%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU364+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 : n026.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 02:20:18 PM UTC 2026
% Result : Theorem 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 21
% Syntax : Number of formulae : 127 ( 15 unt; 19 def)
% Number of atoms : 736 ( 87 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 966 ( 357 ~; 429 |; 150 &)
% ( 24 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 19 prp; 0-5 aty)
% Number of functors : 19 ( 19 usr; 3 con; 0-5 aty)
% Number of variables : 265 ( 195 !; 70 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A,B,C] :
( ( element(C,powerset(B))
& finite(C)
& element(B,powerset(the_carrier(A)))
& rel_str(A)
& transitive_relstr(A)
& ~ empty_carrier(A) )
=> ? [D] :
! [E] :
( in(E,D)
<=> ( ? [F] :
( ? [G] :
( relstr_set_smaller(A,F,G)
& in(G,B)
& element(G,the_carrier(A)) )
& F = E )
& in(E,powerset(C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A,B,C] :
( ( element(C,powerset(B))
& finite(C)
& element(B,powerset(the_carrier(A)))
& rel_str(A)
& transitive_relstr(A)
& ~ empty_carrier(A) )
=> ? [D] :
! [E] :
( in(E,D)
<=> ( ? [F] :
( ? [G] :
( relstr_set_smaller(A,F,G)
& in(G,B)
& element(G,the_carrier(A)) )
& F = E )
& in(E,powerset(C)) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f22,axiom,
! [A,B,C] :
( ( element(C,powerset(B))
& finite(C)
& element(B,powerset(the_carrier(A)))
& rel_str(A)
& transitive_relstr(A)
& ~ empty_carrier(A) )
=> ( ! [D,E,F] :
( ( ? [I] :
( ? [J] :
( relstr_set_smaller(A,I,J)
& in(J,B)
& element(J,the_carrier(A)) )
& I = F )
& D = F
& ? [G] :
( ? [H] :
( relstr_set_smaller(A,G,H)
& in(H,B)
& element(H,the_carrier(A)) )
& G = E )
& D = E )
=> E = F )
=> ? [D] :
! [E] :
( in(E,D)
<=> ? [F] :
( ? [K] :
( ? [L] :
( relstr_set_smaller(A,K,L)
& in(L,B)
& element(L,the_carrier(A)) )
& K = E )
& F = E
& in(F,powerset(C)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,plain,
? [A,B,C] :
( ! [D] :
? [E] :
( in(E,D)
<~> ( ? [F] :
( ? [G] :
( relstr_set_smaller(A,F,G)
& in(G,B)
& element(G,the_carrier(A)) )
& F = E )
& in(E,powerset(C)) ) )
& element(C,powerset(B))
& finite(C)
& element(B,powerset(the_carrier(A)))
& rel_str(A)
& transitive_relstr(A)
& ~ empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f24,plain,
? [A,B,C] :
( ! [D] :
? [E] :
( ( ! [F] :
( ! [G] :
( ~ relstr_set_smaller(A,F,G)
| ~ in(G,B)
| ~ element(G,the_carrier(A)) )
| F != E )
| ~ in(E,powerset(C))
| ~ in(E,D) )
& ( ( ? [F] :
( ? [G] :
( relstr_set_smaller(A,F,G)
& in(G,B)
& element(G,the_carrier(A)) )
& F = E )
& in(E,powerset(C)) )
| in(E,D) ) )
& element(C,powerset(B))
& finite(C)
& element(B,powerset(the_carrier(A)))
& rel_str(A)
& transitive_relstr(A)
& ~ empty_carrier(A) ),
inference(NNF_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
( ! [D] :
( ( ! [F] :
( ! [G] :
( ~ relstr_set_smaller(sK0_skl,F,G)
| ~ in(G,sK1_skl)
| ~ element(G,the_carrier(sK0_skl)) )
| F != sK3_skl(D) )
| ~ in(sK3_skl(D),powerset(sK2_skl))
| ~ in(sK3_skl(D),D) )
& ( ( relstr_set_smaller(sK0_skl,sK4_skl(D),sK5_skl(D))
& in(sK5_skl(D),sK1_skl)
& element(sK5_skl(D),the_carrier(sK0_skl))
& sK4_skl(D) = sK3_skl(D)
& in(sK3_skl(D),powerset(sK2_skl)) )
| in(sK3_skl(D),D) ) )
& element(sK2_skl,powerset(sK1_skl))
& finite(sK2_skl)
& element(sK1_skl,powerset(the_carrier(sK0_skl)))
& rel_str(sK0_skl)
& transitive_relstr(sK0_skl)
& ~ empty_carrier(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(B,sK1_skl),skolemize(C,sK2_skl),skolemize(E,sK3_skl(D)),skolemize(F,sK4_skl(D)),skolemize(G,sK5_skl(D))],[f24]) ).
fof(f26,plain,
~ empty_carrier(sK0_skl),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
transitive_relstr(sK0_skl),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f28,plain,
rel_str(sK0_skl),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f29,plain,
element(sK1_skl,powerset(the_carrier(sK0_skl))),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f30,plain,
finite(sK2_skl),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f31,plain,
element(sK2_skl,powerset(sK1_skl)),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f32,plain,
! [X0] :
( in(sK3_skl(X0),powerset(sK2_skl))
| in(sK3_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f33,plain,
! [X0] :
( sK4_skl(X0) = sK3_skl(X0)
| in(sK3_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f34,plain,
! [X0] :
( element(sK5_skl(X0),the_carrier(sK0_skl))
| in(sK3_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f35,plain,
! [X0] :
( in(sK5_skl(X0),sK1_skl)
| in(sK3_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f36,plain,
! [X0] :
( relstr_set_smaller(sK0_skl,sK4_skl(X0),sK5_skl(X0))
| in(sK3_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ relstr_set_smaller(sK0_skl,X1,X2)
| ~ in(X2,sK1_skl)
| ~ element(X2,the_carrier(sK0_skl))
| X1 != sK3_skl(X0)
| ~ in(sK3_skl(X0),powerset(sK2_skl))
| ~ in(sK3_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f80,plain,
! [A,B,C] :
( ? [D] :
! [E] :
( in(E,D)
<=> ? [F] :
( ? [K] :
( ? [L] :
( relstr_set_smaller(A,K,L)
& in(L,B)
& element(L,the_carrier(A)) )
& K = E )
& F = E
& in(F,powerset(C)) ) )
| ? [D,E,F] :
( E != F
& ? [I] :
( ? [J] :
( relstr_set_smaller(A,I,J)
& in(J,B)
& element(J,the_carrier(A)) )
& I = F )
& D = F
& ? [G] :
( ? [H] :
( relstr_set_smaller(A,G,H)
& in(H,B)
& element(H,the_carrier(A)) )
& G = E )
& D = E )
| ~ element(C,powerset(B))
| ~ finite(C)
| ~ element(B,powerset(the_carrier(A)))
| ~ rel_str(A)
| ~ transitive_relstr(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f81,definition,
! [A,B,D,E,F] :
( sP0_prd(F,E,D,B,A)
<=> ( E != F
& ? [I] :
( ? [J] :
( relstr_set_smaller(A,I,J)
& in(J,B)
& element(J,the_carrier(A)) )
& I = F )
& D = F
& ? [G] :
( ? [H] :
( relstr_set_smaller(A,G,H)
& in(H,B)
& element(H,the_carrier(A)) )
& G = E )
& D = E ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f82,plain,
! [A,B,C] :
( ? [D] :
! [E] :
( in(E,D)
<=> ? [F] :
( ? [K] :
( ? [L] :
( relstr_set_smaller(A,K,L)
& in(L,B)
& element(L,the_carrier(A)) )
& K = E )
& F = E
& in(F,powerset(C)) ) )
| ? [D,E,F] : sP0_prd(F,E,D,B,A)
| ~ element(C,powerset(B))
| ~ finite(C)
| ~ element(B,powerset(the_carrier(A)))
| ~ rel_str(A)
| ~ transitive_relstr(A)
| empty_carrier(A) ),
inference(formula_renaming,[status(thm)],[f80,f81]) ).
fof(f83,plain,
! [A,B,C] :
( ? [D] :
! [E] :
( ( ! [F] :
( ! [K] :
( ! [L] :
( ~ relstr_set_smaller(A,K,L)
| ~ in(L,B)
| ~ element(L,the_carrier(A)) )
| K != E )
| F != E
| ~ in(F,powerset(C)) )
| in(E,D) )
& ( ? [F] :
( ? [K] :
( ? [L] :
( relstr_set_smaller(A,K,L)
& in(L,B)
& element(L,the_carrier(A)) )
& K = E )
& F = E
& in(F,powerset(C)) )
| ~ in(E,D) ) )
| ? [D,E,F] : sP0_prd(F,E,D,B,A)
| ~ element(C,powerset(B))
| ~ finite(C)
| ~ element(B,powerset(the_carrier(A)))
| ~ rel_str(A)
| ~ transitive_relstr(A)
| empty_carrier(A) ),
inference(NNF_transformation,[status(thm)],[f82]) ).
fof(f84,plain,
! [A,B,C] :
( ? [D] :
( ! [E] :
( ! [K] :
( ! [L] :
( ~ relstr_set_smaller(A,K,L)
| ~ in(L,B)
| ~ element(L,the_carrier(A)) )
| K != E )
| ! [F] :
( F != E
| ~ in(F,powerset(C)) )
| in(E,D) )
& ! [E] :
( ( ? [K] :
( ? [L] :
( relstr_set_smaller(A,K,L)
& in(L,B)
& element(L,the_carrier(A)) )
& K = E )
& ? [F] :
( F = E
& in(F,powerset(C)) ) )
| ~ in(E,D) ) )
| ? [D,E,F] : sP0_prd(F,E,D,B,A)
| ~ element(C,powerset(B))
| ~ finite(C)
| ~ element(B,powerset(the_carrier(A)))
| ~ rel_str(A)
| ~ transitive_relstr(A)
| empty_carrier(A) ),
inference(miniscoping,[status(thm)],[f83]) ).
fof(f85,plain,
! [A,B,C] :
( ( ! [E] :
( ! [K] :
( ! [L] :
( ~ relstr_set_smaller(A,K,L)
| ~ in(L,B)
| ~ element(L,the_carrier(A)) )
| K != E )
| ! [F] :
( F != E
| ~ in(F,powerset(C)) )
| in(E,sK18_skl(C,B,A)) )
& ! [E] :
( ( relstr_set_smaller(A,sK20_skl(E,C,B,A),sK21_skl(E,C,B,A))
& in(sK21_skl(E,C,B,A),B)
& element(sK21_skl(E,C,B,A),the_carrier(A))
& sK20_skl(E,C,B,A) = E
& sK19_skl(E,C,B,A) = E
& in(sK19_skl(E,C,B,A),powerset(C)) )
| ~ in(E,sK18_skl(C,B,A)) ) )
| sP0_prd(sK17_skl(C,B,A),sK16_skl(C,B,A),sK15_skl(C,B,A),B,A)
| ~ element(C,powerset(B))
| ~ finite(C)
| ~ element(B,powerset(the_carrier(A)))
| ~ rel_str(A)
| ~ transitive_relstr(A)
| empty_carrier(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl,sK17_skl,sK18_skl,sK19_skl,sK20_skl,sK21_skl]),skolemize(D,sK15_skl(C,B,A)),skolemize(E,sK16_skl(C,B,A)),skolemize(F,sK17_skl(C,B,A)),skolemize(D,sK18_skl(C,B,A)),skolemize(F,sK19_skl(E,C,B,A)),skolemize(K,sK20_skl(E,C,B,A)),skolemize(L,sK21_skl(E,C,B,A))],[f84]) ).
fof(f86,plain,
! [X0,X1,X2,X3] :
( in(sK19_skl(X3,X2,X1,X0),powerset(X2))
| ~ in(X3,sK18_skl(X2,X1,X0))
| sP0_prd(sK17_skl(X2,X1,X0),sK16_skl(X2,X1,X0),sK15_skl(X2,X1,X0),X1,X0)
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f87,plain,
! [X0,X1,X2,X3] :
( sK19_skl(X3,X2,X1,X0) = X3
| ~ in(X3,sK18_skl(X2,X1,X0))
| sP0_prd(sK17_skl(X2,X1,X0),sK16_skl(X2,X1,X0),sK15_skl(X2,X1,X0),X1,X0)
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f88,plain,
! [X0,X1,X2,X3] :
( sK20_skl(X3,X2,X1,X0) = X3
| ~ in(X3,sK18_skl(X2,X1,X0))
| sP0_prd(sK17_skl(X2,X1,X0),sK16_skl(X2,X1,X0),sK15_skl(X2,X1,X0),X1,X0)
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f89,plain,
! [X0,X1,X2,X3] :
( element(sK21_skl(X3,X2,X1,X0),the_carrier(X0))
| ~ in(X3,sK18_skl(X2,X1,X0))
| sP0_prd(sK17_skl(X2,X1,X0),sK16_skl(X2,X1,X0),sK15_skl(X2,X1,X0),X1,X0)
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f90,plain,
! [X0,X1,X2,X3] :
( in(sK21_skl(X3,X2,X1,X0),X1)
| ~ in(X3,sK18_skl(X2,X1,X0))
| sP0_prd(sK17_skl(X2,X1,X0),sK16_skl(X2,X1,X0),sK15_skl(X2,X1,X0),X1,X0)
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( relstr_set_smaller(X0,sK20_skl(X3,X2,X1,X0),sK21_skl(X3,X2,X1,X0))
| ~ in(X3,sK18_skl(X2,X1,X0))
| sP0_prd(sK17_skl(X2,X1,X0),sK16_skl(X2,X1,X0),sK15_skl(X2,X1,X0),X1,X0)
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f92,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ relstr_set_smaller(X0,X5,X6)
| ~ in(X6,X1)
| ~ element(X6,the_carrier(X0))
| X5 != X3
| X4 != X3
| ~ in(X4,powerset(X2))
| in(X3,sK18_skl(X2,X1,X0))
| sP0_prd(sK17_skl(X2,X1,X0),sK16_skl(X2,X1,X0),sK15_skl(X2,X1,X0),X1,X0)
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f93,plain,
! [A,B,D,E,F] :
( ( E = F
| ! [I] :
( ! [J] :
( ~ relstr_set_smaller(A,I,J)
| ~ in(J,B)
| ~ element(J,the_carrier(A)) )
| I != F )
| D != F
| ! [G] :
( ! [H] :
( ~ relstr_set_smaller(A,G,H)
| ~ in(H,B)
| ~ element(H,the_carrier(A)) )
| G != E )
| D != E
| sP0_prd(F,E,D,B,A) )
& ( ( E != F
& ? [I] :
( ? [J] :
( relstr_set_smaller(A,I,J)
& in(J,B)
& element(J,the_carrier(A)) )
& I = F )
& D = F
& ? [G] :
( ? [H] :
( relstr_set_smaller(A,G,H)
& in(H,B)
& element(H,the_carrier(A)) )
& G = E )
& D = E )
| ~ sP0_prd(F,E,D,B,A) ) ),
inference(NNF_transformation,[status(thm)],[f81]) ).
fof(f94,plain,
( ! [A,B,D,E,F] :
( E = F
| ! [I] :
( ! [J] :
( ~ relstr_set_smaller(A,I,J)
| ~ in(J,B)
| ~ element(J,the_carrier(A)) )
| I != F )
| D != F
| ! [G] :
( ! [H] :
( ~ relstr_set_smaller(A,G,H)
| ~ in(H,B)
| ~ element(H,the_carrier(A)) )
| G != E )
| D != E
| sP0_prd(F,E,D,B,A) )
& ! [A,B,D,E,F] :
( ( E != F
& ? [I] :
( ? [J] :
( relstr_set_smaller(A,I,J)
& in(J,B)
& element(J,the_carrier(A)) )
& I = F )
& D = F
& ? [G] :
( ? [H] :
( relstr_set_smaller(A,G,H)
& in(H,B)
& element(H,the_carrier(A)) )
& G = E )
& D = E )
| ~ sP0_prd(F,E,D,B,A) ) ),
inference(miniscoping,[status(thm)],[f93]) ).
fof(f95,plain,
( ! [A,B,D,E,F] :
( E = F
| ! [I] :
( ! [J] :
( ~ relstr_set_smaller(A,I,J)
| ~ in(J,B)
| ~ element(J,the_carrier(A)) )
| I != F )
| D != F
| ! [G] :
( ! [H] :
( ~ relstr_set_smaller(A,G,H)
| ~ in(H,B)
| ~ element(H,the_carrier(A)) )
| G != E )
| D != E
| sP0_prd(F,E,D,B,A) )
& ! [A,B,D,E,F] :
( ( E != F
& relstr_set_smaller(A,sK24_skl(F,E,D,B,A),sK25_skl(F,E,D,B,A))
& in(sK25_skl(F,E,D,B,A),B)
& element(sK25_skl(F,E,D,B,A),the_carrier(A))
& sK24_skl(F,E,D,B,A) = F
& D = F
& relstr_set_smaller(A,sK22_skl(F,E,D,B,A),sK23_skl(F,E,D,B,A))
& in(sK23_skl(F,E,D,B,A),B)
& element(sK23_skl(F,E,D,B,A),the_carrier(A))
& sK22_skl(F,E,D,B,A) = E
& D = E )
| ~ sP0_prd(F,E,D,B,A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22_skl,sK23_skl,sK24_skl,sK25_skl]),skolemize(G,sK22_skl(F,E,D,B,A)),skolemize(H,sK23_skl(F,E,D,B,A)),skolemize(I,sK24_skl(F,E,D,B,A)),skolemize(J,sK25_skl(F,E,D,B,A))],[f94]) ).
fof(f96,plain,
! [X0,X1,X2,X3,X4] :
( X2 = X1
| ~ sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f101,plain,
! [X0,X1,X2,X3,X4] :
( X2 = X0
| ~ sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f106,plain,
! [X0,X1,X2,X3,X4] :
( X1 != X0
| ~ sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f108,plain,
! [X0,X1] :
( ~ relstr_set_smaller(sK0_skl,sK3_skl(X0),X1)
| ~ in(X1,sK1_skl)
| ~ element(X1,the_carrier(sK0_skl))
| ~ in(sK3_skl(X0),powerset(sK2_skl))
| ~ in(sK3_skl(X0),X0) ),
inference(destructive_equality_resolution,[status(thm)],[f37]) ).
fof(f109,plain,
! [X0,X1,X2,X3,X4] :
( ~ relstr_set_smaller(X0,X3,X4)
| ~ in(X4,X1)
| ~ element(X4,the_carrier(X0))
| ~ in(X3,powerset(X2))
| in(X3,sK18_skl(X2,X1,X0))
| sP0_prd(sK17_skl(X2,X1,X0),sK16_skl(X2,X1,X0),sK15_skl(X2,X1,X0),X1,X0)
| ~ element(X2,powerset(X1))
| ~ finite(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| empty_carrier(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f92]) ).
fof(f110,plain,
! [X0,X1,X2,X3] : ~ sP0_prd(X0,X0,X1,X2,X3),
inference(destructive_equality_resolution,[status(thm)],[f106]) ).
fof(f113,plain,
! [X0] :
( in(sK3_skl(X0),X0)
| relstr_set_smaller(sK0_skl,sK3_skl(X0),sK5_skl(X0))
| in(sK3_skl(X0),X0) ),
inference(paramodulation,[status(thm)],[f33,f36]) ).
fof(f114,plain,
! [X0] :
( relstr_set_smaller(sK0_skl,sK3_skl(X0),sK5_skl(X0))
| in(sK3_skl(X0),X0) ),
inference(duplicate_literals_removal,[status(thm)],[f113]) ).
fof(f116,plain,
! [X0,X1,X2,X3] :
( ~ relstr_set_smaller(sK0_skl,X2,X3)
| ~ in(X3,X0)
| ~ element(X3,the_carrier(sK0_skl))
| ~ in(X2,powerset(X1))
| in(X2,sK18_skl(X1,X0,sK0_skl))
| sP0_prd(sK17_skl(X1,X0,sK0_skl),sK16_skl(X1,X0,sK0_skl),sK15_skl(X1,X0,sK0_skl),X0,sK0_skl)
| ~ element(X1,powerset(X0))
| ~ finite(X1)
| ~ element(X0,powerset(the_carrier(sK0_skl)))
| ~ rel_str(sK0_skl)
| empty_carrier(sK0_skl) ),
inference(resolution,[status(thm)],[f109,f27]) ).
fof(f117,definition,
( sQ0_spl
<=> empty_carrier(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ0_spl
| empty_carrier(sK0_skl) ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,definition,
( sQ1_spl
<=> rel_str(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( sQ1_spl
| ~ rel_str(sK0_skl) ),
inference(component_clause,[status(thm)],[f120]) ).
fof(f123,definition,
! [X0,X1,X2,X3] :
( sQ2_spl
<=> ( ~ relstr_set_smaller(sK0_skl,X2,X3)
| ~ in(X3,X0)
| ~ element(X3,the_carrier(sK0_skl))
| ~ in(X2,powerset(X1))
| in(X2,sK18_skl(X1,X0,sK0_skl))
| sP0_prd(sK17_skl(X1,X0,sK0_skl),sK16_skl(X1,X0,sK0_skl),sK15_skl(X1,X0,sK0_skl),X0,sK0_skl)
| ~ element(X1,powerset(X0))
| ~ finite(X1)
| ~ element(X0,powerset(the_carrier(sK0_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( ~ sQ2_spl
| ~ relstr_set_smaller(sK0_skl,X2,X3)
| ~ in(X3,X0)
| ~ element(X3,the_carrier(sK0_skl))
| ~ in(X2,powerset(X1))
| in(X2,sK18_skl(X1,X0,sK0_skl))
| sP0_prd(sK17_skl(X1,X0,sK0_skl),sK16_skl(X1,X0,sK0_skl),sK15_skl(X1,X0,sK0_skl),X0,sK0_skl)
| ~ element(X1,powerset(X0))
| ~ finite(X1)
| ~ element(X0,powerset(the_carrier(sK0_skl))) ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f126,plain,
( sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f116,f117,f120,f123]) ).
fof(f127,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| in(sK3_skl(X1),X1)
| ~ relstr_set_smaller(sK0_skl,sK3_skl(X1),X2)
| ~ in(X2,X0)
| ~ element(X2,the_carrier(sK0_skl))
| in(sK3_skl(X1),sK18_skl(sK2_skl,X0,sK0_skl))
| sP0_prd(sK17_skl(sK2_skl,X0,sK0_skl),sK16_skl(sK2_skl,X0,sK0_skl),sK15_skl(sK2_skl,X0,sK0_skl),X0,sK0_skl)
| ~ element(sK2_skl,powerset(X0))
| ~ finite(sK2_skl)
| ~ element(X0,powerset(the_carrier(sK0_skl))) ),
inference(resolution,[status(thm)],[f124,f32]) ).
fof(f128,definition,
! [X0,X1,X2] :
( sQ3_spl
<=> ( in(sK3_skl(X1),X1)
| ~ relstr_set_smaller(sK0_skl,sK3_skl(X1),X2)
| ~ in(X2,X0)
| ~ element(X2,the_carrier(sK0_skl))
| in(sK3_skl(X1),sK18_skl(sK2_skl,X0,sK0_skl))
| sP0_prd(sK17_skl(sK2_skl,X0,sK0_skl),sK16_skl(sK2_skl,X0,sK0_skl),sK15_skl(sK2_skl,X0,sK0_skl),X0,sK0_skl)
| ~ element(sK2_skl,powerset(X0))
| ~ element(X0,powerset(the_carrier(sK0_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| in(sK3_skl(X1),X1)
| ~ relstr_set_smaller(sK0_skl,sK3_skl(X1),X2)
| ~ in(X2,X0)
| ~ element(X2,the_carrier(sK0_skl))
| in(sK3_skl(X1),sK18_skl(sK2_skl,X0,sK0_skl))
| sP0_prd(sK17_skl(sK2_skl,X0,sK0_skl),sK16_skl(sK2_skl,X0,sK0_skl),sK15_skl(sK2_skl,X0,sK0_skl),X0,sK0_skl)
| ~ element(sK2_skl,powerset(X0))
| ~ element(X0,powerset(the_carrier(sK0_skl))) ),
inference(component_clause,[status(thm)],[f128]) ).
fof(f131,definition,
( sQ4_spl
<=> finite(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f133,plain,
( sQ4_spl
| ~ finite(sK2_skl) ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f134,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f127,f128,f131,f123]) ).
fof(f135,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f133,f30]) ).
fof(f136,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f135]) ).
fof(f137,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f122,f28]) ).
fof(f138,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f137]) ).
fof(f139,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f118,f26]) ).
fof(f140,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f139]) ).
fof(f143,plain,
! [X0,X1] :
( ~ sQ3_spl
| in(sK3_skl(X0),X0)
| ~ relstr_set_smaller(sK0_skl,sK3_skl(X0),X1)
| ~ in(X1,sK1_skl)
| ~ element(X1,the_carrier(sK0_skl))
| in(sK3_skl(X0),sK18_skl(sK2_skl,sK1_skl,sK0_skl))
| sP0_prd(sK17_skl(sK2_skl,sK1_skl,sK0_skl),sK16_skl(sK2_skl,sK1_skl,sK0_skl),sK15_skl(sK2_skl,sK1_skl,sK0_skl),sK1_skl,sK0_skl)
| ~ element(sK1_skl,powerset(the_carrier(sK0_skl))) ),
inference(resolution,[status(thm)],[f129,f31]) ).
fof(f144,definition,
( sQ5_spl
<=> element(sK1_skl,powerset(the_carrier(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( sQ5_spl
| ~ element(sK1_skl,powerset(the_carrier(sK0_skl))) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,definition,
( sQ6_spl
<=> sP0_prd(sK17_skl(sK2_skl,sK1_skl,sK0_skl),sK16_skl(sK2_skl,sK1_skl,sK0_skl),sK15_skl(sK2_skl,sK1_skl,sK0_skl),sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f148,plain,
( ~ sQ6_spl
| sP0_prd(sK17_skl(sK2_skl,sK1_skl,sK0_skl),sK16_skl(sK2_skl,sK1_skl,sK0_skl),sK15_skl(sK2_skl,sK1_skl,sK0_skl),sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,definition,
! [X0,X1] :
( sQ7_spl
<=> ( in(sK3_skl(X0),X0)
| ~ relstr_set_smaller(sK0_skl,sK3_skl(X0),X1)
| ~ in(X1,sK1_skl)
| ~ element(X1,the_carrier(sK0_skl))
| in(sK3_skl(X0),sK18_skl(sK2_skl,sK1_skl,sK0_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f151,plain,
! [X0,X1] :
( ~ sQ7_spl
| in(sK3_skl(X0),X0)
| ~ relstr_set_smaller(sK0_skl,sK3_skl(X0),X1)
| ~ in(X1,sK1_skl)
| ~ element(X1,the_carrier(sK0_skl))
| in(sK3_skl(X0),sK18_skl(sK2_skl,sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,plain,
( ~ sQ3_spl
| sQ7_spl
| sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f143,f144,f147,f150,f128]) ).
fof(f154,plain,
! [X0,X1] :
( ~ sQ7_spl
| in(sK3_skl(X1),X1)
| in(sK3_skl(X0),X0)
| ~ relstr_set_smaller(sK0_skl,sK3_skl(X0),sK5_skl(X1))
| ~ element(sK5_skl(X1),the_carrier(sK0_skl))
| in(sK3_skl(X0),sK18_skl(sK2_skl,sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f151,f35]) ).
fof(f155,plain,
! [X0,X1] :
( ~ sQ7_spl
| in(sK3_skl(X1),X1)
| in(sK3_skl(X0),X0)
| ~ relstr_set_smaller(sK0_skl,sK3_skl(X0),sK5_skl(X1))
| in(sK3_skl(X0),sK18_skl(sK2_skl,sK1_skl,sK0_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f154,f34]) ).
fof(f156,plain,
! [X0] :
( ~ sQ7_spl
| in(sK3_skl(X0),X0)
| in(sK3_skl(X0),X0)
| in(sK3_skl(X0),X0)
| in(sK3_skl(X0),sK18_skl(sK2_skl,sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f155,f114]) ).
fof(f157,plain,
! [X0] :
( ~ sQ7_spl
| in(sK3_skl(X0),X0)
| in(sK3_skl(X0),sK18_skl(sK2_skl,sK1_skl,sK0_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f156]) ).
fof(f166,definition,
( sQ9_spl
<=> transitive_relstr(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f168,plain,
( sQ9_spl
| ~ transitive_relstr(sK0_skl) ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f169,definition,
( sQ10_spl
<=> element(sK2_skl,powerset(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f171,plain,
( sQ10_spl
| ~ element(sK2_skl,powerset(sK1_skl)) ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f189,plain,
( ~ sQ6_spl
| sK15_skl(sK2_skl,sK1_skl,sK0_skl) = sK17_skl(sK2_skl,sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f148,f101]) ).
fof(f190,plain,
( ~ sQ6_spl
| sK15_skl(sK2_skl,sK1_skl,sK0_skl) = sK16_skl(sK2_skl,sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f148,f96]) ).
fof(f191,plain,
( ~ sQ6_spl
| sP0_prd(sK15_skl(sK2_skl,sK1_skl,sK0_skl),sK16_skl(sK2_skl,sK1_skl,sK0_skl),sK15_skl(sK2_skl,sK1_skl,sK0_skl),sK1_skl,sK0_skl) ),
inference(backward_demodulation,[status(thm)],[f189,f148]) ).
fof(f192,plain,
( ~ sQ6_spl
| sP0_prd(sK15_skl(sK2_skl,sK1_skl,sK0_skl),sK15_skl(sK2_skl,sK1_skl,sK0_skl),sK15_skl(sK2_skl,sK1_skl,sK0_skl),sK1_skl,sK0_skl) ),
inference(forward_demodulation,[status(thm)],[f190,f191]) ).
fof(f193,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f192,f110]) ).
fof(f194,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f193]) ).
fof(f195,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f146,f29]) ).
fof(f196,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f195]) ).
fof(f197,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f171,f31]) ).
fof(f198,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f197]) ).
fof(f199,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f168,f27]) ).
fof(f200,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f199]) ).
fof(f294,definition,
( sQ23_spl
<=> sK20_skl(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK2_skl,sK1_skl,sK0_skl) = sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f295,plain,
( ~ sQ23_spl
| sK20_skl(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK2_skl,sK1_skl,sK0_skl) = sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f294]) ).
fof(f297,definition,
( sQ24_spl
<=> in(sK21_skl(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK2_skl,sK1_skl,sK0_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f301,plain,
( ~ sQ23_spl
| relstr_set_smaller(sK0_skl,sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK21_skl(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK2_skl,sK1_skl,sK0_skl))
| ~ in(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK18_skl(sK2_skl,sK1_skl,sK0_skl))
| sP0_prd(sK17_skl(sK2_skl,sK1_skl,sK0_skl),sK16_skl(sK2_skl,sK1_skl,sK0_skl),sK15_skl(sK2_skl,sK1_skl,sK0_skl),sK1_skl,sK0_skl)
| ~ element(sK2_skl,powerset(sK1_skl))
| ~ finite(sK2_skl)
| ~ element(sK1_skl,powerset(the_carrier(sK0_skl)))
| ~ rel_str(sK0_skl)
| ~ transitive_relstr(sK0_skl)
| empty_carrier(sK0_skl) ),
inference(paramodulation,[status(thm)],[f295,f91]) ).
fof(f302,definition,
( sQ25_spl
<=> in(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK18_skl(sK2_skl,sK1_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f303,plain,
( ~ sQ25_spl
| in(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK18_skl(sK2_skl,sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f302]) ).
fof(f304,plain,
( sQ25_spl
| ~ in(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK18_skl(sK2_skl,sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f302]) ).
fof(f305,definition,
( sQ26_spl
<=> relstr_set_smaller(sK0_skl,sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK21_skl(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK2_skl,sK1_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f306,plain,
( ~ sQ26_spl
| relstr_set_smaller(sK0_skl,sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK21_skl(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK2_skl,sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f305]) ).
fof(f308,plain,
( ~ sQ23_spl
| sQ26_spl
| ~ sQ25_spl
| sQ6_spl
| ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f301,f117,f166,f120,f144,f131,f169,f147,f302,f305,f294]) ).
fof(f310,plain,
( ~ sQ26_spl
| ~ in(sK21_skl(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK2_skl,sK1_skl,sK0_skl),sK1_skl)
| ~ element(sK21_skl(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK2_skl,sK1_skl,sK0_skl),the_carrier(sK0_skl))
| ~ in(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),powerset(sK2_skl))
| ~ in(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK18_skl(sK2_skl,sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f306,f108]) ).
fof(f311,definition,
( sQ27_spl
<=> in(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),powerset(sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f313,plain,
( sQ27_spl
| ~ in(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),powerset(sK2_skl)) ),
inference(component_clause,[status(thm)],[f311]) ).
fof(f314,definition,
( sQ28_spl
<=> element(sK21_skl(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK2_skl,sK1_skl,sK0_skl),the_carrier(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f316,plain,
( sQ28_spl
| ~ element(sK21_skl(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK2_skl,sK1_skl,sK0_skl),the_carrier(sK0_skl)) ),
inference(component_clause,[status(thm)],[f314]) ).
fof(f317,plain,
( ~ sQ26_spl
| ~ sQ24_spl
| ~ sQ28_spl
| ~ sQ27_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f310,f302,f311,f314,f297,f305]) ).
fof(f318,plain,
( ~ sQ7_spl
| sQ25_spl
| in(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK18_skl(sK2_skl,sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f304,f157]) ).
fof(f321,plain,
( ~ sQ7_spl
| sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f318,f304]) ).
fof(f322,plain,
( ~ sQ7_spl
| sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f321]) ).
fof(f323,plain,
( ~ sQ25_spl
| in(sK21_skl(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK2_skl,sK1_skl,sK0_skl),sK1_skl)
| sP0_prd(sK17_skl(sK2_skl,sK1_skl,sK0_skl),sK16_skl(sK2_skl,sK1_skl,sK0_skl),sK15_skl(sK2_skl,sK1_skl,sK0_skl),sK1_skl,sK0_skl)
| ~ element(sK2_skl,powerset(sK1_skl))
| ~ finite(sK2_skl)
| ~ element(sK1_skl,powerset(the_carrier(sK0_skl)))
| ~ rel_str(sK0_skl)
| ~ transitive_relstr(sK0_skl)
| empty_carrier(sK0_skl) ),
inference(resolution,[status(thm)],[f303,f90]) ).
fof(f324,plain,
( ~ sQ25_spl
| sK20_skl(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK2_skl,sK1_skl,sK0_skl) = sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl))
| sP0_prd(sK17_skl(sK2_skl,sK1_skl,sK0_skl),sK16_skl(sK2_skl,sK1_skl,sK0_skl),sK15_skl(sK2_skl,sK1_skl,sK0_skl),sK1_skl,sK0_skl)
| ~ element(sK2_skl,powerset(sK1_skl))
| ~ finite(sK2_skl)
| ~ element(sK1_skl,powerset(the_carrier(sK0_skl)))
| ~ rel_str(sK0_skl)
| ~ transitive_relstr(sK0_skl)
| empty_carrier(sK0_skl) ),
inference(resolution,[status(thm)],[f303,f88]) ).
fof(f325,plain,
( ~ sQ25_spl
| sK19_skl(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK2_skl,sK1_skl,sK0_skl) = sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl))
| sP0_prd(sK17_skl(sK2_skl,sK1_skl,sK0_skl),sK16_skl(sK2_skl,sK1_skl,sK0_skl),sK15_skl(sK2_skl,sK1_skl,sK0_skl),sK1_skl,sK0_skl)
| ~ element(sK2_skl,powerset(sK1_skl))
| ~ finite(sK2_skl)
| ~ element(sK1_skl,powerset(the_carrier(sK0_skl)))
| ~ rel_str(sK0_skl)
| ~ transitive_relstr(sK0_skl)
| empty_carrier(sK0_skl) ),
inference(resolution,[status(thm)],[f303,f87]) ).
fof(f326,plain,
( ~ sQ25_spl
| in(sK19_skl(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK2_skl,sK1_skl,sK0_skl),powerset(sK2_skl))
| sP0_prd(sK17_skl(sK2_skl,sK1_skl,sK0_skl),sK16_skl(sK2_skl,sK1_skl,sK0_skl),sK15_skl(sK2_skl,sK1_skl,sK0_skl),sK1_skl,sK0_skl)
| ~ element(sK2_skl,powerset(sK1_skl))
| ~ finite(sK2_skl)
| ~ element(sK1_skl,powerset(the_carrier(sK0_skl)))
| ~ rel_str(sK0_skl)
| ~ transitive_relstr(sK0_skl)
| empty_carrier(sK0_skl) ),
inference(resolution,[status(thm)],[f303,f86]) ).
fof(f328,plain,
( ~ sQ25_spl
| sQ24_spl
| sQ6_spl
| ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f323,f117,f166,f120,f144,f131,f169,f147,f297,f302]) ).
fof(f329,plain,
( ~ sQ25_spl
| sQ23_spl
| sQ6_spl
| ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f324,f117,f166,f120,f144,f131,f169,f147,f294,f302]) ).
fof(f330,definition,
( sQ29_spl
<=> sK19_skl(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK2_skl,sK1_skl,sK0_skl) = sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f331,plain,
( ~ sQ29_spl
| sK19_skl(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK2_skl,sK1_skl,sK0_skl) = sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f330]) ).
fof(f333,plain,
( ~ sQ25_spl
| sQ29_spl
| sQ6_spl
| ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f325,f117,f166,f120,f144,f131,f169,f147,f330,f302]) ).
fof(f334,definition,
( sQ30_spl
<=> in(sK19_skl(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK2_skl,sK1_skl,sK0_skl),powerset(sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f335,plain,
( ~ sQ30_spl
| in(sK19_skl(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK2_skl,sK1_skl,sK0_skl),powerset(sK2_skl)) ),
inference(component_clause,[status(thm)],[f334]) ).
fof(f337,plain,
( ~ sQ25_spl
| sQ30_spl
| sQ6_spl
| ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f326,f117,f166,f120,f144,f131,f169,f147,f334,f302]) ).
fof(f361,plain,
( ~ sQ30_spl
| ~ sQ29_spl
| in(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),powerset(sK2_skl)) ),
inference(backward_demodulation,[status(thm)],[f331,f335]) ).
fof(f369,plain,
( ~ sQ30_spl
| ~ sQ29_spl
| sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f361,f313]) ).
fof(f370,plain,
( ~ sQ30_spl
| ~ sQ29_spl
| sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f369]) ).
fof(f406,plain,
( sQ28_spl
| ~ in(sK3_skl(sK18_skl(sK2_skl,sK1_skl,sK0_skl)),sK18_skl(sK2_skl,sK1_skl,sK0_skl))
| sP0_prd(sK17_skl(sK2_skl,sK1_skl,sK0_skl),sK16_skl(sK2_skl,sK1_skl,sK0_skl),sK15_skl(sK2_skl,sK1_skl,sK0_skl),sK1_skl,sK0_skl)
| ~ element(sK2_skl,powerset(sK1_skl))
| ~ finite(sK2_skl)
| ~ element(sK1_skl,powerset(the_carrier(sK0_skl)))
| ~ rel_str(sK0_skl)
| ~ transitive_relstr(sK0_skl)
| empty_carrier(sK0_skl) ),
inference(resolution,[status(thm)],[f316,f89]) ).
fof(f407,plain,
( sQ28_spl
| ~ sQ25_spl
| sQ6_spl
| ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f406,f117,f166,f120,f144,f131,f169,f147,f302,f314]) ).
fof(f408,plain,
$false,
inference(sat_refutation,[status(thm)],[f126,f134,f136,f138,f140,f153,f194,f196,f198,f200,f308,f317,f322,f328,f329,f333,f337,f370,f407]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU364+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 06:18:21 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.43 % Elapsed time: 0.061034 seconds
% 0.10/0.43 % CPU time: 0.243419 seconds
% 0.10/0.43 % Total memory used: 85.868 MB
% 0.10/0.43 % Net memory used: 85.523 MB
%------------------------------------------------------------------------------