c_2Ebool_2E_5C_2F = f8 ),
inference(definition,[],[]) ).
fof(to_be_clausified_59,plain,
( lhs_atom27
| $false ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2EOR__DEF_0,def_lhs_atom27]) ).
fof(def_lhs_atom28,axiom,
( lhs_atom28
<=> ~ $false ),
inference(definition,[],[]) ).
fof(to_be_clausified_60,plain,
( lhs_atom28
| ! [V0t] :
( mem(V0t,bool)
=> p(V0t) ) ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2EF__DEF_1,def_lhs_atom28]) ).
fof(def_lhs_atom29,axiom,
( lhs_atom29
<=> $false ),
inference(definition,[],[]) ).
fof(to_be_clausified_61,plain,
( lhs_atom29
| ~ ! [V0t] :
( mem(V0t,bool)
=> p(V0t) ) ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2EF__DEF_0,def_lhs_atom29]) ).
fof(def_lhs_atom30,axiom,
! [V0t] :
( lhs_atom30(V0t)
<=> ap(f9,V0t) = ap(ap(c_2Emin_2E_3D_3D_3E,V0t),c_2Ebool_2EF) ),
inference(definition,[],[]) ).
fof(to_be_clausified_62,plain,
! [V0t] :
( lhs_atom30(V0t)
| $false ),
inference(fold_definition,[status(thm)],[lameq_f9_0,def_lhs_atom30]) ).
fof(def_lhs_atom31,axiom,
( lhs_atom31
<=> c_2Ebool_2E_7E = f9 ),
inference(definition,[],[]) ).
fof(to_be_clausified_63,plain,
( lhs_atom31
| $false ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2ENOT__DEF_0,def_lhs_atom31]) ).
fof(def_lhs_atom32,axiom,
! [V0P,A_27a] :
( lhs_atom32(V0P,A_27a)
<=> ~ mem(V0P,arr(A_27a,bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_64,plain,
! [A_27a,V0P] :
( lhs_atom32(V0P,A_27a)
| ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] : ap(f10(A_27a,V0P,V1x),V2y) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(V0P,V1x)),ap(V0P,V2y))),ap(ap(c_2Emin_2E_3D(A_27a),V1x),V2y)) ) ),
inference(fold_definition,[status(thm)],[lameq_f10_0,def_lhs_atom32]) ).
fof(to_be_clausified_65,plain,
! [A_27a,V0P] :
( lhs_atom32(V0P,A_27a)
| ! [V1x] : ap(f11(A_27a,V0P),V1x) = ap(c_2Ebool_2E_21(A_27a),f10(A_27a,V0P,V1x)) ),
inference(fold_definition,[status(thm)],[lameq_f11_0,def_lhs_atom32]) ).
fof(def_lhs_atom33,axiom,
! [V0P,A_27a] :
( lhs_atom33(V0P,A_27a)
<=> ap(f12(A_27a),V0P) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_3F(A_27a),V0P)),ap(c_2Ebool_2E_21(A_27a),f11(A_27a,V0P))) ),
inference(definition,[],[]) ).
fof(to_be_clausified_66,plain,
! [A_27a,V0P] :
( lhs_atom33(V0P,A_27a)
| $false ),
inference(fold_definition,[status(thm)],[lameq_f12_0,def_lhs_atom33]) ).
fof(to_be_clausified_67,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| c_2Ebool_2E_3F_21(A_27a) = f12(A_27a) ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2EEXISTS__UNIQUE__DEF_0,def_lhs_atom7]) ).
fof(def_lhs_atom34,axiom,
! [V0f,A_27b,A_27a] :
( lhs_atom34(V0f,A_27b,A_27a)
<=> ~ mem(V0f,arr(A_27a,A_27b)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_68,plain,
! [A_27a,A_27b,V0f] :
( lhs_atom34(V0f,A_27b,A_27a)
| ! [V1x] : ap(f13(A_27b,A_27a,V0f),V1x) = ap(V0f,V1x) ),
inference(fold_definition,[status(thm)],[lameq_f13_0,def_lhs_atom34]) ).
fof(def_lhs_atom35,axiom,
! [V0f,A_27b,A_27a] :
( lhs_atom35(V0f,A_27b,A_27a)
<=> ap(f14(A_27b,A_27a),V0f) = f13(A_27b,A_27a,V0f) ),
inference(definition,[],[]) ).
fof(to_be_clausified_69,plain,
! [A_27a,A_27b,V0f] :
( lhs_atom35(V0f,A_27b,A_27a)
| $false ),
inference(fold_definition,[status(thm)],[lameq_f14_0,def_lhs_atom35]) ).
fof(to_be_clausified_70,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> c_2Ebool_2ELET(A_27a,A_27b) = f14(A_27b,A_27a) ) ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2ELET__DEF_0,def_lhs_atom7]) ).
fof(def_lhs_atom36,axiom,
! [V1t1,A_27a] :
( lhs_atom36(V1t1,A_27a)
<=> ~ mem(V1t1,A_27a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_71,plain,
! [A_27a,V1t1] :
( lhs_atom36(V1t1,A_27a)
| ! [V2t2] :
( mem(V2t2,A_27a)
=> ! [V0t] :
( mem(V0t,bool)
=> ! [V3x] : ap(f15(A_27a,V1t1,V2t2,V0t),V3x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),V0t),c_2Ebool_2ET)),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V1t1))),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),V0t),c_2Ebool_2EF)),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V2t2))) ) ) ),
inference(fold_definition,[status(thm)],[lameq_f15_0,def_lhs_atom36]) ).
fof(def_lhs_atom37,axiom,
! [V0t] :
( lhs_atom37(V0t)
<=> ~ mem(V0t,bool) ),
inference(definition,[],[]) ).
fof(to_be_clausified_72,plain,
! [A_27a,V0t] :
( lhs_atom37(V0t)
| ! [V1t1] :
( mem(V1t1,A_27a)
=> ! [V2t2] : ap(f16(A_27a,V0t,V1t1),V2t2) = ap(c_2Emin_2E_40(A_27a),f15(A_27a,V1t1,V2t2,V0t)) ) ),
inference(fold_definition,[status(thm)],[lameq_f16_0,def_lhs_atom37]) ).
fof(to_be_clausified_73,plain,
! [A_27a,V0t] :
( lhs_atom37(V0t)
| ! [V1t1] : ap(f17(A_27a,V0t),V1t1) = f16(A_27a,V0t,V1t1) ),
inference(fold_definition,[status(thm)],[lameq_f17_0,def_lhs_atom37]) ).
fof(def_lhs_atom38,axiom,
! [V0t,A_27a] :
( lhs_atom38(V0t,A_27a)
<=> ap(f18(A_27a),V0t) = f17(A_27a,V0t) ),
inference(definition,[],[]) ).
fof(to_be_clausified_74,plain,
! [A_27a,V0t] :
( lhs_atom38(V0t,A_27a)
| $false ),
inference(fold_definition,[status(thm)],[lameq_f18_0,def_lhs_atom38]) ).
fof(to_be_clausified_75,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| c_2Ebool_2ECOND(A_27a) = f18(A_27a) ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2ECOND__DEF_0,def_lhs_atom7]) ).
fof(to_be_clausified_76,plain,
! [A_27a,A_27b,V0f] :
( lhs_atom34(V0f,A_27b,A_27a)
| ! [V1x1] :
( mem(V1x1,A_27a)
=> ! [V2x2] : ap(f19(A_27b,A_27a,V0f,V1x1),V2x2) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(A_27b),ap(V0f,V1x1)),ap(V0f,V2x2))),ap(ap(c_2Emin_2E_3D(A_27a),V1x1),V2x2)) ) ),
inference(fold_definition,[status(thm)],[lameq_f19_0,def_lhs_atom34]) ).
fof(to_be_clausified_77,plain,
! [A_27a,A_27b,V0f] :
( lhs_atom34(V0f,A_27b,A_27a)
| ! [V1x1] : ap(f20(A_27b,A_27a,V0f),V1x1) = ap(c_2Ebool_2E_21(A_27a),f19(A_27b,A_27a,V0f,V1x1)) ),
inference(fold_definition,[status(thm)],[lameq_f20_0,def_lhs_atom34]) ).
fof(def_lhs_atom39,axiom,
! [V0f,A_27b,A_27a] :
( lhs_atom39(V0f,A_27b,A_27a)
<=> ap(f21(A_27b,A_27a),V0f) = ap(c_2Ebool_2E_21(A_27a),f20(A_27b,A_27a,V0f)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_78,plain,
! [A_27a,A_27b,V0f] :
( lhs_atom39(V0f,A_27b,A_27a)
| $false ),
inference(fold_definition,[status(thm)],[lameq_f21_0,def_lhs_atom39]) ).
fof(to_be_clausified_79,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> c_2Ebool_2EONE__ONE(A_27a,A_27b) = f21(A_27b,A_27a) ) ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2EONE__ONE__DEF_0,def_lhs_atom7]) ).
fof(to_be_clausified_80,plain,
! [A_27a,A_27b,V0f] :
( lhs_atom34(V0f,A_27b,A_27a)
| ! [V1y] :
( mem(V1y,A_27b)
=> ! [V2x] : ap(f22(A_27b,A_27a,V0f,V1y),V2x) = ap(ap(c_2Emin_2E_3D(A_27b),V1y),ap(V0f,V2x)) ) ),
inference(fold_definition,[status(thm)],[lameq_f22_0,def_lhs_atom34]) ).
fof(to_be_clausified_81,plain,
! [A_27a,A_27b,V0f] :
( lhs_atom34(V0f,A_27b,A_27a)
| ! [V1y] : ap(f23(A_27a,A_27b,V0f),V1y) = ap(c_2Ebool_2E_3F(A_27a),f22(A_27b,A_27a,V0f,V1y)) ),
inference(fold_definition,[status(thm)],[lameq_f23_0,def_lhs_atom34]) ).
fof(def_lhs_atom40,axiom,
! [V0f,A_27b,A_27a] :
( lhs_atom40(V0f,A_27b,A_27a)
<=> ap(f24(A_27a,A_27b),V0f) = ap(c_2Ebool_2E_21(A_27b),f23(A_27a,A_27b,V0f)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_82,plain,
! [A_27a,A_27b,V0f] :
( lhs_atom40(V0f,A_27b,A_27a)
| $false ),
inference(fold_definition,[status(thm)],[lameq_f24_0,def_lhs_atom40]) ).
fof(to_be_clausified_83,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> c_2Ebool_2EONTO(A_27a,A_27b) = f24(A_27a,A_27b) ) ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2EONTO__DEF_0,def_lhs_atom7]) ).
fof(def_lhs_atom41,axiom,
! [V1rep,A_27b,A_27a] :
( lhs_atom41(V1rep,A_27b,A_27a)
<=> ~ mem(V1rep,arr(A_27b,A_27a)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_84,plain,
! [A_27a,A_27b,V1rep] :
( lhs_atom41(V1rep,A_27b,A_27a)
| ! [V2x_27] :
( mem(V2x_27,A_27b)
=> ! [V3x_27_27] : ap(f25(A_27a,A_27b,V1rep,V2x_27),V3x_27_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(A_27a),ap(V1rep,V2x_27)),ap(V1rep,V3x_27_27))),ap(ap(c_2Emin_2E_3D(A_27b),V2x_27),V3x_27_27)) ) ),
inference(fold_definition,[status(thm)],[lameq_f25_0,def_lhs_atom41]) ).
fof(to_be_clausified_85,plain,
! [A_27a,A_27b,V1rep] :
( lhs_atom41(V1rep,A_27b,A_27a)
| ! [V2x_27] : ap(f26(A_27a,A_27b,V1rep),V2x_27) = ap(c_2Ebool_2E_21(A_27b),f25(A_27a,A_27b,V1rep,V2x_27)) ),
inference(fold_definition,[status(thm)],[lameq_f26_0,def_lhs_atom41]) ).
fof(to_be_clausified_86,plain,
! [A_27a,A_27b,V1rep] :
( lhs_atom41(V1rep,A_27b,A_27a)
| ! [V4x] :
( mem(V4x,A_27a)
=> ! [V5x_27] : ap(f27(A_27a,A_27b,V1rep,V4x),V5x_27) = ap(ap(c_2Emin_2E_3D(A_27a),V4x),ap(V1rep,V5x_27)) ) ),
inference(fold_definition,[status(thm)],[lameq_f27_0,def_lhs_atom41]) ).
fof(to_be_clausified_87,plain,
! [A_27a,A_27b,V0P] :
( lhs_atom32(V0P,A_27a)
| ! [V1rep] :
( mem(V1rep,arr(A_27b,A_27a))
=> ! [V4x] : ap(f28(A_27b,A_27a,V0P,V1rep),V4x) = ap(ap(c_2Emin_2E_3D(bool),ap(V0P,V4x)),ap(c_2Ebool_2E_3F(A_27b),f27(A_27a,A_27b,V1rep,V4x))) ) ),
inference(fold_definition,[status(thm)],[lameq_f28_0,def_lhs_atom32]) ).
fof(to_be_clausified_88,plain,
! [A_27a,A_27b,V0P] :
( lhs_atom32(V0P,A_27a)
| ! [V1rep] : ap(f29(A_27b,A_27a,V0P),V1rep) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_21(A_27b),f26(A_27a,A_27b,V1rep))),ap(c_2Ebool_2E_21(A_27a),f28(A_27b,A_27a,V0P,V1rep))) ),
inference(fold_definition,[status(thm)],[lameq_f29_0,def_lhs_atom32]) ).
fof(def_lhs_atom42,axiom,
! [V0P,A_27b,A_27a] :
( lhs_atom42(V0P,A_27b,A_27a)
<=> ap(f30(A_27b,A_27a),V0P) = f29(A_27b,A_27a,V0P) ),
inference(definition,[],[]) ).
fof(to_be_clausified_89,plain,
! [A_27a,A_27b,V0P] :
( lhs_atom42(V0P,A_27b,A_27a)
| $false ),
inference(fold_definition,[status(thm)],[lameq_f30_0,def_lhs_atom42]) ).
fof(to_be_clausified_90,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> c_2Ebool_2ETYPE__DEFINITION(A_27a,A_27b) = f30(A_27b,A_27a) ) ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2ETYPE__DEFINITION_0,def_lhs_atom7]) ).
fof(to_be_clausified_91,plain,
! [V0t] :
( lhs_atom37(V0t)
| ( p(V0t)
<=> $true )
| ( p(V0t)
<=> $false ) ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2EBOOL__CASES__AX_0,def_lhs_atom37]) ).
fof(def_lhs_atom43,axiom,
! [V0t,A_27b,A_27a] :
( lhs_atom43(V0t,A_27b,A_27a)
<=> ~ mem(V0t,arr(A_27a,A_27b)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_92,plain,
! [A_27a,A_27b,V0t] :
( lhs_atom43(V0t,A_27b,A_27a)
| ! [V1x] : ap(f31(A_27b,A_27a,V0t),V1x) = ap(V0t,V1x) ),
inference(fold_definition,[status(thm)],[lameq_f31_0,def_lhs_atom43]) ).
fof(to_be_clausified_93,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> ! [V0t] :
( mem(V0t,arr(A_27a,A_27b))
=> f31(A_27b,A_27a,V0t) = V0t ) ) ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2EETA__AX_0,def_lhs_atom7]) ).
fof(to_be_clausified_94,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| ! [V0P] :
( mem(V0P,arr(A_27a,bool))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ( p(ap(V0P,V1x))
=> p(ap(V0P,ap(c_2Emin_2E_40(A_27a),V0P))) ) ) ) ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2ESELECT__AX_0,def_lhs_atom7]) ).
fof(to_be_clausified_95,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> c_2Ebool_2Eliteral__case(A_27a,A_27b) = f14(A_27b,A_27a) ) ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2Eliteral__case__DEF_0,def_lhs_atom7]) ).
fof(def_lhs_atom44,axiom,
! [V0x,A_27a] :
( lhs_atom44(V0x,A_27a)
<=> ~ mem(V0x,A_27a) ),
inference(definition,[],[]) ).
fof(to_be_clausified_96,plain,
! [A_27a,V0x] :
( lhs_atom44(V0x,A_27a)
| ! [V1f] : ap(f32(A_27a,V0x),V1f) = ap(V1f,V0x) ),
inference(fold_definition,[status(thm)],[lameq_f32_0,def_lhs_atom44]) ).
fof(def_lhs_atom45,axiom,
! [V0x,A_27a] :
( lhs_atom45(V0x,A_27a)
<=> ap(f33(A_27a),V0x) = f32(A_27a,V0x) ),
inference(definition,[],[]) ).
fof(to_be_clausified_97,plain,
! [A_27a,V0x] :
( lhs_atom45(V0x,A_27a)
| $false ),
inference(fold_definition,[status(thm)],[lameq_f33_0,def_lhs_atom45]) ).
fof(to_be_clausified_98,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| c_2Ebool_2EIN(A_27a) = f33(A_27a) ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2EIN__DEF_0,def_lhs_atom7]) ).
fof(def_lhs_atom46,axiom,
! [V0p,A_27a] :
( lhs_atom46(V0p,A_27a)
<=> ~ mem(V0p,arr(A_27a,bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_99,plain,
! [A_27a,V0p] :
( lhs_atom46(V0p,A_27a)
| ! [V1m] :
( mem(V1m,arr(A_27a,bool))
=> ! [V2x] : ap(f34(A_27a,V0p,V1m),V2x) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0p)),ap(V1m,V2x)) ) ),
inference(fold_definition,[status(thm)],[lameq_f34_0,def_lhs_atom46]) ).
fof(to_be_clausified_100,plain,
! [A_27a,V0p] :
( lhs_atom46(V0p,A_27a)
| ! [V1m] : ap(f35(A_27a,V0p),V1m) = ap(c_2Ebool_2E_21(A_27a),f34(A_27a,V0p,V1m)) ),
inference(fold_definition,[status(thm)],[lameq_f35_0,def_lhs_atom46]) ).
fof(def_lhs_atom47,axiom,
! [V0p,A_27a] :
( lhs_atom47(V0p,A_27a)
<=> ap(f36(A_27a),V0p) = f35(A_27a,V0p) ),
inference(definition,[],[]) ).
fof(to_be_clausified_101,plain,
! [A_27a,V0p] :
( lhs_atom47(V0p,A_27a)
| $false ),
inference(fold_definition,[status(thm)],[lameq_f36_0,def_lhs_atom47]) ).
fof(to_be_clausified_102,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| c_2Ebool_2ERES__FORALL(A_27a) = f36(A_27a) ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2ERES__FORALL__DEF_0,def_lhs_atom7]) ).
fof(to_be_clausified_103,plain,
! [A_27a,V0p] :
( lhs_atom46(V0p,A_27a)
| ! [V1m] :
( mem(V1m,arr(A_27a,bool))
=> ! [V2x] : ap(f37(A_27a,V0p,V1m),V2x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0p)),ap(V1m,V2x)) ) ),
inference(fold_definition,[status(thm)],[lameq_f37_0,def_lhs_atom46]) ).
fof(to_be_clausified_104,plain,
! [A_27a,V0p] :
( lhs_atom46(V0p,A_27a)
| ! [V1m] : ap(f38(A_27a,V0p),V1m) = ap(c_2Ebool_2E_3F(A_27a),f37(A_27a,V0p,V1m)) ),
inference(fold_definition,[status(thm)],[lameq_f38_0,def_lhs_atom46]) ).
fof(def_lhs_atom48,axiom,
! [V0p,A_27a] :
( lhs_atom48(V0p,A_27a)
<=> ap(f39(A_27a),V0p) = f38(A_27a,V0p) ),
inference(definition,[],[]) ).
fof(to_be_clausified_105,plain,
! [A_27a,V0p] :
( lhs_atom48(V0p,A_27a)
| $false ),
inference(fold_definition,[status(thm)],[lameq_f39_0,def_lhs_atom48]) ).
fof(to_be_clausified_106,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| c_2Ebool_2ERES__EXISTS(A_27a) = f39(A_27a) ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2ERES__EXISTS__DEF_0,def_lhs_atom7]) ).
fof(def_lhs_atom49,axiom,
! [V1m,A_27a] :
( lhs_atom49(V1m,A_27a)
<=> ~ mem(V1m,arr(A_27a,bool)) ),
inference(definition,[],[]) ).
fof(to_be_clausified_107,plain,
! [A_27a,V1m] :
( lhs_atom49(V1m,A_27a)
| ! [V2x] : ap(f40(A_27a,V1m),V2x) = ap(V1m,V2x) ),
inference(fold_definition,[status(thm)],[lameq_f40_0,def_lhs_atom49]) ).
fof(to_be_clausified_108,plain,
! [A_27a,V1m] :
( lhs_atom49(V1m,A_27a)
| ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4y] : ap(f41(A_27a,V1m,V3x),V4y) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(V1m,V3x)),ap(V1m,V4y))),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V4y)) ) ),
inference(fold_definition,[status(thm)],[lameq_f41_0,def_lhs_atom49]) ).
fof(to_be_clausified_109,plain,
! [A_27a,V1m] :
( lhs_atom49(V1m,A_27a)
| ! [V0p] :
( mem(V0p,arr(A_27a,bool))
=> ! [V3x] : ap(f42(A_27a,V1m,V0p),V3x) = ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0p),f41(A_27a,V1m,V3x)) ) ),
inference(fold_definition,[status(thm)],[lameq_f42_0,def_lhs_atom49]) ).
fof(to_be_clausified_110,plain,
! [A_27a,V0p] :
( lhs_atom46(V0p,A_27a)
| ! [V1m] : ap(f43(A_27a,V0p),V1m) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0p),f40(A_27a,V1m))),ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0p),f42(A_27a,V1m,V0p))) ),
inference(fold_definition,[status(thm)],[lameq_f43_0,def_lhs_atom46]) ).
fof(def_lhs_atom50,axiom,
! [V0p,A_27a] :
( lhs_atom50(V0p,A_27a)
<=> ap(f44(A_27a),V0p) = f43(A_27a,V0p) ),
inference(definition,[],[]) ).
fof(to_be_clausified_111,plain,
! [A_27a,V0p] :
( lhs_atom50(V0p,A_27a)
| $false ),
inference(fold_definition,[status(thm)],[lameq_f44_0,def_lhs_atom50]) ).
fof(to_be_clausified_112,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a) = f44(A_27a) ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2ERES__EXISTS__UNIQUE__DEF_0,def_lhs_atom7]) ).
fof(to_be_clausified_113,plain,
! [A_27a,V0p] :
( lhs_atom46(V0p,A_27a)
| ! [V1m] : ap(f45(A_27a,V0p),V1m) = ap(c_2Emin_2E_40(A_27a),f37(A_27a,V0p,V1m)) ),
inference(fold_definition,[status(thm)],[lameq_f45_0,def_lhs_atom46]) ).
fof(def_lhs_atom51,axiom,
! [V0p,A_27a] :
( lhs_atom51(V0p,A_27a)
<=> ap(f46(A_27a),V0p) = f45(A_27a,V0p) ),
inference(definition,[],[]) ).
fof(to_be_clausified_114,plain,
! [A_27a,V0p] :
( lhs_atom51(V0p,A_27a)
| $false ),
inference(fold_definition,[status(thm)],[lameq_f46_0,def_lhs_atom51]) ).
fof(to_be_clausified_115,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| c_2Ebool_2ERES__SELECT(A_27a) = f46(A_27a) ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2ERES__SELECT__DEF_0,def_lhs_atom7]) ).
fof(def_lhs_atom52,axiom,
( lhs_atom52
<=> c_2Ebool_2EBOUNDED = k(bool,c_2Ebool_2ET) ),
inference(definition,[],[]) ).
fof(to_be_clausified_116,plain,
( lhs_atom52
| $false ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2EBOUNDED__DEF_0,def_lhs_atom52]) ).
fof(to_be_clausified_117,plain,
! [A_27a] :
( lhs_atom7(A_27a)
| c_2Ebool_2EDATATYPE(A_27a) = k(A_27a,c_2Ebool_2ET) ),
inference(fold_definition,[status(thm)],[ax_thm_2Ebool_2EDATATYPE__TAG__DEF_0,def_lhs_atom7]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X20,X9] :
( lhs_atom36(X20,X9)
| ! [X21] :
( mem(X21,X9)
=> ! [X16] :
( mem(X16,bool)
=> ! [X22] : ap(f15(X9,X20,X21,X16),X22) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),X16),c_2Ebool_2ET)),ap(ap(c_2Emin_2E_3D(X9),X22),X20))),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),X16),c_2Ebool_2EF)),ap(ap(c_2Emin_2E_3D(X9),X22),X21))) ) ) ),
file('<stdin>',to_be_clausified_71) ).
fof(c_0_1,axiom,
! [X3,X2,X1] :
( lhs_atom4(X3,X2,X1)
| ! [X7] :
( mem(X7,arr(X1,X2))
=> ( ! [X4] :
( mem(X4,X1)
=> ap(X3,X4) = ap(X7,X4) )
=> X3 = X7 ) ) ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_2,axiom,
! [X12,X11,X9] :
( lhs_atom32(X12,X9)
| ! [X27] :
( mem(X27,arr(X11,X9))
=> ! [X30] : ap(f28(X11,X9,X12,X27),X30) = ap(ap(c_2Emin_2E_3D(bool),ap(X12,X30)),ap(c_2Ebool_2E_3F(X11),f27(X9,X11,X27,X30))) ) ),
file('<stdin>',to_be_clausified_87) ).
fof(c_0_3,axiom,
! [X12,X11,X9] :
( lhs_atom32(X12,X9)
| ! [X27] : ap(f29(X11,X9,X12),X27) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_21(X11),f26(X9,X11,X27))),ap(c_2Ebool_2E_21(X9),f28(X11,X9,X12,X27))) ),
file('<stdin>',to_be_clausified_88) ).
fof(c_0_4,axiom,
! [X27,X11,X9] :
( lhs_atom41(X27,X11,X9)
| ! [X28] :
( mem(X28,X11)
=> ! [X29] : ap(f25(X9,X11,X27,X28),X29) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(X9),ap(X27,X28)),ap(X27,X29))),ap(ap(c_2Emin_2E_3D(X11),X28),X29)) ) ),
file('<stdin>',to_be_clausified_84) ).
fof(c_0_5,axiom,
! [X19,X11,X9] :
( lhs_atom34(X19,X11,X9)
| ! [X23] :
( mem(X23,X9)
=> ! [X24] : ap(f19(X11,X9,X19,X23),X24) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(X11),ap(X19,X23)),ap(X19,X24))),ap(ap(c_2Emin_2E_3D(X9),X23),X24)) ) ),
file('<stdin>',to_be_clausified_76) ).
fof(c_0_6,axiom,
! [X35,X9] :
( lhs_atom49(X35,X9)
| ! [X22] :
( mem(X22,X9)
=> ! [X36] : ap(f41(X9,X35,X22),X36) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(X35,X22)),ap(X35,X36))),ap(ap(c_2Emin_2E_3D(X9),X22),X36)) ) ),
file('<stdin>',to_be_clausified_108) ).
fof(c_0_7,axiom,
! [X12,X9] :
( lhs_atom32(X12,X9)
| ! [X17] :
( mem(X17,X9)
=> ! [X18] : ap(f10(X9,X12,X17),X18) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(X12,X17)),ap(X12,X18))),ap(ap(c_2Emin_2E_3D(X9),X17),X18)) ) ),
file('<stdin>',to_be_clausified_64) ).
fof(c_0_8,axiom,
! [X34,X9] :
( lhs_atom46(X34,X9)
| ! [X35] : ap(f43(X9,X34),X35) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2ERES__EXISTS(X9),X34),f40(X9,X35))),ap(ap(c_2Ebool_2ERES__FORALL(X9),X34),f42(X9,X35,X34))) ),
file('<stdin>',to_be_clausified_110) ).
fof(c_0_9,axiom,
! [X27,X11,X9] :
( lhs_atom41(X27,X11,X9)
| ! [X28] : ap(f26(X9,X11,X27),X28) = ap(c_2Ebool_2E_21(X11),f25(X9,X11,X27,X28)) ),
file('<stdin>',to_be_clausified_85) ).
fof(c_0_10,axiom,
! [X19,X11,X9] :
( lhs_atom34(X19,X11,X9)
| ! [X25] : ap(f23(X9,X11,X19),X25) = ap(c_2Ebool_2E_3F(X9),f22(X11,X9,X19,X25)) ),
file('<stdin>',to_be_clausified_81) ).
fof(c_0_11,axiom,
! [X19,X11,X9] :
( lhs_atom34(X19,X11,X9)
| ! [X23] : ap(f20(X11,X9,X19),X23) = ap(c_2Ebool_2E_21(X9),f19(X11,X9,X19,X23)) ),
file('<stdin>',to_be_clausified_77) ).
fof(c_0_12,axiom,
! [X27,X11,X9] :
( lhs_atom41(X27,X11,X9)
| ! [X30] :
( mem(X30,X9)
=> ! [X31] : ap(f27(X9,X11,X27,X30),X31) = ap(ap(c_2Emin_2E_3D(X9),X30),ap(X27,X31)) ) ),
file('<stdin>',to_be_clausified_86) ).
fof(c_0_13,axiom,
! [X19,X11,X9] :
( lhs_atom34(X19,X11,X9)
| ! [X25] :
( mem(X25,X11)
=> ! [X26] : ap(f22(X11,X9,X19,X25),X26) = ap(ap(c_2Emin_2E_3D(X11),X25),ap(X19,X26)) ) ),
file('<stdin>',to_be_clausified_80) ).
fof(c_0_14,axiom,
! [X16,X9] :
( lhs_atom37(X16)
| ! [X20] :
( mem(X20,X9)
=> ! [X21] : ap(f16(X9,X16,X20),X21) = ap(c_2Emin_2E_40(X9),f15(X9,X20,X21,X16)) ) ),
file('<stdin>',to_be_clausified_72) ).
fof(c_0_15,axiom,
! [X14] :
( lhs_atom23(X14)
| ! [X13] :
( mem(X13,bool)
=> ! [X15] : ap(f6(X14,X13),X15) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,X14),X15)),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,X13),X15)),X15)) ) ),
file('<stdin>',to_be_clausified_56) ).
fof(c_0_16,axiom,
! [X13] :
( lhs_atom22(X13)
| ! [X14] :
( mem(X14,bool)
=> ! [X15] : ap(f3(X13,X14),X15) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,X14),ap(ap(c_2Emin_2E_3D_3D_3E,X13),X15))),X15) ) ),
file('<stdin>',to_be_clausified_52) ).
fof(c_0_17,axiom,
! [X34,X9] :
( lhs_atom46(X34,X9)
| ! [X35] :
( mem(X35,arr(X9,bool))
=> ! [X26] : ap(f37(X9,X34,X35),X26) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(X9),X26),X34)),ap(X35,X26)) ) ),
file('<stdin>',to_be_clausified_103) ).
fof(c_0_18,axiom,
! [X34,X9] :
( lhs_atom46(X34,X9)
| ! [X35] :
( mem(X35,arr(X9,bool))
=> ! [X26] : ap(f34(X9,X34,X35),X26) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(X9),X26),X34)),ap(X35,X26)) ) ),
file('<stdin>',to_be_clausified_99) ).
fof(c_0_19,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> mem(c_2Ebool_2ERES__ABSTRACT(X9,X11),arr(arr(X9,bool),arr(arr(X9,X11),arr(X9,X11)))) ) ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_20,axiom,
! [X35,X9] :
( lhs_atom49(X35,X9)
| ! [X34] :
( mem(X34,arr(X9,bool))
=> ! [X22] : ap(f42(X9,X35,X34),X22) = ap(ap(c_2Ebool_2ERES__FORALL(X9),X34),f41(X9,X35,X22)) ) ),
file('<stdin>',to_be_clausified_109) ).
fof(c_0_21,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> mem(c_2Ebool_2ETYPE__DEFINITION(X9,X11),arr(arr(X9,bool),arr(arr(X11,X9),bool))) ) ),
file('<stdin>',to_be_clausified_38) ).
fof(c_0_22,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X12] :
( mem(X12,arr(X9,bool))
=> ! [X17] :
( mem(X17,X9)
=> ( p(ap(X12,X17))
=> p(ap(X12,ap(c_2Emin_2E_40(X9),X12))) ) ) ) ),
file('<stdin>',to_be_clausified_94) ).
fof(c_0_23,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2ERES__SELECT(X9),arr(arr(X9,bool),arr(arr(X9,bool),X9))) ),
file('<stdin>',to_be_clausified_35) ).
fof(c_0_24,axiom,
! [X1] :
( lhs_atom3(X1)
| ! [X5] :
( mem(X5,arr(X1,bool))
=> ( p(ap(c_2Ebool_2E_21(X1),X5))
<=> ! [X4] :
( mem(X4,X1)
=> p(ap(X5,X4)) ) ) ) ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_25,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2ERES__FORALL(X9),arr(arr(X9,bool),arr(arr(X9,bool),bool))) ),
file('<stdin>',to_be_clausified_34) ).
fof(c_0_26,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2ERES__EXISTS__UNIQUE(X9),arr(arr(X9,bool),arr(arr(X9,bool),bool))) ),
file('<stdin>',to_be_clausified_33) ).
fof(c_0_27,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2ERES__EXISTS(X9),arr(arr(X9,bool),arr(arr(X9,bool),bool))) ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_28,axiom,
! [X1] :
( lhs_atom3(X1)
| ! [X4] :
( mem(X4,X1)
=> ! [X8] :
( mem(X8,X1)
=> ( p(ap(ap(c_2Emin_2E_3D(X1),X4),X8))
<=> X4 = X8 ) ) ) ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_29,axiom,
! [X1] :
( lhs_atom3(X1)
| ! [X5] :
( mem(X5,arr(X1,bool))
=> ( p(ap(c_2Ebool_2E_3F(X1),X5))
<=> ? [X4] :
( mem(X4,X1)
& p(ap(X5,X4)) ) ) ) ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_30,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2ECOND(X9),arr(bool,arr(X9,arr(X9,X9)))) ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_31,axiom,
! [X16,X11,X9] :
( lhs_atom43(X16,X11,X9)
| ! [X17] : ap(f31(X11,X9,X16),X17) = ap(X16,X17) ),
file('<stdin>',to_be_clausified_92) ).
fof(c_0_32,axiom,
! [X19,X11,X9] :
( lhs_atom34(X19,X11,X9)
| ! [X17] : ap(f13(X11,X9,X19),X17) = ap(X19,X17) ),
file('<stdin>',to_be_clausified_68) ).
fof(c_0_33,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2EIN(X9),arr(X9,arr(arr(X9,bool),bool))) ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_34,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> mem(c_2Ebool_2Eliteral__case(X9,X11),arr(arr(X9,X11),arr(X9,X11))) ) ),
file('<stdin>',to_be_clausified_42) ).
fof(c_0_35,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> mem(c_2Ebool_2ELET(X9,X11),arr(arr(X9,X11),arr(X9,X11))) ) ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_36,axiom,
! [X34,X9] :
( lhs_atom46(X34,X9)
| ! [X35] : ap(f45(X9,X34),X35) = ap(c_2Emin_2E_40(X9),f37(X9,X34,X35)) ),
file('<stdin>',to_be_clausified_113) ).
fof(c_0_37,axiom,
! [X34,X9] :
( lhs_atom46(X34,X9)
| ! [X35] : ap(f38(X9,X34),X35) = ap(c_2Ebool_2E_3F(X9),f37(X9,X34,X35)) ),
file('<stdin>',to_be_clausified_104) ).
fof(c_0_38,axiom,
! [X34,X9] :
( lhs_atom46(X34,X9)
| ! [X35] : ap(f35(X9,X34),X35) = ap(c_2Ebool_2E_21(X9),f34(X9,X34,X35)) ),
file('<stdin>',to_be_clausified_100) ).
fof(c_0_39,axiom,
! [X12,X9] :
( lhs_atom32(X12,X9)
| ! [X17] : ap(f11(X9,X12),X17) = ap(c_2Ebool_2E_21(X9),f10(X9,X12,X17)) ),
file('<stdin>',to_be_clausified_65) ).
fof(c_0_40,axiom,
! [X5] :
( lhs_atom5(X5)
| ! [X6] :
( mem(X6,bool)
=> ( p(ap(ap(c_2Emin_2E_3D_3D_3E,X5),X6))
<=> ( p(X5)
=> p(X6) ) ) ) ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_41,axiom,
! [X5] :
( lhs_atom5(X5)
| ! [X6] :
( mem(X6,bool)
=> ( p(ap(ap(c_2Ebool_2E_5C_2F,X5),X6))
<=> ( p(X5)
| p(X6) ) ) ) ),
file('<stdin>',to_be_clausified_40) ).
fof(c_0_42,axiom,
! [X5] :
( lhs_atom5(X5)
| ! [X6] :
( mem(X6,bool)
=> ( p(ap(ap(c_2Ebool_2E_2F_5C,X5),X6))
<=> ( p(X5)
& p(X6) ) ) ) ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_43,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> mem(c_2Ebool_2Eitself__case(X9,X11),arr(ty_2Ebool_2Eitself(X9),arr(X11,X11))) ) ),
file('<stdin>',to_be_clausified_41) ).
fof(c_0_44,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> ! [X16] :
( mem(X16,arr(X9,X11))
=> f31(X11,X9,X16) = X16 ) ) ),
file('<stdin>',to_be_clausified_93) ).
fof(c_0_45,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> mem(c_2Ebool_2EONTO(X9,X11),arr(arr(X9,X11),bool)) ) ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_46,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> mem(c_2Ebool_2EONE__ONE(X9,X11),arr(arr(X9,X11),bool)) ) ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_47,axiom,
! [X3,X2,X1] :
( lhs_atom4(X3,X2,X1)
| ! [X4] :
( mem(X4,X1)
=> mem(ap(X3,X4),X2) ) ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_48,axiom,
! [X16,X9] :
( lhs_atom37(X16)
| ! [X20] : ap(f17(X9,X16),X20) = f16(X9,X16,X20) ),
file('<stdin>',to_be_clausified_73) ).
fof(c_0_49,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Emin_2E_40(X9),arr(arr(X9,bool),X9)) ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_50,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Emin_2E_3D(X9),arr(X9,arr(X9,bool))) ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_51,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2E_3F_21(X9),arr(arr(X9,bool),bool)) ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_52,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2E_3F(X9),arr(arr(X9,bool),bool)) ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_53,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2E_21(X9),arr(arr(X9,bool),bool)) ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_54,axiom,
! [X35,X9] :
( lhs_atom49(X35,X9)
| ! [X26] : ap(f40(X9,X35),X26) = ap(X35,X26) ),
file('<stdin>',to_be_clausified_107) ).
fof(c_0_55,axiom,
! [X32,X9] :
( lhs_atom44(X32,X9)
| ! [X33] : ap(f32(X9,X32),X33) = ap(X33,X32) ),
file('<stdin>',to_be_clausified_96) ).
fof(c_0_56,axiom,
! [X14] :
( lhs_atom23(X14)
| ! [X13] : ap(f7(X14),X13) = ap(c_2Ebool_2E_21(bool),f6(X14,X13)) ),
file('<stdin>',to_be_clausified_57) ).
fof(c_0_57,axiom,
! [X14] :
( lhs_atom23(X14)
| ! [X13] : ap(f4(X14),X13) = ap(c_2Ebool_2E_21(bool),f3(X13,X14)) ),
file('<stdin>',to_be_clausified_53) ).
fof(c_0_58,axiom,
! [X8,X4,X1] :
( lhs_atom6(X4,X1)
| ap(k(X1,X8),X4) = X8 ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_59,axiom,
! [X12,X11,X9] :
( lhs_atom42(X12,X11,X9)
| ~ $true ),
file('<stdin>',to_be_clausified_89) ).
fof(c_0_60,axiom,
! [X19,X11,X9] :
( lhs_atom40(X19,X11,X9)
| ~ $true ),
file('<stdin>',to_be_clausified_82) ).
fof(c_0_61,axiom,
! [X19,X11,X9] :
( lhs_atom39(X19,X11,X9)
| ~ $true ),
file('<stdin>',to_be_clausified_78) ).
fof(c_0_62,axiom,
! [X19,X11,X9] :
( lhs_atom35(X19,X11,X9)
| ~ $true ),
file('<stdin>',to_be_clausified_69) ).
fof(c_0_63,axiom,
! [X5] :
( lhs_atom5(X5)
| ( p(ap(c_2Ebool_2E_7E,X5))
<=> ~ p(X5) ) ),
file('<stdin>',to_be_clausified_45) ).
fof(c_0_64,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2EDATATYPE(X9),arr(X9,bool)) ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_65,axiom,
! [X1] :
( lhs_atom3(X1)
| ! [X2] :
( ne(X2)
=> ne(arr(X1,X2)) ) ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_66,axiom,
! [X5] :
( lhs_atom5(X5)
| ! [X6] :
( mem(X6,bool)
=> ( ( p(X5)
<=> p(X6) )
=> X5 = X6 ) ) ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_67,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> c_2Ebool_2Eliteral__case(X9,X11) = f14(X11,X9) ) ),
file('<stdin>',to_be_clausified_95) ).
fof(c_0_68,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> c_2Ebool_2ETYPE__DEFINITION(X9,X11) = f30(X11,X9) ) ),
file('<stdin>',to_be_clausified_90) ).
fof(c_0_69,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> c_2Ebool_2EONTO(X9,X11) = f24(X9,X11) ) ),
file('<stdin>',to_be_clausified_83) ).
fof(c_0_70,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> c_2Ebool_2EONE__ONE(X9,X11) = f21(X11,X9) ) ),
file('<stdin>',to_be_clausified_79) ).
fof(c_0_71,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> c_2Ebool_2ELET(X9,X11) = f14(X11,X9) ) ),
file('<stdin>',to_be_clausified_70) ).
fof(c_0_72,axiom,
! [X4,X1] :
( lhs_atom6(X4,X1)
| ap(i(X1),X4) = X4 ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_73,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2Ethe__value(X9),ty_2Ebool_2Eitself(X9)) ),
file('<stdin>',to_be_clausified_43) ).
fof(c_0_74,axiom,
( lhs_atom28
| ! [X16] :
( mem(X16,bool)
=> p(X16) ) ),
file('<stdin>',to_be_clausified_60) ).
fof(c_0_75,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2EARB(X9),X9) ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_76,axiom,
! [X9] :
( lhs_atom7(X9)
| c_2Ebool_2EDATATYPE(X9) = k(X9,c_2Ebool_2ET) ),
file('<stdin>',to_be_clausified_117) ).
fof(c_0_77,axiom,
! [X16] :
( lhs_atom37(X16)
| ( p(X16)
<=> $true )
| ( p(X16)
<=> ~ $true ) ),
file('<stdin>',to_be_clausified_91) ).
fof(c_0_78,axiom,
! [X10] :
( lhs_atom9(X10)
| ne(ty_2Ebool_2Eitself(X10)) ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_79,axiom,
! [X34,X9] :
( lhs_atom51(X34,X9)
| ~ $true ),
file('<stdin>',to_be_clausified_114) ).
fof(c_0_80,axiom,
! [X34,X9] :
( lhs_atom50(X34,X9)
| ~ $true ),
file('<stdin>',to_be_clausified_111) ).
fof(c_0_81,axiom,
! [X34,X9] :
( lhs_atom48(X34,X9)
| ~ $true ),
file('<stdin>',to_be_clausified_105) ).
fof(c_0_82,axiom,
! [X34,X9] :
( lhs_atom47(X34,X9)
| ~ $true ),
file('<stdin>',to_be_clausified_101) ).
fof(c_0_83,axiom,
! [X32,X9] :
( lhs_atom45(X32,X9)
| ~ $true ),
file('<stdin>',to_be_clausified_97) ).
fof(c_0_84,axiom,
! [X16,X9] :
( lhs_atom38(X16,X9)
| ~ $true ),
file('<stdin>',to_be_clausified_74) ).
fof(c_0_85,axiom,
! [X12,X9] :
( lhs_atom33(X12,X9)
| ~ $true ),
file('<stdin>',to_be_clausified_66) ).
fof(c_0_86,axiom,
! [X12,X9] :
( lhs_atom21(X12,X9)
| ~ $true ),
file('<stdin>',to_be_clausified_50) ).
fof(c_0_87,axiom,
! [X12,X9] :
( lhs_atom20(X12,X9)
| ~ $true ),
file('<stdin>',to_be_clausified_48) ).
fof(c_0_88,axiom,
! [X9] :
( lhs_atom7(X9)
| c_2Ebool_2ERES__SELECT(X9) = f46(X9) ),
file('<stdin>',to_be_clausified_115) ).
fof(c_0_89,axiom,
! [X9] :
( lhs_atom7(X9)
| c_2Ebool_2ERES__EXISTS__UNIQUE(X9) = f44(X9) ),
file('<stdin>',to_be_clausified_112) ).
fof(c_0_90,axiom,
! [X9] :
( lhs_atom7(X9)
| c_2Ebool_2ERES__EXISTS(X9) = f39(X9) ),
file('<stdin>',to_be_clausified_106) ).
fof(c_0_91,axiom,
! [X9] :
( lhs_atom7(X9)
| c_2Ebool_2ERES__FORALL(X9) = f36(X9) ),
file('<stdin>',to_be_clausified_102) ).
fof(c_0_92,axiom,
! [X9] :
( lhs_atom7(X9)
| c_2Ebool_2EIN(X9) = f33(X9) ),
file('<stdin>',to_be_clausified_98) ).
fof(c_0_93,axiom,
! [X9] :
( lhs_atom7(X9)
| c_2Ebool_2ECOND(X9) = f18(X9) ),
file('<stdin>',to_be_clausified_75) ).
fof(c_0_94,axiom,
! [X9] :
( lhs_atom7(X9)
| c_2Ebool_2E_3F_21(X9) = f12(X9) ),
file('<stdin>',to_be_clausified_67) ).
fof(c_0_95,axiom,
! [X9] :
( lhs_atom7(X9)
| c_2Ebool_2E_3F(X9) = f2(X9) ),
file('<stdin>',to_be_clausified_51) ).
fof(c_0_96,axiom,
! [X9] :
( lhs_atom7(X9)
| c_2Ebool_2E_21(X9) = f1(X9) ),
file('<stdin>',to_be_clausified_49) ).
fof(c_0_97,axiom,
( lhs_atom29
| ~ ! [X16] :
( mem(X16,bool)
=> p(X16) ) ),
file('<stdin>',to_be_clausified_61) ).
fof(c_0_98,axiom,
( lhs_atom19
| i(bool) != i(bool) ),
file('<stdin>',to_be_clausified_47) ).
fof(c_0_99,axiom,
( lhs_atom18
| i(bool) = i(bool) ),
file('<stdin>',to_be_clausified_46) ).
fof(c_0_100,axiom,
! [X16] :
( lhs_atom30(X16)
| ~ $true ),
file('<stdin>',to_be_clausified_62) ).
fof(c_0_101,axiom,
! [X14] :
( lhs_atom26(X14)
| ~ $true ),
file('<stdin>',to_be_clausified_58) ).
fof(c_0_102,axiom,
! [X14] :
( lhs_atom24(X14)
| ~ $true ),
file('<stdin>',to_be_clausified_54) ).
fof(c_0_103,axiom,
( lhs_atom52
| ~ $true ),
file('<stdin>',to_be_clausified_116) ).
fof(c_0_104,axiom,
( lhs_atom31
| ~ $true ),
file('<stdin>',to_be_clausified_63) ).
fof(c_0_105,axiom,
( lhs_atom27
| ~ $true ),
file('<stdin>',to_be_clausified_59) ).
fof(c_0_106,axiom,
( lhs_atom25
| ~ $true ),
file('<stdin>',to_be_clausified_55) ).
fof(c_0_107,axiom,
( lhs_atom17
| ~ $true ),
file('<stdin>',to_be_clausified_44) ).
fof(c_0_108,axiom,
( lhs_atom16
| ~ $true ),
file('<stdin>',to_be_clausified_39) ).
fof(c_0_109,axiom,
( lhs_atom15
| ~ $true ),
file('<stdin>',to_be_clausified_37) ).
fof(c_0_110,axiom,
( lhs_atom14
| ~ $true ),
file('<stdin>',to_be_clausified_36) ).
fof(c_0_111,axiom,
( lhs_atom13
| ~ $true ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_112,axiom,
( lhs_atom12
| ~ $true ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_113,axiom,
( lhs_atom11
| ~ $true ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_114,axiom,
( lhs_atom10
| ~ $true ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_115,axiom,
( lhs_atom8
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_116,axiom,
( lhs_atom2
| ~ $true ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_117,axiom,
( lhs_atom1
| ~ $true ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_118,axiom,
! [X20,X9] :
( lhs_atom36(X20,X9)
| ! [X21] :
( mem(X21,X9)
=> ! [X16] :
( mem(X16,bool)
=> ! [X22] : ap(f15(X9,X20,X21,X16),X22) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),X16),c_2Ebool_2ET)),ap(ap(c_2Emin_2E_3D(X9),X22),X20))),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),X16),c_2Ebool_2EF)),ap(ap(c_2Emin_2E_3D(X9),X22),X21))) ) ) ),
c_0_0 ).
fof(c_0_119,axiom,
! [X3,X2,X1] :
( lhs_atom4(X3,X2,X1)
| ! [X7] :
( mem(X7,arr(X1,X2))
=> ( ! [X4] :
( mem(X4,X1)
=> ap(X3,X4) = ap(X7,X4) )
=> X3 = X7 ) ) ),
c_0_1 ).
fof(c_0_120,axiom,
! [X12,X11,X9] :
( lhs_atom32(X12,X9)
| ! [X27] :
( mem(X27,arr(X11,X9))
=> ! [X30] : ap(f28(X11,X9,X12,X27),X30) = ap(ap(c_2Emin_2E_3D(bool),ap(X12,X30)),ap(c_2Ebool_2E_3F(X11),f27(X9,X11,X27,X30))) ) ),
c_0_2 ).
fof(c_0_121,axiom,
! [X12,X11,X9] :
( lhs_atom32(X12,X9)
| ! [X27] : ap(f29(X11,X9,X12),X27) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_21(X11),f26(X9,X11,X27))),ap(c_2Ebool_2E_21(X9),f28(X11,X9,X12,X27))) ),
c_0_3 ).
fof(c_0_122,axiom,
! [X27,X11,X9] :
( lhs_atom41(X27,X11,X9)
| ! [X28] :
( mem(X28,X11)
=> ! [X29] : ap(f25(X9,X11,X27,X28),X29) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(X9),ap(X27,X28)),ap(X27,X29))),ap(ap(c_2Emin_2E_3D(X11),X28),X29)) ) ),
c_0_4 ).
fof(c_0_123,axiom,
! [X19,X11,X9] :
( lhs_atom34(X19,X11,X9)
| ! [X23] :
( mem(X23,X9)
=> ! [X24] : ap(f19(X11,X9,X19,X23),X24) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(X11),ap(X19,X23)),ap(X19,X24))),ap(ap(c_2Emin_2E_3D(X9),X23),X24)) ) ),
c_0_5 ).
fof(c_0_124,axiom,
! [X35,X9] :
( lhs_atom49(X35,X9)
| ! [X22] :
( mem(X22,X9)
=> ! [X36] : ap(f41(X9,X35,X22),X36) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(X35,X22)),ap(X35,X36))),ap(ap(c_2Emin_2E_3D(X9),X22),X36)) ) ),
c_0_6 ).
fof(c_0_125,axiom,
! [X12,X9] :
( lhs_atom32(X12,X9)
| ! [X17] :
( mem(X17,X9)
=> ! [X18] : ap(f10(X9,X12,X17),X18) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(X12,X17)),ap(X12,X18))),ap(ap(c_2Emin_2E_3D(X9),X17),X18)) ) ),
c_0_7 ).
fof(c_0_126,axiom,
! [X34,X9] :
( lhs_atom46(X34,X9)
| ! [X35] : ap(f43(X9,X34),X35) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2ERES__EXISTS(X9),X34),f40(X9,X35))),ap(ap(c_2Ebool_2ERES__FORALL(X9),X34),f42(X9,X35,X34))) ),
c_0_8 ).
fof(c_0_127,axiom,
! [X27,X11,X9] :
( lhs_atom41(X27,X11,X9)
| ! [X28] : ap(f26(X9,X11,X27),X28) = ap(c_2Ebool_2E_21(X11),f25(X9,X11,X27,X28)) ),
c_0_9 ).
fof(c_0_128,axiom,
! [X19,X11,X9] :
( lhs_atom34(X19,X11,X9)
| ! [X25] : ap(f23(X9,X11,X19),X25) = ap(c_2Ebool_2E_3F(X9),f22(X11,X9,X19,X25)) ),
c_0_10 ).
fof(c_0_129,axiom,
! [X19,X11,X9] :
( lhs_atom34(X19,X11,X9)
| ! [X23] : ap(f20(X11,X9,X19),X23) = ap(c_2Ebool_2E_21(X9),f19(X11,X9,X19,X23)) ),
c_0_11 ).
fof(c_0_130,axiom,
! [X27,X11,X9] :
( lhs_atom41(X27,X11,X9)
| ! [X30] :
( mem(X30,X9)
=> ! [X31] : ap(f27(X9,X11,X27,X30),X31) = ap(ap(c_2Emin_2E_3D(X9),X30),ap(X27,X31)) ) ),
c_0_12 ).
fof(c_0_131,axiom,
! [X19,X11,X9] :
( lhs_atom34(X19,X11,X9)
| ! [X25] :
( mem(X25,X11)
=> ! [X26] : ap(f22(X11,X9,X19,X25),X26) = ap(ap(c_2Emin_2E_3D(X11),X25),ap(X19,X26)) ) ),
c_0_13 ).
fof(c_0_132,axiom,
! [X16,X9] :
( lhs_atom37(X16)
| ! [X20] :
( mem(X20,X9)
=> ! [X21] : ap(f16(X9,X16,X20),X21) = ap(c_2Emin_2E_40(X9),f15(X9,X20,X21,X16)) ) ),
c_0_14 ).
fof(c_0_133,axiom,
! [X14] :
( lhs_atom23(X14)
| ! [X13] :
( mem(X13,bool)
=> ! [X15] : ap(f6(X14,X13),X15) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,X14),X15)),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,X13),X15)),X15)) ) ),
c_0_15 ).
fof(c_0_134,axiom,
! [X13] :
( lhs_atom22(X13)
| ! [X14] :
( mem(X14,bool)
=> ! [X15] : ap(f3(X13,X14),X15) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,X14),ap(ap(c_2Emin_2E_3D_3D_3E,X13),X15))),X15) ) ),
c_0_16 ).
fof(c_0_135,axiom,
! [X34,X9] :
( lhs_atom46(X34,X9)
| ! [X35] :
( mem(X35,arr(X9,bool))
=> ! [X26] : ap(f37(X9,X34,X35),X26) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(X9),X26),X34)),ap(X35,X26)) ) ),
c_0_17 ).
fof(c_0_136,axiom,
! [X34,X9] :
( lhs_atom46(X34,X9)
| ! [X35] :
( mem(X35,arr(X9,bool))
=> ! [X26] : ap(f34(X9,X34,X35),X26) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(X9),X26),X34)),ap(X35,X26)) ) ),
c_0_18 ).
fof(c_0_137,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> mem(c_2Ebool_2ERES__ABSTRACT(X9,X11),arr(arr(X9,bool),arr(arr(X9,X11),arr(X9,X11)))) ) ),
c_0_19 ).
fof(c_0_138,axiom,
! [X35,X9] :
( lhs_atom49(X35,X9)
| ! [X34] :
( mem(X34,arr(X9,bool))
=> ! [X22] : ap(f42(X9,X35,X34),X22) = ap(ap(c_2Ebool_2ERES__FORALL(X9),X34),f41(X9,X35,X22)) ) ),
c_0_20 ).
fof(c_0_139,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> mem(c_2Ebool_2ETYPE__DEFINITION(X9,X11),arr(arr(X9,bool),arr(arr(X11,X9),bool))) ) ),
c_0_21 ).
fof(c_0_140,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X12] :
( mem(X12,arr(X9,bool))
=> ! [X17] :
( mem(X17,X9)
=> ( p(ap(X12,X17))
=> p(ap(X12,ap(c_2Emin_2E_40(X9),X12))) ) ) ) ),
c_0_22 ).
fof(c_0_141,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2ERES__SELECT(X9),arr(arr(X9,bool),arr(arr(X9,bool),X9))) ),
c_0_23 ).
fof(c_0_142,axiom,
! [X1] :
( lhs_atom3(X1)
| ! [X5] :
( mem(X5,arr(X1,bool))
=> ( p(ap(c_2Ebool_2E_21(X1),X5))
<=> ! [X4] :
( mem(X4,X1)
=> p(ap(X5,X4)) ) ) ) ),
c_0_24 ).
fof(c_0_143,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2ERES__FORALL(X9),arr(arr(X9,bool),arr(arr(X9,bool),bool))) ),
c_0_25 ).
fof(c_0_144,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2ERES__EXISTS__UNIQUE(X9),arr(arr(X9,bool),arr(arr(X9,bool),bool))) ),
c_0_26 ).
fof(c_0_145,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2ERES__EXISTS(X9),arr(arr(X9,bool),arr(arr(X9,bool),bool))) ),
c_0_27 ).
fof(c_0_146,axiom,
! [X1] :
( lhs_atom3(X1)
| ! [X4] :
( mem(X4,X1)
=> ! [X8] :
( mem(X8,X1)
=> ( p(ap(ap(c_2Emin_2E_3D(X1),X4),X8))
<=> X4 = X8 ) ) ) ),
c_0_28 ).
fof(c_0_147,axiom,
! [X1] :
( lhs_atom3(X1)
| ! [X5] :
( mem(X5,arr(X1,bool))
=> ( p(ap(c_2Ebool_2E_3F(X1),X5))
<=> ? [X4] :
( mem(X4,X1)
& p(ap(X5,X4)) ) ) ) ),
c_0_29 ).
fof(c_0_148,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2ECOND(X9),arr(bool,arr(X9,arr(X9,X9)))) ),
c_0_30 ).
fof(c_0_149,axiom,
! [X16,X11,X9] :
( lhs_atom43(X16,X11,X9)
| ! [X17] : ap(f31(X11,X9,X16),X17) = ap(X16,X17) ),
c_0_31 ).
fof(c_0_150,axiom,
! [X19,X11,X9] :
( lhs_atom34(X19,X11,X9)
| ! [X17] : ap(f13(X11,X9,X19),X17) = ap(X19,X17) ),
c_0_32 ).
fof(c_0_151,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2EIN(X9),arr(X9,arr(arr(X9,bool),bool))) ),
c_0_33 ).
fof(c_0_152,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> mem(c_2Ebool_2Eliteral__case(X9,X11),arr(arr(X9,X11),arr(X9,X11))) ) ),
c_0_34 ).
fof(c_0_153,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> mem(c_2Ebool_2ELET(X9,X11),arr(arr(X9,X11),arr(X9,X11))) ) ),
c_0_35 ).
fof(c_0_154,axiom,
! [X34,X9] :
( lhs_atom46(X34,X9)
| ! [X35] : ap(f45(X9,X34),X35) = ap(c_2Emin_2E_40(X9),f37(X9,X34,X35)) ),
c_0_36 ).
fof(c_0_155,axiom,
! [X34,X9] :
( lhs_atom46(X34,X9)
| ! [X35] : ap(f38(X9,X34),X35) = ap(c_2Ebool_2E_3F(X9),f37(X9,X34,X35)) ),
c_0_37 ).
fof(c_0_156,axiom,
! [X34,X9] :
( lhs_atom46(X34,X9)
| ! [X35] : ap(f35(X9,X34),X35) = ap(c_2Ebool_2E_21(X9),f34(X9,X34,X35)) ),
c_0_38 ).
fof(c_0_157,axiom,
! [X12,X9] :
( lhs_atom32(X12,X9)
| ! [X17] : ap(f11(X9,X12),X17) = ap(c_2Ebool_2E_21(X9),f10(X9,X12,X17)) ),
c_0_39 ).
fof(c_0_158,axiom,
! [X5] :
( lhs_atom5(X5)
| ! [X6] :
( mem(X6,bool)
=> ( p(ap(ap(c_2Emin_2E_3D_3D_3E,X5),X6))
<=> ( p(X5)
=> p(X6) ) ) ) ),
c_0_40 ).
fof(c_0_159,axiom,
! [X5] :
( lhs_atom5(X5)
| ! [X6] :
( mem(X6,bool)
=> ( p(ap(ap(c_2Ebool_2E_5C_2F,X5),X6))
<=> ( p(X5)
| p(X6) ) ) ) ),
c_0_41 ).
fof(c_0_160,axiom,
! [X5] :
( lhs_atom5(X5)
| ! [X6] :
( mem(X6,bool)
=> ( p(ap(ap(c_2Ebool_2E_2F_5C,X5),X6))
<=> ( p(X5)
& p(X6) ) ) ) ),
c_0_42 ).
fof(c_0_161,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> mem(c_2Ebool_2Eitself__case(X9,X11),arr(ty_2Ebool_2Eitself(X9),arr(X11,X11))) ) ),
c_0_43 ).
fof(c_0_162,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> ! [X16] :
( mem(X16,arr(X9,X11))
=> f31(X11,X9,X16) = X16 ) ) ),
c_0_44 ).
fof(c_0_163,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> mem(c_2Ebool_2EONTO(X9,X11),arr(arr(X9,X11),bool)) ) ),
c_0_45 ).
fof(c_0_164,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> mem(c_2Ebool_2EONE__ONE(X9,X11),arr(arr(X9,X11),bool)) ) ),
c_0_46 ).
fof(c_0_165,axiom,
! [X3,X2,X1] :
( lhs_atom4(X3,X2,X1)
| ! [X4] :
( mem(X4,X1)
=> mem(ap(X3,X4),X2) ) ),
c_0_47 ).
fof(c_0_166,axiom,
! [X16,X9] :
( lhs_atom37(X16)
| ! [X20] : ap(f17(X9,X16),X20) = f16(X9,X16,X20) ),
c_0_48 ).
fof(c_0_167,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Emin_2E_40(X9),arr(arr(X9,bool),X9)) ),
c_0_49 ).
fof(c_0_168,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Emin_2E_3D(X9),arr(X9,arr(X9,bool))) ),
c_0_50 ).
fof(c_0_169,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2E_3F_21(X9),arr(arr(X9,bool),bool)) ),
c_0_51 ).
fof(c_0_170,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2E_3F(X9),arr(arr(X9,bool),bool)) ),
c_0_52 ).
fof(c_0_171,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2E_21(X9),arr(arr(X9,bool),bool)) ),
c_0_53 ).
fof(c_0_172,axiom,
! [X35,X9] :
( lhs_atom49(X35,X9)
| ! [X26] : ap(f40(X9,X35),X26) = ap(X35,X26) ),
c_0_54 ).
fof(c_0_173,axiom,
! [X32,X9] :
( lhs_atom44(X32,X9)
| ! [X33] : ap(f32(X9,X32),X33) = ap(X33,X32) ),
c_0_55 ).
fof(c_0_174,axiom,
! [X14] :
( lhs_atom23(X14)
| ! [X13] : ap(f7(X14),X13) = ap(c_2Ebool_2E_21(bool),f6(X14,X13)) ),
c_0_56 ).
fof(c_0_175,axiom,
! [X14] :
( lhs_atom23(X14)
| ! [X13] : ap(f4(X14),X13) = ap(c_2Ebool_2E_21(bool),f3(X13,X14)) ),
c_0_57 ).
fof(c_0_176,axiom,
! [X8,X4,X1] :
( lhs_atom6(X4,X1)
| ap(k(X1,X8),X4) = X8 ),
c_0_58 ).
fof(c_0_177,plain,
! [X12,X11,X9] : lhs_atom42(X12,X11,X9),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_178,plain,
! [X19,X11,X9] : lhs_atom40(X19,X11,X9),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_179,plain,
! [X19,X11,X9] : lhs_atom39(X19,X11,X9),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_180,plain,
! [X19,X11,X9] : lhs_atom35(X19,X11,X9),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_181,plain,
! [X5] :
( lhs_atom5(X5)
| ( p(ap(c_2Ebool_2E_7E,X5))
<=> ~ p(X5) ) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_182,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2EDATATYPE(X9),arr(X9,bool)) ),
c_0_64 ).
fof(c_0_183,axiom,
! [X1] :
( lhs_atom3(X1)
| ! [X2] :
( ne(X2)
=> ne(arr(X1,X2)) ) ),
c_0_65 ).
fof(c_0_184,axiom,
! [X5] :
( lhs_atom5(X5)
| ! [X6] :
( mem(X6,bool)
=> ( ( p(X5)
<=> p(X6) )
=> X5 = X6 ) ) ),
c_0_66 ).
fof(c_0_185,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> c_2Ebool_2Eliteral__case(X9,X11) = f14(X11,X9) ) ),
c_0_67 ).
fof(c_0_186,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> c_2Ebool_2ETYPE__DEFINITION(X9,X11) = f30(X11,X9) ) ),
c_0_68 ).
fof(c_0_187,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> c_2Ebool_2EONTO(X9,X11) = f24(X9,X11) ) ),
c_0_69 ).
fof(c_0_188,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> c_2Ebool_2EONE__ONE(X9,X11) = f21(X11,X9) ) ),
c_0_70 ).
fof(c_0_189,axiom,
! [X9] :
( lhs_atom7(X9)
| ! [X11] :
( ne(X11)
=> c_2Ebool_2ELET(X9,X11) = f14(X11,X9) ) ),
c_0_71 ).
fof(c_0_190,axiom,
! [X4,X1] :
( lhs_atom6(X4,X1)
| ap(i(X1),X4) = X4 ),
c_0_72 ).
fof(c_0_191,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2Ethe__value(X9),ty_2Ebool_2Eitself(X9)) ),
c_0_73 ).
fof(c_0_192,axiom,
( lhs_atom28
| ! [X16] :
( mem(X16,bool)
=> p(X16) ) ),
c_0_74 ).
fof(c_0_193,axiom,
! [X9] :
( lhs_atom7(X9)
| mem(c_2Ebool_2EARB(X9),X9) ),
c_0_75 ).
fof(c_0_194,axiom,
! [X9] :
( lhs_atom7(X9)
| c_2Ebool_2EDATATYPE(X9) = k(X9,c_2Ebool_2ET) ),
c_0_76 ).
fof(c_0_195,plain,
! [X16] :
( lhs_atom37(X16)
| p(X16)
| ~ p(X16) ),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_196,axiom,
! [X10] :
( lhs_atom9(X10)
| ne(ty_2Ebool_2Eitself(X10)) ),
c_0_78 ).
fof(c_0_197,plain,
! [X34,X9] : lhs_atom51(X34,X9),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_198,plain,
! [X34,X9] : lhs_atom50(X34,X9),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_199,plain,
! [X34,X9] : lhs_atom48(X34,X9),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_200,plain,
! [X34,X9] : lhs_atom47(X34,X9),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_201,plain,
! [X32,X9] : lhs_atom45(X32,X9),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_202,plain,
! [X16,X9] : lhs_atom38(X16,X9),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_203,plain,
! [X12,X9] : lhs_atom33(X12,X9),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_204,plain,
! [X12,X9] : lhs_atom21(X12,X9),
inference(fof_simplification,[status(thm)],[c_0_86]) ).
fof(c_0_205,plain,
! [X12,X9] : lhs_atom20(X12,X9),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_206,axiom,
! [X9] :
( lhs_atom7(X9)
| c_2Ebool_2ERES__SELECT(X9) = f46(X9) ),
c_0_88 ).
fof(c_0_207,axiom,
! [X9] :
( lhs_atom7(X9)
| c_2Ebool_2ERES__EXISTS__UNIQUE(X9) = f44(X9) ),
c_0_89 ).
fof(c_0_208,axiom,
! [X9] :
( lhs_atom7(X9)
| c_2Ebool_2ERES__EXISTS(X9) = f39(X9) ),
c_0_90 ).
fof(c_0_209,axiom,
! [X9] :
( lhs_atom7(X9)
| c_2Ebool_2ERES__FORALL(X9) = f36(X9) ),
c_0_91 ).
fof(c_0_210,axiom,
! [X9] :
( lhs_atom7(X9)
| c_2Ebool_2EIN(X9) = f33(X9) ),
c_0_92 ).
fof(c_0_211,axiom,
! [X9] :
( lhs_atom7(X9)
| c_2Ebool_2ECOND(X9) = f18(X9) ),
c_0_93 ).
fof(c_0_212,axiom,
! [X9] :
( lhs_atom7(X9)
| c_2Ebool_2E_3F_21(X9) = f12(X9) ),
c_0_94 ).
fof(c_0_213,axiom,
! [X9] :
( lhs_atom7(X9)
| c_2Ebool_2E_3F(X9) = f2(X9) ),
c_0_95 ).
fof(c_0_214,axiom,
! [X9] :
( lhs_atom7(X9)
| c_2Ebool_2E_21(X9) = f1(X9) ),
c_0_96 ).
fof(c_0_215,axiom,
( lhs_atom29
| ~ ! [X16] :
( mem(X16,bool)
=> p(X16) ) ),
c_0_97 ).
fof(c_0_216,plain,
( lhs_atom19
| i(bool) != i(bool) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_217,axiom,
( lhs_atom18
| i(bool) = i(bool) ),
c_0_99 ).
fof(c_0_218,plain,
! [X16] : lhs_atom30(X16),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_219,plain,
! [X14] : lhs_atom26(X14),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_220,plain,
! [X14] : lhs_atom24(X14),
inference(fof_simplification,[status(thm)],[c_0_102]) ).
fof(c_0_221,plain,
lhs_atom52,
inference(fof_simplification,[status(thm)],[c_0_103]) ).
fof(c_0_222,plain,
lhs_atom31,
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_223,plain,
lhs_atom27,
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_224,plain,
lhs_atom25,
inference(fof_simplification,[status(thm)],[c_0_106]) ).
fof(c_0_225,plain,
lhs_atom17,
inference(fof_simplification,[status(thm)],[c_0_107]) ).
fof(c_0_226,plain,
lhs_atom16,
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_227,plain,
lhs_atom15,
inference(fof_simplification,[status(thm)],[c_0_109]) ).
fof(c_0_228,plain,
lhs_atom14,
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_229,plain,
lhs_atom13,
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_230,plain,
lhs_atom12,
inference(fof_simplification,[status(thm)],[c_0_112]) ).
fof(c_0_231,plain,
lhs_atom11,
inference(fof_simplification,[status(thm)],[c_0_113]) ).
fof(c_0_232,plain,
lhs_atom10,
inference(fof_simplification,[status(thm)],[c_0_114]) ).
fof(c_0_233,plain,
lhs_atom8,
inference(fof_simplification,[status(thm)],[c_0_115]) ).
fof(c_0_234,plain,
lhs_atom2,
inference(fof_simplification,[status(thm)],[c_0_116]) ).
fof(c_0_235,plain,
lhs_atom1,
inference(fof_simplification,[status(thm)],[c_0_117]) ).
fof(c_0_236,plain,
! [X23,X24,X25,X26,X27] :
( lhs_atom36(X23,X24)
| ~ mem(X25,X24)
| ~ mem(X26,bool)
| ap(f15(X24,X23,X25,X26),X27) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),X26),c_2Ebool_2ET)),ap(ap(c_2Emin_2E_3D(X24),X27),X23))),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),X26),c_2Ebool_2EF)),ap(ap(c_2Emin_2E_3D(X24),X27),X25))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_118])])]) ).
fof(c_0_237,plain,
! [X8,X9,X10,X11] :
( ( mem(esk1_4(X8,X9,X10,X11),X10)
| X8 = X11
| ~ mem(X11,arr(X10,X9))
| lhs_atom4(X8,X9,X10) )
& ( ap(X8,esk1_4(X8,X9,X10,X11)) != ap(X11,esk1_4(X8,X9,X10,X11))
| X8 = X11
| ~ mem(X11,arr(X10,X9))
| lhs_atom4(X8,X9,X10) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_119])])])])]) ).
fof(c_0_238,plain,
! [X31,X32,X33,X34,X35] :
( lhs_atom32(X31,X33)
| ~ mem(X34,arr(X32,X33))
| ap(f28(X32,X33,X31,X34),X35) = ap(ap(c_2Emin_2E_3D(bool),ap(X31,X35)),ap(c_2Ebool_2E_3F(X32),f27(X33,X32,X34,X35))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_120])])]) ).
fof(c_0_239,plain,
! [X28,X29,X30,X31] :
( lhs_atom32(X28,X30)
| ap(f29(X29,X30,X28),X31) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_21(X29),f26(X30,X29,X31))),ap(c_2Ebool_2E_21(X30),f28(X29,X30,X28,X31))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_121])]) ).
fof(c_0_240,plain,
! [X30,X31,X32,X33,X34] :
( lhs_atom41(X30,X31,X32)
| ~ mem(X33,X31)
| ap(f25(X32,X31,X30,X33),X34) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(X32),ap(X30,X33)),ap(X30,X34))),ap(ap(c_2Emin_2E_3D(X31),X33),X34)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_122])])]) ).
fof(c_0_241,plain,
! [X25,X26,X27,X28,X29] :
( lhs_atom34(X25,X26,X27)
| ~ mem(X28,X27)
| ap(f19(X26,X27,X25,X28),X29) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(X26),ap(X25,X28)),ap(X25,X29))),ap(ap(c_2Emin_2E_3D(X27),X28),X29)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_123])])]) ).
fof(c_0_242,plain,
! [X37,X38,X39,X40] :
( lhs_atom49(X37,X38)
| ~ mem(X39,X38)
| ap(f41(X38,X37,X39),X40) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(X37,X39)),ap(X37,X40))),ap(ap(c_2Emin_2E_3D(X38),X39),X40)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_124])])]) ).
fof(c_0_243,plain,
! [X19,X20,X21,X22] :
( lhs_atom32(X19,X20)
| ~ mem(X21,X20)
| ap(f10(X20,X19,X21),X22) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(X19,X21)),ap(X19,X22))),ap(ap(c_2Emin_2E_3D(X20),X21),X22)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_125])])]) ).
fof(c_0_244,plain,
! [X36,X37,X38] :
( lhs_atom46(X36,X37)
| ap(f43(X37,X36),X38) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2ERES__EXISTS(X37),X36),f40(X37,X38))),ap(ap(c_2Ebool_2ERES__FORALL(X37),X36),f42(X37,X38,X36))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_126])]) ).
fof(c_0_245,plain,
! [X29,X30,X31,X32] :
( lhs_atom41(X29,X30,X31)
| ap(f26(X31,X30,X29),X32) = ap(c_2Ebool_2E_21(X30),f25(X31,X30,X29,X32)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_127])]) ).
fof(c_0_246,plain,
! [X26,X27,X28,X29] :
( lhs_atom34(X26,X27,X28)
| ap(f23(X28,X27,X26),X29) = ap(c_2Ebool_2E_3F(X28),f22(X27,X28,X26,X29)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_128])]) ).
fof(c_0_247,plain,
! [X24,X25,X26,X27] :
( lhs_atom34(X24,X25,X26)
| ap(f20(X25,X26,X24),X27) = ap(c_2Ebool_2E_21(X26),f19(X25,X26,X24,X27)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_129])]) ).
fof(c_0_248,plain,
! [X32,X33,X34,X35,X36] :
( lhs_atom41(X32,X33,X34)
| ~ mem(X35,X34)
| ap(f27(X34,X33,X32,X35),X36) = ap(ap(c_2Emin_2E_3D(X34),X35),ap(X32,X36)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_130])])]) ).
fof(c_0_249,plain,
! [X27,X28,X29,X30,X31] :
( lhs_atom34(X27,X28,X29)
| ~ mem(X30,X28)
| ap(f22(X28,X29,X27,X30),X31) = ap(ap(c_2Emin_2E_3D(X28),X30),ap(X27,X31)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_131])])]) ).
fof(c_0_250,plain,
! [X22,X23,X24,X25] :
( lhs_atom37(X22)
| ~ mem(X24,X23)
| ap(f16(X23,X22,X24),X25) = ap(c_2Emin_2E_40(X23),f15(X23,X24,X25,X22)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_132])])])]) ).
fof(c_0_251,plain,
! [X16,X17,X18] :
( lhs_atom23(X16)
| ~ mem(X17,bool)
| ap(f6(X16,X17),X18) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,X16),X18)),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,X17),X18)),X18)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_133])])]) ).
fof(c_0_252,plain,
! [X16,X17,X18] :
( lhs_atom22(X16)
| ~ mem(X17,bool)
| ap(f3(X16,X17),X18) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,X17),ap(ap(c_2Emin_2E_3D_3D_3E,X16),X18))),X18) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_134])])]) ).
fof(c_0_253,plain,
! [X36,X37,X38,X39] :
( lhs_atom46(X36,X37)
| ~ mem(X38,arr(X37,bool))
| ap(f37(X37,X36,X38),X39) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(X37),X39),X36)),ap(X38,X39)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_135])])]) ).
fof(c_0_254,plain,
! [X36,X37,X38,X39] :
( lhs_atom46(X36,X37)
| ~ mem(X38,arr(X37,bool))
| ap(f34(X37,X36,X38),X39) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(X37),X39),X36)),ap(X38,X39)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_136])])]) ).
fof(c_0_255,plain,
! [X12,X13] :
( lhs_atom7(X12)
| ~ ne(X13)
| mem(c_2Ebool_2ERES__ABSTRACT(X12,X13),arr(arr(X12,bool),arr(arr(X12,X13),arr(X12,X13)))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_137])])]) ).
fof(c_0_256,plain,
! [X36,X37,X38,X39] :
( lhs_atom49(X36,X37)
| ~ mem(X38,arr(X37,bool))
| ap(f42(X37,X36,X38),X39) = ap(ap(c_2Ebool_2ERES__FORALL(X37),X38),f41(X37,X36,X39)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_138])])]) ).
fof(c_0_257,plain,
! [X12,X13] :
( lhs_atom7(X12)
| ~ ne(X13)
| mem(c_2Ebool_2ETYPE__DEFINITION(X12,X13),arr(arr(X12,bool),arr(arr(X13,X12),bool))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_139])])]) ).
fof(c_0_258,plain,
! [X18,X19,X20] :
( lhs_atom7(X18)
| ~ mem(X19,arr(X18,bool))
| ~ mem(X20,X18)
| ~ p(ap(X19,X20))
| p(ap(X19,ap(c_2Emin_2E_40(X18),X19))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_140])])]) ).
fof(c_0_259,plain,
! [X10] :
( lhs_atom7(X10)
| mem(c_2Ebool_2ERES__SELECT(X10),arr(arr(X10,bool),arr(arr(X10,bool),X10))) ),
inference(variable_rename,[status(thm)],[c_0_141]) ).
fof(c_0_260,plain,
! [X6,X7,X8] :
( ( ~ p(ap(c_2Ebool_2E_21(X6),X7))
| ~ mem(X8,X6)
| p(ap(X7,X8))
| ~ mem(X7,arr(X6,bool))
| lhs_atom3(X6) )
& ( mem(esk2_2(X6,X7),X6)
| p(ap(c_2Ebool_2E_21(X6),X7))
| ~ mem(X7,arr(X6,bool))
| lhs_atom3(X6) )
& ( ~ p(ap(X7,esk2_2(X6,X7)))
| p(ap(c_2Ebool_2E_21(X6),X7))
| ~ mem(X7,arr(X6,bool))
| lhs_atom3(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_142])])])])]) ).
fof(c_0_261,plain,
! [X10] :
( lhs_atom7(X10)
| mem(c_2Ebool_2ERES__FORALL(X10),arr(arr(X10,bool),arr(arr(X10,bool),bool))) ),
inference(variable_rename,[status(thm)],[c_0_143]) ).
fof(c_0_262,plain,
! [X10] :
( lhs_atom7(X10)
| mem(c_2Ebool_2ERES__EXISTS__UNIQUE(X10),arr(arr(X10,bool),arr(arr(X10,bool),bool))) ),
inference(variable_rename,[status(thm)],[c_0_144]) ).
fof(c_0_263,plain,
! [X10] :
( lhs_atom7(X10)
| mem(c_2Ebool_2ERES__EXISTS(X10),arr(arr(X10,bool),arr(arr(X10,bool),bool))) ),
inference(variable_rename,[status(thm)],[c_0_145]) ).
fof(c_0_264,plain,
! [X9,X10,X11] :
( ( ~ p(ap(ap(c_2Emin_2E_3D(X9),X10),X11))
| X10 = X11
| ~ mem(X11,X9)
| ~ mem(X10,X9)
| lhs_atom3(X9) )
& ( X10 != X11
| p(ap(ap(c_2Emin_2E_3D(X9),X10),X11))
| ~ mem(X11,X9)
| ~ mem(X10,X9)
| lhs_atom3(X9) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_146])])])]) ).
fof(c_0_265,plain,
! [X6,X7,X9] :
( ( mem(esk3_2(X6,X7),X6)
| ~ p(ap(c_2Ebool_2E_3F(X6),X7))
| ~ mem(X7,arr(X6,bool))
| lhs_atom3(X6) )
& ( p(ap(X7,esk3_2(X6,X7)))
| ~ p(ap(c_2Ebool_2E_3F(X6),X7))
| ~ mem(X7,arr(X6,bool))
| lhs_atom3(X6) )
& ( ~ mem(X9,X6)
| ~ p(ap(X7,X9))
| p(ap(c_2Ebool_2E_3F(X6),X7))
| ~ mem(X7,arr(X6,bool))
| lhs_atom3(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_147])])])])]) ).
fof(c_0_266,plain,
! [X10] :
( lhs_atom7(X10)
| mem(c_2Ebool_2ECOND(X10),arr(bool,arr(X10,arr(X10,X10)))) ),
inference(variable_rename,[status(thm)],[c_0_148]) ).
fof(c_0_267,plain,
! [X18,X19,X20,X21] :
( lhs_atom43(X18,X19,X20)
| ap(f31(X19,X20,X18),X21) = ap(X18,X21) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_149])]) ).
fof(c_0_268,plain,
! [X20,X21,X22,X23] :
( lhs_atom34(X20,X21,X22)
| ap(f13(X21,X22,X20),X23) = ap(X20,X23) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_150])]) ).
fof(c_0_269,plain,
! [X10] :
( lhs_atom7(X10)
| mem(c_2Ebool_2EIN(X10),arr(X10,arr(arr(X10,bool),bool))) ),
inference(variable_rename,[status(thm)],[c_0_151]) ).
fof(c_0_270,plain,
! [X12,X13] :
( lhs_atom7(X12)
| ~ ne(X13)
| mem(c_2Ebool_2Eliteral__case(X12,X13),arr(arr(X12,X13),arr(X12,X13))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_152])])]) ).
fof(c_0_271,plain,
! [X12,X13] :
( lhs_atom7(X12)
| ~ ne(X13)
| mem(c_2Ebool_2ELET(X12,X13),arr(arr(X12,X13),arr(X12,X13))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_153])])]) ).
fof(c_0_272,plain,
! [X36,X37,X38] :
( lhs_atom46(X36,X37)
| ap(f45(X37,X36),X38) = ap(c_2Emin_2E_40(X37),f37(X37,X36,X38)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_154])]) ).
fof(c_0_273,plain,
! [X36,X37,X38] :
( lhs_atom46(X36,X37)
| ap(f38(X37,X36),X38) = ap(c_2Ebool_2E_3F(X37),f37(X37,X36,X38)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_155])]) ).
fof(c_0_274,plain,
! [X36,X37,X38] :
( lhs_atom46(X36,X37)
| ap(f35(X37,X36),X38) = ap(c_2Ebool_2E_21(X37),f34(X37,X36,X38)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_156])]) ).
fof(c_0_275,plain,
! [X18,X19,X20] :
( lhs_atom32(X18,X19)
| ap(f11(X19,X18),X20) = ap(c_2Ebool_2E_21(X19),f10(X19,X18,X20)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_157])]) ).
fof(c_0_276,plain,
! [X7,X8] :
( ( ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X7),X8))
| ~ p(X7)
| p(X8)
| ~ mem(X8,bool)
| lhs_atom5(X7) )
& ( p(X7)
| p(ap(ap(c_2Emin_2E_3D_3D_3E,X7),X8))
| ~ mem(X8,bool)
| lhs_atom5(X7) )
& ( ~ p(X8)
| p(ap(ap(c_2Emin_2E_3D_3D_3E,X7),X8))
| ~ mem(X8,bool)
| lhs_atom5(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_158])])])]) ).
fof(c_0_277,plain,
! [X7,X8] :
( ( ~ p(ap(ap(c_2Ebool_2E_5C_2F,X7),X8))
| p(X7)
| p(X8)
| ~ mem(X8,bool)
| lhs_atom5(X7) )
& ( ~ p(X7)
| p(ap(ap(c_2Ebool_2E_5C_2F,X7),X8))
| ~ mem(X8,bool)
| lhs_atom5(X7) )
& ( ~ p(X8)
| p(ap(ap(c_2Ebool_2E_5C_2F,X7),X8))
| ~ mem(X8,bool)
| lhs_atom5(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_159])])])]) ).
fof(c_0_278,plain,
! [X7,X8] :
( ( p(X7)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X7),X8))
| ~ mem(X8,bool)
| lhs_atom5(X7) )
& ( p(X8)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X7),X8))
| ~ mem(X8,bool)
| lhs_atom5(X7) )
& ( ~ p(X7)
| ~ p(X8)
| p(ap(ap(c_2Ebool_2E_2F_5C,X7),X8))
| ~ mem(X8,bool)
| lhs_atom5(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_160])])])]) ).
fof(c_0_279,plain,
! [X12,X13] :
( lhs_atom7(X12)
| ~ ne(X13)
| mem(c_2Ebool_2Eitself__case(X12,X13),arr(ty_2Ebool_2Eitself(X12),arr(X13,X13))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_161])])]) ).
fof(c_0_280,plain,
! [X17,X18,X19] :
( lhs_atom7(X17)
| ~ ne(X18)
| ~ mem(X19,arr(X17,X18))
| f31(X18,X17,X19) = X19 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_162])])]) ).
fof(c_0_281,plain,
! [X12,X13] :
( lhs_atom7(X12)
| ~ ne(X13)
| mem(c_2Ebool_2EONTO(X12,X13),arr(arr(X12,X13),bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_163])])]) ).
fof(c_0_282,plain,
! [X12,X13] :
( lhs_atom7(X12)
| ~ ne(X13)
| mem(c_2Ebool_2EONE__ONE(X12,X13),arr(arr(X12,X13),bool)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_164])])]) ).
fof(c_0_283,plain,
! [X5,X6,X7,X8] :
( lhs_atom4(X5,X6,X7)
| ~ mem(X8,X7)
| mem(ap(X5,X8),X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_165])])]) ).
fof(c_0_284,plain,
! [X21,X22,X23] :
( lhs_atom37(X21)
| ap(f17(X22,X21),X23) = f16(X22,X21,X23) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_166])])]) ).
fof(c_0_285,plain,
! [X10] :
( lhs_atom7(X10)
| mem(c_2Emin_2E_40(X10),arr(arr(X10,bool),X10)) ),
inference(variable_rename,[status(thm)],[c_0_167]) ).
fof(c_0_286,plain,
! [X10] :
( lhs_atom7(X10)
| mem(c_2Emin_2E_3D(X10),arr(X10,arr(X10,bool))) ),
inference(variable_rename,[status(thm)],[c_0_168]) ).
fof(c_0_287,plain,
! [X10] :
( lhs_atom7(X10)
| mem(c_2Ebool_2E_3F_21(X10),arr(arr(X10,bool),bool)) ),
inference(variable_rename,[status(thm)],[c_0_169]) ).
fof(c_0_288,plain,
! [X10] :
( lhs_atom7(X10)
| mem(c_2Ebool_2E_3F(X10),arr(arr(X10,bool),bool)) ),
inference(variable_rename,[status(thm)],[c_0_170]) ).
fof(c_0_289,plain,
! [X10] :
( lhs_atom7(X10)
| mem(c_2Ebool_2E_21(X10),arr(arr(X10,bool),bool)) ),
inference(variable_rename,[status(thm)],[c_0_171]) ).
fof(c_0_290,plain,
! [X36,X37,X38] :
( lhs_atom49(X36,X37)
| ap(f40(X37,X36),X38) = ap(X36,X38) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_172])]) ).
fof(c_0_291,plain,
! [X34,X35,X36] :
( lhs_atom44(X34,X35)
| ap(f32(X35,X34),X36) = ap(X36,X34) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_173])]) ).
fof(c_0_292,plain,
! [X15,X16] :
( lhs_atom23(X15)
| ap(f7(X15),X16) = ap(c_2Ebool_2E_21(bool),f6(X15,X16)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_174])]) ).
fof(c_0_293,plain,
! [X15,X16] :
( lhs_atom23(X15)
| ap(f4(X15),X16) = ap(c_2Ebool_2E_21(bool),f3(X16,X15)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_175])]) ).
fof(c_0_294,plain,
! [X9,X10,X11] :
( lhs_atom6(X10,X11)
| ap(k(X11,X9),X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_176]) ).
fof(c_0_295,plain,
! [X13,X14,X15] : lhs_atom42(X13,X14,X15),
inference(variable_rename,[status(thm)],[c_0_177]) ).
fof(c_0_296,plain,
! [X20,X21,X22] : lhs_atom40(X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_178]) ).
fof(c_0_297,plain,
! [X20,X21,X22] : lhs_atom39(X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_179]) ).
fof(c_0_298,plain,
! [X20,X21,X22] : lhs_atom35(X20,X21,X22),
inference(variable_rename,[status(thm)],[c_0_180]) ).
fof(c_0_299,plain,
! [X6] :
( ( ~ p(ap(c_2Ebool_2E_7E,X6))
| ~ p(X6)
| lhs_atom5(X6) )
& ( p(X6)
| p(ap(c_2Ebool_2E_7E,X6))
| lhs_atom5(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_181])])]) ).
fof(c_0_300,plain,
! [X10] :
( lhs_atom7(X10)
| mem(c_2Ebool_2EDATATYPE(X10),arr(X10,bool)) ),
inference(variable_rename,[status(thm)],[c_0_182]) ).
fof(c_0_301,plain,
! [X3,X4] :
( lhs_atom3(X3)
| ~ ne(X4)
| ne(arr(X3,X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_183])])]) ).
fof(c_0_302,plain,
! [X7,X8] :
( ( ~ p(X7)
| ~ p(X8)
| X7 = X8
| ~ mem(X8,bool)
| lhs_atom5(X7) )
& ( p(X7)
| p(X8)
| X7 = X8
| ~ mem(X8,bool)
| lhs_atom5(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_184])])])]) ).
fof(c_0_303,plain,
! [X12,X13] :
( lhs_atom7(X12)
| ~ ne(X13)
| c_2Ebool_2Eliteral__case(X12,X13) = f14(X13,X12) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_185])])]) ).
fof(c_0_304,plain,
! [X12,X13] :
( lhs_atom7(X12)
| ~ ne(X13)
| c_2Ebool_2ETYPE__DEFINITION(X12,X13) = f30(X13,X12) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_186])])]) ).
fof(c_0_305,plain,
! [X12,X13] :
( lhs_atom7(X12)
| ~ ne(X13)
| c_2Ebool_2EONTO(X12,X13) = f24(X12,X13) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_187])])]) ).
fof(c_0_306,plain,
! [X12,X13] :
( lhs_atom7(X12)
| ~ ne(X13)
| c_2Ebool_2EONE__ONE(X12,X13) = f21(X13,X12) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_188])])]) ).
fof(c_0_307,plain,
! [X12,X13] :
( lhs_atom7(X12)
| ~ ne(X13)
| c_2Ebool_2ELET(X12,X13) = f14(X13,X12) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_189])])]) ).
fof(c_0_308,plain,
! [X5,X6] :
( lhs_atom6(X5,X6)
| ap(i(X6),X5) = X5 ),
inference(variable_rename,[status(thm)],[c_0_190]) ).
fof(c_0_309,plain,
! [X10] :
( lhs_atom7(X10)
| mem(c_2Ebool_2Ethe__value(X10),ty_2Ebool_2Eitself(X10)) ),
inference(variable_rename,[status(thm)],[c_0_191]) ).
fof(c_0_310,plain,
! [X17] :
( lhs_atom28
| ~ mem(X17,bool)
| p(X17) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_192])])]) ).
fof(c_0_311,plain,
! [X10] :
( lhs_atom7(X10)
| mem(c_2Ebool_2EARB(X10),X10) ),
inference(variable_rename,[status(thm)],[c_0_193]) ).
fof(c_0_312,plain,
! [X10] :
( lhs_atom7(X10)
| c_2Ebool_2EDATATYPE(X10) = k(X10,c_2Ebool_2ET) ),
inference(variable_rename,[status(thm)],[c_0_194]) ).
fof(c_0_313,plain,
! [X17] :
( lhs_atom37(X17)
| p(X17)
| ~ p(X17) ),
inference(variable_rename,[status(thm)],[c_0_195]) ).
fof(c_0_314,plain,
! [X11] :
( lhs_atom9(X11)
| ne(ty_2Ebool_2Eitself(X11)) ),
inference(variable_rename,[status(thm)],[c_0_196]) ).
fof(c_0_315,plain,
! [X35,X36] : lhs_atom51(X35,X36),
inference(variable_rename,[status(thm)],[c_0_197]) ).
fof(c_0_316,plain,
! [X35,X36] : lhs_atom50(X35,X36),
inference(variable_rename,[status(thm)],[c_0_198]) ).
fof(c_0_317,plain,
! [X35,X36] : lhs_atom48(X35,X36),
inference(variable_rename,[status(thm)],[c_0_199]) ).
fof(c_0_318,plain,
! [X35,X36] : lhs_atom47(X35,X36),
inference(variable_rename,[status(thm)],[c_0_200]) ).
fof(c_0_319,plain,
! [X33,X34] : lhs_atom45(X33,X34),
inference(variable_rename,[status(thm)],[c_0_201]) ).
fof(c_0_320,plain,
! [X17,X18] : lhs_atom38(X17,X18),
inference(variable_rename,[status(thm)],[c_0_202]) ).
fof(c_0_321,plain,
! [X13,X14] : lhs_atom33(X13,X14),
inference(variable_rename,[status(thm)],[c_0_203]) ).
fof(c_0_322,plain,
! [X13,X14] : lhs_atom21(X13,X14),
inference(variable_rename,[status(thm)],[c_0_204]) ).
fof(c_0_323,plain,
! [X13,X14] : lhs_atom20(X13,X14),
inference(variable_rename,[status(thm)],[c_0_205]) ).
fof(c_0_324,plain,
! [X10] :
( lhs_atom7(X10)
| c_2Ebool_2ERES__SELECT(X10) = f46(X10) ),
inference(variable_rename,[status(thm)],[c_0_206]) ).
fof(c_0_325,plain,
! [X10] :
( lhs_atom7(X10)
| c_2Ebool_2ERES__EXISTS__UNIQUE(X10) = f44(X10) ),
inference(variable_rename,[status(thm)],[c_0_207]) ).
fof(c_0_326,plain,
! [X10] :
( lhs_atom7(X10)
| c_2Ebool_2ERES__EXISTS(X10) = f39(X10) ),
inference(variable_rename,[status(thm)],[c_0_208]) ).
fof(c_0_327,plain,
! [X10] :
( lhs_atom7(X10)
| c_2Ebool_2ERES__FORALL(X10) = f36(X10) ),
inference(variable_rename,[status(thm)],[c_0_209]) ).
fof(c_0_328,plain,
! [X10] :
( lhs_atom7(X10)
| c_2Ebool_2EIN(X10) = f33(X10) ),
inference(variable_rename,[status(thm)],[c_0_210]) ).
fof(c_0_329,plain,
! [X10] :
( lhs_atom7(X10)
| c_2Ebool_2ECOND(X10) = f18(X10) ),
inference(variable_rename,[status(thm)],[c_0_211]) ).
fof(c_0_330,plain,
! [X10] :
( lhs_atom7(X10)
| c_2Ebool_2E_3F_21(X10) = f12(X10) ),
inference(variable_rename,[status(thm)],[c_0_212]) ).
fof(c_0_331,plain,
! [X10] :
( lhs_atom7(X10)
| c_2Ebool_2E_3F(X10) = f2(X10) ),
inference(variable_rename,[status(thm)],[c_0_213]) ).
fof(c_0_332,plain,
! [X10] :
( lhs_atom7(X10)
| c_2Ebool_2E_21(X10) = f1(X10) ),
inference(variable_rename,[status(thm)],[c_0_214]) ).
fof(c_0_333,plain,
( ( mem(esk4_0,bool)
| lhs_atom29 )
& ( ~ p(esk4_0)
| lhs_atom29 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_215])])])]) ).
fof(c_0_334,plain,
( lhs_atom19
| i(bool) != i(bool) ),
c_0_216 ).
fof(c_0_335,axiom,
( lhs_atom18
| i(bool) = i(bool) ),
c_0_217 ).
fof(c_0_336,plain,
! [X17] : lhs_atom30(X17),
inference(variable_rename,[status(thm)],[c_0_218]) ).
fof(c_0_337,plain,
! [X15] : lhs_atom26(X15),
inference(variable_rename,[status(thm)],[c_0_219]) ).
fof(c_0_338,plain,
! [X15] : lhs_atom24(X15),
inference(variable_rename,[status(thm)],[c_0_220]) ).
fof(c_0_339,plain,
lhs_atom52,
c_0_221 ).
fof(c_0_340,plain,
lhs_atom31,
c_0_222 ).
fof(c_0_341,plain,
lhs_atom27,
c_0_223 ).
fof(c_0_342,plain,
lhs_atom25,
c_0_224 ).
fof(c_0_343,plain,
lhs_atom17,
c_0_225 ).
fof(c_0_344,plain,
lhs_atom16,
c_0_226 ).
fof(c_0_345,plain,
lhs_atom15,
c_0_227 ).
fof(c_0_346,plain,
lhs_atom14,
c_0_228 ).
fof(c_0_347,plain,
lhs_atom13,
c_0_229 ).
fof(c_0_348,plain,
lhs_atom12,
c_0_230 ).
fof(c_0_349,plain,
lhs_atom11,
c_0_231 ).
fof(c_0_350,plain,
lhs_atom10,
c_0_232 ).
fof(c_0_351,plain,
lhs_atom8,
c_0_233 ).
fof(c_0_352,plain,
lhs_atom2,
c_0_234 ).
fof(c_0_353,plain,
lhs_atom1,
c_0_235 ).
cnf(c_0_354,plain,
( ap(f15(X1,X2,X3,X4),X5) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),X4),c_2Ebool_2ET)),ap(ap(c_2Emin_2E_3D(X1),X5),X2))),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),X4),c_2Ebool_2EF)),ap(ap(c_2Emin_2E_3D(X1),X5),X3)))
| lhs_atom36(X2,X1)
| ~ mem(X4,bool)
| ~ mem(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_236]) ).
cnf(c_0_355,plain,
( lhs_atom4(X1,X2,X3)
| X1 = X4
| ~ mem(X4,arr(X3,X2))
| ap(X1,esk1_4(X1,X2,X3,X4)) != ap(X4,esk1_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_237]) ).
cnf(c_0_356,plain,
( ap(f28(X1,X2,X3,X4),X5) = ap(ap(c_2Emin_2E_3D(bool),ap(X3,X5)),ap(c_2Ebool_2E_3F(X1),f27(X2,X1,X4,X5)))
| lhs_atom32(X3,X2)
| ~ mem(X4,arr(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_238]) ).
cnf(c_0_357,plain,
( ap(f29(X1,X2,X3),X4) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_21(X1),f26(X2,X1,X4))),ap(c_2Ebool_2E_21(X2),f28(X1,X2,X3,X4)))
| lhs_atom32(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_239]) ).
cnf(c_0_358,plain,
( ap(f25(X1,X2,X3,X4),X5) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(X1),ap(X3,X4)),ap(X3,X5))),ap(ap(c_2Emin_2E_3D(X2),X4),X5))
| lhs_atom41(X3,X2,X1)
| ~ mem(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_240]) ).
cnf(c_0_359,plain,
( ap(f19(X1,X2,X3,X4),X5) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(X1),ap(X3,X4)),ap(X3,X5))),ap(ap(c_2Emin_2E_3D(X2),X4),X5))
| lhs_atom34(X3,X1,X2)
| ~ mem(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_241]) ).
cnf(c_0_360,plain,
( ap(f41(X1,X2,X3),X4) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(X2,X3)),ap(X2,X4))),ap(ap(c_2Emin_2E_3D(X1),X3),X4))
| lhs_atom49(X2,X1)
| ~ mem(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_242]) ).
cnf(c_0_361,plain,
( ap(f10(X1,X2,X3),X4) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(X2,X3)),ap(X2,X4))),ap(ap(c_2Emin_2E_3D(X1),X3),X4))
| lhs_atom32(X2,X1)
| ~ mem(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_243]) ).
cnf(c_0_362,plain,
( ap(f43(X1,X2),X3) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2ERES__EXISTS(X1),X2),f40(X1,X3))),ap(ap(c_2Ebool_2ERES__FORALL(X1),X2),f42(X1,X3,X2)))
| lhs_atom46(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_244]) ).
cnf(c_0_363,plain,
( ap(f26(X1,X2,X3),X4) = ap(c_2Ebool_2E_21(X2),f25(X1,X2,X3,X4))
| lhs_atom41(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_245]) ).
cnf(c_0_364,plain,
( ap(f23(X1,X2,X3),X4) = ap(c_2Ebool_2E_3F(X1),f22(X2,X1,X3,X4))
| lhs_atom34(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_246]) ).
cnf(c_0_365,plain,
( ap(f20(X1,X2,X3),X4) = ap(c_2Ebool_2E_21(X2),f19(X1,X2,X3,X4))
| lhs_atom34(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_247]) ).
cnf(c_0_366,plain,
( ap(f27(X1,X2,X3,X4),X5) = ap(ap(c_2Emin_2E_3D(X1),X4),ap(X3,X5))
| lhs_atom41(X3,X2,X1)
| ~ mem(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_248]) ).
cnf(c_0_367,plain,
( ap(f22(X1,X2,X3,X4),X5) = ap(ap(c_2Emin_2E_3D(X1),X4),ap(X3,X5))
| lhs_atom34(X3,X1,X2)
| ~ mem(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_249]) ).
cnf(c_0_368,plain,
( ap(f16(X1,X2,X3),X4) = ap(c_2Emin_2E_40(X1),f15(X1,X3,X4,X2))
| lhs_atom37(X2)
| ~ mem(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_250]) ).
cnf(c_0_369,plain,
( lhs_atom4(X1,X2,X3)
| X1 = X4
| mem(esk1_4(X1,X2,X3,X4),X3)
| ~ mem(X4,arr(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_237]) ).
cnf(c_0_370,plain,
( ap(f6(X1,X2),X3) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,X1),X3)),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,X2),X3)),X3))
| lhs_atom23(X1)
| ~ mem(X2,bool) ),
inference(split_conjunct,[status(thm)],[c_0_251]) ).
cnf(c_0_371,plain,
( ap(f3(X1,X2),X3) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,X2),ap(ap(c_2Emin_2E_3D_3D_3E,X1),X3))),X3)
| lhs_atom22(X1)
| ~ mem(X2,bool) ),
inference(split_conjunct,[status(thm)],[c_0_252]) ).
cnf(c_0_372,plain,
( ap(f37(X1,X2,X3),X4) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(X1),X4),X2)),ap(X3,X4))
| lhs_atom46(X2,X1)
| ~ mem(X3,arr(X1,bool)) ),
inference(split_conjunct,[status(thm)],[c_0_253]) ).
cnf(c_0_373,plain,
( ap(f34(X1,X2,X3),X4) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(X1),X4),X2)),ap(X3,X4))
| lhs_atom46(X2,X1)
| ~ mem(X3,arr(X1,bool)) ),
inference(split_conjunct,[status(thm)],[c_0_254]) ).
cnf(c_0_374,plain,
( mem(c_2Ebool_2ERES__ABSTRACT(X1,X2),arr(arr(X1,bool),arr(arr(X1,X2),arr(X1,X2))))
| lhs_atom7(X1)
| ~ ne(X2) ),
inference(split_conjunct,[status(thm)],[c_0_255]) ).
cnf(c_0_375,plain,
( ap(f42(X1,X2,X3),X4) = ap(ap(c_2Ebool_2ERES__FORALL(X1),X3),f41(X1,X2,X4))
| lhs_atom49(X2,X1)
| ~ mem(X3,arr(X1,bool)) ),
inference(split_conjunct,[status(thm)],[c_0_256]) ).
cnf(c_0_376,plain,
( mem(c_2Ebool_2ETYPE__DEFINITION(X1,X2),arr(arr(X1,bool),arr(arr(X2,X1),bool)))
| lhs_atom7(X1)
| ~ ne(X2) ),
inference(split_conjunct,[status(thm)],[c_0_257]) ).
cnf(c_0_377,plain,
( p(ap(X1,ap(c_2Emin_2E_40(X2),X1)))
| lhs_atom7(X2)
| ~ p(ap(X1,X3))
| ~ mem(X3,X2)
| ~ mem(X1,arr(X2,bool)) ),
inference(split_conjunct,[status(thm)],[c_0_258]) ).
cnf(c_0_378,plain,
( mem(c_2Ebool_2ERES__SELECT(X1),arr(arr(X1,bool),arr(arr(X1,bool),X1)))
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_259]) ).
cnf(c_0_379,plain,
( lhs_atom3(X1)
| p(ap(c_2Ebool_2E_21(X1),X2))
| ~ mem(X2,arr(X1,bool))
| ~ p(ap(X2,esk2_2(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_260]) ).
cnf(c_0_380,plain,
( mem(c_2Ebool_2ERES__FORALL(X1),arr(arr(X1,bool),arr(arr(X1,bool),bool)))
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_381,plain,
( mem(c_2Ebool_2ERES__EXISTS__UNIQUE(X1),arr(arr(X1,bool),arr(arr(X1,bool),bool)))
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_262]) ).
cnf(c_0_382,plain,
( mem(c_2Ebool_2ERES__EXISTS(X1),arr(arr(X1,bool),arr(arr(X1,bool),bool)))
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_263]) ).
cnf(c_0_383,plain,
( lhs_atom3(X1)
| X2 = X3
| ~ mem(X2,X1)
| ~ mem(X3,X1)
| ~ p(ap(ap(c_2Emin_2E_3D(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_264]) ).
cnf(c_0_384,plain,
( lhs_atom3(X1)
| p(ap(X2,esk3_2(X1,X2)))
| ~ mem(X2,arr(X1,bool))
| ~ p(ap(c_2Ebool_2E_3F(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_265]) ).
cnf(c_0_385,plain,
( mem(c_2Ebool_2ECOND(X1),arr(bool,arr(X1,arr(X1,X1))))
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_266]) ).
cnf(c_0_386,plain,
( ap(f31(X1,X2,X3),X4) = ap(X3,X4)
| lhs_atom43(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_267]) ).
cnf(c_0_387,plain,
( ap(f13(X1,X2,X3),X4) = ap(X3,X4)
| lhs_atom34(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_268]) ).
cnf(c_0_388,plain,
( mem(c_2Ebool_2EIN(X1),arr(X1,arr(arr(X1,bool),bool)))
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_269]) ).
cnf(c_0_389,plain,
( lhs_atom3(X1)
| p(ap(X2,X3))
| ~ mem(X2,arr(X1,bool))
| ~ mem(X3,X1)
| ~ p(ap(c_2Ebool_2E_21(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_260]) ).
cnf(c_0_390,plain,
( mem(c_2Ebool_2Eliteral__case(X1,X2),arr(arr(X1,X2),arr(X1,X2)))
| lhs_atom7(X1)
| ~ ne(X2) ),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_391,plain,
( mem(c_2Ebool_2ELET(X1,X2),arr(arr(X1,X2),arr(X1,X2)))
| lhs_atom7(X1)
| ~ ne(X2) ),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_392,plain,
( ap(f45(X1,X2),X3) = ap(c_2Emin_2E_40(X1),f37(X1,X2,X3))
| lhs_atom46(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_272]) ).
cnf(c_0_393,plain,
( ap(f38(X1,X2),X3) = ap(c_2Ebool_2E_3F(X1),f37(X1,X2,X3))
| lhs_atom46(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_394,plain,
( ap(f35(X1,X2),X3) = ap(c_2Ebool_2E_21(X1),f34(X1,X2,X3))
| lhs_atom46(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_274]) ).
cnf(c_0_395,plain,
( ap(f11(X1,X2),X3) = ap(c_2Ebool_2E_21(X1),f10(X1,X2,X3))
| lhs_atom32(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_275]) ).
cnf(c_0_396,plain,
( lhs_atom3(X1)
| p(ap(c_2Ebool_2E_3F(X1),X2))
| ~ mem(X2,arr(X1,bool))
| ~ p(ap(X2,X3))
| ~ mem(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_265]) ).
cnf(c_0_397,plain,
( lhs_atom3(X1)
| mem(esk3_2(X1,X2),X1)
| ~ mem(X2,arr(X1,bool))
| ~ p(ap(c_2Ebool_2E_3F(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_265]) ).
cnf(c_0_398,plain,
( lhs_atom3(X1)
| p(ap(ap(c_2Emin_2E_3D(X1),X2),X3))
| ~ mem(X2,X1)
| ~ mem(X3,X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_264]) ).
cnf(c_0_399,plain,
( lhs_atom5(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_276]) ).
cnf(c_0_400,plain,
( lhs_atom5(X1)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(ap(ap(c_2Ebool_2E_5C_2F,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_277]) ).
cnf(c_0_401,plain,
( lhs_atom5(X1)
| p(X1)
| ~ mem(X2,bool)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_402,plain,
( lhs_atom5(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_403,plain,
( lhs_atom3(X1)
| p(ap(c_2Ebool_2E_21(X1),X2))
| mem(esk2_2(X1,X2),X1)
| ~ mem(X2,arr(X1,bool)) ),
inference(split_conjunct,[status(thm)],[c_0_260]) ).
cnf(c_0_404,plain,
( mem(c_2Ebool_2Eitself__case(X1,X2),arr(ty_2Ebool_2Eitself(X1),arr(X2,X2)))
| lhs_atom7(X1)
| ~ ne(X2) ),
inference(split_conjunct,[status(thm)],[c_0_279]) ).
cnf(c_0_405,plain,
( f31(X1,X2,X3) = X3
| lhs_atom7(X2)
| ~ mem(X3,arr(X2,X1))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_406,plain,
( mem(c_2Ebool_2EONTO(X1,X2),arr(arr(X1,X2),bool))
| lhs_atom7(X1)
| ~ ne(X2) ),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
cnf(c_0_407,plain,
( mem(c_2Ebool_2EONE__ONE(X1,X2),arr(arr(X1,X2),bool))
| lhs_atom7(X1)
| ~ ne(X2) ),
inference(split_conjunct,[status(thm)],[c_0_282]) ).
cnf(c_0_408,plain,
( mem(ap(X1,X2),X3)
| lhs_atom4(X1,X3,X4)
| ~ mem(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_409,plain,
( lhs_atom5(X1)
| p(ap(ap(c_2Ebool_2E_2F_5C,X1),X2))
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_410,plain,
( lhs_atom5(X1)
| p(ap(ap(c_2Ebool_2E_5C_2F,X1),X2))
| ~ mem(X2,bool)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_277]) ).
cnf(c_0_411,plain,
( lhs_atom5(X1)
| p(ap(ap(c_2Ebool_2E_5C_2F,X1),X2))
| ~ mem(X2,bool)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_277]) ).
cnf(c_0_412,plain,
( lhs_atom5(X1)
| p(ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2))
| ~ mem(X2,bool)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_276]) ).
cnf(c_0_413,plain,
( lhs_atom5(X1)
| p(ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2))
| p(X1)
| ~ mem(X2,bool) ),
inference(split_conjunct,[status(thm)],[c_0_276]) ).
cnf(c_0_414,plain,
( ap(f17(X1,X2),X3) = f16(X1,X2,X3)
| lhs_atom37(X2) ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
cnf(c_0_415,plain,
( mem(c_2Emin_2E_40(X1),arr(arr(X1,bool),X1))
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
cnf(c_0_416,plain,
( mem(c_2Emin_2E_3D(X1),arr(X1,arr(X1,bool)))
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_286]) ).
cnf(c_0_417,plain,
( mem(c_2Ebool_2E_3F_21(X1),arr(arr(X1,bool),bool))
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_287]) ).
cnf(c_0_418,plain,
( mem(c_2Ebool_2E_3F(X1),arr(arr(X1,bool),bool))
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_288]) ).
cnf(c_0_419,plain,
( mem(c_2Ebool_2E_21(X1),arr(arr(X1,bool),bool))
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_289]) ).
cnf(c_0_420,plain,
( ap(f40(X1,X2),X3) = ap(X2,X3)
| lhs_atom49(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_290]) ).
cnf(c_0_421,plain,
( ap(f32(X1,X2),X3) = ap(X3,X2)
| lhs_atom44(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_291]) ).
cnf(c_0_422,plain,
( ap(f7(X1),X2) = ap(c_2Ebool_2E_21(bool),f6(X1,X2))
| lhs_atom23(X1) ),
inference(split_conjunct,[status(thm)],[c_0_292]) ).
cnf(c_0_423,plain,
( ap(f4(X1),X2) = ap(c_2Ebool_2E_21(bool),f3(X2,X1))
| lhs_atom23(X1) ),
inference(split_conjunct,[status(thm)],[c_0_293]) ).
cnf(c_0_424,plain,
( ap(k(X1,X2),X3) = X2
| lhs_atom6(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_294]) ).
cnf(c_0_425,plain,
lhs_atom42(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_295]) ).
cnf(c_0_426,plain,
lhs_atom40(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_296]) ).
cnf(c_0_427,plain,
lhs_atom39(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_297]) ).
cnf(c_0_428,plain,
lhs_atom35(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_298]) ).
cnf(c_0_429,plain,
( lhs_atom5(X1)
| ~ p(X1)
| ~ p(ap(c_2Ebool_2E_7E,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_299]) ).
cnf(c_0_430,plain,
( mem(c_2Ebool_2EDATATYPE(X1),arr(X1,bool))
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_300]) ).
cnf(c_0_431,plain,
( ne(arr(X1,X2))
| lhs_atom3(X1)
| ~ ne(X2) ),
inference(split_conjunct,[status(thm)],[c_0_301]) ).
cnf(c_0_432,plain,
( lhs_atom5(X1)
| X1 = X2
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_302]) ).
cnf(c_0_433,plain,
( c_2Ebool_2Eliteral__case(X1,X2) = f14(X2,X1)
| lhs_atom7(X1)
| ~ ne(X2) ),
inference(split_conjunct,[status(thm)],[c_0_303]) ).
cnf(c_0_434,plain,
( c_2Ebool_2ETYPE__DEFINITION(X1,X2) = f30(X2,X1)
| lhs_atom7(X1)
| ~ ne(X2) ),
inference(split_conjunct,[status(thm)],[c_0_304]) ).
cnf(c_0_435,plain,
( c_2Ebool_2EONTO(X1,X2) = f24(X1,X2)
| lhs_atom7(X1)
| ~ ne(X2) ),
inference(split_conjunct,[status(thm)],[c_0_305]) ).
cnf(c_0_436,plain,
( c_2Ebool_2EONE__ONE(X1,X2) = f21(X2,X1)
| lhs_atom7(X1)
| ~ ne(X2) ),
inference(split_conjunct,[status(thm)],[c_0_306]) ).
cnf(c_0_437,plain,
( c_2Ebool_2ELET(X1,X2) = f14(X2,X1)
| lhs_atom7(X1)
| ~ ne(X2) ),
inference(split_conjunct,[status(thm)],[c_0_307]) ).
cnf(c_0_438,plain,
( lhs_atom5(X1)
| p(ap(c_2Ebool_2E_7E,X1))
| p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_299]) ).
cnf(c_0_439,plain,
( lhs_atom5(X1)
| X1 = X2
| p(X2)
| p(X1)
| ~ mem(X2,bool) ),
inference(split_conjunct,[status(thm)],[c_0_302]) ).
cnf(c_0_440,plain,
( ap(i(X1),X2) = X2
| lhs_atom6(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_308]) ).
cnf(c_0_441,plain,
( mem(c_2Ebool_2Ethe__value(X1),ty_2Ebool_2Eitself(X1))
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_309]) ).
cnf(c_0_442,plain,
( p(X1)
| lhs_atom28
| ~ mem(X1,bool) ),
inference(split_conjunct,[status(thm)],[c_0_310]) ).
cnf(c_0_443,plain,
( mem(c_2Ebool_2EARB(X1),X1)
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_311]) ).
cnf(c_0_444,plain,
( c_2Ebool_2EDATATYPE(X1) = k(X1,c_2Ebool_2ET)
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_312]) ).
cnf(c_0_445,plain,
( p(X1)
| lhs_atom37(X1)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_313]) ).
cnf(c_0_446,plain,
( ne(ty_2Ebool_2Eitself(X1))
| lhs_atom9(X1) ),
inference(split_conjunct,[status(thm)],[c_0_314]) ).
cnf(c_0_447,plain,
lhs_atom51(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
cnf(c_0_448,plain,
lhs_atom50(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_316]) ).
cnf(c_0_449,plain,
lhs_atom48(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_317]) ).
cnf(c_0_450,plain,
lhs_atom47(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_318]) ).
cnf(c_0_451,plain,
lhs_atom45(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_319]) ).
cnf(c_0_452,plain,
lhs_atom38(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_320]) ).
cnf(c_0_453,plain,
lhs_atom33(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_321]) ).
cnf(c_0_454,plain,
lhs_atom21(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_322]) ).
cnf(c_0_455,plain,
lhs_atom20(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_323]) ).
cnf(c_0_456,plain,
( c_2Ebool_2ERES__SELECT(X1) = f46(X1)
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_324]) ).
cnf(c_0_457,plain,
( c_2Ebool_2ERES__EXISTS__UNIQUE(X1) = f44(X1)
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_325]) ).
cnf(c_0_458,plain,
( c_2Ebool_2ERES__EXISTS(X1) = f39(X1)
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_326]) ).
cnf(c_0_459,plain,
( c_2Ebool_2ERES__FORALL(X1) = f36(X1)
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_327]) ).
cnf(c_0_460,plain,
( c_2Ebool_2EIN(X1) = f33(X1)
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
cnf(c_0_461,plain,
( c_2Ebool_2ECOND(X1) = f18(X1)
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_329]) ).
cnf(c_0_462,plain,
( c_2Ebool_2E_3F_21(X1) = f12(X1)
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_330]) ).
cnf(c_0_463,plain,
( c_2Ebool_2E_3F(X1) = f2(X1)
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_331]) ).
cnf(c_0_464,plain,
( c_2Ebool_2E_21(X1) = f1(X1)
| lhs_atom7(X1) ),
inference(split_conjunct,[status(thm)],[c_0_332]) ).
cnf(c_0_465,plain,
( lhs_atom29
| mem(esk4_0,bool) ),
inference(split_conjunct,[status(thm)],[c_0_333]) ).
cnf(c_0_466,plain,
( lhs_atom19
| $false ),
inference(split_conjunct,[status(thm)],[c_0_334]) ).
cnf(c_0_467,plain,
( i(bool) = i(bool)
| lhs_atom18 ),
inference(split_conjunct,[status(thm)],[c_0_335]) ).
cnf(c_0_468,plain,
( lhs_atom29
| ~ p(esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_333]) ).
cnf(c_0_469,plain,
lhs_atom30(X1),
inference(split_conjunct,[status(thm)],[c_0_336]) ).
cnf(c_0_470,plain,
lhs_atom26(X1),
inference(split_conjunct,[status(thm)],[c_0_337]) ).
cnf(c_0_471,plain,
lhs_atom24(X1),
inference(split_conjunct,[status(thm)],[c_0_338]) ).
cnf(c_0_472,plain,
lhs_atom52,
inference(split_conjunct,[status(thm)],[c_0_339]) ).
cnf(c_0_473,plain,
lhs_atom31,
inference(split_conjunct,[status(thm)],[c_0_340]) ).
cnf(c_0_474,plain,
lhs_atom27,
inference(split_conjunct,[status(thm)],[c_0_341]) ).
cnf(c_0_475,plain,
lhs_atom25,
inference(split_conjunct,[status(thm)],[c_0_342]) ).
cnf(c_0_476,plain,
lhs_atom17,
inference(split_conjunct,[status(thm)],[c_0_343]) ).
cnf(c_0_477,plain,
lhs_atom16,
inference(split_conjunct,[status(thm)],[c_0_344]) ).
cnf(c_0_478,plain,
lhs_atom15,
inference(split_conjunct,[status(thm)],[c_0_345]) ).
cnf(c_0_479,plain,
lhs_atom14,
inference(split_conjunct,[status(thm)],[c_0_346]) ).
cnf(c_0_480,plain,
lhs_atom13,
inference(split_conjunct,[status(thm)],[c_0_347]) ).
cnf(c_0_481,plain,
lhs_atom12,
inference(split_conjunct,[status(thm)],[c_0_348]) ).
cnf(c_0_482,plain,
lhs_atom11,
inference(split_conjunct,[status(thm)],[c_0_349]) ).
cnf(c_0_483,plain,
lhs_atom10,
inference(split_conjunct,[status(thm)],[c_0_350]) ).
cnf(c_0_484,plain,
lhs_atom8,
inference(split_conjunct,[status(thm)],[c_0_351]) ).
cnf(c_0_485,plain,
lhs_atom2,
inference(split_conjunct,[status(thm)],[c_0_352]) ).
cnf(c_0_486,plain,
lhs_atom1,
inference(split_conjunct,[status(thm)],[c_0_353]) ).
cnf(c_0_487,plain,
( ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),X4),c_2Ebool_2ET)),ap(ap(c_2Emin_2E_3D(X1),X5),X2))),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),X4),c_2Ebool_2EF)),ap(ap(c_2Emin_2E_3D(X1),X5),X3))) = ap(f15(X1,X2,X3,X4),X5)
| lhs_atom36(X2,X1)
| ~ mem(X4,bool)
| ~ mem(X3,X1) ),
c_0_354,
[final] ).
cnf(c_0_488,plain,
( lhs_atom4(X1,X2,X3)
| X1 = X4
| ~ mem(X4,arr(X3,X2))
| ap(X1,esk1_4(X1,X2,X3,X4)) != ap(X4,esk1_4(X1,X2,X3,X4)) ),
c_0_355,
[final] ).
cnf(c_0_489,plain,
( ap(ap(c_2Emin_2E_3D(bool),ap(X3,X5)),ap(c_2Ebool_2E_3F(X1),f27(X2,X1,X4,X5))) = ap(f28(X1,X2,X3,X4),X5)
| lhs_atom32(X3,X2)
| ~ mem(X4,arr(X1,X2)) ),
c_0_356,
[final] ).
cnf(c_0_490,plain,
( ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_21(X1),f26(X2,X1,X4))),ap(c_2Ebool_2E_21(X2),f28(X1,X2,X3,X4))) = ap(f29(X1,X2,X3),X4)
| lhs_atom32(X3,X2) ),
c_0_357,
[final] ).
cnf(c_0_491,plain,
( ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(X1),ap(X3,X4)),ap(X3,X5))),ap(ap(c_2Emin_2E_3D(X2),X4),X5)) = ap(f25(X1,X2,X3,X4),X5)
| lhs_atom41(X3,X2,X1)
| ~ mem(X4,X2) ),
c_0_358,
[final] ).
cnf(c_0_492,plain,
( ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(X1),ap(X3,X4)),ap(X3,X5))),ap(ap(c_2Emin_2E_3D(X2),X4),X5)) = ap(f19(X1,X2,X3,X4),X5)
| lhs_atom34(X3,X1,X2)
| ~ mem(X4,X2) ),
c_0_359,
[final] ).
cnf(c_0_493,plain,
( ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(X2,X3)),ap(X2,X4))),ap(ap(c_2Emin_2E_3D(X1),X3),X4)) = ap(f41(X1,X2,X3),X4)
| lhs_atom49(X2,X1)
| ~ mem(X3,X1) ),
c_0_360,
[final] ).
cnf(c_0_494,plain,
( ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(X2,X3)),ap(X2,X4))),ap(ap(c_2Emin_2E_3D(X1),X3),X4)) = ap(f10(X1,X2,X3),X4)
| lhs_atom32(X2,X1)
| ~ mem(X3,X1) ),
c_0_361,
[final] ).
cnf(c_0_495,plain,
( ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2ERES__EXISTS(X1),X2),f40(X1,X3))),ap(ap(c_2Ebool_2ERES__FORALL(X1),X2),f42(X1,X3,X2))) = ap(f43(X1,X2),X3)
| lhs_atom46(X2,X1) ),
c_0_362,
[final] ).
cnf(c_0_496,plain,
( ap(c_2Ebool_2E_21(X2),f25(X1,X2,X3,X4)) = ap(f26(X1,X2,X3),X4)
| lhs_atom41(X3,X2,X1) ),
c_0_363,
[final] ).
cnf(c_0_497,plain,
( ap(c_2Ebool_2E_3F(X1),f22(X2,X1,X3,X4)) = ap(f23(X1,X2,X3),X4)
| lhs_atom34(X3,X2,X1) ),
c_0_364,
[final] ).
cnf(c_0_498,plain,
( ap(c_2Ebool_2E_21(X2),f19(X1,X2,X3,X4)) = ap(f20(X1,X2,X3),X4)
| lhs_atom34(X3,X1,X2) ),
c_0_365,
[final] ).
cnf(c_0_499,plain,
( ap(f27(X1,X2,X3,X4),X5) = ap(ap(c_2Emin_2E_3D(X1),X4),ap(X3,X5))
| lhs_atom41(X3,X2,X1)
| ~ mem(X4,X1) ),
c_0_366,
[final] ).
cnf(c_0_500,plain,
( ap(f22(X1,X2,X3,X4),X5) = ap(ap(c_2Emin_2E_3D(X1),X4),ap(X3,X5))
| lhs_atom34(X3,X1,X2)
| ~ mem(X4,X1) ),
c_0_367,
[final] ).
cnf(c_0_501,plain,
( ap(c_2Emin_2E_40(X1),f15(X1,X3,X4,X2)) = ap(f16(X1,X2,X3),X4)
| lhs_atom37(X2)
| ~ mem(X3,X1) ),
c_0_368,
[final] ).
cnf(c_0_502,plain,
( lhs_atom4(X1,X2,X3)
| X1 = X4
| mem(esk1_4(X1,X2,X3,X4),X3)
| ~ mem(X4,arr(X3,X2)) ),
c_0_369,
[final] ).
cnf(c_0_503,plain,
( ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,X1),X3)),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,X2),X3)),X3)) = ap(f6(X1,X2),X3)
| lhs_atom23(X1)
| ~ mem(X2,bool) ),
c_0_370,
[final] ).
cnf(c_0_504,plain,
( ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,X2),ap(ap(c_2Emin_2E_3D_3D_3E,X1),X3))),X3) = ap(f3(X1,X2),X3)
| lhs_atom22(X1)
| ~ mem(X2,bool) ),
c_0_371,
[final] ).
cnf(c_0_505,plain,
( ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(X1),X4),X2)),ap(X3,X4)) = ap(f37(X1,X2,X3),X4)
| lhs_atom46(X2,X1)
| ~ mem(X3,arr(X1,bool)) ),
c_0_372,
[final] ).
cnf(c_0_506,plain,
( ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(X1),X4),X2)),ap(X3,X4)) = ap(f34(X1,X2,X3),X4)
| lhs_atom46(X2,X1)
| ~ mem(X3,arr(X1,bool)) ),
c_0_373,
[final] ).
cnf(c_0_507,plain,
( mem(c_2Ebool_2ERES__ABSTRACT(X1,X2),arr(arr(X1,bool),arr(arr(X1,X2),arr(X1,X2))))
| lhs_atom7(X1)
| ~ ne(X2) ),
c_0_374,
[final] ).
cnf(c_0_508,plain,
( ap(ap(c_2Ebool_2ERES__FORALL(X1),X3),f41(X1,X2,X4)) = ap(f42(X1,X2,X3),X4)
| lhs_atom49(X2,X1)
| ~ mem(X3,arr(X1,bool)) ),
c_0_375,
[final] ).
cnf(c_0_509,plain,
( mem(c_2Ebool_2ETYPE__DEFINITION(X1,X2),arr(arr(X1,bool),arr(arr(X2,X1),bool)))
| lhs_atom7(X1)
| ~ ne(X2) ),
c_0_376,
[final] ).
cnf(c_0_510,plain,
( p(ap(X1,ap(c_2Emin_2E_40(X2),X1)))
| lhs_atom7(X2)
| ~ p(ap(X1,X3))
| ~ mem(X3,X2)
| ~ mem(X1,arr(X2,bool)) ),
c_0_377,
[final] ).
cnf(c_0_511,plain,
( mem(c_2Ebool_2ERES__SELECT(X1),arr(arr(X1,bool),arr(arr(X1,bool),X1)))
| lhs_atom7(X1) ),
c_0_378,
[final] ).
cnf(c_0_512,plain,
( lhs_atom3(X1)
| p(ap(c_2Ebool_2E_21(X1),X2))
| ~ mem(X2,arr(X1,bool))
| ~ p(ap(X2,esk2_2(X1,X2))) ),
c_0_379,
[final] ).
cnf(c_0_513,plain,
( mem(c_2Ebool_2ERES__FORALL(X1),arr(arr(X1,bool),arr(arr(X1,bool),bool)))
| lhs_atom7(X1) ),
c_0_380,
[final] ).
cnf(c_0_514,plain,
( mem(c_2Ebool_2ERES__EXISTS__UNIQUE(X1),arr(arr(X1,bool),arr(arr(X1,bool),bool)))
| lhs_atom7(X1) ),
c_0_381,
[final] ).
cnf(c_0_515,plain,
( mem(c_2Ebool_2ERES__EXISTS(X1),arr(arr(X1,bool),arr(arr(X1,bool),bool)))
| lhs_atom7(X1) ),
c_0_382,
[final] ).
cnf(c_0_516,plain,
( lhs_atom3(X1)
| X2 = X3
| ~ mem(X2,X1)
| ~ mem(X3,X1)
| ~ p(ap(ap(c_2Emin_2E_3D(X1),X2),X3)) ),
c_0_383,
[final] ).
cnf(c_0_517,plain,
( lhs_atom3(X1)
| p(ap(X2,esk3_2(X1,X2)))
| ~ mem(X2,arr(X1,bool))
| ~ p(ap(c_2Ebool_2E_3F(X1),X2)) ),
c_0_384,
[final] ).
cnf(c_0_518,plain,
( mem(c_2Ebool_2ECOND(X1),arr(bool,arr(X1,arr(X1,X1))))
| lhs_atom7(X1) ),
c_0_385,
[final] ).
cnf(c_0_519,plain,
( ap(f31(X1,X2,X3),X4) = ap(X3,X4)
| lhs_atom43(X3,X1,X2) ),
c_0_386,
[final] ).
cnf(c_0_520,plain,
( ap(f13(X1,X2,X3),X4) = ap(X3,X4)
| lhs_atom34(X3,X1,X2) ),
c_0_387,
[final] ).
cnf(c_0_521,plain,
( mem(c_2Ebool_2EIN(X1),arr(X1,arr(arr(X1,bool),bool)))
| lhs_atom7(X1) ),
c_0_388,
[final] ).
cnf(c_0_522,plain,
( lhs_atom3(X1)
| p(ap(X2,X3))
| ~ mem(X2,arr(X1,bool))
| ~ mem(X3,X1)
| ~ p(ap(c_2Ebool_2E_21(X1),X2)) ),
c_0_389,
[final] ).
cnf(c_0_523,plain,
( mem(c_2Ebool_2Eliteral__case(X1,X2),arr(arr(X1,X2),arr(X1,X2)))
| lhs_atom7(X1)
| ~ ne(X2) ),
c_0_390,
[final] ).
cnf(c_0_524,plain,
( mem(c_2Ebool_2ELET(X1,X2),arr(arr(X1,X2),arr(X1,X2)))
| lhs_atom7(X1)
| ~ ne(X2) ),
c_0_391,
[final] ).
cnf(c_0_525,plain,
( ap(c_2Emin_2E_40(X1),f37(X1,X2,X3)) = ap(f45(X1,X2),X3)
| lhs_atom46(X2,X1) ),
c_0_392,
[final] ).
cnf(c_0_526,plain,
( ap(c_2Ebool_2E_3F(X1),f37(X1,X2,X3)) = ap(f38(X1,X2),X3)
| lhs_atom46(X2,X1) ),
c_0_393,
[final] ).
cnf(c_0_527,plain,
( ap(c_2Ebool_2E_21(X1),f34(X1,X2,X3)) = ap(f35(X1,X2),X3)
| lhs_atom46(X2,X1) ),
c_0_394,
[final] ).
cnf(c_0_528,plain,
( ap(c_2Ebool_2E_21(X1),f10(X1,X2,X3)) = ap(f11(X1,X2),X3)
| lhs_atom32(X2,X1) ),
c_0_395,
[final] ).
cnf(c_0_529,plain,
( lhs_atom3(X1)
| p(ap(c_2Ebool_2E_3F(X1),X2))
| ~ mem(X2,arr(X1,bool))
| ~ p(ap(X2,X3))
| ~ mem(X3,X1) ),
c_0_396,
[final] ).
cnf(c_0_530,plain,
( lhs_atom3(X1)
| mem(esk3_2(X1,X2),X1)
| ~ mem(X2,arr(X1,bool))
| ~ p(ap(c_2Ebool_2E_3F(X1),X2)) ),
c_0_397,
[final] ).
cnf(c_0_531,plain,
( lhs_atom3(X1)
| p(ap(ap(c_2Emin_2E_3D(X1),X2),X3))
| ~ mem(X2,X1)
| ~ mem(X3,X1)
| X2 != X3 ),
c_0_398,
[final] ).
cnf(c_0_532,plain,
( lhs_atom5(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2)) ),
c_0_399,
[final] ).
cnf(c_0_533,plain,
( lhs_atom5(X1)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(ap(ap(c_2Ebool_2E_5C_2F,X1),X2)) ),
c_0_400,
[final] ).
cnf(c_0_534,plain,
( lhs_atom5(X1)
| p(X1)
| ~ mem(X2,bool)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X1),X2)) ),
c_0_401,
[final] ).
cnf(c_0_535,plain,
( lhs_atom5(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X1),X2)) ),
c_0_402,
[final] ).
cnf(c_0_536,plain,
( lhs_atom3(X1)
| p(ap(c_2Ebool_2E_21(X1),X2))
| mem(esk2_2(X1,X2),X1)
| ~ mem(X2,arr(X1,bool)) ),
c_0_403,
[final] ).
cnf(c_0_537,plain,
( mem(c_2Ebool_2Eitself__case(X1,X2),arr(ty_2Ebool_2Eitself(X1),arr(X2,X2)))
| lhs_atom7(X1)
| ~ ne(X2) ),
c_0_404,
[final] ).
cnf(c_0_538,plain,
( f31(X1,X2,X3) = X3
| lhs_atom7(X2)
| ~ mem(X3,arr(X2,X1))
| ~ ne(X1) ),
c_0_405,
[final] ).
cnf(c_0_539,plain,
( mem(c_2Ebool_2EONTO(X1,X2),arr(arr(X1,X2),bool))
| lhs_atom7(X1)
| ~ ne(X2) ),
c_0_406,
[final] ).
cnf(c_0_540,plain,
( mem(c_2Ebool_2EONE__ONE(X1,X2),arr(arr(X1,X2),bool))
| lhs_atom7(X1)
| ~ ne(X2) ),
c_0_407,
[final] ).
cnf(c_0_541,plain,
( mem(ap(X1,X2),X3)
| lhs_atom4(X1,X3,X4)
| ~ mem(X2,X4) ),
c_0_408,
[final] ).
cnf(c_0_542,plain,
( lhs_atom5(X1)
| p(ap(ap(c_2Ebool_2E_2F_5C,X1),X2))
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X1) ),
c_0_409,
[final] ).
cnf(c_0_543,plain,
( lhs_atom5(X1)
| p(ap(ap(c_2Ebool_2E_5C_2F,X1),X2))
| ~ mem(X2,bool)
| ~ p(X1) ),
c_0_410,
[final] ).
cnf(c_0_544,plain,
( lhs_atom5(X1)
| p(ap(ap(c_2Ebool_2E_5C_2F,X1),X2))
| ~ mem(X2,bool)
| ~ p(X2) ),
c_0_411,
[final] ).
cnf(c_0_545,plain,
( lhs_atom5(X1)
| p(ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2))
| ~ mem(X2,bool)
| ~ p(X2) ),
c_0_412,
[final] ).
cnf(c_0_546,plain,
( lhs_atom5(X1)
| p(ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2))
| p(X1)
| ~ mem(X2,bool) ),
c_0_413,
[final] ).
cnf(c_0_547,plain,
( ap(f17(X1,X2),X3) = f16(X1,X2,X3)
| lhs_atom37(X2) ),
c_0_414,
[final] ).
cnf(c_0_548,plain,
( mem(c_2Emin_2E_40(X1),arr(arr(X1,bool),X1))
| lhs_atom7(X1) ),
c_0_415,
[final] ).
cnf(c_0_549,plain,
( mem(c_2Emin_2E_3D(X1),arr(X1,arr(X1,bool)))
| lhs_atom7(X1) ),
c_0_416,
[final] ).
cnf(c_0_550,plain,
( mem(c_2Ebool_2E_3F_21(X1),arr(arr(X1,bool),bool))
| lhs_atom7(X1) ),
c_0_417,
[final] ).
cnf(c_0_551,plain,
( mem(c_2Ebool_2E_3F(X1),arr(arr(X1,bool),bool))
| lhs_atom7(X1) ),
c_0_418,
[final] ).
cnf(c_0_552,plain,
( mem(c_2Ebool_2E_21(X1),arr(arr(X1,bool),bool))
| lhs_atom7(X1) ),
c_0_419,
[final] ).
cnf(c_0_553,plain,
( ap(f40(X1,X2),X3) = ap(X2,X3)
| lhs_atom49(X2,X1) ),
c_0_420,
[final] ).
cnf(c_0_554,plain,
( ap(f32(X1,X2),X3) = ap(X3,X2)
| lhs_atom44(X2,X1) ),
c_0_421,
[final] ).
cnf(c_0_555,plain,
( ap(c_2Ebool_2E_21(bool),f6(X1,X2)) = ap(f7(X1),X2)
| lhs_atom23(X1) ),
c_0_422,
[final] ).
cnf(c_0_556,plain,
( ap(c_2Ebool_2E_21(bool),f3(X2,X1)) = ap(f4(X1),X2)
| lhs_atom23(X1) ),
c_0_423,
[final] ).
cnf(c_0_557,plain,
( ap(k(X1,X2),X3) = X2
| lhs_atom6(X3,X1) ),
c_0_424,
[final] ).
cnf(c_0_558,plain,
lhs_atom42(X1,X2,X3),
c_0_425,
[final] ).
cnf(c_0_559,plain,
lhs_atom40(X1,X2,X3),
c_0_426,
[final] ).
cnf(c_0_560,plain,
lhs_atom39(X1,X2,X3),
c_0_427,
[final] ).
cnf(c_0_561,plain,
lhs_atom35(X1,X2,X3),
c_0_428,
[final] ).
cnf(c_0_562,plain,
( lhs_atom5(X1)
| ~ p(X1)
| ~ p(ap(c_2Ebool_2E_7E,X1)) ),
c_0_429,
[final] ).
cnf(c_0_563,plain,
( mem(c_2Ebool_2EDATATYPE(X1),arr(X1,bool))
| lhs_atom7(X1) ),
c_0_430,
[final] ).
cnf(c_0_564,plain,
( ne(arr(X1,X2))
| lhs_atom3(X1)
| ~ ne(X2) ),
c_0_431,
[final] ).
cnf(c_0_565,plain,
( lhs_atom5(X1)
| X1 = X2
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X1) ),
c_0_432,
[final] ).
cnf(c_0_566,plain,
( f14(X2,X1) = c_2Ebool_2Eliteral__case(X1,X2)
| lhs_atom7(X1)
| ~ ne(X2) ),
c_0_433,
[final] ).
cnf(c_0_567,plain,
( f30(X2,X1) = c_2Ebool_2ETYPE__DEFINITION(X1,X2)
| lhs_atom7(X1)
| ~ ne(X2) ),
c_0_434,
[final] ).
cnf(c_0_568,plain,
( f24(X1,X2) = c_2Ebool_2EONTO(X1,X2)
| lhs_atom7(X1)
| ~ ne(X2) ),
c_0_435,
[final] ).
cnf(c_0_569,plain,
( f21(X2,X1) = c_2Ebool_2EONE__ONE(X1,X2)
| lhs_atom7(X1)
| ~ ne(X2) ),
c_0_436,
[final] ).
cnf(c_0_570,plain,
( f14(X2,X1) = c_2Ebool_2ELET(X1,X2)
| lhs_atom7(X1)
| ~ ne(X2) ),
c_0_437,
[final] ).
cnf(c_0_571,plain,
( lhs_atom5(X1)
| p(ap(c_2Ebool_2E_7E,X1))
| p(X1) ),
c_0_438,
[final] ).
cnf(c_0_572,plain,
( lhs_atom5(X1)
| X1 = X2
| p(X2)
| p(X1)
| ~ mem(X2,bool) ),
c_0_439,
[final] ).
cnf(c_0_573,plain,
( ap(i(X1),X2) = X2
| lhs_atom6(X2,X1) ),
c_0_440,
[final] ).
cnf(c_0_574,plain,
( mem(c_2Ebool_2Ethe__value(X1),ty_2Ebool_2Eitself(X1))
| lhs_atom7(X1) ),
c_0_441,
[final] ).
cnf(c_0_575,plain,
( p(X1)
| lhs_atom28
| ~ mem(X1,bool) ),
c_0_442,
[final] ).
cnf(c_0_576,plain,
( mem(c_2Ebool_2EARB(X1),X1)
| lhs_atom7(X1) ),
c_0_443,
[final] ).
cnf(c_0_577,plain,
( k(X1,c_2Ebool_2ET) = c_2Ebool_2EDATATYPE(X1)
| lhs_atom7(X1) ),
c_0_444,
[final] ).
cnf(c_0_578,plain,
( p(X1)
| lhs_atom37(X1)
| ~ p(X1) ),
c_0_445,
[final] ).
cnf(c_0_579,plain,
( ne(ty_2Ebool_2Eitself(X1))
| lhs_atom9(X1) ),
c_0_446,
[final] ).
cnf(c_0_580,plain,
lhs_atom51(X1,X2),
c_0_447,
[final] ).
cnf(c_0_581,plain,
lhs_atom50(X1,X2),
c_0_448,
[final] ).
cnf(c_0_582,plain,
lhs_atom48(X1,X2),
c_0_449,
[final] ).
cnf(c_0_583,plain,
lhs_atom47(X1,X2),
c_0_450,
[final] ).
cnf(c_0_584,plain,
lhs_atom45(X1,X2),
c_0_451,
[final] ).
cnf(c_0_585,plain,
lhs_atom38(X1,X2),
c_0_452,
[final] ).
cnf(c_0_586,plain,
lhs_atom33(X1,X2),
c_0_453,
[final] ).
cnf(c_0_587,plain,
lhs_atom21(X1,X2),
c_0_454,
[final] ).
cnf(c_0_588,plain,
lhs_atom20(X1,X2),
c_0_455,
[final] ).
cnf(c_0_589,plain,
( c_2Ebool_2ERES__SELECT(X1) = f46(X1)
| lhs_atom7(X1) ),
c_0_456,
[final] ).
cnf(c_0_590,plain,
( f44(X1) = c_2Ebool_2ERES__EXISTS__UNIQUE(X1)
| lhs_atom7(X1) ),
c_0_457,
[final] ).
cnf(c_0_591,plain,
( f39(X1) = c_2Ebool_2ERES__EXISTS(X1)
| lhs_atom7(X1) ),
c_0_458,
[final] ).
cnf(c_0_592,plain,
( f36(X1) = c_2Ebool_2ERES__FORALL(X1)
| lhs_atom7(X1) ),
c_0_459,
[final] ).
cnf(c_0_593,plain,
( f33(X1) = c_2Ebool_2EIN(X1)
| lhs_atom7(X1) ),
c_0_460,
[final] ).
cnf(c_0_594,plain,
( f18(X1) = c_2Ebool_2ECOND(X1)
| lhs_atom7(X1) ),
c_0_461,
[final] ).
cnf(c_0_595,plain,
( f12(X1) = c_2Ebool_2E_3F_21(X1)
| lhs_atom7(X1) ),
c_0_462,
[final] ).
cnf(c_0_596,plain,
( f2(X1) = c_2Ebool_2E_3F(X1)
| lhs_atom7(X1) ),
c_0_463,
[final] ).
cnf(c_0_597,plain,
( f1(X1) = c_2Ebool_2E_21(X1)
| lhs_atom7(X1) ),
c_0_464,
[final] ).
cnf(c_0_598,plain,
( lhs_atom29
| mem(esk4_0,bool) ),
c_0_465,
[final] ).
cnf(c_0_599,plain,
( lhs_atom19
| $false ),
c_0_466,
[final] ).
cnf(c_0_600,plain,
( i(bool) = i(bool)
| lhs_atom18 ),
c_0_467,
[final] ).
cnf(c_0_601,plain,
( lhs_atom29
| ~ p(esk4_0) ),
c_0_468,
[final] ).
cnf(c_0_602,plain,
lhs_atom30(X1),
c_0_469,
[final] ).
cnf(c_0_603,plain,
lhs_atom26(X1),
c_0_470,
[final] ).
cnf(c_0_604,plain,
lhs_atom24(X1),
c_0_471,
[final] ).
cnf(c_0_605,plain,
lhs_atom52,
c_0_472,
[final] ).
cnf(c_0_606,plain,
lhs_atom31,
c_0_473,
[final] ).
cnf(c_0_607,plain,
lhs_atom27,
c_0_474,
[final] ).
cnf(c_0_608,plain,
lhs_atom25,
c_0_475,
[final] ).
cnf(c_0_609,plain,
lhs_atom17,
c_0_476,
[final] ).
cnf(c_0_610,plain,
lhs_atom16,
c_0_477,
[final] ).
cnf(c_0_611,plain,
lhs_atom15,
c_0_478,
[final] ).
cnf(c_0_612,plain,
lhs_atom14,
c_0_479,
[final] ).
cnf(c_0_613,plain,
lhs_atom13,
c_0_480,
[final] ).
cnf(c_0_614,plain,
lhs_atom12,
c_0_481,
[final] ).
cnf(c_0_615,plain,
lhs_atom11,
c_0_482,
[final] ).
cnf(c_0_616,plain,
lhs_atom10,
c_0_483,
[final] ).
cnf(c_0_617,plain,
lhs_atom8,
c_0_484,
[final] ).
cnf(c_0_618,plain,
lhs_atom2,
c_0_485,
[final] ).
cnf(c_0_619,plain,
lhs_atom1,
c_0_486,
[final] ).
% End CNF derivation
cnf(c_0_487_0,axiom,
( ~ mem(X2,X1)
| ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),X4),c_2Ebool_2ET)),ap(ap(c_2Emin_2E_3D(X1),X5),X2))),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),X4),c_2Ebool_2EF)),ap(ap(c_2Emin_2E_3D(X1),X5),X3))) = ap(f15(X1,X2,X3,X4),X5)
| ~ mem(X4,bool)
| ~ mem(X3,X1) ),
inference(unfold_definition,[status(thm)],[c_0_487,def_lhs_atom36]) ).
cnf(c_0_488_0,axiom,
( ~ mem(X1,arr(X3,X2))
| X1 = X4
| ~ mem(X4,arr(X3,X2))
| ap(X1,sk1_esk1_4(X1,X2,X3,X4)) != ap(X4,sk1_esk1_4(X1,X2,X3,X4)) ),
inference(unfold_definition,[status(thm)],[c_0_488,def_lhs_atom4]) ).
cnf(c_0_489_0,axiom,
( ~ mem(X3,arr(X2,bool))
| ap(ap(c_2Emin_2E_3D(bool),ap(X3,X5)),ap(c_2Ebool_2E_3F(X1),f27(X2,X1,X4,X5))) = ap(f28(X1,X2,X3,X4),X5)
| ~ mem(X4,arr(X1,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_489,def_lhs_atom32]) ).
cnf(c_0_490_0,axiom,
( ~ mem(X3,arr(X2,bool))
| ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_21(X1),f26(X2,X1,X4))),ap(c_2Ebool_2E_21(X2),f28(X1,X2,X3,X4))) = ap(f29(X1,X2,X3),X4) ),
inference(unfold_definition,[status(thm)],[c_0_490,def_lhs_atom32]) ).
cnf(c_0_491_0,axiom,
( ~ mem(X3,arr(X2,X1))
| ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(X1),ap(X3,X4)),ap(X3,X5))),ap(ap(c_2Emin_2E_3D(X2),X4),X5)) = ap(f25(X1,X2,X3,X4),X5)
| ~ mem(X4,X2) ),
inference(unfold_definition,[status(thm)],[c_0_491,def_lhs_atom41]) ).
cnf(c_0_492_0,axiom,
( ~ mem(X3,arr(X2,X1))
| ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(X1),ap(X3,X4)),ap(X3,X5))),ap(ap(c_2Emin_2E_3D(X2),X4),X5)) = ap(f19(X1,X2,X3,X4),X5)
| ~ mem(X4,X2) ),
inference(unfold_definition,[status(thm)],[c_0_492,def_lhs_atom34]) ).
cnf(c_0_493_0,axiom,
( ~ mem(X2,arr(X1,bool))
| ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(X2,X3)),ap(X2,X4))),ap(ap(c_2Emin_2E_3D(X1),X3),X4)) = ap(f41(X1,X2,X3),X4)
| ~ mem(X3,X1) ),
inference(unfold_definition,[status(thm)],[c_0_493,def_lhs_atom49]) ).
cnf(c_0_494_0,axiom,
( ~ mem(X2,arr(X1,bool))
| ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(X2,X3)),ap(X2,X4))),ap(ap(c_2Emin_2E_3D(X1),X3),X4)) = ap(f10(X1,X2,X3),X4)
| ~ mem(X3,X1) ),
inference(unfold_definition,[status(thm)],[c_0_494,def_lhs_atom32]) ).
cnf(c_0_495_0,axiom,
( ~ mem(X2,arr(X1,bool))
| ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2ERES__EXISTS(X1),X2),f40(X1,X3))),ap(ap(c_2Ebool_2ERES__FORALL(X1),X2),f42(X1,X3,X2))) = ap(f43(X1,X2),X3) ),
inference(unfold_definition,[status(thm)],[c_0_495,def_lhs_atom46]) ).
cnf(c_0_496_0,axiom,
( ~ mem(X3,arr(X2,X1))
| ap(c_2Ebool_2E_21(X2),f25(X1,X2,X3,X4)) = ap(f26(X1,X2,X3),X4) ),
inference(unfold_definition,[status(thm)],[c_0_496,def_lhs_atom41]) ).
cnf(c_0_497_0,axiom,
( ~ mem(X3,arr(X1,X2))
| ap(c_2Ebool_2E_3F(X1),f22(X2,X1,X3,X4)) = ap(f23(X1,X2,X3),X4) ),
inference(unfold_definition,[status(thm)],[c_0_497,def_lhs_atom34]) ).
cnf(c_0_498_0,axiom,
( ~ mem(X3,arr(X2,X1))
| ap(c_2Ebool_2E_21(X2),f19(X1,X2,X3,X4)) = ap(f20(X1,X2,X3),X4) ),
inference(unfold_definition,[status(thm)],[c_0_498,def_lhs_atom34]) ).
cnf(c_0_499_0,axiom,
( ~ mem(X3,arr(X2,X1))
| ap(f27(X1,X2,X3,X4),X5) = ap(ap(c_2Emin_2E_3D(X1),X4),ap(X3,X5))
| ~ mem(X4,X1) ),
inference(unfold_definition,[status(thm)],[c_0_499,def_lhs_atom41]) ).
cnf(c_0_500_0,axiom,
( ~ mem(X3,arr(X2,X1))
| ap(f22(X1,X2,X3,X4),X5) = ap(ap(c_2Emin_2E_3D(X1),X4),ap(X3,X5))
| ~ mem(X4,X1) ),
inference(unfold_definition,[status(thm)],[c_0_500,def_lhs_atom34]) ).
cnf(c_0_501_0,axiom,
( ~ mem(X2,bool)
| ap(c_2Emin_2E_40(X1),f15(X1,X3,X4,X2)) = ap(f16(X1,X2,X3),X4)
| ~ mem(X3,X1) ),
inference(unfold_definition,[status(thm)],[c_0_501,def_lhs_atom37]) ).
cnf(c_0_502_0,axiom,
( ~ mem(X1,arr(X3,X2))
| X1 = X4
| mem(sk1_esk1_4(X1,X2,X3,X4),X3)
| ~ mem(X4,arr(X3,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_502,def_lhs_atom4]) ).
cnf(c_0_503_0,axiom,
( ~ mem(X1,bool)
| ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,X1),X3)),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,X2),X3)),X3)) = ap(f6(X1,X2),X3)
| ~ mem(X2,bool) ),
inference(unfold_definition,[status(thm)],[c_0_503,def_lhs_atom23]) ).
cnf(c_0_504_0,axiom,
( ~ mem(X1,bool)
| ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,X2),ap(ap(c_2Emin_2E_3D_3D_3E,X1),X3))),X3) = ap(f3(X1,X2),X3)
| ~ mem(X2,bool) ),
inference(unfold_definition,[status(thm)],[c_0_504,def_lhs_atom22]) ).
cnf(c_0_505_0,axiom,
( ~ mem(X2,arr(X1,bool))
| ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(X1),X4),X2)),ap(X3,X4)) = ap(f37(X1,X2,X3),X4)
| ~ mem(X3,arr(X1,bool)) ),
inference(unfold_definition,[status(thm)],[c_0_505,def_lhs_atom46]) ).
cnf(c_0_506_0,axiom,
( ~ mem(X2,arr(X1,bool))
| ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(X1),X4),X2)),ap(X3,X4)) = ap(f34(X1,X2,X3),X4)
| ~ mem(X3,arr(X1,bool)) ),
inference(unfold_definition,[status(thm)],[c_0_506,def_lhs_atom46]) ).
cnf(c_0_507_0,axiom,
( ~ ne(X1)
| mem(c_2Ebool_2ERES__ABSTRACT(X1,X2),arr(arr(X1,bool),arr(arr(X1,X2),arr(X1,X2))))
| ~ ne(X2) ),
inference(unfold_definition,[status(thm)],[c_0_507,def_lhs_atom7]) ).
cnf(c_0_508_0,axiom,
( ~ mem(X2,arr(X1,bool))
| ap(ap(c_2Ebool_2ERES__FORALL(X1),X3),f41(X1,X2,X4)) = ap(f42(X1,X2,X3),X4)
| ~ mem(X3,arr(X1,bool)) ),
inference(unfold_definition,[status(thm)],[c_0_508,def_lhs_atom49]) ).
cnf(c_0_509_0,axiom,
( ~ ne(X1)
| mem(c_2Ebool_2ETYPE__DEFINITION(X1,X2),arr(arr(X1,bool),arr(arr(X2,X1),bool)))
| ~ ne(X2) ),
inference(unfold_definition,[status(thm)],[c_0_509,def_lhs_atom7]) ).
cnf(c_0_510_0,axiom,
( ~ ne(X2)
| p(ap(X1,ap(c_2Emin_2E_40(X2),X1)))
| ~ p(ap(X1,X3))
| ~ mem(X3,X2)
| ~ mem(X1,arr(X2,bool)) ),
inference(unfold_definition,[status(thm)],[c_0_510,def_lhs_atom7]) ).
cnf(c_0_511_0,axiom,
( ~ ne(X1)
| mem(c_2Ebool_2ERES__SELECT(X1),arr(arr(X1,bool),arr(arr(X1,bool),X1))) ),
inference(unfold_definition,[status(thm)],[c_0_511,def_lhs_atom7]) ).
cnf(c_0_512_0,axiom,
( ~ ne(X1)
| p(ap(c_2Ebool_2E_21(X1),X2))
| ~ mem(X2,arr(X1,bool))
| ~ p(ap(X2,sk1_esk2_2(X1,X2))) ),
inference(unfold_definition,[status(thm)],[c_0_512,def_lhs_atom3]) ).
cnf(c_0_513_0,axiom,
( ~ ne(X1)
| mem(c_2Ebool_2ERES__FORALL(X1),arr(arr(X1,bool),arr(arr(X1,bool),bool))) ),
inference(unfold_definition,[status(thm)],[c_0_513,def_lhs_atom7]) ).
cnf(c_0_514_0,axiom,
( ~ ne(X1)
| mem(c_2Ebool_2ERES__EXISTS__UNIQUE(X1),arr(arr(X1,bool),arr(arr(X1,bool),bool))) ),
inference(unfold_definition,[status(thm)],[c_0_514,def_lhs_atom7]) ).
cnf(c_0_515_0,axiom,
( ~ ne(X1)
| mem(c_2Ebool_2ERES__EXISTS(X1),arr(arr(X1,bool),arr(arr(X1,bool),bool))) ),
inference(unfold_definition,[status(thm)],[c_0_515,def_lhs_atom7]) ).
cnf(c_0_516_0,axiom,
( ~ ne(X1)
| X2 = X3
| ~ mem(X2,X1)
| ~ mem(X3,X1)
| ~ p(ap(ap(c_2Emin_2E_3D(X1),X2),X3)) ),
inference(unfold_definition,[status(thm)],[c_0_516,def_lhs_atom3]) ).
cnf(c_0_517_0,axiom,
( ~ ne(X1)
| p(ap(X2,sk1_esk3_2(X1,X2)))
| ~ mem(X2,arr(X1,bool))
| ~ p(ap(c_2Ebool_2E_3F(X1),X2)) ),
inference(unfold_definition,[status(thm)],[c_0_517,def_lhs_atom3]) ).
cnf(c_0_518_0,axiom,
( ~ ne(X1)
| mem(c_2Ebool_2ECOND(X1),arr(bool,arr(X1,arr(X1,X1)))) ),
inference(unfold_definition,[status(thm)],[c_0_518,def_lhs_atom7]) ).
cnf(c_0_519_0,axiom,
( ~ mem(X3,arr(X2,X1))
| ap(f31(X1,X2,X3),X4) = ap(X3,X4) ),
inference(unfold_definition,[status(thm)],[c_0_519,def_lhs_atom43]) ).
cnf(c_0_520_0,axiom,
( ~ mem(X3,arr(X2,X1))
| ap(f13(X1,X2,X3),X4) = ap(X3,X4) ),
inference(unfold_definition,[status(thm)],[c_0_520,def_lhs_atom34]) ).
cnf(c_0_521_0,axiom,
( ~ ne(X1)
| mem(c_2Ebool_2EIN(X1),arr(X1,arr(arr(X1,bool),bool))) ),
inference(unfold_definition,[status(thm)],[c_0_521,def_lhs_atom7]) ).
cnf(c_0_522_0,axiom,
( ~ ne(X1)
| p(ap(X2,X3))
| ~ mem(X2,arr(X1,bool))
| ~ mem(X3,X1)
| ~ p(ap(c_2Ebool_2E_21(X1),X2)) ),
inference(unfold_definition,[status(thm)],[c_0_522,def_lhs_atom3]) ).
cnf(c_0_523_0,axiom,
( ~ ne(X1)
| mem(c_2Ebool_2Eliteral__case(X1,X2),arr(arr(X1,X2),arr(X1,X2)))
| ~ ne(X2) ),
inference(unfold_definition,[status(thm)],[c_0_523,def_lhs_atom7]) ).
cnf(c_0_524_0,axiom,
( ~ ne(X1)
| mem(c_2Ebool_2ELET(X1,X2),arr(arr(X1,X2),arr(X1,X2)))
| ~ ne(X2) ),
inference(unfold_definition,[status(thm)],[c_0_524,def_lhs_atom7]) ).
cnf(c_0_525_0,axiom,
( ~ mem(X2,arr(X1,bool))
| ap(c_2Emin_2E_40(X1),f37(X1,X2,X3)) = ap(f45(X1,X2),X3) ),
inference(unfold_definition,[status(thm)],[c_0_525,def_lhs_atom46]) ).
cnf(c_0_526_0,axiom,
( ~ mem(X2,arr(X1,bool))
| ap(c_2Ebool_2E_3F(X1),f37(X1,X2,X3)) = ap(f38(X1,X2),X3) ),
inference(unfold_definition,[status(thm)],[c_0_526,def_lhs_atom46]) ).
cnf(c_0_527_0,axiom,
( ~ mem(X2,arr(X1,bool))
| ap(c_2Ebool_2E_21(X1),f34(X1,X2,X3)) = ap(f35(X1,X2),X3) ),
inference(unfold_definition,[status(thm)],[c_0_527,def_lhs_atom46]) ).
cnf(c_0_528_0,axiom,
( ~ mem(X2,arr(X1,bool))
| ap(c_2Ebool_2E_21(X1),f10(X1,X2,X3)) = ap(f11(X1,X2),X3) ),
inference(unfold_definition,[status(thm)],[c_0_528,def_lhs_atom32]) ).
cnf(c_0_529_0,axiom,
( ~ ne(X1)
| p(ap(c_2Ebool_2E_3F(X1),X2))
| ~ mem(X2,arr(X1,bool))
| ~ p(ap(X2,X3))
| ~ mem(X3,X1) ),
inference(unfold_definition,[status(thm)],[c_0_529,def_lhs_atom3]) ).
cnf(c_0_530_0,axiom,
( ~ ne(X1)
| mem(sk1_esk3_2(X1,X2),X1)
| ~ mem(X2,arr(X1,bool))
| ~ p(ap(c_2Ebool_2E_3F(X1),X2)) ),
inference(unfold_definition,[status(thm)],[c_0_530,def_lhs_atom3]) ).
cnf(c_0_531_0,axiom,
( ~ ne(X1)
| p(ap(ap(c_2Emin_2E_3D(X1),X2),X3))
| ~ mem(X2,X1)
| ~ mem(X3,X1)
| X2 != X3 ),
inference(unfold_definition,[status(thm)],[c_0_531,def_lhs_atom3]) ).
cnf(c_0_532_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2)) ),
inference(unfold_definition,[status(thm)],[c_0_532,def_lhs_atom5]) ).
cnf(c_0_533_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(ap(ap(c_2Ebool_2E_5C_2F,X1),X2)) ),
inference(unfold_definition,[status(thm)],[c_0_533,def_lhs_atom5]) ).
cnf(c_0_534_0,axiom,
( ~ mem(X1,bool)
| p(X1)
| ~ mem(X2,bool)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X1),X2)) ),
inference(unfold_definition,[status(thm)],[c_0_534,def_lhs_atom5]) ).
cnf(c_0_535_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| ~ mem(X2,bool)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X1),X2)) ),
inference(unfold_definition,[status(thm)],[c_0_535,def_lhs_atom5]) ).
cnf(c_0_536_0,axiom,
( ~ ne(X1)
| p(ap(c_2Ebool_2E_21(X1),X2))
| mem(sk1_esk2_2(X1,X2),X1)
| ~ mem(X2,arr(X1,bool)) ),
inference(unfold_definition,[status(thm)],[c_0_536,def_lhs_atom3]) ).
cnf(c_0_537_0,axiom,
( ~ ne(X1)
| mem(c_2Ebool_2Eitself__case(X1,X2),arr(ty_2Ebool_2Eitself(X1),arr(X2,X2)))
| ~ ne(X2) ),
inference(unfold_definition,[status(thm)],[c_0_537,def_lhs_atom7]) ).
cnf(c_0_538_0,axiom,
( ~ ne(X2)
| f31(X1,X2,X3) = X3
| ~ mem(X3,arr(X2,X1))
| ~ ne(X1) ),
inference(unfold_definition,[status(thm)],[c_0_538,def_lhs_atom7]) ).
cnf(c_0_539_0,axiom,
( ~ ne(X1)
| mem(c_2Ebool_2EONTO(X1,X2),arr(arr(X1,X2),bool))
| ~ ne(X2) ),
inference(unfold_definition,[status(thm)],[c_0_539,def_lhs_atom7]) ).
cnf(c_0_540_0,axiom,
( ~ ne(X1)
| mem(c_2Ebool_2EONE__ONE(X1,X2),arr(arr(X1,X2),bool))
| ~ ne(X2) ),
inference(unfold_definition,[status(thm)],[c_0_540,def_lhs_atom7]) ).
cnf(c_0_541_0,axiom,
( ~ mem(X1,arr(X4,X3))
| mem(ap(X1,X2),X3)
| ~ mem(X2,X4) ),
inference(unfold_definition,[status(thm)],[c_0_541,def_lhs_atom4]) ).
cnf(c_0_542_0,axiom,
( ~ mem(X1,bool)
| p(ap(ap(c_2Ebool_2E_2F_5C,X1),X2))
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_542,def_lhs_atom5]) ).
cnf(c_0_543_0,axiom,
( ~ mem(X1,bool)
| p(ap(ap(c_2Ebool_2E_5C_2F,X1),X2))
| ~ mem(X2,bool)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_543,def_lhs_atom5]) ).
cnf(c_0_544_0,axiom,
( ~ mem(X1,bool)
| p(ap(ap(c_2Ebool_2E_5C_2F,X1),X2))
| ~ mem(X2,bool)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_544,def_lhs_atom5]) ).
cnf(c_0_545_0,axiom,
( ~ mem(X1,bool)
| p(ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2))
| ~ mem(X2,bool)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_545,def_lhs_atom5]) ).
cnf(c_0_546_0,axiom,
( ~ mem(X1,bool)
| p(ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2))
| p(X1)
| ~ mem(X2,bool) ),
inference(unfold_definition,[status(thm)],[c_0_546,def_lhs_atom5]) ).
cnf(c_0_547_0,axiom,
( ~ mem(X2,bool)
| ap(f17(X1,X2),X3) = f16(X1,X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_547,def_lhs_atom37]) ).
cnf(c_0_548_0,axiom,
( ~ ne(X1)
| mem(c_2Emin_2E_40(X1),arr(arr(X1,bool),X1)) ),
inference(unfold_definition,[status(thm)],[c_0_548,def_lhs_atom7]) ).
cnf(c_0_549_0,axiom,
( ~ ne(X1)
| mem(c_2Emin_2E_3D(X1),arr(X1,arr(X1,bool))) ),
inference(unfold_definition,[status(thm)],[c_0_549,def_lhs_atom7]) ).
cnf(c_0_550_0,axiom,
( ~ ne(X1)
| mem(c_2Ebool_2E_3F_21(X1),arr(arr(X1,bool),bool)) ),
inference(unfold_definition,[status(thm)],[c_0_550,def_lhs_atom7]) ).
cnf(c_0_551_0,axiom,
( ~ ne(X1)
| mem(c_2Ebool_2E_3F(X1),arr(arr(X1,bool),bool)) ),
inference(unfold_definition,[status(thm)],[c_0_551,def_lhs_atom7]) ).
cnf(c_0_552_0,axiom,
( ~ ne(X1)
| mem(c_2Ebool_2E_21(X1),arr(arr(X1,bool),bool)) ),
inference(unfold_definition,[status(thm)],[c_0_552,def_lhs_atom7]) ).
cnf(c_0_553_0,axiom,
( ~ mem(X2,arr(X1,bool))
| ap(f40(X1,X2),X3) = ap(X2,X3) ),
inference(unfold_definition,[status(thm)],[c_0_553,def_lhs_atom49]) ).
cnf(c_0_554_0,axiom,
( ~ mem(X2,X1)
| ap(f32(X1,X2),X3) = ap(X3,X2) ),
inference(unfold_definition,[status(thm)],[c_0_554,def_lhs_atom44]) ).
cnf(c_0_555_0,axiom,
( ~ mem(X1,bool)
| ap(c_2Ebool_2E_21(bool),f6(X1,X2)) = ap(f7(X1),X2) ),
inference(unfold_definition,[status(thm)],[c_0_555,def_lhs_atom23]) ).
cnf(c_0_556_0,axiom,
( ~ mem(X1,bool)
| ap(c_2Ebool_2E_21(bool),f3(X2,X1)) = ap(f4(X1),X2) ),
inference(unfold_definition,[status(thm)],[c_0_556,def_lhs_atom23]) ).
cnf(c_0_557_0,axiom,
( ~ mem(X3,X1)
| ap(k(X1,X2),X3) = X2 ),
inference(unfold_definition,[status(thm)],[c_0_557,def_lhs_atom6]) ).
cnf(c_0_562_0,axiom,
( ~ mem(X1,bool)
| ~ p(X1)
| ~ p(ap(c_2Ebool_2E_7E,X1)) ),
inference(unfold_definition,[status(thm)],[c_0_562,def_lhs_atom5]) ).
cnf(c_0_563_0,axiom,
( ~ ne(X1)
| mem(c_2Ebool_2EDATATYPE(X1),arr(X1,bool)) ),
inference(unfold_definition,[status(thm)],[c_0_563,def_lhs_atom7]) ).
cnf(c_0_564_0,axiom,
( ~ ne(X1)
| ne(arr(X1,X2))
| ~ ne(X2) ),
inference(unfold_definition,[status(thm)],[c_0_564,def_lhs_atom3]) ).
cnf(c_0_565_0,axiom,
( ~ mem(X1,bool)
| X1 = X2
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_565,def_lhs_atom5]) ).
cnf(c_0_566_0,axiom,
( ~ ne(X1)
| f14(X2,X1) = c_2Ebool_2Eliteral__case(X1,X2)
| ~ ne(X2) ),
inference(unfold_definition,[status(thm)],[c_0_566,def_lhs_atom7]) ).
cnf(c_0_567_0,axiom,
( ~ ne(X1)
| f30(X2,X1) = c_2Ebool_2ETYPE__DEFINITION(X1,X2)
| ~ ne(X2) ),
inference(unfold_definition,[status(thm)],[c_0_567,def_lhs_atom7]) ).
cnf(c_0_568_0,axiom,
( ~ ne(X1)
| f24(X1,X2) = c_2Ebool_2EONTO(X1,X2)
| ~ ne(X2) ),
inference(unfold_definition,[status(thm)],[c_0_568,def_lhs_atom7]) ).
cnf(c_0_569_0,axiom,
( ~ ne(X1)
| f21(X2,X1) = c_2Ebool_2EONE__ONE(X1,X2)
| ~ ne(X2) ),
inference(unfold_definition,[status(thm)],[c_0_569,def_lhs_atom7]) ).
cnf(c_0_570_0,axiom,
( ~ ne(X1)
| f14(X2,X1) = c_2Ebool_2ELET(X1,X2)
| ~ ne(X2) ),
inference(unfold_definition,[status(thm)],[c_0_570,def_lhs_atom7]) ).
cnf(c_0_571_0,axiom,
( ~ mem(X1,bool)
| p(ap(c_2Ebool_2E_7E,X1))
| p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_571,def_lhs_atom5]) ).
cnf(c_0_572_0,axiom,
( ~ mem(X1,bool)
| X1 = X2
| p(X2)
| p(X1)
| ~ mem(X2,bool) ),
inference(unfold_definition,[status(thm)],[c_0_572,def_lhs_atom5]) ).
cnf(c_0_573_0,axiom,
( ~ mem(X2,X1)
| ap(i(X1),X2) = X2 ),
inference(unfold_definition,[status(thm)],[c_0_573,def_lhs_atom6]) ).
cnf(c_0_574_0,axiom,
( ~ ne(X1)
| mem(c_2Ebool_2Ethe__value(X1),ty_2Ebool_2Eitself(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_574,def_lhs_atom7]) ).
cnf(c_0_575_0,axiom,
( ~ $false
| p(X1)
| ~ mem(X1,bool) ),
inference(unfold_definition,[status(thm)],[c_0_575,def_lhs_atom28]) ).
cnf(c_0_576_0,axiom,
( ~ ne(X1)
| mem(c_2Ebool_2EARB(X1),X1) ),
inference(unfold_definition,[status(thm)],[c_0_576,def_lhs_atom7]) ).
cnf(c_0_577_0,axiom,
( ~ ne(X1)
| k(X1,c_2Ebool_2ET) = c_2Ebool_2EDATATYPE(X1) ),
inference(unfold_definition,[status(thm)],[c_0_577,def_lhs_atom7]) ).
cnf(c_0_578_0,axiom,
( ~ mem(X1,bool)
| p(X1)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_578,def_lhs_atom37]) ).
cnf(c_0_579_0,axiom,
( ~ ne(X1)
| ne(ty_2Ebool_2Eitself(X1)) ),
inference(unfold_definition,[status(thm)],[c_0_579,def_lhs_atom9]) ).
cnf(c_0_589_0,axiom,
( ~ ne(X1)
| c_2Ebool_2ERES__SELECT(X1) = f46(X1) ),
inference(unfold_definition,[status(thm)],[c_0_589,def_lhs_atom7]) ).
cnf(c_0_590_0,axiom,
( ~ ne(X1)
| f44(X1) = c_2Ebool_2ERES__EXISTS__UNIQUE(X1) ),
inference(unfold_definition,[status(thm)],[c_0_590,def_lhs_atom7]) ).
cnf(c_0_591_0,axiom,
( ~ ne(X1)
| f39(X1) = c_2Ebool_2ERES__EXISTS(X1) ),
inference(unfold_definition,[status(thm)],[c_0_591,def_lhs_atom7]) ).
cnf(c_0_592_0,axiom,
( ~ ne(X1)
| f36(X1) = c_2Ebool_2ERES__FORALL(X1) ),
inference(unfold_definition,[status(thm)],[c_0_592,def_lhs_atom7]) ).
cnf(c_0_593_0,axiom,
( ~ ne(X1)
| f33(X1) = c_2Ebool_2EIN(X1) ),
inference(unfold_definition,[status(thm)],[c_0_593,def_lhs_atom7]) ).
cnf(c_0_594_0,axiom,
( ~ ne(X1)
| f18(X1) = c_2Ebool_2ECOND(X1) ),
inference(unfold_definition,[status(thm)],[c_0_594,def_lhs_atom7]) ).
cnf(c_0_595_0,axiom,
( ~ ne(X1)
| f12(X1) = c_2Ebool_2E_3F_21(X1) ),
inference(unfold_definition,[status(thm)],[c_0_595,def_lhs_atom7]) ).
cnf(c_0_596_0,axiom,
( ~ ne(X1)
| f2(X1) = c_2Ebool_2E_3F(X1) ),
inference(unfold_definition,[status(thm)],[c_0_596,def_lhs_atom7]) ).
cnf(c_0_597_0,axiom,
( ~ ne(X1)
| f1(X1) = c_2Ebool_2E_21(X1) ),
inference(unfold_definition,[status(thm)],[c_0_597,def_lhs_atom7]) ).
cnf(c_0_598_0,axiom,
mem(sk1_esk4_0,bool),
inference(unfold_definition,[status(thm)],[c_0_598,def_lhs_atom29]) ).
cnf(c_0_599_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_599,def_lhs_atom19]) ).
cnf(c_0_600_0,axiom,
( ~ $true
| i(bool) = i(bool) ),
inference(unfold_definition,[status(thm)],[c_0_600,def_lhs_atom18]) ).
cnf(c_0_601_0,axiom,
~ p(sk1_esk4_0),
inference(unfold_definition,[status(thm)],[c_0_601,def_lhs_atom29]) ).
cnf(c_0_558_0,axiom,
ap(f30(X2,X3),X1) = f29(X2,X3,X1),
inference(unfold_definition,[status(thm)],[c_0_558,def_lhs_atom42]) ).
cnf(c_0_559_0,axiom,
ap(f24(X3,X2),X1) = ap(c_2Ebool_2E_21(X2),f23(X3,X2,X1)),
inference(unfold_definition,[status(thm)],[c_0_559,def_lhs_atom40]) ).
cnf(c_0_560_0,axiom,
ap(f21(X2,X3),X1) = ap(c_2Ebool_2E_21(X3),f20(X2,X3,X1)),
inference(unfold_definition,[status(thm)],[c_0_560,def_lhs_atom39]) ).
cnf(c_0_561_0,axiom,
ap(f14(X2,X3),X1) = f13(X2,X3,X1),
inference(unfold_definition,[status(thm)],[c_0_561,def_lhs_atom35]) ).
cnf(c_0_580_0,axiom,
ap(f46(X2),X1) = f45(X2,X1),
inference(unfold_definition,[status(thm)],[c_0_580,def_lhs_atom51]) ).
cnf(c_0_581_0,axiom,
ap(f44(X2),X1) = f43(X2,X1),
inference(unfold_definition,[status(thm)],[c_0_581,def_lhs_atom50]) ).
cnf(c_0_582_0,axiom,
ap(f39(X2),X1) = f38(X2,X1),
inference(unfold_definition,[status(thm)],[c_0_582,def_lhs_atom48]) ).
cnf(c_0_583_0,axiom,
ap(f36(X2),X1) = f35(X2,X1),
inference(unfold_definition,[status(thm)],[c_0_583,def_lhs_atom47]) ).
cnf(c_0_584_0,axiom,
ap(f33(X2),X1) = f32(X2,X1),
inference(unfold_definition,[status(thm)],[c_0_584,def_lhs_atom45]) ).
cnf(c_0_585_0,axiom,
ap(f18(X2),X1) = f17(X2,X1),
inference(unfold_definition,[status(thm)],[c_0_585,def_lhs_atom38]) ).
cnf(c_0_586_0,axiom,
ap(f12(X2),X1) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_3F(X2),X1)),ap(c_2Ebool_2E_21(X2),f11(X2,X1))),
inference(unfold_definition,[status(thm)],[c_0_586,def_lhs_atom33]) ).
cnf(c_0_587_0,axiom,
ap(f2(X2),X1) = ap(X1,ap(c_2Emin_2E_40(X2),X1)),
inference(unfold_definition,[status(thm)],[c_0_587,def_lhs_atom21]) ).
cnf(c_0_588_0,axiom,
ap(f1(X2),X1) = ap(ap(c_2Emin_2E_3D(arr(X2,bool)),X1),k(X2,c_2Ebool_2ET)),
inference(unfold_definition,[status(thm)],[c_0_588,def_lhs_atom20]) ).
cnf(c_0_602_0,axiom,
ap(f9,X1) = ap(ap(c_2Emin_2E_3D_3D_3E,X1),c_2Ebool_2EF),
inference(unfold_definition,[status(thm)],[c_0_602,def_lhs_atom30]) ).
cnf(c_0_603_0,axiom,
ap(f8,X1) = f7(X1),
inference(unfold_definition,[status(thm)],[c_0_603,def_lhs_atom26]) ).
cnf(c_0_604_0,axiom,
ap(f5,X1) = f4(X1),
inference(unfold_definition,[status(thm)],[c_0_604,def_lhs_atom24]) ).
cnf(c_0_605_0,axiom,
c_2Ebool_2EBOUNDED = k(bool,c_2Ebool_2ET),
inference(unfold_definition,[status(thm)],[c_0_605,def_lhs_atom52]) ).
cnf(c_0_606_0,axiom,
c_2Ebool_2E_7E = f9,
inference(unfold_definition,[status(thm)],[c_0_606,def_lhs_atom31]) ).
cnf(c_0_607_0,axiom,
c_2Ebool_2E_5C_2F = f8,
inference(unfold_definition,[status(thm)],[c_0_607,def_lhs_atom27]) ).
cnf(c_0_608_0,axiom,
c_2Ebool_2E_2F_5C = f5,
inference(unfold_definition,[status(thm)],[c_0_608,def_lhs_atom25]) ).
cnf(c_0_609_0,axiom,
mem(c_2Ebool_2E_7E,arr(bool,bool)),
inference(unfold_definition,[status(thm)],[c_0_609,def_lhs_atom17]) ).
cnf(c_0_610_0,axiom,
mem(c_2Ebool_2E_5C_2F,arr(bool,arr(bool,bool))),
inference(unfold_definition,[status(thm)],[c_0_610,def_lhs_atom16]) ).
cnf(c_0_611_0,axiom,
p(c_2Ebool_2ET),
inference(unfold_definition,[status(thm)],[c_0_611,def_lhs_atom15]) ).
cnf(c_0_612_0,axiom,
mem(c_2Ebool_2ET,bool),
inference(unfold_definition,[status(thm)],[c_0_612,def_lhs_atom14]) ).
cnf(c_0_613_0,axiom,
~ p(c_2Ebool_2EF),
inference(unfold_definition,[status(thm)],[c_0_613,def_lhs_atom13]) ).
cnf(c_0_614_0,axiom,
mem(c_2Ebool_2EF,bool),
inference(unfold_definition,[status(thm)],[c_0_614,def_lhs_atom12]) ).
cnf(c_0_615_0,axiom,
mem(c_2Ebool_2EBOUNDED,arr(bool,bool)),
inference(unfold_definition,[status(thm)],[c_0_615,def_lhs_atom11]) ).
cnf(c_0_616_0,axiom,
mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))),
inference(unfold_definition,[status(thm)],[c_0_616,def_lhs_atom10]) ).
cnf(c_0_617_0,axiom,
mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))),
inference(unfold_definition,[status(thm)],[c_0_617,def_lhs_atom8]) ).
cnf(c_0_618_0,axiom,
ne(ind),
inference(unfold_definition,[status(thm)],[c_0_618,def_lhs_atom2]) ).
cnf(c_0_619_0,axiom,
ne(bool),
inference(unfold_definition,[status(thm)],[c_0_619,def_lhs_atom1]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
? [X1] :
( mem(X1,arr(ind,ind))
& p(ap(c_2Ebool_2EONE__ONE(ind,ind),X1))
& ~ p(ap(c_2Ebool_2EONTO(ind,ind),X1)) ),
file('<stdin>',ax_thm_2Ebool_2EINFINITY__AX) ).
fof(c_0_1_002,plain,
? [X1] :
( mem(X1,arr(ind,ind))
& p(ap(c_2Ebool_2EONE__ONE(ind,ind),X1))
& ~ p(ap(c_2Ebool_2EONTO(ind,ind),X1)) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_2_003,plain,
( mem(esk1_0,arr(ind,ind))
& p(ap(c_2Ebool_2EONE__ONE(ind,ind),esk1_0))
& ~ p(ap(c_2Ebool_2EONTO(ind,ind),esk1_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_1])]) ).
cnf(c_0_3_004,plain,
~ p(ap(c_2Ebool_2EONTO(ind,ind),esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_005,plain,
p(ap(c_2Ebool_2EONE__ONE(ind,ind),esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5_006,plain,
mem(esk1_0,arr(ind,ind)),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_6_007,plain,
~ p(ap(c_2Ebool_2EONTO(ind,ind),esk1_0)),
c_0_3,
[final] ).
cnf(c_0_7_008,plain,
p(ap(c_2Ebool_2EONE__ONE(ind,ind),esk1_0)),
c_0_4,
[final] ).
cnf(c_0_8_009,plain,
mem(esk1_0,arr(ind,ind)),
c_0_5,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_6_0,axiom,
~ p(ap(c_2Ebool_2EONTO(ind,ind),sk2_esk1_0)),
inference(literals_permutation,[status(thm)],[c_0_6]) ).
cnf(c_0_7_0,axiom,
p(ap(c_2Ebool_2EONE__ONE(ind,ind),sk2_esk1_0)),
inference(literals_permutation,[status(thm)],[c_0_7]) ).
cnf(c_0_8_0,axiom,
mem(sk2_esk1_0,arr(ind,ind)),
inference(literals_permutation,[status(thm)],[c_0_8]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_010,conjecture,
$true,
file('<stdin>',conj_thm_2Ebool_2ETRUTH) ).
fof(c_0_1_011,negated_conjecture,
~ $true,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[c_0_0])]) ).
fof(c_0_2_012,negated_conjecture,
~ $true,
c_0_1 ).
cnf(c_0_3_013,negated_conjecture,
$false,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_014,negated_conjecture,
$false,
c_0_3,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_136,negated_conjecture,
$false,
file('/export/starexec/sandbox2/tmp/iprover_modulo_c587f5.p',c_0_4) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP001+5 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.07/0.13 % Command : iprover_modulo %s %d
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 4 02:06:45 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Running in mono-core mode
% 0.21/0.43 % Orienting using strategy Equiv(ClausalAll)
% 0.21/0.43 % FOF problem with conjecture
% 0.21/0.43 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_8bc0a7.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_c587f5.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_2a039c | grep -v "SZS"
% 0.21/0.45
% 0.21/0.45 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.21/0.45
% 0.21/0.45 %
% 0.21/0.45 % ------ iProver source info
% 0.21/0.45
% 0.21/0.45 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.21/0.45 % git: non_committed_changes: true
% 0.21/0.45 % git: last_make_outside_of_git: true
% 0.21/0.45
% 0.21/0.45 %
% 0.21/0.45 % ------ Input Options
% 0.21/0.45
% 0.21/0.45 % --out_options all
% 0.21/0.45 % --tptp_safe_out true
% 0.21/0.45 % --problem_path ""
% 0.21/0.45 % --include_path ""
% 0.21/0.45 % --clausifier .//eprover
% 0.21/0.45 % --clausifier_options --tstp-format
% 0.21/0.45 % --stdin false
% 0.21/0.45 % --dbg_backtrace false
% 0.21/0.45 % --dbg_dump_prop_clauses false
% 0.21/0.45 % --dbg_dump_prop_clauses_file -
% 0.21/0.45 % --dbg_out_stat false
% 0.21/0.45
% 0.21/0.45 % ------ General Options
% 0.21/0.45
% 0.21/0.45 % --fof false
% 0.21/0.45 % --time_out_real 150.
% 0.21/0.45 % --time_out_prep_mult 0.2
% 0.21/0.45 % --time_out_virtual -1.
% 0.21/0.45 % --schedule none
% 0.21/0.45 % --ground_splitting input
% 0.21/0.45 % --splitting_nvd 16
% 0.21/0.45 % --non_eq_to_eq false
% 0.21/0.45 % --prep_gs_sim true
% 0.21/0.45 % --prep_unflatten false
% 0.21/0.45 % --prep_res_sim true
% 0.21/0.45 % --prep_upred true
% 0.21/0.45 % --res_sim_input true
% 0.21/0.45 % --clause_weak_htbl true
% 0.21/0.45 % --gc_record_bc_elim false
% 0.21/0.45 % --symbol_type_check false
% 0.21/0.45 % --clausify_out false
% 0.21/0.45 % --large_theory_mode false
% 0.21/0.45 % --prep_sem_filter none
% 0.21/0.45 % --prep_sem_filter_out false
% 0.21/0.45 % --preprocessed_out false
% 0.21/0.45 % --sub_typing false
% 0.21/0.45 % --brand_transform false
% 0.21/0.45 % --pure_diseq_elim true
% 0.21/0.45 % --min_unsat_core false
% 0.21/0.45 % --pred_elim true
% 0.21/0.45 % --add_important_lit false
% 0.21/0.45 % --soft_assumptions false
% 0.21/0.45 % --reset_solvers false
% 0.21/0.45 % --bc_imp_inh []
% 0.21/0.45 % --conj_cone_tolerance 1.5
% 0.21/0.45 % --prolific_symb_bound 500
% 0.21/0.45 % --lt_threshold 2000
% 0.21/0.45
% 0.21/0.45 % ------ SAT Options
% 0.21/0.45
% 0.21/0.45 % --sat_mode false
% 0.21/0.45 % --sat_fm_restart_options ""
% 0.21/0.45 % --sat_gr_def false
% 0.21/0.45 % --sat_epr_types true
% 0.21/0.45 % --sat_non_cyclic_types false
% 0.21/0.45 % --sat_finite_models false
% 0.21/0.45 % --sat_fm_lemmas false
% 0.21/0.45 % --sat_fm_prep false
% 0.21/0.45 % --sat_fm_uc_incr true
% 0.21/0.45 % --sat_out_model small
% 0.21/0.45 % --sat_out_clauses false
% 0.21/0.45
% 0.21/0.45 % ------ QBF Options
% 0.21/0.45
% 0.21/0.45 % --qbf_mode false
% 0.21/0.45 % --qbf_elim_univ true
% 0.21/0.45 % --qbf_sk_in true
% 0.21/0.45 % --qbf_pred_elim true
% 0.21/0.45 % --qbf_split 32
% 0.21/0.45
% 0.21/0.45 % ------ BMC1 Options
% 0.21/0.45
% 0.21/0.45 % --bmc1_incremental false
% 0.21/0.45 % --bmc1_axioms reachable_all
% 0.21/0.45 % --bmc1_min_bound 0
% 0.21/0.45 % --bmc1_max_bound -1
% 0.21/0.45 % --bmc1_max_bound_default -1
% 0.21/0.45 % --bmc1_symbol_reachability true
% 0.21/0.45 % --bmc1_property_lemmas false
% 0.21/0.45 % --bmc1_k_induction false
% 0.21/0.45 % --bmc1_non_equiv_states false
% 0.21/0.45 % --bmc1_deadlock false
% 0.21/0.45 % --bmc1_ucm false
% 0.21/0.45 % --bmc1_add_unsat_core none
% 0.21/0.45 % --bmc1_unsat_core_children false
% 0.21/0.45 % --bmc1_unsat_core_extrapolate_axioms false
% 0.21/0.45 % --bmc1_out_stat full
% 0.21/0.45 % --bmc1_ground_init false
% 0.21/0.45 % --bmc1_pre_inst_next_state false
% 0.21/0.45 % --bmc1_pre_inst_state false
% 0.21/0.45 % --bmc1_pre_inst_reach_state false
% 0.21/0.45 % --bmc1_out_unsat_core false
% 0.21/0.45 % --bmc1_aig_witness_out false
% 0.21/0.45 % --bmc1_verbose false
% 0.21/0.45 % --bmc1_dump_clauses_tptp false
% 0.21/0.46 % --bmc1_dump_unsat_core_tptp false
% 0.21/0.46 % --bmc1_dump_file -
% 0.21/0.46 % --bmc1_ucm_expand_uc_limit 128
% 0.21/0.46 % --bmc1_ucm_n_expand_iterations 6
% 0.21/0.46 % --bmc1_ucm_extend_mode 1
% 0.21/0.46 % --bmc1_ucm_init_mode 2
% 0.21/0.46 % --bmc1_ucm_cone_mode none
% 0.21/0.46 % --bmc1_ucm_reduced_relation_type 0
% 0.21/0.46 % --bmc1_ucm_relax_model 4
% 0.21/0.46 % --bmc1_ucm_full_tr_after_sat true
% 0.21/0.46 % --bmc1_ucm_expand_neg_assumptions false
% 0.21/0.46 % --bmc1_ucm_layered_model none
% 0.21/0.46 % --bmc1_ucm_max_lemma_size 10
% 0.21/0.46
% 0.21/0.46 % ------ AIG Options
% 0.21/0.46
% 0.21/0.46 % --aig_mode false
% 0.21/0.46
% 0.21/0.46 % ------ Instantiation Options
% 0.21/0.46
% 0.21/0.46 % --instantiation_flag true
% 0.21/0.46 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.21/0.46 % --inst_solver_per_active 750
% 0.21/0.46 % --inst_solver_calls_frac 0.5
% 0.21/0.46 % --inst_passive_queue_type priority_queues
% 0.21/0.46 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.21/0.46 % --inst_passive_queues_freq [25;2]
% 0.21/0.46 % --inst_dismatching true
% 0.21/0.46 % --inst_eager_unprocessed_to_passive true
% 0.21/0.46 % --inst_prop_sim_given true
% 0.21/0.46 % --inst_prop_sim_new false
% 0.21/0.46 % --inst_orphan_elimination true
% 0.21/0.46 % --inst_learning_loop_flag true
% 0.21/0.46 % --inst_learning_start 3000
% 0.21/0.46 % --inst_learning_factor 2
% 0.21/0.46 % --inst_start_prop_sim_after_learn 3
% 0.21/0.46 % --inst_sel_renew solver
% 0.21/0.46 % --inst_lit_activity_flag true
% 0.21/0.46 % --inst_out_proof true
% 0.21/0.46
% 0.21/0.46 % ------ Resolution Options
% 0.21/0.46
% 0.21/0.46 % --resolution_flag true
% 0.21/0.46 % --res_lit_sel kbo_max
% 0.21/0.46 % --res_to_prop_solver none
% 0.21/0.46 % --res_prop_simpl_new false
% 0.21/0.46 % --res_prop_simpl_given false
% 0.21/0.46 % --res_passive_queue_type priority_queues
% 0.21/0.46 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.21/0.46 % --res_passive_queues_freq [15;5]
% 0.21/0.46 % --res_forward_subs full
% 0.21/0.46 % --res_backward_subs full
% 0.21/0.46 % --res_forward_subs_resolution true
% 0.21/0.46 % --res_backward_subs_resolution true
% 0.21/0.46 % --res_orphan_elimination false
% 0.21/0.46 % --res_time_limit 1000.
% 0.21/0.46 % --res_out_proof true
% 0.21/0.46 % --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_8bc0a7.s
% 0.21/0.46 % --modulo true
% 0.21/0.46
% 0.21/0.46 % ------ Combination Options
% 0.21/0.46
% 0.21/0.46 % --comb_res_mult 1000
% 0.21/0.46 % --comb_inst_mult 300
% 0.21/0.46 % ------
% 0.21/0.46
% 0.21/0.46 % ------ Parsing...%
% 0.21/0.46
% 0.21/0.46
% 0.21/0.46 % Resolution empty clause
% 0.21/0.46
% 0.21/0.46 % ------ Statistics
% 0.21/0.46
% 0.21/0.46 % ------ General
% 0.21/0.46
% 0.21/0.46 % num_of_input_clauses: 137
% 0.21/0.46 % num_of_input_neg_conjectures: 1
% 0.21/0.46 % num_of_splits: 0
% 0.21/0.46 % num_of_split_atoms: 0
% 0.21/0.46 % num_of_sem_filtered_clauses: 0
% 0.21/0.46 % num_of_subtypes: 0
% 0.21/0.46 % monotx_restored_types: 0
% 0.21/0.46 % sat_num_of_epr_types: 0
% 0.21/0.46 % sat_num_of_non_cyclic_types: 0
% 0.21/0.46 % sat_guarded_non_collapsed_types: 0
% 0.21/0.46 % is_epr: 0
% 0.21/0.46 % is_horn: 0
% 0.21/0.46 % has_eq: 0
% 0.21/0.46 % num_pure_diseq_elim: 0
% 0.21/0.46 % simp_replaced_by: 0
% 0.21/0.46 % res_preprocessed: 0
% 0.21/0.46 % prep_upred: 0
% 0.21/0.46 % prep_unflattend: 0
% 0.21/0.46 % pred_elim_cands: 0
% 0.21/0.46 % pred_elim: 0
% 0.21/0.46 % pred_elim_cl: 0
% 0.21/0.46 % pred_elim_cycles: 0
% 0.21/0.46 % forced_gc_time: 0
% 0.21/0.46 % gc_basic_clause_elim: 0
% 0.21/0.46 % parsing_time: 0.
% 0.21/0.46 % sem_filter_time: 0.
% 0.21/0.46 % pred_elim_time: 0.
% 0.21/0.46 % out_proof_time: 0.
% 0.21/0.46 % monotx_time: 0.
% 0.21/0.46 % subtype_inf_time: 0.
% 0.21/0.46 % unif_index_cands_time: 0.
% 0.21/0.46 % unif_index_add_time: 0.
% 0.21/0.46 % total_time: 0.027
% 0.21/0.46 % num_of_symbols: 114
% 0.21/0.46 % num_of_terms: 723
% 0.21/0.46
% 0.21/0.46 % ------ Propositional Solver
% 0.21/0.46
% 0.21/0.46 % prop_solver_calls: 0
% 0.21/0.46 % prop_fast_solver_calls: 0
% 0.21/0.46 % prop_num_of_clauses: 0
% 0.21/0.46 % prop_preprocess_simplified: 0
% 0.21/0.46 % prop_fo_subsumed: 0
% 0.21/0.46 % prop_solver_time: 0.
% 0.21/0.46 % prop_fast_solver_time: 0.
% 0.21/0.46 % prop_unsat_core_time: 0.
% 0.21/0.46
% 0.21/0.46 % ------ QBF
% 0.21/0.46
% 0.21/0.46 % qbf_q_res: 0
% 0.21/0.46 % qbf_num_tautologies: 0
% 0.21/0.46 % qbf_prep_cycles: 0
% 0.21/0.46
% 0.21/0.46 % ------ BMC1
% 0.21/0.46
% 0.21/0.46 % bmc1_current_bound: -1
% 0.21/0.46 % bmc1_last_solved_bound: -1
% 0.21/0.46 % bmc1_unsat_core_size: -1
% 0.21/0.46 % bmc1_unsat_core_parents_size: -1
% 0.21/0.46 % bmc1_merge_next_fun: 0
% 0.21/0.46 % bmc1_unsat_core_clauses_time: 0.
% 0.21/0.46
% 0.21/0.46 % ------ Instantiation
% 0.21/0.46
% 0.21/0.46 % inst_num_of_clauses: undef
% 0.21/0.46 % inst_num_in_passive: undef
% 0.21/0.46 % inst_num_in_active: 0
% 0.21/0.46 % inst_num_in_unprocessed: 0
% 0.21/0.46 % inst_num_of_loops: 0
% 0.21/0.46 % inst_num_of_learning_restarts: 0
% 0.21/0.46 % inst_num_moves_active_passive: 0
% 0.21/0.46 % inst_lit_activity: 0
% 0.21/0.46 % inst_lit_activity_moves: 0
% 0.21/0.46 % inst_num_tautologies: 0
% 0.21/0.46 % inst_num_prop_implied: 0
% 0.21/0.46 % inst_num_existing_simplified: 0
% 0.21/0.46 % inst_num_eq_res_simplified: 0
% 0.21/0.46 % inst_num_child_elim: 0
% 0.21/0.46 % inst_num_of_dismatching_blockings: 0
% 0.21/0.46 % inst_num_of_non_proper_insts: 0
% 0.21/0.46 % inst_num_of_duplicates: 0
% 0.21/0.46 % inst_inst_num_from_inst_to_res: 0
% 0.21/0.46 % inst_dismatching_checking_time: 0.
% 0.21/0.46
% 0.21/0.46 % ------ Resolution
% 0.21/0.46
% 0.21/0.46 % res_num_of_clauses: undef
% 0.21/0.46 % res_num_in_passive: undef
% 0.21/0.46 % res_num_in_active: 0
% 0.21/0.46 % res_num_of_loops: 0
% 0.21/0.46 % res_forward_subset_subsumed: 0
% 0.21/0.46 % res_backward_subset_subsumed: 0
% 0.21/0.46 % res_forward_subsumed: 0
% 0.21/0.46 % res_backward_subsumed: 0
% 0.21/0.46 % res_forward_subsumption_resolution: 0
% 0.21/0.46 % res_backward_subsumption_resolution: 0
% 0.21/0.46 % res_clause_to_clause_subsumption: 0
% 0.21/0.46 % res_orphan_elimination: 0
% 0.21/0.46 % res_tautology_del: 0
% 0.21/0.46 % res_num_eq_res_simplified: 0
% 0.21/0.46 % res_num_sel_changes: 0
% 0.21/0.46 % res_moves_from_active_to_pass: 0
% 0.21/0.46
% 0.21/0.46 % Status Unsatisfiable
% 0.21/0.46 % SZS status Theorem
% 0.21/0.46 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------