%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU299+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 02:20:04 PM UTC 2026
% Result : Theorem 3.93s 25.87s
% Output : CNFRefutation 3.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 102
% Syntax : Number of formulae : 441 ( 33 unt; 86 def)
% Number of atoms : 2045 ( 363 equ)
% Maximal formula atoms : 44 ( 4 avg)
% Number of connectives : 2557 ( 953 ~;1232 |; 256 &)
% ( 91 <=>; 24 =>; 0 <=; 1 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 101 ( 99 usr; 86 prp; 0-3 aty)
% Number of functors : 35 ( 35 usr; 7 con; 0-5 aty)
% Number of variables : 462 ( 377 !; 85 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A] :
( ordinal(A)
=> ? [B] :
! [C] :
( in(C,B)
<=> ( ? [D] :
( ( in(D,omega)
=> ! [E] :
( element(E,powerset(powerset(D)))
=> ~ ( ! [F] :
~ ( ! [G] :
( ( subset(F,G)
& in(G,E) )
=> G = F )
& in(F,E) )
& E != empty_set ) ) )
& C = D
& ordinal(D) )
& in(C,succ(A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ? [B] :
! [C] :
( in(C,B)
<=> ( ? [D] :
( ( in(D,omega)
=> ! [E] :
( element(E,powerset(powerset(D)))
=> ~ ( ! [F] :
~ ( ! [G] :
( ( subset(F,G)
& in(G,E) )
=> G = F )
& in(F,E) )
& E != empty_set ) ) )
& C = D
& ordinal(D) )
& in(C,succ(A)) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f4,axiom,
! [A] :
? [B] :
( finite(B)
& natural(B)
& ordinal(B)
& epsilon_connected(B)
& epsilon_transitive(B)
& one_to_one(B)
& function(B)
& relation(B)
& empty(B)
& element(B,powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
=> ordinal(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
( ~ empty(omega)
& ordinal(omega)
& epsilon_connected(omega)
& epsilon_transitive(omega) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [A] :
( ordinal(A)
=> ( ! [B,C,D] :
( ( ? [I] :
( ( in(I,omega)
=> ! [J] :
( element(J,powerset(powerset(I)))
=> ~ ( ! [K] :
~ ( ! [L] :
( ( subset(K,L)
& in(L,J) )
=> L = K )
& in(K,J) )
& J != empty_set ) ) )
& D = I
& ordinal(I) )
& B = D
& ? [E] :
( ( in(E,omega)
=> ! [F] :
( element(F,powerset(powerset(E)))
=> ~ ( ! [G] :
~ ( ! [H] :
( ( subset(G,H)
& in(H,F) )
=> H = G )
& in(G,F) )
& F != empty_set ) ) )
& C = E
& ordinal(E) )
& B = C )
=> C = D )
=> ? [B] :
! [C] :
( in(C,B)
<=> ? [D] :
( ? [M] :
( ( in(M,omega)
=> ! [N] :
( element(N,powerset(powerset(M)))
=> ~ ( ! [O] :
~ ( ! [P] :
( ( subset(O,P)
& in(P,N) )
=> P = O )
& in(O,N) )
& N != empty_set ) ) )
& C = M
& ordinal(M) )
& D = C
& in(D,succ(A)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,plain,
? [A] :
( ! [B] :
? [C] :
( in(C,B)
<~> ( ? [D] :
( ( ! [E] :
( ? [F] :
( ! [G] :
( G = F
| ~ subset(F,G)
| ~ in(G,E) )
& in(F,E) )
| E = empty_set
| ~ element(E,powerset(powerset(D))) )
| ~ in(D,omega) )
& C = D
& ordinal(D) )
& in(C,succ(A)) ) )
& ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f50,plain,
? [A] :
( ! [B] :
? [C] :
( ( ! [D] :
( ( ? [E] :
( ! [F] :
( ? [G] :
( G != F
& subset(F,G)
& in(G,E) )
| ~ in(F,E) )
& E != empty_set
& element(E,powerset(powerset(D))) )
& in(D,omega) )
| C != D
| ~ ordinal(D) )
| ~ in(C,succ(A))
| ~ in(C,B) )
& ( ( ? [D] :
( ( ! [E] :
( ? [F] :
( ! [G] :
( G = F
| ~ subset(F,G)
| ~ in(G,E) )
& in(F,E) )
| E = empty_set
| ~ element(E,powerset(powerset(D))) )
| ~ in(D,omega) )
& C = D
& ordinal(D) )
& in(C,succ(A)) )
| in(C,B) ) )
& ordinal(A) ),
inference(NNF_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
( ! [B] :
( ( ! [D] :
( ( ! [F] :
( ( sK5_skl(F,D,B) != F
& subset(F,sK5_skl(F,D,B))
& in(sK5_skl(F,D,B),sK4_skl(D,B)) )
| ~ in(F,sK4_skl(D,B)) )
& sK4_skl(D,B) != empty_set
& element(sK4_skl(D,B),powerset(powerset(D)))
& in(D,omega) )
| sK1_skl(B) != D
| ~ ordinal(D) )
| ~ in(sK1_skl(B),succ(sK0_skl))
| ~ in(sK1_skl(B),B) )
& ( ( ( ! [E] :
( ( ! [G] :
( G = sK3_skl(E,B)
| ~ subset(sK3_skl(E,B),G)
| ~ in(G,E) )
& in(sK3_skl(E,B),E) )
| E = empty_set
| ~ element(E,powerset(powerset(sK2_skl(B)))) )
| ~ in(sK2_skl(B),omega) )
& sK1_skl(B) = sK2_skl(B)
& ordinal(sK2_skl(B))
& in(sK1_skl(B),succ(sK0_skl)) )
| in(sK1_skl(B),B) ) )
& ordinal(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(A,sK0_skl),skolemize(C,sK1_skl(B)),skolemize(D,sK2_skl(B)),skolemize(F,sK3_skl(E,B)),skolemize(E,sK4_skl(D,B)),skolemize(G,sK5_skl(F,D,B))],[f50]) ).
fof(f52,plain,
ordinal(sK0_skl),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0] :
( in(sK1_skl(X0),succ(sK0_skl))
| in(sK1_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f54,plain,
! [X0] :
( ordinal(sK2_skl(X0))
| in(sK1_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f55,plain,
! [X0] :
( sK1_skl(X0) = sK2_skl(X0)
| in(sK1_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f56,plain,
! [X0,X1] :
( in(sK3_skl(X1,X0),X1)
| X1 = empty_set
| ~ element(X1,powerset(powerset(sK2_skl(X0))))
| ~ in(sK2_skl(X0),omega)
| in(sK1_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f57,plain,
! [X0,X1,X2] :
( X2 = sK3_skl(X1,X0)
| ~ subset(sK3_skl(X1,X0),X2)
| ~ in(X2,X1)
| X1 = empty_set
| ~ element(X1,powerset(powerset(sK2_skl(X0))))
| ~ in(sK2_skl(X0),omega)
| in(sK1_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f58,plain,
! [X0,X1] :
( in(X1,omega)
| sK1_skl(X0) != X1
| ~ ordinal(X1)
| ~ in(sK1_skl(X0),succ(sK0_skl))
| ~ in(sK1_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f59,plain,
! [X0,X1] :
( element(sK4_skl(X1,X0),powerset(powerset(X1)))
| sK1_skl(X0) != X1
| ~ ordinal(X1)
| ~ in(sK1_skl(X0),succ(sK0_skl))
| ~ in(sK1_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f60,plain,
! [X0,X1] :
( sK4_skl(X1,X0) != empty_set
| sK1_skl(X0) != X1
| ~ ordinal(X1)
| ~ in(sK1_skl(X0),succ(sK0_skl))
| ~ in(sK1_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f61,plain,
! [X0,X1,X2] :
( in(sK5_skl(X2,X1,X0),sK4_skl(X1,X0))
| ~ in(X2,sK4_skl(X1,X0))
| sK1_skl(X0) != X1
| ~ ordinal(X1)
| ~ in(sK1_skl(X0),succ(sK0_skl))
| ~ in(sK1_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f62,plain,
! [X0,X1,X2] :
( subset(X2,sK5_skl(X2,X1,X0))
| ~ in(X2,sK4_skl(X1,X0))
| sK1_skl(X0) != X1
| ~ ordinal(X1)
| ~ in(sK1_skl(X0),succ(sK0_skl))
| ~ in(sK1_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f63,plain,
! [X0,X1,X2] :
( sK5_skl(X2,X1,X0) != X2
| ~ in(X2,sK4_skl(X1,X0))
| sK1_skl(X0) != X1
| ~ ordinal(X1)
| ~ in(sK1_skl(X0),succ(sK0_skl))
| ~ in(sK1_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f67,plain,
! [A] :
( finite(sK7_skl(A))
& natural(sK7_skl(A))
& ordinal(sK7_skl(A))
& epsilon_connected(sK7_skl(A))
& epsilon_transitive(sK7_skl(A))
& one_to_one(sK7_skl(A))
& function(sK7_skl(A))
& relation(sK7_skl(A))
& empty(sK7_skl(A))
& element(sK7_skl(A),powerset(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(B,sK7_skl(A))],[f4]) ).
fof(f68,plain,
! [X0] : element(sK7_skl(X0),powerset(X0)),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f78,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f79,plain,
! [A] :
( ( finite(sK8_skl(A))
& ~ empty(sK8_skl(A))
& element(sK8_skl(A),powerset(A)) )
| empty(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(B,sK8_skl(A))],[f78]) ).
fof(f80,plain,
! [X0] :
( element(sK8_skl(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f81,plain,
! [X0] :
( ~ empty(sK8_skl(X0))
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f124,plain,
( natural(sK16_skl)
& ordinal(sK16_skl)
& epsilon_connected(sK16_skl)
& epsilon_transitive(sK16_skl)
& ~ empty(sK16_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(A,sK16_skl)],[f19]) ).
fof(f126,plain,
epsilon_transitive(sK16_skl),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f127,plain,
epsilon_connected(sK16_skl),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f136,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f137,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f138,plain,
( ordinal(sK17_skl)
& epsilon_connected(sK17_skl)
& epsilon_transitive(sK17_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl]),skolemize(A,sK17_skl)],[f22]) ).
fof(f139,plain,
epsilon_transitive(sK17_skl),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f140,plain,
epsilon_connected(sK17_skl),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f142,plain,
( ordinal(sK18_skl)
& epsilon_connected(sK18_skl)
& epsilon_transitive(sK18_skl)
& empty(sK18_skl)
& one_to_one(sK18_skl)
& function(sK18_skl)
& relation(sK18_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl]),skolemize(A,sK18_skl)],[f23]) ).
fof(f147,plain,
epsilon_transitive(sK18_skl),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f148,plain,
epsilon_connected(sK18_skl),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f154,plain,
( ordinal(sK19_skl)
& epsilon_connected(sK19_skl)
& epsilon_transitive(sK19_skl)
& ~ empty(sK19_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl]),skolemize(A,sK19_skl)],[f25]) ).
fof(f156,plain,
epsilon_transitive(sK19_skl),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f157,plain,
epsilon_connected(sK19_skl),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f159,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f160,plain,
! [A] :
( ( ~ empty(sK20_skl(A))
& element(sK20_skl(A),powerset(A)) )
| empty(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl]),skolemize(B,sK20_skl(A))],[f159]) ).
fof(f161,plain,
! [X0] :
( element(sK20_skl(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f162,plain,
! [X0] :
( ~ empty(sK20_skl(X0))
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f163,plain,
! [A] :
( empty(sK21_skl(A))
& element(sK21_skl(A),powerset(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl]),skolemize(B,sK21_skl(A))],[f27]) ).
fof(f164,plain,
! [X0] : element(sK21_skl(X0),powerset(X0)),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f172,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f173,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f174,plain,
epsilon_transitive(omega),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f175,plain,
epsilon_connected(omega),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f178,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f201,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f202,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f209,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f211,plain,
! [A] :
( ? [B] :
! [C] :
( in(C,B)
<=> ? [D] :
( ? [M] :
( ( ! [N] :
( ? [O] :
( ! [P] :
( P = O
| ~ subset(O,P)
| ~ in(P,N) )
& in(O,N) )
| N = empty_set
| ~ element(N,powerset(powerset(M))) )
| ~ in(M,omega) )
& C = M
& ordinal(M) )
& D = C
& in(D,succ(A)) ) )
| ? [B,C,D] :
( C != D
& ? [I] :
( ( ! [J] :
( ? [K] :
( ! [L] :
( L = K
| ~ subset(K,L)
| ~ in(L,J) )
& in(K,J) )
| J = empty_set
| ~ element(J,powerset(powerset(I))) )
| ~ in(I,omega) )
& D = I
& ordinal(I) )
& B = D
& ? [E] :
( ( ! [F] :
( ? [G] :
( ! [H] :
( H = G
| ~ subset(G,H)
| ~ in(H,F) )
& in(G,F) )
| F = empty_set
| ~ element(F,powerset(powerset(E))) )
| ~ in(E,omega) )
& C = E
& ordinal(E) )
& B = C )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f212,definition,
! [B,C,D] :
( sP0_prd(D,C,B)
<=> ( C != D
& ? [I] :
( ( ! [J] :
( ? [K] :
( ! [L] :
( L = K
| ~ subset(K,L)
| ~ in(L,J) )
& in(K,J) )
| J = empty_set
| ~ element(J,powerset(powerset(I))) )
| ~ in(I,omega) )
& D = I
& ordinal(I) )
& B = D
& ? [E] :
( ( ! [F] :
( ? [G] :
( ! [H] :
( H = G
| ~ subset(G,H)
| ~ in(H,F) )
& in(G,F) )
| F = empty_set
| ~ element(F,powerset(powerset(E))) )
| ~ in(E,omega) )
& C = E
& ordinal(E) )
& B = C ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f213,plain,
! [A] :
( ? [B] :
! [C] :
( in(C,B)
<=> ? [D] :
( ? [M] :
( ( ! [N] :
( ? [O] :
( ! [P] :
( P = O
| ~ subset(O,P)
| ~ in(P,N) )
& in(O,N) )
| N = empty_set
| ~ element(N,powerset(powerset(M))) )
| ~ in(M,omega) )
& C = M
& ordinal(M) )
& D = C
& in(D,succ(A)) ) )
| ? [B,C,D] : sP0_prd(D,C,B)
| ~ ordinal(A) ),
inference(formula_renaming,[status(thm)],[f211,f212]) ).
fof(f214,plain,
! [A] :
( ? [B] :
! [C] :
( ( ! [D] :
( ! [M] :
( ( ? [N] :
( ! [O] :
( ? [P] :
( P != O
& subset(O,P)
& in(P,N) )
| ~ in(O,N) )
& N != empty_set
& element(N,powerset(powerset(M))) )
& in(M,omega) )
| C != M
| ~ ordinal(M) )
| D != C
| ~ in(D,succ(A)) )
| in(C,B) )
& ( ? [D] :
( ? [M] :
( ( ! [N] :
( ? [O] :
( ! [P] :
( P = O
| ~ subset(O,P)
| ~ in(P,N) )
& in(O,N) )
| N = empty_set
| ~ element(N,powerset(powerset(M))) )
| ~ in(M,omega) )
& C = M
& ordinal(M) )
& D = C
& in(D,succ(A)) )
| ~ in(C,B) ) )
| ? [B,C,D] : sP0_prd(D,C,B)
| ~ ordinal(A) ),
inference(NNF_transformation,[status(thm)],[f213]) ).
fof(f215,plain,
! [A] :
( ? [B] :
( ! [C] :
( ! [M] :
( ( ? [N] :
( ! [O] :
( ? [P] :
( P != O
& subset(O,P)
& in(P,N) )
| ~ in(O,N) )
& N != empty_set
& element(N,powerset(powerset(M))) )
& in(M,omega) )
| C != M
| ~ ordinal(M) )
| ! [D] :
( D != C
| ~ in(D,succ(A)) )
| in(C,B) )
& ! [C] :
( ( ? [M] :
( ( ! [N] :
( ? [O] :
( ! [P] :
( P = O
| ~ subset(O,P)
| ~ in(P,N) )
& in(O,N) )
| N = empty_set
| ~ element(N,powerset(powerset(M))) )
| ~ in(M,omega) )
& C = M
& ordinal(M) )
& ? [D] :
( D = C
& in(D,succ(A)) ) )
| ~ in(C,B) ) )
| ? [B,C,D] : sP0_prd(D,C,B)
| ~ ordinal(A) ),
inference(miniscoping,[status(thm)],[f214]) ).
fof(f216,plain,
! [A] :
( ( ! [C] :
( ! [M] :
( ( ! [O] :
( ( sK32_skl(O,M,C,A) != O
& subset(O,sK32_skl(O,M,C,A))
& in(sK32_skl(O,M,C,A),sK31_skl(M,C,A)) )
| ~ in(O,sK31_skl(M,C,A)) )
& sK31_skl(M,C,A) != empty_set
& element(sK31_skl(M,C,A),powerset(powerset(M)))
& in(M,omega) )
| C != M
| ~ ordinal(M) )
| ! [D] :
( D != C
| ~ in(D,succ(A)) )
| in(C,sK27_skl(A)) )
& ! [C] :
( ( ( ! [N] :
( ( ! [P] :
( P = sK30_skl(N,C,A)
| ~ subset(sK30_skl(N,C,A),P)
| ~ in(P,N) )
& in(sK30_skl(N,C,A),N) )
| N = empty_set
| ~ element(N,powerset(powerset(sK29_skl(C,A)))) )
| ~ in(sK29_skl(C,A),omega) )
& C = sK29_skl(C,A)
& ordinal(sK29_skl(C,A))
& sK28_skl(C,A) = C
& in(sK28_skl(C,A),succ(A)) )
| ~ in(C,sK27_skl(A)) ) )
| sP0_prd(sK26_skl(A),sK25_skl(A),sK24_skl(A))
| ~ ordinal(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl,sK25_skl,sK26_skl,sK27_skl,sK28_skl,sK29_skl,sK30_skl,sK31_skl,sK32_skl]),skolemize(B,sK24_skl(A)),skolemize(C,sK25_skl(A)),skolemize(D,sK26_skl(A)),skolemize(B,sK27_skl(A)),skolemize(D,sK28_skl(C,A)),skolemize(M,sK29_skl(C,A)),skolemize(O,sK30_skl(N,C,A)),skolemize(N,sK31_skl(M,C,A)),skolemize(P,sK32_skl(O,M,C,A))],[f215]) ).
fof(f217,plain,
! [X0,X1] :
( in(sK28_skl(X1,X0),succ(X0))
| ~ in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f216]) ).
fof(f218,plain,
! [X0,X1] :
( sK28_skl(X1,X0) = X1
| ~ in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f216]) ).
fof(f219,plain,
! [X0,X1] :
( ordinal(sK29_skl(X1,X0))
| ~ in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f216]) ).
fof(f220,plain,
! [X0,X1] :
( X1 = sK29_skl(X1,X0)
| ~ in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f216]) ).
fof(f221,plain,
! [X0,X1,X2] :
( in(sK30_skl(X2,X1,X0),X2)
| X2 = empty_set
| ~ element(X2,powerset(powerset(sK29_skl(X1,X0))))
| ~ in(sK29_skl(X1,X0),omega)
| ~ in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f216]) ).
fof(f222,plain,
! [X0,X1,X2,X3] :
( X3 = sK30_skl(X2,X1,X0)
| ~ subset(sK30_skl(X2,X1,X0),X3)
| ~ in(X3,X2)
| X2 = empty_set
| ~ element(X2,powerset(powerset(sK29_skl(X1,X0))))
| ~ in(sK29_skl(X1,X0),omega)
| ~ in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f216]) ).
fof(f223,plain,
! [X0,X1,X2,X3] :
( in(X3,omega)
| X1 != X3
| ~ ordinal(X3)
| X2 != X1
| ~ in(X2,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f216]) ).
fof(f224,plain,
! [X0,X1,X2,X3] :
( element(sK31_skl(X3,X1,X0),powerset(powerset(X3)))
| X1 != X3
| ~ ordinal(X3)
| X2 != X1
| ~ in(X2,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f216]) ).
fof(f225,plain,
! [X0,X1,X2,X3] :
( sK31_skl(X3,X1,X0) != empty_set
| X1 != X3
| ~ ordinal(X3)
| X2 != X1
| ~ in(X2,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f216]) ).
fof(f226,plain,
! [X0,X1,X2,X3,X4] :
( in(sK32_skl(X4,X3,X1,X0),sK31_skl(X3,X1,X0))
| ~ in(X4,sK31_skl(X3,X1,X0))
| X1 != X3
| ~ ordinal(X3)
| X2 != X1
| ~ in(X2,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f216]) ).
fof(f227,plain,
! [X0,X1,X2,X3,X4] :
( subset(X4,sK32_skl(X4,X3,X1,X0))
| ~ in(X4,sK31_skl(X3,X1,X0))
| X1 != X3
| ~ ordinal(X3)
| X2 != X1
| ~ in(X2,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f216]) ).
fof(f228,plain,
! [X0,X1,X2,X3,X4] :
( sK32_skl(X4,X3,X1,X0) != X4
| ~ in(X4,sK31_skl(X3,X1,X0))
| X1 != X3
| ~ ordinal(X3)
| X2 != X1
| ~ in(X2,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f216]) ).
fof(f229,plain,
! [B,C,D] :
( ( C = D
| ! [I] :
( ( ? [J] :
( ! [K] :
( ? [L] :
( L != K
& subset(K,L)
& in(L,J) )
| ~ in(K,J) )
& J != empty_set
& element(J,powerset(powerset(I))) )
& in(I,omega) )
| D != I
| ~ ordinal(I) )
| B != D
| ! [E] :
( ( ? [F] :
( ! [G] :
( ? [H] :
( H != G
& subset(G,H)
& in(H,F) )
| ~ in(G,F) )
& F != empty_set
& element(F,powerset(powerset(E))) )
& in(E,omega) )
| C != E
| ~ ordinal(E) )
| B != C
| sP0_prd(D,C,B) )
& ( ( C != D
& ? [I] :
( ( ! [J] :
( ? [K] :
( ! [L] :
( L = K
| ~ subset(K,L)
| ~ in(L,J) )
& in(K,J) )
| J = empty_set
| ~ element(J,powerset(powerset(I))) )
| ~ in(I,omega) )
& D = I
& ordinal(I) )
& B = D
& ? [E] :
( ( ! [F] :
( ? [G] :
( ! [H] :
( H = G
| ~ subset(G,H)
| ~ in(H,F) )
& in(G,F) )
| F = empty_set
| ~ element(F,powerset(powerset(E))) )
| ~ in(E,omega) )
& C = E
& ordinal(E) )
& B = C )
| ~ sP0_prd(D,C,B) ) ),
inference(NNF_transformation,[status(thm)],[f212]) ).
fof(f230,plain,
( ! [B,C,D] :
( C = D
| ! [I] :
( ( ? [J] :
( ! [K] :
( ? [L] :
( L != K
& subset(K,L)
& in(L,J) )
| ~ in(K,J) )
& J != empty_set
& element(J,powerset(powerset(I))) )
& in(I,omega) )
| D != I
| ~ ordinal(I) )
| B != D
| ! [E] :
( ( ? [F] :
( ! [G] :
( ? [H] :
( H != G
& subset(G,H)
& in(H,F) )
| ~ in(G,F) )
& F != empty_set
& element(F,powerset(powerset(E))) )
& in(E,omega) )
| C != E
| ~ ordinal(E) )
| B != C
| sP0_prd(D,C,B) )
& ! [B,C,D] :
( ( C != D
& ? [I] :
( ( ! [J] :
( ? [K] :
( ! [L] :
( L = K
| ~ subset(K,L)
| ~ in(L,J) )
& in(K,J) )
| J = empty_set
| ~ element(J,powerset(powerset(I))) )
| ~ in(I,omega) )
& D = I
& ordinal(I) )
& B = D
& ? [E] :
( ( ! [F] :
( ? [G] :
( ! [H] :
( H = G
| ~ subset(G,H)
| ~ in(H,F) )
& in(G,F) )
| F = empty_set
| ~ element(F,powerset(powerset(E))) )
| ~ in(E,omega) )
& C = E
& ordinal(E) )
& B = C )
| ~ sP0_prd(D,C,B) ) ),
inference(miniscoping,[status(thm)],[f229]) ).
fof(f231,plain,
( ! [B,C,D] :
( C = D
| ! [I] :
( ( ! [K] :
( ( sK40_skl(K,I,D,C,B) != K
& subset(K,sK40_skl(K,I,D,C,B))
& in(sK40_skl(K,I,D,C,B),sK39_skl(I,D,C,B)) )
| ~ in(K,sK39_skl(I,D,C,B)) )
& sK39_skl(I,D,C,B) != empty_set
& element(sK39_skl(I,D,C,B),powerset(powerset(I)))
& in(I,omega) )
| D != I
| ~ ordinal(I) )
| B != D
| ! [E] :
( ( ! [G] :
( ( sK38_skl(G,E,D,C,B) != G
& subset(G,sK38_skl(G,E,D,C,B))
& in(sK38_skl(G,E,D,C,B),sK37_skl(E,D,C,B)) )
| ~ in(G,sK37_skl(E,D,C,B)) )
& sK37_skl(E,D,C,B) != empty_set
& element(sK37_skl(E,D,C,B),powerset(powerset(E)))
& in(E,omega) )
| C != E
| ~ ordinal(E) )
| B != C
| sP0_prd(D,C,B) )
& ! [B,C,D] :
( ( C != D
& ( ! [J] :
( ( ! [L] :
( L = sK36_skl(J,D,C,B)
| ~ subset(sK36_skl(J,D,C,B),L)
| ~ in(L,J) )
& in(sK36_skl(J,D,C,B),J) )
| J = empty_set
| ~ element(J,powerset(powerset(sK35_skl(D,C,B)))) )
| ~ in(sK35_skl(D,C,B),omega) )
& D = sK35_skl(D,C,B)
& ordinal(sK35_skl(D,C,B))
& B = D
& ( ! [F] :
( ( ! [H] :
( H = sK34_skl(F,D,C,B)
| ~ subset(sK34_skl(F,D,C,B),H)
| ~ in(H,F) )
& in(sK34_skl(F,D,C,B),F) )
| F = empty_set
| ~ element(F,powerset(powerset(sK33_skl(D,C,B)))) )
| ~ in(sK33_skl(D,C,B),omega) )
& C = sK33_skl(D,C,B)
& ordinal(sK33_skl(D,C,B))
& B = C )
| ~ sP0_prd(D,C,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33_skl,sK34_skl,sK35_skl,sK36_skl,sK37_skl,sK38_skl,sK39_skl,sK40_skl]),skolemize(E,sK33_skl(D,C,B)),skolemize(G,sK34_skl(F,D,C,B)),skolemize(I,sK35_skl(D,C,B)),skolemize(K,sK36_skl(J,D,C,B)),skolemize(F,sK37_skl(E,D,C,B)),skolemize(H,sK38_skl(G,E,D,C,B)),skolemize(J,sK39_skl(I,D,C,B)),skolemize(L,sK40_skl(K,I,D,C,B))],[f230]) ).
fof(f232,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f237,plain,
! [X0,X1,X2] :
( X2 = X0
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f242,plain,
! [X0,X1,X2] :
( X1 != X0
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f279,plain,
! [X0] :
( in(sK1_skl(X0),omega)
| ~ ordinal(sK1_skl(X0))
| ~ in(sK1_skl(X0),succ(sK0_skl))
| ~ in(sK1_skl(X0),X0) ),
inference(destructive_equality_resolution,[status(thm)],[f58]) ).
fof(f280,plain,
! [X0] :
( element(sK4_skl(sK1_skl(X0),X0),powerset(powerset(sK1_skl(X0))))
| ~ ordinal(sK1_skl(X0))
| ~ in(sK1_skl(X0),succ(sK0_skl))
| ~ in(sK1_skl(X0),X0) ),
inference(destructive_equality_resolution,[status(thm)],[f59]) ).
fof(f281,plain,
! [X0] :
( sK4_skl(sK1_skl(X0),X0) != empty_set
| ~ ordinal(sK1_skl(X0))
| ~ in(sK1_skl(X0),succ(sK0_skl))
| ~ in(sK1_skl(X0),X0) ),
inference(destructive_equality_resolution,[status(thm)],[f60]) ).
fof(f282,plain,
! [X0,X1] :
( in(sK5_skl(X1,sK1_skl(X0),X0),sK4_skl(sK1_skl(X0),X0))
| ~ in(X1,sK4_skl(sK1_skl(X0),X0))
| ~ ordinal(sK1_skl(X0))
| ~ in(sK1_skl(X0),succ(sK0_skl))
| ~ in(sK1_skl(X0),X0) ),
inference(destructive_equality_resolution,[status(thm)],[f61]) ).
fof(f283,plain,
! [X0,X1] :
( subset(X1,sK5_skl(X1,sK1_skl(X0),X0))
| ~ in(X1,sK4_skl(sK1_skl(X0),X0))
| ~ ordinal(sK1_skl(X0))
| ~ in(sK1_skl(X0),succ(sK0_skl))
| ~ in(sK1_skl(X0),X0) ),
inference(destructive_equality_resolution,[status(thm)],[f62]) ).
fof(f284,plain,
! [X0,X1] :
( sK5_skl(X1,sK1_skl(X0),X0) != X1
| ~ in(X1,sK4_skl(sK1_skl(X0),X0))
| ~ ordinal(sK1_skl(X0))
| ~ in(sK1_skl(X0),succ(sK0_skl))
| ~ in(sK1_skl(X0),X0) ),
inference(destructive_equality_resolution,[status(thm)],[f63]) ).
fof(f288,plain,
! [X0,X1] :
( in(X1,omega)
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f223]) ).
fof(f289,plain,
! [X0,X1] :
( element(sK31_skl(X1,X1,X0),powerset(powerset(X1)))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f224]) ).
fof(f290,plain,
! [X0,X1] :
( sK31_skl(X1,X1,X0) != empty_set
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f225]) ).
fof(f291,plain,
! [X0,X1,X2] :
( in(sK32_skl(X2,X1,X1,X0),sK31_skl(X1,X1,X0))
| ~ in(X2,sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f226]) ).
fof(f292,plain,
! [X0,X1,X2] :
( subset(X2,sK32_skl(X2,X1,X1,X0))
| ~ in(X2,sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f227]) ).
fof(f293,plain,
! [X0,X1,X2] :
( sK32_skl(X2,X1,X1,X0) != X2
| ~ in(X2,sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f228]) ).
fof(f294,plain,
! [X0,X1] : ~ sP0_prd(X0,X0,X1),
inference(destructive_equality_resolution,[status(thm)],[f242]) ).
fof(f306,plain,
( ordinal(sK17_skl)
| ~ epsilon_transitive(sK17_skl) ),
inference(resolution,[status(thm)],[f137,f140]) ).
fof(f307,plain,
( ordinal(sK16_skl)
| ~ epsilon_transitive(sK16_skl) ),
inference(resolution,[status(thm)],[f137,f127]) ).
fof(f309,definition,
( sQ0_spl
<=> epsilon_transitive(sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f311,plain,
( sQ0_spl
| ~ epsilon_transitive(sK17_skl) ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f312,definition,
( sQ1_spl
<=> ordinal(sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f315,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f306,f309,f312]) ).
fof(f316,definition,
( sQ2_spl
<=> epsilon_transitive(sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f318,plain,
( sQ2_spl
| ~ epsilon_transitive(sK16_skl) ),
inference(component_clause,[status(thm)],[f316]) ).
fof(f319,definition,
( sQ3_spl
<=> ordinal(sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f322,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f307,f316,f319]) ).
fof(f323,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f318,f126]) ).
fof(f324,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f323]) ).
fof(f325,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f311,f139]) ).
fof(f326,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f325]) ).
fof(f327,plain,
( ordinal(sK18_skl)
| ~ epsilon_transitive(sK18_skl) ),
inference(resolution,[status(thm)],[f148,f137]) ).
fof(f328,definition,
( sQ4_spl
<=> epsilon_transitive(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f330,plain,
( sQ4_spl
| ~ epsilon_transitive(sK18_skl) ),
inference(component_clause,[status(thm)],[f328]) ).
fof(f331,definition,
( sQ5_spl
<=> ordinal(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f334,plain,
( sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f327,f328,f331]) ).
fof(f335,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f330,f147]) ).
fof(f336,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f335]) ).
fof(f337,plain,
( ordinal(sK19_skl)
| ~ epsilon_transitive(sK19_skl) ),
inference(resolution,[status(thm)],[f157,f137]) ).
fof(f338,definition,
( sQ6_spl
<=> epsilon_transitive(sK19_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f340,plain,
( sQ6_spl
| ~ epsilon_transitive(sK19_skl) ),
inference(component_clause,[status(thm)],[f338]) ).
fof(f341,definition,
( sQ7_spl
<=> ordinal(sK19_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f344,plain,
( sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f337,f338,f341]) ).
fof(f345,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f340,f156]) ).
fof(f346,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f345]) ).
fof(f348,plain,
( ordinal(omega)
| ~ epsilon_transitive(omega) ),
inference(resolution,[status(thm)],[f175,f137]) ).
fof(f349,definition,
( sQ8_spl
<=> epsilon_transitive(omega) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f351,plain,
( sQ8_spl
| ~ epsilon_transitive(omega) ),
inference(component_clause,[status(thm)],[f349]) ).
fof(f352,definition,
( sQ9_spl
<=> ordinal(omega) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f355,plain,
( sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f348,f349,f352]) ).
fof(f356,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f351,f174]) ).
fof(f357,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f356]) ).
fof(f360,plain,
( ordinal(empty_set)
| ~ epsilon_transitive(empty_set) ),
inference(resolution,[status(thm)],[f202,f137]) ).
fof(f361,definition,
( sQ10_spl
<=> epsilon_transitive(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f363,plain,
( sQ10_spl
| ~ epsilon_transitive(empty_set) ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f364,definition,
( sQ11_spl
<=> ordinal(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f367,plain,
( sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f360,f361,f364]) ).
fof(f368,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f363,f201]) ).
fof(f369,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f368]) ).
fof(f374,plain,
! [X0] :
( sK1_skl(sK27_skl(X0)) = sK2_skl(sK27_skl(X0))
| sK28_skl(sK1_skl(sK27_skl(X0)),X0) = sK1_skl(sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f218,f55]) ).
fof(f378,plain,
! [X0] :
( sK1_skl(sK27_skl(X0)) = sK2_skl(sK27_skl(X0))
| sK1_skl(sK27_skl(X0)) = sK29_skl(sK1_skl(sK27_skl(X0)),X0)
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f220,f55]) ).
fof(f382,plain,
! [X0,X1] :
( ~ in(omega,X1)
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f288,f173]) ).
fof(f385,plain,
! [X0,X1] :
( ~ ordinal(omega)
| ~ in(omega,succ(X1))
| in(omega,sK27_skl(X1))
| sP0_prd(sK26_skl(X1),sK25_skl(X1),sK24_skl(X1))
| ~ ordinal(X1)
| ~ ordinal(omega)
| ~ in(omega,succ(X0))
| in(omega,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f382,f288]) ).
fof(f386,definition,
! [X0] :
( sQ12_spl
<=> ( ~ in(omega,succ(X0))
| in(omega,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f389,plain,
( ~ sQ9_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f385,f386,f352]) ).
fof(f391,plain,
! [X0] :
( in(sK1_skl(X0),X0)
| sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl) != empty_set
| ~ ordinal(sK1_skl(X0))
| in(sK1_skl(X0),sK27_skl(sK0_skl))
| sP0_prd(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))
| ~ ordinal(sK0_skl) ),
inference(resolution,[status(thm)],[f290,f53]) ).
fof(f394,definition,
( sQ13_spl
<=> ordinal(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f396,plain,
( sQ13_spl
| ~ ordinal(sK0_skl) ),
inference(component_clause,[status(thm)],[f394]) ).
fof(f397,definition,
( sQ14_spl
<=> sP0_prd(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f398,plain,
( ~ sQ14_spl
| sP0_prd(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)) ),
inference(component_clause,[status(thm)],[f397]) ).
fof(f399,plain,
( sQ14_spl
| ~ sP0_prd(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)) ),
inference(component_clause,[status(thm)],[f397]) ).
fof(f400,definition,
! [X0] :
( sQ15_spl
<=> ( in(sK1_skl(X0),X0)
| sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl) != empty_set
| ~ ordinal(sK1_skl(X0))
| in(sK1_skl(X0),sK27_skl(sK0_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f401,plain,
! [X0] :
( ~ sQ15_spl
| in(sK1_skl(X0),X0)
| sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl) != empty_set
| ~ ordinal(sK1_skl(X0))
| in(sK1_skl(X0),sK27_skl(sK0_skl)) ),
inference(component_clause,[status(thm)],[f400]) ).
fof(f403,plain,
( sQ15_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f391,f394,f397,f400]) ).
fof(f419,plain,
! [X0,X1] :
( sK1_skl(sK31_skl(X1,X1,X0)) = sK2_skl(sK31_skl(X1,X1,X0))
| sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0) != sK1_skl(sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f293,f55]) ).
fof(f420,plain,
! [X0,X1] :
( sK1_skl(sK31_skl(X1,X1,X0)) = sK2_skl(sK31_skl(X1,X1,X0))
| in(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f291,f55]) ).
fof(f428,plain,
! [X0] :
( in(sK1_skl(X0),X0)
| sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)) = sK2_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl))
| sK32_skl(sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)),sK1_skl(X0),sK1_skl(X0),sK0_skl) != sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl))
| ~ ordinal(sK1_skl(X0))
| in(sK1_skl(X0),sK27_skl(sK0_skl))
| sP0_prd(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))
| ~ ordinal(sK0_skl) ),
inference(resolution,[status(thm)],[f419,f53]) ).
fof(f431,definition,
! [X0] :
( sQ16_spl
<=> ( in(sK1_skl(X0),X0)
| sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)) = sK2_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl))
| sK32_skl(sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)),sK1_skl(X0),sK1_skl(X0),sK0_skl) != sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl))
| ~ ordinal(sK1_skl(X0))
| in(sK1_skl(X0),sK27_skl(sK0_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f434,plain,
( sQ16_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f428,f394,f397,f431]) ).
fof(f435,plain,
! [X0,X1] :
( in(sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0),sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0)
| sK1_skl(sK31_skl(X1,X1,X0)) = sK2_skl(sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f420,f291]) ).
fof(f436,plain,
! [X0,X1] :
( sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0) != sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0)
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0)
| sK1_skl(sK31_skl(X1,X1,X0)) = sK2_skl(sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f420,f293]) ).
fof(f438,plain,
! [X0,X1] :
( in(sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0),sK31_skl(X1,X1,X0))
| sK1_skl(sK31_skl(X1,X1,X0)) = sK2_skl(sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f435]) ).
fof(f439,plain,
! [X0,X1] :
( sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0) != sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0)
| sK1_skl(sK31_skl(X1,X1,X0)) = sK2_skl(sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f436]) ).
fof(f443,plain,
( ~ sQ14_spl
| sK24_skl(sK0_skl) = sK26_skl(sK0_skl) ),
inference(resolution,[status(thm)],[f398,f237]) ).
fof(f444,plain,
( ~ sQ14_spl
| sK24_skl(sK0_skl) = sK25_skl(sK0_skl) ),
inference(resolution,[status(thm)],[f398,f232]) ).
fof(f445,definition,
( sQ17_spl
<=> in(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),omega) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( sQ17_spl
| ~ in(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),omega) ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f448,definition,
! [X0] :
( sQ18_spl
<=> ( in(sK36_skl(X0,sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),X0)
| X0 = empty_set
| ~ element(X0,powerset(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))))) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f449,plain,
! [X0] :
( ~ sQ18_spl
| in(sK36_skl(X0,sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),X0)
| X0 = empty_set
| ~ element(X0,powerset(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))))) ),
inference(component_clause,[status(thm)],[f448]) ).
fof(f452,plain,
( ~ sQ14_spl
| sP0_prd(sK24_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)) ),
inference(backward_demodulation,[status(thm)],[f443,f398]) ).
fof(f455,plain,
( ~ sQ14_spl
| sP0_prd(sK24_skl(sK0_skl),sK24_skl(sK0_skl),sK24_skl(sK0_skl)) ),
inference(forward_demodulation,[status(thm)],[f444,f452]) ).
fof(f456,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f455,f294]) ).
fof(f457,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f456]) ).
fof(f458,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f396,f52]) ).
fof(f459,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f458]) ).
fof(f460,plain,
( sQ14_spl
| sK1_skl(sK27_skl(sK0_skl)) = sK2_skl(sK27_skl(sK0_skl))
| sK1_skl(sK27_skl(sK0_skl)) = sK29_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl)
| ~ ordinal(sK0_skl) ),
inference(resolution,[status(thm)],[f399,f378]) ).
fof(f461,plain,
( sQ14_spl
| sK1_skl(sK27_skl(sK0_skl)) = sK2_skl(sK27_skl(sK0_skl))
| sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl) = sK1_skl(sK27_skl(sK0_skl))
| ~ ordinal(sK0_skl) ),
inference(resolution,[status(thm)],[f399,f374]) ).
fof(f462,definition,
( sQ19_spl
<=> sK1_skl(sK27_skl(sK0_skl)) = sK29_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f463,plain,
( ~ sQ19_spl
| sK1_skl(sK27_skl(sK0_skl)) = sK29_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl) ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,definition,
( sQ20_spl
<=> sK1_skl(sK27_skl(sK0_skl)) = sK2_skl(sK27_skl(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( ~ sQ20_spl
| sK1_skl(sK27_skl(sK0_skl)) = sK2_skl(sK27_skl(sK0_skl)) ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f468,plain,
( sQ14_spl
| sQ20_spl
| sQ19_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f460,f394,f462,f465,f397]) ).
fof(f469,definition,
( sQ21_spl
<=> sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl) = sK1_skl(sK27_skl(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f470,plain,
( ~ sQ21_spl
| sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl) = sK1_skl(sK27_skl(sK0_skl)) ),
inference(component_clause,[status(thm)],[f469]) ).
fof(f472,plain,
( sQ14_spl
| sQ20_spl
| sQ21_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f461,f394,f469,f465,f397]) ).
fof(f475,plain,
! [X0,X1] :
( ~ sQ20_spl
| X1 = sK3_skl(X0,sK27_skl(sK0_skl))
| ~ subset(sK3_skl(X0,sK27_skl(sK0_skl)),X1)
| ~ in(X1,X0)
| X0 = empty_set
| ~ element(X0,powerset(powerset(sK2_skl(sK27_skl(sK0_skl)))))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),omega)
| in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) ),
inference(paramodulation,[status(thm)],[f466,f57]) ).
fof(f476,plain,
! [X0] :
( ~ sQ20_spl
| in(sK3_skl(X0,sK27_skl(sK0_skl)),X0)
| X0 = empty_set
| ~ element(X0,powerset(powerset(sK2_skl(sK27_skl(sK0_skl)))))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),omega)
| in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) ),
inference(paramodulation,[status(thm)],[f466,f56]) ).
fof(f477,plain,
( ~ sQ20_spl
| ordinal(sK1_skl(sK27_skl(sK0_skl)))
| in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) ),
inference(paramodulation,[status(thm)],[f466,f54]) ).
fof(f481,definition,
( sQ23_spl
<=> in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f482,plain,
( ~ sQ23_spl
| in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f483,plain,
( sQ23_spl
| ~ in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f484,definition,
! [X1] :
( sQ24_spl
<=> ( in(sK3_skl(X1,sK27_skl(sK0_skl)),X1)
| X1 = empty_set
| ~ element(X1,powerset(powerset(sK2_skl(sK27_skl(sK0_skl))))) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f485,plain,
! [X0] :
( ~ sQ24_spl
| in(sK3_skl(X0,sK27_skl(sK0_skl)),X0)
| X0 = empty_set
| ~ element(X0,powerset(powerset(sK2_skl(sK27_skl(sK0_skl))))) ),
inference(component_clause,[status(thm)],[f484]) ).
fof(f488,definition,
! [X1,X2] :
( sQ25_spl
<=> ( X2 = sK3_skl(X1,sK27_skl(sK0_skl))
| ~ subset(sK3_skl(X1,sK27_skl(sK0_skl)),X2)
| ~ in(X2,X1)
| X1 = empty_set
| ~ element(X1,powerset(powerset(sK2_skl(sK27_skl(sK0_skl))))) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f489,plain,
! [X0,X1] :
( ~ sQ25_spl
| X1 = sK3_skl(X0,sK27_skl(sK0_skl))
| ~ subset(sK3_skl(X0,sK27_skl(sK0_skl)),X1)
| ~ in(X1,X0)
| X0 = empty_set
| ~ element(X0,powerset(powerset(sK2_skl(sK27_skl(sK0_skl))))) ),
inference(component_clause,[status(thm)],[f488]) ).
fof(f492,definition,
( sQ26_spl
<=> in(sK1_skl(sK27_skl(sK0_skl)),omega) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f494,plain,
( sQ26_spl
| ~ in(sK1_skl(sK27_skl(sK0_skl)),omega) ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f495,plain,
( ~ sQ20_spl
| sQ25_spl
| ~ sQ26_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f475,f481,f492,f488,f465]) ).
fof(f496,plain,
( ~ sQ20_spl
| sQ24_spl
| ~ sQ26_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f476,f481,f492,f484,f465]) ).
fof(f497,definition,
( sQ27_spl
<=> ordinal(sK1_skl(sK27_skl(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f498,plain,
( ~ sQ27_spl
| ordinal(sK1_skl(sK27_skl(sK0_skl))) ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f500,plain,
( ~ sQ20_spl
| sQ27_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f477,f481,f497,f465]) ).
fof(f501,plain,
( ~ sQ23_spl
| sK1_skl(sK27_skl(sK0_skl)) = sK29_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl)
| sP0_prd(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))
| ~ ordinal(sK0_skl) ),
inference(resolution,[status(thm)],[f482,f220]) ).
fof(f502,plain,
( ~ sQ23_spl
| sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl) = sK1_skl(sK27_skl(sK0_skl))
| sP0_prd(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))
| ~ ordinal(sK0_skl) ),
inference(resolution,[status(thm)],[f482,f218]) ).
fof(f504,plain,
( ~ sQ23_spl
| sQ19_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f501,f394,f397,f462,f481]) ).
fof(f505,plain,
( ~ sQ23_spl
| sQ21_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f502,f394,f397,f469,f481]) ).
fof(f508,plain,
! [X0,X1] :
( ~ sQ19_spl
| X1 = sK30_skl(X0,sK1_skl(sK27_skl(sK0_skl)),sK0_skl)
| ~ subset(sK30_skl(X0,sK1_skl(sK27_skl(sK0_skl)),sK0_skl),X1)
| ~ in(X1,X0)
| X0 = empty_set
| ~ element(X0,powerset(powerset(sK29_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl))))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),omega)
| ~ in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))
| sP0_prd(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))
| ~ ordinal(sK0_skl) ),
inference(paramodulation,[status(thm)],[f463,f222]) ).
fof(f509,plain,
! [X0] :
( ~ sQ19_spl
| in(sK30_skl(X0,sK1_skl(sK27_skl(sK0_skl)),sK0_skl),X0)
| X0 = empty_set
| ~ element(X0,powerset(powerset(sK29_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl))))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),omega)
| ~ in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))
| sP0_prd(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))
| ~ ordinal(sK0_skl) ),
inference(paramodulation,[status(thm)],[f463,f221]) ).
fof(f510,plain,
( ~ sQ19_spl
| ordinal(sK1_skl(sK27_skl(sK0_skl)))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))
| sP0_prd(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))
| ~ ordinal(sK0_skl) ),
inference(paramodulation,[status(thm)],[f463,f219]) ).
fof(f511,definition,
! [X0,X1] :
( sQ28_spl
<=> ( X1 = sK30_skl(X0,sK1_skl(sK27_skl(sK0_skl)),sK0_skl)
| ~ subset(sK30_skl(X0,sK1_skl(sK27_skl(sK0_skl)),sK0_skl),X1)
| ~ in(X1,X0)
| X0 = empty_set
| ~ element(X0,powerset(powerset(sK29_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f512,plain,
! [X0,X1] :
( ~ sQ28_spl
| X1 = sK30_skl(X0,sK1_skl(sK27_skl(sK0_skl)),sK0_skl)
| ~ subset(sK30_skl(X0,sK1_skl(sK27_skl(sK0_skl)),sK0_skl),X1)
| ~ in(X1,X0)
| X0 = empty_set
| ~ element(X0,powerset(powerset(sK29_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl)))) ),
inference(component_clause,[status(thm)],[f511]) ).
fof(f514,plain,
( ~ sQ19_spl
| sQ28_spl
| ~ sQ26_spl
| ~ sQ23_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f508,f394,f397,f481,f492,f511,f462]) ).
fof(f515,definition,
! [X0] :
( sQ29_spl
<=> ( in(sK30_skl(X0,sK1_skl(sK27_skl(sK0_skl)),sK0_skl),X0)
| X0 = empty_set
| ~ element(X0,powerset(powerset(sK29_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f516,plain,
! [X0] :
( ~ sQ29_spl
| in(sK30_skl(X0,sK1_skl(sK27_skl(sK0_skl)),sK0_skl),X0)
| X0 = empty_set
| ~ element(X0,powerset(powerset(sK29_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl)))) ),
inference(component_clause,[status(thm)],[f515]) ).
fof(f518,plain,
( ~ sQ19_spl
| sQ29_spl
| ~ sQ26_spl
| ~ sQ23_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f509,f394,f397,f481,f492,f515,f462]) ).
fof(f519,plain,
( ~ sQ19_spl
| sQ27_spl
| ~ sQ23_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f510,f394,f397,f481,f497,f462]) ).
fof(f520,plain,
! [X0] :
( ~ sQ24_spl
| ~ sQ20_spl
| in(sK3_skl(X0,sK27_skl(sK0_skl)),X0)
| X0 = empty_set
| ~ element(X0,powerset(powerset(sK1_skl(sK27_skl(sK0_skl))))) ),
inference(forward_demodulation,[status(thm)],[f466,f485]) ).
fof(f522,plain,
( ~ sQ15_spl
| ~ sQ27_spl
| in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))
| sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl) != empty_set
| in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f498,f401]) ).
fof(f524,plain,
! [X0] :
( ~ sQ27_spl
| subset(X0,sK5_skl(X0,sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)))
| ~ in(X0,sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),succ(sK0_skl))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f498,f283]) ).
fof(f525,plain,
! [X0] :
( ~ sQ27_spl
| in(sK5_skl(X0,sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)))
| ~ in(X0,sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),succ(sK0_skl))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f498,f282]) ).
fof(f526,plain,
! [X0] :
( ~ sQ27_spl
| sK5_skl(X0,sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) != X0
| ~ in(X0,sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),succ(sK0_skl))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f498,f284]) ).
fof(f527,plain,
( ~ sQ27_spl
| sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) != empty_set
| ~ in(sK1_skl(sK27_skl(sK0_skl)),succ(sK0_skl))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f498,f281]) ).
fof(f528,definition,
( sQ30_spl
<=> sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f531,plain,
( ~ sQ15_spl
| ~ sQ27_spl
| ~ sQ30_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f522,f481,f528,f497,f400]) ).
fof(f538,definition,
( sQ33_spl
<=> in(sK1_skl(sK27_skl(sK0_skl)),succ(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f540,plain,
( sQ33_spl
| ~ in(sK1_skl(sK27_skl(sK0_skl)),succ(sK0_skl)) ),
inference(component_clause,[status(thm)],[f538]) ).
fof(f542,definition,
! [X0] :
( sQ34_spl
<=> ( subset(X0,sK5_skl(X0,sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)))
| ~ in(X0,sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f543,plain,
! [X0] :
( ~ sQ34_spl
| subset(X0,sK5_skl(X0,sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)))
| ~ in(X0,sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))) ),
inference(component_clause,[status(thm)],[f542]) ).
fof(f545,plain,
( ~ sQ27_spl
| sQ34_spl
| ~ sQ33_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f524,f481,f538,f542,f497]) ).
fof(f546,definition,
! [X0] :
( sQ35_spl
<=> ( in(sK5_skl(X0,sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)))
| ~ in(X0,sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f547,plain,
! [X0] :
( ~ sQ35_spl
| in(sK5_skl(X0,sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)))
| ~ in(X0,sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))) ),
inference(component_clause,[status(thm)],[f546]) ).
fof(f549,plain,
( ~ sQ27_spl
| sQ35_spl
| ~ sQ33_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f525,f481,f538,f546,f497]) ).
fof(f550,definition,
! [X0] :
( sQ36_spl
<=> ( sK5_skl(X0,sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) != X0
| ~ in(X0,sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f551,plain,
! [X0] :
( ~ sQ36_spl
| sK5_skl(X0,sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) != X0
| ~ in(X0,sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))) ),
inference(component_clause,[status(thm)],[f550]) ).
fof(f553,plain,
( ~ sQ27_spl
| sQ36_spl
| ~ sQ33_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f526,f481,f538,f550,f497]) ).
fof(f554,definition,
( sQ37_spl
<=> sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f557,plain,
( ~ sQ27_spl
| ~ sQ37_spl
| ~ sQ33_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f527,f481,f538,f554,f497]) ).
fof(f558,plain,
( sQ26_spl
| ~ ordinal(sK1_skl(sK27_skl(sK0_skl)))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),succ(sK0_skl))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f494,f279]) ).
fof(f559,plain,
! [X0] :
( sQ26_spl
| ~ ordinal(sK1_skl(sK27_skl(sK0_skl)))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),succ(X0))
| in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f494,f288]) ).
fof(f560,plain,
( sQ26_spl
| ~ sQ27_spl
| ~ sQ33_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f558,f481,f538,f497,f492]) ).
fof(f561,definition,
! [X0] :
( sQ38_spl
<=> ( ~ in(sK1_skl(sK27_skl(sK0_skl)),succ(X0))
| in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f562,plain,
! [X0] :
( ~ sQ38_spl
| ~ in(sK1_skl(sK27_skl(sK0_skl)),succ(X0))
| in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(component_clause,[status(thm)],[f561]) ).
fof(f564,plain,
( sQ26_spl
| ~ sQ27_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f559,f561,f497,f492]) ).
fof(f565,plain,
( sQ33_spl
| in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f540,f53]) ).
fof(f577,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ19_spl
| in(sK30_skl(X0,sK1_skl(sK27_skl(sK0_skl)),sK0_skl),X0)
| X0 = empty_set
| ~ element(X0,powerset(powerset(sK1_skl(sK27_skl(sK0_skl))))) ),
inference(forward_demodulation,[status(thm)],[f463,f516]) ).
fof(f578,plain,
! [X0,X1] :
( ~ sQ28_spl
| ~ sQ19_spl
| X1 = sK30_skl(X0,sK1_skl(sK27_skl(sK0_skl)),sK0_skl)
| ~ subset(sK30_skl(X0,sK1_skl(sK27_skl(sK0_skl)),sK0_skl),X1)
| ~ in(X1,X0)
| X0 = empty_set
| ~ element(X0,powerset(powerset(sK1_skl(sK27_skl(sK0_skl))))) ),
inference(forward_demodulation,[status(thm)],[f463,f512]) ).
fof(f583,plain,
( sQ23_spl
| sK1_skl(sK27_skl(sK0_skl)) = sK2_skl(sK27_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f483,f55]) ).
fof(f584,plain,
( sQ23_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f583,f465,f481]) ).
fof(f599,plain,
! [X0] :
( ~ sQ24_spl
| ~ sQ20_spl
| ~ ordinal(sK1_skl(sK27_skl(sK0_skl)))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),succ(X0))
| in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0)
| in(sK3_skl(sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),X0),sK27_skl(sK0_skl)),sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),X0))
| sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),X0) = empty_set ),
inference(resolution,[status(thm)],[f520,f289]) ).
fof(f605,definition,
! [X0] :
( sQ40_spl
<=> ( ~ in(sK1_skl(sK27_skl(sK0_skl)),succ(X0))
| in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0)
| in(sK3_skl(sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),X0),sK27_skl(sK0_skl)),sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),X0))
| sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f606,plain,
! [X0] :
( ~ sQ40_spl
| ~ in(sK1_skl(sK27_skl(sK0_skl)),succ(X0))
| in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0)
| in(sK3_skl(sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),X0),sK27_skl(sK0_skl)),sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),X0))
| sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),X0) = empty_set ),
inference(component_clause,[status(thm)],[f605]) ).
fof(f608,plain,
( ~ sQ24_spl
| ~ sQ20_spl
| ~ sQ27_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f599,f605,f497,f465,f484]) ).
fof(f616,definition,
( sQ43_spl
<=> sK20_skl(powerset(sK1_skl(sK27_skl(sK0_skl)))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f617,plain,
( ~ sQ43_spl
| sK20_skl(powerset(sK1_skl(sK27_skl(sK0_skl)))) = empty_set ),
inference(component_clause,[status(thm)],[f616]) ).
fof(f622,definition,
( sQ45_spl
<=> empty(powerset(sK1_skl(sK27_skl(sK0_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f623,plain,
( ~ sQ45_spl
| empty(powerset(sK1_skl(sK27_skl(sK0_skl)))) ),
inference(component_clause,[status(thm)],[f622]) ).
fof(f626,definition,
( sQ46_spl
<=> sK8_skl(powerset(sK1_skl(sK27_skl(sK0_skl)))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f627,plain,
( ~ sQ46_spl
| sK8_skl(powerset(sK1_skl(sK27_skl(sK0_skl)))) = empty_set ),
inference(component_clause,[status(thm)],[f626]) ).
fof(f657,plain,
( ~ sQ21_spl
| in(sK1_skl(sK27_skl(sK0_skl)),succ(sK0_skl))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))
| sP0_prd(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))
| ~ ordinal(sK0_skl) ),
inference(paramodulation,[status(thm)],[f470,f217]) ).
fof(f676,plain,
( ~ sQ21_spl
| sQ33_spl
| ~ sQ23_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f657,f394,f397,f481,f538,f469]) ).
fof(f679,plain,
! [X0,X1] :
( in(sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0),X1,X1,X0),sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0)
| sK1_skl(sK31_skl(X1,X1,X0)) = sK2_skl(sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f438,f291]) ).
fof(f680,plain,
! [X0,X1] :
( sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0),X1,X1,X0) != sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0)
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0)
| sK1_skl(sK31_skl(X1,X1,X0)) = sK2_skl(sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f438,f293]) ).
fof(f682,plain,
! [X0,X1] :
( in(sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0),X1,X1,X0),sK31_skl(X1,X1,X0))
| sK1_skl(sK31_skl(X1,X1,X0)) = sK2_skl(sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f679]) ).
fof(f683,plain,
! [X0,X1] :
( sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0),X1,X1,X0) != sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0)
| sK1_skl(sK31_skl(X1,X1,X0)) = sK2_skl(sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f680]) ).
fof(f701,plain,
! [X0,X1] :
( ~ ordinal(sK27_skl(X0))
| ~ in(sK27_skl(X0),succ(X1))
| in(sK27_skl(X0),sK27_skl(X1))
| sP0_prd(sK26_skl(X1),sK25_skl(X1),sK24_skl(X1))
| ~ ordinal(X1)
| sK32_skl(sK32_skl(sK1_skl(sK31_skl(omega,omega,X0)),omega,omega,X0),omega,omega,X0) != sK32_skl(sK1_skl(sK31_skl(omega,omega,X0)),omega,omega,X0)
| sK1_skl(sK31_skl(omega,omega,X0)) = sK2_skl(sK31_skl(omega,omega,X0))
| ~ ordinal(omega)
| ~ in(omega,succ(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f439,f382]) ).
fof(f702,plain,
! [X0,X1] :
( X1 = sK29_skl(X1,X0)
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0)
| sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0) != sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0)
| sK1_skl(sK31_skl(X1,X1,X0)) = sK2_skl(sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f439,f220]) ).
fof(f703,plain,
! [X0,X1] :
( sK28_skl(X1,X0) = X1
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0)
| sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0) != sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0)
| sK1_skl(sK31_skl(X1,X1,X0)) = sK2_skl(sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f439,f218]) ).
fof(f705,definition,
! [X0,X1] :
( sQ58_spl
<=> ( ~ ordinal(sK27_skl(X0))
| ~ in(sK27_skl(X0),succ(X1))
| in(sK27_skl(X0),sK27_skl(X1))
| sP0_prd(sK26_skl(X1),sK25_skl(X1),sK24_skl(X1))
| ~ ordinal(X1)
| sK32_skl(sK32_skl(sK1_skl(sK31_skl(omega,omega,X0)),omega,omega,X0),omega,omega,X0) != sK32_skl(sK1_skl(sK31_skl(omega,omega,X0)),omega,omega,X0)
| sK1_skl(sK31_skl(omega,omega,X0)) = sK2_skl(sK31_skl(omega,omega,X0))
| ~ in(omega,succ(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f708,plain,
( ~ sQ9_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f701,f705,f352]) ).
fof(f709,plain,
! [X0,X1] :
( X1 = sK29_skl(X1,X0)
| sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0) != sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0)
| sK1_skl(sK31_skl(X1,X1,X0)) = sK2_skl(sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f702]) ).
fof(f710,plain,
! [X0,X1] :
( sK28_skl(X1,X0) = X1
| sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0) != sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0)
| sK1_skl(sK31_skl(X1,X1,X0)) = sK2_skl(sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f703]) ).
fof(f724,plain,
( ~ sQ29_spl
| ~ sQ19_spl
| ~ ordinal(sK1_skl(sK27_skl(sK0_skl)))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),succ(sK0_skl))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))
| in(sK30_skl(sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)))
| sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) = empty_set ),
inference(resolution,[status(thm)],[f577,f280]) ).
fof(f745,definition,
( sQ66_spl
<=> in(sK30_skl(sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f746,plain,
( ~ sQ66_spl
| in(sK30_skl(sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))) ),
inference(component_clause,[status(thm)],[f745]) ).
fof(f748,plain,
( ~ sQ29_spl
| ~ sQ19_spl
| ~ sQ27_spl
| ~ sQ33_spl
| ~ sQ23_spl
| sQ66_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f724,f554,f745,f481,f538,f497,f462,f515]) ).
fof(f749,plain,
( ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f623,f209]) ).
fof(f750,plain,
~ sQ45_spl,
inference(contradiction_clause,[status(thm)],[f749]) ).
fof(f774,plain,
( ~ sQ43_spl
| ~ empty(empty_set)
| empty(powerset(sK1_skl(sK27_skl(sK0_skl)))) ),
inference(paramodulation,[status(thm)],[f617,f162]) ).
fof(f777,definition,
( sQ68_spl
<=> empty(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f779,plain,
( sQ68_spl
| ~ empty(empty_set) ),
inference(component_clause,[status(thm)],[f777]) ).
fof(f780,plain,
( ~ sQ43_spl
| ~ sQ68_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f774,f622,f777,f616]) ).
fof(f785,plain,
( sQ68_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f779,f178]) ).
fof(f786,plain,
sQ68_spl,
inference(contradiction_clause,[status(thm)],[f785]) ).
fof(f789,plain,
( ~ sQ46_spl
| ~ empty(empty_set)
| empty(powerset(sK1_skl(sK27_skl(sK0_skl)))) ),
inference(paramodulation,[status(thm)],[f627,f81]) ).
fof(f796,plain,
( ~ sQ46_spl
| ~ sQ68_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f789,f622,f777,f626]) ).
fof(f839,plain,
! [X0,X1] :
( in(sK32_skl(sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0),X1,X1,X0),X1,X1,X0),sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0)
| sK1_skl(sK31_skl(X1,X1,X0)) = sK2_skl(sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f682,f291]) ).
fof(f842,plain,
! [X0,X1] :
( in(sK32_skl(sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0),X1,X1,X0),X1,X1,X0),sK31_skl(X1,X1,X0))
| sK1_skl(sK31_skl(X1,X1,X0)) = sK2_skl(sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f839]) ).
fof(f845,plain,
! [X0,X1] :
( ~ ordinal(sK27_skl(X0))
| ~ in(sK27_skl(X0),succ(X1))
| in(sK27_skl(X0),sK27_skl(X1))
| sP0_prd(sK26_skl(X1),sK25_skl(X1),sK24_skl(X1))
| ~ ordinal(X1)
| sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(omega,omega,X0)),omega,omega,X0),omega,omega,X0),omega,omega,X0) != sK32_skl(sK32_skl(sK1_skl(sK31_skl(omega,omega,X0)),omega,omega,X0),omega,omega,X0)
| sK1_skl(sK31_skl(omega,omega,X0)) = sK2_skl(sK31_skl(omega,omega,X0))
| ~ ordinal(omega)
| ~ in(omega,succ(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f683,f382]) ).
fof(f846,plain,
! [X0,X1] :
( X1 = sK29_skl(X1,X0)
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0)
| sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0),X1,X1,X0) != sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0)
| sK1_skl(sK31_skl(X1,X1,X0)) = sK2_skl(sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f683,f220]) ).
fof(f847,plain,
! [X0,X1] :
( sK28_skl(X1,X0) = X1
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0)
| sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0),X1,X1,X0) != sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0)
| sK1_skl(sK31_skl(X1,X1,X0)) = sK2_skl(sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f683,f218]) ).
fof(f849,definition,
! [X0,X1] :
( sQ73_spl
<=> ( ~ ordinal(sK27_skl(X0))
| ~ in(sK27_skl(X0),succ(X1))
| in(sK27_skl(X0),sK27_skl(X1))
| sP0_prd(sK26_skl(X1),sK25_skl(X1),sK24_skl(X1))
| ~ ordinal(X1)
| sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(omega,omega,X0)),omega,omega,X0),omega,omega,X0),omega,omega,X0) != sK32_skl(sK32_skl(sK1_skl(sK31_skl(omega,omega,X0)),omega,omega,X0),omega,omega,X0)
| sK1_skl(sK31_skl(omega,omega,X0)) = sK2_skl(sK31_skl(omega,omega,X0))
| ~ in(omega,succ(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f852,plain,
( ~ sQ9_spl
| sQ73_spl ),
inference(split_clause,[status(thm)],[f845,f849,f352]) ).
fof(f853,plain,
! [X0,X1] :
( X1 = sK29_skl(X1,X0)
| sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0),X1,X1,X0) != sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0)
| sK1_skl(sK31_skl(X1,X1,X0)) = sK2_skl(sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f846]) ).
fof(f854,plain,
! [X0,X1] :
( sK28_skl(X1,X0) = X1
| sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0),X1,X1,X0) != sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0)
| sK1_skl(sK31_skl(X1,X1,X0)) = sK2_skl(sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f847]) ).
fof(f942,plain,
! [X0] :
( in(sK1_skl(X0),X0)
| sK1_skl(X0) = sK29_skl(sK1_skl(X0),sK0_skl)
| sK32_skl(sK32_skl(sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl) != sK32_skl(sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)),sK1_skl(X0),sK1_skl(X0),sK0_skl)
| sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)) = sK2_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl))
| ~ ordinal(sK1_skl(X0))
| sP0_prd(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))
| ~ ordinal(sK0_skl) ),
inference(resolution,[status(thm)],[f709,f53]) ).
fof(f949,definition,
! [X0] :
( sQ93_spl
<=> ( in(sK1_skl(X0),X0)
| sK1_skl(X0) = sK29_skl(sK1_skl(X0),sK0_skl)
| sK32_skl(sK32_skl(sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl) != sK32_skl(sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)),sK1_skl(X0),sK1_skl(X0),sK0_skl)
| sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)) = sK2_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl))
| ~ ordinal(sK1_skl(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f952,plain,
( sQ93_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f942,f394,f397,f949]) ).
fof(f971,plain,
! [X0] :
( in(sK1_skl(X0),X0)
| sK28_skl(sK1_skl(X0),sK0_skl) = sK1_skl(X0)
| sK32_skl(sK32_skl(sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl) != sK32_skl(sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)),sK1_skl(X0),sK1_skl(X0),sK0_skl)
| sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)) = sK2_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl))
| ~ ordinal(sK1_skl(X0))
| sP0_prd(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))
| ~ ordinal(sK0_skl) ),
inference(resolution,[status(thm)],[f710,f53]) ).
fof(f975,definition,
! [X0] :
( sQ96_spl
<=> ( in(sK1_skl(X0),X0)
| sK28_skl(sK1_skl(X0),sK0_skl) = sK1_skl(X0)
| sK32_skl(sK32_skl(sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl) != sK32_skl(sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)),sK1_skl(X0),sK1_skl(X0),sK0_skl)
| sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)) = sK2_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl))
| ~ ordinal(sK1_skl(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f978,plain,
( sQ96_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f971,f394,f397,f975]) ).
fof(f1024,definition,
( sQ103_spl
<=> in(sK2_skl(sK27_skl(sK0_skl)),omega) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1026,plain,
( sQ103_spl
| ~ in(sK2_skl(sK27_skl(sK0_skl)),omega) ),
inference(component_clause,[status(thm)],[f1024]) ).
fof(f1029,definition,
( sQ104_spl
<=> ordinal(sK2_skl(sK27_skl(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f1031,plain,
( sQ104_spl
| ~ ordinal(sK2_skl(sK27_skl(sK0_skl))) ),
inference(component_clause,[status(thm)],[f1029]) ).
fof(f1036,plain,
! [X0] :
( sQ103_spl
| ~ ordinal(sK2_skl(sK27_skl(sK0_skl)))
| ~ in(sK2_skl(sK27_skl(sK0_skl)),succ(X0))
| in(sK2_skl(sK27_skl(sK0_skl)),sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f1026,f288]) ).
fof(f1037,definition,
! [X0] :
( sQ105_spl
<=> ( ~ in(sK2_skl(sK27_skl(sK0_skl)),succ(X0))
| in(sK2_skl(sK27_skl(sK0_skl)),sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f1040,plain,
( sQ103_spl
| ~ sQ104_spl
| sQ105_spl ),
inference(split_clause,[status(thm)],[f1036,f1037,f1029,f1024]) ).
fof(f1087,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ in(sK3_skl(X0,sK27_skl(sK0_skl)),sK31_skl(X1,X1,X2))
| ~ ordinal(X1)
| ~ in(X1,succ(X2))
| in(X1,sK27_skl(X2))
| sP0_prd(sK26_skl(X2),sK25_skl(X2),sK24_skl(X2))
| ~ ordinal(X2)
| sK32_skl(sK3_skl(X0,sK27_skl(sK0_skl)),X1,X1,X2) = sK3_skl(X0,sK27_skl(sK0_skl))
| ~ in(sK32_skl(sK3_skl(X0,sK27_skl(sK0_skl)),X1,X1,X2),X0)
| X0 = empty_set
| ~ element(X0,powerset(powerset(sK2_skl(sK27_skl(sK0_skl))))) ),
inference(resolution,[status(thm)],[f489,f292]) ).
fof(f1089,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ in(sK3_skl(X0,sK27_skl(sK0_skl)),sK31_skl(X1,X1,X2))
| ~ ordinal(X1)
| ~ in(X1,succ(X2))
| in(X1,sK27_skl(X2))
| sP0_prd(sK26_skl(X2),sK25_skl(X2),sK24_skl(X2))
| ~ ordinal(X2)
| ~ in(sK32_skl(sK3_skl(X0,sK27_skl(sK0_skl)),X1,X1,X2),X0)
| X0 = empty_set
| ~ element(X0,powerset(powerset(sK2_skl(sK27_skl(sK0_skl))))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1087,f293]) ).
fof(f1102,plain,
( ~ sQ35_spl
| ~ sQ66_spl
| in(sK5_skl(sK30_skl(sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))) ),
inference(resolution,[status(thm)],[f746,f547]) ).
fof(f1103,plain,
( ~ sQ34_spl
| ~ sQ66_spl
| subset(sK30_skl(sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK5_skl(sK30_skl(sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))) ),
inference(resolution,[status(thm)],[f746,f543]) ).
fof(f1104,plain,
( ~ sQ36_spl
| ~ sQ66_spl
| sK5_skl(sK30_skl(sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) != sK30_skl(sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl) ),
inference(resolution,[status(thm)],[f746,f551]) ).
fof(f1149,definition,
( sQ122_spl
<=> sK20_skl(powerset(sK2_skl(sK27_skl(sK0_skl)))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f1150,plain,
( ~ sQ122_spl
| sK20_skl(powerset(sK2_skl(sK27_skl(sK0_skl)))) = empty_set ),
inference(component_clause,[status(thm)],[f1149]) ).
fof(f1155,definition,
( sQ124_spl
<=> empty(powerset(sK2_skl(sK27_skl(sK0_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f1156,plain,
( ~ sQ124_spl
| empty(powerset(sK2_skl(sK27_skl(sK0_skl)))) ),
inference(component_clause,[status(thm)],[f1155]) ).
fof(f1159,definition,
( sQ125_spl
<=> sK8_skl(powerset(sK2_skl(sK27_skl(sK0_skl)))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1160,plain,
( ~ sQ125_spl
| sK8_skl(powerset(sK2_skl(sK27_skl(sK0_skl)))) = empty_set ),
inference(component_clause,[status(thm)],[f1159]) ).
fof(f1173,plain,
( ~ sQ124_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1156,f209]) ).
fof(f1174,plain,
~ sQ124_spl,
inference(contradiction_clause,[status(thm)],[f1173]) ).
fof(f1197,plain,
( ~ sQ125_spl
| ~ empty(empty_set)
| empty(powerset(sK2_skl(sK27_skl(sK0_skl)))) ),
inference(paramodulation,[status(thm)],[f1160,f81]) ).
fof(f1204,plain,
( ~ sQ125_spl
| ~ sQ68_spl
| sQ124_spl ),
inference(split_clause,[status(thm)],[f1197,f1155,f777,f1159]) ).
fof(f1216,plain,
( ~ sQ122_spl
| ~ empty(empty_set)
| empty(powerset(sK2_skl(sK27_skl(sK0_skl)))) ),
inference(paramodulation,[status(thm)],[f1150,f162]) ).
fof(f1219,plain,
( ~ sQ122_spl
| ~ sQ68_spl
| sQ124_spl ),
inference(split_clause,[status(thm)],[f1216,f1155,f777,f1149]) ).
fof(f1229,plain,
! [X0,X1] :
( sK32_skl(sK32_skl(sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0),X1,X1,X0),X1,X1,X0),X1,X1,X0) != sK32_skl(sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0),X1,X1,X0),X1,X1,X0)
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0)
| sK1_skl(sK31_skl(X1,X1,X0)) = sK2_skl(sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f842,f293]) ).
fof(f1232,plain,
! [X0,X1] :
( sK32_skl(sK32_skl(sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0),X1,X1,X0),X1,X1,X0),X1,X1,X0) != sK32_skl(sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(X1,X1,X0)),X1,X1,X0),X1,X1,X0),X1,X1,X0),X1,X1,X0)
| sK1_skl(sK31_skl(X1,X1,X0)) = sK2_skl(sK31_skl(X1,X1,X0))
| ~ ordinal(X1)
| ~ in(X1,succ(X0))
| in(X1,sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1229]) ).
fof(f1301,plain,
! [X0] :
( in(sK1_skl(X0),X0)
| sK1_skl(X0) = sK29_skl(sK1_skl(X0),sK0_skl)
| sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl) != sK32_skl(sK32_skl(sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl)
| sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)) = sK2_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl))
| ~ ordinal(sK1_skl(X0))
| sP0_prd(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))
| ~ ordinal(sK0_skl) ),
inference(resolution,[status(thm)],[f853,f53]) ).
fof(f1312,definition,
! [X0] :
( sQ144_spl
<=> ( in(sK1_skl(X0),X0)
| sK1_skl(X0) = sK29_skl(sK1_skl(X0),sK0_skl)
| sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl) != sK32_skl(sK32_skl(sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl)
| sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)) = sK2_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl))
| ~ ordinal(sK1_skl(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f1315,plain,
( sQ144_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1301,f394,f397,f1312]) ).
fof(f1319,plain,
! [X0] :
( in(sK1_skl(X0),X0)
| sK28_skl(sK1_skl(X0),sK0_skl) = sK1_skl(X0)
| sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl) != sK32_skl(sK32_skl(sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl)
| sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)) = sK2_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl))
| ~ ordinal(sK1_skl(X0))
| sP0_prd(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))
| ~ ordinal(sK0_skl) ),
inference(resolution,[status(thm)],[f854,f53]) ).
fof(f1324,definition,
! [X0] :
( sQ145_spl
<=> ( in(sK1_skl(X0),X0)
| sK28_skl(sK1_skl(X0),sK0_skl) = sK1_skl(X0)
| sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl) != sK32_skl(sK32_skl(sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl)
| sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)) = sK2_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl))
| ~ ordinal(sK1_skl(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1327,plain,
( sQ145_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1319,f394,f397,f1324]) ).
fof(f1436,plain,
( ~ sQ38_spl
| in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))
| in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))
| sP0_prd(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))
| ~ ordinal(sK0_skl) ),
inference(resolution,[status(thm)],[f562,f53]) ).
fof(f1438,plain,
( ~ sQ38_spl
| sQ23_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1436,f394,f397,f481,f561]) ).
fof(f1530,plain,
! [X0] :
( ~ sQ18_spl
| ~ ordinal(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))
| ~ in(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),succ(X0))
| in(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0)
| in(sK36_skl(sK31_skl(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),X0),sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),sK31_skl(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),X0))
| sK31_skl(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),X0) = empty_set ),
inference(resolution,[status(thm)],[f449,f289]) ).
fof(f1531,plain,
( ~ sQ18_spl
| in(sK36_skl(sK21_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))),sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),sK21_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))))
| sK21_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))) = empty_set ),
inference(resolution,[status(thm)],[f449,f164]) ).
fof(f1532,plain,
( ~ sQ18_spl
| empty(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))))
| in(sK36_skl(sK20_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))),sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),sK20_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))))
| sK20_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))) = empty_set ),
inference(resolution,[status(thm)],[f449,f161]) ).
fof(f1533,plain,
( ~ sQ18_spl
| empty(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))))
| in(sK36_skl(sK8_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))),sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),sK8_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))))
| sK8_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))) = empty_set ),
inference(resolution,[status(thm)],[f449,f80]) ).
fof(f1534,plain,
( ~ sQ18_spl
| in(sK36_skl(sK7_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))),sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),sK7_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))))
| sK7_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))) = empty_set ),
inference(resolution,[status(thm)],[f449,f68]) ).
fof(f1535,definition,
! [X0] :
( sQ178_spl
<=> ( ~ in(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),succ(X0))
| in(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0)
| in(sK36_skl(sK31_skl(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),X0),sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),sK31_skl(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),X0))
| sK31_skl(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f1538,definition,
( sQ179_spl
<=> ordinal(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f1541,plain,
( ~ sQ18_spl
| ~ sQ179_spl
| sQ178_spl ),
inference(split_clause,[status(thm)],[f1530,f1535,f1538,f448]) ).
fof(f1542,definition,
( sQ180_spl
<=> sK21_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f1545,definition,
( sQ181_spl
<=> in(sK36_skl(sK21_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))),sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),sK21_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f1548,plain,
( ~ sQ18_spl
| sQ181_spl
| sQ180_spl ),
inference(split_clause,[status(thm)],[f1531,f1542,f1545,f448]) ).
fof(f1549,definition,
( sQ182_spl
<=> sK20_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f1550,plain,
( ~ sQ182_spl
| sK20_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))) = empty_set ),
inference(component_clause,[status(thm)],[f1549]) ).
fof(f1552,definition,
( sQ183_spl
<=> in(sK36_skl(sK20_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))),sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),sK20_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f1555,definition,
( sQ184_spl
<=> empty(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f1556,plain,
( ~ sQ184_spl
| empty(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))) ),
inference(component_clause,[status(thm)],[f1555]) ).
fof(f1558,plain,
( ~ sQ18_spl
| sQ184_spl
| sQ183_spl
| sQ182_spl ),
inference(split_clause,[status(thm)],[f1532,f1549,f1552,f1555,f448]) ).
fof(f1559,definition,
( sQ185_spl
<=> sK8_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition]) ).
fof(f1560,plain,
( ~ sQ185_spl
| sK8_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))) = empty_set ),
inference(component_clause,[status(thm)],[f1559]) ).
fof(f1562,definition,
( sQ186_spl
<=> in(sK36_skl(sK8_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))),sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),sK8_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f1565,plain,
( ~ sQ18_spl
| sQ184_spl
| sQ186_spl
| sQ185_spl ),
inference(split_clause,[status(thm)],[f1533,f1559,f1562,f1555,f448]) ).
fof(f1566,definition,
( sQ187_spl
<=> sK7_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f1569,definition,
( sQ188_spl
<=> in(sK36_skl(sK7_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))),sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),sK7_skl(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition]) ).
fof(f1572,plain,
( ~ sQ18_spl
| sQ188_spl
| sQ187_spl ),
inference(split_clause,[status(thm)],[f1534,f1566,f1569,f448]) ).
fof(f1573,plain,
( ~ sQ184_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1556,f209]) ).
fof(f1574,plain,
~ sQ184_spl,
inference(contradiction_clause,[status(thm)],[f1573]) ).
fof(f1585,plain,
! [X0] :
( sQ17_spl
| ~ ordinal(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))
| ~ in(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),succ(X0))
| in(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f447,f288]) ).
fof(f1586,definition,
! [X0] :
( sQ189_spl
<=> ( ~ in(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),succ(X0))
| in(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)),sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f1589,plain,
( sQ17_spl
| ~ sQ179_spl
| sQ189_spl ),
inference(split_clause,[status(thm)],[f1585,f1586,f1538,f445]) ).
fof(f1612,plain,
( ~ sQ185_spl
| ~ empty(empty_set)
| empty(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))) ),
inference(paramodulation,[status(thm)],[f1560,f81]) ).
fof(f1619,plain,
( ~ sQ185_spl
| ~ sQ68_spl
| sQ184_spl ),
inference(split_clause,[status(thm)],[f1612,f1555,f777,f1559]) ).
fof(f1625,plain,
( ~ sQ182_spl
| ~ empty(empty_set)
| empty(powerset(sK35_skl(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl)))) ),
inference(paramodulation,[status(thm)],[f1550,f162]) ).
fof(f1628,plain,
( ~ sQ182_spl
| ~ sQ68_spl
| sQ184_spl ),
inference(split_clause,[status(thm)],[f1625,f1555,f777,f1549]) ).
fof(f1693,plain,
( ~ sQ40_spl
| in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))
| in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))
| sP0_prd(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))
| ~ ordinal(sK0_skl)
| in(sK3_skl(sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK27_skl(sK0_skl)),sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl))
| sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl) = empty_set ),
inference(resolution,[status(thm)],[f606,f53]) ).
fof(f1694,definition,
( sQ199_spl
<=> in(sK3_skl(sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK27_skl(sK0_skl)),sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ199_spl])],[split_symbol_definition]) ).
fof(f1695,plain,
( ~ sQ199_spl
| in(sK3_skl(sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK27_skl(sK0_skl)),sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl)) ),
inference(component_clause,[status(thm)],[f1694]) ).
fof(f1698,plain,
( ~ sQ40_spl
| sQ23_spl
| sQ14_spl
| ~ sQ13_spl
| sQ199_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f1693,f528,f1694,f394,f397,f481,f605]) ).
fof(f1815,plain,
( ~ sQ28_spl
| ~ sQ19_spl
| ~ sQ34_spl
| ~ sQ66_spl
| sK5_skl(sK30_skl(sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) = sK30_skl(sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl)
| ~ in(sK5_skl(sK30_skl(sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)))
| sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) = empty_set
| ~ element(sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),powerset(powerset(sK1_skl(sK27_skl(sK0_skl))))) ),
inference(resolution,[status(thm)],[f1103,f578]) ).
fof(f1816,definition,
( sQ218_spl
<=> element(sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),powerset(powerset(sK1_skl(sK27_skl(sK0_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f1818,plain,
( sQ218_spl
| ~ element(sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),powerset(powerset(sK1_skl(sK27_skl(sK0_skl))))) ),
inference(component_clause,[status(thm)],[f1816]) ).
fof(f1819,definition,
( sQ219_spl
<=> in(sK5_skl(sK30_skl(sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition]) ).
fof(f1821,plain,
( sQ219_spl
| ~ in(sK5_skl(sK30_skl(sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))) ),
inference(component_clause,[status(thm)],[f1819]) ).
fof(f1822,definition,
( sQ220_spl
<=> sK5_skl(sK30_skl(sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) = sK30_skl(sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f1823,plain,
( ~ sQ220_spl
| sK5_skl(sK30_skl(sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) = sK30_skl(sK4_skl(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl) ),
inference(component_clause,[status(thm)],[f1822]) ).
fof(f1825,plain,
( ~ sQ28_spl
| ~ sQ19_spl
| ~ sQ34_spl
| ~ sQ66_spl
| sQ220_spl
| ~ sQ219_spl
| sQ37_spl
| ~ sQ218_spl ),
inference(split_clause,[status(thm)],[f1815,f1816,f554,f1819,f1822,f745,f542,f462,f511]) ).
fof(f1826,plain,
( ~ sQ220_spl
| ~ sQ36_spl
| ~ sQ66_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1823,f1104]) ).
fof(f1827,plain,
( ~ sQ220_spl
| ~ sQ36_spl
| ~ sQ66_spl ),
inference(contradiction_clause,[status(thm)],[f1826]) ).
fof(f1828,plain,
( sQ219_spl
| ~ sQ35_spl
| ~ sQ66_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1821,f1102]) ).
fof(f1829,plain,
( sQ219_spl
| ~ sQ35_spl
| ~ sQ66_spl ),
inference(contradiction_clause,[status(thm)],[f1828]) ).
fof(f1830,plain,
( sQ218_spl
| ~ ordinal(sK1_skl(sK27_skl(sK0_skl)))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),succ(sK0_skl))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl)) ),
inference(resolution,[status(thm)],[f1818,f280]) ).
fof(f1831,plain,
( sQ218_spl
| ~ sQ27_spl
| ~ sQ33_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1830,f481,f538,f497,f1816]) ).
fof(f1841,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ20_spl
| ~ in(sK3_skl(X0,sK27_skl(sK0_skl)),sK31_skl(X1,X1,X2))
| ~ ordinal(X1)
| ~ in(X1,succ(X2))
| in(X1,sK27_skl(X2))
| sP0_prd(sK26_skl(X2),sK25_skl(X2),sK24_skl(X2))
| ~ ordinal(X2)
| ~ in(sK32_skl(sK3_skl(X0,sK27_skl(sK0_skl)),X1,X1,X2),X0)
| X0 = empty_set
| ~ element(X0,powerset(powerset(sK1_skl(sK27_skl(sK0_skl))))) ),
inference(backward_demodulation,[status(thm)],[f466,f1089]) ).
fof(f2102,plain,
( sQ33_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f565,f481,f538]) ).
fof(f2122,plain,
( sQ104_spl
| ~ sQ20_spl
| ~ ordinal(sK1_skl(sK27_skl(sK0_skl))) ),
inference(forward_demodulation,[status(thm)],[f466,f1031]) ).
fof(f2123,plain,
( sQ104_spl
| ~ sQ20_spl
| ~ sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2122,f498]) ).
fof(f2124,plain,
( sQ104_spl
| ~ sQ20_spl
| ~ sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f2123]) ).
fof(f2278,plain,
! [X0] :
( in(sK1_skl(X0),X0)
| sK32_skl(sK32_skl(sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl) != sK32_skl(sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl)
| sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)) = sK2_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl))
| ~ ordinal(sK1_skl(X0))
| in(sK1_skl(X0),sK27_skl(sK0_skl))
| sP0_prd(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))
| ~ ordinal(sK0_skl) ),
inference(resolution,[status(thm)],[f1232,f53]) ).
fof(f2285,definition,
! [X0] :
( sQ222_spl
<=> ( in(sK1_skl(X0),X0)
| sK32_skl(sK32_skl(sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl) != sK32_skl(sK32_skl(sK32_skl(sK32_skl(sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl),sK1_skl(X0),sK1_skl(X0),sK0_skl)
| sK1_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl)) = sK2_skl(sK31_skl(sK1_skl(X0),sK1_skl(X0),sK0_skl))
| ~ ordinal(sK1_skl(X0))
| in(sK1_skl(X0),sK27_skl(sK0_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition]) ).
fof(f2288,plain,
( sQ222_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2278,f394,f397,f2285]) ).
fof(f2467,definition,
! [X1] :
( sQ242_spl
<=> ( in(sK3_skl(X1,sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),X1)
| X1 = empty_set
| ~ element(X1,powerset(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl))))) ) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f2468,plain,
! [X0] :
( ~ sQ242_spl
| in(sK3_skl(X0,sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),X0)
| X0 = empty_set
| ~ element(X0,powerset(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl))))) ),
inference(component_clause,[status(thm)],[f2467]) ).
fof(f2492,plain,
! [X0] :
( ~ sQ242_spl
| ~ ordinal(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))
| ~ in(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),succ(X0))
| in(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0)
| in(sK3_skl(sK31_skl(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),X0),sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),sK31_skl(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),X0))
| sK31_skl(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),X0) = empty_set ),
inference(resolution,[status(thm)],[f2468,f289]) ).
fof(f2493,plain,
( ~ sQ242_spl
| in(sK3_skl(sK21_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))),sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),sK21_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))))
| sK21_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))) = empty_set ),
inference(resolution,[status(thm)],[f2468,f164]) ).
fof(f2494,plain,
( ~ sQ242_spl
| empty(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl))))
| in(sK3_skl(sK20_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))),sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),sK20_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))))
| sK20_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))) = empty_set ),
inference(resolution,[status(thm)],[f2468,f161]) ).
fof(f2495,plain,
( ~ sQ242_spl
| empty(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl))))
| in(sK3_skl(sK8_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))),sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),sK8_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))))
| sK8_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))) = empty_set ),
inference(resolution,[status(thm)],[f2468,f80]) ).
fof(f2496,plain,
( ~ sQ242_spl
| in(sK3_skl(sK7_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))),sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),sK7_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))))
| sK7_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))) = empty_set ),
inference(resolution,[status(thm)],[f2468,f68]) ).
fof(f2497,definition,
! [X0] :
( sQ247_spl
<=> ( ~ in(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),succ(X0))
| in(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),sK27_skl(X0))
| sP0_prd(sK26_skl(X0),sK25_skl(X0),sK24_skl(X0))
| ~ ordinal(X0)
| in(sK3_skl(sK31_skl(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),X0),sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),sK31_skl(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),X0))
| sK31_skl(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f2500,definition,
( sQ248_spl
<=> ordinal(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f2503,plain,
( ~ sQ242_spl
| ~ sQ248_spl
| sQ247_spl ),
inference(split_clause,[status(thm)],[f2492,f2497,f2500,f2467]) ).
fof(f2504,definition,
( sQ249_spl
<=> sK21_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f2507,definition,
( sQ250_spl
<=> in(sK3_skl(sK21_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))),sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),sK21_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f2510,plain,
( ~ sQ242_spl
| sQ250_spl
| sQ249_spl ),
inference(split_clause,[status(thm)],[f2493,f2504,f2507,f2467]) ).
fof(f2511,definition,
( sQ251_spl
<=> sK20_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f2512,plain,
( ~ sQ251_spl
| sK20_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))) = empty_set ),
inference(component_clause,[status(thm)],[f2511]) ).
fof(f2514,definition,
( sQ252_spl
<=> in(sK3_skl(sK20_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))),sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),sK20_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f2517,definition,
( sQ253_spl
<=> empty(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f2518,plain,
( ~ sQ253_spl
| empty(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))) ),
inference(component_clause,[status(thm)],[f2517]) ).
fof(f2520,plain,
( ~ sQ242_spl
| sQ253_spl
| sQ252_spl
| sQ251_spl ),
inference(split_clause,[status(thm)],[f2494,f2511,f2514,f2517,f2467]) ).
fof(f2521,definition,
( sQ254_spl
<=> sK8_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f2522,plain,
( ~ sQ254_spl
| sK8_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))) = empty_set ),
inference(component_clause,[status(thm)],[f2521]) ).
fof(f2524,definition,
( sQ255_spl
<=> in(sK3_skl(sK8_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))),sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),sK8_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f2527,plain,
( ~ sQ242_spl
| sQ253_spl
| sQ255_spl
| sQ254_spl ),
inference(split_clause,[status(thm)],[f2495,f2521,f2524,f2517,f2467]) ).
fof(f2528,definition,
( sQ256_spl
<=> sK7_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f2531,definition,
( sQ257_spl
<=> in(sK3_skl(sK7_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))),sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)),sK7_skl(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f2534,plain,
( ~ sQ242_spl
| sQ257_spl
| sQ256_spl ),
inference(split_clause,[status(thm)],[f2496,f2528,f2531,f2467]) ).
fof(f2535,plain,
( ~ sQ253_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2518,f209]) ).
fof(f2536,plain,
~ sQ253_spl,
inference(contradiction_clause,[status(thm)],[f2535]) ).
fof(f2941,plain,
( ~ sQ251_spl
| ~ empty(empty_set)
| empty(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))) ),
inference(paramodulation,[status(thm)],[f2512,f162]) ).
fof(f2944,plain,
( ~ sQ251_spl
| ~ sQ68_spl
| sQ253_spl ),
inference(split_clause,[status(thm)],[f2941,f2517,f777,f2511]) ).
fof(f2951,plain,
( ~ sQ254_spl
| ~ empty(empty_set)
| empty(powerset(sK2_skl(sK31_skl(sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK28_skl(sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK0_skl)))) ),
inference(paramodulation,[status(thm)],[f2522,f81]) ).
fof(f2955,plain,
( ~ sQ254_spl
| ~ sQ68_spl
| sQ253_spl ),
inference(split_clause,[status(thm)],[f2951,f2517,f777,f2521]) ).
fof(f2968,plain,
( ~ sQ25_spl
| ~ sQ20_spl
| ~ sQ199_spl
| ~ ordinal(sK1_skl(sK27_skl(sK0_skl)))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),succ(sK0_skl))
| in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))
| sP0_prd(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))
| ~ ordinal(sK0_skl)
| ~ in(sK32_skl(sK3_skl(sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl))
| sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl) = empty_set
| ~ element(sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),powerset(powerset(sK1_skl(sK27_skl(sK0_skl))))) ),
inference(resolution,[status(thm)],[f1695,f1841]) ).
fof(f2969,plain,
( ~ sQ199_spl
| in(sK32_skl(sK3_skl(sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl))
| ~ ordinal(sK1_skl(sK27_skl(sK0_skl)))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),succ(sK0_skl))
| in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))
| sP0_prd(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))
| ~ ordinal(sK0_skl) ),
inference(resolution,[status(thm)],[f1695,f291]) ).
fof(f2972,definition,
( sQ285_spl
<=> element(sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),powerset(powerset(sK1_skl(sK27_skl(sK0_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f2974,plain,
( sQ285_spl
| ~ element(sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),powerset(powerset(sK1_skl(sK27_skl(sK0_skl))))) ),
inference(component_clause,[status(thm)],[f2972]) ).
fof(f2975,definition,
( sQ286_spl
<=> in(sK32_skl(sK3_skl(sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl),sK31_skl(sK1_skl(sK27_skl(sK0_skl)),sK1_skl(sK27_skl(sK0_skl)),sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f2978,plain,
( ~ sQ25_spl
| ~ sQ20_spl
| ~ sQ199_spl
| ~ sQ27_spl
| ~ sQ33_spl
| sQ23_spl
| sQ14_spl
| ~ sQ13_spl
| ~ sQ286_spl
| sQ30_spl
| ~ sQ285_spl ),
inference(split_clause,[status(thm)],[f2968,f2972,f528,f2975,f394,f397,f481,f538,f497,f1694,f465,f488]) ).
fof(f2979,plain,
( ~ sQ199_spl
| sQ286_spl
| ~ sQ27_spl
| ~ sQ33_spl
| sQ23_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2969,f394,f397,f481,f538,f497,f2975,f1694]) ).
fof(f2996,plain,
( sQ285_spl
| ~ ordinal(sK1_skl(sK27_skl(sK0_skl)))
| ~ in(sK1_skl(sK27_skl(sK0_skl)),succ(sK0_skl))
| in(sK1_skl(sK27_skl(sK0_skl)),sK27_skl(sK0_skl))
| sP0_prd(sK26_skl(sK0_skl),sK25_skl(sK0_skl),sK24_skl(sK0_skl))
| ~ ordinal(sK0_skl) ),
inference(resolution,[status(thm)],[f2974,f289]) ).
fof(f2997,plain,
( sQ285_spl
| ~ sQ27_spl
| ~ sQ33_spl
| sQ23_spl
| sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2996,f394,f397,f481,f538,f497,f2972]) ).
fof(f2998,plain,
$false,
inference(sat_refutation,[status(thm)],[f315,f322,f324,f326,f334,f336,f344,f346,f355,f357,f367,f369,f389,f403,f434,f457,f459,f468,f472,f495,f496,f500,f504,f505,f514,f518,f519,f531,f545,f549,f553,f557,f560,f564,f584,f608,f676,f708,f748,f750,f780,f786,f796,f852,f952,f978,f1040,f1174,f1204,f1219,f1315,f1327,f1438,f1541,f1548,f1558,f1565,f1572,f1574,f1589,f1619,f1628,f1698,f1825,f1827,f1829,f1831,f2102,f2124,f2288,f2503,f2510,f2520,f2527,f2534,f2536,f2944,f2955,f2978,f2979,f2997]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU299+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.06/25.27 % CPULimit : 300
% 0.06/25.27 % WCLimit : 300
% 0.06/25.27 % DateTime : Mon Sep 21 06:09:18 UTC 2026
% 0.06/25.27 % CPUTime :
% 0.06/25.28 % Drodi V4.1.1
% 3.93/25.87 % Refutation found
% 3.93/25.87 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.93/25.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.45/25.91 % Elapsed time: 0.625531 seconds
% 0.45/25.91 % CPU time: 4.760578 seconds
% 0.45/25.91 % Total memory used: 219.593 MB
% 0.45/25.91 % Net memory used: 214.447 MB
%------------------------------------------------------------------------------