%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ITP021+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 : n010.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 12:50:19 PM UTC 2026
% Result : Theorem 18.10s 2.93s
% Output : CNFRefutation 18.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 281
% Syntax : Number of formulae : 1192 ( 55 unt; 245 def)
% Number of atoms : 4305 ( 204 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 5449 (2336 ~;2572 |; 171 &)
% ( 303 <=>; 65 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 251 ( 248 usr; 233 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 13 con; 0-4 aty)
% Number of variables : 1058 (1050 !; 8 ?)
% 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(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,
ne(ty_2Eextreal_2Eextreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
mem(c_2Eextreal_2Eextreal__le,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2ECOND(A_27a),arr(bool,arr(A_27a,arr(A_27a,A_27a)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
mem(c_2Ebool_2EF,bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
~ p(c_2Ebool_2EF),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,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(f19,axiom,
mem(c_2Ebool_2E_5C_2F,arr(bool,arr(bool,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,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(f21,axiom,
mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [Q] :
( mem(Q,bool)
=> ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Ebool_2E_2F_5C,Q),R))
<=> ( p(R)
& p(Q) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
mem(c_2Ebool_2E_7E,arr(bool,bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [Q] :
( mem(Q,bool)
=> ( p(ap(c_2Ebool_2E_7E,Q))
<=> ~ p(Q) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,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(f26,axiom,
! [A] :
( ne(A)
=> ! [X] :
( mem(X,A)
=> ! [Y] :
( mem(Y,A)
=> ( p(ap(ap(c_2Emin_2E_3D(A),X),Y))
<=> X = Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,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(f28,axiom,
! [A] :
( ne(A)
=> ! [Q] :
( mem(Q,arr(A,bool))
=> ( p(ap(c_2Ebool_2E_21(A),Q))
<=> ! [X] :
( mem(X,A)
=> p(ap(Q,X)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0t1] :
( mem(V0t1,A_27a)
=> ! [V1t2] :
( mem(V1t2,A_27a)
=> ( ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V0t1),V1t2) = V1t2
& ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2ET),V0t1),V1t2) = V0t1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [V0x] :
( mem(V0x,ty_2Eextreal_2Eextreal)
=> ! [V1y] :
( mem(V1y,ty_2Eextreal_2Eextreal)
=> ! [V2z] :
( mem(V2z,ty_2Eextreal_2Eextreal)
=> ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),V2z))
& p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y)) )
=> p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V2z)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [V0x] :
( mem(V0x,ty_2Eextreal_2Eextreal)
=> ! [V1y] :
( mem(V1y,ty_2Eextreal_2Eextreal)
=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),V0x))
| p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [V0x] :
( mem(V0x,ty_2Eextreal_2Eextreal)
=> ! [V1y] :
( mem(V1y,ty_2Eextreal_2Eextreal)
=> ap(ap(c_2Eextreal_2Eextreal__max,V0x),V1y) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y)),V1y),V0x) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [V0A] :
( mem(V0A,bool)
=> ( ( ~ p(V0A)
=> $false )
=> ( ( p(V0A)
=> $false )
=> $false ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,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(f52,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ! [V2r] :
( mem(V2r,bool)
=> ( ( p(V0p)
<=> ( p(V2r)
& p(V1q) ) )
<=> ( ( ~ p(V0p)
| p(V2r) )
& ( ~ p(V0p)
| p(V1q) )
& ( ~ p(V2r)
| ~ p(V1q)
| p(V0p) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ! [V2r] :
( mem(V2r,bool)
=> ( ( p(V0p)
<=> ( p(V2r)
| p(V1q) ) )
<=> ( ( ~ p(V0p)
| p(V2r)
| p(V1q) )
& ( ~ p(V2r)
| p(V0p) )
& ( ~ p(V1q)
| p(V0p) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ! [V2r] :
( mem(V2r,bool)
=> ( ( p(V0p)
<=> ( p(V1q)
=> p(V2r) ) )
<=> ( ( ~ p(V0p)
| p(V2r)
| ~ p(V1q) )
& ( ~ p(V2r)
| p(V0p) )
& ( p(V1q)
| p(V0p) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ( ( p(V0p)
<=> ~ p(V1q) )
<=> ( ( ~ p(V0p)
| ~ p(V1q) )
& ( p(V1q)
| p(V0p) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,conjecture,
! [V0z] :
( mem(V0z,ty_2Eextreal_2Eextreal)
=> ! [V1x] :
( mem(V1x,ty_2Eextreal_2Eextreal)
=> ! [V2y] :
( mem(V2y,ty_2Eextreal_2Eextreal)
=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,V1x),V2y)),V0z))
<=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,V2y),V0z))
& p(ap(ap(c_2Eextreal_2Eextreal__le,V1x),V0z)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,negated_conjecture,
~ ! [V0z] :
( mem(V0z,ty_2Eextreal_2Eextreal)
=> ! [V1x] :
( mem(V1x,ty_2Eextreal_2Eextreal)
=> ! [V2y] :
( mem(V2y,ty_2Eextreal_2Eextreal)
=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,V1x),V2y)),V0z))
<=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,V2y),V0z))
& p(ap(ap(c_2Eextreal_2Eextreal__le,V1x),V0z)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f58,plain,
ne(bool),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f60,plain,
! [A] :
( ! [B] :
( ne(arr(A,B))
| ~ ne(B) )
| ~ ne(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f61,plain,
! [X0,X1] :
( ne(arr(X0,X1))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f62,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(f63,plain,
! [X0,X1,X2,X3] :
( mem(ap(X0,X3),X2)
| ~ mem(X3,X1)
| ~ mem(X0,arr(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
! [Q] :
( ! [R] :
( Q = R
| ( p(Q)
<~> p(R) )
| ~ mem(R,bool) )
| ~ mem(Q,bool) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f65,plain,
! [Q] :
( ! [R] :
( Q = R
| ( ( ~ p(R)
| ~ p(Q) )
& ( p(R)
| p(Q) ) )
| ~ mem(R,bool) )
| ~ mem(Q,bool) ),
inference(NNF_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( X0 = X1
| p(X1)
| p(X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_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)],[f65]) ).
fof(f68,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(f69,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))],[f68]) ).
fof(f70,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)],[f69]) ).
fof(f71,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)],[f69]) ).
fof(f77,plain,
mem(c_2Ebool_2ET,bool),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f78,plain,
p(c_2Ebool_2ET),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f79,plain,
ne(ty_2Eextreal_2Eextreal),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f80,plain,
mem(c_2Eextreal_2Eextreal__le,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f81,plain,
! [A_27a] :
( mem(c_2Ebool_2ECOND(A_27a),arr(bool,arr(A_27a,arr(A_27a,A_27a))))
| ~ ne(A_27a) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f82,plain,
! [X0] :
( mem(c_2Ebool_2ECOND(X0),arr(bool,arr(X0,arr(X0,X0))))
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f83,plain,
mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f84,plain,
mem(c_2Ebool_2EF,bool),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f85,plain,
~ p(c_2Ebool_2EF),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f86,plain,
mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f87,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)],[f18]) ).
fof(f88,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)],[f87]) ).
fof(f89,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)],[f88]) ).
fof(f90,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)],[f88]) ).
fof(f92,plain,
mem(c_2Ebool_2E_5C_2F,arr(bool,arr(bool,bool))),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f93,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)],[f20]) ).
fof(f94,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)],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( p(X1)
| p(X0)
| ~ p(ap(ap(c_2Ebool_2E_5C_2F,X0),X1))
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f96,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)],[f94]) ).
fof(f98,plain,
mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f99,plain,
! [Q] :
( ! [R] :
( ( p(ap(ap(c_2Ebool_2E_2F_5C,Q),R))
<=> ( p(R)
& p(Q) ) )
| ~ mem(R,bool) )
| ~ mem(Q,bool) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f100,plain,
! [Q] :
( ! [R] :
( ( ( ~ p(R)
| ~ p(Q)
| p(ap(ap(c_2Ebool_2E_2F_5C,Q),R)) )
& ( ( p(R)
& p(Q) )
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,Q),R)) ) )
| ~ mem(R,bool) )
| ~ mem(Q,bool) ),
inference(NNF_transformation,[status(thm)],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( p(X0)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f102,plain,
! [X0,X1] :
( p(X1)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),X1))
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f104,plain,
mem(c_2Ebool_2E_7E,arr(bool,bool)),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f105,plain,
! [Q] :
( ( p(ap(c_2Ebool_2E_7E,Q))
<=> ~ p(Q) )
| ~ mem(Q,bool) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f106,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)],[f105]) ).
fof(f107,plain,
! [X0] :
( ~ p(X0)
| ~ p(ap(c_2Ebool_2E_7E,X0))
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
! [X0] :
( p(X0)
| p(ap(c_2Ebool_2E_7E,X0))
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f109,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)],[f25]) ).
fof(f110,plain,
! [X0] :
( mem(c_2Emin_2E_3D(X0),arr(X0,arr(X0,bool)))
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f111,plain,
! [A] :
( ! [X] :
( ! [Y] :
( ( p(ap(ap(c_2Emin_2E_3D(A),X),Y))
<=> X = Y )
| ~ mem(Y,A) )
| ~ mem(X,A) )
| ~ ne(A) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f112,plain,
! [A] :
( ! [X] :
( ! [Y] :
( ( ( X != Y
| p(ap(ap(c_2Emin_2E_3D(A),X),Y)) )
& ( X = Y
| ~ p(ap(ap(c_2Emin_2E_3D(A),X),Y)) ) )
| ~ mem(Y,A) )
| ~ mem(X,A) )
| ~ ne(A) ),
inference(NNF_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ p(ap(ap(c_2Emin_2E_3D(X0),X1),X2))
| ~ mem(X2,X0)
| ~ mem(X1,X0)
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f115,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)],[f27]) ).
fof(f116,plain,
! [X0] :
( mem(c_2Ebool_2E_21(X0),arr(arr(X0,bool),bool))
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
! [A] :
( ! [Q] :
( ( p(ap(c_2Ebool_2E_21(A),Q))
<=> ! [X] :
( p(ap(Q,X))
| ~ mem(X,A) ) )
| ~ mem(Q,arr(A,bool)) )
| ~ ne(A) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f118,plain,
! [A] :
( ! [Q] :
( ( ( ? [X] :
( ~ p(ap(Q,X))
& mem(X,A) )
| p(ap(c_2Ebool_2E_21(A),Q)) )
& ( ! [X] :
( p(ap(Q,X))
| ~ mem(X,A) )
| ~ p(ap(c_2Ebool_2E_21(A),Q)) ) )
| ~ mem(Q,arr(A,bool)) )
| ~ ne(A) ),
inference(NNF_transformation,[status(thm)],[f117]) ).
fof(f119,plain,
! [A] :
( ! [Q] :
( ( ( ( ~ p(ap(Q,sK1_skl(Q,A)))
& mem(sK1_skl(Q,A),A) )
| p(ap(c_2Ebool_2E_21(A),Q)) )
& ( ! [X] :
( p(ap(Q,X))
| ~ mem(X,A) )
| ~ p(ap(c_2Ebool_2E_21(A),Q)) ) )
| ~ mem(Q,arr(A,bool)) )
| ~ ne(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(X,sK1_skl(Q,A))],[f118]) ).
fof(f120,plain,
! [X0,X1,X2] :
( p(ap(X1,X2))
| ~ mem(X2,X0)
| ~ p(ap(c_2Ebool_2E_21(X0),X1))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
! [X0,X1] :
( mem(sK1_skl(X1,X0),X0)
| p(ap(c_2Ebool_2E_21(X0),X1))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f122,plain,
! [X0,X1] :
( ~ p(ap(X1,sK1_skl(X1,X0)))
| p(ap(c_2Ebool_2E_21(X0),X1))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f169,plain,
! [A_27a] :
( ! [V0t1] :
( ! [V1t2] :
( ( ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V0t1),V1t2) = V1t2
& ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2ET),V0t1),V1t2) = V0t1 )
| ~ mem(V1t2,A_27a) )
| ~ mem(V0t1,A_27a) )
| ~ ne(A_27a) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f170,plain,
! [X0,X1,X2] :
( ap(ap(ap(c_2Ebool_2ECOND(X0),c_2Ebool_2ET),X1),X2) = X1
| ~ mem(X2,X0)
| ~ mem(X1,X0)
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f169]) ).
fof(f171,plain,
! [X0,X1,X2] :
( ap(ap(ap(c_2Ebool_2ECOND(X0),c_2Ebool_2EF),X1),X2) = X2
| ~ mem(X2,X0)
| ~ mem(X1,X0)
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f169]) ).
fof(f196,plain,
! [V0x] :
( ! [V1y] :
( ! [V2z] :
( p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V2z))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),V2z))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y))
| ~ mem(V2z,ty_2Eextreal_2Eextreal) )
| ~ mem(V1y,ty_2Eextreal_2Eextreal) )
| ~ mem(V0x,ty_2Eextreal_2Eextreal) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f197,plain,
! [X0,X1,X2] :
( p(ap(ap(c_2Eextreal_2Eextreal__le,X0),X2))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X1),X2))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X0),X1))
| ~ mem(X2,ty_2Eextreal_2Eextreal)
| ~ mem(X1,ty_2Eextreal_2Eextreal)
| ~ mem(X0,ty_2Eextreal_2Eextreal) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f198,plain,
! [V0x] :
( ! [V1y] :
( p(ap(ap(c_2Eextreal_2Eextreal__le,V1y),V0x))
| p(ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y))
| ~ mem(V1y,ty_2Eextreal_2Eextreal) )
| ~ mem(V0x,ty_2Eextreal_2Eextreal) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f199,plain,
! [X0,X1] :
( p(ap(ap(c_2Eextreal_2Eextreal__le,X1),X0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X0),X1))
| ~ mem(X1,ty_2Eextreal_2Eextreal)
| ~ mem(X0,ty_2Eextreal_2Eextreal) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f200,plain,
! [V0x] :
( ! [V1y] :
( ap(ap(c_2Eextreal_2Eextreal__max,V0x),V1y) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Eextreal_2Eextreal__le,V0x),V1y)),V1y),V0x)
| ~ mem(V1y,ty_2Eextreal_2Eextreal) )
| ~ mem(V0x,ty_2Eextreal_2Eextreal) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f201,plain,
! [X0,X1] :
( ap(ap(c_2Eextreal_2Eextreal__max,X0),X1) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Eextreal_2Eextreal__le,X0),X1)),X1),X0)
| ~ mem(X1,ty_2Eextreal_2Eextreal)
| ~ mem(X0,ty_2Eextreal_2Eextreal) ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f224,plain,
! [V0A] :
( $false
| ( $true
& p(V0A) )
| ( $true
& ~ p(V0A) )
| ~ mem(V0A,bool) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f225,definition,
! [V0A] :
( sP4_prd(V0A)
<=> ( $true
& ~ p(V0A) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f229,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)],[f51]) ).
fof(f230,definition,
! [V0p,V1q,V2r] :
( sP5_prd(V2r,V1q,V0p)
<=> ( p(V0p)
<=> ( p(V1q)
<=> p(V2r) ) ) ),
introduced(definition,[new_symbols(definition,[sP5_prd])],[]) ).
fof(f231,plain,
! [V0p] :
( ! [V1q] :
( ! [V2r] :
( ( sP5_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)],[f229,f230]) ).
fof(f232,definition,
! [V0p,V1q,V2r] :
( sP6_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,[sP6_prd])],[]) ).
fof(f233,plain,
! [V0p] :
( ! [V1q] :
( ! [V2r] :
( ( sP5_prd(V2r,V1q,V0p)
<=> ( ( ~ p(V0p)
| ~ p(V1q)
| p(V2r) )
& sP6_prd(V2r,V1q,V0p) ) )
| ~ mem(V2r,bool) )
| ~ mem(V1q,bool) )
| ~ mem(V0p,bool) ),
inference(formula_renaming,[status(thm)],[f231,f232]) ).
fof(f234,plain,
! [V0p] :
( ! [V1q] :
( ! [V2r] :
( ( ( ( p(V0p)
& p(V1q)
& ~ p(V2r) )
| ~ sP6_prd(V2r,V1q,V0p)
| sP5_prd(V2r,V1q,V0p) )
& ( ( ( ~ p(V0p)
| ~ p(V1q)
| p(V2r) )
& sP6_prd(V2r,V1q,V0p) )
| ~ sP5_prd(V2r,V1q,V0p) ) )
| ~ mem(V2r,bool) )
| ~ mem(V1q,bool) )
| ~ mem(V0p,bool) ),
inference(NNF_transformation,[status(thm)],[f233]) ).
fof(f235,plain,
! [X0,X1,X2] :
( sP6_prd(X2,X1,X0)
| ~ sP5_prd(X2,X1,X0)
| ~ mem(X2,bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f236,plain,
! [X0,X1,X2] :
( ~ p(X0)
| ~ p(X1)
| p(X2)
| ~ sP5_prd(X2,X1,X0)
| ~ mem(X2,bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f237,plain,
! [X0,X1,X2] :
( ~ p(X2)
| ~ sP6_prd(X2,X1,X0)
| sP5_prd(X2,X1,X0)
| ~ mem(X2,bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f238,plain,
! [X0,X1,X2] :
( p(X1)
| ~ sP6_prd(X2,X1,X0)
| sP5_prd(X2,X1,X0)
| ~ mem(X2,bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f239,plain,
! [X0,X1,X2] :
( p(X0)
| ~ sP6_prd(X2,X1,X0)
| sP5_prd(X2,X1,X0)
| ~ mem(X2,bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f240,plain,
! [V0p] :
( ! [V1q] :
( ! [V2r] :
( ( ( p(V0p)
<=> ( p(V2r)
& p(V1q) ) )
<=> ( ( ~ p(V0p)
| p(V2r) )
& ( ~ p(V0p)
| p(V1q) )
& ( ~ p(V2r)
| ~ p(V1q)
| p(V0p) ) ) )
| ~ mem(V2r,bool) )
| ~ mem(V1q,bool) )
| ~ mem(V0p,bool) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f241,definition,
! [V0p,V1q,V2r] :
( sP7_prd(V2r,V1q,V0p)
<=> ( p(V0p)
<=> ( p(V2r)
& p(V1q) ) ) ),
introduced(definition,[new_symbols(definition,[sP7_prd])],[]) ).
fof(f242,plain,
! [V0p] :
( ! [V1q] :
( ! [V2r] :
( ( sP7_prd(V2r,V1q,V0p)
<=> ( ( ~ p(V0p)
| p(V2r) )
& ( ~ p(V0p)
| p(V1q) )
& ( ~ p(V2r)
| ~ p(V1q)
| p(V0p) ) ) )
| ~ mem(V2r,bool) )
| ~ mem(V1q,bool) )
| ~ mem(V0p,bool) ),
inference(formula_renaming,[status(thm)],[f240,f241]) ).
fof(f243,definition,
! [V0p,V1q,V2r] :
( sP8_prd(V2r,V1q,V0p)
<=> ( ( ~ p(V0p)
| p(V1q) )
& ( ~ p(V2r)
| ~ p(V1q)
| p(V0p) ) ) ),
introduced(definition,[new_symbols(definition,[sP8_prd])],[]) ).
fof(f244,plain,
! [V0p] :
( ! [V1q] :
( ! [V2r] :
( ( sP7_prd(V2r,V1q,V0p)
<=> ( ( ~ p(V0p)
| p(V2r) )
& sP8_prd(V2r,V1q,V0p) ) )
| ~ mem(V2r,bool) )
| ~ mem(V1q,bool) )
| ~ mem(V0p,bool) ),
inference(formula_renaming,[status(thm)],[f242,f243]) ).
fof(f245,plain,
! [V0p] :
( ! [V1q] :
( ! [V2r] :
( ( ( ( p(V0p)
& ~ p(V2r) )
| ~ sP8_prd(V2r,V1q,V0p)
| sP7_prd(V2r,V1q,V0p) )
& ( ( ( ~ p(V0p)
| 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)],[f244]) ).
fof(f246,plain,
! [X0,X1,X2] :
( sP8_prd(X2,X1,X0)
| ~ sP7_prd(X2,X1,X0)
| ~ mem(X2,bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f245]) ).
fof(f249,plain,
! [X0,X1,X2] :
( p(X0)
| ~ sP8_prd(X2,X1,X0)
| sP7_prd(X2,X1,X0)
| ~ mem(X2,bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f245]) ).
fof(f250,plain,
! [V0p] :
( ! [V1q] :
( ! [V2r] :
( ( ( p(V0p)
<=> ( p(V2r)
| p(V1q) ) )
<=> ( ( ~ p(V0p)
| p(V2r)
| p(V1q) )
& ( ~ p(V2r)
| p(V0p) )
& ( ~ p(V1q)
| p(V0p) ) ) )
| ~ mem(V2r,bool) )
| ~ mem(V1q,bool) )
| ~ mem(V0p,bool) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f251,definition,
! [V0p,V1q,V2r] :
( sP9_prd(V2r,V1q,V0p)
<=> ( p(V0p)
<=> ( p(V2r)
| p(V1q) ) ) ),
introduced(definition,[new_symbols(definition,[sP9_prd])],[]) ).
fof(f252,plain,
! [V0p] :
( ! [V1q] :
( ! [V2r] :
( ( sP9_prd(V2r,V1q,V0p)
<=> ( ( ~ p(V0p)
| p(V2r)
| p(V1q) )
& ( ~ p(V2r)
| p(V0p) )
& ( ~ p(V1q)
| p(V0p) ) ) )
| ~ mem(V2r,bool) )
| ~ mem(V1q,bool) )
| ~ mem(V0p,bool) ),
inference(formula_renaming,[status(thm)],[f250,f251]) ).
fof(f253,definition,
! [V0p,V1q,V2r] :
( sP10_prd(V2r,V1q,V0p)
<=> ( ( ~ p(V2r)
| p(V0p) )
& ( ~ p(V1q)
| p(V0p) ) ) ),
introduced(definition,[new_symbols(definition,[sP10_prd])],[]) ).
fof(f254,plain,
! [V0p] :
( ! [V1q] :
( ! [V2r] :
( ( sP9_prd(V2r,V1q,V0p)
<=> ( ( ~ p(V0p)
| p(V2r)
| p(V1q) )
& sP10_prd(V2r,V1q,V0p) ) )
| ~ mem(V2r,bool) )
| ~ mem(V1q,bool) )
| ~ mem(V0p,bool) ),
inference(formula_renaming,[status(thm)],[f252,f253]) ).
fof(f255,plain,
! [V0p] :
( ! [V1q] :
( ! [V2r] :
( ( ( ( p(V0p)
& ~ p(V2r)
& ~ p(V1q) )
| ~ sP10_prd(V2r,V1q,V0p)
| sP9_prd(V2r,V1q,V0p) )
& ( ( ( ~ p(V0p)
| p(V2r)
| p(V1q) )
& sP10_prd(V2r,V1q,V0p) )
| ~ sP9_prd(V2r,V1q,V0p) ) )
| ~ mem(V2r,bool) )
| ~ mem(V1q,bool) )
| ~ mem(V0p,bool) ),
inference(NNF_transformation,[status(thm)],[f254]) ).
fof(f256,plain,
! [X0,X1,X2] :
( sP10_prd(X2,X1,X0)
| ~ sP9_prd(X2,X1,X0)
| ~ mem(X2,bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f260,plain,
! [X0,X1,X2] :
( p(X0)
| ~ sP10_prd(X2,X1,X0)
| sP9_prd(X2,X1,X0)
| ~ mem(X2,bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f261,plain,
! [V0p] :
( ! [V1q] :
( ! [V2r] :
( ( ( p(V0p)
<=> ( p(V2r)
| ~ p(V1q) ) )
<=> ( ( ~ p(V0p)
| p(V2r)
| ~ p(V1q) )
& ( ~ p(V2r)
| p(V0p) )
& ( p(V1q)
| p(V0p) ) ) )
| ~ mem(V2r,bool) )
| ~ mem(V1q,bool) )
| ~ mem(V0p,bool) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f262,definition,
! [V0p,V1q,V2r] :
( sP11_prd(V2r,V1q,V0p)
<=> ( p(V0p)
<=> ( p(V2r)
| ~ p(V1q) ) ) ),
introduced(definition,[new_symbols(definition,[sP11_prd])],[]) ).
fof(f263,plain,
! [V0p] :
( ! [V1q] :
( ! [V2r] :
( ( sP11_prd(V2r,V1q,V0p)
<=> ( ( ~ p(V0p)
| p(V2r)
| ~ p(V1q) )
& ( ~ p(V2r)
| p(V0p) )
& ( p(V1q)
| p(V0p) ) ) )
| ~ mem(V2r,bool) )
| ~ mem(V1q,bool) )
| ~ mem(V0p,bool) ),
inference(formula_renaming,[status(thm)],[f261,f262]) ).
fof(f264,definition,
! [V0p,V1q,V2r] :
( sP12_prd(V2r,V1q,V0p)
<=> ( ( ~ p(V2r)
| p(V0p) )
& ( p(V1q)
| p(V0p) ) ) ),
introduced(definition,[new_symbols(definition,[sP12_prd])],[]) ).
fof(f265,plain,
! [V0p] :
( ! [V1q] :
( ! [V2r] :
( ( sP11_prd(V2r,V1q,V0p)
<=> ( ( ~ p(V0p)
| p(V2r)
| ~ p(V1q) )
& sP12_prd(V2r,V1q,V0p) ) )
| ~ mem(V2r,bool) )
| ~ mem(V1q,bool) )
| ~ mem(V0p,bool) ),
inference(formula_renaming,[status(thm)],[f263,f264]) ).
fof(f266,plain,
! [V0p] :
( ! [V1q] :
( ! [V2r] :
( ( ( ( p(V0p)
& ~ p(V2r)
& p(V1q) )
| ~ sP12_prd(V2r,V1q,V0p)
| sP11_prd(V2r,V1q,V0p) )
& ( ( ( ~ p(V0p)
| p(V2r)
| ~ p(V1q) )
& sP12_prd(V2r,V1q,V0p) )
| ~ sP11_prd(V2r,V1q,V0p) ) )
| ~ mem(V2r,bool) )
| ~ mem(V1q,bool) )
| ~ mem(V0p,bool) ),
inference(NNF_transformation,[status(thm)],[f265]) ).
fof(f267,plain,
! [X0,X1,X2] :
( sP12_prd(X2,X1,X0)
| ~ sP11_prd(X2,X1,X0)
| ~ mem(X2,bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f269,plain,
! [X0,X1,X2] :
( p(X1)
| ~ sP12_prd(X2,X1,X0)
| sP11_prd(X2,X1,X0)
| ~ mem(X2,bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f272,plain,
! [V0p] :
( ! [V1q] :
( ( ( p(V0p)
<=> ~ p(V1q) )
<=> ( ( ~ p(V0p)
| ~ p(V1q) )
& ( p(V1q)
| p(V0p) ) ) )
| ~ mem(V1q,bool) )
| ~ mem(V0p,bool) ),
inference(pre_NNF_transformation,[status(thm)],[f55]) ).
fof(f273,definition,
! [V0p,V1q] :
( sP13_prd(V1q,V0p)
<=> ( p(V0p)
<=> ~ p(V1q) ) ),
introduced(definition,[new_symbols(definition,[sP13_prd])],[]) ).
fof(f274,plain,
! [V0p] :
( ! [V1q] :
( ( sP13_prd(V1q,V0p)
<=> ( ( ~ p(V0p)
| ~ p(V1q) )
& ( p(V1q)
| p(V0p) ) ) )
| ~ mem(V1q,bool) )
| ~ mem(V0p,bool) ),
inference(formula_renaming,[status(thm)],[f272,f273]) ).
fof(f275,plain,
! [V0p] :
( ! [V1q] :
( ( ( ( p(V0p)
& p(V1q) )
| ( ~ p(V1q)
& ~ p(V0p) )
| sP13_prd(V1q,V0p) )
& ( ( ( ~ p(V0p)
| ~ p(V1q) )
& ( p(V1q)
| p(V0p) ) )
| ~ sP13_prd(V1q,V0p) ) )
| ~ mem(V1q,bool) )
| ~ mem(V0p,bool) ),
inference(NNF_transformation,[status(thm)],[f274]) ).
fof(f278,plain,
! [X0,X1] :
( p(X1)
| ~ p(X0)
| sP13_prd(X1,X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f275]) ).
fof(f281,plain,
! [X0,X1] :
( p(X0)
| ~ p(X1)
| sP13_prd(X1,X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(cnf_transformation,[status(thm)],[f275]) ).
fof(f282,plain,
? [V0z] :
( ? [V1x] :
( ? [V2y] :
( ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,V1x),V2y)),V0z))
<~> ( p(ap(ap(c_2Eextreal_2Eextreal__le,V2y),V0z))
& p(ap(ap(c_2Eextreal_2Eextreal__le,V1x),V0z)) ) )
& mem(V2y,ty_2Eextreal_2Eextreal) )
& mem(V1x,ty_2Eextreal_2Eextreal) )
& mem(V0z,ty_2Eextreal_2Eextreal) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f283,plain,
? [V0z] :
( ? [V1x] :
( ? [V2y] :
( ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V2y),V0z))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,V1x),V0z))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,V1x),V2y)),V0z)) )
& ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,V2y),V0z))
& p(ap(ap(c_2Eextreal_2Eextreal__le,V1x),V0z)) )
| p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,V1x),V2y)),V0z)) )
& mem(V2y,ty_2Eextreal_2Eextreal) )
& mem(V1x,ty_2Eextreal_2Eextreal) )
& mem(V0z,ty_2Eextreal_2Eextreal) ),
inference(NNF_transformation,[status(thm)],[f282]) ).
fof(f284,plain,
( ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK4_skl),sK2_skl))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl)),sK2_skl)) )
& ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,sK4_skl),sK2_skl))
& p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl)) )
| p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl)),sK2_skl)) )
& mem(sK4_skl,ty_2Eextreal_2Eextreal)
& mem(sK3_skl,ty_2Eextreal_2Eextreal)
& mem(sK2_skl,ty_2Eextreal_2Eextreal) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(V0z,sK2_skl),skolemize(V1x,sK3_skl),skolemize(V2y,sK4_skl)],[f283]) ).
fof(f285,plain,
mem(sK2_skl,ty_2Eextreal_2Eextreal),
inference(cnf_transformation,[status(thm)],[f284]) ).
fof(f286,plain,
mem(sK3_skl,ty_2Eextreal_2Eextreal),
inference(cnf_transformation,[status(thm)],[f284]) ).
fof(f287,plain,
mem(sK4_skl,ty_2Eextreal_2Eextreal),
inference(cnf_transformation,[status(thm)],[f284]) ).
fof(f288,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl))
| p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl)),sK2_skl)) ),
inference(cnf_transformation,[status(thm)],[f284]) ).
fof(f289,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,sK4_skl),sK2_skl))
| p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl)),sK2_skl)) ),
inference(cnf_transformation,[status(thm)],[f284]) ).
fof(f290,plain,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK4_skl),sK2_skl))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl)),sK2_skl)) ),
inference(cnf_transformation,[status(thm)],[f284]) ).
fof(f312,plain,
! [V0A] :
( ( $false
| p(V0A)
| sP4_prd(V0A) )
& ( ( $true
& ~ p(V0A) )
| ~ sP4_prd(V0A) ) ),
inference(NNF_transformation,[status(thm)],[f225]) ).
fof(f313,plain,
( ! [V0A] :
( $false
| p(V0A)
| sP4_prd(V0A) )
& ! [V0A] :
( ( $true
& ~ p(V0A) )
| ~ sP4_prd(V0A) ) ),
inference(miniscoping,[status(thm)],[f312]) ).
fof(f314,plain,
( ! [V0A] :
( p(V0A)
| sP4_prd(V0A) )
& ! [V0A] :
( ~ p(V0A)
| ~ sP4_prd(V0A) ) ),
inference(true_and_false_simplification,[status(thm)],[f313]) ).
fof(f315,plain,
! [X0] :
( ~ p(X0)
| ~ sP4_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f314]) ).
fof(f316,plain,
! [X0] :
( p(X0)
| sP4_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f314]) ).
fof(f317,definition,
! [V1q,V2r] :
( sP14_prd(V2r,V1q)
<=> ( p(V1q)
<=> p(V2r) ) ),
introduced(definition,[new_symbols(definition,[sP14_prd])],[]) ).
fof(f318,plain,
! [V0p,V1q,V2r] :
( sP5_prd(V2r,V1q,V0p)
<=> ( p(V0p)
<=> sP14_prd(V2r,V1q) ) ),
inference(formula_renaming,[status(thm)],[f230,f317]) ).
fof(f319,plain,
! [V0p,V1q,V2r] :
( ( ( ( sP14_prd(V2r,V1q)
| p(V0p) )
& ( ~ sP14_prd(V2r,V1q)
| ~ p(V0p) ) )
| sP5_prd(V2r,V1q,V0p) )
& ( ( ( ~ sP14_prd(V2r,V1q)
| p(V0p) )
& ( sP14_prd(V2r,V1q)
| ~ p(V0p) ) )
| ~ sP5_prd(V2r,V1q,V0p) ) ),
inference(NNF_transformation,[status(thm)],[f318]) ).
fof(f320,plain,
( ! [V0p,V1q,V2r] :
( ( ( sP14_prd(V2r,V1q)
| p(V0p) )
& ( ~ sP14_prd(V2r,V1q)
| ~ p(V0p) ) )
| sP5_prd(V2r,V1q,V0p) )
& ! [V0p,V1q,V2r] :
( ( ( ~ sP14_prd(V2r,V1q)
| p(V0p) )
& ( sP14_prd(V2r,V1q)
| ~ p(V0p) ) )
| ~ sP5_prd(V2r,V1q,V0p) ) ),
inference(miniscoping,[status(thm)],[f319]) ).
fof(f321,plain,
! [X0,X1,X2] :
( sP14_prd(X0,X1)
| ~ p(X2)
| ~ sP5_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f322,plain,
! [X0,X1,X2] :
( ~ sP14_prd(X0,X1)
| p(X2)
| ~ sP5_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f323,plain,
! [X0,X1,X2] :
( ~ sP14_prd(X0,X1)
| ~ p(X2)
| sP5_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f324,plain,
! [X0,X1,X2] :
( sP14_prd(X0,X1)
| p(X2)
| sP5_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f325,definition,
! [V0p,V1q,V2r] :
( sP15_prd(V2r,V1q,V0p)
<=> ( ( ~ p(V1q)
| ~ p(V2r)
| p(V0p) )
& ( p(V2r)
| p(V1q)
| p(V0p) ) ) ),
introduced(definition,[new_symbols(definition,[sP15_prd])],[]) ).
fof(f326,plain,
! [V0p,V1q,V2r] :
( sP6_prd(V2r,V1q,V0p)
<=> ( ( ~ p(V0p)
| ~ p(V2r)
| p(V1q) )
& sP15_prd(V2r,V1q,V0p) ) ),
inference(formula_renaming,[status(thm)],[f232,f325]) ).
fof(f327,plain,
! [V0p,V1q,V2r] :
( ( ( p(V0p)
& p(V2r)
& ~ p(V1q) )
| ~ sP15_prd(V2r,V1q,V0p)
| sP6_prd(V2r,V1q,V0p) )
& ( ( ( ~ p(V0p)
| ~ p(V2r)
| p(V1q) )
& sP15_prd(V2r,V1q,V0p) )
| ~ sP6_prd(V2r,V1q,V0p) ) ),
inference(NNF_transformation,[status(thm)],[f326]) ).
fof(f328,plain,
( ! [V0p,V1q,V2r] :
( ( p(V0p)
& p(V2r)
& ~ p(V1q) )
| ~ sP15_prd(V2r,V1q,V0p)
| sP6_prd(V2r,V1q,V0p) )
& ! [V0p,V1q,V2r] :
( ( ( ~ p(V0p)
| ~ p(V2r)
| p(V1q) )
& sP15_prd(V2r,V1q,V0p) )
| ~ sP6_prd(V2r,V1q,V0p) ) ),
inference(miniscoping,[status(thm)],[f327]) ).
fof(f329,plain,
! [X0,X1,X2] :
( sP15_prd(X0,X1,X2)
| ~ sP6_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f328]) ).
fof(f330,plain,
! [X0,X1,X2] :
( ~ p(X2)
| ~ p(X0)
| p(X1)
| ~ sP6_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f328]) ).
fof(f331,plain,
! [X0,X1,X2] :
( ~ p(X1)
| ~ sP15_prd(X0,X1,X2)
| sP6_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f328]) ).
fof(f332,plain,
! [X0,X1,X2] :
( p(X0)
| ~ sP15_prd(X0,X1,X2)
| sP6_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f328]) ).
fof(f333,plain,
! [X0,X1,X2] :
( p(X2)
| ~ sP15_prd(X0,X1,X2)
| sP6_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f328]) ).
fof(f334,plain,
! [V0p,V1q,V2r] :
( ( ( ( ( p(V2r)
& p(V1q) )
| p(V0p) )
& ( ~ p(V2r)
| ~ p(V1q)
| ~ p(V0p) ) )
| sP7_prd(V2r,V1q,V0p) )
& ( ( ( ~ p(V2r)
| ~ p(V1q)
| p(V0p) )
& ( ( p(V2r)
& p(V1q) )
| ~ p(V0p) ) )
| ~ sP7_prd(V2r,V1q,V0p) ) ),
inference(NNF_transformation,[status(thm)],[f241]) ).
fof(f335,plain,
( ! [V0p,V1q,V2r] :
( ( ( ( p(V2r)
& p(V1q) )
| p(V0p) )
& ( ~ p(V2r)
| ~ p(V1q)
| ~ p(V0p) ) )
| sP7_prd(V2r,V1q,V0p) )
& ! [V0p,V1q,V2r] :
( ( ( ~ p(V2r)
| ~ p(V1q)
| p(V0p) )
& ( ( p(V2r)
& p(V1q) )
| ~ p(V0p) ) )
| ~ sP7_prd(V2r,V1q,V0p) ) ),
inference(miniscoping,[status(thm)],[f334]) ).
fof(f338,plain,
! [X0,X1,X2] :
( ~ p(X0)
| ~ p(X1)
| p(X2)
| ~ sP7_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f335]) ).
fof(f339,plain,
! [X0,X1,X2] :
( ~ p(X0)
| ~ p(X1)
| ~ p(X2)
| sP7_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f335]) ).
fof(f340,plain,
! [X0,X1,X2] :
( p(X1)
| p(X2)
| sP7_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f335]) ).
fof(f342,definition,
! [V0p,V1q,V2r] :
( sP16_prd(V2r,V1q,V0p)
<=> ( ~ p(V2r)
| ~ p(V1q)
| p(V0p) ) ),
introduced(definition,[new_symbols(definition,[sP16_prd])],[]) ).
fof(f343,plain,
! [V0p,V1q,V2r] :
( sP8_prd(V2r,V1q,V0p)
<=> ( ( ~ p(V0p)
| p(V1q) )
& sP16_prd(V2r,V1q,V0p) ) ),
inference(formula_renaming,[status(thm)],[f243,f342]) ).
fof(f344,plain,
! [V0p,V1q,V2r] :
( ( ( p(V0p)
& ~ p(V1q) )
| ~ sP16_prd(V2r,V1q,V0p)
| sP8_prd(V2r,V1q,V0p) )
& ( ( ( ~ p(V0p)
| p(V1q) )
& sP16_prd(V2r,V1q,V0p) )
| ~ sP8_prd(V2r,V1q,V0p) ) ),
inference(NNF_transformation,[status(thm)],[f343]) ).
fof(f345,plain,
( ! [V0p,V1q,V2r] :
( ( p(V0p)
& ~ p(V1q) )
| ~ sP16_prd(V2r,V1q,V0p)
| sP8_prd(V2r,V1q,V0p) )
& ! [V0p,V1q,V2r] :
( ( ( ~ p(V0p)
| p(V1q) )
& sP16_prd(V2r,V1q,V0p) )
| ~ sP8_prd(V2r,V1q,V0p) ) ),
inference(miniscoping,[status(thm)],[f344]) ).
fof(f346,plain,
! [X0,X1,X2] :
( sP16_prd(X0,X1,X2)
| ~ sP8_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f345]) ).
fof(f348,plain,
! [X0,X1,X2] :
( ~ p(X1)
| ~ sP16_prd(X0,X1,X2)
| sP8_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f345]) ).
fof(f349,plain,
! [X0,X1,X2] :
( p(X2)
| ~ sP16_prd(X0,X1,X2)
| sP8_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f345]) ).
fof(f382,plain,
! [V0p,V1q] :
( ( ( ( ~ p(V1q)
| p(V0p) )
& ( p(V1q)
| ~ p(V0p) ) )
| sP13_prd(V1q,V0p) )
& ( ( ( p(V1q)
| p(V0p) )
& ( ~ p(V1q)
| ~ p(V0p) ) )
| ~ sP13_prd(V1q,V0p) ) ),
inference(NNF_transformation,[status(thm)],[f273]) ).
fof(f383,plain,
( ! [V0p,V1q] :
( ( ( ~ p(V1q)
| p(V0p) )
& ( p(V1q)
| ~ p(V0p) ) )
| sP13_prd(V1q,V0p) )
& ! [V0p,V1q] :
( ( ( p(V1q)
| p(V0p) )
& ( ~ p(V1q)
| ~ p(V0p) ) )
| ~ sP13_prd(V1q,V0p) ) ),
inference(miniscoping,[status(thm)],[f382]) ).
fof(f384,plain,
! [X0,X1] :
( ~ p(X0)
| ~ p(X1)
| ~ sP13_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f383]) ).
fof(f385,plain,
! [X0,X1] :
( p(X0)
| p(X1)
| ~ sP13_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f383]) ).
fof(f386,plain,
! [X0,X1] :
( p(X0)
| ~ p(X1)
| sP13_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f383]) ).
fof(f388,plain,
! [V1q,V2r] :
( ( ( ( p(V2r)
| p(V1q) )
& ( ~ p(V2r)
| ~ p(V1q) ) )
| sP14_prd(V2r,V1q) )
& ( ( ( ~ p(V2r)
| p(V1q) )
& ( p(V2r)
| ~ p(V1q) ) )
| ~ sP14_prd(V2r,V1q) ) ),
inference(NNF_transformation,[status(thm)],[f317]) ).
fof(f389,plain,
( ! [V1q,V2r] :
( ( ( p(V2r)
| p(V1q) )
& ( ~ p(V2r)
| ~ p(V1q) ) )
| sP14_prd(V2r,V1q) )
& ! [V1q,V2r] :
( ( ( ~ p(V2r)
| p(V1q) )
& ( p(V2r)
| ~ p(V1q) ) )
| ~ sP14_prd(V2r,V1q) ) ),
inference(miniscoping,[status(thm)],[f388]) ).
fof(f390,plain,
! [X0,X1] :
( p(X0)
| ~ p(X1)
| ~ sP14_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f389]) ).
fof(f391,plain,
! [X0,X1] :
( ~ p(X0)
| p(X1)
| ~ sP14_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f389]) ).
fof(f392,plain,
! [X0,X1] :
( ~ p(X0)
| ~ p(X1)
| sP14_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f389]) ).
fof(f393,plain,
! [X0,X1] :
( p(X0)
| p(X1)
| sP14_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f389]) ).
fof(f394,definition,
! [V0p,V1q,V2r] :
( sP17_prd(V2r,V1q,V0p)
<=> ( p(V2r)
| p(V1q)
| p(V0p) ) ),
introduced(definition,[new_symbols(definition,[sP17_prd])],[]) ).
fof(f395,plain,
! [V0p,V1q,V2r] :
( sP15_prd(V2r,V1q,V0p)
<=> ( ( ~ p(V1q)
| ~ p(V2r)
| p(V0p) )
& sP17_prd(V2r,V1q,V0p) ) ),
inference(formula_renaming,[status(thm)],[f325,f394]) ).
fof(f396,plain,
! [V0p,V1q,V2r] :
( ( ( p(V1q)
& p(V2r)
& ~ p(V0p) )
| ~ sP17_prd(V2r,V1q,V0p)
| sP15_prd(V2r,V1q,V0p) )
& ( ( ( ~ p(V1q)
| ~ p(V2r)
| p(V0p) )
& sP17_prd(V2r,V1q,V0p) )
| ~ sP15_prd(V2r,V1q,V0p) ) ),
inference(NNF_transformation,[status(thm)],[f395]) ).
fof(f397,plain,
( ! [V0p,V1q,V2r] :
( ( p(V1q)
& p(V2r)
& ~ p(V0p) )
| ~ sP17_prd(V2r,V1q,V0p)
| sP15_prd(V2r,V1q,V0p) )
& ! [V0p,V1q,V2r] :
( ( ( ~ p(V1q)
| ~ p(V2r)
| p(V0p) )
& sP17_prd(V2r,V1q,V0p) )
| ~ sP15_prd(V2r,V1q,V0p) ) ),
inference(miniscoping,[status(thm)],[f396]) ).
fof(f398,plain,
! [X0,X1,X2] :
( sP17_prd(X0,X1,X2)
| ~ sP15_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f397]) ).
fof(f399,plain,
! [X0,X1,X2] :
( ~ p(X1)
| ~ p(X0)
| p(X2)
| ~ sP15_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f397]) ).
fof(f400,plain,
! [X0,X1,X2] :
( ~ p(X2)
| ~ sP17_prd(X0,X1,X2)
| sP15_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f397]) ).
fof(f401,plain,
! [X0,X1,X2] :
( p(X0)
| ~ sP17_prd(X0,X1,X2)
| sP15_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f397]) ).
fof(f402,plain,
! [X0,X1,X2] :
( p(X1)
| ~ sP17_prd(X0,X1,X2)
| sP15_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f397]) ).
fof(f403,plain,
! [V0p,V1q,V2r] :
( ( ( p(V2r)
& p(V1q)
& ~ p(V0p) )
| sP16_prd(V2r,V1q,V0p) )
& ( ~ p(V2r)
| ~ p(V1q)
| p(V0p)
| ~ sP16_prd(V2r,V1q,V0p) ) ),
inference(NNF_transformation,[status(thm)],[f342]) ).
fof(f404,plain,
( ! [V0p,V1q,V2r] :
( ( p(V2r)
& p(V1q)
& ~ p(V0p) )
| sP16_prd(V2r,V1q,V0p) )
& ! [V0p,V1q,V2r] :
( ~ p(V2r)
| ~ p(V1q)
| p(V0p)
| ~ sP16_prd(V2r,V1q,V0p) ) ),
inference(miniscoping,[status(thm)],[f403]) ).
fof(f405,plain,
! [X0,X1,X2] :
( ~ p(X0)
| ~ p(X1)
| p(X2)
| ~ sP16_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f404]) ).
fof(f409,plain,
! [V0p,V1q,V2r] :
( ( ( ~ p(V2r)
& ~ p(V1q)
& ~ p(V0p) )
| sP17_prd(V2r,V1q,V0p) )
& ( p(V2r)
| p(V1q)
| p(V0p)
| ~ sP17_prd(V2r,V1q,V0p) ) ),
inference(NNF_transformation,[status(thm)],[f394]) ).
fof(f410,plain,
( ! [V0p,V1q,V2r] :
( ( ~ p(V2r)
& ~ p(V1q)
& ~ p(V0p) )
| sP17_prd(V2r,V1q,V0p) )
& ! [V0p,V1q,V2r] :
( p(V2r)
| p(V1q)
| p(V0p)
| ~ sP17_prd(V2r,V1q,V0p) ) ),
inference(miniscoping,[status(thm)],[f409]) ).
fof(f411,plain,
! [X0,X1,X2] :
( p(X0)
| p(X1)
| p(X2)
| ~ sP17_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f410]) ).
fof(f412,plain,
! [X0,X1,X2] :
( ~ p(X2)
| sP17_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f410]) ).
fof(f415,definition,
! [X0] :
( sQ0_spl
<=> ( p(X0)
| ~ p(X0)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f446,definition,
( sQ3_spl
<=> p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl)),sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( ~ sQ3_spl
| p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl)),sK2_skl)) ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f448,plain,
( sQ3_spl
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl)),sK2_skl)) ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f449,definition,
( sQ4_spl
<=> p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f451,plain,
( sQ4_spl
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl)) ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,plain,
( sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f288,f446,f449]) ).
fof(f453,definition,
( sQ5_spl
<=> p(ap(ap(c_2Eextreal_2Eextreal__le,sK4_skl),sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( sQ5_spl
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK4_skl),sK2_skl)) ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,plain,
( sQ5_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f289,f446,f453]) ).
fof(f457,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f290,f446,f449,f453]) ).
fof(f463,definition,
( sQ6_spl
<=> mem(sK2_skl,ty_2Eextreal_2Eextreal) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( sQ6_spl
| ~ mem(sK2_skl,ty_2Eextreal_2Eextreal) ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f466,definition,
( sQ7_spl
<=> mem(sK3_skl,ty_2Eextreal_2Eextreal) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f468,plain,
( sQ7_spl
| ~ mem(sK3_skl,ty_2Eextreal_2Eextreal) ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f473,plain,
! [X0] :
( sQ4_spl
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X0),sK2_skl))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),X0))
| ~ mem(sK2_skl,ty_2Eextreal_2Eextreal)
| ~ mem(X0,ty_2Eextreal_2Eextreal)
| ~ mem(sK3_skl,ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[f197,f451]) ).
fof(f474,definition,
! [X0] :
( sQ9_spl
<=> ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X0),sK2_skl))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),X0))
| ~ mem(X0,ty_2Eextreal_2Eextreal) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f475,plain,
! [X0] :
( ~ sQ9_spl
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X0),sK2_skl))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),X0))
| ~ mem(X0,ty_2Eextreal_2Eextreal) ),
inference(component_clause,[status(thm)],[f474]) ).
fof(f477,plain,
( sQ4_spl
| ~ sQ6_spl
| sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f473,f466,f474,f463,f449]) ).
fof(f480,plain,
! [X0] :
( X0 = c_2Ebool_2EF
| p(X0)
| ~ mem(c_2Ebool_2EF,bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f66,f85]) ).
fof(f481,definition,
! [X0] :
( sQ10_spl
<=> ( X0 = c_2Ebool_2EF
| p(X0)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f482,plain,
! [X0] :
( ~ sQ10_spl
| X0 = c_2Ebool_2EF
| p(X0)
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f484,definition,
( sQ11_spl
<=> mem(c_2Ebool_2EF,bool) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f486,plain,
( sQ11_spl
| ~ mem(c_2Ebool_2EF,bool) ),
inference(component_clause,[status(thm)],[f484]) ).
fof(f487,plain,
( ~ sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f480,f481,f484]) ).
fof(f492,definition,
( sQ12_spl
<=> mem(ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl),ty_2Eextreal_2Eextreal) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f493,plain,
( ~ sQ12_spl
| mem(ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl),ty_2Eextreal_2Eextreal) ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f494,plain,
( sQ12_spl
| ~ mem(ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl),ty_2Eextreal_2Eextreal) ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f510,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f465,f285]) ).
fof(f511,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f510]) ).
fof(f512,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f468,f286]) ).
fof(f513,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f512]) ).
fof(f521,plain,
! [X0] :
( sQ12_spl
| ~ mem(sK4_skl,X0)
| ~ mem(ap(c_2Eextreal_2Eextreal__max,sK3_skl),arr(X0,ty_2Eextreal_2Eextreal)) ),
inference(resolution,[status(thm)],[f494,f63]) ).
fof(f522,plain,
! [X0,X1] :
( sQ12_spl
| ~ mem(sK3_skl,X1)
| ~ mem(c_2Eextreal_2Eextreal__max,arr(X1,arr(X0,ty_2Eextreal_2Eextreal)))
| ~ mem(sK4_skl,X0) ),
inference(resolution,[status(thm)],[f521,f63]) ).
fof(f524,plain,
( sQ12_spl
| ~ mem(sK3_skl,ty_2Eextreal_2Eextreal)
| ~ mem(sK4_skl,ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[f522,f83]) ).
fof(f525,definition,
( sQ17_spl
<=> mem(sK4_skl,ty_2Eextreal_2Eextreal) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f527,plain,
( sQ17_spl
| ~ mem(sK4_skl,ty_2Eextreal_2Eextreal) ),
inference(component_clause,[status(thm)],[f525]) ).
fof(f528,plain,
( sQ12_spl
| ~ sQ7_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f524,f525,f466,f492]) ).
fof(f529,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f527,f287]) ).
fof(f530,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f529]) ).
fof(f533,plain,
! [X0] :
( sQ4_spl
| X0 = ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl)
| p(X0)
| ~ mem(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl),bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f451,f66]) ).
fof(f537,definition,
! [X0] :
( sQ18_spl
<=> ( X0 = ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl)
| p(X0)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f538,plain,
! [X0] :
( ~ sQ18_spl
| X0 = ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl)
| p(X0)
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f537]) ).
fof(f540,definition,
( sQ19_spl
<=> mem(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl),bool) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f541,plain,
( ~ sQ19_spl
| mem(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl),bool) ),
inference(component_clause,[status(thm)],[f540]) ).
fof(f542,plain,
( sQ19_spl
| ~ mem(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl),bool) ),
inference(component_clause,[status(thm)],[f540]) ).
fof(f543,plain,
( sQ4_spl
| ~ sQ19_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f533,f537,f540,f449]) ).
fof(f544,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,f63]) ).
fof(f546,plain,
! [X0] :
( X0 = c_2Ebool_2ET
| ~ p(c_2Ebool_2ET)
| ~ p(X0)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f67,f77]) ).
fof(f550,definition,
( sQ21_spl
<=> p(c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f554,definition,
! [X0] :
( sQ22_spl
<=> ( X0 = c_2Ebool_2ET
| ~ p(X0)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f555,plain,
! [X0] :
( ~ sQ22_spl
| X0 = c_2Ebool_2ET
| ~ p(X0)
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f554]) ).
fof(f557,definition,
( sQ23_spl
<=> p(c_2Ebool_2ET) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f559,plain,
( sQ23_spl
| ~ p(c_2Ebool_2ET) ),
inference(component_clause,[status(thm)],[f557]) ).
fof(f560,plain,
( ~ sQ23_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f546,f554,f557]) ).
fof(f561,plain,
! [X0,X1,X2,X3] :
( X3 = sK0_skl(X2,X0,X1,bool)
| ~ p(sK0_skl(X2,X0,X1,bool))
| ~ p(X3)
| ~ mem(X3,bool)
| X0 = X2
| ~ mem(X2,arr(bool,X1))
| ~ mem(X0,arr(bool,X1)) ),
inference(resolution,[status(thm)],[f70,f67]) ).
fof(f564,plain,
! [X0] :
( X0 = c_2Eextreal_2Eextreal__max
| ap(X0,sK0_skl(c_2Eextreal_2Eextreal__max,X0,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal),ty_2Eextreal_2Eextreal)) != ap(c_2Eextreal_2Eextreal__max,sK0_skl(c_2Eextreal_2Eextreal__max,X0,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal),ty_2Eextreal_2Eextreal))
| ~ mem(X0,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))) ),
inference(resolution,[status(thm)],[f71,f83]) ).
fof(f565,plain,
! [X0] :
( X0 = c_2Eextreal_2Eextreal__le
| ap(X0,sK0_skl(c_2Eextreal_2Eextreal__le,X0,arr(ty_2Eextreal_2Eextreal,bool),ty_2Eextreal_2Eextreal)) != ap(c_2Eextreal_2Eextreal__le,sK0_skl(c_2Eextreal_2Eextreal__le,X0,arr(ty_2Eextreal_2Eextreal,bool),ty_2Eextreal_2Eextreal))
| ~ mem(X0,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ),
inference(resolution,[status(thm)],[f71,f80]) ).
fof(f568,plain,
! [X0] :
( ~ sQ9_spl
| p(ap(ap(c_2Eextreal_2Eextreal__le,X0),sK3_skl))
| ~ mem(sK3_skl,ty_2Eextreal_2Eextreal)
| ~ mem(X0,ty_2Eextreal_2Eextreal)
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X0),sK2_skl))
| ~ mem(X0,ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[f475,f199]) ).
fof(f575,definition,
! [X0] :
( sQ25_spl
<=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,X0),sK3_skl))
| ~ mem(X0,ty_2Eextreal_2Eextreal)
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X0),sK2_skl))
| ~ mem(X0,ty_2Eextreal_2Eextreal) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f576,plain,
! [X0] :
( ~ sQ25_spl
| p(ap(ap(c_2Eextreal_2Eextreal__le,X0),sK3_skl))
| ~ mem(X0,ty_2Eextreal_2Eextreal)
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X0),sK2_skl))
| ~ mem(X0,ty_2Eextreal_2Eextreal) ),
inference(component_clause,[status(thm)],[f575]) ).
fof(f578,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f568,f575,f466,f474]) ).
fof(f580,plain,
! [X0] :
( ~ sQ25_spl
| p(ap(ap(c_2Eextreal_2Eextreal__le,X0),sK3_skl))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X0),sK2_skl))
| ~ mem(X0,ty_2Eextreal_2Eextreal) ),
inference(duplicate_literals_removal,[status(thm)],[f576]) ).
fof(f583,plain,
( ~ sQ18_spl
| c_2Ebool_2EF = ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl)
| ~ mem(c_2Ebool_2EF,bool) ),
inference(resolution,[status(thm)],[f538,f85]) ).
fof(f584,definition,
( sQ26_spl
<=> ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl) = ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f588,definition,
( sQ27_spl
<=> c_2Ebool_2EF = ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f589,plain,
( ~ sQ27_spl
| c_2Ebool_2EF = ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f588]) ).
fof(f591,plain,
( ~ sQ18_spl
| sQ27_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f583,f484,f588,f537]) ).
fof(f592,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f486,f84]) ).
fof(f593,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f592]) ).
fof(f597,plain,
! [X0] :
( ~ sQ27_spl
| p(c_2Ebool_2EF)
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X0),sK2_skl))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),X0))
| ~ mem(sK2_skl,ty_2Eextreal_2Eextreal)
| ~ mem(X0,ty_2Eextreal_2Eextreal)
| ~ mem(sK3_skl,ty_2Eextreal_2Eextreal) ),
inference(paramodulation,[status(thm)],[f589,f197]) ).
fof(f600,definition,
( sQ28_spl
<=> p(ap(ap(c_2Eextreal_2Eextreal__le,sK2_skl),sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f601,plain,
( ~ sQ28_spl
| p(ap(ap(c_2Eextreal_2Eextreal__le,sK2_skl),sK2_skl)) ),
inference(component_clause,[status(thm)],[f600]) ).
fof(f602,plain,
( sQ28_spl
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK2_skl),sK2_skl)) ),
inference(component_clause,[status(thm)],[f600]) ).
fof(f604,plain,
( ~ sQ27_spl
| sQ21_spl
| ~ sQ6_spl
| sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f597,f466,f474,f463,f550,f588]) ).
fof(f607,plain,
( sQ28_spl
| p(ap(ap(c_2Eextreal_2Eextreal__le,sK2_skl),sK2_skl))
| ~ mem(sK2_skl,ty_2Eextreal_2Eextreal)
| ~ mem(sK2_skl,ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[f602,f199]) ).
fof(f614,plain,
( sQ28_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f607,f463,f600]) ).
fof(f631,plain,
! [X0,X1,X2] :
( ~ mem(X1,X2)
| ~ mem(X0,arr(X2,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))))
| ap(X0,X1) = c_2Eextreal_2Eextreal__max
| ap(ap(X0,X1),sK0_skl(c_2Eextreal_2Eextreal__max,ap(X0,X1),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal),ty_2Eextreal_2Eextreal)) != ap(c_2Eextreal_2Eextreal__max,sK0_skl(c_2Eextreal_2Eextreal__max,ap(X0,X1),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal),ty_2Eextreal_2Eextreal)) ),
inference(resolution,[status(thm)],[f564,f63]) ).
fof(f632,plain,
( c_2Eextreal_2Eextreal__max = c_2Eextreal_2Eextreal__max
| ap(c_2Eextreal_2Eextreal__max,sK0_skl(c_2Eextreal_2Eextreal__max,c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal),ty_2Eextreal_2Eextreal)) != ap(c_2Eextreal_2Eextreal__max,sK0_skl(c_2Eextreal_2Eextreal__max,c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal),ty_2Eextreal_2Eextreal)) ),
inference(resolution,[status(thm)],[f564,f83]) ).
fof(f633,definition,
( sQ32_spl
<=> ap(c_2Eextreal_2Eextreal__max,sK0_skl(c_2Eextreal_2Eextreal__max,c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal),ty_2Eextreal_2Eextreal)) = ap(c_2Eextreal_2Eextreal__max,sK0_skl(c_2Eextreal_2Eextreal__max,c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal),ty_2Eextreal_2Eextreal)) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f635,plain,
( sQ32_spl
| ap(c_2Eextreal_2Eextreal__max,sK0_skl(c_2Eextreal_2Eextreal__max,c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal),ty_2Eextreal_2Eextreal)) != ap(c_2Eextreal_2Eextreal__max,sK0_skl(c_2Eextreal_2Eextreal__max,c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal),ty_2Eextreal_2Eextreal)) ),
inference(component_clause,[status(thm)],[f633]) ).
fof(f636,definition,
( sQ33_spl
<=> c_2Eextreal_2Eextreal__max = c_2Eextreal_2Eextreal__max ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f639,plain,
( sQ33_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f632,f633,f636]) ).
fof(f640,plain,
( sQ32_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f635]) ).
fof(f641,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f640]) ).
fof(f644,plain,
( c_2Eextreal_2Eextreal__le = c_2Eextreal_2Eextreal__le
| ap(c_2Eextreal_2Eextreal__le,sK0_skl(c_2Eextreal_2Eextreal__le,c_2Eextreal_2Eextreal__le,arr(ty_2Eextreal_2Eextreal,bool),ty_2Eextreal_2Eextreal)) != ap(c_2Eextreal_2Eextreal__le,sK0_skl(c_2Eextreal_2Eextreal__le,c_2Eextreal_2Eextreal__le,arr(ty_2Eextreal_2Eextreal,bool),ty_2Eextreal_2Eextreal)) ),
inference(resolution,[status(thm)],[f565,f80]) ).
fof(f645,definition,
( sQ34_spl
<=> ap(c_2Eextreal_2Eextreal__le,sK0_skl(c_2Eextreal_2Eextreal__le,c_2Eextreal_2Eextreal__le,arr(ty_2Eextreal_2Eextreal,bool),ty_2Eextreal_2Eextreal)) = ap(c_2Eextreal_2Eextreal__le,sK0_skl(c_2Eextreal_2Eextreal__le,c_2Eextreal_2Eextreal__le,arr(ty_2Eextreal_2Eextreal,bool),ty_2Eextreal_2Eextreal)) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f647,plain,
( sQ34_spl
| ap(c_2Eextreal_2Eextreal__le,sK0_skl(c_2Eextreal_2Eextreal__le,c_2Eextreal_2Eextreal__le,arr(ty_2Eextreal_2Eextreal,bool),ty_2Eextreal_2Eextreal)) != ap(c_2Eextreal_2Eextreal__le,sK0_skl(c_2Eextreal_2Eextreal__le,c_2Eextreal_2Eextreal__le,arr(ty_2Eextreal_2Eextreal,bool),ty_2Eextreal_2Eextreal)) ),
inference(component_clause,[status(thm)],[f645]) ).
fof(f648,definition,
( sQ35_spl
<=> c_2Eextreal_2Eextreal__le = c_2Eextreal_2Eextreal__le ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f651,plain,
( sQ35_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f644,f645,f648]) ).
fof(f652,plain,
( sQ34_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f647]) ).
fof(f653,plain,
sQ34_spl,
inference(contradiction_clause,[status(thm)],[f652]) ).
fof(f654,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)],[f104,f71]) ).
fof(f660,definition,
! [X1] :
( sQ37_spl
<=> ( ~ p(X1)
| p(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f696,plain,
! [X0] :
( sQ19_spl
| ~ mem(sK2_skl,X0)
| ~ mem(ap(c_2Eextreal_2Eextreal__le,sK3_skl),arr(X0,bool)) ),
inference(resolution,[status(thm)],[f542,f63]) ).
fof(f716,plain,
! [X0,X1] :
( ~ p(X1)
| ~ p(X0)
| p(X1)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f386,f384]) ).
fof(f717,definition,
! [X1] :
( sQ39_spl
<=> ( p(X1)
| p(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f718,plain,
! [X0] :
( ~ sQ39_spl
| p(X0)
| p(X0) ),
inference(component_clause,[status(thm)],[f717]) ).
fof(f721,definition,
! [X0] :
( sQ40_spl
<=> ( ~ p(X0)
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f722,plain,
! [X0] :
( ~ sQ40_spl
| ~ p(X0)
| ~ p(X0) ),
inference(component_clause,[status(thm)],[f721]) ).
fof(f724,plain,
( sQ37_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f716,f721,f660]) ).
fof(f729,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)],[f86,f71]) ).
fof(f742,plain,
! [X0,X1] :
( sQ19_spl
| ~ mem(sK3_skl,X1)
| ~ mem(c_2Eextreal_2Eextreal__le,arr(X1,arr(X0,bool)))
| ~ mem(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f696,f63]) ).
fof(f778,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)],[f92,f71]) ).
fof(f783,plain,
( sQ19_spl
| ~ mem(sK3_skl,ty_2Eextreal_2Eextreal)
| ~ mem(sK2_skl,ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[f742,f80]) ).
fof(f784,plain,
( sQ19_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f783,f463,f466,f540]) ).
fof(f795,definition,
( sQ46_spl
<=> sP4_prd(c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f804,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ27_spl
| X0 = c_2Ebool_2EF
| p(X0)
| ~ mem(X0,bool) ),
inference(forward_demodulation,[status(thm)],[f589,f538]) ).
fof(f809,definition,
( sQ47_spl
<=> c_2Ebool_2EF = c_2Ebool_2EF ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f813,definition,
( sQ48_spl
<=> c_2Ebool_2ET = c_2Ebool_2EF ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f814,plain,
( ~ sQ48_spl
| c_2Ebool_2ET = c_2Ebool_2EF ),
inference(component_clause,[status(thm)],[f813]) ).
fof(f823,plain,
( ~ sQ48_spl
| ~ p(c_2Ebool_2ET) ),
inference(backward_demodulation,[status(thm)],[f814,f85]) ).
fof(f825,plain,
( ~ sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f823,f78]) ).
fof(f826,plain,
~ sQ48_spl,
inference(contradiction_clause,[status(thm)],[f825]) ).
fof(f846,plain,
( ~ sQ9_spl
| ~ sQ25_spl
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl))
| ~ mem(sK3_skl,ty_2Eextreal_2Eextreal)
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl))
| ~ mem(sK3_skl,ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[f580,f475]) ).
fof(f848,plain,
( ~ sQ9_spl
| ~ sQ25_spl
| ~ sQ4_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f846,f466,f449,f575,f474]) ).
fof(f865,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)],[f98,f71]) ).
fof(f874,plain,
! [X0] :
( ~ ne(ty_2Eextreal_2Eextreal)
| ~ mem(X0,bool)
| ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),X0) = c_2Eextreal_2Eextreal__max
| ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),X0),sK0_skl(c_2Eextreal_2Eextreal__max,ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),X0),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal),ty_2Eextreal_2Eextreal)) != ap(c_2Eextreal_2Eextreal__max,sK0_skl(c_2Eextreal_2Eextreal__max,ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),X0),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal),ty_2Eextreal_2Eextreal)) ),
inference(resolution,[status(thm)],[f631,f82]) ).
fof(f877,definition,
! [X0] :
( sQ49_spl
<=> ( ~ mem(X0,bool)
| ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),X0) = c_2Eextreal_2Eextreal__max
| ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),X0),sK0_skl(c_2Eextreal_2Eextreal__max,ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),X0),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal),ty_2Eextreal_2Eextreal)) != ap(c_2Eextreal_2Eextreal__max,sK0_skl(c_2Eextreal_2Eextreal__max,ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),X0),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal),ty_2Eextreal_2Eextreal)) ) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f880,definition,
( sQ50_spl
<=> ne(ty_2Eextreal_2Eextreal) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f882,plain,
( sQ50_spl
| ~ ne(ty_2Eextreal_2Eextreal) ),
inference(component_clause,[status(thm)],[f880]) ).
fof(f883,plain,
( ~ sQ50_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f874,f877,f880]) ).
fof(f973,plain,
! [X0] :
( sP4_prd(ap(c_2Ebool_2E_7E,X0))
| ~ p(X0)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f107,f316]) ).
fof(f979,plain,
mem(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))),
inference(resolution,[status(thm)],[f110,f79]) ).
fof(f988,definition,
( sQ55_spl
<=> mem(c_2Ebool_2ET,bool) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f990,plain,
( sQ55_spl
| ~ mem(c_2Ebool_2ET,bool) ),
inference(component_clause,[status(thm)],[f988]) ).
fof(f995,plain,
( sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f990,f77]) ).
fof(f996,plain,
sQ55_spl,
inference(contradiction_clause,[status(thm)],[f995]) ).
fof(f1001,definition,
( sQ56_spl
<=> ap(c_2Ebool_2E_7E,c_2Ebool_2EF) = c_2Ebool_2EF ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f1002,plain,
( ~ sQ56_spl
| ap(c_2Ebool_2E_7E,c_2Ebool_2EF) = c_2Ebool_2EF ),
inference(component_clause,[status(thm)],[f1001]) ).
fof(f1005,definition,
( sQ57_spl
<=> ap(c_2Ebool_2E_7E,c_2Ebool_2ET) = c_2Ebool_2EF ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f1006,plain,
( ~ sQ57_spl
| ap(c_2Ebool_2E_7E,c_2Ebool_2ET) = c_2Ebool_2EF ),
inference(component_clause,[status(thm)],[f1005]) ).
fof(f1021,plain,
! [X0] :
( X0 = c_2Emin_2E_3D(ty_2Eextreal_2Eextreal)
| ap(X0,sK0_skl(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),X0,arr(ty_2Eextreal_2Eextreal,bool),ty_2Eextreal_2Eextreal)) != ap(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),sK0_skl(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),X0,arr(ty_2Eextreal_2Eextreal,bool),ty_2Eextreal_2Eextreal))
| ~ mem(X0,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))) ),
inference(resolution,[status(thm)],[f979,f71]) ).
fof(f1037,plain,
( c_2Emin_2E_3D(ty_2Eextreal_2Eextreal) = c_2Emin_2E_3D(ty_2Eextreal_2Eextreal)
| ap(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),sK0_skl(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),arr(ty_2Eextreal_2Eextreal,bool),ty_2Eextreal_2Eextreal)) != ap(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),sK0_skl(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),arr(ty_2Eextreal_2Eextreal,bool),ty_2Eextreal_2Eextreal)) ),
inference(resolution,[status(thm)],[f1021,f979]) ).
fof(f1041,definition,
( sQ60_spl
<=> ap(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),sK0_skl(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),arr(ty_2Eextreal_2Eextreal,bool),ty_2Eextreal_2Eextreal)) = ap(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),sK0_skl(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),arr(ty_2Eextreal_2Eextreal,bool),ty_2Eextreal_2Eextreal)) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f1043,plain,
( sQ60_spl
| ap(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),sK0_skl(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),arr(ty_2Eextreal_2Eextreal,bool),ty_2Eextreal_2Eextreal)) != ap(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),sK0_skl(c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),c_2Emin_2E_3D(ty_2Eextreal_2Eextreal),arr(ty_2Eextreal_2Eextreal,bool),ty_2Eextreal_2Eextreal)) ),
inference(component_clause,[status(thm)],[f1041]) ).
fof(f1044,definition,
( sQ61_spl
<=> c_2Emin_2E_3D(ty_2Eextreal_2Eextreal) = c_2Emin_2E_3D(ty_2Eextreal_2Eextreal) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f1047,plain,
( sQ61_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f1037,f1041,f1044]) ).
fof(f1052,plain,
( sQ60_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1043]) ).
fof(f1053,plain,
sQ60_spl,
inference(contradiction_clause,[status(thm)],[f1052]) ).
fof(f1073,plain,
( ~ sQ22_spl
| c_2Ebool_2ET = c_2Ebool_2ET
| ~ p(c_2Ebool_2ET) ),
inference(resolution,[status(thm)],[f555,f77]) ).
fof(f1075,definition,
( sQ63_spl
<=> c_2Ebool_2ET = c_2Ebool_2ET ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1078,plain,
( ~ sQ22_spl
| sQ63_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1073,f557,f1075,f554]) ).
fof(f1086,plain,
( sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f882,f79]) ).
fof(f1087,plain,
sQ50_spl,
inference(contradiction_clause,[status(thm)],[f1086]) ).
fof(f1101,definition,
( sQ65_spl
<=> ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET) = c_2Ebool_2EF ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f1102,plain,
( ~ sQ65_spl
| ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET) = c_2Ebool_2EF ),
inference(component_clause,[status(thm)],[f1101]) ).
fof(f1155,plain,
! [X0,X1,X2] :
( p(X0)
| p(X1)
| ~ p(X2)
| sP5_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f323,f393]) ).
fof(f1156,plain,
! [X0,X1,X2] :
( ~ p(X0)
| ~ p(X1)
| ~ p(X2)
| sP5_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f323,f392]) ).
fof(f1159,definition,
! [X1,X2] :
( sQ69_spl
<=> ( ~ sP14_prd(X1,X2)
| sP14_prd(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1167,plain,
! [X0] :
( ~ sQ39_spl
| p(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f718]) ).
fof(f1198,plain,
( ~ sQ39_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f85,f1167]) ).
fof(f1211,plain,
~ sQ39_spl,
inference(contradiction_clause,[status(thm)],[f1198]) ).
fof(f1212,plain,
~ sP4_prd(c_2Ebool_2ET),
inference(resolution,[status(thm)],[f315,f78]) ).
fof(f1215,plain,
! [X0,X1] :
( ~ sP4_prd(ap(c_2Ebool_2E_21(X0),X1))
| mem(sK1_skl(X1,X0),X0)
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(resolution,[status(thm)],[f121,f315]) ).
fof(f1226,plain,
( ~ sQ3_spl
| ~ sP4_prd(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl)),sK2_skl)) ),
inference(resolution,[status(thm)],[f447,f315]) ).
fof(f1251,plain,
! [X0,X1,X2] :
( ~ sP4_prd(ap(ap(c_2Eextreal_2Eextreal__le,X0),X2))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X1),X2))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X0),X1))
| ~ mem(X2,ty_2Eextreal_2Eextreal)
| ~ mem(X1,ty_2Eextreal_2Eextreal)
| ~ mem(X0,ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[f197,f315]) ).
fof(f1267,plain,
! [X0,X1] :
( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),X0),X1) = X0
| ~ mem(X1,ty_2Eextreal_2Eextreal)
| ~ mem(X0,ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[f170,f79]) ).
fof(f1307,plain,
! [X0,X1] :
( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),X0),X1) = X1
| ~ mem(X1,ty_2Eextreal_2Eextreal)
| ~ mem(X0,ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[f171,f79]) ).
fof(f1311,plain,
! [X0] :
( ap(ap(c_2Eextreal_2Eextreal__max,X0),sK4_skl) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Eextreal_2Eextreal__le,X0),sK4_skl)),sK4_skl),X0)
| ~ mem(X0,ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[f201,f287]) ).
fof(f1313,plain,
! [X0] :
( ap(ap(c_2Eextreal_2Eextreal__max,X0),sK2_skl) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Eextreal_2Eextreal__le,X0),sK2_skl)),sK2_skl),X0)
| ~ mem(X0,ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[f201,f285]) ).
fof(f1328,plain,
ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK4_skl)),sK4_skl),sK3_skl),
inference(resolution,[status(thm)],[f1311,f286]) ).
fof(f1334,plain,
! [X0] :
( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),X0),sK3_skl) = X0
| ~ mem(X0,ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[f1267,f286]) ).
fof(f1348,plain,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),sK4_skl),sK3_skl) = sK4_skl,
inference(resolution,[status(thm)],[f1334,f287]) ).
fof(f1400,plain,
! [X0] :
( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),X0),sK3_skl) = sK3_skl
| ~ mem(X0,ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[f1307,f286]) ).
fof(f1445,plain,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),sK4_skl),sK3_skl) = sK3_skl,
inference(resolution,[status(thm)],[f1400,f287]) ).
fof(f1539,definition,
! [X0] :
( sQ74_spl
<=> ( ~ p(X0)
| ~ p(X0)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1540,plain,
! [X0] :
( ~ sQ74_spl
| ~ p(X0)
| ~ p(X0)
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f1539]) ).
fof(f1562,plain,
! [X0,X1,X2] :
( p(X2)
| sP7_prd(X0,X1,X2)
| ~ mem(X0,bool)
| ~ mem(X1,bool)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ sP16_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f348,f249]) ).
fof(f1565,plain,
! [X0,X1,X2] :
( p(X2)
| sP7_prd(X0,X1,X2)
| ~ mem(X0,bool)
| ~ mem(X1,bool)
| ~ mem(X2,bool)
| ~ sP16_prd(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1562,f340]) ).
fof(f1571,plain,
! [X0,X1,X2] :
( ~ p(X2)
| sP15_prd(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f400,f412]) ).
fof(f1574,plain,
! [X0,X1,X2] :
( ~ p(X2)
| sP6_prd(X1,X2,X0)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f1571,f331]) ).
fof(f1590,plain,
! [X0,X1,X2] :
( p(X2)
| sP6_prd(X0,X1,X2)
| p(X1)
| ~ sP17_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f402,f333]) ).
fof(f1649,definition,
( sQ78_spl
<=> mem(ap(c_2Ebool_2E_7E,c_2Ebool_2EF),bool) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1650,plain,
( ~ sQ78_spl
| mem(ap(c_2Ebool_2E_7E,c_2Ebool_2EF),bool) ),
inference(component_clause,[status(thm)],[f1649]) ).
fof(f1651,plain,
( sQ78_spl
| ~ mem(ap(c_2Ebool_2E_7E,c_2Ebool_2EF),bool) ),
inference(component_clause,[status(thm)],[f1649]) ).
fof(f1663,plain,
! [X0,X1,X2] :
( ~ sP5_prd(X1,X0,X2)
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X1)
| p(X0) ),
inference(resolution,[status(thm)],[f330,f235]) ).
fof(f1740,plain,
! [X0,X1,X2] :
( ~ sP15_prd(X2,X1,X0)
| p(X2)
| p(X1)
| p(X0) ),
inference(resolution,[status(thm)],[f411,f398]) ).
fof(f1746,plain,
! [X0,X1,X2] :
( sP14_prd(X2,X1)
| ~ p(X0)
| p(X2)
| p(X1)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f1155,f321]) ).
fof(f1749,definition,
! [X1,X2] :
( sQ79_spl
<=> ( sP14_prd(X2,X1)
| p(X2)
| p(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1752,plain,
( sQ79_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f1746,f721,f1749]) ).
fof(f1757,definition,
! [X2] :
( sQ81_spl
<=> ( p(X2)
| ~ mem(X2,bool)
| p(X2) ) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1758,plain,
! [X0] :
( ~ sQ81_spl
| p(X0)
| ~ mem(X0,bool)
| p(X0) ),
inference(component_clause,[status(thm)],[f1757]) ).
fof(f1761,plain,
! [X0] :
( ~ sQ40_spl
| ~ p(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f722]) ).
fof(f1803,plain,
( ~ sQ28_spl
| ~ sQ40_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f601,f1761]) ).
fof(f1839,definition,
( sQ82_spl
<=> p(ap(c_2Ebool_2E_7E,c_2Ebool_2EF)) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1840,plain,
( ~ sQ82_spl
| p(ap(c_2Ebool_2E_7E,c_2Ebool_2EF)) ),
inference(component_clause,[status(thm)],[f1839]) ).
fof(f1841,plain,
( sQ82_spl
| ~ p(ap(c_2Ebool_2E_7E,c_2Ebool_2EF)) ),
inference(component_clause,[status(thm)],[f1839]) ).
fof(f1843,definition,
( sQ83_spl
<=> p(ap(c_2Ebool_2E_7E,c_2Ebool_2ET)) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1845,plain,
( sQ83_spl
| ~ p(ap(c_2Ebool_2E_7E,c_2Ebool_2ET)) ),
inference(component_clause,[status(thm)],[f1843]) ).
fof(f1871,plain,
! [X0] :
( ~ p(X0)
| sP13_prd(c_2Ebool_2EF,X0)
| ~ mem(c_2Ebool_2EF,bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f278,f85]) ).
fof(f1876,definition,
! [X0] :
( sQ86_spl
<=> ( ~ p(X0)
| sP13_prd(c_2Ebool_2EF,X0)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1877,plain,
! [X0] :
( ~ sQ86_spl
| ~ p(X0)
| sP13_prd(c_2Ebool_2EF,X0)
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f1876]) ).
fof(f1879,plain,
( ~ sQ11_spl
| sQ86_spl ),
inference(split_clause,[status(thm)],[f1871,f1876,f484]) ).
fof(f1881,plain,
! [X0] :
( ~ p(X0)
| sP13_prd(X0,c_2Ebool_2EF)
| ~ mem(X0,bool)
| ~ mem(c_2Ebool_2EF,bool) ),
inference(resolution,[status(thm)],[f281,f85]) ).
fof(f1886,definition,
! [X0] :
( sQ88_spl
<=> ( ~ p(X0)
| sP13_prd(X0,c_2Ebool_2EF)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f1889,plain,
( sQ88_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1881,f484,f1886]) ).
fof(f1901,plain,
( ~ sQ82_spl
| ~ sQ56_spl
| p(c_2Ebool_2EF) ),
inference(forward_demodulation,[status(thm)],[f1002,f1840]) ).
fof(f1902,plain,
( ~ sQ82_spl
| ~ sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1901,f85]) ).
fof(f1903,plain,
( ~ sQ82_spl
| ~ sQ56_spl ),
inference(contradiction_clause,[status(thm)],[f1902]) ).
fof(f1910,plain,
( ~ sQ9_spl
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK4_skl),sK2_skl))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK4_skl)) ),
inference(resolution,[status(thm)],[f475,f287]) ).
fof(f1912,plain,
( ~ sQ9_spl
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK2_skl),sK2_skl))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl)) ),
inference(resolution,[status(thm)],[f475,f285]) ).
fof(f1917,definition,
( sQ90_spl
<=> p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f1919,plain,
( sQ90_spl
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK4_skl)) ),
inference(component_clause,[status(thm)],[f1917]) ).
fof(f1920,plain,
( ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ90_spl ),
inference(split_clause,[status(thm)],[f1910,f1917,f453,f474]) ).
fof(f1925,plain,
( ~ sQ9_spl
| ~ sQ28_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1912,f449,f600,f474]) ).
fof(f1926,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f559,f78]) ).
fof(f1927,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f1926]) ).
fof(f1928,plain,
( ~ sQ28_spl
| ~ sQ40_spl ),
inference(contradiction_clause,[status(thm)],[f1803]) ).
fof(f1947,plain,
! [X0] :
( ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),c_2Ebool_2EF))
| ~ mem(c_2Ebool_2EF,bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f102,f85]) ).
fof(f1952,definition,
! [X0] :
( sQ95_spl
<=> ( ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),c_2Ebool_2EF))
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f1953,plain,
! [X0] :
( ~ sQ95_spl
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),c_2Ebool_2EF))
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f1952]) ).
fof(f1955,plain,
( ~ sQ11_spl
| sQ95_spl ),
inference(split_clause,[status(thm)],[f1947,f1952,f484]) ).
fof(f1957,plain,
! [X0] :
( ~ p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),X0))
| ~ mem(X0,bool)
| ~ mem(c_2Ebool_2EF,bool) ),
inference(resolution,[status(thm)],[f101,f85]) ).
fof(f1962,definition,
! [X0] :
( sQ97_spl
<=> ( ~ p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),X0))
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f1965,plain,
( sQ97_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1957,f484,f1962]) ).
fof(f1980,definition,
( sQ99_spl
<=> p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl)),sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f1981,plain,
( ~ sQ99_spl
| p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl)),sK4_skl)) ),
inference(component_clause,[status(thm)],[f1980]) ).
fof(f1982,plain,
( sQ99_spl
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl)),sK4_skl)) ),
inference(component_clause,[status(thm)],[f1980]) ).
fof(f1991,plain,
( sQ99_spl
| p(ap(ap(c_2Eextreal_2Eextreal__le,sK4_skl),ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl)))
| ~ mem(ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl),ty_2Eextreal_2Eextreal)
| ~ mem(sK4_skl,ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[f1982,f199]) ).
fof(f1998,definition,
( sQ101_spl
<=> p(ap(ap(c_2Eextreal_2Eextreal__le,sK4_skl),ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f2001,plain,
( sQ99_spl
| sQ101_spl
| ~ sQ12_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1991,f525,f492,f1998,f1980]) ).
fof(f2140,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)],[f66,f63]) ).
fof(f2255,plain,
! [X0] :
( ~ sQ78_spl
| X0 = ap(c_2Ebool_2E_7E,c_2Ebool_2EF)
| ~ p(ap(c_2Ebool_2E_7E,c_2Ebool_2EF))
| ~ p(X0)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f67,f1650]) ).
fof(f2256,plain,
! [X0] :
( ~ sQ19_spl
| X0 = ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl)
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl))
| ~ p(X0)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f67,f541]) ).
fof(f2260,definition,
! [X0] :
( sQ119_spl
<=> ( X0 = ap(c_2Ebool_2E_7E,c_2Ebool_2EF)
| ~ p(X0)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f2261,plain,
! [X0] :
( ~ sQ119_spl
| X0 = ap(c_2Ebool_2E_7E,c_2Ebool_2EF)
| ~ p(X0)
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f2260]) ).
fof(f2263,plain,
( ~ sQ78_spl
| ~ sQ82_spl
| sQ119_spl ),
inference(split_clause,[status(thm)],[f2255,f2260,f1839,f1649]) ).
fof(f2264,definition,
! [X0] :
( sQ120_spl
<=> ( X0 = ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl)
| ~ p(X0)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f2265,plain,
! [X0] :
( ~ sQ120_spl
| X0 = ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl)
| ~ p(X0)
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f2264]) ).
fof(f2267,plain,
( ~ sQ19_spl
| ~ sQ4_spl
| sQ120_spl ),
inference(split_clause,[status(thm)],[f2256,f2264,f449,f540]) ).
fof(f2275,plain,
( ~ sQ78_spl
| ~ sQ119_spl
| ap(c_2Ebool_2E_7E,c_2Ebool_2EF) = ap(c_2Ebool_2E_7E,c_2Ebool_2EF)
| ~ p(ap(c_2Ebool_2E_7E,c_2Ebool_2EF)) ),
inference(resolution,[status(thm)],[f2261,f1650]) ).
fof(f2276,plain,
( ~ sQ19_spl
| ~ sQ119_spl
| ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl) = ap(c_2Ebool_2E_7E,c_2Ebool_2EF)
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl)) ),
inference(resolution,[status(thm)],[f2261,f541]) ).
fof(f2278,plain,
( ~ sQ119_spl
| c_2Ebool_2ET = ap(c_2Ebool_2E_7E,c_2Ebool_2EF)
| ~ p(c_2Ebool_2ET) ),
inference(resolution,[status(thm)],[f2261,f77]) ).
fof(f2280,definition,
( sQ121_spl
<=> ap(c_2Ebool_2E_7E,c_2Ebool_2EF) = ap(c_2Ebool_2E_7E,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f2283,plain,
( ~ sQ78_spl
| ~ sQ119_spl
| sQ121_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f2275,f1839,f2280,f2260,f1649]) ).
fof(f2284,definition,
( sQ122_spl
<=> ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl) = ap(c_2Ebool_2E_7E,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f2285,plain,
( ~ sQ122_spl
| ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl) = ap(c_2Ebool_2E_7E,c_2Ebool_2EF) ),
inference(component_clause,[status(thm)],[f2284]) ).
fof(f2287,plain,
( ~ sQ19_spl
| ~ sQ119_spl
| sQ122_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f2276,f449,f2284,f2260,f540]) ).
fof(f2288,definition,
( sQ123_spl
<=> c_2Ebool_2ET = ap(c_2Ebool_2E_7E,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f2289,plain,
( ~ sQ123_spl
| c_2Ebool_2ET = ap(c_2Ebool_2E_7E,c_2Ebool_2EF) ),
inference(component_clause,[status(thm)],[f2288]) ).
fof(f2291,plain,
( ~ sQ119_spl
| sQ123_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f2278,f557,f2288,f2260]) ).
fof(f2292,plain,
! [X0] :
( sQ78_spl
| ~ mem(c_2Ebool_2EF,X0)
| ~ mem(c_2Ebool_2E_7E,arr(X0,bool)) ),
inference(resolution,[status(thm)],[f1651,f63]) ).
fof(f2293,plain,
( sQ78_spl
| ~ mem(c_2Ebool_2EF,bool) ),
inference(resolution,[status(thm)],[f2292,f104]) ).
fof(f2294,plain,
( sQ78_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2293,f484,f1649]) ).
fof(f2297,plain,
( ~ sQ19_spl
| ~ sQ120_spl
| ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl) = ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl)
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl)) ),
inference(resolution,[status(thm)],[f2265,f541]) ).
fof(f2299,plain,
( ~ sQ120_spl
| c_2Ebool_2ET = ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl)
| ~ p(c_2Ebool_2ET) ),
inference(resolution,[status(thm)],[f2265,f77]) ).
fof(f2301,plain,
( ~ sQ19_spl
| ~ sQ120_spl
| sQ26_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f2297,f449,f584,f2264,f540]) ).
fof(f2302,definition,
( sQ124_spl
<=> c_2Ebool_2ET = ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f2303,plain,
( ~ sQ124_spl
| c_2Ebool_2ET = ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f2302]) ).
fof(f2305,plain,
( ~ sQ120_spl
| sQ124_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f2299,f557,f2302,f2264]) ).
fof(f2307,plain,
( sQ82_spl
| p(c_2Ebool_2EF)
| ~ mem(c_2Ebool_2EF,bool) ),
inference(resolution,[status(thm)],[f1841,f108]) ).
fof(f2311,plain,
( sQ82_spl
| sQ21_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2307,f484,f550,f1839]) ).
fof(f2326,plain,
! [X0] :
( sQ83_spl
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_7E,c_2Ebool_2ET)),X0))
| ~ mem(X0,bool)
| ~ mem(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),bool) ),
inference(resolution,[status(thm)],[f1845,f101]) ).
fof(f2327,plain,
! [X0] :
( sQ83_spl
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),ap(c_2Ebool_2E_7E,c_2Ebool_2ET)))
| ~ mem(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f1845,f102]) ).
fof(f2330,definition,
( sQ127_spl
<=> mem(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),bool) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f2331,plain,
( ~ sQ127_spl
| mem(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),bool) ),
inference(component_clause,[status(thm)],[f2330]) ).
fof(f2332,plain,
( sQ127_spl
| ~ mem(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),bool) ),
inference(component_clause,[status(thm)],[f2330]) ).
fof(f2333,definition,
! [X0] :
( sQ128_spl
<=> ( ~ p(ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_7E,c_2Ebool_2ET)),X0))
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f2334,plain,
! [X0] :
( ~ sQ128_spl
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_7E,c_2Ebool_2ET)),X0))
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f2333]) ).
fof(f2336,plain,
( sQ83_spl
| sQ128_spl
| ~ sQ127_spl ),
inference(split_clause,[status(thm)],[f2326,f2330,f2333,f1843]) ).
fof(f2337,definition,
! [X0] :
( sQ129_spl
<=> ( ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),ap(c_2Ebool_2E_7E,c_2Ebool_2ET)))
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f2340,plain,
( sQ83_spl
| ~ sQ127_spl
| sQ129_spl ),
inference(split_clause,[status(thm)],[f2327,f2337,f2330,f1843]) ).
fof(f2374,plain,
! [X0] :
( ~ sQ128_spl
| ~ sQ57_spl
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),X0))
| ~ mem(X0,bool) ),
inference(forward_demodulation,[status(thm)],[f1006,f2334]) ).
fof(f2377,plain,
( ~ sQ10_spl
| c_2Ebool_2EF = c_2Ebool_2EF
| p(c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f482,f84]) ).
fof(f2382,plain,
( ~ sQ10_spl
| sQ47_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f2377,f550,f809,f481]) ).
fof(f2385,plain,
! [X0] :
( ~ sQ81_spl
| ~ mem(X0,bool)
| p(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1758]) ).
fof(f2386,plain,
! [X0] :
( ~ sQ74_spl
| ~ p(X0)
| ~ mem(X0,bool) ),
inference(duplicate_literals_removal,[status(thm)],[f1540]) ).
fof(f2387,plain,
( ~ sQ122_spl
| ~ sQ123_spl
| ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl) = c_2Ebool_2ET ),
inference(forward_demodulation,[status(thm)],[f2289,f2285]) ).
fof(f2395,plain,
( ~ sQ81_spl
| p(c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f2385,f84]) ).
fof(f2402,plain,
( ~ sQ81_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2395,f85]) ).
fof(f2403,plain,
~ sQ81_spl,
inference(contradiction_clause,[status(thm)],[f2402]) ).
fof(f2408,plain,
( ~ sQ74_spl
| ~ p(c_2Ebool_2ET) ),
inference(resolution,[status(thm)],[f2386,f77]) ).
fof(f2410,plain,
( ~ sQ74_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f2408,f557,f1539]) ).
fof(f2420,plain,
! [X0,X1] :
( ~ p(X0)
| ~ p(X1)
| ~ sP16_prd(X0,X1,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f405,f85]) ).
fof(f2422,plain,
! [X0,X1] :
( ~ p(X1)
| ~ p(X0)
| ~ sP15_prd(X0,X1,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f399,f85]) ).
fof(f2450,plain,
! [X0] :
( sQ5_spl
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X0),sK2_skl))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK4_skl),X0))
| ~ mem(sK2_skl,ty_2Eextreal_2Eextreal)
| ~ mem(X0,ty_2Eextreal_2Eextreal)
| ~ mem(sK4_skl,ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[f455,f197]) ).
fof(f2455,plain,
( sQ5_spl
| sP4_prd(ap(ap(c_2Eextreal_2Eextreal__le,sK4_skl),sK2_skl)) ),
inference(resolution,[status(thm)],[f455,f316]) ).
fof(f2464,definition,
! [X0] :
( sQ135_spl
<=> ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X0),sK2_skl))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK4_skl),X0))
| ~ mem(X0,ty_2Eextreal_2Eextreal) ) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f2465,plain,
! [X0] :
( ~ sQ135_spl
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X0),sK2_skl))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK4_skl),X0))
| ~ mem(X0,ty_2Eextreal_2Eextreal) ),
inference(component_clause,[status(thm)],[f2464]) ).
fof(f2467,plain,
( sQ5_spl
| ~ sQ6_spl
| sQ135_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f2450,f525,f2464,f463,f453]) ).
fof(f2482,plain,
! [X0,X1,X2] :
( sP14_prd(X1,X2)
| ~ p(X0)
| ~ sP14_prd(X1,X2)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f323,f321]) ).
fof(f2483,plain,
( sQ69_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f2482,f721,f1159]) ).
fof(f2489,plain,
! [X0,X1,X2] :
( ~ p(X0)
| p(X1)
| p(X2)
| sP5_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f324,f391]) ).
fof(f2490,plain,
! [X0,X1,X2] :
( p(X0)
| ~ p(X1)
| p(X2)
| sP5_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f324,f390]) ).
fof(f2528,plain,
! [X0,X1] :
( ~ sP8_prd(X1,X0,c_2Ebool_2EF)
| ~ p(X1)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f2420,f346]) ).
fof(f2533,plain,
! [X0,X1] :
( ~ sP6_prd(X0,X1,c_2Ebool_2EF)
| ~ p(X1)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f2422,f329]) ).
fof(f2545,plain,
! [X0,X1] :
( ~ sP7_prd(X1,X0,c_2Ebool_2EF)
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| ~ mem(c_2Ebool_2EF,bool)
| ~ p(X1)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f2528,f246]) ).
fof(f2546,definition,
! [X0,X1] :
( sQ139_spl
<=> ( ~ sP7_prd(X1,X0,c_2Ebool_2EF)
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| ~ p(X1)
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f2549,plain,
( ~ sQ11_spl
| sQ139_spl ),
inference(split_clause,[status(thm)],[f2545,f2546,f484]) ).
fof(f2553,plain,
! [X0,X1] :
( ~ sP5_prd(X0,X1,c_2Ebool_2EF)
| ~ mem(X0,bool)
| ~ mem(X1,bool)
| ~ mem(c_2Ebool_2EF,bool)
| ~ p(X1)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f2533,f235]) ).
fof(f2557,definition,
! [X0,X1] :
( sQ140_spl
<=> ( ~ sP5_prd(X0,X1,c_2Ebool_2EF)
| ~ mem(X0,bool)
| ~ mem(X1,bool)
| ~ p(X1)
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f2560,plain,
( ~ sQ11_spl
| sQ140_spl ),
inference(split_clause,[status(thm)],[f2553,f2557,f484]) ).
fof(f2567,plain,
! [X0,X1,X2,X3,X4] :
( X3 = X4
| ~ mem(X4,X2)
| ~ mem(X3,X2)
| ~ ne(X2)
| ~ p(X0)
| ~ p(X1)
| ~ sP7_prd(X0,X1,ap(ap(c_2Emin_2E_3D(X2),X3),X4)) ),
inference(resolution,[status(thm)],[f338,f113]) ).
fof(f2571,plain,
! [X0,X1] :
( ~ p(X1)
| ~ p(X0)
| ~ sP6_prd(X0,c_2Ebool_2EF,X1) ),
inference(resolution,[status(thm)],[f330,f85]) ).
fof(f2614,plain,
! [X0,X1] :
( ~ sP5_prd(X0,c_2Ebool_2EF,X1)
| ~ mem(X0,bool)
| ~ mem(c_2Ebool_2EF,bool)
| ~ mem(X1,bool)
| ~ p(X1)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f2571,f235]) ).
fof(f2622,definition,
! [X0,X1] :
( sQ142_spl
<=> ( ~ sP5_prd(X0,c_2Ebool_2EF,X1)
| ~ mem(X0,bool)
| ~ mem(X1,bool)
| ~ p(X1)
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f2625,plain,
( ~ sQ11_spl
| sQ142_spl ),
inference(split_clause,[status(thm)],[f2614,f2622,f484]) ).
fof(f2630,plain,
! [X0,X1] :
( ~ p(X0)
| ~ p(X1)
| p(c_2Ebool_2EF)
| ~ sP16_prd(X0,X1,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f349,f2528]) ).
fof(f2632,definition,
! [X0,X1] :
( sQ143_spl
<=> ( ~ p(X0)
| ~ p(X1)
| ~ sP16_prd(X0,X1,c_2Ebool_2EF) ) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f2635,plain,
( sQ21_spl
| sQ143_spl ),
inference(split_clause,[status(thm)],[f2630,f2632,f550]) ).
fof(f2637,plain,
! [X0,X1] :
( ~ p(X1)
| ~ p(X0)
| p(c_2Ebool_2EF)
| ~ sP15_prd(X0,X1,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f333,f2533]) ).
fof(f2638,definition,
! [X0,X1] :
( sQ144_spl
<=> ( ~ p(X1)
| ~ p(X0)
| ~ sP15_prd(X0,X1,c_2Ebool_2EF) ) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f2641,plain,
( sQ21_spl
| sQ144_spl ),
inference(split_clause,[status(thm)],[f2637,f2638,f550]) ).
fof(f2644,plain,
! [X0] :
( ~ sQ86_spl
| p(c_2Ebool_2EF)
| p(X0)
| ~ p(X0)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f1877,f385]) ).
fof(f2646,plain,
( ~ sQ86_spl
| sQ21_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f2644,f415,f550,f1876]) ).
fof(f2655,plain,
! [X0,X1,X2] :
( ~ sP14_prd(X2,X1)
| p(X0)
| ~ p(X2)
| ~ sP6_prd(X2,X1,X0)
| ~ mem(X2,bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f237,f322]) ).
fof(f2656,plain,
! [X0,X1,X2] :
( sP14_prd(X2,X1)
| ~ p(X0)
| ~ p(X2)
| ~ sP6_prd(X2,X1,X0)
| ~ mem(X2,bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f237,f321]) ).
fof(f2688,plain,
( ~ sQ12_spl
| ~ sQ135_spl
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl)),sK2_skl))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK4_skl),ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl))) ),
inference(resolution,[status(thm)],[f2465,f493]) ).
fof(f2692,plain,
( ~ sQ135_spl
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK2_skl),sK2_skl))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK4_skl),sK2_skl)) ),
inference(resolution,[status(thm)],[f2465,f285]) ).
fof(f2693,plain,
( ~ sQ12_spl
| ~ sQ135_spl
| ~ sQ3_spl
| ~ sQ101_spl ),
inference(split_clause,[status(thm)],[f2688,f1998,f446,f2464,f492]) ).
fof(f2702,plain,
( ~ sQ135_spl
| ~ sQ28_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2692,f453,f600,f2464]) ).
fof(f2709,plain,
( ~ sQ18_spl
| ~ sQ27_spl
| sQ90_spl
| ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK4_skl) = c_2Ebool_2EF
| ~ mem(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK4_skl),bool) ),
inference(resolution,[status(thm)],[f1919,f804]) ).
fof(f2723,definition,
( sQ149_spl
<=> mem(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK4_skl),bool) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f2724,plain,
( ~ sQ149_spl
| mem(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK4_skl),bool) ),
inference(component_clause,[status(thm)],[f2723]) ).
fof(f2725,plain,
( sQ149_spl
| ~ mem(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK4_skl),bool) ),
inference(component_clause,[status(thm)],[f2723]) ).
fof(f2726,definition,
( sQ150_spl
<=> ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK4_skl) = c_2Ebool_2EF ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f2727,plain,
( ~ sQ150_spl
| ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK4_skl) = c_2Ebool_2EF ),
inference(component_clause,[status(thm)],[f2726]) ).
fof(f2729,plain,
( ~ sQ18_spl
| ~ sQ27_spl
| sQ90_spl
| sQ150_spl
| ~ sQ149_spl ),
inference(split_clause,[status(thm)],[f2709,f2723,f2726,f1917,f588,f537]) ).
fof(f2738,plain,
! [X0,X1,X2] :
( sP14_prd(X2,X1)
| ~ p(X0)
| ~ p(X2)
| ~ p(X1)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f1156,f321]) ).
fof(f2743,definition,
! [X1,X2] :
( sQ152_spl
<=> ( sP14_prd(X2,X1)
| ~ p(X2)
| ~ p(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f2746,plain,
( sQ152_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f2738,f721,f2743]) ).
fof(f2753,plain,
! [X0,X1] :
( ~ p(X0)
| ~ p(X1)
| ~ sP5_prd(c_2Ebool_2EF,X1,X0)
| ~ mem(c_2Ebool_2EF,bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f236,f85]) ).
fof(f2758,definition,
! [X0,X1] :
( sQ154_spl
<=> ( ~ p(X0)
| ~ p(X1)
| ~ sP5_prd(c_2Ebool_2EF,X1,X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f2759,plain,
! [X0,X1] :
( ~ sQ154_spl
| ~ p(X0)
| ~ p(X1)
| ~ sP5_prd(c_2Ebool_2EF,X1,X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f2758]) ).
fof(f2761,plain,
( ~ sQ11_spl
| sQ154_spl ),
inference(split_clause,[status(thm)],[f2753,f2758,f484]) ).
fof(f2762,plain,
! [X0,X1,X2,X3] :
( ~ ne(X2)
| ~ ne(X1)
| p(ap(X0,X3))
| ~ mem(X3,arr(X1,X2))
| ~ p(ap(c_2Ebool_2E_21(arr(X1,X2)),X0))
| ~ mem(X0,arr(arr(X1,X2),bool)) ),
inference(resolution,[status(thm)],[f120,f61]) ).
fof(f2764,plain,
! [X0,X1] :
( p(ap(X0,X1))
| ~ mem(X1,bool)
| ~ p(ap(c_2Ebool_2E_21(bool),X0))
| ~ mem(X0,arr(bool,bool)) ),
inference(resolution,[status(thm)],[f120,f58]) ).
fof(f2766,plain,
! [X0] :
( sQ149_spl
| ~ mem(sK4_skl,X0)
| ~ mem(ap(c_2Eextreal_2Eextreal__le,sK3_skl),arr(X0,bool)) ),
inference(resolution,[status(thm)],[f2725,f63]) ).
fof(f2773,plain,
! [X0,X1] :
( sQ149_spl
| ~ mem(sK3_skl,X1)
| ~ mem(c_2Eextreal_2Eextreal__le,arr(X1,arr(X0,bool)))
| ~ mem(sK4_skl,X0) ),
inference(resolution,[status(thm)],[f2766,f63]) ).
fof(f2780,definition,
( sQ155_spl
<=> sP4_prd(c_2Ebool_2ET) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f2813,plain,
! [X0] :
( ~ sP15_prd(c_2Ebool_2EF,c_2Ebool_2EF,X0)
| p(X0) ),
inference(resolution,[status(thm)],[f1740,f85]) ).
fof(f2814,plain,
! [X0,X1] :
( ~ sP15_prd(X1,c_2Ebool_2EF,X0)
| p(X1)
| p(X0) ),
inference(resolution,[status(thm)],[f1740,f85]) ).
fof(f2817,plain,
! [X0,X1] :
( ~ sP15_prd(c_2Ebool_2EF,X1,X0)
| p(X1)
| p(X0) ),
inference(resolution,[status(thm)],[f1740,f85]) ).
fof(f2820,plain,
~ sP15_prd(c_2Ebool_2EF,c_2Ebool_2EF,c_2Ebool_2EF),
inference(resolution,[status(thm)],[f2813,f85]) ).
fof(f2821,plain,
( p(c_2Ebool_2EF)
| ~ sP17_prd(c_2Ebool_2EF,c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f2820,f401]) ).
fof(f2824,plain,
~ sP6_prd(c_2Ebool_2EF,c_2Ebool_2EF,c_2Ebool_2EF),
inference(resolution,[status(thm)],[f2820,f329]) ).
fof(f2825,definition,
( sQ157_spl
<=> sP17_prd(c_2Ebool_2EF,c_2Ebool_2EF,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f2828,plain,
( sQ21_spl
| ~ sQ157_spl ),
inference(split_clause,[status(thm)],[f2821,f2825,f550]) ).
fof(f2830,plain,
( p(c_2Ebool_2EF)
| ~ sP15_prd(c_2Ebool_2EF,c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f2824,f332]) ).
fof(f2835,plain,
( ~ p(c_2Ebool_2EF)
| ~ p(c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f2824,f1574]) ).
fof(f2837,plain,
( ~ sP5_prd(c_2Ebool_2EF,c_2Ebool_2EF,c_2Ebool_2EF)
| ~ mem(c_2Ebool_2EF,bool)
| ~ mem(c_2Ebool_2EF,bool)
| ~ mem(c_2Ebool_2EF,bool) ),
inference(resolution,[status(thm)],[f2824,f235]) ).
fof(f2838,definition,
( sQ158_spl
<=> sP15_prd(c_2Ebool_2EF,c_2Ebool_2EF,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f2841,plain,
( sQ21_spl
| ~ sQ158_spl ),
inference(split_clause,[status(thm)],[f2830,f2838,f550]) ).
fof(f2846,plain,
~ sQ21_spl,
inference(split_clause,[status(thm)],[f2835,f550]) ).
fof(f2848,definition,
( sQ159_spl
<=> sP5_prd(c_2Ebool_2EF,c_2Ebool_2EF,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f2850,plain,
( sQ159_spl
| ~ sP5_prd(c_2Ebool_2EF,c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(component_clause,[status(thm)],[f2848]) ).
fof(f2851,plain,
( ~ sQ159_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2837,f484,f2848]) ).
fof(f2862,definition,
( sQ160_spl
<=> sP6_prd(c_2Ebool_2EF,c_2Ebool_2EF,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f2875,plain,
! [X0,X1] :
( p(X0)
| p(X1)
| ~ sP17_prd(X0,X1,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f411,f85]) ).
fof(f2878,plain,
! [X0,X1] :
( ~ sP12_prd(X1,c_2Ebool_2EF,X0)
| sP11_prd(X1,c_2Ebool_2EF,X0)
| ~ mem(X1,bool)
| ~ mem(c_2Ebool_2EF,bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f269,f85]) ).
fof(f2883,definition,
! [X0,X1] :
( sQ163_spl
<=> ( ~ sP12_prd(X1,c_2Ebool_2EF,X0)
| sP11_prd(X1,c_2Ebool_2EF,X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f2884,plain,
! [X0,X1] :
( ~ sQ163_spl
| ~ sP12_prd(X1,c_2Ebool_2EF,X0)
| sP11_prd(X1,c_2Ebool_2EF,X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f2883]) ).
fof(f2886,plain,
( ~ sQ11_spl
| sQ163_spl ),
inference(split_clause,[status(thm)],[f2878,f2883,f484]) ).
fof(f2975,plain,
! [X0] :
( p(X0)
| ~ sP17_prd(X0,c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f2875,f85]) ).
fof(f2993,plain,
! [X0,X1] :
( ~ p(X0)
| p(X1)
| sP5_prd(X0,X1,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f2489,f85]) ).
fof(f2996,plain,
! [X0] :
( ~ p(X0)
| sP5_prd(X0,c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f2993,f85]) ).
fof(f2999,plain,
! [X0,X1] :
( ~ sP10_prd(X1,X0,c_2Ebool_2EF)
| sP9_prd(X1,X0,c_2Ebool_2EF)
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| ~ mem(c_2Ebool_2EF,bool) ),
inference(resolution,[status(thm)],[f260,f85]) ).
fof(f3004,definition,
! [X0,X1] :
( sQ171_spl
<=> ( ~ sP10_prd(X1,X0,c_2Ebool_2EF)
| sP9_prd(X1,X0,c_2Ebool_2EF)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f3005,plain,
! [X0,X1] :
( ~ sQ171_spl
| ~ sP10_prd(X1,X0,c_2Ebool_2EF)
| sP9_prd(X1,X0,c_2Ebool_2EF)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f3004]) ).
fof(f3007,plain,
( sQ171_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2999,f484,f3004]) ).
fof(f3010,plain,
! [X0,X1] :
( ~ sP8_prd(X1,X0,c_2Ebool_2EF)
| sP7_prd(X1,X0,c_2Ebool_2EF)
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| ~ mem(c_2Ebool_2EF,bool) ),
inference(resolution,[status(thm)],[f249,f85]) ).
fof(f3015,definition,
! [X0,X1] :
( sQ173_spl
<=> ( ~ sP8_prd(X1,X0,c_2Ebool_2EF)
| sP7_prd(X1,X0,c_2Ebool_2EF)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f3016,plain,
! [X0,X1] :
( ~ sQ173_spl
| ~ sP8_prd(X1,X0,c_2Ebool_2EF)
| sP7_prd(X1,X0,c_2Ebool_2EF)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f3015]) ).
fof(f3018,plain,
( sQ173_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3010,f484,f3015]) ).
fof(f3021,plain,
! [X0,X1] :
( ~ sP6_prd(X1,X0,c_2Ebool_2EF)
| sP5_prd(X1,X0,c_2Ebool_2EF)
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| ~ mem(c_2Ebool_2EF,bool) ),
inference(resolution,[status(thm)],[f239,f85]) ).
fof(f3026,definition,
! [X0,X1] :
( sQ175_spl
<=> ( ~ sP6_prd(X1,X0,c_2Ebool_2EF)
| sP5_prd(X1,X0,c_2Ebool_2EF)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f3029,plain,
( sQ175_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3021,f484,f3026]) ).
fof(f3107,plain,
! [X0] :
( ~ sP14_prd(X0,c_2Ebool_2EF)
| p(c_2Ebool_2EF)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f2996,f322]) ).
fof(f3109,definition,
! [X0] :
( sQ181_spl
<=> ( ~ sP14_prd(X0,c_2Ebool_2EF)
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f3112,plain,
( sQ21_spl
| sQ181_spl ),
inference(split_clause,[status(thm)],[f3107,f3109,f550]) ).
fof(f3127,plain,
! [X0,X1] :
( p(X0)
| ~ p(X1)
| sP5_prd(X0,X1,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f2490,f85]) ).
fof(f3130,plain,
! [X0] :
( ~ p(X0)
| sP5_prd(c_2Ebool_2EF,X0,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f3127,f85]) ).
fof(f3132,plain,
! [X0] :
( ~ sP14_prd(c_2Ebool_2EF,X0)
| p(c_2Ebool_2EF)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f3130,f322]) ).
fof(f3134,definition,
! [X0] :
( sQ183_spl
<=> ( ~ sP14_prd(c_2Ebool_2EF,X0)
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f3137,plain,
( sQ21_spl
| sQ183_spl ),
inference(split_clause,[status(thm)],[f3132,f3134,f550]) ).
fof(f3152,plain,
( ~ sQ57_spl
| sP4_prd(c_2Ebool_2EF)
| ~ p(c_2Ebool_2ET)
| ~ mem(c_2Ebool_2ET,bool) ),
inference(paramodulation,[status(thm)],[f1006,f973]) ).
fof(f3155,plain,
( ~ sQ57_spl
| sQ46_spl
| ~ sQ23_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f3152,f988,f557,f795,f1005]) ).
fof(f3159,plain,
! [X0,X1] :
( ~ sP6_prd(X1,c_2Ebool_2EF,X0)
| sP5_prd(X1,c_2Ebool_2EF,X0)
| ~ mem(X1,bool)
| ~ mem(c_2Ebool_2EF,bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f238,f85]) ).
fof(f3164,definition,
! [X0,X1] :
( sQ186_spl
<=> ( ~ sP6_prd(X1,c_2Ebool_2EF,X0)
| sP5_prd(X1,c_2Ebool_2EF,X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f3165,plain,
! [X0,X1] :
( ~ sQ186_spl
| ~ sP6_prd(X1,c_2Ebool_2EF,X0)
| sP5_prd(X1,c_2Ebool_2EF,X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f3164]) ).
fof(f3167,plain,
( ~ sQ11_spl
| sQ186_spl ),
inference(split_clause,[status(thm)],[f3159,f3164,f484]) ).
fof(f3344,plain,
( ~ p(c_2Ebool_2ET)
| ~ p(ap(c_2Ebool_2E_7E,c_2Ebool_2ET)) ),
inference(resolution,[status(thm)],[f107,f77]) ).
fof(f3346,plain,
( ~ sQ23_spl
| ~ sQ83_spl ),
inference(split_clause,[status(thm)],[f3344,f1843,f557]) ).
fof(f3348,plain,
! [X0] :
( sQ83_spl
| X0 = ap(c_2Ebool_2E_7E,c_2Ebool_2ET)
| p(X0)
| ~ mem(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f1845,f66]) ).
fof(f3349,plain,
! [X0,X1] :
( sQ83_spl
| ~ sP6_prd(X1,ap(c_2Ebool_2E_7E,c_2Ebool_2ET),X0)
| sP5_prd(X1,ap(c_2Ebool_2E_7E,c_2Ebool_2ET),X0)
| ~ mem(X1,bool)
| ~ mem(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f1845,f238]) ).
fof(f3351,plain,
! [X0] :
( sQ83_spl
| ~ p(X0)
| sP5_prd(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),X0,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f1845,f3127]) ).
fof(f3357,plain,
! [X0,X1] :
( sQ83_spl
| ~ sP6_prd(X1,X0,ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| sP5_prd(X1,X0,ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| ~ mem(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),bool) ),
inference(resolution,[status(thm)],[f1845,f239]) ).
fof(f3358,plain,
! [X0,X1] :
( sQ83_spl
| ~ sP8_prd(X1,X0,ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| sP7_prd(X1,X0,ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| ~ mem(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),bool) ),
inference(resolution,[status(thm)],[f1845,f249]) ).
fof(f3359,plain,
! [X0,X1] :
( sQ83_spl
| ~ sP10_prd(X1,X0,ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| sP9_prd(X1,X0,ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| ~ mem(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),bool) ),
inference(resolution,[status(thm)],[f1845,f260]) ).
fof(f3360,plain,
! [X0] :
( sQ83_spl
| ~ p(X0)
| sP5_prd(X0,ap(c_2Ebool_2E_7E,c_2Ebool_2ET),c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f1845,f2993]) ).
fof(f3364,plain,
( sQ83_spl
| ~ sP17_prd(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f1845,f2975]) ).
fof(f3365,plain,
! [X0] :
( sQ83_spl
| p(X0)
| ~ sP17_prd(X0,ap(c_2Ebool_2E_7E,c_2Ebool_2ET),c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f1845,f2875]) ).
fof(f3366,plain,
! [X0] :
( sQ83_spl
| ~ sP15_prd(c_2Ebool_2EF,ap(c_2Ebool_2E_7E,c_2Ebool_2ET),X0)
| p(X0) ),
inference(resolution,[status(thm)],[f1845,f2817]) ).
fof(f3369,plain,
! [X0,X1] :
( sQ83_spl
| ~ sP12_prd(X1,ap(c_2Ebool_2E_7E,c_2Ebool_2ET),X0)
| sP11_prd(X1,ap(c_2Ebool_2E_7E,c_2Ebool_2ET),X0)
| ~ mem(X1,bool)
| ~ mem(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f1845,f269]) ).
fof(f3371,plain,
! [X0] :
( sQ83_spl
| ~ sP15_prd(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),c_2Ebool_2EF,X0)
| p(X0) ),
inference(resolution,[status(thm)],[f1845,f2814]) ).
fof(f3372,plain,
( sQ83_spl
| ~ sP15_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(c_2Ebool_2E_7E,c_2Ebool_2ET)) ),
inference(resolution,[status(thm)],[f1845,f2813]) ).
fof(f3379,plain,
! [X0,X1] :
( sQ83_spl
| ~ p(X0)
| ~ p(X1)
| ~ sP5_prd(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),X1,X0)
| ~ mem(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f1845,f236]) ).
fof(f3388,definition,
! [X0] :
( sQ204_spl
<=> ( X0 = ap(c_2Ebool_2E_7E,c_2Ebool_2ET)
| p(X0)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f3391,plain,
( sQ83_spl
| ~ sQ127_spl
| sQ204_spl ),
inference(split_clause,[status(thm)],[f3348,f3388,f2330,f1843]) ).
fof(f3392,definition,
! [X0,X1] :
( sQ205_spl
<=> ( ~ sP6_prd(X1,ap(c_2Ebool_2E_7E,c_2Ebool_2ET),X0)
| sP5_prd(X1,ap(c_2Ebool_2E_7E,c_2Ebool_2ET),X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition]) ).
fof(f3395,plain,
( sQ83_spl
| ~ sQ127_spl
| sQ205_spl ),
inference(split_clause,[status(thm)],[f3349,f3392,f2330,f1843]) ).
fof(f3396,definition,
! [X0,X1] :
( sQ206_spl
<=> ( ~ sP6_prd(X1,X0,ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| sP5_prd(X1,X0,ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f3399,plain,
( sQ83_spl
| sQ206_spl
| ~ sQ127_spl ),
inference(split_clause,[status(thm)],[f3357,f2330,f3396,f1843]) ).
fof(f3400,definition,
! [X0,X1] :
( sQ207_spl
<=> ( ~ sP8_prd(X1,X0,ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| sP7_prd(X1,X0,ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f3403,plain,
( sQ83_spl
| sQ207_spl
| ~ sQ127_spl ),
inference(split_clause,[status(thm)],[f3358,f2330,f3400,f1843]) ).
fof(f3404,definition,
! [X0,X1] :
( sQ208_spl
<=> ( ~ sP10_prd(X1,X0,ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| sP9_prd(X1,X0,ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition]) ).
fof(f3407,plain,
( sQ83_spl
| sQ208_spl
| ~ sQ127_spl ),
inference(split_clause,[status(thm)],[f3359,f2330,f3404,f1843]) ).
fof(f3408,definition,
! [X0,X1] :
( sQ209_spl
<=> ( ~ sP12_prd(X1,ap(c_2Ebool_2E_7E,c_2Ebool_2ET),X0)
| sP11_prd(X1,ap(c_2Ebool_2E_7E,c_2Ebool_2ET),X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f3411,plain,
( sQ83_spl
| ~ sQ127_spl
| sQ209_spl ),
inference(split_clause,[status(thm)],[f3369,f3408,f2330,f1843]) ).
fof(f3412,definition,
! [X0,X1] :
( sQ210_spl
<=> ( ~ p(X0)
| ~ p(X1)
| ~ sP5_prd(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),X1,X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f3415,plain,
( sQ83_spl
| ~ sQ127_spl
| sQ210_spl ),
inference(split_clause,[status(thm)],[f3379,f3412,f2330,f1843]) ).
fof(f3417,plain,
! [X0] :
( sQ127_spl
| ~ mem(c_2Ebool_2ET,X0)
| ~ mem(c_2Ebool_2E_7E,arr(X0,bool)) ),
inference(resolution,[status(thm)],[f2332,f63]) ).
fof(f3424,plain,
! [X0] :
( p(c_2Ebool_2EF)
| ~ p(X0)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),c_2Ebool_2EF))
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f89,f84]) ).
fof(f3426,plain,
! [X0,X1,X2,X3] :
( ~ mem(X2,X3)
| ~ mem(X1,arr(X3,bool))
| p(ap(X1,X2))
| ~ p(X0)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),ap(X1,X2)))
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f89,f63]) ).
fof(f3428,definition,
! [X0] :
( sQ211_spl
<=> ( ~ p(X0)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),c_2Ebool_2EF))
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f3429,plain,
! [X0] :
( ~ sQ211_spl
| ~ p(X0)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),c_2Ebool_2EF))
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f3428]) ).
fof(f3431,plain,
( sQ21_spl
| sQ211_spl ),
inference(split_clause,[status(thm)],[f3424,f3428,f550]) ).
fof(f3436,plain,
! [X0] :
( p(c_2Ebool_2EF)
| p(X0)
| ~ p(ap(ap(c_2Ebool_2E_5C_2F,X0),c_2Ebool_2EF))
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f95,f84]) ).
fof(f3438,plain,
! [X0,X1,X2,X3] :
( ~ mem(X2,X3)
| ~ mem(X1,arr(X3,bool))
| p(ap(X1,X2))
| p(X0)
| ~ p(ap(ap(c_2Ebool_2E_5C_2F,X0),ap(X1,X2)))
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f95,f63]) ).
fof(f3440,definition,
! [X0] :
( sQ213_spl
<=> ( p(X0)
| ~ p(ap(ap(c_2Ebool_2E_5C_2F,X0),c_2Ebool_2EF))
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition]) ).
fof(f3441,plain,
! [X0] :
( ~ sQ213_spl
| p(X0)
| ~ p(ap(ap(c_2Ebool_2E_5C_2F,X0),c_2Ebool_2EF))
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f3440]) ).
fof(f3443,plain,
( sQ21_spl
| sQ213_spl ),
inference(split_clause,[status(thm)],[f3436,f3440,f550]) ).
fof(f3448,plain,
( ~ sQ124_spl
| ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK2_skl) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),sK2_skl),sK3_skl)
| ~ mem(sK3_skl,ty_2Eextreal_2Eextreal) ),
inference(paramodulation,[status(thm)],[f2303,f1313]) ).
fof(f3450,plain,
! [X0] :
( ~ sQ124_spl
| ~ sP4_prd(c_2Ebool_2ET)
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X0),sK2_skl))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),X0))
| ~ mem(sK2_skl,ty_2Eextreal_2Eextreal)
| ~ mem(X0,ty_2Eextreal_2Eextreal)
| ~ mem(sK3_skl,ty_2Eextreal_2Eextreal) ),
inference(paramodulation,[status(thm)],[f2303,f1251]) ).
fof(f3454,definition,
( sQ215_spl
<=> ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK2_skl) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),sK2_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f3457,plain,
( ~ sQ124_spl
| sQ215_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3448,f466,f3454,f2302]) ).
fof(f3459,plain,
( ~ sQ124_spl
| ~ sQ155_spl
| ~ sQ6_spl
| sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3450,f466,f474,f463,f2780,f2302]) ).
fof(f3505,plain,
( sQ3_spl
| sP4_prd(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl)),sK2_skl)) ),
inference(resolution,[status(thm)],[f448,f316]) ).
fof(f3544,plain,
( sQ83_spl
| ~ sP15_prd(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f3364,f398]) ).
fof(f3545,plain,
( sQ83_spl
| p(c_2Ebool_2EF)
| ~ sP17_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(c_2Ebool_2E_7E,c_2Ebool_2ET)) ),
inference(resolution,[status(thm)],[f3372,f401]) ).
fof(f3548,plain,
( sQ83_spl
| ~ sP6_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(c_2Ebool_2E_7E,c_2Ebool_2ET)) ),
inference(resolution,[status(thm)],[f3372,f329]) ).
fof(f3549,definition,
( sQ222_spl
<=> sP17_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(c_2Ebool_2E_7E,c_2Ebool_2ET)) ),
introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition]) ).
fof(f3552,plain,
( sQ83_spl
| sQ21_spl
| ~ sQ222_spl ),
inference(split_clause,[status(thm)],[f3545,f3549,f550,f1843]) ).
fof(f3555,plain,
( sQ83_spl
| p(ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| ~ sP17_prd(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f3544,f401]) ).
fof(f3558,plain,
( sQ83_spl
| ~ sP6_prd(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f3544,f329]) ).
fof(f3559,definition,
( sQ223_spl
<=> sP17_prd(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),c_2Ebool_2EF,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f3562,plain,
( sQ83_spl
| ~ sQ223_spl ),
inference(split_clause,[status(thm)],[f3555,f3559,f1843]) ).
fof(f3566,plain,
( sQ83_spl
| p(ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| ~ sP15_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(c_2Ebool_2E_7E,c_2Ebool_2ET)) ),
inference(resolution,[status(thm)],[f3548,f333]) ).
fof(f3572,plain,
( sQ83_spl
| ~ sP5_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| ~ mem(c_2Ebool_2EF,bool)
| ~ mem(c_2Ebool_2EF,bool)
| ~ mem(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),bool) ),
inference(resolution,[status(thm)],[f3548,f235]) ).
fof(f3573,definition,
( sQ224_spl
<=> sP15_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(c_2Ebool_2E_7E,c_2Ebool_2ET)) ),
introduced(definition,[new_symbols(definition,[sQ224_spl])],[split_symbol_definition]) ).
fof(f3577,plain,
( sQ83_spl
| ~ sQ224_spl ),
inference(split_clause,[status(thm)],[f3566,f3573,f1843]) ).
fof(f3583,definition,
( sQ225_spl
<=> sP5_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(c_2Ebool_2E_7E,c_2Ebool_2ET)) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f3586,plain,
( sQ83_spl
| ~ sQ225_spl
| ~ sQ11_spl
| ~ sQ127_spl ),
inference(split_clause,[status(thm)],[f3572,f2330,f484,f3583,f1843]) ).
fof(f3591,plain,
( sQ83_spl
| p(ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| ~ sP15_prd(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f3558,f332]) ).
fof(f3598,plain,
( sQ83_spl
| ~ sP5_prd(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),c_2Ebool_2EF,c_2Ebool_2EF)
| ~ mem(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),bool)
| ~ mem(c_2Ebool_2EF,bool)
| ~ mem(c_2Ebool_2EF,bool) ),
inference(resolution,[status(thm)],[f3558,f235]) ).
fof(f3599,definition,
( sQ226_spl
<=> sP15_prd(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),c_2Ebool_2EF,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f3602,plain,
( sQ83_spl
| ~ sQ226_spl ),
inference(split_clause,[status(thm)],[f3591,f3599,f1843]) ).
fof(f3609,definition,
( sQ227_spl
<=> sP5_prd(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),c_2Ebool_2EF,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f3612,plain,
( sQ83_spl
| ~ sQ227_spl
| ~ sQ127_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3598,f484,f2330,f3609,f1843]) ).
fof(f3618,plain,
! [X0] :
( sQ83_spl
| ~ sP14_prd(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),X0)
| p(c_2Ebool_2EF)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f3351,f322]) ).
fof(f3620,definition,
! [X0] :
( sQ228_spl
<=> ( ~ sP14_prd(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),X0)
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f3623,plain,
( sQ83_spl
| sQ21_spl
| sQ228_spl ),
inference(split_clause,[status(thm)],[f3618,f3620,f550,f1843]) ).
fof(f3637,plain,
! [X0] :
( sQ83_spl
| ~ sP14_prd(X0,ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| p(c_2Ebool_2EF)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f3360,f322]) ).
fof(f3639,definition,
! [X0] :
( sQ230_spl
<=> ( ~ sP14_prd(X0,ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f3642,plain,
( sQ83_spl
| sQ21_spl
| sQ230_spl ),
inference(split_clause,[status(thm)],[f3637,f3639,f550,f1843]) ).
fof(f3677,plain,
! [X0] :
( sQ83_spl
| ~ sP15_prd(X0,ap(c_2Ebool_2E_7E,c_2Ebool_2ET),c_2Ebool_2EF)
| p(X0) ),
inference(resolution,[status(thm)],[f3365,f398]) ).
fof(f3684,plain,
! [X0] :
( sQ83_spl
| p(ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| ~ sP17_prd(c_2Ebool_2EF,ap(c_2Ebool_2E_7E,c_2Ebool_2ET),X0)
| p(X0) ),
inference(resolution,[status(thm)],[f3366,f402]) ).
fof(f3686,plain,
! [X0] :
( sQ83_spl
| ~ sP6_prd(c_2Ebool_2EF,ap(c_2Ebool_2E_7E,c_2Ebool_2ET),X0)
| p(X0) ),
inference(resolution,[status(thm)],[f3366,f329]) ).
fof(f3687,definition,
! [X0] :
( sQ233_spl
<=> ( ~ sP17_prd(c_2Ebool_2EF,ap(c_2Ebool_2E_7E,c_2Ebool_2ET),X0)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f3691,plain,
( sQ83_spl
| sQ233_spl ),
inference(split_clause,[status(thm)],[f3684,f3687,f1843]) ).
fof(f3692,plain,
! [X0] :
( sQ83_spl
| p(ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| ~ sP17_prd(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),c_2Ebool_2EF,X0)
| p(X0) ),
inference(resolution,[status(thm)],[f3371,f401]) ).
fof(f3696,definition,
! [X0] :
( sQ234_spl
<=> ( ~ sP17_prd(ap(c_2Ebool_2E_7E,c_2Ebool_2ET),c_2Ebool_2EF,X0)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f3699,plain,
( sQ83_spl
| sQ234_spl ),
inference(split_clause,[status(thm)],[f3692,f3696,f1843]) ).
fof(f3707,plain,
( sQ127_spl
| ~ mem(c_2Ebool_2ET,bool) ),
inference(resolution,[status(thm)],[f3417,f104]) ).
fof(f3708,plain,
( sQ127_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f3707,f988,f2330]) ).
fof(f3849,definition,
! [X0] :
( sQ241_spl
<=> ( X0 = ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET)
| p(X0)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ241_spl])],[split_symbol_definition]) ).
fof(f3852,definition,
( sQ242_spl
<=> mem(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),bool) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f3853,plain,
( ~ sQ242_spl
| mem(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),bool) ),
inference(component_clause,[status(thm)],[f3852]) ).
fof(f3854,plain,
( sQ242_spl
| ~ mem(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),bool) ),
inference(component_clause,[status(thm)],[f3852]) ).
fof(f3856,definition,
! [X0,X1] :
( sQ243_spl
<=> ( ~ sP6_prd(X1,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),X0)
| sP5_prd(X1,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition]) ).
fof(f3860,definition,
! [X0,X1] :
( sQ244_spl
<=> ( ~ sP6_prd(X1,X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET))
| sP5_prd(X1,X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET))
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition]) ).
fof(f3864,definition,
! [X0,X1] :
( sQ245_spl
<=> ( ~ sP8_prd(X1,X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET))
| sP7_prd(X1,X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET))
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f3868,definition,
! [X0,X1] :
( sQ246_spl
<=> ( ~ sP10_prd(X1,X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET))
| sP9_prd(X1,X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET))
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ246_spl])],[split_symbol_definition]) ).
fof(f3872,definition,
! [X0,X1] :
( sQ247_spl
<=> ( ~ sP12_prd(X1,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),X0)
| sP11_prd(X1,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f3876,definition,
! [X0,X1] :
( sQ248_spl
<=> ( ~ p(X0)
| ~ p(X1)
| ~ sP5_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),X1,X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f3931,plain,
! [X0] :
( sQ83_spl
| ~ sQ57_spl
| ~ sP15_prd(X0,c_2Ebool_2EF,c_2Ebool_2EF)
| p(X0) ),
inference(forward_demodulation,[status(thm)],[f1006,f3677]) ).
fof(f3936,plain,
! [X0] :
( sQ83_spl
| ~ sQ57_spl
| ~ sP6_prd(c_2Ebool_2EF,c_2Ebool_2EF,X0)
| p(X0) ),
inference(forward_demodulation,[status(thm)],[f1006,f3686]) ).
fof(f3947,plain,
( sQ242_spl
| ~ sQ65_spl
| ~ mem(c_2Ebool_2EF,bool) ),
inference(forward_demodulation,[status(thm)],[f1102,f3854]) ).
fof(f3948,plain,
( sQ242_spl
| ~ sQ65_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3947,f84]) ).
fof(f3949,plain,
( sQ242_spl
| ~ sQ65_spl ),
inference(contradiction_clause,[status(thm)],[f3948]) ).
fof(f3979,plain,
! [X0,X1] :
( sP6_prd(X0,X1,c_2Ebool_2EF)
| p(X1)
| ~ sP17_prd(X0,X1,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f1590,f85]) ).
fof(f3982,plain,
! [X0] :
( sP6_prd(X0,c_2Ebool_2EF,c_2Ebool_2EF)
| ~ sP17_prd(X0,c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f3979,f85]) ).
fof(f3986,plain,
! [X0] :
( ~ sP15_prd(X0,c_2Ebool_2EF,c_2Ebool_2EF)
| sP6_prd(X0,c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f3982,f398]) ).
fof(f4001,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)],[f544,f77]) ).
fof(f4006,definition,
! [X0,X1,X2] :
( sQ251_spl
<=> ( ~ mem(X1,X2)
| ~ mem(X0,arr(X2,bool))
| c_2Ebool_2ET = ap(X0,X1)
| ~ p(ap(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f4009,plain,
( sQ251_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f4001,f557,f4006]) ).
fof(f4013,plain,
! [X0,X1,X2] :
( c_2Ebool_2ET = sK0_skl(X2,X0,X1,bool)
| ~ p(sK0_skl(X2,X0,X1,bool))
| ~ p(c_2Ebool_2ET)
| X0 = X2
| ~ mem(X2,arr(bool,X1))
| ~ mem(X0,arr(bool,X1)) ),
inference(resolution,[status(thm)],[f561,f77]) ).
fof(f4018,definition,
! [X0,X1,X2] :
( sQ253_spl
<=> ( c_2Ebool_2ET = sK0_skl(X2,X0,X1,bool)
| ~ p(sK0_skl(X2,X0,X1,bool))
| X0 = X2
| ~ mem(X2,arr(bool,X1))
| ~ mem(X0,arr(bool,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f4021,plain,
( ~ sQ23_spl
| sQ253_spl ),
inference(split_clause,[status(thm)],[f4013,f4018,f557]) ).
fof(f4047,plain,
! [X0] :
( p(c_2Ebool_2EF)
| ~ sP17_prd(X0,c_2Ebool_2EF,c_2Ebool_2EF)
| sP6_prd(X0,c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f3986,f402]) ).
fof(f4050,definition,
! [X0] :
( sQ254_spl
<=> ( ~ sP17_prd(X0,c_2Ebool_2EF,c_2Ebool_2EF)
| sP6_prd(X0,c_2Ebool_2EF,c_2Ebool_2EF) ) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f4053,plain,
( sQ21_spl
| sQ254_spl ),
inference(split_clause,[status(thm)],[f4047,f4050,f550]) ).
fof(f4072,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)],[f654,f104]) ).
fof(f4075,definition,
( sQ255_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,[sQ255_spl])],[split_symbol_definition]) ).
fof(f4077,plain,
( sQ255_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)],[f4075]) ).
fof(f4078,definition,
( sQ256_spl
<=> c_2Ebool_2E_7E = c_2Ebool_2E_7E ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f4081,plain,
( sQ256_spl
| ~ sQ255_spl ),
inference(split_clause,[status(thm)],[f4072,f4075,f4078]) ).
fof(f4082,plain,
( sQ255_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f4077]) ).
fof(f4083,plain,
sQ255_spl,
inference(contradiction_clause,[status(thm)],[f4082]) ).
fof(f4153,definition,
( sQ257_spl
<=> mem(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E),bool) ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f4154,plain,
( ~ sQ257_spl
| mem(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E),bool) ),
inference(component_clause,[status(thm)],[f4153]) ).
fof(f4155,plain,
( sQ257_spl
| ~ mem(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E),bool) ),
inference(component_clause,[status(thm)],[f4153]) ).
fof(f4156,definition,
( sQ258_spl
<=> p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E)) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f4222,definition,
! [X0,X1] :
( sQ261_spl
<=> ( ~ sP16_prd(X1,X0,c_2Ebool_2EF)
| sP7_prd(X1,X0,c_2Ebool_2EF)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f4226,definition,
! [X0,X1] :
( sQ262_spl
<=> ( ~ sP7_prd(X1,X0,c_2Ebool_2EF)
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| sP7_prd(X1,X0,c_2Ebool_2EF)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f4239,definition,
! [X0,X1] :
( sQ264_spl
<=> ( ~ sP9_prd(X1,X0,c_2Ebool_2EF)
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| sP9_prd(X1,X0,c_2Ebool_2EF)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f4252,plain,
( ~ sQ211_spl
| ~ p(c_2Ebool_2ET)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF)) ),
inference(resolution,[status(thm)],[f3429,f77]) ).
fof(f4257,definition,
( sQ266_spl
<=> p(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF)) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f4259,plain,
( sQ266_spl
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF)) ),
inference(component_clause,[status(thm)],[f4257]) ).
fof(f4260,plain,
( ~ sQ211_spl
| ~ sQ23_spl
| ~ sQ266_spl ),
inference(split_clause,[status(thm)],[f4252,f4257,f557,f3428]) ).
fof(f4266,plain,
( sQ83_spl
| ~ sQ57_spl
| sQ266_spl
| ~ sP6_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF)) ),
inference(resolution,[status(thm)],[f4259,f3936]) ).
fof(f4267,plain,
( sQ83_spl
| ~ sQ57_spl
| sQ266_spl
| ~ sP15_prd(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f4259,f3931]) ).
fof(f4271,plain,
! [X0] :
( sQ266_spl
| ~ p(X0)
| sP5_prd(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),X0,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f4259,f3127]) ).
fof(f4280,plain,
! [X0] :
( sQ266_spl
| ~ p(X0)
| sP5_prd(X0,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f4259,f2993]) ).
fof(f4285,plain,
! [X0] :
( sQ266_spl
| p(X0)
| ~ sP17_prd(X0,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f4259,f2875]) ).
fof(f4286,plain,
! [X0] :
( sQ266_spl
| ~ sP15_prd(c_2Ebool_2EF,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),X0)
| p(X0) ),
inference(resolution,[status(thm)],[f4259,f2817]) ).
fof(f4291,plain,
! [X0] :
( sQ266_spl
| ~ sP15_prd(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF,X0)
| p(X0) ),
inference(resolution,[status(thm)],[f4259,f2814]) ).
fof(f4292,plain,
( sQ266_spl
| ~ sP15_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF)) ),
inference(resolution,[status(thm)],[f4259,f2813]) ).
fof(f4347,plain,
( sQ83_spl
| ~ sQ57_spl
| sQ266_spl
| p(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF))
| ~ sP15_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF)) ),
inference(resolution,[status(thm)],[f4266,f333]) ).
fof(f4354,definition,
( sQ275_spl
<=> sP15_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF)) ),
introduced(definition,[new_symbols(definition,[sQ275_spl])],[split_symbol_definition]) ).
fof(f4358,plain,
( sQ83_spl
| ~ sQ57_spl
| sQ266_spl
| ~ sQ275_spl ),
inference(split_clause,[status(thm)],[f4347,f4354,f4257,f1005,f1843]) ).
fof(f4359,definition,
( sQ276_spl
<=> sP17_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF)) ),
introduced(definition,[new_symbols(definition,[sQ276_spl])],[split_symbol_definition]) ).
fof(f4478,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)],[f729,f92]) ).
fof(f4479,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)],[f729,f86]) ).
fof(f4496,definition,
( sQ282_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,[sQ282_spl])],[split_symbol_definition]) ).
fof(f4499,definition,
( sQ283_spl
<=> c_2Ebool_2E_5C_2F = c_2Emin_2E_3D_3D_3E ),
introduced(definition,[new_symbols(definition,[sQ283_spl])],[split_symbol_definition]) ).
fof(f4500,plain,
( ~ sQ283_spl
| c_2Ebool_2E_5C_2F = c_2Emin_2E_3D_3D_3E ),
inference(component_clause,[status(thm)],[f4499]) ).
fof(f4502,plain,
( sQ283_spl
| ~ sQ282_spl ),
inference(split_clause,[status(thm)],[f4478,f4496,f4499]) ).
fof(f4503,definition,
( sQ284_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,[sQ284_spl])],[split_symbol_definition]) ).
fof(f4505,plain,
( sQ284_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)],[f4503]) ).
fof(f4506,definition,
( sQ285_spl
<=> c_2Emin_2E_3D_3D_3E = c_2Emin_2E_3D_3D_3E ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f4509,plain,
( sQ285_spl
| ~ sQ284_spl ),
inference(split_clause,[status(thm)],[f4479,f4503,f4506]) ).
fof(f4510,plain,
( sQ284_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f4505]) ).
fof(f4511,plain,
sQ284_spl,
inference(contradiction_clause,[status(thm)],[f4510]) ).
fof(f4519,plain,
! [X0] :
( ~ sQ127_spl
| p(ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| p(X0)
| ~ p(ap(ap(c_2Ebool_2E_5C_2F,X0),ap(c_2Ebool_2E_7E,c_2Ebool_2ET)))
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f2331,f95]) ).
fof(f4520,plain,
! [X0] :
( ~ sQ127_spl
| p(ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| ~ p(X0)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),ap(c_2Ebool_2E_7E,c_2Ebool_2ET)))
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f2331,f89]) ).
fof(f4521,plain,
( ~ sQ10_spl
| ~ sQ127_spl
| ap(c_2Ebool_2E_7E,c_2Ebool_2ET) = c_2Ebool_2EF
| p(ap(c_2Ebool_2E_7E,c_2Ebool_2ET)) ),
inference(resolution,[status(thm)],[f2331,f482]) ).
fof(f4543,definition,
! [X0] :
( sQ290_spl
<=> ( p(X0)
| ~ p(ap(ap(c_2Ebool_2E_5C_2F,X0),ap(c_2Ebool_2E_7E,c_2Ebool_2ET)))
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ290_spl])],[split_symbol_definition]) ).
fof(f4546,plain,
( ~ sQ127_spl
| sQ83_spl
| sQ290_spl ),
inference(split_clause,[status(thm)],[f4519,f4543,f1843,f2330]) ).
fof(f4547,definition,
! [X0] :
( sQ291_spl
<=> ( ~ p(X0)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),ap(c_2Ebool_2E_7E,c_2Ebool_2ET)))
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f4550,plain,
( ~ sQ127_spl
| sQ83_spl
| sQ291_spl ),
inference(split_clause,[status(thm)],[f4520,f4547,f1843,f2330]) ).
fof(f4551,plain,
( ~ sQ10_spl
| ~ sQ127_spl
| sQ57_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f4521,f1843,f1005,f2330,f481]) ).
fof(f4570,plain,
! [X0] :
( sQ83_spl
| ~ sQ57_spl
| p(c_2Ebool_2EF)
| ~ sP17_prd(X0,c_2Ebool_2EF,c_2Ebool_2EF)
| p(X0) ),
inference(resolution,[status(thm)],[f3931,f402]) ).
fof(f4572,plain,
! [X0] :
( sQ83_spl
| ~ sQ57_spl
| ~ sP6_prd(X0,c_2Ebool_2EF,c_2Ebool_2EF)
| p(X0) ),
inference(resolution,[status(thm)],[f3931,f329]) ).
fof(f4574,definition,
! [X0] :
( sQ294_spl
<=> ( ~ sP17_prd(X0,c_2Ebool_2EF,c_2Ebool_2EF)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f4577,plain,
( sQ83_spl
| ~ sQ57_spl
| sQ21_spl
| sQ294_spl ),
inference(split_clause,[status(thm)],[f4570,f4574,f550,f1005,f1843]) ).
fof(f4590,plain,
( sQ266_spl
| sQ83_spl
| ~ sQ57_spl
| ~ sP6_prd(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f4572,f4259]) ).
fof(f4596,plain,
( ~ sQ211_spl
| ~ sQ19_spl
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl))
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl)),c_2Ebool_2EF)) ),
inference(resolution,[status(thm)],[f541,f3429]) ).
fof(f4598,plain,
! [X0,X1,X2] :
( ~ sQ19_spl
| ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl) = sK0_skl(X2,X0,X1,bool)
| ~ p(sK0_skl(X2,X0,X1,bool))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl))
| X0 = X2
| ~ mem(X2,arr(bool,X1))
| ~ mem(X0,arr(bool,X1)) ),
inference(resolution,[status(thm)],[f541,f561]) ).
fof(f4599,plain,
! [X0,X1,X2] :
( ~ sQ19_spl
| ~ mem(X1,X2)
| ~ mem(X0,arr(X2,bool))
| ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl) = ap(X0,X1)
| ~ p(ap(X0,X1))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl)) ),
inference(resolution,[status(thm)],[f541,f544]) ).
fof(f4602,plain,
! [X0] :
( ~ sQ19_spl
| p(X0)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl)))
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f541,f101]) ).
fof(f4606,plain,
( ~ sQ19_spl
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl))
| ~ p(ap(c_2Ebool_2E_7E,ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl))) ),
inference(resolution,[status(thm)],[f541,f107]) ).
fof(f4610,definition,
( sQ295_spl
<=> p(ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl)),c_2Ebool_2EF)) ),
introduced(definition,[new_symbols(definition,[sQ295_spl])],[split_symbol_definition]) ).
fof(f4613,plain,
( ~ sQ211_spl
| ~ sQ19_spl
| ~ sQ4_spl
| ~ sQ295_spl ),
inference(split_clause,[status(thm)],[f4596,f4610,f449,f540,f3428]) ).
fof(f4614,definition,
! [X0,X1,X2] :
( sQ296_spl
<=> ( ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl) = sK0_skl(X2,X0,X1,bool)
| ~ p(sK0_skl(X2,X0,X1,bool))
| X0 = X2
| ~ mem(X2,arr(bool,X1))
| ~ mem(X0,arr(bool,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ296_spl])],[split_symbol_definition]) ).
fof(f4617,plain,
( ~ sQ19_spl
| ~ sQ4_spl
| sQ296_spl ),
inference(split_clause,[status(thm)],[f4598,f4614,f449,f540]) ).
fof(f4618,definition,
! [X0,X1,X2] :
( sQ297_spl
<=> ( ~ mem(X1,X2)
| ~ mem(X0,arr(X2,bool))
| ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl) = ap(X0,X1)
| ~ p(ap(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ297_spl])],[split_symbol_definition]) ).
fof(f4621,plain,
( ~ sQ19_spl
| sQ297_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f4599,f449,f4618,f540]) ).
fof(f4633,definition,
( sQ300_spl
<=> p(ap(c_2Ebool_2E_7E,ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl))) ),
introduced(definition,[new_symbols(definition,[sQ300_spl])],[split_symbol_definition]) ).
fof(f4636,plain,
( ~ sQ19_spl
| ~ sQ4_spl
| ~ sQ300_spl ),
inference(split_clause,[status(thm)],[f4606,f4633,f449,f540]) ).
fof(f4663,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)],[f778,f92]) ).
fof(f4664,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)],[f778,f86]) ).
fof(f4681,definition,
( sQ305_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,[sQ305_spl])],[split_symbol_definition]) ).
fof(f4683,plain,
( sQ305_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)],[f4681]) ).
fof(f4684,definition,
( sQ306_spl
<=> c_2Ebool_2E_5C_2F = c_2Ebool_2E_5C_2F ),
introduced(definition,[new_symbols(definition,[sQ306_spl])],[split_symbol_definition]) ).
fof(f4687,plain,
( sQ306_spl
| ~ sQ305_spl ),
inference(split_clause,[status(thm)],[f4663,f4681,f4684]) ).
fof(f4688,definition,
( sQ307_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,[sQ307_spl])],[split_symbol_definition]) ).
fof(f4691,plain,
( sQ283_spl
| ~ sQ307_spl ),
inference(split_clause,[status(thm)],[f4664,f4688,f4499]) ).
fof(f4692,plain,
( sQ305_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f4683]) ).
fof(f4693,plain,
sQ305_spl,
inference(contradiction_clause,[status(thm)],[f4692]) ).
fof(f4738,plain,
! [X0,X1] :
( ~ sQ283_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)],[f4500,f96]) ).
fof(f4745,plain,
! [X0,X1] :
( ~ sQ283_spl
| p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),X1))
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(forward_subsumption_resolution,[status(thm)],[f4738,f90]) ).
fof(f4756,plain,
( sQ266_spl
| ~ sQ283_spl
| ~ mem(c_2Ebool_2EF,bool)
| ~ mem(c_2Ebool_2ET,bool) ),
inference(resolution,[status(thm)],[f4745,f4259]) ).
fof(f4758,plain,
( sQ266_spl
| ~ sQ283_spl
| ~ sQ11_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f4756,f988,f484,f4499,f4257]) ).
fof(f4780,plain,
! [X0] :
( ~ sQ242_spl
| p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET))
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET)))
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f3853,f102]) ).
fof(f4782,plain,
( ~ sQ10_spl
| ~ sQ242_spl
| ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET) = c_2Ebool_2EF
| p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET)) ),
inference(resolution,[status(thm)],[f3853,f482]) ).
fof(f4790,definition,
( sQ311_spl
<=> p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET)) ),
introduced(definition,[new_symbols(definition,[sQ311_spl])],[split_symbol_definition]) ).
fof(f4792,plain,
( sQ311_spl
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET)) ),
inference(component_clause,[status(thm)],[f4790]) ).
fof(f4806,definition,
! [X0] :
( sQ315_spl
<=> ( ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET)))
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ315_spl])],[split_symbol_definition]) ).
fof(f4809,plain,
( ~ sQ242_spl
| sQ311_spl
| sQ315_spl ),
inference(split_clause,[status(thm)],[f4780,f4806,f4790,f3852]) ).
fof(f4810,plain,
( ~ sQ10_spl
| ~ sQ242_spl
| sQ65_spl
| sQ311_spl ),
inference(split_clause,[status(thm)],[f4782,f4790,f1101,f3852,f481]) ).
fof(f4820,plain,
( sQ83_spl
| ~ sQ57_spl
| sQ311_spl
| ~ sP6_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f4792,f4572]) ).
fof(f4821,plain,
( sQ83_spl
| ~ sQ57_spl
| sQ311_spl
| ~ sP6_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET)) ),
inference(resolution,[status(thm)],[f4792,f3936]) ).
fof(f4827,plain,
! [X0] :
( sQ311_spl
| ~ p(X0)
| sP5_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),X0,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f4792,f3127]) ).
fof(f4836,plain,
! [X0] :
( sQ311_spl
| ~ p(X0)
| sP5_prd(X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f4792,f2993]) ).
fof(f4840,plain,
( sQ311_spl
| ~ sP17_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f4792,f2975]) ).
fof(f4842,plain,
! [X0] :
( sQ311_spl
| ~ sP15_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),X0)
| p(X0) ),
inference(resolution,[status(thm)],[f4792,f2817]) ).
fof(f4847,plain,
! [X0] :
( sQ311_spl
| ~ sP15_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),c_2Ebool_2EF,X0)
| p(X0) ),
inference(resolution,[status(thm)],[f4792,f2814]) ).
fof(f4848,plain,
( sQ311_spl
| ~ sP15_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET)) ),
inference(resolution,[status(thm)],[f4792,f2813]) ).
fof(f4939,plain,
( sQ266_spl
| p(c_2Ebool_2EF)
| ~ sP17_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF)) ),
inference(resolution,[status(thm)],[f4292,f401]) ).
fof(f4943,plain,
( sQ266_spl
| sQ21_spl
| ~ sQ276_spl ),
inference(split_clause,[status(thm)],[f4939,f4359,f550,f4257]) ).
fof(f4945,plain,
( ~ sQ95_spl
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF)) ),
inference(resolution,[status(thm)],[f1953,f84]) ).
fof(f4948,plain,
( ~ sQ95_spl
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF)) ),
inference(resolution,[status(thm)],[f1953,f77]) ).
fof(f4950,plain,
( sQ83_spl
| ~ sQ57_spl
| ~ sQ95_spl
| ~ sP6_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f4945,f4572]) ).
fof(f4951,plain,
( sQ83_spl
| ~ sQ57_spl
| ~ sQ95_spl
| ~ sP6_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF)) ),
inference(resolution,[status(thm)],[f4945,f3936]) ).
fof(f4957,plain,
! [X0] :
( ~ sQ95_spl
| ~ p(X0)
| sP5_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),X0,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f4945,f3127]) ).
fof(f4966,plain,
! [X0] :
( ~ sQ95_spl
| ~ p(X0)
| sP5_prd(X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f4945,f2993]) ).
fof(f4971,plain,
! [X0] :
( ~ sQ95_spl
| p(X0)
| ~ sP17_prd(X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f4945,f2875]) ).
fof(f4972,plain,
! [X0] :
( ~ sQ95_spl
| ~ sP15_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),X0)
| p(X0) ),
inference(resolution,[status(thm)],[f4945,f2817]) ).
fof(f4977,plain,
! [X0] :
( ~ sQ95_spl
| ~ sP15_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),c_2Ebool_2EF,X0)
| p(X0) ),
inference(resolution,[status(thm)],[f4945,f2814]) ).
fof(f4978,plain,
( ~ sQ95_spl
| ~ sP15_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF)) ),
inference(resolution,[status(thm)],[f4945,f2813]) ).
fof(f5026,plain,
( sQ83_spl
| ~ sQ57_spl
| ~ sQ95_spl
| ~ sP6_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f4948,f4572]) ).
fof(f5027,plain,
( sQ83_spl
| ~ sQ57_spl
| ~ sQ95_spl
| ~ sP6_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF)) ),
inference(resolution,[status(thm)],[f4948,f3936]) ).
fof(f5033,plain,
! [X0] :
( ~ sQ95_spl
| ~ p(X0)
| sP5_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),X0,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f4948,f3127]) ).
fof(f5042,plain,
! [X0] :
( ~ sQ95_spl
| ~ p(X0)
| sP5_prd(X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f4948,f2993]) ).
fof(f5047,plain,
! [X0] :
( ~ sQ95_spl
| p(X0)
| ~ sP17_prd(X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f4948,f2875]) ).
fof(f5048,plain,
! [X0] :
( ~ sQ95_spl
| ~ sP15_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),X0)
| p(X0) ),
inference(resolution,[status(thm)],[f4948,f2817]) ).
fof(f5053,plain,
! [X0] :
( ~ sQ95_spl
| ~ sP15_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF,X0)
| p(X0) ),
inference(resolution,[status(thm)],[f4948,f2814]) ).
fof(f5054,plain,
( ~ sQ95_spl
| ~ sP15_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF)) ),
inference(resolution,[status(thm)],[f4948,f2813]) ).
fof(f5145,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)],[f865,f98]) ).
fof(f5160,definition,
( sQ337_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,[sQ337_spl])],[split_symbol_definition]) ).
fof(f5162,plain,
( sQ337_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)],[f5160]) ).
fof(f5163,definition,
( sQ338_spl
<=> c_2Ebool_2E_2F_5C = c_2Ebool_2E_2F_5C ),
introduced(definition,[new_symbols(definition,[sQ338_spl])],[split_symbol_definition]) ).
fof(f5166,plain,
( sQ338_spl
| ~ sQ337_spl ),
inference(split_clause,[status(thm)],[f5145,f5160,f5163]) ).
fof(f5171,plain,
( sQ337_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f5162]) ).
fof(f5172,plain,
sQ337_spl,
inference(contradiction_clause,[status(thm)],[f5171]) ).
fof(f5337,plain,
( sQ83_spl
| ~ sQ57_spl
| sQ266_spl
| p(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF))
| ~ sP17_prd(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f4267,f401]) ).
fof(f5341,definition,
( sQ340_spl
<=> sP17_prd(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ340_spl])],[split_symbol_definition]) ).
fof(f5344,plain,
( sQ83_spl
| ~ sQ57_spl
| sQ266_spl
| ~ sQ340_spl ),
inference(split_clause,[status(thm)],[f5337,f5341,f4257,f1005,f1843]) ).
fof(f5383,plain,
( sQ266_spl
| sQ83_spl
| ~ sQ57_spl
| p(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF))
| ~ sP15_prd(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f4590,f332]) ).
fof(f5391,definition,
( sQ341_spl
<=> sP15_prd(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ341_spl])],[split_symbol_definition]) ).
fof(f5394,plain,
( sQ83_spl
| ~ sQ57_spl
| sQ266_spl
| ~ sQ341_spl ),
inference(split_clause,[status(thm)],[f5383,f5391,f4257,f1005,f1843]) ).
fof(f5426,plain,
( sQ83_spl
| ~ sQ57_spl
| ~ sQ95_spl
| p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF))
| ~ sP15_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f4950,f332]) ).
fof(f5434,definition,
( sQ343_spl
<=> sP15_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),c_2Ebool_2EF,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ343_spl])],[split_symbol_definition]) ).
fof(f5436,plain,
( sQ343_spl
| ~ sP15_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(component_clause,[status(thm)],[f5434]) ).
fof(f5437,definition,
( sQ344_spl
<=> p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF)) ),
introduced(definition,[new_symbols(definition,[sQ344_spl])],[split_symbol_definition]) ).
fof(f5438,plain,
( ~ sQ344_spl
| p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF)) ),
inference(component_clause,[status(thm)],[f5437]) ).
fof(f5440,plain,
( sQ83_spl
| ~ sQ57_spl
| ~ sQ95_spl
| sQ344_spl
| ~ sQ343_spl ),
inference(split_clause,[status(thm)],[f5426,f5434,f5437,f1952,f1005,f1843]) ).
fof(f5442,definition,
( sQ345_spl
<=> sP17_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),c_2Ebool_2EF,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ345_spl])],[split_symbol_definition]) ).
fof(f5454,plain,
( ~ sQ344_spl
| ~ sQ95_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5438,f4945]) ).
fof(f5455,plain,
( ~ sQ344_spl
| ~ sQ95_spl ),
inference(contradiction_clause,[status(thm)],[f5454]) ).
fof(f5456,plain,
( sQ83_spl
| ~ sQ57_spl
| ~ sQ95_spl
| p(c_2Ebool_2EF)
| ~ sP15_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF)) ),
inference(resolution,[status(thm)],[f4951,f332]) ).
fof(f5464,definition,
( sQ347_spl
<=> sP15_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF)) ),
introduced(definition,[new_symbols(definition,[sQ347_spl])],[split_symbol_definition]) ).
fof(f5467,plain,
( sQ83_spl
| ~ sQ57_spl
| ~ sQ95_spl
| sQ21_spl
| ~ sQ347_spl ),
inference(split_clause,[status(thm)],[f5456,f5464,f550,f1952,f1005,f1843]) ).
fof(f5469,definition,
( sQ348_spl
<=> sP17_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF)) ),
introduced(definition,[new_symbols(definition,[sQ348_spl])],[split_symbol_definition]) ).
fof(f5482,plain,
( sQ83_spl
| ~ sQ57_spl
| ~ sQ95_spl
| p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF))
| ~ sP15_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f5026,f332]) ).
fof(f5490,definition,
( sQ350_spl
<=> sP15_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ350_spl])],[split_symbol_definition]) ).
fof(f5492,plain,
( sQ350_spl
| ~ sP15_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(component_clause,[status(thm)],[f5490]) ).
fof(f5493,definition,
( sQ351_spl
<=> p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF)) ),
introduced(definition,[new_symbols(definition,[sQ351_spl])],[split_symbol_definition]) ).
fof(f5494,plain,
( ~ sQ351_spl
| p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF)) ),
inference(component_clause,[status(thm)],[f5493]) ).
fof(f5496,plain,
( sQ83_spl
| ~ sQ57_spl
| ~ sQ95_spl
| sQ351_spl
| ~ sQ350_spl ),
inference(split_clause,[status(thm)],[f5482,f5490,f5493,f1952,f1005,f1843]) ).
fof(f5498,definition,
( sQ352_spl
<=> sP17_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ352_spl])],[split_symbol_definition]) ).
fof(f5510,plain,
( ~ sQ351_spl
| ~ sQ95_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5494,f4948]) ).
fof(f5511,plain,
( ~ sQ351_spl
| ~ sQ95_spl ),
inference(contradiction_clause,[status(thm)],[f5510]) ).
fof(f5512,plain,
( sQ83_spl
| ~ sQ57_spl
| ~ sQ95_spl
| p(c_2Ebool_2EF)
| ~ sP15_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF)) ),
inference(resolution,[status(thm)],[f5027,f332]) ).
fof(f5520,definition,
( sQ354_spl
<=> sP15_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF)) ),
introduced(definition,[new_symbols(definition,[sQ354_spl])],[split_symbol_definition]) ).
fof(f5523,plain,
( sQ83_spl
| ~ sQ57_spl
| ~ sQ95_spl
| sQ21_spl
| ~ sQ354_spl ),
inference(split_clause,[status(thm)],[f5512,f5520,f550,f1952,f1005,f1843]) ).
fof(f5525,definition,
( sQ355_spl
<=> sP17_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF)) ),
introduced(definition,[new_symbols(definition,[sQ355_spl])],[split_symbol_definition]) ).
fof(f5551,plain,
( ~ sQ95_spl
| p(c_2Ebool_2EF)
| ~ sP17_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF)) ),
inference(resolution,[status(thm)],[f4978,f401]) ).
fof(f5555,plain,
( ~ sQ95_spl
| sQ21_spl
| ~ sQ348_spl ),
inference(split_clause,[status(thm)],[f5551,f5469,f550,f1952]) ).
fof(f5567,plain,
( ~ sQ95_spl
| p(c_2Ebool_2EF)
| ~ sP17_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF)) ),
inference(resolution,[status(thm)],[f5054,f401]) ).
fof(f5571,plain,
( ~ sQ95_spl
| sQ21_spl
| ~ sQ355_spl ),
inference(split_clause,[status(thm)],[f5567,f5525,f550,f1952]) ).
fof(f5580,plain,
( sQ343_spl
| p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF))
| ~ sP17_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f5436,f401]) ).
fof(f5584,plain,
( sQ343_spl
| sQ344_spl
| ~ sQ345_spl ),
inference(split_clause,[status(thm)],[f5580,f5442,f5437,f5434]) ).
fof(f5590,plain,
( sQ350_spl
| p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF))
| ~ sP17_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f5492,f401]) ).
fof(f5594,plain,
( sQ350_spl
| sQ351_spl
| ~ sQ352_spl ),
inference(split_clause,[status(thm)],[f5590,f5498,f5493,f5490]) ).
fof(f5648,plain,
! [X0] :
( sQ266_spl
| ~ sP14_prd(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),X0)
| p(c_2Ebool_2EF)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f4271,f322]) ).
fof(f5650,definition,
! [X0] :
( sQ359_spl
<=> ( ~ sP14_prd(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),X0)
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ359_spl])],[split_symbol_definition]) ).
fof(f5653,plain,
( sQ266_spl
| sQ21_spl
| sQ359_spl ),
inference(split_clause,[status(thm)],[f5648,f5650,f550,f4257]) ).
fof(f5667,plain,
! [X0] :
( sQ266_spl
| ~ sP14_prd(X0,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF))
| p(c_2Ebool_2EF)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f4280,f322]) ).
fof(f5669,definition,
! [X0] :
( sQ361_spl
<=> ( ~ sP14_prd(X0,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF))
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ361_spl])],[split_symbol_definition]) ).
fof(f5672,plain,
( sQ266_spl
| sQ21_spl
| sQ361_spl ),
inference(split_clause,[status(thm)],[f5667,f5669,f550,f4257]) ).
fof(f5723,plain,
! [X0] :
( sQ266_spl
| ~ sP15_prd(X0,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF)
| p(X0) ),
inference(resolution,[status(thm)],[f4285,f398]) ).
fof(f5727,plain,
! [X0] :
( sQ266_spl
| p(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF))
| ~ sP17_prd(c_2Ebool_2EF,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),X0)
| p(X0) ),
inference(resolution,[status(thm)],[f4286,f402]) ).
fof(f5729,plain,
! [X0] :
( sQ266_spl
| ~ sP6_prd(c_2Ebool_2EF,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),X0)
| p(X0) ),
inference(resolution,[status(thm)],[f4286,f329]) ).
fof(f5730,definition,
! [X0] :
( sQ366_spl
<=> ( ~ sP17_prd(c_2Ebool_2EF,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),X0)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ366_spl])],[split_symbol_definition]) ).
fof(f5734,plain,
( sQ266_spl
| sQ366_spl ),
inference(split_clause,[status(thm)],[f5727,f5730,f4257]) ).
fof(f5735,plain,
! [X0] :
( sQ266_spl
| p(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF))
| ~ sP17_prd(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF,X0)
| p(X0) ),
inference(resolution,[status(thm)],[f4291,f401]) ).
fof(f5739,definition,
! [X0] :
( sQ367_spl
<=> ( ~ sP17_prd(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF,X0)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ367_spl])],[split_symbol_definition]) ).
fof(f5742,plain,
( sQ266_spl
| sQ367_spl ),
inference(split_clause,[status(thm)],[f5735,f5739,f4257]) ).
fof(f5863,plain,
! [X0] :
( ~ sQ95_spl
| ~ sP14_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),X0)
| p(c_2Ebool_2EF)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f4957,f322]) ).
fof(f5865,definition,
! [X0] :
( sQ376_spl
<=> ( ~ sP14_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),X0)
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ376_spl])],[split_symbol_definition]) ).
fof(f5868,plain,
( ~ sQ95_spl
| sQ21_spl
| sQ376_spl ),
inference(split_clause,[status(thm)],[f5863,f5865,f550,f1952]) ).
fof(f5882,plain,
! [X0] :
( ~ sQ95_spl
| ~ sP14_prd(X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF))
| p(c_2Ebool_2EF)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f4966,f322]) ).
fof(f5884,definition,
! [X0] :
( sQ378_spl
<=> ( ~ sP14_prd(X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF))
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ378_spl])],[split_symbol_definition]) ).
fof(f5887,plain,
( ~ sQ95_spl
| sQ21_spl
| sQ378_spl ),
inference(split_clause,[status(thm)],[f5882,f5884,f550,f1952]) ).
fof(f5970,plain,
! [X0] :
( ~ sQ95_spl
| ~ sP15_prd(X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),c_2Ebool_2EF)
| p(X0) ),
inference(resolution,[status(thm)],[f4971,f398]) ).
fof(f5974,plain,
! [X0] :
( ~ sQ95_spl
| p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF))
| ~ sP17_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),X0)
| p(X0) ),
inference(resolution,[status(thm)],[f4972,f402]) ).
fof(f5976,plain,
! [X0] :
( ~ sQ95_spl
| ~ sP6_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),X0)
| p(X0) ),
inference(resolution,[status(thm)],[f4972,f329]) ).
fof(f5977,definition,
! [X0] :
( sQ382_spl
<=> ( ~ sP17_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),X0)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ382_spl])],[split_symbol_definition]) ).
fof(f5981,plain,
( ~ sQ95_spl
| sQ344_spl
| sQ382_spl ),
inference(split_clause,[status(thm)],[f5974,f5977,f5437,f1952]) ).
fof(f5982,plain,
! [X0] :
( ~ sQ95_spl
| p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF))
| ~ sP17_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),c_2Ebool_2EF,X0)
| p(X0) ),
inference(resolution,[status(thm)],[f4977,f401]) ).
fof(f5986,definition,
! [X0] :
( sQ383_spl
<=> ( ~ sP17_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),c_2Ebool_2EF,X0)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ383_spl])],[split_symbol_definition]) ).
fof(f5989,plain,
( ~ sQ95_spl
| sQ344_spl
| sQ383_spl ),
inference(split_clause,[status(thm)],[f5982,f5986,f5437,f1952]) ).
fof(f6001,plain,
! [X0] :
( ~ sQ95_spl
| ~ sP14_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),X0)
| p(c_2Ebool_2EF)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f5033,f322]) ).
fof(f6003,definition,
! [X0] :
( sQ384_spl
<=> ( ~ sP14_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),X0)
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ384_spl])],[split_symbol_definition]) ).
fof(f6006,plain,
( ~ sQ95_spl
| sQ21_spl
| sQ384_spl ),
inference(split_clause,[status(thm)],[f6001,f6003,f550,f1952]) ).
fof(f6020,plain,
! [X0] :
( ~ sQ95_spl
| ~ sP14_prd(X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF))
| p(c_2Ebool_2EF)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f5042,f322]) ).
fof(f6022,definition,
! [X0] :
( sQ386_spl
<=> ( ~ sP14_prd(X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF))
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ386_spl])],[split_symbol_definition]) ).
fof(f6025,plain,
( ~ sQ95_spl
| sQ21_spl
| sQ386_spl ),
inference(split_clause,[status(thm)],[f6020,f6022,f550,f1952]) ).
fof(f6073,plain,
! [X0] :
( ~ sQ95_spl
| ~ sP15_prd(X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF)
| p(X0) ),
inference(resolution,[status(thm)],[f5047,f398]) ).
fof(f6077,plain,
! [X0] :
( ~ sQ95_spl
| p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF))
| ~ sP17_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),X0)
| p(X0) ),
inference(resolution,[status(thm)],[f5048,f402]) ).
fof(f6079,plain,
! [X0] :
( ~ sQ95_spl
| ~ sP6_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),X0)
| p(X0) ),
inference(resolution,[status(thm)],[f5048,f329]) ).
fof(f6080,definition,
! [X0] :
( sQ388_spl
<=> ( ~ sP17_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),X0)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ388_spl])],[split_symbol_definition]) ).
fof(f6084,plain,
( ~ sQ95_spl
| sQ351_spl
| sQ388_spl ),
inference(split_clause,[status(thm)],[f6077,f6080,f5493,f1952]) ).
fof(f6085,plain,
! [X0] :
( ~ sQ95_spl
| p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF))
| ~ sP17_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF,X0)
| p(X0) ),
inference(resolution,[status(thm)],[f5053,f401]) ).
fof(f6089,definition,
! [X0] :
( sQ389_spl
<=> ( ~ sP17_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF,X0)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ389_spl])],[split_symbol_definition]) ).
fof(f6092,plain,
( ~ sQ95_spl
| sQ351_spl
| sQ389_spl ),
inference(split_clause,[status(thm)],[f6085,f6089,f5493,f1952]) ).
fof(f6103,plain,
! [X0,X1] :
( p(c_2Ebool_2EF)
| sP7_prd(X0,X1,c_2Ebool_2EF)
| ~ mem(X0,bool)
| ~ mem(X1,bool)
| ~ sP16_prd(X0,X1,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f1565,f84]) ).
fof(f6107,plain,
( sQ21_spl
| sQ261_spl ),
inference(split_clause,[status(thm)],[f6103,f4222,f550]) ).
fof(f6289,plain,
! [X0,X1] :
( ~ sP5_prd(X1,X0,c_2Ebool_2ET)
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| ~ p(c_2Ebool_2ET)
| ~ p(X1)
| p(X0) ),
inference(resolution,[status(thm)],[f1663,f77]) ).
fof(f6294,definition,
! [X0,X1] :
( sQ406_spl
<=> ( ~ sP5_prd(X1,X0,c_2Ebool_2ET)
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| ~ p(X1)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ406_spl])],[split_symbol_definition]) ).
fof(f6297,plain,
( ~ sQ23_spl
| sQ406_spl ),
inference(split_clause,[status(thm)],[f6289,f6294,f557]) ).
fof(f6380,plain,
! [X0] :
( sQ266_spl
| p(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF))
| ~ sP17_prd(X0,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF)
| p(X0) ),
inference(resolution,[status(thm)],[f5723,f402]) ).
fof(f6382,plain,
! [X0] :
( sQ266_spl
| ~ sP6_prd(X0,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF)
| p(X0) ),
inference(resolution,[status(thm)],[f5723,f329]) ).
fof(f6384,definition,
! [X0] :
( sQ414_spl
<=> ( ~ sP17_prd(X0,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ414_spl])],[split_symbol_definition]) ).
fof(f6387,plain,
( sQ266_spl
| sQ414_spl ),
inference(split_clause,[status(thm)],[f6380,f6384,f4257]) ).
fof(f6389,plain,
! [X0] :
( sQ266_spl
| p(c_2Ebool_2EF)
| ~ sP15_prd(c_2Ebool_2EF,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),X0)
| p(X0) ),
inference(resolution,[status(thm)],[f5729,f332]) ).
fof(f6397,definition,
! [X0] :
( sQ415_spl
<=> ( ~ sP15_prd(c_2Ebool_2EF,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),X0)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ415_spl])],[split_symbol_definition]) ).
fof(f6400,plain,
( sQ266_spl
| sQ21_spl
| sQ415_spl ),
inference(split_clause,[status(thm)],[f6389,f6397,f550,f4257]) ).
fof(f6502,plain,
! [X0] :
( ~ sQ95_spl
| p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF))
| ~ sP17_prd(X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),c_2Ebool_2EF)
| p(X0) ),
inference(resolution,[status(thm)],[f5970,f402]) ).
fof(f6504,plain,
! [X0] :
( ~ sQ95_spl
| ~ sP6_prd(X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),c_2Ebool_2EF)
| p(X0) ),
inference(resolution,[status(thm)],[f5970,f329]) ).
fof(f6506,definition,
! [X0] :
( sQ419_spl
<=> ( ~ sP17_prd(X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),c_2Ebool_2EF)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ419_spl])],[split_symbol_definition]) ).
fof(f6509,plain,
( ~ sQ95_spl
| sQ344_spl
| sQ419_spl ),
inference(split_clause,[status(thm)],[f6502,f6506,f5437,f1952]) ).
fof(f6511,plain,
! [X0] :
( ~ sQ95_spl
| p(c_2Ebool_2EF)
| ~ sP15_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),X0)
| p(X0) ),
inference(resolution,[status(thm)],[f5976,f332]) ).
fof(f6519,definition,
! [X0] :
( sQ420_spl
<=> ( ~ sP15_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),X0)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ420_spl])],[split_symbol_definition]) ).
fof(f6522,plain,
( ~ sQ95_spl
| sQ21_spl
| sQ420_spl ),
inference(split_clause,[status(thm)],[f6511,f6519,f550,f1952]) ).
fof(f6555,plain,
! [X0] :
( ~ sQ95_spl
| p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF))
| ~ sP17_prd(X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF)
| p(X0) ),
inference(resolution,[status(thm)],[f6073,f402]) ).
fof(f6557,plain,
! [X0] :
( ~ sQ95_spl
| ~ sP6_prd(X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF)
| p(X0) ),
inference(resolution,[status(thm)],[f6073,f329]) ).
fof(f6559,definition,
! [X0] :
( sQ422_spl
<=> ( ~ sP17_prd(X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ422_spl])],[split_symbol_definition]) ).
fof(f6562,plain,
( ~ sQ95_spl
| sQ351_spl
| sQ422_spl ),
inference(split_clause,[status(thm)],[f6555,f6559,f5493,f1952]) ).
fof(f6564,plain,
! [X0] :
( ~ sQ95_spl
| p(c_2Ebool_2EF)
| ~ sP15_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),X0)
| p(X0) ),
inference(resolution,[status(thm)],[f6079,f332]) ).
fof(f6572,definition,
! [X0] :
( sQ423_spl
<=> ( ~ sP15_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),X0)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ423_spl])],[split_symbol_definition]) ).
fof(f6575,plain,
( ~ sQ95_spl
| sQ21_spl
| sQ423_spl ),
inference(split_clause,[status(thm)],[f6564,f6572,f550,f1952]) ).
fof(f6592,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)],[f2140,f84]) ).
fof(f6596,definition,
! [X0,X1,X2] :
( sQ425_spl
<=> ( ~ mem(X1,X2)
| ~ mem(X0,arr(X2,bool))
| c_2Ebool_2EF = ap(X0,X1)
| p(ap(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ425_spl])],[split_symbol_definition]) ).
fof(f6599,plain,
( sQ425_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f6592,f550,f6596]) ).
fof(f6644,plain,
( sQ149_spl
| ~ mem(sK3_skl,ty_2Eextreal_2Eextreal)
| ~ mem(sK4_skl,ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[f2773,f80]) ).
fof(f6645,plain,
( sQ149_spl
| ~ sQ7_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f6644,f525,f466,f2723]) ).
fof(f6663,plain,
( ~ sQ10_spl
| ~ sQ149_spl
| ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK4_skl) = c_2Ebool_2EF
| p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK4_skl)) ),
inference(resolution,[status(thm)],[f2724,f482]) ).
fof(f6665,plain,
( ~ sQ22_spl
| ~ sQ149_spl
| ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK4_skl) = c_2Ebool_2ET
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK4_skl)) ),
inference(resolution,[status(thm)],[f2724,f555]) ).
fof(f6708,plain,
( ~ sQ10_spl
| ~ sQ149_spl
| sQ150_spl
| sQ90_spl ),
inference(split_clause,[status(thm)],[f6663,f1917,f2726,f2723,f481]) ).
fof(f6713,definition,
( sQ441_spl
<=> ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK4_skl) = c_2Ebool_2ET ),
introduced(definition,[new_symbols(definition,[sQ441_spl])],[split_symbol_definition]) ).
fof(f6714,plain,
( ~ sQ441_spl
| ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK4_skl) = c_2Ebool_2ET ),
inference(component_clause,[status(thm)],[f6713]) ).
fof(f6716,plain,
( ~ sQ22_spl
| ~ sQ149_spl
| sQ441_spl
| ~ sQ90_spl ),
inference(split_clause,[status(thm)],[f6665,f1917,f6713,f2723,f554]) ).
fof(f6777,plain,
( ~ sQ150_spl
| ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),sK4_skl),sK3_skl) ),
inference(backward_demodulation,[status(thm)],[f2727,f1328]) ).
fof(f6783,plain,
( ~ sQ150_spl
| ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl) = sK3_skl ),
inference(forward_demodulation,[status(thm)],[f1445,f6777]) ).
fof(f6817,plain,
( sQ3_spl
| ~ sQ150_spl
| sP4_prd(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl)) ),
inference(backward_demodulation,[status(thm)],[f6783,f3505]) ).
fof(f6862,plain,
( sQ3_spl
| ~ sQ150_spl
| ~ sQ122_spl
| ~ sQ123_spl
| sP4_prd(c_2Ebool_2ET) ),
inference(forward_demodulation,[status(thm)],[f2387,f6817]) ).
fof(f6863,plain,
( sQ3_spl
| ~ sQ150_spl
| ~ sQ122_spl
| ~ sQ123_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6862,f1212]) ).
fof(f6864,plain,
( sQ3_spl
| ~ sQ150_spl
| ~ sQ122_spl
| ~ sQ123_spl ),
inference(contradiction_clause,[status(thm)],[f6863]) ).
fof(f6917,plain,
( ~ sQ3_spl
| ~ sQ150_spl
| p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK2_skl)) ),
inference(forward_demodulation,[status(thm)],[f6783,f447]) ).
fof(f6919,plain,
( ~ sQ99_spl
| ~ sQ150_spl
| p(ap(ap(c_2Eextreal_2Eextreal__le,sK3_skl),sK4_skl)) ),
inference(forward_demodulation,[status(thm)],[f6783,f1981]) ).
fof(f6920,plain,
( ~ sQ99_spl
| ~ sQ150_spl
| p(c_2Ebool_2EF) ),
inference(forward_demodulation,[status(thm)],[f2727,f6919]) ).
fof(f6921,plain,
( ~ sQ99_spl
| ~ sQ150_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6920,f85]) ).
fof(f6922,plain,
( ~ sQ99_spl
| ~ sQ150_spl ),
inference(contradiction_clause,[status(thm)],[f6921]) ).
fof(f7202,plain,
( ~ sQ3_spl
| ~ sQ150_spl
| ~ sQ27_spl
| p(c_2Ebool_2EF) ),
inference(backward_demodulation,[status(thm)],[f589,f6917]) ).
fof(f7209,plain,
( ~ sQ3_spl
| ~ sQ150_spl
| ~ sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7202,f85]) ).
fof(f7210,plain,
( ~ sQ3_spl
| ~ sQ150_spl
| ~ sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f7209]) ).
fof(f7314,definition,
! [X0,X1] :
( sQ450_spl
<=> ( ~ sP11_prd(X1,c_2Ebool_2EF,X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| sP11_prd(X1,c_2Ebool_2EF,X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ450_spl])],[split_symbol_definition]) ).
fof(f7327,definition,
! [X0] :
( sQ452_spl
<=> ( ~ p(X0)
| ~ sP5_prd(c_2Ebool_2EF,c_2Ebool_2ET,X0)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ452_spl])],[split_symbol_definition]) ).
fof(f7328,plain,
! [X0] :
( ~ sQ452_spl
| ~ p(X0)
| ~ sP5_prd(c_2Ebool_2EF,c_2Ebool_2ET,X0)
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f7327]) ).
fof(f7490,plain,
( ~ sQ452_spl
| ~ p(c_2Ebool_2ET)
| ~ sP5_prd(c_2Ebool_2EF,c_2Ebool_2ET,c_2Ebool_2ET) ),
inference(resolution,[status(thm)],[f7328,f77]) ).
fof(f7495,definition,
( sQ465_spl
<=> sP5_prd(c_2Ebool_2EF,c_2Ebool_2ET,c_2Ebool_2ET) ),
introduced(definition,[new_symbols(definition,[sQ465_spl])],[split_symbol_definition]) ).
fof(f7497,plain,
( sQ465_spl
| ~ sP5_prd(c_2Ebool_2EF,c_2Ebool_2ET,c_2Ebool_2ET) ),
inference(component_clause,[status(thm)],[f7495]) ).
fof(f7498,plain,
( ~ sQ452_spl
| ~ sQ23_spl
| ~ sQ465_spl ),
inference(split_clause,[status(thm)],[f7490,f7495,f557,f7327]) ).
fof(f7502,plain,
( sQ465_spl
| ~ sP14_prd(c_2Ebool_2EF,c_2Ebool_2ET)
| ~ p(c_2Ebool_2ET) ),
inference(resolution,[status(thm)],[f7497,f323]) ).
fof(f7509,definition,
( sQ467_spl
<=> sP14_prd(c_2Ebool_2EF,c_2Ebool_2ET) ),
introduced(definition,[new_symbols(definition,[sQ467_spl])],[split_symbol_definition]) ).
fof(f7512,plain,
( sQ465_spl
| ~ sQ467_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f7502,f557,f7509,f7495]) ).
fof(f7702,definition,
! [X2,X3,X4] :
( sQ480_spl
<=> ( ~ p(ap(ap(c_2Emin_2E_3D(X2),X3),X4))
| X3 = X4
| ~ mem(X4,X2)
| ~ mem(X3,X2)
| ~ ne(X2) ) ),
introduced(definition,[new_symbols(definition,[sQ480_spl])],[split_symbol_definition]) ).
fof(f7711,plain,
! [X0,X1,X2,X3,X4] :
( ~ p(X1)
| ~ p(X0)
| ~ p(ap(ap(c_2Emin_2E_3D(X2),X3),X4))
| X3 = X4
| ~ mem(X4,X2)
| ~ mem(X3,X2)
| ~ ne(X2)
| ~ p(X1)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f2567,f339]) ).
fof(f7714,plain,
( sQ480_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f7711,f721,f7702]) ).
fof(f7736,plain,
! [X0] :
( sQ257_spl
| ~ mem(c_2Ebool_2E_7E,X0)
| ~ mem(c_2Ebool_2E_21(bool),arr(X0,bool)) ),
inference(resolution,[status(thm)],[f4155,f63]) ).
fof(f7741,plain,
( sQ257_spl
| ~ ne(bool)
| ~ mem(c_2Ebool_2E_7E,arr(bool,bool)) ),
inference(resolution,[status(thm)],[f7736,f116]) ).
fof(f7742,definition,
( sQ483_spl
<=> mem(c_2Ebool_2E_7E,arr(bool,bool)) ),
introduced(definition,[new_symbols(definition,[sQ483_spl])],[split_symbol_definition]) ).
fof(f7744,plain,
( sQ483_spl
| ~ mem(c_2Ebool_2E_7E,arr(bool,bool)) ),
inference(component_clause,[status(thm)],[f7742]) ).
fof(f7745,definition,
( sQ484_spl
<=> ne(bool) ),
introduced(definition,[new_symbols(definition,[sQ484_spl])],[split_symbol_definition]) ).
fof(f7747,plain,
( sQ484_spl
| ~ ne(bool) ),
inference(component_clause,[status(thm)],[f7745]) ).
fof(f7748,plain,
( sQ257_spl
| ~ sQ484_spl
| ~ sQ483_spl ),
inference(split_clause,[status(thm)],[f7741,f7742,f7745,f4153]) ).
fof(f7749,plain,
( sQ483_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7744,f104]) ).
fof(f7750,plain,
sQ483_spl,
inference(contradiction_clause,[status(thm)],[f7749]) ).
fof(f7751,plain,
( sQ484_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7747,f58]) ).
fof(f7752,plain,
sQ484_spl,
inference(contradiction_clause,[status(thm)],[f7751]) ).
fof(f7870,plain,
! [X0,X1,X2] :
( ~ sQ257_spl
| ~ mem(X1,X2)
| ~ mem(X0,arr(X2,bool))
| ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E) = ap(X0,X1)
| p(ap(X0,X1))
| p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E)) ),
inference(resolution,[status(thm)],[f4154,f2140]) ).
fof(f7873,plain,
! [X0,X1] :
( ~ sQ257_spl
| p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E))
| sP7_prd(X0,X1,ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E))
| ~ mem(X0,bool)
| ~ mem(X1,bool)
| ~ sP16_prd(X0,X1,ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E)) ),
inference(resolution,[status(thm)],[f4154,f1565]) ).
fof(f7879,plain,
! [X0] :
( ~ sQ257_spl
| p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E))
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E)))
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f4154,f102]) ).
fof(f7880,plain,
! [X0] :
( ~ sQ257_spl
| p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E))
| p(X0)
| ~ p(ap(ap(c_2Ebool_2E_5C_2F,X0),ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E)))
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f4154,f95]) ).
fof(f7881,plain,
! [X0] :
( ~ sQ257_spl
| p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E))
| ~ p(X0)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E)))
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f4154,f89]) ).
fof(f7887,plain,
( ~ sQ10_spl
| ~ sQ257_spl
| ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E) = c_2Ebool_2EF
| p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E)) ),
inference(resolution,[status(thm)],[f4154,f482]) ).
fof(f7892,definition,
! [X0,X1,X2] :
( sQ485_spl
<=> ( ~ mem(X1,X2)
| ~ mem(X0,arr(X2,bool))
| ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E) = ap(X0,X1)
| p(ap(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ485_spl])],[split_symbol_definition]) ).
fof(f7895,plain,
( ~ sQ257_spl
| sQ485_spl
| sQ258_spl ),
inference(split_clause,[status(thm)],[f7870,f4156,f7892,f4153]) ).
fof(f7900,definition,
! [X0,X1] :
( sQ487_spl
<=> ( sP7_prd(X0,X1,ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E))
| ~ mem(X0,bool)
| ~ mem(X1,bool)
| ~ sP16_prd(X0,X1,ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E)) ) ),
introduced(definition,[new_symbols(definition,[sQ487_spl])],[split_symbol_definition]) ).
fof(f7903,plain,
( ~ sQ257_spl
| sQ258_spl
| sQ487_spl ),
inference(split_clause,[status(thm)],[f7873,f7900,f4156,f4153]) ).
fof(f7904,definition,
! [X0] :
( sQ488_spl
<=> ( ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E)))
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ488_spl])],[split_symbol_definition]) ).
fof(f7907,plain,
( ~ sQ257_spl
| sQ258_spl
| sQ488_spl ),
inference(split_clause,[status(thm)],[f7879,f7904,f4156,f4153]) ).
fof(f7908,definition,
! [X0] :
( sQ489_spl
<=> ( p(X0)
| ~ p(ap(ap(c_2Ebool_2E_5C_2F,X0),ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E)))
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ489_spl])],[split_symbol_definition]) ).
fof(f7911,plain,
( ~ sQ257_spl
| sQ258_spl
| sQ489_spl ),
inference(split_clause,[status(thm)],[f7880,f7908,f4156,f4153]) ).
fof(f7912,definition,
! [X0] :
( sQ490_spl
<=> ( ~ p(X0)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X0),ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E)))
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ490_spl])],[split_symbol_definition]) ).
fof(f7915,plain,
( ~ sQ257_spl
| sQ258_spl
| sQ490_spl ),
inference(split_clause,[status(thm)],[f7881,f7912,f4156,f4153]) ).
fof(f7932,definition,
( sQ495_spl
<=> ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E) = c_2Ebool_2EF ),
introduced(definition,[new_symbols(definition,[sQ495_spl])],[split_symbol_definition]) ).
fof(f7933,plain,
( ~ sQ495_spl
| ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E) = c_2Ebool_2EF ),
inference(component_clause,[status(thm)],[f7932]) ).
fof(f7935,plain,
( ~ sQ10_spl
| ~ sQ257_spl
| sQ495_spl
| sQ258_spl ),
inference(split_clause,[status(thm)],[f7887,f4156,f7932,f4153,f481]) ).
fof(f7949,definition,
( sQ498_spl
<=> mem(sK1_skl(c_2Ebool_2E_7E,bool),bool) ),
introduced(definition,[new_symbols(definition,[sQ498_spl])],[split_symbol_definition]) ).
fof(f7950,plain,
( ~ sQ498_spl
| mem(sK1_skl(c_2Ebool_2E_7E,bool),bool) ),
inference(component_clause,[status(thm)],[f7949]) ).
fof(f7954,definition,
( sQ499_spl
<=> p(ap(c_2Ebool_2E_7E,sK1_skl(c_2Ebool_2E_7E,bool))) ),
introduced(definition,[new_symbols(definition,[sQ499_spl])],[split_symbol_definition]) ).
fof(f7956,plain,
( sQ499_spl
| ~ p(ap(c_2Ebool_2E_7E,sK1_skl(c_2Ebool_2E_7E,bool))) ),
inference(component_clause,[status(thm)],[f7954]) ).
fof(f8023,plain,
! [X0] :
( sP14_prd(c_2Ebool_2ET,c_2Ebool_2ET)
| ~ p(X0)
| ~ p(c_2Ebool_2ET)
| ~ sP6_prd(c_2Ebool_2ET,c_2Ebool_2ET,X0)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f2656,f77]) ).
fof(f8028,plain,
! [X0,X1] :
( sP14_prd(c_2Ebool_2ET,X1)
| ~ p(X0)
| ~ p(c_2Ebool_2ET)
| ~ sP6_prd(c_2Ebool_2ET,X1,X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f2656,f77]) ).
fof(f8035,definition,
! [X0] :
( sQ501_spl
<=> ( ~ p(X0)
| ~ sP6_prd(c_2Ebool_2ET,c_2Ebool_2ET,X0)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ501_spl])],[split_symbol_definition]) ).
fof(f8036,plain,
! [X0] :
( ~ sQ501_spl
| ~ p(X0)
| ~ sP6_prd(c_2Ebool_2ET,c_2Ebool_2ET,X0)
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f8035]) ).
fof(f8038,definition,
( sQ502_spl
<=> sP14_prd(c_2Ebool_2ET,c_2Ebool_2ET) ),
introduced(definition,[new_symbols(definition,[sQ502_spl])],[split_symbol_definition]) ).
fof(f8039,plain,
( ~ sQ502_spl
| sP14_prd(c_2Ebool_2ET,c_2Ebool_2ET) ),
inference(component_clause,[status(thm)],[f8038]) ).
fof(f8041,plain,
( sQ502_spl
| ~ sQ23_spl
| sQ501_spl ),
inference(split_clause,[status(thm)],[f8023,f8035,f557,f8038]) ).
fof(f8046,definition,
! [X0,X1] :
( sQ504_spl
<=> ( sP14_prd(c_2Ebool_2ET,X1)
| ~ p(X0)
| ~ sP6_prd(c_2Ebool_2ET,X1,X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ504_spl])],[split_symbol_definition]) ).
fof(f8049,plain,
( ~ sQ23_spl
| sQ504_spl ),
inference(split_clause,[status(thm)],[f8028,f8046,f557]) ).
fof(f8159,plain,
( ~ sQ501_spl
| ~ p(c_2Ebool_2ET)
| ~ sP6_prd(c_2Ebool_2ET,c_2Ebool_2ET,c_2Ebool_2ET) ),
inference(resolution,[status(thm)],[f8036,f77]) ).
fof(f8160,definition,
( sQ507_spl
<=> sP6_prd(c_2Ebool_2ET,c_2Ebool_2ET,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ507_spl])],[split_symbol_definition]) ).
fof(f8162,plain,
( sQ507_spl
| ~ sP6_prd(c_2Ebool_2ET,c_2Ebool_2ET,c_2Ebool_2EF) ),
inference(component_clause,[status(thm)],[f8160]) ).
fof(f8164,definition,
( sQ508_spl
<=> sP6_prd(c_2Ebool_2ET,c_2Ebool_2ET,c_2Ebool_2ET) ),
introduced(definition,[new_symbols(definition,[sQ508_spl])],[split_symbol_definition]) ).
fof(f8166,plain,
( sQ508_spl
| ~ sP6_prd(c_2Ebool_2ET,c_2Ebool_2ET,c_2Ebool_2ET) ),
inference(component_clause,[status(thm)],[f8164]) ).
fof(f8167,plain,
( ~ sQ501_spl
| ~ sQ23_spl
| ~ sQ508_spl ),
inference(split_clause,[status(thm)],[f8159,f8164,f557,f8035]) ).
fof(f8173,plain,
( sQ508_spl
| ~ p(c_2Ebool_2ET)
| ~ p(c_2Ebool_2ET) ),
inference(resolution,[status(thm)],[f8166,f1574]) ).
fof(f8187,plain,
( sQ508_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f8173,f557,f8164]) ).
fof(f8193,plain,
! [X0] :
( ~ sQ502_spl
| p(X0)
| ~ p(c_2Ebool_2ET)
| ~ sP6_prd(c_2Ebool_2ET,c_2Ebool_2ET,X0)
| ~ mem(c_2Ebool_2ET,bool)
| ~ mem(c_2Ebool_2ET,bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f8039,f2655]) ).
fof(f8196,definition,
! [X0] :
( sQ512_spl
<=> ( p(X0)
| ~ sP6_prd(c_2Ebool_2ET,c_2Ebool_2ET,X0)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ512_spl])],[split_symbol_definition]) ).
fof(f8197,plain,
! [X0] :
( ~ sQ512_spl
| p(X0)
| ~ sP6_prd(c_2Ebool_2ET,c_2Ebool_2ET,X0)
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f8196]) ).
fof(f8199,plain,
( ~ sQ502_spl
| ~ sQ23_spl
| ~ sQ55_spl
| sQ512_spl ),
inference(split_clause,[status(thm)],[f8193,f8196,f988,f557,f8038]) ).
fof(f8202,plain,
( ~ sQ512_spl
| p(c_2Ebool_2EF)
| ~ sP6_prd(c_2Ebool_2ET,c_2Ebool_2ET,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f8197,f84]) ).
fof(f8206,plain,
( ~ sQ512_spl
| sQ21_spl
| ~ sQ507_spl ),
inference(split_clause,[status(thm)],[f8202,f8160,f550,f8196]) ).
fof(f8209,plain,
( sQ507_spl
| p(c_2Ebool_2EF)
| ~ sP15_prd(c_2Ebool_2ET,c_2Ebool_2ET,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f8162,f333]) ).
fof(f8215,plain,
( sQ507_spl
| ~ sP5_prd(c_2Ebool_2ET,c_2Ebool_2ET,c_2Ebool_2EF)
| ~ mem(c_2Ebool_2ET,bool)
| ~ mem(c_2Ebool_2ET,bool)
| ~ mem(c_2Ebool_2EF,bool) ),
inference(resolution,[status(thm)],[f8162,f235]) ).
fof(f8216,definition,
( sQ513_spl
<=> sP15_prd(c_2Ebool_2ET,c_2Ebool_2ET,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ513_spl])],[split_symbol_definition]) ).
fof(f8220,plain,
( sQ507_spl
| sQ21_spl
| ~ sQ513_spl ),
inference(split_clause,[status(thm)],[f8209,f8216,f550,f8160]) ).
fof(f8229,definition,
( sQ515_spl
<=> sP5_prd(c_2Ebool_2ET,c_2Ebool_2ET,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ515_spl])],[split_symbol_definition]) ).
fof(f8232,plain,
( sQ507_spl
| ~ sQ515_spl
| ~ sQ55_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8215,f484,f988,f8229,f8160]) ).
fof(f8257,plain,
! [X0] :
( ~ sQ154_spl
| ~ p(X0)
| ~ p(c_2Ebool_2ET)
| ~ sP5_prd(c_2Ebool_2EF,c_2Ebool_2ET,X0)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f2759,f77]) ).
fof(f8259,plain,
( ~ sQ154_spl
| ~ sQ23_spl
| sQ452_spl ),
inference(split_clause,[status(thm)],[f8257,f7327,f557,f2758]) ).
fof(f8260,plain,
! [X0,X1] :
( ~ ne(X0)
| ~ ne(bool)
| ~ ne(X0)
| p(ap(c_2Ebool_2E_21(X0),X1))
| ~ mem(X1,arr(X0,bool))
| ~ p(ap(c_2Ebool_2E_21(arr(X0,bool)),c_2Ebool_2E_21(X0))) ),
inference(resolution,[status(thm)],[f2762,f116]) ).
fof(f8263,definition,
! [X0,X1] :
( sQ516_spl
<=> ( ~ ne(X0)
| ~ ne(X0)
| p(ap(c_2Ebool_2E_21(X0),X1))
| ~ mem(X1,arr(X0,bool))
| ~ p(ap(c_2Ebool_2E_21(arr(X0,bool)),c_2Ebool_2E_21(X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ516_spl])],[split_symbol_definition]) ).
fof(f8266,plain,
( ~ sQ484_spl
| sQ516_spl ),
inference(split_clause,[status(thm)],[f8260,f8263,f7745]) ).
fof(f8325,plain,
! [X0] :
( p(ap(c_2Ebool_2E_7E,X0))
| ~ mem(X0,bool)
| ~ p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E)) ),
inference(resolution,[status(thm)],[f2764,f104]) ).
fof(f8328,definition,
! [X0] :
( sQ517_spl
<=> ( p(ap(c_2Ebool_2E_7E,X0))
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ517_spl])],[split_symbol_definition]) ).
fof(f8329,plain,
! [X0] :
( ~ sQ517_spl
| p(ap(c_2Ebool_2E_7E,X0))
| ~ mem(X0,bool) ),
inference(component_clause,[status(thm)],[f8328]) ).
fof(f8331,plain,
( sQ517_spl
| ~ sQ258_spl ),
inference(split_clause,[status(thm)],[f8325,f4156,f8328]) ).
fof(f8388,plain,
( ~ sQ57_spl
| ~ sQ517_spl
| p(c_2Ebool_2EF)
| ~ mem(c_2Ebool_2ET,bool) ),
inference(paramodulation,[status(thm)],[f1006,f8329]) ).
fof(f8390,plain,
( ~ sQ57_spl
| ~ sQ517_spl
| sQ21_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f8388,f988,f550,f8328,f1005]) ).
fof(f8392,plain,
( ~ sQ495_spl
| ~ sP4_prd(c_2Ebool_2EF)
| mem(sK1_skl(c_2Ebool_2E_7E,bool),bool)
| ~ mem(c_2Ebool_2E_7E,arr(bool,bool))
| ~ ne(bool) ),
inference(paramodulation,[status(thm)],[f7933,f1215]) ).
fof(f8394,plain,
( ~ sQ495_spl
| ~ p(ap(c_2Ebool_2E_7E,sK1_skl(c_2Ebool_2E_7E,bool)))
| p(c_2Ebool_2EF)
| ~ mem(c_2Ebool_2E_7E,arr(bool,bool))
| ~ ne(bool) ),
inference(paramodulation,[status(thm)],[f7933,f122]) ).
fof(f8396,plain,
( ~ sQ495_spl
| ~ sQ46_spl
| sQ498_spl
| ~ sQ483_spl
| ~ sQ484_spl ),
inference(split_clause,[status(thm)],[f8392,f7745,f7742,f7949,f795,f7932]) ).
fof(f8398,plain,
( ~ sQ495_spl
| ~ sQ499_spl
| sQ21_spl
| ~ sQ483_spl
| ~ sQ484_spl ),
inference(split_clause,[status(thm)],[f8394,f7745,f7742,f550,f7954,f7932]) ).
fof(f8400,plain,
( ~ sQ452_spl
| ~ sQ498_spl
| ~ p(sK1_skl(c_2Ebool_2E_7E,bool))
| ~ sP5_prd(c_2Ebool_2EF,c_2Ebool_2ET,sK1_skl(c_2Ebool_2E_7E,bool)) ),
inference(resolution,[status(thm)],[f7950,f7328]) ).
fof(f8401,plain,
! [X0] :
( ~ sQ154_spl
| ~ sQ498_spl
| ~ p(X0)
| ~ p(sK1_skl(c_2Ebool_2E_7E,bool))
| ~ sP5_prd(c_2Ebool_2EF,sK1_skl(c_2Ebool_2E_7E,bool),X0)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f7950,f2759]) ).
fof(f8404,plain,
! [X0,X1] :
( ~ sQ498_spl
| sP14_prd(sK1_skl(c_2Ebool_2E_7E,bool),X1)
| ~ p(X0)
| ~ p(sK1_skl(c_2Ebool_2E_7E,bool))
| ~ sP6_prd(sK1_skl(c_2Ebool_2E_7E,bool),X1,X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f7950,f2656]) ).
fof(f8408,plain,
! [X0,X1] :
( ~ sQ498_spl
| ~ sP5_prd(X1,X0,sK1_skl(c_2Ebool_2E_7E,bool))
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| ~ p(sK1_skl(c_2Ebool_2E_7E,bool))
| ~ p(X1)
| p(X0) ),
inference(resolution,[status(thm)],[f7950,f1663]) ).
fof(f8413,plain,
( ~ sQ128_spl
| ~ sQ57_spl
| ~ sQ498_spl
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),sK1_skl(c_2Ebool_2E_7E,bool))) ),
inference(resolution,[status(thm)],[f7950,f2374]) ).
fof(f8419,plain,
( ~ sQ211_spl
| ~ sQ498_spl
| ~ p(sK1_skl(c_2Ebool_2E_7E,bool))
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,sK1_skl(c_2Ebool_2E_7E,bool)),c_2Ebool_2EF)) ),
inference(resolution,[status(thm)],[f7950,f3429]) ).
fof(f8421,plain,
! [X0,X1,X2] :
( ~ sQ498_spl
| sK1_skl(c_2Ebool_2E_7E,bool) = sK0_skl(X2,X0,X1,bool)
| ~ p(sK0_skl(X2,X0,X1,bool))
| ~ p(sK1_skl(c_2Ebool_2E_7E,bool))
| X0 = X2
| ~ mem(X2,arr(bool,X1))
| ~ mem(X0,arr(bool,X1)) ),
inference(resolution,[status(thm)],[f7950,f561]) ).
fof(f8422,plain,
! [X0,X1,X2] :
( ~ sQ498_spl
| ~ mem(X1,X2)
| ~ mem(X0,arr(X2,bool))
| sK1_skl(c_2Ebool_2E_7E,bool) = ap(X0,X1)
| ~ p(ap(X0,X1))
| ~ p(sK1_skl(c_2Ebool_2E_7E,bool)) ),
inference(resolution,[status(thm)],[f7950,f544]) ).
fof(f8423,plain,
! [X0] :
( ~ sQ498_spl
| X0 = sK1_skl(c_2Ebool_2E_7E,bool)
| ~ p(sK1_skl(c_2Ebool_2E_7E,bool))
| ~ p(X0)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f7950,f67]) ).
fof(f8424,plain,
( ~ sQ10_spl
| ~ sQ498_spl
| sK1_skl(c_2Ebool_2E_7E,bool) = c_2Ebool_2EF
| p(sK1_skl(c_2Ebool_2E_7E,bool)) ),
inference(resolution,[status(thm)],[f7950,f482]) ).
fof(f8425,plain,
( ~ sQ22_spl
| ~ sQ498_spl
| sK1_skl(c_2Ebool_2E_7E,bool) = c_2Ebool_2ET
| ~ p(sK1_skl(c_2Ebool_2E_7E,bool)) ),
inference(resolution,[status(thm)],[f7950,f555]) ).
fof(f8428,definition,
( sQ522_spl
<=> sP5_prd(c_2Ebool_2EF,c_2Ebool_2ET,sK1_skl(c_2Ebool_2E_7E,bool)) ),
introduced(definition,[new_symbols(definition,[sQ522_spl])],[split_symbol_definition]) ).
fof(f8431,definition,
( sQ523_spl
<=> p(sK1_skl(c_2Ebool_2E_7E,bool)) ),
introduced(definition,[new_symbols(definition,[sQ523_spl])],[split_symbol_definition]) ).
fof(f8434,plain,
( ~ sQ452_spl
| ~ sQ498_spl
| ~ sQ523_spl
| ~ sQ522_spl ),
inference(split_clause,[status(thm)],[f8400,f8428,f8431,f7949,f7327]) ).
fof(f8435,definition,
! [X0] :
( sQ524_spl
<=> ( ~ p(X0)
| ~ sP5_prd(c_2Ebool_2EF,sK1_skl(c_2Ebool_2E_7E,bool),X0)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ524_spl])],[split_symbol_definition]) ).
fof(f8438,plain,
( ~ sQ154_spl
| ~ sQ498_spl
| ~ sQ523_spl
| sQ524_spl ),
inference(split_clause,[status(thm)],[f8401,f8435,f8431,f7949,f2758]) ).
fof(f8450,definition,
! [X0,X1] :
( sQ528_spl
<=> ( sP14_prd(sK1_skl(c_2Ebool_2E_7E,bool),X1)
| ~ p(X0)
| ~ sP6_prd(sK1_skl(c_2Ebool_2E_7E,bool),X1,X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ528_spl])],[split_symbol_definition]) ).
fof(f8453,plain,
( ~ sQ498_spl
| ~ sQ523_spl
| sQ528_spl ),
inference(split_clause,[status(thm)],[f8404,f8450,f8431,f7949]) ).
fof(f8459,definition,
! [X0,X1] :
( sQ530_spl
<=> ( ~ sP5_prd(X1,X0,sK1_skl(c_2Ebool_2E_7E,bool))
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| ~ p(X1)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ530_spl])],[split_symbol_definition]) ).
fof(f8462,plain,
( ~ sQ498_spl
| ~ sQ523_spl
| sQ530_spl ),
inference(split_clause,[status(thm)],[f8408,f8459,f8431,f7949]) ).
fof(f8479,definition,
( sQ535_spl
<=> p(ap(ap(c_2Emin_2E_3D_3D_3E,sK1_skl(c_2Ebool_2E_7E,bool)),c_2Ebool_2EF)) ),
introduced(definition,[new_symbols(definition,[sQ535_spl])],[split_symbol_definition]) ).
fof(f8482,plain,
( ~ sQ211_spl
| ~ sQ498_spl
| ~ sQ523_spl
| ~ sQ535_spl ),
inference(split_clause,[status(thm)],[f8419,f8479,f8431,f7949,f3428]) ).
fof(f8483,definition,
! [X0,X1,X2] :
( sQ536_spl
<=> ( sK1_skl(c_2Ebool_2E_7E,bool) = sK0_skl(X2,X0,X1,bool)
| ~ p(sK0_skl(X2,X0,X1,bool))
| X0 = X2
| ~ mem(X2,arr(bool,X1))
| ~ mem(X0,arr(bool,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ536_spl])],[split_symbol_definition]) ).
fof(f8486,plain,
( ~ sQ498_spl
| ~ sQ523_spl
| sQ536_spl ),
inference(split_clause,[status(thm)],[f8421,f8483,f8431,f7949]) ).
fof(f8487,definition,
! [X0,X1,X2] :
( sQ537_spl
<=> ( ~ mem(X1,X2)
| ~ mem(X0,arr(X2,bool))
| sK1_skl(c_2Ebool_2E_7E,bool) = ap(X0,X1)
| ~ p(ap(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ537_spl])],[split_symbol_definition]) ).
fof(f8490,plain,
( ~ sQ498_spl
| sQ537_spl
| ~ sQ523_spl ),
inference(split_clause,[status(thm)],[f8422,f8431,f8487,f7949]) ).
fof(f8491,definition,
! [X0] :
( sQ538_spl
<=> ( X0 = sK1_skl(c_2Ebool_2E_7E,bool)
| ~ p(X0)
| ~ mem(X0,bool) ) ),
introduced(definition,[new_symbols(definition,[sQ538_spl])],[split_symbol_definition]) ).
fof(f8494,plain,
( ~ sQ498_spl
| ~ sQ523_spl
| sQ538_spl ),
inference(split_clause,[status(thm)],[f8423,f8491,f8431,f7949]) ).
fof(f8495,definition,
( sQ539_spl
<=> sK1_skl(c_2Ebool_2E_7E,bool) = c_2Ebool_2EF ),
introduced(definition,[new_symbols(definition,[sQ539_spl])],[split_symbol_definition]) ).
fof(f8496,plain,
( ~ sQ539_spl
| sK1_skl(c_2Ebool_2E_7E,bool) = c_2Ebool_2EF ),
inference(component_clause,[status(thm)],[f8495]) ).
fof(f8498,plain,
( ~ sQ10_spl
| ~ sQ498_spl
| sQ539_spl
| sQ523_spl ),
inference(split_clause,[status(thm)],[f8424,f8431,f8495,f7949,f481]) ).
fof(f8499,definition,
( sQ540_spl
<=> sK1_skl(c_2Ebool_2E_7E,bool) = c_2Ebool_2ET ),
introduced(definition,[new_symbols(definition,[sQ540_spl])],[split_symbol_definition]) ).
fof(f8500,plain,
( ~ sQ540_spl
| sK1_skl(c_2Ebool_2E_7E,bool) = c_2Ebool_2ET ),
inference(component_clause,[status(thm)],[f8499]) ).
fof(f8502,plain,
( ~ sQ22_spl
| ~ sQ498_spl
| sQ540_spl
| ~ sQ523_spl ),
inference(split_clause,[status(thm)],[f8425,f8431,f8499,f7949,f554]) ).
fof(f8506,plain,
( sQ499_spl
| ~ sQ539_spl
| ~ p(ap(c_2Ebool_2E_7E,c_2Ebool_2EF)) ),
inference(forward_demodulation,[status(thm)],[f8496,f7956]) ).
fof(f8507,plain,
( sQ499_spl
| ~ sQ539_spl
| ~ sQ123_spl
| ~ p(c_2Ebool_2ET) ),
inference(forward_demodulation,[status(thm)],[f2289,f8506]) ).
fof(f8508,plain,
( sQ499_spl
| ~ sQ539_spl
| ~ sQ123_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8507,f78]) ).
fof(f8509,plain,
( sQ499_spl
| ~ sQ539_spl
| ~ sQ123_spl ),
inference(contradiction_clause,[status(thm)],[f8508]) ).
fof(f8530,plain,
( ~ sQ128_spl
| ~ sQ57_spl
| ~ sQ498_spl
| ~ sQ540_spl
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET)) ),
inference(forward_demodulation,[status(thm)],[f8500,f8413]) ).
fof(f8532,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ122_spl
| ~ sQ123_spl
| p(X0)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X0),c_2Ebool_2ET))
| ~ mem(X0,bool) ),
inference(forward_demodulation,[status(thm)],[f2387,f4602]) ).
fof(f8533,plain,
( ~ sQ19_spl
| ~ sQ122_spl
| ~ sQ123_spl
| p(c_2Ebool_2EF)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET)) ),
inference(resolution,[status(thm)],[f8532,f84]) ).
fof(f8537,plain,
( ~ sQ19_spl
| ~ sQ122_spl
| ~ sQ123_spl
| sQ21_spl
| ~ sQ311_spl ),
inference(split_clause,[status(thm)],[f8533,f4790,f550,f2288,f2284,f540]) ).
fof(f8548,plain,
! [X0] :
( ~ sQ128_spl
| ~ sQ57_spl
| ~ sQ498_spl
| ~ sQ540_spl
| X0 = ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET)
| p(X0)
| ~ mem(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f8530,f66]) ).
fof(f8549,plain,
! [X0,X1] :
( ~ sQ128_spl
| ~ sQ57_spl
| ~ sQ498_spl
| ~ sQ540_spl
| ~ sP6_prd(X1,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),X0)
| sP5_prd(X1,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),X0)
| ~ mem(X1,bool)
| ~ mem(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f8530,f238]) ).
fof(f8554,plain,
! [X0,X1] :
( ~ sQ128_spl
| ~ sQ57_spl
| ~ sQ498_spl
| ~ sQ540_spl
| ~ sP6_prd(X1,X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET))
| sP5_prd(X1,X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET))
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| ~ mem(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),bool) ),
inference(resolution,[status(thm)],[f8530,f239]) ).
fof(f8555,plain,
! [X0,X1] :
( ~ sQ128_spl
| ~ sQ57_spl
| ~ sQ498_spl
| ~ sQ540_spl
| ~ sP8_prd(X1,X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET))
| sP7_prd(X1,X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET))
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| ~ mem(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),bool) ),
inference(resolution,[status(thm)],[f8530,f249]) ).
fof(f8556,plain,
! [X0,X1] :
( ~ sQ128_spl
| ~ sQ57_spl
| ~ sQ498_spl
| ~ sQ540_spl
| ~ sP10_prd(X1,X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET))
| sP9_prd(X1,X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET))
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| ~ mem(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),bool) ),
inference(resolution,[status(thm)],[f8530,f260]) ).
fof(f8565,plain,
! [X0,X1] :
( ~ sQ128_spl
| ~ sQ57_spl
| ~ sQ498_spl
| ~ sQ540_spl
| ~ sP12_prd(X1,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),X0)
| sP11_prd(X1,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),X0)
| ~ mem(X1,bool)
| ~ mem(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f8530,f269]) ).
fof(f8575,plain,
! [X0,X1] :
( ~ sQ128_spl
| ~ sQ57_spl
| ~ sQ498_spl
| ~ sQ540_spl
| ~ p(X0)
| ~ p(X1)
| ~ sP5_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),X1,X0)
| ~ mem(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),bool)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f8530,f236]) ).
fof(f8584,plain,
( ~ sQ128_spl
| ~ sQ57_spl
| ~ sQ498_spl
| ~ sQ540_spl
| ~ sQ242_spl
| sQ241_spl ),
inference(split_clause,[status(thm)],[f8548,f3849,f3852,f8499,f7949,f1005,f2333]) ).
fof(f8585,plain,
( ~ sQ128_spl
| ~ sQ57_spl
| ~ sQ498_spl
| ~ sQ540_spl
| ~ sQ242_spl
| sQ243_spl ),
inference(split_clause,[status(thm)],[f8549,f3856,f3852,f8499,f7949,f1005,f2333]) ).
fof(f8586,plain,
( ~ sQ128_spl
| ~ sQ57_spl
| ~ sQ498_spl
| ~ sQ540_spl
| sQ244_spl
| ~ sQ242_spl ),
inference(split_clause,[status(thm)],[f8554,f3852,f3860,f8499,f7949,f1005,f2333]) ).
fof(f8587,plain,
( ~ sQ128_spl
| ~ sQ57_spl
| ~ sQ498_spl
| ~ sQ540_spl
| sQ245_spl
| ~ sQ242_spl ),
inference(split_clause,[status(thm)],[f8555,f3852,f3864,f8499,f7949,f1005,f2333]) ).
fof(f8588,plain,
( ~ sQ128_spl
| ~ sQ57_spl
| ~ sQ498_spl
| ~ sQ540_spl
| sQ246_spl
| ~ sQ242_spl ),
inference(split_clause,[status(thm)],[f8556,f3852,f3868,f8499,f7949,f1005,f2333]) ).
fof(f8589,plain,
( ~ sQ128_spl
| ~ sQ57_spl
| ~ sQ498_spl
| ~ sQ540_spl
| ~ sQ242_spl
| sQ247_spl ),
inference(split_clause,[status(thm)],[f8565,f3872,f3852,f8499,f7949,f1005,f2333]) ).
fof(f8590,plain,
( ~ sQ128_spl
| ~ sQ57_spl
| ~ sQ498_spl
| ~ sQ540_spl
| ~ sQ242_spl
| sQ248_spl ),
inference(split_clause,[status(thm)],[f8575,f3876,f3852,f8499,f7949,f1005,f2333]) ).
fof(f8595,plain,
! [X0,X1] :
( ~ sQ163_spl
| ~ sP11_prd(X1,c_2Ebool_2EF,X0)
| ~ mem(X1,bool)
| ~ mem(c_2Ebool_2EF,bool)
| ~ mem(X0,bool)
| sP11_prd(X1,c_2Ebool_2EF,X0)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f2884,f267]) ).
fof(f8597,plain,
( ~ sQ163_spl
| ~ sQ11_spl
| sQ450_spl ),
inference(split_clause,[status(thm)],[f8595,f7314,f484,f2883]) ).
fof(f8607,plain,
( sQ311_spl
| p(c_2Ebool_2EF)
| ~ sP17_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET)) ),
inference(resolution,[status(thm)],[f4848,f401]) ).
fof(f8611,definition,
( sQ542_spl
<=> sP17_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET)) ),
introduced(definition,[new_symbols(definition,[sQ542_spl])],[split_symbol_definition]) ).
fof(f8614,plain,
( sQ311_spl
| sQ21_spl
| ~ sQ542_spl ),
inference(split_clause,[status(thm)],[f8607,f8611,f550,f4790]) ).
fof(f8621,plain,
( sQ311_spl
| ~ sP15_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f4840,f398]) ).
fof(f8629,plain,
( sQ83_spl
| ~ sQ57_spl
| sQ311_spl
| p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET))
| ~ sP15_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET)) ),
inference(resolution,[status(thm)],[f4821,f333]) ).
fof(f8635,plain,
( sQ83_spl
| ~ sQ57_spl
| sQ311_spl
| ~ sP5_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET))
| ~ mem(c_2Ebool_2EF,bool)
| ~ mem(c_2Ebool_2EF,bool)
| ~ mem(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),bool) ),
inference(resolution,[status(thm)],[f4821,f235]) ).
fof(f8636,definition,
( sQ543_spl
<=> sP15_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET)) ),
introduced(definition,[new_symbols(definition,[sQ543_spl])],[split_symbol_definition]) ).
fof(f8640,plain,
( sQ83_spl
| ~ sQ57_spl
| sQ311_spl
| ~ sQ543_spl ),
inference(split_clause,[status(thm)],[f8629,f8636,f4790,f1005,f1843]) ).
fof(f8646,definition,
( sQ544_spl
<=> sP5_prd(c_2Ebool_2EF,c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET)) ),
introduced(definition,[new_symbols(definition,[sQ544_spl])],[split_symbol_definition]) ).
fof(f8649,plain,
( sQ83_spl
| ~ sQ57_spl
| sQ311_spl
| ~ sQ544_spl
| ~ sQ11_spl
| ~ sQ242_spl ),
inference(split_clause,[status(thm)],[f8635,f3852,f484,f8646,f4790,f1005,f1843]) ).
fof(f8651,plain,
( sQ83_spl
| ~ sQ57_spl
| sQ311_spl
| p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET))
| ~ sP15_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f4820,f332]) ).
fof(f8658,plain,
( sQ83_spl
| ~ sQ57_spl
| sQ311_spl
| ~ sP5_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),c_2Ebool_2EF,c_2Ebool_2EF)
| ~ mem(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),bool)
| ~ mem(c_2Ebool_2EF,bool)
| ~ mem(c_2Ebool_2EF,bool) ),
inference(resolution,[status(thm)],[f4820,f235]) ).
fof(f8659,definition,
( sQ545_spl
<=> sP15_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),c_2Ebool_2EF,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ545_spl])],[split_symbol_definition]) ).
fof(f8662,plain,
( sQ83_spl
| ~ sQ57_spl
| sQ311_spl
| ~ sQ545_spl ),
inference(split_clause,[status(thm)],[f8651,f8659,f4790,f1005,f1843]) ).
fof(f8664,definition,
( sQ546_spl
<=> sP17_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),c_2Ebool_2EF,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ546_spl])],[split_symbol_definition]) ).
fof(f8672,definition,
( sQ547_spl
<=> sP5_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),c_2Ebool_2EF,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ547_spl])],[split_symbol_definition]) ).
fof(f8675,plain,
( sQ83_spl
| ~ sQ57_spl
| sQ311_spl
| ~ sQ547_spl
| ~ sQ242_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8658,f484,f3852,f8672,f4790,f1005,f1843]) ).
fof(f8685,plain,
( sQ311_spl
| p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET))
| ~ sP17_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),c_2Ebool_2EF,c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f8621,f401]) ).
fof(f8689,plain,
( sQ311_spl
| ~ sQ546_spl ),
inference(split_clause,[status(thm)],[f8685,f8664,f4790]) ).
fof(f8693,plain,
! [X0,X1] :
( ~ sQ171_spl
| ~ sP9_prd(X1,X0,c_2Ebool_2EF)
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| ~ mem(c_2Ebool_2EF,bool)
| sP9_prd(X1,X0,c_2Ebool_2EF)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f3005,f256]) ).
fof(f8695,plain,
( ~ sQ171_spl
| ~ sQ11_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f8693,f4239,f484,f3004]) ).
fof(f8699,plain,
! [X0,X1] :
( ~ sQ173_spl
| ~ sP7_prd(X1,X0,c_2Ebool_2EF)
| ~ mem(X1,bool)
| ~ mem(X0,bool)
| ~ mem(c_2Ebool_2EF,bool)
| sP7_prd(X1,X0,c_2Ebool_2EF)
| ~ mem(X1,bool)
| ~ mem(X0,bool) ),
inference(resolution,[status(thm)],[f3016,f246]) ).
fof(f8701,plain,
( ~ sQ173_spl
| ~ sQ11_spl
| sQ262_spl ),
inference(split_clause,[status(thm)],[f8699,f4226,f484,f3015]) ).
fof(f8791,plain,
( sQ266_spl
| ~ sP6_prd(c_2Ebool_2EF,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f6382,f85]) ).
fof(f8792,plain,
( sQ266_spl
| p(c_2Ebool_2EF)
| ~ sP15_prd(c_2Ebool_2EF,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f8791,f332]) ).
fof(f8800,definition,
( sQ554_spl
<=> sP15_prd(c_2Ebool_2EF,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ554_spl])],[split_symbol_definition]) ).
fof(f8802,plain,
( sQ554_spl
| ~ sP15_prd(c_2Ebool_2EF,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF) ),
inference(component_clause,[status(thm)],[f8800]) ).
fof(f8803,plain,
( sQ266_spl
| sQ21_spl
| ~ sQ554_spl ),
inference(split_clause,[status(thm)],[f8792,f8800,f550,f4257]) ).
fof(f8805,definition,
( sQ555_spl
<=> sP17_prd(c_2Ebool_2EF,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ555_spl])],[split_symbol_definition]) ).
fof(f8817,plain,
( sQ554_spl
| p(c_2Ebool_2EF)
| ~ sP17_prd(c_2Ebool_2EF,ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f8802,f401]) ).
fof(f8821,plain,
( sQ554_spl
| sQ21_spl
| ~ sQ555_spl ),
inference(split_clause,[status(thm)],[f8817,f8805,f550,f8800]) ).
fof(f8834,plain,
( ~ sQ95_spl
| ~ sP6_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f6504,f85]) ).
fof(f8835,plain,
( ~ sQ95_spl
| p(c_2Ebool_2EF)
| ~ sP15_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f8834,f332]) ).
fof(f8843,definition,
( sQ557_spl
<=> sP15_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ557_spl])],[split_symbol_definition]) ).
fof(f8845,plain,
( sQ557_spl
| ~ sP15_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),c_2Ebool_2EF) ),
inference(component_clause,[status(thm)],[f8843]) ).
fof(f8846,plain,
( ~ sQ95_spl
| sQ21_spl
| ~ sQ557_spl ),
inference(split_clause,[status(thm)],[f8835,f8843,f550,f1952]) ).
fof(f8848,definition,
( sQ558_spl
<=> sP17_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ558_spl])],[split_symbol_definition]) ).
fof(f8860,plain,
( sQ557_spl
| p(c_2Ebool_2EF)
| ~ sP17_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2EF),c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f8845,f401]) ).
fof(f8864,plain,
( sQ557_spl
| sQ21_spl
| ~ sQ558_spl ),
inference(split_clause,[status(thm)],[f8860,f8848,f550,f8843]) ).
fof(f8939,plain,
( ~ sQ95_spl
| ~ sP6_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f6557,f85]) ).
fof(f8940,plain,
( ~ sQ95_spl
| p(c_2Ebool_2EF)
| ~ sP15_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f8939,f332]) ).
fof(f8948,definition,
( sQ564_spl
<=> sP15_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ564_spl])],[split_symbol_definition]) ).
fof(f8950,plain,
( sQ564_spl
| ~ sP15_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF) ),
inference(component_clause,[status(thm)],[f8948]) ).
fof(f8951,plain,
( ~ sQ95_spl
| sQ21_spl
| ~ sQ564_spl ),
inference(split_clause,[status(thm)],[f8940,f8948,f550,f1952]) ).
fof(f8953,definition,
( sQ565_spl
<=> sP17_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ565_spl])],[split_symbol_definition]) ).
fof(f8965,plain,
( sQ564_spl
| p(c_2Ebool_2EF)
| ~ sP17_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2ET),c_2Ebool_2EF),c_2Ebool_2EF) ),
inference(resolution,[status(thm)],[f8950,f401]) ).
fof(f8969,plain,
( sQ564_spl
| sQ21_spl
| ~ sQ565_spl ),
inference(split_clause,[status(thm)],[f8965,f8953,f550,f8948]) ).
fof(f8979,plain,
( sQ159_spl
| ~ sQ186_spl
| ~ sP6_prd(c_2Ebool_2EF,c_2Ebool_2EF,c_2Ebool_2EF)
| ~ mem(c_2Ebool_2EF,bool)
| ~ mem(c_2Ebool_2EF,bool) ),
inference(resolution,[status(thm)],[f3165,f2850]) ).
fof(f8982,plain,
( sQ159_spl
| ~ sQ186_spl
| ~ sQ160_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8979,f484,f2862,f3164,f2848]) ).
fof(f9060,plain,
! [X0] :
( sQ311_spl
| p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET))
| ~ sP17_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),c_2Ebool_2EF,X0)
| p(X0) ),
inference(resolution,[status(thm)],[f4847,f401]) ).
fof(f9064,definition,
! [X0] :
( sQ567_spl
<=> ( ~ sP17_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),c_2Ebool_2EF,X0)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ567_spl])],[split_symbol_definition]) ).
fof(f9067,plain,
( sQ311_spl
| sQ567_spl ),
inference(split_clause,[status(thm)],[f9060,f9064,f4790]) ).
fof(f9070,plain,
! [X0] :
( sQ311_spl
| p(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET))
| ~ sP17_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),X0)
| p(X0) ),
inference(resolution,[status(thm)],[f4842,f402]) ).
fof(f9073,definition,
! [X0] :
( sQ568_spl
<=> ( ~ sP17_prd(c_2Ebool_2EF,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),X0)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ568_spl])],[split_symbol_definition]) ).
fof(f9077,plain,
( sQ311_spl
| sQ568_spl ),
inference(split_clause,[status(thm)],[f9070,f9073,f4790]) ).
fof(f9160,plain,
! [X0,X1,X2] :
( ~ mem(X1,X2)
| ~ mem(X0,arr(X2,bool))
| p(ap(X0,X1))
| ~ p(c_2Ebool_2ET)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),ap(X0,X1))) ),
inference(resolution,[status(thm)],[f3426,f77]) ).
fof(f9165,definition,
! [X0,X1,X2] :
( sQ570_spl
<=> ( ~ mem(X1,X2)
| ~ mem(X0,arr(X2,bool))
| p(ap(X0,X1))
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,c_2Ebool_2ET),ap(X0,X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ570_spl])],[split_symbol_definition]) ).
fof(f9168,plain,
( ~ sQ23_spl
| sQ570_spl ),
inference(split_clause,[status(thm)],[f9160,f9165,f557]) ).
fof(f9169,plain,
! [X0] :
( sQ311_spl
| ~ sP14_prd(X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET))
| p(c_2Ebool_2EF)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f4836,f322]) ).
fof(f9171,definition,
! [X0] :
( sQ571_spl
<=> ( ~ sP14_prd(X0,ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET))
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ571_spl])],[split_symbol_definition]) ).
fof(f9174,plain,
( sQ311_spl
| sQ21_spl
| sQ571_spl ),
inference(split_clause,[status(thm)],[f9169,f9171,f550,f4790]) ).
fof(f9194,plain,
! [X0] :
( sQ311_spl
| ~ sP14_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),X0)
| p(c_2Ebool_2EF)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f4827,f322]) ).
fof(f9196,definition,
! [X0] :
( sQ573_spl
<=> ( ~ sP14_prd(ap(ap(c_2Ebool_2E_2F_5C,c_2Ebool_2EF),c_2Ebool_2ET),X0)
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ573_spl])],[split_symbol_definition]) ).
fof(f9199,plain,
( sQ311_spl
| sQ21_spl
| sQ573_spl ),
inference(split_clause,[status(thm)],[f9194,f9196,f550,f4790]) ).
fof(f9277,plain,
! [X0,X1,X2] :
( ~ mem(X1,X2)
| ~ mem(X0,arr(X2,bool))
| p(ap(X0,X1))
| p(c_2Ebool_2EF)
| ~ p(ap(ap(c_2Ebool_2E_5C_2F,c_2Ebool_2EF),ap(X0,X1))) ),
inference(resolution,[status(thm)],[f3438,f84]) ).
fof(f9281,definition,
! [X0,X1,X2] :
( sQ575_spl
<=> ( ~ mem(X1,X2)
| ~ mem(X0,arr(X2,bool))
| p(ap(X0,X1))
| ~ p(ap(ap(c_2Ebool_2E_5C_2F,c_2Ebool_2EF),ap(X0,X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ575_spl])],[split_symbol_definition]) ).
fof(f9284,plain,
( sQ21_spl
| sQ575_spl ),
inference(split_clause,[status(thm)],[f9277,f9281,f550]) ).
fof(f9289,plain,
( ~ sQ213_spl
| p(c_2Ebool_2EF)
| ~ p(ap(ap(c_2Ebool_2E_5C_2F,c_2Ebool_2EF),c_2Ebool_2EF)) ),
inference(resolution,[status(thm)],[f3441,f84]) ).
fof(f9293,definition,
( sQ577_spl
<=> p(ap(ap(c_2Ebool_2E_5C_2F,c_2Ebool_2EF),c_2Ebool_2EF)) ),
introduced(definition,[new_symbols(definition,[sQ577_spl])],[split_symbol_definition]) ).
fof(f9296,plain,
( ~ sQ213_spl
| sQ21_spl
| ~ sQ577_spl ),
inference(split_clause,[status(thm)],[f9289,f9293,f550,f3440]) ).
fof(f9335,plain,
( ~ sQ441_spl
| ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),sK4_skl),sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f6714,f1328]) ).
fof(f9345,plain,
( ~ sQ3_spl
| ~ sQ441_spl
| ~ sP4_prd(ap(ap(c_2Eextreal_2Eextreal__le,sK4_skl),sK2_skl)) ),
inference(backward_demodulation,[status(thm)],[f9348,f1226]) ).
fof(f9348,plain,
( ~ sQ441_spl
| ap(ap(c_2Eextreal_2Eextreal__max,sK3_skl),sK4_skl) = sK4_skl ),
inference(forward_demodulation,[status(thm)],[f1348,f9335]) ).
fof(f9358,plain,
( ~ sQ3_spl
| ~ sQ441_spl
| sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9345,f2455]) ).
fof(f9359,plain,
( ~ sQ3_spl
| ~ sQ441_spl
| sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f9358]) ).
fof(f9442,plain,
( sQ3_spl
| ~ sQ441_spl
| sP4_prd(ap(ap(c_2Eextreal_2Eextreal__le,sK4_skl),sK2_skl)) ),
inference(forward_demodulation,[status(thm)],[f9348,f3505]) ).
fof(f9634,plain,
! [X0] :
( sQ3_spl
| ~ sQ441_spl
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X0),sK2_skl))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,sK4_skl),X0))
| ~ mem(sK2_skl,ty_2Eextreal_2Eextreal)
| ~ mem(X0,ty_2Eextreal_2Eextreal)
| ~ mem(sK4_skl,ty_2Eextreal_2Eextreal) ),
inference(resolution,[status(thm)],[f9442,f1251]) ).
fof(f9636,plain,
( sQ3_spl
| ~ sQ441_spl
| ~ sQ6_spl
| sQ135_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f9634,f525,f2464,f463,f6713,f446]) ).
fof(f9638,plain,
$false,
inference(sat_refutation,[status(thm)],[f452,f456,f457,f477,f487,f511,f513,f528,f530,f543,f560,f578,f591,f593,f604,f614,f639,f641,f651,f653,f724,f784,f826,f848,f883,f996,f1047,f1053,f1078,f1087,f1211,f1752,f1879,f1889,f1903,f1920,f1925,f1927,f1928,f1955,f1965,f2001,f2263,f2267,f2283,f2287,f2291,f2294,f2301,f2305,f2311,f2336,f2340,f2382,f2403,f2410,f2467,f2483,f2549,f2560,f2625,f2635,f2641,f2646,f2693,f2702,f2729,f2746,f2761,f2828,f2841,f2846,f2851,f2886,f3007,f3018,f3029,f3112,f3137,f3155,f3167,f3346,f3391,f3395,f3399,f3403,f3407,f3411,f3415,f3431,f3443,f3457,f3459,f3552,f3562,f3577,f3586,f3602,f3612,f3623,f3642,f3691,f3699,f3708,f3949,f4009,f4021,f4053,f4081,f4083,f4260,f4358,f4502,f4509,f4511,f4546,f4550,f4551,f4577,f4613,f4617,f4621,f4636,f4687,f4691,f4693,f4758,f4809,f4810,f4943,f5166,f5172,f5344,f5394,f5440,f5455,f5467,f5496,f5511,f5523,f5555,f5571,f5584,f5594,f5653,f5672,f5734,f5742,f5868,f5887,f5981,f5989,f6006,f6025,f6084,f6092,f6107,f6297,f6387,f6400,f6509,f6522,f6562,f6575,f6599,f6645,f6708,f6716,f6864,f6922,f7210,f7498,f7512,f7714,f7748,f7750,f7752,f7895,f7903,f7907,f7911,f7915,f7935,f8041,f8049,f8167,f8187,f8199,f8206,f8220,f8232,f8259,f8266,f8331,f8390,f8396,f8398,f8434,f8438,f8453,f8462,f8482,f8486,f8490,f8494,f8498,f8502,f8509,f8537,f8584,f8585,f8586,f8587,f8588,f8589,f8590,f8597,f8614,f8640,f8649,f8662,f8675,f8689,f8695,f8701,f8803,f8821,f8846,f8864,f8951,f8969,f8982,f9067,f9077,f9168,f9174,f9199,f9284,f9296,f9359,f9636]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP021+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n010.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Sun Sep 20 21:53:41 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.59 % Drodi V4.1.1
% 18.10/2.93 % Refutation found
% 18.10/2.93 % SZS status Theorem for theBenchmark: Theorem is valid
% 18.10/2.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.97/3.01 % Elapsed time: 2.421242 seconds
% 3.97/3.01 % CPU time: 18.627714 seconds
% 3.97/3.01 % Total memory used: 245.328 MB
% 3.97/3.01 % Net memory used: 232.085 MB
%------------------------------------------------------------------------------