%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ITP012+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:50:09 PM UTC 2026
% Result : Theorem 5.59s 1.23s
% Output : CNFRefutation 5.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 133
% Syntax : Number of formulae : 529 ( 58 unt; 100 def)
% Number of atoms : 1726 ( 203 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 2072 ( 875 ~; 950 |; 67 &)
% ( 132 <=>; 46 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 105 ( 103 usr; 98 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 15 con; 0-4 aty)
% Number of variables : 474 ( 464 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
ne(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] :
( ne(A)
=> ! [B] :
( ne(B)
=> ne(arr(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,F] :
( mem(F,arr(A,B))
=> ! [X] :
( mem(X,A)
=> mem(ap(F,X),B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Q] :
( mem(Q,bool)
=> ! [R] :
( mem(R,bool)
=> ( ( p(Q)
<=> p(R) )
=> Q = R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,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 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,Y,X] :
( mem(X,A)
=> ap(k(A,Y),X) = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,X] :
( mem(X,A)
=> ap(i(A),X) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
mem(c_2Ebool_2ET,bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
p(c_2Ebool_2ET),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2E_3F(A_27a),arr(arr(A_27a,bool),bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] :
( ne(A)
=> ! [Q] :
( mem(Q,arr(A,bool))
=> ( p(ap(c_2Ebool_2E_3F(A),Q))
<=> ? [X] :
( p(ap(Q,X))
& mem(X,A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
ne(ty_2Einteger_2Eint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
mem(c_2Einteger_2Eint__sub,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
mem(c_2Einteger_2Eint__add,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
mem(c_2Einteger_2Eint__neg,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
mem(c_2Einteger_2Eint__divides,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
mem(c_2Ebool_2EF,bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
~ p(c_2Ebool_2EF),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Q] :
( mem(Q,bool)
=> ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R))
<=> ( p(Q)
=> p(R) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
mem(c_2Ebool_2E_5C_2F,arr(bool,arr(bool,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [Q] :
( mem(Q,bool)
=> ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Ebool_2E_5C_2F,Q),R))
<=> ( p(R)
| p(Q) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
mem(c_2Ebool_2E_7E,arr(bool,bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [Q] :
( mem(Q,bool)
=> ( p(ap(c_2Ebool_2E_7E,Q))
<=> ~ p(Q) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [V0A] :
( mem(V0A,bool)
=> ! [V1B] :
( mem(V1B,bool)
=> ! [V2C] :
( mem(V2C,bool)
=> ( ( p(V2C)
| p(V1B)
| p(V0A) )
<=> ( p(V2C)
| p(V1B)
| p(V0A) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [V0x] :
( mem(V0x,ty_2Einteger_2Eint)
=> ! [V1y] :
( mem(V1y,ty_2Einteger_2Eint)
=> ap(ap(c_2Einteger_2Eint__sub,V0x),V1y) = ap(ap(c_2Einteger_2Eint__add,V0x),ap(c_2Einteger_2Eint__neg,V1y)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [V0p] :
( mem(V0p,ty_2Einteger_2Eint)
=> ! [V1q] :
( mem(V1q,ty_2Einteger_2Eint)
=> ! [V2r] :
( mem(V2r,ty_2Einteger_2Eint)
=> ( p(ap(ap(c_2Einteger_2Eint__divides,V0p),V1q))
=> ( p(ap(ap(c_2Einteger_2Eint__divides,V0p),ap(ap(c_2Einteger_2Eint__add,V2r),V1q)))
<=> p(ap(ap(c_2Einteger_2Eint__divides,V0p),V2r)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [V0p] :
( mem(V0p,ty_2Einteger_2Eint)
=> ! [V1q] :
( mem(V1q,ty_2Einteger_2Eint)
=> ( ( p(ap(ap(c_2Einteger_2Eint__divides,ap(c_2Einteger_2Eint__neg,V0p)),V1q))
<=> p(ap(ap(c_2Einteger_2Eint__divides,V0p),V1q)) )
& ( p(ap(ap(c_2Einteger_2Eint__divides,V0p),ap(c_2Einteger_2Eint__neg,V1q)))
<=> p(ap(ap(c_2Einteger_2Eint__divides,V0p),V1q)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ! [V2r] :
( mem(V2r,bool)
=> ( ( p(V0p)
<=> ( p(V1q)
<=> p(V2r) ) )
<=> ( ( ~ p(V0p)
| ~ p(V1q)
| p(V2r) )
& ( ~ p(V0p)
| ~ p(V2r)
| p(V1q) )
& ( ~ p(V1q)
| ~ p(V2r)
| p(V0p) )
& ( p(V2r)
| p(V1q)
| p(V0p) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,conjecture,
! [V0p] :
( mem(V0p,ty_2Einteger_2Eint)
=> ! [V1q] :
( mem(V1q,ty_2Einteger_2Eint)
=> ! [V2r] :
( mem(V2r,ty_2Einteger_2Eint)
=> ( p(ap(ap(c_2Einteger_2Eint__divides,V0p),V1q))
=> ( p(ap(ap(c_2Einteger_2Eint__divides,V0p),ap(ap(c_2Einteger_2Eint__sub,V2r),V1q)))
<=> p(ap(ap(c_2Einteger_2Eint__divides,V0p),V2r)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,negated_conjecture,
~ ! [V0p] :
( mem(V0p,ty_2Einteger_2Eint)
=> ! [V1q] :
( mem(V1q,ty_2Einteger_2Eint)
=> ! [V2r] :
( mem(V2r,ty_2Einteger_2Eint)
=> ( p(ap(ap(c_2Einteger_2Eint__divides,V0p),V1q))
=> ( p(ap(ap(c_2Einteger_2Eint__divides,V0p),ap(ap(c_2Einteger_2Eint__sub,V2r),V1q)))
<=> p(ap(ap(c_2Einteger_2Eint__divides,V0p),V2r)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f57]) ).
fof(f59,plain,
ne(bool),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f61,plain,
! [A] :
( ! [B] :
( ne(arr(A,B))
| ~ ne(B) )
| ~ ne(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f62,plain,
! [X0,X1] :
( ne(arr(X0,X1))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
! [A,B,F] :
( ! [X] :
( mem(ap(F,X),B)
| ~ mem(X,A) )
| ~ mem(F,arr(A,B)) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f64,plain,
! [X0,X1,X2,X3] :
( mem(ap(X0,X3),X2)
| ~ mem(X3,X1)
| ~ mem(X0,arr(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f65,plain,
! [Q] :
( ! [R] :
( Q = R
| ( p(Q)
<~> p(R) )
| ~ mem(R,bool) )
| ~ mem(Q,bool) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f66,plain,
! [Q] :
( ! [R] :
( Q = R
| ( ( ~ p(R)
| ~ p(Q) )
& ( p(R)
| p(Q) ) )
| ~ mem(R,bool) )
| ~ mem(Q,bool) ),
inference(NNF_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( X0 = X1
| p(X1)
| p(X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( X0 = X1
| ~ p(X1)
| ~ p(X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f69,plain,
! [A,B,F] :
( ! [G] :
( F = G
| ? [X] :
( ap(F,X) != ap(G,X)
& mem(X,A) )
| ~ mem(G,arr(A,B)) )
| ~ mem(F,arr(A,B)) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f70,plain,
! [A,B,F] :
( ! [G] :
( F = G
| ( ap(F,sK0_skl(G,F,B,A)) != ap(G,sK0_skl(G,F,B,A))
& mem(sK0_skl(G,F,B,A),A) )
| ~ mem(G,arr(A,B)) )
| ~ mem(F,arr(A,B)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(G,F,B,A))],[f69]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| mem(sK0_skl(X3,X0,X2,X1),X1)
| ~ mem(X3,arr(X1,X2))
| ~ mem(X0,arr(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| ap(X0,sK0_skl(X3,X0,X2,X1)) != ap(X3,sK0_skl(X3,X0,X2,X1))
| ~ mem(X3,arr(X1,X2))
| ~ mem(X0,arr(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f73,plain,
! [A,Y,X] :
( ap(k(A,Y),X) = Y
| ~ mem(X,A) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f74,plain,
! [A,X] :
( ! [Y] : ap(k(A,Y),X) = Y
| ~ mem(X,A) ),
inference(miniscoping,[status(thm)],[f73]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ap(k(X1,X2),X0) = X2
| ~ mem(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f76,plain,
! [A,X] :
( ap(i(A),X) = X
| ~ mem(X,A) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f77,plain,
! [X0,X1] :
( ap(i(X1),X0) = X0
| ~ mem(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
mem(c_2Ebool_2ET,bool),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f79,plain,
p(c_2Ebool_2ET),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f80,plain,
! [A_27a] :
( mem(c_2Ebool_2E_3F(A_27a),arr(arr(A_27a,bool),bool))
| ~ ne(A_27a) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f81,plain,
! [X0] :
( mem(c_2Ebool_2E_3F(X0),arr(arr(X0,bool),bool))
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f82,plain,
! [A] :
( ! [Q] :
( ( p(ap(c_2Ebool_2E_3F(A),Q))
<=> ? [X] :
( p(ap(Q,X))
& mem(X,A) ) )
| ~ mem(Q,arr(A,bool)) )
| ~ ne(A) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f83,plain,
! [A] :
( ! [Q] :
( ( ( ! [X] :
( ~ p(ap(Q,X))
| ~ mem(X,A) )
| p(ap(c_2Ebool_2E_3F(A),Q)) )
& ( ? [X] :
( p(ap(Q,X))
& mem(X,A) )
| ~ p(ap(c_2Ebool_2E_3F(A),Q)) ) )
| ~ mem(Q,arr(A,bool)) )
| ~ ne(A) ),
inference(NNF_transformation,[status(thm)],[f82]) ).
fof(f84,plain,
! [A] :
( ! [Q] :
( ( ( ! [X] :
( ~ p(ap(Q,X))
| ~ mem(X,A) )
| p(ap(c_2Ebool_2E_3F(A),Q)) )
& ( ( p(ap(Q,sK1_skl(Q,A)))
& mem(sK1_skl(Q,A),A) )
| ~ p(ap(c_2Ebool_2E_3F(A),Q)) ) )
| ~ mem(Q,arr(A,bool)) )
| ~ ne(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(X,sK1_skl(Q,A))],[f83]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ~ p(ap(X1,X2))
| ~ mem(X2,X0)
| p(ap(c_2Ebool_2E_3F(X0),X1))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f88,plain,
ne(ty_2Einteger_2Eint),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f89,plain,
mem(c_2Einteger_2Eint__sub,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint))),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f90,plain,
mem(c_2Einteger_2Eint__add,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint))),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f91,plain,
mem(c_2Einteger_2Eint__neg,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint)),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f92,plain,
mem(c_2Einteger_2Eint__divides,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,bool))),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f93,plain,
mem(c_2Ebool_2EF,bool),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f94,plain,
~ p(c_2Ebool_2EF),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f95,plain,
mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f96,plain,
! [Q] :
( ! [R] :
( ( p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R))
<=> ( p(R)
| ~ p(Q) ) )
| ~ mem(R,bool) )
| ~ mem(Q,bool) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f97,plain,
! [Q] :
( ! [R] :
( ( ( ( ~ p(R)
& p(Q) )
| p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R)) )
& ( p(R)
| ~ p(Q)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R)) ) )
| ~ mem(R,bool) )
| ~ mem(Q,bool) ),
inference(NNF_transformation,[status(thm)],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( p(X1)
| ~ p(X0)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),X1))
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( p(X0)
| p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),X1))
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f101,plain,
mem(c_2Ebool_2E_5C_2F,arr(bool,arr(bool,bool))),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f102,plain,
! [Q] :
( ! [R] :
( ( p(ap(ap(c_2Ebool_2E_5C_2F,Q),R))
<=> ( p(R)
| p(Q) ) )
| ~ mem(R,bool) )
| ~ mem(Q,bool) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f103,plain,
! [Q] :
( ! [R] :
( ( ( ( ~ p(R)
& ~ p(Q) )
| p(ap(ap(c_2Ebool_2E_5C_2F,Q),R)) )
& ( p(R)
| p(Q)
| ~ p(ap(ap(c_2Ebool_2E_5C_2F,Q),R)) ) )
| ~ mem(R,bool) )
| ~ mem(Q,bool) ),
inference(NNF_transformation,[status(thm)],[f102]) ).
fof(f105,plain,
! [X0,X1] :
( ~ p(X0)
| p(ap(ap(c_2Ebool_2E_5C_2F,X0),X1))
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f107,plain,
mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f113,plain,
mem(c_2Ebool_2E_7E,arr(bool,bool)),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f114,plain,
! [Q] :
( ( p(ap(c_2Ebool_2E_7E,Q))
<=> ~ p(Q) )
| ~ mem(Q,bool) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f115,plain,
! [Q] :
( ( ( p(Q)
| p(ap(c_2Ebool_2E_7E,Q)) )
& ( ~ p(Q)
| ~ p(ap(c_2Ebool_2E_7E,Q)) ) )
| ~ mem(Q,bool) ),
inference(NNF_transformation,[status(thm)],[f114]) ).
fof(f117,plain,
! [X0] :
( p(X0)
| p(ap(c_2Ebool_2E_7E,X0))
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f118,plain,
! [A_27a] :
( mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool)))
| ~ ne(A_27a) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f119,plain,
! [X0] :
( mem(c_2Emin_2E_3D(X0),arr(X0,arr(X0,bool)))
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f124,plain,
! [A_27a] :
( mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool))
| ~ ne(A_27a) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f125,plain,
! [X0] :
( mem(c_2Ebool_2E_21(X0),arr(arr(X0,bool),bool))
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f186,plain,
! [V0A] :
( ! [V1B] :
( ! [V2C] :
( ( ( p(V2C)
| p(V1B)
| p(V0A) )
<=> ( p(V2C)
| p(V1B)
| p(V0A) ) )
| ~ mem(V2C,bool) )
| ~ mem(V1B,bool) )
| ~ mem(V0A,bool) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f187,plain,
! [V0A] :
( ! [V1B] :
( ! [V2C] :
( ( ( ( ~ p(V2C)
& ~ p(V1B)
& ~ p(V0A) )
| p(V2C)
| p(V1B)
| p(V0A) )
& ( p(V2C)
| p(V1B)
| p(V0A)
| ( ~ p(V2C)
& ~ p(V1B)
& ~ p(V0A) ) ) )
| ~ mem(V2C,bool) )
| ~ mem(V1B,bool) )
| ~ mem(V0A,bool) ),
inference(NNF_transformation,[status(thm)],[f186]) ).
fof(f188,plain,
! [X0,X1,X2] :
( p(X2)
| p(X1)
| p(X0)
| ~ p(X0)
| ~ mem(X2,bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f210,plain,
! [V0x] :
( ! [V1y] :
( ap(ap(c_2Einteger_2Eint__sub,V0x),V1y) = ap(ap(c_2Einteger_2Eint__add,V0x),ap(c_2Einteger_2Eint__neg,V1y))
| ~ mem(V1y,ty_2Einteger_2Eint) )
| ~ mem(V0x,ty_2Einteger_2Eint) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f211,plain,
! [X0,X1] :
( ap(ap(c_2Einteger_2Eint__sub,X0),X1) = ap(ap(c_2Einteger_2Eint__add,X0),ap(c_2Einteger_2Eint__neg,X1))
| ~ mem(X1,ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f212,plain,
! [V0p] :
( ! [V1q] :
( ! [V2r] :
( ( p(ap(ap(c_2Einteger_2Eint__divides,V0p),ap(ap(c_2Einteger_2Eint__add,V2r),V1q)))
<=> p(ap(ap(c_2Einteger_2Eint__divides,V0p),V2r)) )
| ~ p(ap(ap(c_2Einteger_2Eint__divides,V0p),V1q))
| ~ mem(V2r,ty_2Einteger_2Eint) )
| ~ mem(V1q,ty_2Einteger_2Eint) )
| ~ mem(V0p,ty_2Einteger_2Eint) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f213,plain,
! [V0p] :
( ! [V1q] :
( ! [V2r] :
( ( ( ~ p(ap(ap(c_2Einteger_2Eint__divides,V0p),V2r))
| p(ap(ap(c_2Einteger_2Eint__divides,V0p),ap(ap(c_2Einteger_2Eint__add,V2r),V1q))) )
& ( p(ap(ap(c_2Einteger_2Eint__divides,V0p),V2r))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,V0p),ap(ap(c_2Einteger_2Eint__add,V2r),V1q))) ) )
| ~ p(ap(ap(c_2Einteger_2Eint__divides,V0p),V1q))
| ~ mem(V2r,ty_2Einteger_2Eint) )
| ~ mem(V1q,ty_2Einteger_2Eint) )
| ~ mem(V0p,ty_2Einteger_2Eint) ),
inference(NNF_transformation,[status(thm)],[f212]) ).
fof(f214,plain,
! [X0,X1,X2] :
( p(ap(ap(c_2Einteger_2Eint__divides,X0),X2))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__add,X2),X1)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),X1))
| ~ mem(X2,ty_2Einteger_2Eint)
| ~ mem(X1,ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(cnf_transformation,[status(thm)],[f213]) ).
fof(f215,plain,
! [X0,X1,X2] :
( ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),X2))
| p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__add,X2),X1)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),X1))
| ~ mem(X2,ty_2Einteger_2Eint)
| ~ mem(X1,ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(cnf_transformation,[status(thm)],[f213]) ).
fof(f216,plain,
! [V0p] :
( ! [V1q] :
( ( ( p(ap(ap(c_2Einteger_2Eint__divides,ap(c_2Einteger_2Eint__neg,V0p)),V1q))
<=> p(ap(ap(c_2Einteger_2Eint__divides,V0p),V1q)) )
& ( p(ap(ap(c_2Einteger_2Eint__divides,V0p),ap(c_2Einteger_2Eint__neg,V1q)))
<=> p(ap(ap(c_2Einteger_2Eint__divides,V0p),V1q)) ) )
| ~ mem(V1q,ty_2Einteger_2Eint) )
| ~ mem(V0p,ty_2Einteger_2Eint) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f217,plain,
! [V0p] :
( ! [V1q] :
( ( ( ~ p(ap(ap(c_2Einteger_2Eint__divides,V0p),V1q))
| p(ap(ap(c_2Einteger_2Eint__divides,ap(c_2Einteger_2Eint__neg,V0p)),V1q)) )
& ( p(ap(ap(c_2Einteger_2Eint__divides,V0p),V1q))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,ap(c_2Einteger_2Eint__neg,V0p)),V1q)) )
& ( ~ p(ap(ap(c_2Einteger_2Eint__divides,V0p),V1q))
| p(ap(ap(c_2Einteger_2Eint__divides,V0p),ap(c_2Einteger_2Eint__neg,V1q))) )
& ( p(ap(ap(c_2Einteger_2Eint__divides,V0p),V1q))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,V0p),ap(c_2Einteger_2Eint__neg,V1q))) ) )
| ~ mem(V1q,ty_2Einteger_2Eint) )
| ~ mem(V0p,ty_2Einteger_2Eint) ),
inference(NNF_transformation,[status(thm)],[f216]) ).
fof(f219,plain,
! [X0,X1] :
( ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),X1))
| p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,X1)))
| ~ mem(X1,ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(cnf_transformation,[status(thm)],[f217]) ).
fof(f220,plain,
! [X0,X1] :
( p(ap(ap(c_2Einteger_2Eint__divides,X0),X1))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,ap(c_2Einteger_2Eint__neg,X0)),X1))
| ~ mem(X1,ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(cnf_transformation,[status(thm)],[f217]) ).
fof(f221,plain,
! [X0,X1] :
( ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),X1))
| p(ap(ap(c_2Einteger_2Eint__divides,ap(c_2Einteger_2Eint__neg,X0)),X1))
| ~ mem(X1,ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(cnf_transformation,[status(thm)],[f217]) ).
fof(f249,plain,
! [V0p] :
( ! [V1q] :
( ! [V2r] :
( ( ( p(V0p)
<=> ( p(V1q)
<=> p(V2r) ) )
<=> ( ( ~ p(V0p)
| ~ p(V1q)
| p(V2r) )
& ( ~ p(V0p)
| ~ p(V2r)
| p(V1q) )
& ( ~ p(V1q)
| ~ p(V2r)
| p(V0p) )
& ( p(V2r)
| p(V1q)
| p(V0p) ) ) )
| ~ mem(V2r,bool) )
| ~ mem(V1q,bool) )
| ~ mem(V0p,bool) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f250,definition,
! [V0p,V1q,V2r] :
( sP7_prd(V2r,V1q,V0p)
<=> ( p(V0p)
<=> ( p(V1q)
<=> p(V2r) ) ) ),
introduced(definition,[new_symbols(definition,[sP7_prd])],[]) ).
fof(f251,plain,
! [V0p] :
( ! [V1q] :
( ! [V2r] :
( ( sP7_prd(V2r,V1q,V0p)
<=> ( ( ~ p(V0p)
| ~ p(V1q)
| p(V2r) )
& ( ~ p(V0p)
| ~ p(V2r)
| p(V1q) )
& ( ~ p(V1q)
| ~ p(V2r)
| p(V0p) )
& ( p(V2r)
| p(V1q)
| p(V0p) ) ) )
| ~ mem(V2r,bool) )
| ~ mem(V1q,bool) )
| ~ mem(V0p,bool) ),
inference(formula_renaming,[status(thm)],[f249,f250]) ).
fof(f252,definition,
! [V0p,V1q,V2r] :
( sP8_prd(V2r,V1q,V0p)
<=> ( ( ~ p(V0p)
| ~ p(V2r)
| p(V1q) )
& ( ~ p(V1q)
| ~ p(V2r)
| p(V0p) )
& ( p(V2r)
| p(V1q)
| p(V0p) ) ) ),
introduced(definition,[new_symbols(definition,[sP8_prd])],[]) ).
fof(f253,plain,
! [V0p] :
( ! [V1q] :
( ! [V2r] :
( ( sP7_prd(V2r,V1q,V0p)
<=> ( ( ~ p(V0p)
| ~ p(V1q)
| p(V2r) )
& sP8_prd(V2r,V1q,V0p) ) )
| ~ mem(V2r,bool) )
| ~ mem(V1q,bool) )
| ~ mem(V0p,bool) ),
inference(formula_renaming,[status(thm)],[f251,f252]) ).
fof(f254,plain,
! [V0p] :
( ! [V1q] :
( ! [V2r] :
( ( ( ( p(V0p)
& p(V1q)
& ~ p(V2r) )
| ~ sP8_prd(V2r,V1q,V0p)
| sP7_prd(V2r,V1q,V0p) )
& ( ( ( ~ p(V0p)
| ~ p(V1q)
| p(V2r) )
& sP8_prd(V2r,V1q,V0p) )
| ~ sP7_prd(V2r,V1q,V0p) ) )
| ~ mem(V2r,bool) )
| ~ mem(V1q,bool) )
| ~ mem(V0p,bool) ),
inference(NNF_transformation,[status(thm)],[f253]) ).
fof(f256,plain,
! [X0,X1,X2] :
( ~ p(X0)
| ~ p(X1)
| p(X2)
| ~ sP7_prd(X2,X1,X0)
| ~ mem(X2,bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f302,plain,
? [V0p] :
( ? [V1q] :
( ? [V2r] :
( ( p(ap(ap(c_2Einteger_2Eint__divides,V0p),ap(ap(c_2Einteger_2Eint__sub,V2r),V1q)))
<~> p(ap(ap(c_2Einteger_2Eint__divides,V0p),V2r)) )
& p(ap(ap(c_2Einteger_2Eint__divides,V0p),V1q))
& mem(V2r,ty_2Einteger_2Eint) )
& mem(V1q,ty_2Einteger_2Eint) )
& mem(V0p,ty_2Einteger_2Eint) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f303,plain,
? [V0p] :
( ? [V1q] :
( ? [V2r] :
( ( ~ p(ap(ap(c_2Einteger_2Eint__divides,V0p),V2r))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,V0p),ap(ap(c_2Einteger_2Eint__sub,V2r),V1q))) )
& ( p(ap(ap(c_2Einteger_2Eint__divides,V0p),V2r))
| p(ap(ap(c_2Einteger_2Eint__divides,V0p),ap(ap(c_2Einteger_2Eint__sub,V2r),V1q))) )
& p(ap(ap(c_2Einteger_2Eint__divides,V0p),V1q))
& mem(V2r,ty_2Einteger_2Eint) )
& mem(V1q,ty_2Einteger_2Eint) )
& mem(V0p,ty_2Einteger_2Eint) ),
inference(NNF_transformation,[status(thm)],[f302]) ).
fof(f304,plain,
( ( ~ p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),sK8_skl))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl))) )
& ( p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),sK8_skl))
| p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl))) )
& p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),sK7_skl))
& mem(sK8_skl,ty_2Einteger_2Eint)
& mem(sK7_skl,ty_2Einteger_2Eint)
& mem(sK6_skl,ty_2Einteger_2Eint) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl,sK8_skl]),skolemize(V0p,sK6_skl),skolemize(V1q,sK7_skl),skolemize(V2r,sK8_skl)],[f303]) ).
fof(f305,plain,
mem(sK6_skl,ty_2Einteger_2Eint),
inference(cnf_transformation,[status(thm)],[f304]) ).
fof(f306,plain,
mem(sK7_skl,ty_2Einteger_2Eint),
inference(cnf_transformation,[status(thm)],[f304]) ).
fof(f307,plain,
mem(sK8_skl,ty_2Einteger_2Eint),
inference(cnf_transformation,[status(thm)],[f304]) ).
fof(f308,plain,
p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),sK7_skl)),
inference(cnf_transformation,[status(thm)],[f304]) ).
fof(f309,plain,
( p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),sK8_skl))
| p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl))) ),
inference(cnf_transformation,[status(thm)],[f304]) ).
fof(f310,plain,
( ~ p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),sK8_skl))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl))) ),
inference(cnf_transformation,[status(thm)],[f304]) ).
fof(f351,definition,
! [V1q,V2r] :
( sP16_prd(V2r,V1q)
<=> ( p(V1q)
<=> p(V2r) ) ),
introduced(definition,[new_symbols(definition,[sP16_prd])],[]) ).
fof(f352,plain,
! [V0p,V1q,V2r] :
( sP7_prd(V2r,V1q,V0p)
<=> ( p(V0p)
<=> sP16_prd(V2r,V1q) ) ),
inference(formula_renaming,[status(thm)],[f250,f351]) ).
fof(f353,plain,
! [V0p,V1q,V2r] :
( ( ( ( sP16_prd(V2r,V1q)
| p(V0p) )
& ( ~ sP16_prd(V2r,V1q)
| ~ p(V0p) ) )
| sP7_prd(V2r,V1q,V0p) )
& ( ( ( ~ sP16_prd(V2r,V1q)
| p(V0p) )
& ( sP16_prd(V2r,V1q)
| ~ p(V0p) ) )
| ~ sP7_prd(V2r,V1q,V0p) ) ),
inference(NNF_transformation,[status(thm)],[f352]) ).
fof(f354,plain,
( ! [V0p,V1q,V2r] :
( ( ( sP16_prd(V2r,V1q)
| p(V0p) )
& ( ~ sP16_prd(V2r,V1q)
| ~ p(V0p) ) )
| sP7_prd(V2r,V1q,V0p) )
& ! [V0p,V1q,V2r] :
( ( ( ~ sP16_prd(V2r,V1q)
| p(V0p) )
& ( sP16_prd(V2r,V1q)
| ~ p(V0p) ) )
| ~ sP7_prd(V2r,V1q,V0p) ) ),
inference(miniscoping,[status(thm)],[f353]) ).
fof(f355,plain,
! [X0,X1,X2] :
( sP16_prd(X0,X1)
| ~ p(X2)
| ~ sP7_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f354]) ).
fof(f357,plain,
! [X0,X1,X2] :
( ~ sP16_prd(X0,X1)
| ~ p(X2)
| sP7_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f354]) ).
fof(f358,plain,
! [X0,X1,X2] :
( sP16_prd(X0,X1)
| p(X2)
| sP7_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f354]) ).
fof(f422,plain,
! [V1q,V2r] :
( ( ( ( p(V2r)
| p(V1q) )
& ( ~ p(V2r)
| ~ p(V1q) ) )
| sP16_prd(V2r,V1q) )
& ( ( ( ~ p(V2r)
| p(V1q) )
& ( p(V2r)
| ~ p(V1q) ) )
| ~ sP16_prd(V2r,V1q) ) ),
inference(NNF_transformation,[status(thm)],[f351]) ).
fof(f423,plain,
( ! [V1q,V2r] :
( ( ( p(V2r)
| p(V1q) )
& ( ~ p(V2r)
| ~ p(V1q) ) )
| sP16_prd(V2r,V1q) )
& ! [V1q,V2r] :
( ( ( ~ p(V2r)
| p(V1q) )
& ( p(V2r)
| ~ p(V1q) ) )
| ~ sP16_prd(V2r,V1q) ) ),
inference(miniscoping,[status(thm)],[f422]) ).
fof(f424,plain,
! [X0,X1] :
( p(X0)
| ~ p(X1)
| ~ sP16_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f423]) ).
fof(f425,plain,
! [X0,X1] :
( ~ p(X0)
| p(X1)
| ~ sP16_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f423]) ).
fof(f427,plain,
! [X0,X1] :
( p(X0)
| p(X1)
| sP16_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f423]) ).
fof(f449,definition,
! [X0] :
( sQ0_spl
<=> ( p(X0)
| ~ p(X0)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f452,definition,
! [X1] :
( sQ1_spl
<=> ( p(X1)
| ~ mem(X1,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f453,plain,
! [X0] :
( ~ sQ1_spl
| p(X0)
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f452]) ).
fof(f455,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f188,f449,f452]) ).
fof(f465,definition,
! [X1] :
( sQ2_spl
<=> ( ~ p(X1)
| ~ mem(X1,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f466,plain,
! [X0] :
( ~ sQ2_spl
| ~ p(X0)
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f480,definition,
( sQ3_spl
<=> p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f483,definition,
( sQ4_spl
<=> p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f485,plain,
( sQ4_spl
| ~ p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),sK8_skl)) ),
inference(component_clause,[status(thm)],[f483]) ).
fof(f486,plain,
( sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f309,f480,f483]) ).
fof(f487,plain,
( ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f310,f480,f483]) ).
fof(f492,plain,
! [X0,X1,X2,X3] :
( ~ mem(X2,X3)
| ~ mem(X1,arr(X3,bool))
| X0 = ap(X1,X2)
| p(ap(X1,X2))
| p(X0)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f67,f64]) ).
fof(f493,plain,
! [X0,X1,X2,X3] :
( ~ mem(X2,X3)
| ~ mem(X1,arr(X3,bool))
| X0 = ap(X1,X2)
| ~ p(ap(X1,X2))
| ~ p(X0)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f68,f64]) ).
fof(f497,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ mem(X4,X5)
| ~ mem(X3,arr(X5,arr(X1,X2)))
| X0 = ap(X3,X4)
| ap(X0,sK0_skl(ap(X3,X4),X0,X2,X1)) != ap(ap(X3,X4),sK0_skl(ap(X3,X4),X0,X2,X1))
| ~ mem(X0,arr(X1,X2)) ),
inference(resolution,[status(thm)],[f72,f64]) ).
fof(f498,plain,
! [X0] :
( X0 = c_2Einteger_2Eint__divides
| ap(X0,sK0_skl(c_2Einteger_2Eint__divides,X0,arr(ty_2Einteger_2Eint,bool),ty_2Einteger_2Eint)) != ap(c_2Einteger_2Eint__divides,sK0_skl(c_2Einteger_2Eint__divides,X0,arr(ty_2Einteger_2Eint,bool),ty_2Einteger_2Eint))
| ~ mem(X0,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,bool))) ),
inference(resolution,[status(thm)],[f72,f92]) ).
fof(f499,plain,
! [X0] :
( X0 = c_2Einteger_2Eint__sub
| ap(X0,sK0_skl(c_2Einteger_2Eint__sub,X0,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint),ty_2Einteger_2Eint)) != ap(c_2Einteger_2Eint__sub,sK0_skl(c_2Einteger_2Eint__sub,X0,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint),ty_2Einteger_2Eint))
| ~ mem(X0,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint))) ),
inference(resolution,[status(thm)],[f72,f89]) ).
fof(f502,plain,
( c_2Einteger_2Eint__divides = c_2Einteger_2Eint__divides
| ap(c_2Einteger_2Eint__divides,sK0_skl(c_2Einteger_2Eint__divides,c_2Einteger_2Eint__divides,arr(ty_2Einteger_2Eint,bool),ty_2Einteger_2Eint)) != ap(c_2Einteger_2Eint__divides,sK0_skl(c_2Einteger_2Eint__divides,c_2Einteger_2Eint__divides,arr(ty_2Einteger_2Eint,bool),ty_2Einteger_2Eint)) ),
inference(resolution,[status(thm)],[f498,f92]) ).
fof(f503,definition,
( sQ5_spl
<=> ap(c_2Einteger_2Eint__divides,sK0_skl(c_2Einteger_2Eint__divides,c_2Einteger_2Eint__divides,arr(ty_2Einteger_2Eint,bool),ty_2Einteger_2Eint)) = ap(c_2Einteger_2Eint__divides,sK0_skl(c_2Einteger_2Eint__divides,c_2Einteger_2Eint__divides,arr(ty_2Einteger_2Eint,bool),ty_2Einteger_2Eint)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f505,plain,
( sQ5_spl
| ap(c_2Einteger_2Eint__divides,sK0_skl(c_2Einteger_2Eint__divides,c_2Einteger_2Eint__divides,arr(ty_2Einteger_2Eint,bool),ty_2Einteger_2Eint)) != ap(c_2Einteger_2Eint__divides,sK0_skl(c_2Einteger_2Eint__divides,c_2Einteger_2Eint__divides,arr(ty_2Einteger_2Eint,bool),ty_2Einteger_2Eint)) ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f506,definition,
( sQ6_spl
<=> c_2Einteger_2Eint__divides = c_2Einteger_2Eint__divides ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f509,plain,
( sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f502,f503,f506]) ).
fof(f510,plain,
( sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f505]) ).
fof(f511,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f510]) ).
fof(f514,plain,
( c_2Einteger_2Eint__sub = c_2Einteger_2Eint__sub
| ap(c_2Einteger_2Eint__sub,sK0_skl(c_2Einteger_2Eint__sub,c_2Einteger_2Eint__sub,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint),ty_2Einteger_2Eint)) != ap(c_2Einteger_2Eint__sub,sK0_skl(c_2Einteger_2Eint__sub,c_2Einteger_2Eint__sub,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint),ty_2Einteger_2Eint)) ),
inference(resolution,[status(thm)],[f499,f89]) ).
fof(f515,definition,
( sQ7_spl
<=> ap(c_2Einteger_2Eint__sub,sK0_skl(c_2Einteger_2Eint__sub,c_2Einteger_2Eint__sub,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint),ty_2Einteger_2Eint)) = ap(c_2Einteger_2Eint__sub,sK0_skl(c_2Einteger_2Eint__sub,c_2Einteger_2Eint__sub,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint),ty_2Einteger_2Eint)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f517,plain,
( sQ7_spl
| ap(c_2Einteger_2Eint__sub,sK0_skl(c_2Einteger_2Eint__sub,c_2Einteger_2Eint__sub,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint),ty_2Einteger_2Eint)) != ap(c_2Einteger_2Eint__sub,sK0_skl(c_2Einteger_2Eint__sub,c_2Einteger_2Eint__sub,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint),ty_2Einteger_2Eint)) ),
inference(component_clause,[status(thm)],[f515]) ).
fof(f518,definition,
( sQ8_spl
<=> c_2Einteger_2Eint__sub = c_2Einteger_2Eint__sub ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f521,plain,
( sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f514,f515,f518]) ).
fof(f522,plain,
( sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f517]) ).
fof(f523,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f522]) ).
fof(f528,plain,
! [X0] :
( X0 = c_2Ebool_2ET
| ~ p(c_2Ebool_2ET)
| ~ p(X0)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f78,f68]) ).
fof(f530,definition,
! [X0] :
( sQ9_spl
<=> ( X0 = c_2Ebool_2ET
| ~ p(X0)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f531,plain,
! [X0] :
( ~ sQ9_spl
| X0 = c_2Ebool_2ET
| ~ p(X0)
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f530]) ).
fof(f533,definition,
( sQ10_spl
<=> p(c_2Ebool_2ET) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f536,plain,
( ~ sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f528,f530,f533]) ).
fof(f537,definition,
! [X0] :
( sQ11_spl
<=> ( X0 = c_2Ebool_2ET
| p(X0)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f538,plain,
! [X0] :
( ~ sQ11_spl
| X0 = c_2Ebool_2ET
| p(X0)
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f537]) ).
fof(f543,plain,
! [X0,X1,X2,X3,X4] :
( ~ mem(X3,X4)
| ~ mem(X2,arr(X4,X0))
| ap(k(X0,X1),ap(X2,X3)) = X1 ),
inference(resolution,[status(thm)],[f75,f64]) ).
fof(f551,plain,
! [X0,X1,X2,X3] :
( ~ mem(X2,X3)
| ~ mem(X1,arr(X3,X0))
| ap(i(X0),ap(X1,X2)) = ap(X1,X2) ),
inference(resolution,[status(thm)],[f77,f64]) ).
fof(f574,plain,
! [X0] :
( X0 = c_2Ebool_2EF
| p(c_2Ebool_2EF)
| p(X0)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f93,f67]) ).
fof(f580,definition,
( sQ13_spl
<=> p(c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f581,plain,
( ~ sQ13_spl
| p(c_2Ebool_2EF) ),
inference(component_clause,[status(thm)],[f580]) ).
fof(f584,definition,
! [X0] :
( sQ14_spl
<=> ( X0 = c_2Ebool_2EF
| p(X0)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f585,plain,
! [X0] :
( ~ sQ14_spl
| X0 = c_2Ebool_2EF
| p(X0)
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f584]) ).
fof(f587,plain,
( sQ13_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f574,f584,f580]) ).
fof(f590,plain,
! [X0] :
( X0 = c_2Einteger_2Eint__add
| ap(X0,sK0_skl(c_2Einteger_2Eint__add,X0,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint),ty_2Einteger_2Eint)) != ap(c_2Einteger_2Eint__add,sK0_skl(c_2Einteger_2Eint__add,X0,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint),ty_2Einteger_2Eint))
| ~ mem(X0,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint))) ),
inference(resolution,[status(thm)],[f90,f72]) ).
fof(f600,plain,
! [X0] :
( X0 = c_2Einteger_2Eint__neg
| ap(X0,sK0_skl(c_2Einteger_2Eint__neg,X0,ty_2Einteger_2Eint,ty_2Einteger_2Eint)) != ap(c_2Einteger_2Eint__neg,sK0_skl(c_2Einteger_2Eint__neg,X0,ty_2Einteger_2Eint,ty_2Einteger_2Eint))
| ~ mem(X0,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint)) ),
inference(resolution,[status(thm)],[f91,f72]) ).
fof(f603,plain,
! [X0] :
( X0 = c_2Emin_2E_3D_3D_3E
| ap(X0,sK0_skl(c_2Emin_2E_3D_3D_3E,X0,arr(bool,bool),bool)) != ap(c_2Emin_2E_3D_3D_3E,sK0_skl(c_2Emin_2E_3D_3D_3E,X0,arr(bool,bool),bool))
| ~ mem(X0,arr(bool,arr(bool,bool))) ),
inference(resolution,[status(thm)],[f95,f72]) ).
fof(f620,plain,
! [X0] :
( X0 = c_2Ebool_2E_5C_2F
| ap(X0,sK0_skl(c_2Ebool_2E_5C_2F,X0,arr(bool,bool),bool)) != ap(c_2Ebool_2E_5C_2F,sK0_skl(c_2Ebool_2E_5C_2F,X0,arr(bool,bool),bool))
| ~ mem(X0,arr(bool,arr(bool,bool))) ),
inference(resolution,[status(thm)],[f101,f72]) ).
fof(f627,plain,
! [X0] :
( X0 = c_2Ebool_2E_2F_5C
| ap(X0,sK0_skl(c_2Ebool_2E_2F_5C,X0,arr(bool,bool),bool)) != ap(c_2Ebool_2E_2F_5C,sK0_skl(c_2Ebool_2E_2F_5C,X0,arr(bool,bool),bool))
| ~ mem(X0,arr(bool,arr(bool,bool))) ),
inference(resolution,[status(thm)],[f107,f72]) ).
fof(f640,plain,
! [X0] :
( X0 = c_2Ebool_2E_7E
| ap(X0,sK0_skl(c_2Ebool_2E_7E,X0,bool,bool)) != ap(c_2Ebool_2E_7E,sK0_skl(c_2Ebool_2E_7E,X0,bool,bool))
| ~ mem(X0,arr(bool,bool)) ),
inference(resolution,[status(thm)],[f113,f72]) ).
fof(f648,definition,
( sQ20_spl
<=> ne(ty_2Einteger_2Eint) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f650,plain,
( sQ20_spl
| ~ ne(ty_2Einteger_2Eint) ),
inference(component_clause,[status(thm)],[f648]) ).
fof(f663,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f650,f88]) ).
fof(f664,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f663]) ).
fof(f726,plain,
! [X0] :
( sQ4_spl
| ~ p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),ap(ap(c_2Einteger_2Eint__add,sK8_skl),X0)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),X0))
| ~ mem(sK8_skl,ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint)
| ~ mem(sK6_skl,ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f214,f485]) ).
fof(f727,definition,
( sQ24_spl
<=> mem(sK6_skl,ty_2Einteger_2Eint) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f729,plain,
( sQ24_spl
| ~ mem(sK6_skl,ty_2Einteger_2Eint) ),
inference(component_clause,[status(thm)],[f727]) ).
fof(f730,definition,
! [X0] :
( sQ25_spl
<=> ( ~ p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),ap(ap(c_2Einteger_2Eint__add,sK8_skl),X0)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),X0))
| ~ mem(X0,ty_2Einteger_2Eint) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f731,plain,
! [X0] :
( ~ sQ25_spl
| ~ p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),ap(ap(c_2Einteger_2Eint__add,sK8_skl),X0)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),X0))
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(component_clause,[status(thm)],[f730]) ).
fof(f733,definition,
( sQ26_spl
<=> mem(sK8_skl,ty_2Einteger_2Eint) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f735,plain,
( sQ26_spl
| ~ mem(sK8_skl,ty_2Einteger_2Eint) ),
inference(component_clause,[status(thm)],[f733]) ).
fof(f736,plain,
( sQ4_spl
| ~ sQ26_spl
| sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f726,f727,f730,f733,f483]) ).
fof(f739,definition,
( sQ27_spl
<=> mem(ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl),ty_2Einteger_2Eint) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f740,plain,
( ~ sQ27_spl
| mem(ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl),ty_2Einteger_2Eint) ),
inference(component_clause,[status(thm)],[f739]) ).
fof(f741,plain,
( sQ27_spl
| ~ mem(ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl),ty_2Einteger_2Eint) ),
inference(component_clause,[status(thm)],[f739]) ).
fof(f750,plain,
( sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f729,f305]) ).
fof(f751,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f750]) ).
fof(f759,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f735,f307]) ).
fof(f760,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f759]) ).
fof(f765,plain,
! [X0] :
( sQ27_spl
| ~ mem(sK7_skl,X0)
| ~ mem(ap(c_2Einteger_2Eint__sub,sK8_skl),arr(X0,ty_2Einteger_2Eint)) ),
inference(resolution,[status(thm)],[f741,f64]) ).
fof(f766,plain,
! [X0,X1] :
( sQ27_spl
| ~ mem(sK8_skl,X1)
| ~ mem(c_2Einteger_2Eint__sub,arr(X1,arr(X0,ty_2Einteger_2Eint)))
| ~ mem(sK7_skl,X0) ),
inference(resolution,[status(thm)],[f765,f64]) ).
fof(f767,plain,
( sQ27_spl
| ~ mem(sK8_skl,ty_2Einteger_2Eint)
| ~ mem(sK7_skl,ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f766,f89]) ).
fof(f768,definition,
( sQ31_spl
<=> mem(sK7_skl,ty_2Einteger_2Eint) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f770,plain,
( sQ31_spl
| ~ mem(sK7_skl,ty_2Einteger_2Eint) ),
inference(component_clause,[status(thm)],[f768]) ).
fof(f771,plain,
( sQ27_spl
| ~ sQ26_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f767,f768,f733,f739]) ).
fof(f772,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f770,f306]) ).
fof(f773,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f772]) ).
fof(f779,definition,
! [X1] :
( sQ33_spl
<=> ( ~ p(X1)
| p(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f804,definition,
! [X0] :
( sQ36_spl
<=> ( ~ p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),X0))
| ~ mem(X0,ty_2Einteger_2Eint)
| ~ p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),X0))
| ~ mem(X0,ty_2Einteger_2Eint) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f805,plain,
! [X0] :
( ~ sQ36_spl
| ~ p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),X0))
| ~ mem(X0,ty_2Einteger_2Eint)
| ~ p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),X0))
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(component_clause,[status(thm)],[f804]) ).
fof(f827,definition,
( sQ40_spl
<=> mem(ap(c_2Einteger_2Eint__neg,sK8_skl),ty_2Einteger_2Eint) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f828,plain,
( ~ sQ40_spl
| mem(ap(c_2Einteger_2Eint__neg,sK8_skl),ty_2Einteger_2Eint) ),
inference(component_clause,[status(thm)],[f827]) ).
fof(f829,plain,
( sQ40_spl
| ~ mem(ap(c_2Einteger_2Eint__neg,sK8_skl),ty_2Einteger_2Eint) ),
inference(component_clause,[status(thm)],[f827]) ).
fof(f847,definition,
( sQ44_spl
<=> mem(ap(c_2Einteger_2Eint__neg,sK6_skl),ty_2Einteger_2Eint) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f848,plain,
( ~ sQ44_spl
| mem(ap(c_2Einteger_2Eint__neg,sK6_skl),ty_2Einteger_2Eint) ),
inference(component_clause,[status(thm)],[f847]) ).
fof(f849,plain,
( sQ44_spl
| ~ mem(ap(c_2Einteger_2Eint__neg,sK6_skl),ty_2Einteger_2Eint) ),
inference(component_clause,[status(thm)],[f847]) ).
fof(f875,plain,
! [X0] :
( sQ40_spl
| ~ mem(sK8_skl,X0)
| ~ mem(c_2Einteger_2Eint__neg,arr(X0,ty_2Einteger_2Eint)) ),
inference(resolution,[status(thm)],[f829,f64]) ).
fof(f878,plain,
! [X0] :
( sQ44_spl
| ~ mem(sK6_skl,X0)
| ~ mem(c_2Einteger_2Eint__neg,arr(X0,ty_2Einteger_2Eint)) ),
inference(resolution,[status(thm)],[f849,f64]) ).
fof(f879,plain,
( sQ40_spl
| ~ mem(sK8_skl,ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f875,f91]) ).
fof(f880,plain,
( sQ40_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f879,f733,f827]) ).
fof(f895,definition,
( sQ48_spl
<=> mem(ap(c_2Einteger_2Eint__neg,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)),ty_2Einteger_2Eint) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f896,plain,
( ~ sQ48_spl
| mem(ap(c_2Einteger_2Eint__neg,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)),ty_2Einteger_2Eint) ),
inference(component_clause,[status(thm)],[f895]) ).
fof(f897,plain,
( sQ48_spl
| ~ mem(ap(c_2Einteger_2Eint__neg,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)),ty_2Einteger_2Eint) ),
inference(component_clause,[status(thm)],[f895]) ).
fof(f933,plain,
! [X0] :
( sQ48_spl
| ~ mem(ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl),X0)
| ~ mem(c_2Einteger_2Eint__neg,arr(X0,ty_2Einteger_2Eint)) ),
inference(resolution,[status(thm)],[f897,f64]) ).
fof(f957,definition,
! [X0] :
( sQ58_spl
<=> ( ~ p(X0)
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f958,plain,
! [X0] :
( ~ sQ58_spl
| ~ p(X0)
| ~ p(X0) ),
inference(component_clause,[status(thm)],[f957]) ).
fof(f970,plain,
( sQ44_spl
| ~ mem(sK6_skl,ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f878,f91]) ).
fof(f971,plain,
( sQ44_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f970,f727,f847]) ).
fof(f998,definition,
( sQ62_spl
<=> mem(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,sK6_skl)),ty_2Einteger_2Eint) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1000,plain,
( sQ62_spl
| ~ mem(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,sK6_skl)),ty_2Einteger_2Eint) ),
inference(component_clause,[status(thm)],[f998]) ).
fof(f1047,plain,
( sQ48_spl
| ~ mem(ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl),ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f933,f91]) ).
fof(f1048,plain,
( sQ48_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f1047,f739,f895]) ).
fof(f1054,definition,
( sQ70_spl
<=> mem(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl))),ty_2Einteger_2Eint) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f1056,plain,
( sQ70_spl
| ~ mem(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl))),ty_2Einteger_2Eint) ),
inference(component_clause,[status(thm)],[f1054]) ).
fof(f1066,plain,
! [X0] :
( sQ62_spl
| ~ mem(ap(c_2Einteger_2Eint__neg,sK6_skl),X0)
| ~ mem(c_2Einteger_2Eint__neg,arr(X0,ty_2Einteger_2Eint)) ),
inference(resolution,[status(thm)],[f1000,f64]) ).
fof(f1085,plain,
! [X0] :
( ~ sQ36_spl
| ~ p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),X0))
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(duplicate_literals_removal,[status(thm)],[f805]) ).
fof(f1090,plain,
( ~ sQ36_spl
| ~ mem(sK7_skl,ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f1085,f308]) ).
fof(f1098,plain,
( ~ sQ36_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f1090,f768,f804]) ).
fof(f1139,plain,
( sQ62_spl
| ~ mem(ap(c_2Einteger_2Eint__neg,sK6_skl),ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f1066,f91]) ).
fof(f1140,plain,
( sQ62_spl
| ~ sQ44_spl ),
inference(split_clause,[status(thm)],[f1139,f847,f998]) ).
fof(f1163,plain,
! [X0,X1,X2] :
( p(X0)
| p(X1)
| ~ p(X2)
| sP7_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f357,f427]) ).
fof(f1166,plain,
! [X0,X1,X2] :
( ~ p(X0)
| p(X1)
| p(X2)
| sP7_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f358,f425]) ).
fof(f1168,plain,
! [X0] :
( sQ70_spl
| ~ mem(ap(c_2Einteger_2Eint__neg,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)),X0)
| ~ mem(c_2Einteger_2Eint__neg,arr(X0,ty_2Einteger_2Eint)) ),
inference(resolution,[status(thm)],[f1056,f64]) ).
fof(f1255,plain,
( sQ70_spl
| ~ mem(ap(c_2Einteger_2Eint__neg,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)),ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f1168,f91]) ).
fof(f1256,plain,
( sQ70_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f1255,f895,f1054]) ).
fof(f1309,definition,
( sQ90_spl
<=> mem(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,sK6_skl))),ty_2Einteger_2Eint) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f1311,plain,
( sQ90_spl
| ~ mem(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,sK6_skl))),ty_2Einteger_2Eint) ),
inference(component_clause,[status(thm)],[f1309]) ).
fof(f1346,plain,
! [X0] :
( sQ90_spl
| ~ mem(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,sK6_skl)),X0)
| ~ mem(c_2Einteger_2Eint__neg,arr(X0,ty_2Einteger_2Eint)) ),
inference(resolution,[status(thm)],[f1311,f64]) ).
fof(f1347,plain,
( sQ90_spl
| ~ mem(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,sK6_skl)),ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f1346,f91]) ).
fof(f1348,plain,
( sQ90_spl
| ~ sQ62_spl ),
inference(split_clause,[status(thm)],[f1347,f998,f1309]) ).
fof(f1354,definition,
( sQ98_spl
<=> mem(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)))),ty_2Einteger_2Eint) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f1356,plain,
( sQ98_spl
| ~ mem(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)))),ty_2Einteger_2Eint) ),
inference(component_clause,[status(thm)],[f1354]) ).
fof(f1463,plain,
! [X0] :
( sQ98_spl
| ~ mem(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl))),X0)
| ~ mem(c_2Einteger_2Eint__neg,arr(X0,ty_2Einteger_2Eint)) ),
inference(resolution,[status(thm)],[f1356,f64]) ).
fof(f1465,plain,
( sQ98_spl
| ~ mem(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl))),ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f1463,f91]) ).
fof(f1466,plain,
( sQ98_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f1465,f1054,f1354]) ).
fof(f1489,plain,
( ~ sQ11_spl
| c_2Ebool_2EF = c_2Ebool_2ET
| p(c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f538,f93]) ).
fof(f1493,definition,
( sQ110_spl
<=> c_2Ebool_2EF = c_2Ebool_2ET ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1494,plain,
( ~ sQ110_spl
| c_2Ebool_2EF = c_2Ebool_2ET ),
inference(component_clause,[status(thm)],[f1493]) ).
fof(f1496,plain,
( ~ sQ11_spl
| sQ110_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f1489,f580,f1493,f537]) ).
fof(f1497,definition,
( sQ111_spl
<=> c_2Ebool_2ET = c_2Ebool_2ET ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f1501,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f581,f94]) ).
fof(f1502,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f1501]) ).
fof(f1506,plain,
( ~ sQ110_spl
| ~ p(c_2Ebool_2ET) ),
inference(backward_demodulation,[status(thm)],[f1494,f94]) ).
fof(f1508,plain,
( ~ sQ110_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1506,f79]) ).
fof(f1509,plain,
~ sQ110_spl,
inference(contradiction_clause,[status(thm)],[f1508]) ).
fof(f1538,plain,
! [X0,X1,X2] :
( ~ mem(X1,X2)
| ~ mem(X0,arr(X2,bool))
| c_2Ebool_2EF = ap(X0,X1)
| p(ap(X0,X1))
| p(c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f492,f93]) ).
fof(f1542,definition,
! [X0,X1,X2] :
( sQ112_spl
<=> ( ~ mem(X1,X2)
| ~ mem(X0,arr(X2,bool))
| c_2Ebool_2EF = ap(X0,X1)
| p(ap(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f1545,plain,
( sQ112_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f1538,f580,f1542]) ).
fof(f1598,plain,
! [X0,X1,X2] :
( ~ mem(X1,X2)
| ~ mem(X0,arr(X2,bool))
| c_2Ebool_2ET = ap(X0,X1)
| ~ p(ap(X0,X1))
| ~ p(c_2Ebool_2ET) ),
inference(resolution,[status(thm)],[f493,f78]) ).
fof(f1605,definition,
! [X0,X1,X2] :
( sQ121_spl
<=> ( ~ mem(X1,X2)
| ~ mem(X0,arr(X2,bool))
| c_2Ebool_2ET = ap(X0,X1)
| ~ p(ap(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f1608,plain,
( sQ121_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1598,f533,f1605]) ).
fof(f1623,plain,
! [X0,X1] :
( ~ mem(X1,ty_2Einteger_2Eint)
| X0 = ap(c_2Einteger_2Eint__divides,X1)
| ap(X0,sK0_skl(ap(c_2Einteger_2Eint__divides,X1),X0,bool,ty_2Einteger_2Eint)) != ap(ap(c_2Einteger_2Eint__divides,X1),sK0_skl(ap(c_2Einteger_2Eint__divides,X1),X0,bool,ty_2Einteger_2Eint))
| ~ mem(X0,arr(ty_2Einteger_2Eint,bool)) ),
inference(resolution,[status(thm)],[f497,f92]) ).
fof(f1626,plain,
( ~ sQ9_spl
| c_2Ebool_2ET = c_2Ebool_2ET
| ~ p(c_2Ebool_2ET) ),
inference(resolution,[status(thm)],[f531,f78]) ).
fof(f1630,plain,
( ~ sQ9_spl
| sQ111_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1626,f533,f1497,f530]) ).
fof(f1675,definition,
( sQ128_spl
<=> mem(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,sK6_skl)))),ty_2Einteger_2Eint) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1677,plain,
( sQ128_spl
| ~ mem(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,sK6_skl)))),ty_2Einteger_2Eint) ),
inference(component_clause,[status(thm)],[f1675]) ).
fof(f1687,plain,
! [X0,X1,X2,X3] :
( X1 = X0
| ~ mem(X0,arr(arr(ty_2Einteger_2Eint,bool),X2))
| ~ mem(X1,arr(arr(ty_2Einteger_2Eint,bool),X2))
| ~ mem(X3,ty_2Einteger_2Eint)
| sK0_skl(X0,X1,X2,arr(ty_2Einteger_2Eint,bool)) = ap(c_2Einteger_2Eint__divides,X3)
| ap(sK0_skl(X0,X1,X2,arr(ty_2Einteger_2Eint,bool)),sK0_skl(ap(c_2Einteger_2Eint__divides,X3),sK0_skl(X0,X1,X2,arr(ty_2Einteger_2Eint,bool)),bool,ty_2Einteger_2Eint)) != ap(ap(c_2Einteger_2Eint__divides,X3),sK0_skl(ap(c_2Einteger_2Eint__divides,X3),sK0_skl(X0,X1,X2,arr(ty_2Einteger_2Eint,bool)),bool,ty_2Einteger_2Eint)) ),
inference(resolution,[status(thm)],[f1623,f71]) ).
fof(f1688,plain,
! [X0,X1,X2,X3] :
( ~ mem(X1,X3)
| ~ mem(X0,arr(X3,arr(ty_2Einteger_2Eint,bool)))
| ~ mem(X2,ty_2Einteger_2Eint)
| ap(X0,X1) = ap(c_2Einteger_2Eint__divides,X2)
| ap(ap(X0,X1),sK0_skl(ap(c_2Einteger_2Eint__divides,X2),ap(X0,X1),bool,ty_2Einteger_2Eint)) != ap(ap(c_2Einteger_2Eint__divides,X2),sK0_skl(ap(c_2Einteger_2Eint__divides,X2),ap(X0,X1),bool,ty_2Einteger_2Eint)) ),
inference(resolution,[status(thm)],[f1623,f64]) ).
fof(f1692,plain,
! [X0,X1] :
( ~ ne(ty_2Einteger_2Eint)
| c_2Ebool_2E_21(ty_2Einteger_2Eint) = X0
| ~ mem(X0,arr(arr(ty_2Einteger_2Eint,bool),bool))
| ~ mem(X1,ty_2Einteger_2Eint)
| sK0_skl(X0,c_2Ebool_2E_21(ty_2Einteger_2Eint),bool,arr(ty_2Einteger_2Eint,bool)) = ap(c_2Einteger_2Eint__divides,X1)
| ap(sK0_skl(X0,c_2Ebool_2E_21(ty_2Einteger_2Eint),bool,arr(ty_2Einteger_2Eint,bool)),sK0_skl(ap(c_2Einteger_2Eint__divides,X1),sK0_skl(X0,c_2Ebool_2E_21(ty_2Einteger_2Eint),bool,arr(ty_2Einteger_2Eint,bool)),bool,ty_2Einteger_2Eint)) != ap(ap(c_2Einteger_2Eint__divides,X1),sK0_skl(ap(c_2Einteger_2Eint__divides,X1),sK0_skl(X0,c_2Ebool_2E_21(ty_2Einteger_2Eint),bool,arr(ty_2Einteger_2Eint,bool)),bool,ty_2Einteger_2Eint)) ),
inference(resolution,[status(thm)],[f1687,f125]) ).
fof(f1694,plain,
! [X0,X1] :
( ~ ne(ty_2Einteger_2Eint)
| c_2Ebool_2E_3F(ty_2Einteger_2Eint) = X0
| ~ mem(X0,arr(arr(ty_2Einteger_2Eint,bool),bool))
| ~ mem(X1,ty_2Einteger_2Eint)
| sK0_skl(X0,c_2Ebool_2E_3F(ty_2Einteger_2Eint),bool,arr(ty_2Einteger_2Eint,bool)) = ap(c_2Einteger_2Eint__divides,X1)
| ap(sK0_skl(X0,c_2Ebool_2E_3F(ty_2Einteger_2Eint),bool,arr(ty_2Einteger_2Eint,bool)),sK0_skl(ap(c_2Einteger_2Eint__divides,X1),sK0_skl(X0,c_2Ebool_2E_3F(ty_2Einteger_2Eint),bool,arr(ty_2Einteger_2Eint,bool)),bool,ty_2Einteger_2Eint)) != ap(ap(c_2Einteger_2Eint__divides,X1),sK0_skl(ap(c_2Einteger_2Eint__divides,X1),sK0_skl(X0,c_2Ebool_2E_3F(ty_2Einteger_2Eint),bool,arr(ty_2Einteger_2Eint,bool)),bool,ty_2Einteger_2Eint)) ),
inference(resolution,[status(thm)],[f1687,f81]) ).
fof(f1697,definition,
! [X0,X1] :
( sQ131_spl
<=> ( c_2Ebool_2E_21(ty_2Einteger_2Eint) = X0
| ~ mem(X0,arr(arr(ty_2Einteger_2Eint,bool),bool))
| ~ mem(X1,ty_2Einteger_2Eint)
| sK0_skl(X0,c_2Ebool_2E_21(ty_2Einteger_2Eint),bool,arr(ty_2Einteger_2Eint,bool)) = ap(c_2Einteger_2Eint__divides,X1)
| ap(sK0_skl(X0,c_2Ebool_2E_21(ty_2Einteger_2Eint),bool,arr(ty_2Einteger_2Eint,bool)),sK0_skl(ap(c_2Einteger_2Eint__divides,X1),sK0_skl(X0,c_2Ebool_2E_21(ty_2Einteger_2Eint),bool,arr(ty_2Einteger_2Eint,bool)),bool,ty_2Einteger_2Eint)) != ap(ap(c_2Einteger_2Eint__divides,X1),sK0_skl(ap(c_2Einteger_2Eint__divides,X1),sK0_skl(X0,c_2Ebool_2E_21(ty_2Einteger_2Eint),bool,arr(ty_2Einteger_2Eint,bool)),bool,ty_2Einteger_2Eint)) ) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f1700,plain,
( ~ sQ20_spl
| sQ131_spl ),
inference(split_clause,[status(thm)],[f1692,f1697,f648]) ).
fof(f1708,definition,
! [X0,X1] :
( sQ134_spl
<=> ( c_2Ebool_2E_3F(ty_2Einteger_2Eint) = X0
| ~ mem(X0,arr(arr(ty_2Einteger_2Eint,bool),bool))
| ~ mem(X1,ty_2Einteger_2Eint)
| sK0_skl(X0,c_2Ebool_2E_3F(ty_2Einteger_2Eint),bool,arr(ty_2Einteger_2Eint,bool)) = ap(c_2Einteger_2Eint__divides,X1)
| ap(sK0_skl(X0,c_2Ebool_2E_3F(ty_2Einteger_2Eint),bool,arr(ty_2Einteger_2Eint,bool)),sK0_skl(ap(c_2Einteger_2Eint__divides,X1),sK0_skl(X0,c_2Ebool_2E_3F(ty_2Einteger_2Eint),bool,arr(ty_2Einteger_2Eint,bool)),bool,ty_2Einteger_2Eint)) != ap(ap(c_2Einteger_2Eint__divides,X1),sK0_skl(ap(c_2Einteger_2Eint__divides,X1),sK0_skl(X0,c_2Ebool_2E_3F(ty_2Einteger_2Eint),bool,arr(ty_2Einteger_2Eint,bool)),bool,ty_2Einteger_2Eint)) ) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f1711,plain,
( ~ sQ20_spl
| sQ134_spl ),
inference(split_clause,[status(thm)],[f1694,f1708,f648]) ).
fof(f1712,plain,
! [X0,X1] :
( ~ ne(ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint)
| ~ mem(X1,ty_2Einteger_2Eint)
| ap(c_2Emin_2E_3D(ty_2Einteger_2Eint),X0) = ap(c_2Einteger_2Eint__divides,X1)
| ap(ap(c_2Emin_2E_3D(ty_2Einteger_2Eint),X0),sK0_skl(ap(c_2Einteger_2Eint__divides,X1),ap(c_2Emin_2E_3D(ty_2Einteger_2Eint),X0),bool,ty_2Einteger_2Eint)) != ap(ap(c_2Einteger_2Eint__divides,X1),sK0_skl(ap(c_2Einteger_2Eint__divides,X1),ap(c_2Emin_2E_3D(ty_2Einteger_2Eint),X0),bool,ty_2Einteger_2Eint)) ),
inference(resolution,[status(thm)],[f1688,f119]) ).
fof(f1716,definition,
! [X0,X1] :
( sQ135_spl
<=> ( ~ mem(X0,ty_2Einteger_2Eint)
| ~ mem(X1,ty_2Einteger_2Eint)
| ap(c_2Emin_2E_3D(ty_2Einteger_2Eint),X0) = ap(c_2Einteger_2Eint__divides,X1)
| ap(ap(c_2Emin_2E_3D(ty_2Einteger_2Eint),X0),sK0_skl(ap(c_2Einteger_2Eint__divides,X1),ap(c_2Emin_2E_3D(ty_2Einteger_2Eint),X0),bool,ty_2Einteger_2Eint)) != ap(ap(c_2Einteger_2Eint__divides,X1),sK0_skl(ap(c_2Einteger_2Eint__divides,X1),ap(c_2Emin_2E_3D(ty_2Einteger_2Eint),X0),bool,ty_2Einteger_2Eint)) ) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f1719,plain,
( ~ sQ20_spl
| sQ135_spl ),
inference(split_clause,[status(thm)],[f1712,f1716,f648]) ).
fof(f1720,plain,
( ~ sQ14_spl
| c_2Ebool_2EF = c_2Ebool_2EF
| p(c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f585,f93]) ).
fof(f1721,plain,
( ~ sQ14_spl
| c_2Ebool_2ET = c_2Ebool_2EF
| p(c_2Ebool_2ET) ),
inference(resolution,[status(thm)],[f585,f78]) ).
fof(f1724,definition,
( sQ136_spl
<=> c_2Ebool_2EF = c_2Ebool_2EF ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f1727,plain,
( ~ sQ14_spl
| sQ136_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f1720,f580,f1724,f584]) ).
fof(f1728,plain,
( ~ sQ14_spl
| sQ110_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f1721,f533,f1493,f584]) ).
fof(f1753,plain,
! [X0,X1] :
( ~ mem(X1,ty_2Einteger_2Eint)
| ap(k(arr(ty_2Einteger_2Eint,bool),X0),ap(c_2Einteger_2Eint__divides,X1)) = X0 ),
inference(resolution,[status(thm)],[f543,f92]) ).
fof(f1754,plain,
! [X0,X1] :
( ~ mem(X1,ty_2Einteger_2Eint)
| ap(k(arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint),X0),ap(c_2Einteger_2Eint__sub,X1)) = X0 ),
inference(resolution,[status(thm)],[f543,f89]) ).
fof(f1780,plain,
! [X0] :
( ~ mem(X0,ty_2Einteger_2Eint)
| ap(i(arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint)),ap(c_2Einteger_2Eint__sub,X0)) = ap(c_2Einteger_2Eint__sub,X0) ),
inference(resolution,[status(thm)],[f551,f89]) ).
fof(f1789,plain,
! [X0] :
( sQ128_spl
| ~ mem(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,sK6_skl))),X0)
| ~ mem(c_2Einteger_2Eint__neg,arr(X0,ty_2Einteger_2Eint)) ),
inference(resolution,[status(thm)],[f1677,f64]) ).
fof(f1792,plain,
! [X0,X1,X2,X3] :
( X2 = X1
| ~ mem(X1,arr(ty_2Einteger_2Eint,X3))
| ~ mem(X2,arr(ty_2Einteger_2Eint,X3))
| ap(k(arr(ty_2Einteger_2Eint,bool),X0),ap(c_2Einteger_2Eint__divides,sK0_skl(X1,X2,X3,ty_2Einteger_2Eint))) = X0 ),
inference(resolution,[status(thm)],[f1753,f71]) ).
fof(f1830,plain,
! [X0,X1,X2,X3] :
( X2 = X1
| ~ mem(X1,arr(ty_2Einteger_2Eint,X3))
| ~ mem(X2,arr(ty_2Einteger_2Eint,X3))
| ap(k(arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint),X0),ap(c_2Einteger_2Eint__sub,sK0_skl(X1,X2,X3,ty_2Einteger_2Eint))) = X0 ),
inference(resolution,[status(thm)],[f1754,f71]) ).
fof(f1951,definition,
( sQ147_spl
<=> p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f1953,plain,
( sQ147_spl
| ~ p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),sK7_skl)) ),
inference(component_clause,[status(thm)],[f1951]) ).
fof(f1982,plain,
! [X0,X1,X2,X3] :
( ~ mem(X2,X3)
| ~ mem(X1,arr(X3,ty_2Einteger_2Eint))
| ap(ap(c_2Einteger_2Eint__sub,X0),ap(X1,X2)) = ap(ap(c_2Einteger_2Eint__add,X0),ap(c_2Einteger_2Eint__neg,ap(X1,X2)))
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f211,f64]) ).
fof(f1984,plain,
! [X0] :
( ap(ap(c_2Einteger_2Eint__sub,X0),sK7_skl) = ap(ap(c_2Einteger_2Eint__add,X0),ap(c_2Einteger_2Eint__neg,sK7_skl))
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f211,f306]) ).
fof(f1999,plain,
! [X0,X1,X2,X3,X4,X5] :
( X2 = X1
| ~ mem(X1,arr(arr(X4,ty_2Einteger_2Eint),X3))
| ~ mem(X2,arr(arr(X4,ty_2Einteger_2Eint),X3))
| ~ mem(X5,X4)
| ap(ap(c_2Einteger_2Eint__sub,X0),ap(sK0_skl(X1,X2,X3,arr(X4,ty_2Einteger_2Eint)),X5)) = ap(ap(c_2Einteger_2Eint__add,X0),ap(c_2Einteger_2Eint__neg,ap(sK0_skl(X1,X2,X3,arr(X4,ty_2Einteger_2Eint)),X5)))
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f1982,f71]) ).
fof(f2006,plain,
( ~ sQ48_spl
| ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__neg,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl))),sK7_skl) = ap(ap(c_2Einteger_2Eint__add,ap(c_2Einteger_2Eint__neg,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl))),ap(c_2Einteger_2Eint__neg,sK7_skl)) ),
inference(resolution,[status(thm)],[f1984,f896]) ).
fof(f2007,plain,
( ~ sQ44_spl
| ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__neg,sK6_skl)),sK7_skl) = ap(ap(c_2Einteger_2Eint__add,ap(c_2Einteger_2Eint__neg,sK6_skl)),ap(c_2Einteger_2Eint__neg,sK7_skl)) ),
inference(resolution,[status(thm)],[f1984,f848]) ).
fof(f2008,plain,
( ~ sQ40_spl
| ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__neg,sK8_skl)),sK7_skl) = ap(ap(c_2Einteger_2Eint__add,ap(c_2Einteger_2Eint__neg,sK8_skl)),ap(c_2Einteger_2Eint__neg,sK7_skl)) ),
inference(resolution,[status(thm)],[f1984,f828]) ).
fof(f2009,plain,
( ~ sQ27_spl
| ap(ap(c_2Einteger_2Eint__sub,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)),sK7_skl) = ap(ap(c_2Einteger_2Eint__add,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)),ap(c_2Einteger_2Eint__neg,sK7_skl)) ),
inference(resolution,[status(thm)],[f1984,f740]) ).
fof(f2010,plain,
! [X0,X1,X2] :
( ~ mem(X1,X2)
| ~ mem(X0,arr(X2,ty_2Einteger_2Eint))
| ap(ap(c_2Einteger_2Eint__sub,ap(X0,X1)),sK7_skl) = ap(ap(c_2Einteger_2Eint__add,ap(X0,X1)),ap(c_2Einteger_2Eint__neg,sK7_skl)) ),
inference(resolution,[status(thm)],[f1984,f64]) ).
fof(f2011,plain,
ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl) = ap(ap(c_2Einteger_2Eint__add,sK8_skl),ap(c_2Einteger_2Eint__neg,sK7_skl)),
inference(resolution,[status(thm)],[f1984,f307]) ).
fof(f2012,plain,
ap(ap(c_2Einteger_2Eint__sub,sK7_skl),sK7_skl) = ap(ap(c_2Einteger_2Eint__add,sK7_skl),ap(c_2Einteger_2Eint__neg,sK7_skl)),
inference(resolution,[status(thm)],[f1984,f306]) ).
fof(f2013,plain,
ap(ap(c_2Einteger_2Eint__sub,sK6_skl),sK7_skl) = ap(ap(c_2Einteger_2Eint__add,sK6_skl),ap(c_2Einteger_2Eint__neg,sK7_skl)),
inference(resolution,[status(thm)],[f1984,f305]) ).
fof(f2040,plain,
( c_2Einteger_2Eint__add = c_2Einteger_2Eint__add
| ap(c_2Einteger_2Eint__add,sK0_skl(c_2Einteger_2Eint__add,c_2Einteger_2Eint__add,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint),ty_2Einteger_2Eint)) != ap(c_2Einteger_2Eint__add,sK0_skl(c_2Einteger_2Eint__add,c_2Einteger_2Eint__add,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint),ty_2Einteger_2Eint)) ),
inference(resolution,[status(thm)],[f590,f90]) ).
fof(f2044,definition,
( sQ148_spl
<=> ap(c_2Einteger_2Eint__add,sK0_skl(c_2Einteger_2Eint__add,c_2Einteger_2Eint__add,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint),ty_2Einteger_2Eint)) = ap(c_2Einteger_2Eint__add,sK0_skl(c_2Einteger_2Eint__add,c_2Einteger_2Eint__add,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint),ty_2Einteger_2Eint)) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f2046,plain,
( sQ148_spl
| ap(c_2Einteger_2Eint__add,sK0_skl(c_2Einteger_2Eint__add,c_2Einteger_2Eint__add,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint),ty_2Einteger_2Eint)) != ap(c_2Einteger_2Eint__add,sK0_skl(c_2Einteger_2Eint__add,c_2Einteger_2Eint__add,arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint),ty_2Einteger_2Eint)) ),
inference(component_clause,[status(thm)],[f2044]) ).
fof(f2047,definition,
( sQ149_spl
<=> c_2Einteger_2Eint__add = c_2Einteger_2Eint__add ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f2050,plain,
( sQ149_spl
| ~ sQ148_spl ),
inference(split_clause,[status(thm)],[f2040,f2044,f2047]) ).
fof(f2055,plain,
( sQ148_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2046]) ).
fof(f2056,plain,
sQ148_spl,
inference(contradiction_clause,[status(thm)],[f2055]) ).
fof(f2059,plain,
( c_2Einteger_2Eint__neg = c_2Einteger_2Eint__neg
| ap(c_2Einteger_2Eint__neg,sK0_skl(c_2Einteger_2Eint__neg,c_2Einteger_2Eint__neg,ty_2Einteger_2Eint,ty_2Einteger_2Eint)) != ap(c_2Einteger_2Eint__neg,sK0_skl(c_2Einteger_2Eint__neg,c_2Einteger_2Eint__neg,ty_2Einteger_2Eint,ty_2Einteger_2Eint)) ),
inference(resolution,[status(thm)],[f600,f91]) ).
fof(f2062,definition,
( sQ151_spl
<=> ap(c_2Einteger_2Eint__neg,sK0_skl(c_2Einteger_2Eint__neg,c_2Einteger_2Eint__neg,ty_2Einteger_2Eint,ty_2Einteger_2Eint)) = ap(c_2Einteger_2Eint__neg,sK0_skl(c_2Einteger_2Eint__neg,c_2Einteger_2Eint__neg,ty_2Einteger_2Eint,ty_2Einteger_2Eint)) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f2064,plain,
( sQ151_spl
| ap(c_2Einteger_2Eint__neg,sK0_skl(c_2Einteger_2Eint__neg,c_2Einteger_2Eint__neg,ty_2Einteger_2Eint,ty_2Einteger_2Eint)) != ap(c_2Einteger_2Eint__neg,sK0_skl(c_2Einteger_2Eint__neg,c_2Einteger_2Eint__neg,ty_2Einteger_2Eint,ty_2Einteger_2Eint)) ),
inference(component_clause,[status(thm)],[f2062]) ).
fof(f2065,definition,
( sQ152_spl
<=> c_2Einteger_2Eint__neg = c_2Einteger_2Eint__neg ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f2068,plain,
( sQ152_spl
| ~ sQ151_spl ),
inference(split_clause,[status(thm)],[f2059,f2062,f2065]) ).
fof(f2069,plain,
( sQ151_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2064]) ).
fof(f2070,plain,
sQ151_spl,
inference(contradiction_clause,[status(thm)],[f2069]) ).
fof(f2089,plain,
! [X0,X1,X2] :
( X1 = X0
| ~ mem(X0,arr(ty_2Einteger_2Eint,X2))
| ~ mem(X1,arr(ty_2Einteger_2Eint,X2))
| ap(i(arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint)),ap(c_2Einteger_2Eint__sub,sK0_skl(X0,X1,X2,ty_2Einteger_2Eint))) = ap(c_2Einteger_2Eint__sub,sK0_skl(X0,X1,X2,ty_2Einteger_2Eint)) ),
inference(resolution,[status(thm)],[f1780,f71]) ).
fof(f2105,plain,
( c_2Ebool_2E_2F_5C = c_2Emin_2E_3D_3D_3E
| ap(c_2Ebool_2E_2F_5C,sK0_skl(c_2Emin_2E_3D_3D_3E,c_2Ebool_2E_2F_5C,arr(bool,bool),bool)) != ap(c_2Emin_2E_3D_3D_3E,sK0_skl(c_2Emin_2E_3D_3D_3E,c_2Ebool_2E_2F_5C,arr(bool,bool),bool)) ),
inference(resolution,[status(thm)],[f603,f107]) ).
fof(f2106,plain,
( c_2Ebool_2E_5C_2F = c_2Emin_2E_3D_3D_3E
| ap(c_2Ebool_2E_5C_2F,sK0_skl(c_2Emin_2E_3D_3D_3E,c_2Ebool_2E_5C_2F,arr(bool,bool),bool)) != ap(c_2Emin_2E_3D_3D_3E,sK0_skl(c_2Emin_2E_3D_3D_3E,c_2Ebool_2E_5C_2F,arr(bool,bool),bool)) ),
inference(resolution,[status(thm)],[f603,f101]) ).
fof(f2107,plain,
( c_2Emin_2E_3D_3D_3E = c_2Emin_2E_3D_3D_3E
| ap(c_2Emin_2E_3D_3D_3E,sK0_skl(c_2Emin_2E_3D_3D_3E,c_2Emin_2E_3D_3D_3E,arr(bool,bool),bool)) != ap(c_2Emin_2E_3D_3D_3E,sK0_skl(c_2Emin_2E_3D_3D_3E,c_2Emin_2E_3D_3D_3E,arr(bool,bool),bool)) ),
inference(resolution,[status(thm)],[f603,f95]) ).
fof(f2116,definition,
( sQ155_spl
<=> ne(bool) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f2118,plain,
( sQ155_spl
| ~ ne(bool) ),
inference(component_clause,[status(thm)],[f2116]) ).
fof(f2120,definition,
( sQ156_spl
<=> ap(c_2Ebool_2E_2F_5C,sK0_skl(c_2Emin_2E_3D_3D_3E,c_2Ebool_2E_2F_5C,arr(bool,bool),bool)) = ap(c_2Emin_2E_3D_3D_3E,sK0_skl(c_2Emin_2E_3D_3D_3E,c_2Ebool_2E_2F_5C,arr(bool,bool),bool)) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f2123,definition,
( sQ157_spl
<=> c_2Ebool_2E_2F_5C = c_2Emin_2E_3D_3D_3E ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f2124,plain,
( ~ sQ157_spl
| c_2Ebool_2E_2F_5C = c_2Emin_2E_3D_3D_3E ),
inference(component_clause,[status(thm)],[f2123]) ).
fof(f2126,plain,
( sQ157_spl
| ~ sQ156_spl ),
inference(split_clause,[status(thm)],[f2105,f2120,f2123]) ).
fof(f2127,definition,
( sQ158_spl
<=> ap(c_2Ebool_2E_5C_2F,sK0_skl(c_2Emin_2E_3D_3D_3E,c_2Ebool_2E_5C_2F,arr(bool,bool),bool)) = ap(c_2Emin_2E_3D_3D_3E,sK0_skl(c_2Emin_2E_3D_3D_3E,c_2Ebool_2E_5C_2F,arr(bool,bool),bool)) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f2130,definition,
( sQ159_spl
<=> c_2Ebool_2E_5C_2F = c_2Emin_2E_3D_3D_3E ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f2131,plain,
( ~ sQ159_spl
| c_2Ebool_2E_5C_2F = c_2Emin_2E_3D_3D_3E ),
inference(component_clause,[status(thm)],[f2130]) ).
fof(f2132,plain,
( sQ159_spl
| c_2Ebool_2E_5C_2F != c_2Emin_2E_3D_3D_3E ),
inference(component_clause,[status(thm)],[f2130]) ).
fof(f2133,plain,
( sQ159_spl
| ~ sQ158_spl ),
inference(split_clause,[status(thm)],[f2106,f2127,f2130]) ).
fof(f2134,definition,
( sQ160_spl
<=> ap(c_2Emin_2E_3D_3D_3E,sK0_skl(c_2Emin_2E_3D_3D_3E,c_2Emin_2E_3D_3D_3E,arr(bool,bool),bool)) = ap(c_2Emin_2E_3D_3D_3E,sK0_skl(c_2Emin_2E_3D_3D_3E,c_2Emin_2E_3D_3D_3E,arr(bool,bool),bool)) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f2136,plain,
( sQ160_spl
| ap(c_2Emin_2E_3D_3D_3E,sK0_skl(c_2Emin_2E_3D_3D_3E,c_2Emin_2E_3D_3D_3E,arr(bool,bool),bool)) != ap(c_2Emin_2E_3D_3D_3E,sK0_skl(c_2Emin_2E_3D_3D_3E,c_2Emin_2E_3D_3D_3E,arr(bool,bool),bool)) ),
inference(component_clause,[status(thm)],[f2134]) ).
fof(f2137,definition,
( sQ161_spl
<=> c_2Emin_2E_3D_3D_3E = c_2Emin_2E_3D_3D_3E ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f2140,plain,
( sQ161_spl
| ~ sQ160_spl ),
inference(split_clause,[status(thm)],[f2107,f2134,f2137]) ).
fof(f2144,plain,
( sQ160_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2136]) ).
fof(f2145,plain,
sQ160_spl,
inference(contradiction_clause,[status(thm)],[f2144]) ).
fof(f2146,plain,
( sQ155_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2118,f59]) ).
fof(f2147,plain,
sQ155_spl,
inference(contradiction_clause,[status(thm)],[f2146]) ).
fof(f2151,plain,
( c_2Ebool_2E_2F_5C = c_2Ebool_2E_5C_2F
| ap(c_2Ebool_2E_2F_5C,sK0_skl(c_2Ebool_2E_5C_2F,c_2Ebool_2E_2F_5C,arr(bool,bool),bool)) != ap(c_2Ebool_2E_5C_2F,sK0_skl(c_2Ebool_2E_5C_2F,c_2Ebool_2E_2F_5C,arr(bool,bool),bool)) ),
inference(resolution,[status(thm)],[f620,f107]) ).
fof(f2152,plain,
( c_2Ebool_2E_5C_2F = c_2Ebool_2E_5C_2F
| ap(c_2Ebool_2E_5C_2F,sK0_skl(c_2Ebool_2E_5C_2F,c_2Ebool_2E_5C_2F,arr(bool,bool),bool)) != ap(c_2Ebool_2E_5C_2F,sK0_skl(c_2Ebool_2E_5C_2F,c_2Ebool_2E_5C_2F,arr(bool,bool),bool)) ),
inference(resolution,[status(thm)],[f620,f101]) ).
fof(f2153,plain,
( c_2Emin_2E_3D_3D_3E = c_2Ebool_2E_5C_2F
| ap(c_2Emin_2E_3D_3D_3E,sK0_skl(c_2Ebool_2E_5C_2F,c_2Emin_2E_3D_3D_3E,arr(bool,bool),bool)) != ap(c_2Ebool_2E_5C_2F,sK0_skl(c_2Ebool_2E_5C_2F,c_2Emin_2E_3D_3D_3E,arr(bool,bool),bool)) ),
inference(resolution,[status(thm)],[f620,f95]) ).
fof(f2163,definition,
( sQ164_spl
<=> ap(c_2Ebool_2E_2F_5C,sK0_skl(c_2Ebool_2E_5C_2F,c_2Ebool_2E_2F_5C,arr(bool,bool),bool)) = ap(c_2Ebool_2E_5C_2F,sK0_skl(c_2Ebool_2E_5C_2F,c_2Ebool_2E_2F_5C,arr(bool,bool),bool)) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f2166,definition,
( sQ165_spl
<=> c_2Ebool_2E_2F_5C = c_2Ebool_2E_5C_2F ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f2167,plain,
( ~ sQ165_spl
| c_2Ebool_2E_2F_5C = c_2Ebool_2E_5C_2F ),
inference(component_clause,[status(thm)],[f2166]) ).
fof(f2169,plain,
( sQ165_spl
| ~ sQ164_spl ),
inference(split_clause,[status(thm)],[f2151,f2163,f2166]) ).
fof(f2170,definition,
( sQ166_spl
<=> ap(c_2Ebool_2E_5C_2F,sK0_skl(c_2Ebool_2E_5C_2F,c_2Ebool_2E_5C_2F,arr(bool,bool),bool)) = ap(c_2Ebool_2E_5C_2F,sK0_skl(c_2Ebool_2E_5C_2F,c_2Ebool_2E_5C_2F,arr(bool,bool),bool)) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f2172,plain,
( sQ166_spl
| ap(c_2Ebool_2E_5C_2F,sK0_skl(c_2Ebool_2E_5C_2F,c_2Ebool_2E_5C_2F,arr(bool,bool),bool)) != ap(c_2Ebool_2E_5C_2F,sK0_skl(c_2Ebool_2E_5C_2F,c_2Ebool_2E_5C_2F,arr(bool,bool),bool)) ),
inference(component_clause,[status(thm)],[f2170]) ).
fof(f2173,definition,
( sQ167_spl
<=> c_2Ebool_2E_5C_2F = c_2Ebool_2E_5C_2F ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f2176,plain,
( sQ167_spl
| ~ sQ166_spl ),
inference(split_clause,[status(thm)],[f2152,f2170,f2173]) ).
fof(f2177,definition,
( sQ168_spl
<=> ap(c_2Emin_2E_3D_3D_3E,sK0_skl(c_2Ebool_2E_5C_2F,c_2Emin_2E_3D_3D_3E,arr(bool,bool),bool)) = ap(c_2Ebool_2E_5C_2F,sK0_skl(c_2Ebool_2E_5C_2F,c_2Emin_2E_3D_3D_3E,arr(bool,bool),bool)) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f2180,plain,
( sQ159_spl
| ~ sQ168_spl ),
inference(split_clause,[status(thm)],[f2153,f2177,f2130]) ).
fof(f2181,plain,
( sQ166_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2172]) ).
fof(f2182,plain,
sQ166_spl,
inference(contradiction_clause,[status(thm)],[f2181]) ).
fof(f2223,plain,
! [X0,X1,X2,X3] :
( ~ ne(arr(X2,ty_2Einteger_2Eint))
| c_2Emin_2E_3D(arr(X2,ty_2Einteger_2Eint)) = X1
| ~ mem(X1,arr(arr(X2,ty_2Einteger_2Eint),arr(arr(X2,ty_2Einteger_2Eint),bool)))
| ~ mem(X3,X2)
| ap(ap(c_2Einteger_2Eint__sub,X0),ap(sK0_skl(X1,c_2Emin_2E_3D(arr(X2,ty_2Einteger_2Eint)),arr(arr(X2,ty_2Einteger_2Eint),bool),arr(X2,ty_2Einteger_2Eint)),X3)) = ap(ap(c_2Einteger_2Eint__add,X0),ap(c_2Einteger_2Eint__neg,ap(sK0_skl(X1,c_2Emin_2E_3D(arr(X2,ty_2Einteger_2Eint)),arr(arr(X2,ty_2Einteger_2Eint),bool),arr(X2,ty_2Einteger_2Eint)),X3)))
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f1999,f119]) ).
fof(f2229,plain,
! [X0,X1] :
( ~ sQ159_spl
| ~ p(X0)
| p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),X1))
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(backward_demodulation,[status(thm)],[f2131,f105]) ).
fof(f2236,plain,
! [X0,X1] :
( ~ sQ159_spl
| p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),X1))
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(forward_subsumption_resolution,[status(thm)],[f2229,f99]) ).
fof(f2240,plain,
! [X0,X1] :
( ~ sQ159_spl
| p(X1)
| ~ p(X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(backward_subsumption_resolution,[status(thm)],[f98,f2236]) ).
fof(f2241,plain,
( ~ sQ159_spl
| sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f2240,f465,f452,f2130]) ).
fof(f2253,plain,
( ~ sQ1_spl
| p(c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f453,f93]) ).
fof(f2259,plain,
( ~ sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f2253,f580,f452]) ).
fof(f2269,plain,
! [X0] :
( ~ sQ27_spl
| p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl),ty_2Einteger_2Eint)
| ~ mem(ap(c_2Einteger_2Eint__neg,sK7_skl),ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(paramodulation,[status(thm)],[f2009,f214]) ).
fof(f2270,plain,
! [X0] :
( ~ sQ27_spl
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)))
| p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl),ty_2Einteger_2Eint)
| ~ mem(ap(c_2Einteger_2Eint__neg,sK7_skl),ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(paramodulation,[status(thm)],[f2009,f215]) ).
fof(f2272,definition,
( sQ174_spl
<=> mem(ap(c_2Einteger_2Eint__neg,sK7_skl),ty_2Einteger_2Eint) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f2274,plain,
( sQ174_spl
| ~ mem(ap(c_2Einteger_2Eint__neg,sK7_skl),ty_2Einteger_2Eint) ),
inference(component_clause,[status(thm)],[f2272]) ).
fof(f2275,definition,
( sQ175_spl
<=> p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),ap(c_2Einteger_2Eint__neg,sK7_skl))) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f2276,plain,
( ~ sQ175_spl
| p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),ap(c_2Einteger_2Eint__neg,sK7_skl))) ),
inference(component_clause,[status(thm)],[f2275]) ).
fof(f2277,plain,
( sQ175_spl
| ~ p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),ap(c_2Einteger_2Eint__neg,sK7_skl))) ),
inference(component_clause,[status(thm)],[f2275]) ).
fof(f2297,definition,
! [X0] :
( sQ181_spl
<=> ( p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(X0,ty_2Einteger_2Eint) ) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f2300,plain,
( ~ sQ27_spl
| ~ sQ174_spl
| sQ181_spl ),
inference(split_clause,[status(thm)],[f2269,f2297,f2272,f739]) ).
fof(f2301,definition,
! [X0] :
( sQ182_spl
<=> ( ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)))
| p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(X0,ty_2Einteger_2Eint) ) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f2304,plain,
( ~ sQ27_spl
| ~ sQ174_spl
| sQ182_spl ),
inference(split_clause,[status(thm)],[f2270,f2301,f2272,f739]) ).
fof(f2305,plain,
! [X0] :
( sQ174_spl
| ~ mem(sK7_skl,X0)
| ~ mem(c_2Einteger_2Eint__neg,arr(X0,ty_2Einteger_2Eint)) ),
inference(resolution,[status(thm)],[f2274,f64]) ).
fof(f2306,plain,
( sQ174_spl
| ~ mem(sK7_skl,ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f2305,f91]) ).
fof(f2307,plain,
( sQ174_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f2306,f768,f2272]) ).
fof(f2312,plain,
! [X0] :
( ~ mem(X0,ty_2Einteger_2Eint)
| ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__neg,X0)),sK7_skl) = ap(ap(c_2Einteger_2Eint__add,ap(c_2Einteger_2Eint__neg,X0)),ap(c_2Einteger_2Eint__neg,sK7_skl)) ),
inference(resolution,[status(thm)],[f2010,f91]) ).
fof(f2315,plain,
! [X0] :
( p(ap(ap(c_2Einteger_2Eint__divides,X0),sK8_skl))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(sK8_skl,ty_2Einteger_2Eint)
| ~ mem(ap(c_2Einteger_2Eint__neg,sK7_skl),ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(paramodulation,[status(thm)],[f2011,f214]) ).
fof(f2316,plain,
! [X0] :
( ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),sK8_skl))
| p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(sK8_skl,ty_2Einteger_2Eint)
| ~ mem(ap(c_2Einteger_2Eint__neg,sK7_skl),ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(paramodulation,[status(thm)],[f2011,f215]) ).
fof(f2318,definition,
! [X0] :
( sQ183_spl
<=> ( p(ap(ap(c_2Einteger_2Eint__divides,X0),sK8_skl))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(X0,ty_2Einteger_2Eint) ) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f2319,plain,
! [X0] :
( ~ sQ183_spl
| p(ap(ap(c_2Einteger_2Eint__divides,X0),sK8_skl))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(component_clause,[status(thm)],[f2318]) ).
fof(f2321,plain,
( ~ sQ26_spl
| ~ sQ174_spl
| sQ183_spl ),
inference(split_clause,[status(thm)],[f2315,f2318,f2272,f733]) ).
fof(f2322,definition,
! [X0] :
( sQ184_spl
<=> ( ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),sK8_skl))
| p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(X0,ty_2Einteger_2Eint) ) ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f2323,plain,
! [X0] :
( ~ sQ184_spl
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),sK8_skl))
| p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(component_clause,[status(thm)],[f2322]) ).
fof(f2325,plain,
( ~ sQ26_spl
| ~ sQ174_spl
| sQ184_spl ),
inference(split_clause,[status(thm)],[f2316,f2322,f2272,f733]) ).
fof(f2326,plain,
! [X0] :
( p(ap(ap(c_2Einteger_2Eint__divides,X0),sK7_skl))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,sK7_skl),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(sK7_skl,ty_2Einteger_2Eint)
| ~ mem(ap(c_2Einteger_2Eint__neg,sK7_skl),ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(paramodulation,[status(thm)],[f2012,f214]) ).
fof(f2327,plain,
! [X0] :
( ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),sK7_skl))
| p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,sK7_skl),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(sK7_skl,ty_2Einteger_2Eint)
| ~ mem(ap(c_2Einteger_2Eint__neg,sK7_skl),ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(paramodulation,[status(thm)],[f2012,f215]) ).
fof(f2329,definition,
! [X0] :
( sQ185_spl
<=> ( p(ap(ap(c_2Einteger_2Eint__divides,X0),sK7_skl))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,sK7_skl),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(X0,ty_2Einteger_2Eint) ) ),
introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition]) ).
fof(f2332,plain,
( ~ sQ31_spl
| ~ sQ174_spl
| sQ185_spl ),
inference(split_clause,[status(thm)],[f2326,f2329,f2272,f768]) ).
fof(f2333,definition,
! [X0] :
( sQ186_spl
<=> ( ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),sK7_skl))
| p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,sK7_skl),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(X0,ty_2Einteger_2Eint) ) ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f2336,plain,
( ~ sQ31_spl
| ~ sQ174_spl
| sQ186_spl ),
inference(split_clause,[status(thm)],[f2327,f2333,f2272,f768]) ).
fof(f2339,plain,
( ~ sQ2_spl
| ~ p(c_2Ebool_2ET) ),
inference(resolution,[status(thm)],[f466,f78]) ).
fof(f2342,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2339,f79]) ).
fof(f2343,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f2342]) ).
fof(f2374,plain,
! [X0] :
( p(ap(ap(c_2Einteger_2Eint__divides,X0),sK6_skl))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,sK6_skl),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(sK6_skl,ty_2Einteger_2Eint)
| ~ mem(ap(c_2Einteger_2Eint__neg,sK7_skl),ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(paramodulation,[status(thm)],[f2013,f214]) ).
fof(f2375,plain,
! [X0] :
( ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),sK6_skl))
| p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,sK6_skl),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(sK6_skl,ty_2Einteger_2Eint)
| ~ mem(ap(c_2Einteger_2Eint__neg,sK7_skl),ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(paramodulation,[status(thm)],[f2013,f215]) ).
fof(f2377,definition,
! [X0] :
( sQ187_spl
<=> ( p(ap(ap(c_2Einteger_2Eint__divides,X0),sK6_skl))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,sK6_skl),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(X0,ty_2Einteger_2Eint) ) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f2380,plain,
( ~ sQ24_spl
| ~ sQ174_spl
| sQ187_spl ),
inference(split_clause,[status(thm)],[f2374,f2377,f2272,f727]) ).
fof(f2381,definition,
! [X0] :
( sQ188_spl
<=> ( ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),sK6_skl))
| p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,sK6_skl),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(X0,ty_2Einteger_2Eint) ) ),
introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition]) ).
fof(f2384,plain,
( ~ sQ24_spl
| ~ sQ174_spl
| sQ188_spl ),
inference(split_clause,[status(thm)],[f2375,f2381,f2272,f727]) ).
fof(f2386,plain,
( sQ175_spl
| ~ p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),sK7_skl))
| ~ mem(sK7_skl,ty_2Einteger_2Eint)
| ~ mem(sK6_skl,ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f2277,f219]) ).
fof(f2389,plain,
( sQ175_spl
| ~ sQ147_spl
| ~ sQ31_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f2386,f727,f768,f1951,f2275]) ).
fof(f2398,plain,
( sQ147_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1953,f308]) ).
fof(f2399,plain,
sQ147_spl,
inference(contradiction_clause,[status(thm)],[f2398]) ).
fof(f2506,plain,
! [X0,X1,X2] :
( sP16_prd(X2,X1)
| ~ p(X0)
| p(X2)
| p(X1)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f1163,f355]) ).
fof(f2507,definition,
! [X0] :
( sQ192_spl
<=> ( ~ p(X0)
| ~ mem(X0,bool)
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ192_spl])],[split_symbol_definition]) ).
fof(f2508,plain,
! [X0] :
( ~ sQ192_spl
| ~ p(X0)
| ~ mem(X0,bool)
| ~ p(X0) ),
inference(component_clause,[status(thm)],[f2507]) ).
fof(f2518,definition,
! [X1,X2] :
( sQ195_spl
<=> ( sP16_prd(X2,X1)
| p(X2)
| p(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f2521,plain,
( sQ195_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f2506,f957,f2518]) ).
fof(f2522,plain,
! [X0] :
( ~ sQ58_spl
| ~ p(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f958]) ).
fof(f2560,plain,
( ~ sQ58_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f79,f2522]) ).
fof(f2580,plain,
~ sQ58_spl,
inference(contradiction_clause,[status(thm)],[f2560]) ).
fof(f2821,plain,
( ~ sQ25_spl
| ~ p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(ap(c_2Einteger_2Eint__neg,sK7_skl),ty_2Einteger_2Eint) ),
inference(paramodulation,[status(thm)],[f2011,f731]) ).
fof(f2836,plain,
( ~ sQ25_spl
| ~ sQ3_spl
| ~ sQ175_spl
| ~ sQ174_spl ),
inference(split_clause,[status(thm)],[f2821,f2272,f2275,f480,f730]) ).
fof(f3039,plain,
! [X0,X1,X2] :
( ~ p(X0)
| ~ p(X2)
| p(X1)
| ~ mem(X1,bool)
| ~ mem(X2,bool)
| ~ mem(X0,bool)
| ~ sP16_prd(X1,X2)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f357,f256]) ).
fof(f3040,definition,
! [X1,X2] :
( sQ235_spl
<=> ( ~ p(X2)
| p(X1)
| ~ mem(X1,bool)
| ~ mem(X2,bool)
| ~ sP16_prd(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f3043,plain,
( sQ235_spl
| sQ192_spl ),
inference(split_clause,[status(thm)],[f3039,f2507,f3040]) ).
fof(f3044,plain,
! [X0] :
( ~ sQ192_spl
| ~ mem(X0,bool)
| ~ p(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2508]) ).
fof(f3045,plain,
! [X0,X1,X2] :
( p(X0)
| ~ p(X1)
| ~ p(X2)
| ~ sP7_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f355,f424]) ).
fof(f3046,plain,
! [X0,X1,X2] :
( ~ p(X0)
| p(X1)
| ~ p(X2)
| ~ sP7_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f355,f425]) ).
fof(f3118,plain,
( ~ sQ192_spl
| ~ p(c_2Ebool_2ET) ),
inference(resolution,[status(thm)],[f3044,f78]) ).
fof(f3122,plain,
( ~ sQ192_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3118,f79]) ).
fof(f3123,plain,
~ sQ192_spl,
inference(contradiction_clause,[status(thm)],[f3122]) ).
fof(f3238,plain,
( sQ128_spl
| ~ mem(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__neg,sK6_skl))),ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f1789,f91]) ).
fof(f3239,plain,
( sQ128_spl
| ~ sQ90_spl ),
inference(split_clause,[status(thm)],[f3238,f1309,f1675]) ).
fof(f3253,plain,
! [X0,X1] :
( ~ ne(ty_2Einteger_2Eint)
| c_2Emin_2E_3D(ty_2Einteger_2Eint) = X1
| ~ mem(X1,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,bool)))
| ap(k(arr(ty_2Einteger_2Eint,bool),X0),ap(c_2Einteger_2Eint__divides,sK0_skl(X1,c_2Emin_2E_3D(ty_2Einteger_2Eint),arr(ty_2Einteger_2Eint,bool),ty_2Einteger_2Eint))) = X0 ),
inference(resolution,[status(thm)],[f1792,f119]) ).
fof(f3259,definition,
! [X0,X1] :
( sQ249_spl
<=> ( c_2Emin_2E_3D(ty_2Einteger_2Eint) = X1
| ~ mem(X1,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,bool)))
| ap(k(arr(ty_2Einteger_2Eint,bool),X0),ap(c_2Einteger_2Eint__divides,sK0_skl(X1,c_2Emin_2E_3D(ty_2Einteger_2Eint),arr(ty_2Einteger_2Eint,bool),ty_2Einteger_2Eint))) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f3262,plain,
( ~ sQ20_spl
| sQ249_spl ),
inference(split_clause,[status(thm)],[f3253,f3259,f648]) ).
fof(f3361,plain,
! [X0,X1] :
( ~ ne(ty_2Einteger_2Eint)
| c_2Emin_2E_3D(ty_2Einteger_2Eint) = X1
| ~ mem(X1,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,bool)))
| ap(k(arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint),X0),ap(c_2Einteger_2Eint__sub,sK0_skl(X1,c_2Emin_2E_3D(ty_2Einteger_2Eint),arr(ty_2Einteger_2Eint,bool),ty_2Einteger_2Eint))) = X0 ),
inference(resolution,[status(thm)],[f1830,f119]) ).
fof(f3367,definition,
! [X0,X1] :
( sQ254_spl
<=> ( c_2Emin_2E_3D(ty_2Einteger_2Eint) = X1
| ~ mem(X1,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,bool)))
| ap(k(arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint),X0),ap(c_2Einteger_2Eint__sub,sK0_skl(X1,c_2Emin_2E_3D(ty_2Einteger_2Eint),arr(ty_2Einteger_2Eint,bool),ty_2Einteger_2Eint))) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f3370,plain,
( ~ sQ20_spl
| sQ254_spl ),
inference(split_clause,[status(thm)],[f3361,f3367,f648]) ).
fof(f3404,plain,
! [X0] :
( ~ sQ48_spl
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl))))
| p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__neg,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl))),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(ap(c_2Einteger_2Eint__neg,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)),ty_2Einteger_2Eint)
| ~ mem(ap(c_2Einteger_2Eint__neg,sK7_skl),ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(paramodulation,[status(thm)],[f2006,f215]) ).
fof(f3410,definition,
! [X0] :
( sQ256_spl
<=> ( ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl))))
| p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__neg,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl))),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(X0,ty_2Einteger_2Eint) ) ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f3413,plain,
( ~ sQ48_spl
| ~ sQ174_spl
| sQ256_spl ),
inference(split_clause,[status(thm)],[f3404,f3410,f2272,f895]) ).
fof(f3414,plain,
! [X0] :
( ~ sQ44_spl
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK6_skl)))
| p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__neg,sK6_skl)),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(ap(c_2Einteger_2Eint__neg,sK6_skl),ty_2Einteger_2Eint)
| ~ mem(ap(c_2Einteger_2Eint__neg,sK7_skl),ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(paramodulation,[status(thm)],[f2007,f215]) ).
fof(f3416,definition,
! [X0] :
( sQ257_spl
<=> ( ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK6_skl)))
| p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__neg,sK6_skl)),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(X0,ty_2Einteger_2Eint) ) ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f3419,plain,
( ~ sQ44_spl
| ~ sQ174_spl
| sQ257_spl ),
inference(split_clause,[status(thm)],[f3414,f3416,f2272,f847]) ).
fof(f3436,plain,
! [X0] :
( ~ sQ40_spl
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK8_skl)))
| p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__neg,sK8_skl)),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(ap(c_2Einteger_2Eint__neg,sK8_skl),ty_2Einteger_2Eint)
| ~ mem(ap(c_2Einteger_2Eint__neg,sK7_skl),ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(paramodulation,[status(thm)],[f2008,f215]) ).
fof(f3438,definition,
! [X0] :
( sQ258_spl
<=> ( ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK8_skl)))
| p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__neg,sK8_skl)),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(X0,ty_2Einteger_2Eint) ) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f3441,plain,
( ~ sQ40_spl
| ~ sQ174_spl
| sQ258_spl ),
inference(split_clause,[status(thm)],[f3436,f3438,f2272,f827]) ).
fof(f3450,plain,
! [X0,X1] :
( ~ p(X0)
| ~ p(c_2Ebool_2ET)
| p(X1)
| ~ sP7_prd(X1,c_2Ebool_2ET,X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f256,f78]) ).
fof(f3455,plain,
! [X0,X1] :
( ~ p(X0)
| ~ p(X1)
| p(c_2Ebool_2EF)
| ~ sP7_prd(c_2Ebool_2EF,X1,X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f256,f93]) ).
fof(f3472,definition,
! [X0,X1] :
( sQ262_spl
<=> ( ~ p(X0)
| p(X1)
| ~ sP7_prd(X1,c_2Ebool_2ET,X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f3475,plain,
( ~ sQ10_spl
| sQ262_spl ),
inference(split_clause,[status(thm)],[f3450,f3472,f533]) ).
fof(f3476,definition,
! [X0,X1] :
( sQ263_spl
<=> ( ~ p(X0)
| ~ p(X1)
| ~ sP7_prd(c_2Ebool_2EF,X1,X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f3479,plain,
( sQ13_spl
| sQ263_spl ),
inference(split_clause,[status(thm)],[f3455,f3476,f580]) ).
fof(f3501,plain,
! [X0] :
( ~ ne(ty_2Einteger_2Eint)
| c_2Emin_2E_3D(ty_2Einteger_2Eint) = X0
| ~ mem(X0,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,bool)))
| ap(i(arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint)),ap(c_2Einteger_2Eint__sub,sK0_skl(X0,c_2Emin_2E_3D(ty_2Einteger_2Eint),arr(ty_2Einteger_2Eint,bool),ty_2Einteger_2Eint))) = ap(c_2Einteger_2Eint__sub,sK0_skl(X0,c_2Emin_2E_3D(ty_2Einteger_2Eint),arr(ty_2Einteger_2Eint,bool),ty_2Einteger_2Eint)) ),
inference(resolution,[status(thm)],[f2089,f119]) ).
fof(f3507,definition,
! [X0] :
( sQ265_spl
<=> ( c_2Emin_2E_3D(ty_2Einteger_2Eint) = X0
| ~ mem(X0,arr(ty_2Einteger_2Eint,arr(ty_2Einteger_2Eint,bool)))
| ap(i(arr(ty_2Einteger_2Eint,ty_2Einteger_2Eint)),ap(c_2Einteger_2Eint__sub,sK0_skl(X0,c_2Emin_2E_3D(ty_2Einteger_2Eint),arr(ty_2Einteger_2Eint,bool),ty_2Einteger_2Eint))) = ap(c_2Einteger_2Eint__sub,sK0_skl(X0,c_2Emin_2E_3D(ty_2Einteger_2Eint),arr(ty_2Einteger_2Eint,bool),ty_2Einteger_2Eint)) ) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f3510,plain,
( ~ sQ20_spl
| sQ265_spl ),
inference(split_clause,[status(thm)],[f3501,f3507,f648]) ).
fof(f3577,definition,
( sQ268_spl
<=> mem(c_2Ebool_2ET,bool) ),
introduced(definition,[new_symbols(definition,[sQ268_spl])],[split_symbol_definition]) ).
fof(f3579,plain,
( sQ268_spl
| ~ mem(c_2Ebool_2ET,bool) ),
inference(component_clause,[status(thm)],[f3577]) ).
fof(f3585,plain,
( sQ268_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3579,f78]) ).
fof(f3586,plain,
sQ268_spl,
inference(contradiction_clause,[status(thm)],[f3585]) ).
fof(f3590,plain,
! [X0,X1,X2,X3] :
( ~ ne(ty_2Einteger_2Eint)
| ~ ne(X2)
| c_2Emin_2E_3D(arr(X2,ty_2Einteger_2Eint)) = X1
| ~ mem(X1,arr(arr(X2,ty_2Einteger_2Eint),arr(arr(X2,ty_2Einteger_2Eint),bool)))
| ~ mem(X3,X2)
| ap(ap(c_2Einteger_2Eint__sub,X0),ap(sK0_skl(X1,c_2Emin_2E_3D(arr(X2,ty_2Einteger_2Eint)),arr(arr(X2,ty_2Einteger_2Eint),bool),arr(X2,ty_2Einteger_2Eint)),X3)) = ap(ap(c_2Einteger_2Eint__add,X0),ap(c_2Einteger_2Eint__neg,ap(sK0_skl(X1,c_2Emin_2E_3D(arr(X2,ty_2Einteger_2Eint)),arr(arr(X2,ty_2Einteger_2Eint),bool),arr(X2,ty_2Einteger_2Eint)),X3)))
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f2223,f62]) ).
fof(f3591,definition,
! [X0,X1,X2,X3] :
( sQ269_spl
<=> ( ~ ne(X2)
| c_2Emin_2E_3D(arr(X2,ty_2Einteger_2Eint)) = X1
| ~ mem(X1,arr(arr(X2,ty_2Einteger_2Eint),arr(arr(X2,ty_2Einteger_2Eint),bool)))
| ~ mem(X3,X2)
| ap(ap(c_2Einteger_2Eint__sub,X0),ap(sK0_skl(X1,c_2Emin_2E_3D(arr(X2,ty_2Einteger_2Eint)),arr(arr(X2,ty_2Einteger_2Eint),bool),arr(X2,ty_2Einteger_2Eint)),X3)) = ap(ap(c_2Einteger_2Eint__add,X0),ap(c_2Einteger_2Eint__neg,ap(sK0_skl(X1,c_2Emin_2E_3D(arr(X2,ty_2Einteger_2Eint)),arr(arr(X2,ty_2Einteger_2Eint),bool),arr(X2,ty_2Einteger_2Eint)),X3)))
| ~ mem(X0,ty_2Einteger_2Eint) ) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f3594,plain,
( ~ sQ20_spl
| sQ269_spl ),
inference(split_clause,[status(thm)],[f3590,f3591,f648]) ).
fof(f3706,plain,
! [X0,X1,X2] :
( ~ p(X2)
| p(X1)
| p(X0)
| p(X2)
| ~ p(X1)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f3045,f1166]) ).
fof(f3711,plain,
! [X0,X1,X2] :
( ~ sP16_prd(X2,X1)
| ~ p(X0)
| p(X2)
| ~ p(X1)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f3045,f357]) ).
fof(f3714,plain,
sQ33_spl,
inference(split_clause,[status(thm)],[f3706,f779]) ).
fof(f3720,definition,
! [X1,X2] :
( sQ275_spl
<=> ( ~ sP16_prd(X2,X1)
| p(X2)
| ~ p(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ275_spl])],[split_symbol_definition]) ).
fof(f3723,plain,
( sQ275_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f3711,f957,f3720]) ).
fof(f3732,plain,
! [X0,X1,X2] :
( ~ sP16_prd(X2,X1)
| ~ p(X0)
| ~ p(X2)
| p(X1)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f3046,f357]) ).
fof(f3743,definition,
! [X1,X2] :
( sQ277_spl
<=> ( ~ sP16_prd(X2,X1)
| ~ p(X2)
| p(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ277_spl])],[split_symbol_definition]) ).
fof(f3746,plain,
( sQ277_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f3732,f957,f3743]) ).
fof(f3747,plain,
( c_2Ebool_2E_5C_2F = c_2Ebool_2E_2F_5C
| ap(c_2Ebool_2E_5C_2F,sK0_skl(c_2Ebool_2E_2F_5C,c_2Ebool_2E_5C_2F,arr(bool,bool),bool)) != ap(c_2Ebool_2E_2F_5C,sK0_skl(c_2Ebool_2E_2F_5C,c_2Ebool_2E_5C_2F,arr(bool,bool),bool)) ),
inference(resolution,[status(thm)],[f627,f101]) ).
fof(f3749,plain,
( c_2Ebool_2E_2F_5C = c_2Ebool_2E_2F_5C
| ap(c_2Ebool_2E_2F_5C,sK0_skl(c_2Ebool_2E_2F_5C,c_2Ebool_2E_2F_5C,arr(bool,bool),bool)) != ap(c_2Ebool_2E_2F_5C,sK0_skl(c_2Ebool_2E_2F_5C,c_2Ebool_2E_2F_5C,arr(bool,bool),bool)) ),
inference(resolution,[status(thm)],[f627,f107]) ).
fof(f3750,plain,
( c_2Emin_2E_3D_3D_3E = c_2Ebool_2E_2F_5C
| ap(c_2Emin_2E_3D_3D_3E,sK0_skl(c_2Ebool_2E_2F_5C,c_2Emin_2E_3D_3D_3E,arr(bool,bool),bool)) != ap(c_2Ebool_2E_2F_5C,sK0_skl(c_2Ebool_2E_2F_5C,c_2Emin_2E_3D_3D_3E,arr(bool,bool),bool)) ),
inference(resolution,[status(thm)],[f627,f95]) ).
fof(f3753,definition,
( sQ278_spl
<=> ap(c_2Ebool_2E_5C_2F,sK0_skl(c_2Ebool_2E_2F_5C,c_2Ebool_2E_5C_2F,arr(bool,bool),bool)) = ap(c_2Ebool_2E_2F_5C,sK0_skl(c_2Ebool_2E_2F_5C,c_2Ebool_2E_5C_2F,arr(bool,bool),bool)) ),
introduced(definition,[new_symbols(definition,[sQ278_spl])],[split_symbol_definition]) ).
fof(f3756,plain,
( sQ165_spl
| ~ sQ278_spl ),
inference(split_clause,[status(thm)],[f3747,f3753,f2166]) ).
fof(f3764,definition,
( sQ281_spl
<=> ap(c_2Ebool_2E_2F_5C,sK0_skl(c_2Ebool_2E_2F_5C,c_2Ebool_2E_2F_5C,arr(bool,bool),bool)) = ap(c_2Ebool_2E_2F_5C,sK0_skl(c_2Ebool_2E_2F_5C,c_2Ebool_2E_2F_5C,arr(bool,bool),bool)) ),
introduced(definition,[new_symbols(definition,[sQ281_spl])],[split_symbol_definition]) ).
fof(f3766,plain,
( sQ281_spl
| ap(c_2Ebool_2E_2F_5C,sK0_skl(c_2Ebool_2E_2F_5C,c_2Ebool_2E_2F_5C,arr(bool,bool),bool)) != ap(c_2Ebool_2E_2F_5C,sK0_skl(c_2Ebool_2E_2F_5C,c_2Ebool_2E_2F_5C,arr(bool,bool),bool)) ),
inference(component_clause,[status(thm)],[f3764]) ).
fof(f3767,definition,
( sQ282_spl
<=> c_2Ebool_2E_2F_5C = c_2Ebool_2E_2F_5C ),
introduced(definition,[new_symbols(definition,[sQ282_spl])],[split_symbol_definition]) ).
fof(f3770,plain,
( sQ282_spl
| ~ sQ281_spl ),
inference(split_clause,[status(thm)],[f3749,f3764,f3767]) ).
fof(f3771,definition,
( sQ283_spl
<=> ap(c_2Emin_2E_3D_3D_3E,sK0_skl(c_2Ebool_2E_2F_5C,c_2Emin_2E_3D_3D_3E,arr(bool,bool),bool)) = ap(c_2Ebool_2E_2F_5C,sK0_skl(c_2Ebool_2E_2F_5C,c_2Emin_2E_3D_3D_3E,arr(bool,bool),bool)) ),
introduced(definition,[new_symbols(definition,[sQ283_spl])],[split_symbol_definition]) ).
fof(f3774,plain,
( sQ157_spl
| ~ sQ283_spl ),
inference(split_clause,[status(thm)],[f3750,f3771,f2123]) ).
fof(f3775,plain,
( sQ281_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3766]) ).
fof(f3776,plain,
sQ281_spl,
inference(contradiction_clause,[status(thm)],[f3775]) ).
fof(f3779,plain,
( c_2Ebool_2E_7E = c_2Ebool_2E_7E
| ap(c_2Ebool_2E_7E,sK0_skl(c_2Ebool_2E_7E,c_2Ebool_2E_7E,bool,bool)) != ap(c_2Ebool_2E_7E,sK0_skl(c_2Ebool_2E_7E,c_2Ebool_2E_7E,bool,bool)) ),
inference(resolution,[status(thm)],[f640,f113]) ).
fof(f3782,definition,
( sQ284_spl
<=> ap(c_2Ebool_2E_7E,sK0_skl(c_2Ebool_2E_7E,c_2Ebool_2E_7E,bool,bool)) = ap(c_2Ebool_2E_7E,sK0_skl(c_2Ebool_2E_7E,c_2Ebool_2E_7E,bool,bool)) ),
introduced(definition,[new_symbols(definition,[sQ284_spl])],[split_symbol_definition]) ).
fof(f3784,plain,
( sQ284_spl
| ap(c_2Ebool_2E_7E,sK0_skl(c_2Ebool_2E_7E,c_2Ebool_2E_7E,bool,bool)) != ap(c_2Ebool_2E_7E,sK0_skl(c_2Ebool_2E_7E,c_2Ebool_2E_7E,bool,bool)) ),
inference(component_clause,[status(thm)],[f3782]) ).
fof(f3785,definition,
( sQ285_spl
<=> c_2Ebool_2E_7E = c_2Ebool_2E_7E ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f3788,plain,
( sQ285_spl
| ~ sQ284_spl ),
inference(split_clause,[status(thm)],[f3779,f3782,f3785]) ).
fof(f3789,plain,
( sQ284_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3784]) ).
fof(f3790,plain,
sQ284_spl,
inference(contradiction_clause,[status(thm)],[f3789]) ).
fof(f3802,definition,
( sQ286_spl
<=> ap(c_2Ebool_2E_3F(bool),c_2Ebool_2E_7E) = c_2Ebool_2EF ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f3803,plain,
( ~ sQ286_spl
| ap(c_2Ebool_2E_3F(bool),c_2Ebool_2E_7E) = c_2Ebool_2EF ),
inference(component_clause,[status(thm)],[f3802]) ).
fof(f3809,plain,
( ~ sQ40_spl
| ~ mem(sK8_skl,ty_2Einteger_2Eint)
| ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__neg,sK8_skl)),sK7_skl) = ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__neg,sK8_skl)),sK7_skl) ),
inference(paramodulation,[status(thm)],[f2008,f2312]) ).
fof(f3810,plain,
( ~ sQ44_spl
| ~ mem(sK6_skl,ty_2Einteger_2Eint)
| ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__neg,sK6_skl)),sK7_skl) = ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__neg,sK6_skl)),sK7_skl) ),
inference(paramodulation,[status(thm)],[f2007,f2312]) ).
fof(f3811,plain,
( ~ sQ48_spl
| ~ mem(ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl),ty_2Einteger_2Eint)
| ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__neg,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl))),sK7_skl) = ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__neg,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl))),sK7_skl) ),
inference(paramodulation,[status(thm)],[f2006,f2312]) ).
fof(f3812,definition,
( sQ288_spl
<=> ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__neg,sK8_skl)),sK7_skl) = ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__neg,sK8_skl)),sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ288_spl])],[split_symbol_definition]) ).
fof(f3815,plain,
( ~ sQ40_spl
| ~ sQ26_spl
| sQ288_spl ),
inference(split_clause,[status(thm)],[f3809,f3812,f733,f827]) ).
fof(f3816,definition,
( sQ289_spl
<=> ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__neg,sK6_skl)),sK7_skl) = ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__neg,sK6_skl)),sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ289_spl])],[split_symbol_definition]) ).
fof(f3819,plain,
( ~ sQ44_spl
| ~ sQ24_spl
| sQ289_spl ),
inference(split_clause,[status(thm)],[f3810,f3816,f727,f847]) ).
fof(f3820,definition,
( sQ290_spl
<=> ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__neg,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl))),sK7_skl) = ap(ap(c_2Einteger_2Eint__sub,ap(c_2Einteger_2Eint__neg,ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl))),sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ290_spl])],[split_symbol_definition]) ).
fof(f3823,plain,
( ~ sQ48_spl
| ~ sQ27_spl
| sQ290_spl ),
inference(split_clause,[status(thm)],[f3811,f3820,f739,f895]) ).
fof(f3830,plain,
! [X0] :
( ~ sQ286_spl
| ~ p(ap(c_2Ebool_2E_7E,X0))
| ~ mem(X0,bool)
| p(c_2Ebool_2EF)
| ~ mem(c_2Ebool_2E_7E,arr(bool,bool))
| ~ ne(bool) ),
inference(paramodulation,[status(thm)],[f3803,f87]) ).
fof(f3832,definition,
( sQ291_spl
<=> mem(c_2Ebool_2E_7E,arr(bool,bool)) ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f3834,plain,
( sQ291_spl
| ~ mem(c_2Ebool_2E_7E,arr(bool,bool)) ),
inference(component_clause,[status(thm)],[f3832]) ).
fof(f3841,definition,
! [X0] :
( sQ293_spl
<=> ( ~ p(ap(c_2Ebool_2E_7E,X0))
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f3842,plain,
! [X0] :
( ~ sQ293_spl
| ~ p(ap(c_2Ebool_2E_7E,X0))
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f3841]) ).
fof(f3844,plain,
( ~ sQ286_spl
| sQ293_spl
| sQ13_spl
| ~ sQ291_spl
| ~ sQ155_spl ),
inference(split_clause,[status(thm)],[f3830,f2116,f3832,f580,f3841,f3802]) ).
fof(f3845,plain,
( sQ291_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3834,f113]) ).
fof(f3846,plain,
sQ291_spl,
inference(contradiction_clause,[status(thm)],[f3845]) ).
fof(f3847,plain,
! [X0] :
( ~ sQ293_spl
| p(X0)
| ~ mem(X0,bool) ),
inference(backward_subsumption_resolution,[status(thm)],[f117,f3842]) ).
fof(f3850,plain,
( ~ sQ293_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f3847,f452,f3841]) ).
fof(f3858,plain,
! [X0] :
( ~ sQ183_spl
| p(ap(ap(c_2Einteger_2Eint__divides,X0),sK8_skl))
| ~ mem(sK8_skl,ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint)
| ~ p(ap(ap(c_2Einteger_2Eint__divides,ap(c_2Einteger_2Eint__neg,X0)),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,ap(c_2Einteger_2Eint__neg,X0)),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(ap(c_2Einteger_2Eint__neg,X0),ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f2319,f220]) ).
fof(f3860,definition,
! [X0] :
( sQ294_spl
<=> ( p(ap(ap(c_2Einteger_2Eint__divides,X0),sK8_skl))
| ~ mem(X0,ty_2Einteger_2Eint)
| ~ p(ap(ap(c_2Einteger_2Eint__divides,ap(c_2Einteger_2Eint__neg,X0)),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,ap(c_2Einteger_2Eint__neg,X0)),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(ap(c_2Einteger_2Eint__neg,X0),ty_2Einteger_2Eint) ) ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f3863,plain,
( ~ sQ183_spl
| ~ sQ26_spl
| sQ294_spl ),
inference(split_clause,[status(thm)],[f3858,f3860,f733,f2318]) ).
fof(f3876,plain,
( ~ sQ165_spl
| ~ sQ157_spl
| c_2Emin_2E_3D_3D_3E = c_2Ebool_2E_5C_2F ),
inference(forward_demodulation,[status(thm)],[f2124,f2167]) ).
fof(f3877,plain,
( ~ sQ165_spl
| ~ sQ157_spl
| sQ159_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3876,f2132]) ).
fof(f3878,plain,
( ~ sQ165_spl
| ~ sQ157_spl
| sQ159_spl ),
inference(contradiction_clause,[status(thm)],[f3877]) ).
fof(f3933,plain,
! [X0] :
( ~ sQ184_spl
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(ap(c_2Einteger_2Eint__neg,sK7_skl),ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint)
| ~ p(ap(ap(c_2Einteger_2Eint__divides,ap(c_2Einteger_2Eint__neg,X0)),sK8_skl))
| p(ap(ap(c_2Einteger_2Eint__divides,ap(c_2Einteger_2Eint__neg,X0)),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)))
| ~ mem(ap(c_2Einteger_2Eint__neg,X0),ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f2323,f221]) ).
fof(f3934,plain,
( ~ sQ175_spl
| ~ sQ184_spl
| ~ p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),sK8_skl))
| p(ap(ap(c_2Einteger_2Eint__divides,sK6_skl),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)))
| ~ mem(sK6_skl,ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f2323,f2276]) ).
fof(f3935,plain,
! [X0] :
( ~ sQ184_spl
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),sK7_skl))
| ~ mem(sK7_skl,ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint)
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),sK8_skl))
| p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)))
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f2323,f219]) ).
fof(f3936,plain,
! [X0,X1] :
( ~ sQ184_spl
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__add,ap(c_2Einteger_2Eint__neg,sK7_skl)),X1)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),X1))
| ~ mem(ap(c_2Einteger_2Eint__neg,sK7_skl),ty_2Einteger_2Eint)
| ~ mem(X1,ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint)
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),sK8_skl))
| p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)))
| ~ mem(X0,ty_2Einteger_2Eint) ),
inference(resolution,[status(thm)],[f2323,f214]) ).
fof(f3937,definition,
! [X0] :
( sQ302_spl
<=> ( ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(c_2Einteger_2Eint__neg,sK7_skl)))
| ~ mem(X0,ty_2Einteger_2Eint)
| ~ p(ap(ap(c_2Einteger_2Eint__divides,ap(c_2Einteger_2Eint__neg,X0)),sK8_skl))
| p(ap(ap(c_2Einteger_2Eint__divides,ap(c_2Einteger_2Eint__neg,X0)),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)))
| ~ mem(ap(c_2Einteger_2Eint__neg,X0),ty_2Einteger_2Eint) ) ),
introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition]) ).
fof(f3940,plain,
( ~ sQ184_spl
| ~ sQ174_spl
| sQ302_spl ),
inference(split_clause,[status(thm)],[f3933,f3937,f2272,f2322]) ).
fof(f3941,plain,
( ~ sQ175_spl
| ~ sQ184_spl
| ~ sQ4_spl
| sQ3_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f3934,f727,f480,f483,f2322,f2275]) ).
fof(f3942,definition,
! [X0] :
( sQ303_spl
<=> ( ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),sK7_skl))
| ~ mem(X0,ty_2Einteger_2Eint)
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),sK8_skl))
| p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)))
| ~ mem(X0,ty_2Einteger_2Eint) ) ),
introduced(definition,[new_symbols(definition,[sQ303_spl])],[split_symbol_definition]) ).
fof(f3945,plain,
( ~ sQ184_spl
| ~ sQ31_spl
| sQ303_spl ),
inference(split_clause,[status(thm)],[f3935,f3942,f768,f2322]) ).
fof(f3946,definition,
! [X0,X1] :
( sQ304_spl
<=> ( ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__add,ap(c_2Einteger_2Eint__neg,sK7_skl)),X1)))
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),X1))
| ~ mem(X1,ty_2Einteger_2Eint)
| ~ mem(X0,ty_2Einteger_2Eint)
| ~ p(ap(ap(c_2Einteger_2Eint__divides,X0),sK8_skl))
| p(ap(ap(c_2Einteger_2Eint__divides,X0),ap(ap(c_2Einteger_2Eint__sub,sK8_skl),sK7_skl)))
| ~ mem(X0,ty_2Einteger_2Eint) ) ),
introduced(definition,[new_symbols(definition,[sQ304_spl])],[split_symbol_definition]) ).
fof(f3949,plain,
( ~ sQ184_spl
| ~ sQ174_spl
| sQ304_spl ),
inference(split_clause,[status(thm)],[f3936,f3946,f2272,f2322]) ).
fof(f3950,plain,
$false,
inference(sat_refutation,[status(thm)],[f455,f486,f487,f509,f511,f521,f523,f536,f587,f664,f736,f751,f760,f771,f773,f880,f971,f1048,f1098,f1140,f1256,f1348,f1466,f1496,f1502,f1509,f1545,f1608,f1630,f1700,f1711,f1719,f1727,f1728,f2050,f2056,f2068,f2070,f2126,f2133,f2140,f2145,f2147,f2169,f2176,f2180,f2182,f2241,f2259,f2300,f2304,f2307,f2321,f2325,f2332,f2336,f2343,f2380,f2384,f2389,f2399,f2521,f2580,f2836,f3043,f3123,f3239,f3262,f3370,f3413,f3419,f3441,f3475,f3479,f3510,f3586,f3594,f3714,f3723,f3746,f3756,f3770,f3774,f3776,f3788,f3790,f3815,f3819,f3823,f3844,f3846,f3850,f3863,f3878,f3940,f3941,f3945,f3949]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP012+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n002.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 20 21:48:17 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 5.59/1.23 % Refutation found
% 5.59/1.23 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.59/1.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.59/1.26 % Elapsed time: 0.908713 seconds
% 5.59/1.26 % CPU time: 6.857355 seconds
% 5.59/1.26 % Total memory used: 187.084 MB
% 5.59/1.26 % Net memory used: 179.303 MB
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