%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LAT310+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 01:02:40 PM UTC 2026
% Result : Theorem 0.23s 5.89s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 35
% Syntax : Number of formulae : 153 ( 34 unt; 23 def)
% Number of atoms : 511 ( 8 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 592 ( 234 ~; 249 |; 60 &)
% ( 26 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 36 ( 34 usr; 24 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 110 ( 105 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B) )
=> ! [C] :
( ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(C) )
=> ! [D] :
( ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(D) )
=> ( r1_tarski(k19_filter_2(A,k19_filter_2(A,B)),k19_filter_2(A,B))
& ( r1_tarski(C,D)
=> r1_tarski(k19_filter_2(A,C),k19_filter_2(A,D)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B) )
=> ! [C] :
( ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(C) )
=> ! [D] :
( ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(D) )
=> ( r1_tarski(k19_filter_2(A,k19_filter_2(A,B)),k19_filter_2(A,B))
& ( r1_tarski(C,D)
=> r1_tarski(k19_filter_2(A,C),k19_filter_2(A,D)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f7,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B) )
=> ! [C] :
( m2_filter_2(C,A)
=> ( C = k19_filter_2(A,B)
<=> ( ! [D] :
( m2_filter_2(D,A)
=> ( r1_tarski(B,D)
=> r1_tarski(C,D) ) )
& r1_tarski(B,C) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> m2_filter_2(k19_filter_2(A,B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] :
( l1_lattices(A)
=> l1_struct_0(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] :
( l3_lattices(A)
=> ( l2_lattices(A)
& l1_lattices(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_filter_2(B,A)
=> ( m2_lattice4(B,A)
& ~ v1_xboole_0(B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_lattice4(B,A)
=> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
v1_xboole_0(k1_xboole_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A,B] : r1_tarski(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [A,B,C] :
( ( r1_tarski(B,C)
& r1_tarski(A,B) )
=> r1_tarski(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,plain,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ( ~ r1_tarski(k19_filter_2(A,k19_filter_2(A,B)),k19_filter_2(A,B))
| ( ~ r1_tarski(k19_filter_2(A,C),k19_filter_2(A,D))
& r1_tarski(C,D) ) )
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(D) )
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(C) )
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B) )
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f47,plain,
( ( ~ r1_tarski(k19_filter_2(sK0_skl,k19_filter_2(sK0_skl,sK1_skl)),k19_filter_2(sK0_skl,sK1_skl))
| ( ~ r1_tarski(k19_filter_2(sK0_skl,sK2_skl),k19_filter_2(sK0_skl,sK3_skl))
& r1_tarski(sK2_skl,sK3_skl) ) )
& m1_subset_1(sK3_skl,k1_zfmisc_1(u1_struct_0(sK0_skl)))
& ~ v1_xboole_0(sK3_skl)
& m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK0_skl)))
& ~ v1_xboole_0(sK2_skl)
& m1_subset_1(sK1_skl,k1_zfmisc_1(u1_struct_0(sK0_skl)))
& ~ v1_xboole_0(sK1_skl)
& l3_lattices(sK0_skl)
& v10_lattices(sK0_skl)
& ~ v3_struct_0(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(C,sK2_skl),skolemize(D,sK3_skl)],[f46]) ).
fof(f48,plain,
~ v3_struct_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
v10_lattices(sK0_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
l3_lattices(sK0_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,plain,
~ v1_xboole_0(sK1_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f52,plain,
m1_subset_1(sK1_skl,k1_zfmisc_1(u1_struct_0(sK0_skl))),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f53,plain,
~ v1_xboole_0(sK2_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f54,plain,
m1_subset_1(sK2_skl,k1_zfmisc_1(u1_struct_0(sK0_skl))),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f55,plain,
~ v1_xboole_0(sK3_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f56,plain,
m1_subset_1(sK3_skl,k1_zfmisc_1(u1_struct_0(sK0_skl))),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f57,plain,
( ~ r1_tarski(k19_filter_2(sK0_skl,k19_filter_2(sK0_skl,sK1_skl)),k19_filter_2(sK0_skl,sK1_skl))
| r1_tarski(sK2_skl,sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f58,plain,
( ~ r1_tarski(k19_filter_2(sK0_skl,k19_filter_2(sK0_skl,sK1_skl)),k19_filter_2(sK0_skl,sK1_skl))
| ~ r1_tarski(k19_filter_2(sK0_skl,sK2_skl),k19_filter_2(sK0_skl,sK3_skl)) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f74,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( C = k19_filter_2(A,B)
<=> ( ! [D] :
( r1_tarski(C,D)
| ~ r1_tarski(B,D)
| ~ m2_filter_2(D,A) )
& r1_tarski(B,C) ) )
| ~ m2_filter_2(C,A) )
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| v1_xboole_0(B) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f75,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ r1_tarski(C,D)
& r1_tarski(B,D)
& m2_filter_2(D,A) )
| ~ r1_tarski(B,C)
| C = k19_filter_2(A,B) )
& ( ( ! [D] :
( r1_tarski(C,D)
| ~ r1_tarski(B,D)
| ~ m2_filter_2(D,A) )
& r1_tarski(B,C) )
| C != k19_filter_2(A,B) ) )
| ~ m2_filter_2(C,A) )
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| v1_xboole_0(B) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(NNF_transformation,[status(thm)],[f74]) ).
fof(f76,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ( ~ r1_tarski(C,sK4_skl(C,B,A))
& r1_tarski(B,sK4_skl(C,B,A))
& m2_filter_2(sK4_skl(C,B,A),A) )
| ~ r1_tarski(B,C)
| C = k19_filter_2(A,B) )
& ( ( ! [D] :
( r1_tarski(C,D)
| ~ r1_tarski(B,D)
| ~ m2_filter_2(D,A) )
& r1_tarski(B,C) )
| C != k19_filter_2(A,B) ) )
| ~ m2_filter_2(C,A) )
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| v1_xboole_0(B) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(D,sK4_skl(C,B,A))],[f75]) ).
fof(f77,plain,
! [X0,X1,X2] :
( r1_tarski(X1,X2)
| X2 != k19_filter_2(X0,X1)
| ~ m2_filter_2(X2,X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
! [X0,X1,X2,X3] :
( r1_tarski(X2,X3)
| ~ r1_tarski(X1,X3)
| ~ m2_filter_2(X3,X0)
| X2 != k19_filter_2(X0,X1)
| ~ m2_filter_2(X2,X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f82,plain,
! [A,B] :
( m2_filter_2(k19_filter_2(A,B),A)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| v1_xboole_0(B)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f83,plain,
! [X0,X1] :
( m2_filter_2(k19_filter_2(X0,X1),X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f84,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_lattices(A) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f85,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_lattices(X0) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f88,plain,
! [A] :
( ( l2_lattices(A)
& l1_lattices(A) )
| ~ l3_lattices(A) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f89,plain,
! [X0] :
( l1_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f91,plain,
! [A] :
( ! [B] :
( ( m2_lattice4(B,A)
& ~ v1_xboole_0(B) )
| ~ m2_filter_2(B,A) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f92,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| ~ m2_filter_2(X1,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
! [X0,X1] :
( m2_lattice4(X1,X0)
| ~ m2_filter_2(X1,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f94,plain,
! [A] :
( ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| ~ m2_lattice4(B,A) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f95,plain,
! [X0,X1] :
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_lattice4(X1,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f114,plain,
! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f115,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f138,plain,
! [A] : r1_tarski(A,A),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f139,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f142,plain,
! [A,B,C] :
( r1_tarski(A,C)
| ~ r1_tarski(B,C)
| ~ r1_tarski(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f143,plain,
! [A,C] :
( r1_tarski(A,C)
| ! [B] :
( ~ r1_tarski(B,C)
| ~ r1_tarski(A,B) ) ),
inference(miniscoping,[status(thm)],[f142]) ).
fof(f144,plain,
! [X0,X1,X2] :
( r1_tarski(X0,X2)
| ~ r1_tarski(X1,X2)
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f147,plain,
! [A,B] :
( ( ~ r1_tarski(A,B)
| m1_subset_1(A,k1_zfmisc_1(B)) )
& ( r1_tarski(A,B)
| ~ m1_subset_1(A,k1_zfmisc_1(B)) ) ),
inference(NNF_transformation,[status(thm)],[f40]) ).
fof(f148,plain,
( ! [A,B] :
( ~ r1_tarski(A,B)
| m1_subset_1(A,k1_zfmisc_1(B)) )
& ! [A,B] :
( r1_tarski(A,B)
| ~ m1_subset_1(A,k1_zfmisc_1(B)) ) ),
inference(miniscoping,[status(thm)],[f147]) ).
fof(f149,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f150,plain,
! [X0,X1] :
( ~ r1_tarski(X0,X1)
| m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f165,definition,
( sQ0_spl
<=> r1_tarski(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f168,definition,
( sQ1_spl
<=> r1_tarski(k19_filter_2(sK0_skl,k19_filter_2(sK0_skl,sK1_skl)),k19_filter_2(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( sQ1_spl
| ~ r1_tarski(k19_filter_2(sK0_skl,k19_filter_2(sK0_skl,sK1_skl)),k19_filter_2(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f57,f165,f168]) ).
fof(f172,definition,
( sQ2_spl
<=> r1_tarski(k19_filter_2(sK0_skl,sK2_skl),k19_filter_2(sK0_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( sQ2_spl
| ~ r1_tarski(k19_filter_2(sK0_skl,sK2_skl),k19_filter_2(sK0_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,plain,
( ~ sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f58,f172,f168]) ).
fof(f176,plain,
! [X0,X1] :
( r1_tarski(X1,k19_filter_2(X0,X1))
| ~ m2_filter_2(k19_filter_2(X0,X1),X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f77]) ).
fof(f177,plain,
! [X0,X1,X2] :
( r1_tarski(k19_filter_2(X0,X1),X2)
| ~ r1_tarski(X1,X2)
| ~ m2_filter_2(X2,X0)
| ~ m2_filter_2(k19_filter_2(X0,X1),X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f78]) ).
fof(f189,plain,
r1_tarski(sK2_skl,u1_struct_0(sK0_skl)),
inference(resolution,[status(thm)],[f149,f54]) ).
fof(f190,plain,
r1_tarski(sK1_skl,u1_struct_0(sK0_skl)),
inference(resolution,[status(thm)],[f149,f52]) ).
fof(f208,definition,
( sQ6_spl
<=> v3_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f209,plain,
( ~ sQ6_spl
| v3_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,definition,
( sQ7_spl
<=> v10_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( sQ7_spl
| ~ v10_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f218,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f213,f49]) ).
fof(f219,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f218]) ).
fof(f220,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f209,f48]) ).
fof(f221,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f220]) ).
fof(f287,plain,
l1_lattices(sK0_skl),
inference(resolution,[status(thm)],[f89,f50]) ).
fof(f289,plain,
l1_struct_0(sK0_skl),
inference(resolution,[status(thm)],[f287,f85]) ).
fof(f298,definition,
( sQ19_spl
<=> l3_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f300,plain,
( sQ19_spl
| ~ l3_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f298]) ).
fof(f352,definition,
( sQ22_spl
<=> v1_xboole_0(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( ~ sQ22_spl
| v1_xboole_0(sK3_skl) ),
inference(component_clause,[status(thm)],[f352]) ).
fof(f362,definition,
( sQ25_spl
<=> v1_xboole_0(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f363,plain,
( ~ sQ25_spl
| v1_xboole_0(sK2_skl) ),
inference(component_clause,[status(thm)],[f362]) ).
fof(f372,definition,
( sQ28_spl
<=> v1_xboole_0(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f373,plain,
( ~ sQ28_spl
| v1_xboole_0(sK1_skl) ),
inference(component_clause,[status(thm)],[f372]) ).
fof(f382,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f300,f50]) ).
fof(f383,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f382]) ).
fof(f384,plain,
( ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f373,f51]) ).
fof(f385,plain,
~ sQ28_spl,
inference(contradiction_clause,[status(thm)],[f384]) ).
fof(f386,plain,
( ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f363,f53]) ).
fof(f387,plain,
~ sQ25_spl,
inference(contradiction_clause,[status(thm)],[f386]) ).
fof(f396,plain,
! [X0,X1,X2] :
( r1_tarski(k19_filter_2(X0,X1),X2)
| ~ r1_tarski(X1,X2)
| ~ m2_filter_2(X2,X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f177,f83]) ).
fof(f397,plain,
! [X0,X1] :
( r1_tarski(X1,k19_filter_2(X0,X1))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f176,f83]) ).
fof(f400,plain,
( m2_filter_2(k19_filter_2(sK0_skl,sK3_skl),sK0_skl)
| v1_xboole_0(sK3_skl)
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f83,f56]) ).
fof(f402,plain,
( m2_filter_2(k19_filter_2(sK0_skl,sK1_skl),sK0_skl)
| v1_xboole_0(sK1_skl)
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f83,f52]) ).
fof(f408,definition,
( sQ32_spl
<=> m2_filter_2(k19_filter_2(sK0_skl,sK3_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f411,plain,
( sQ32_spl
| sQ22_spl
| ~ sQ19_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f400,f208,f211,f298,f352,f408]) ).
fof(f416,definition,
( sQ34_spl
<=> m2_filter_2(k19_filter_2(sK0_skl,sK1_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f417,plain,
( ~ sQ34_spl
| m2_filter_2(k19_filter_2(sK0_skl,sK1_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f416]) ).
fof(f419,plain,
( sQ34_spl
| sQ28_spl
| ~ sQ19_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f402,f208,f211,f298,f372,f416]) ).
fof(f420,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f353,f55]) ).
fof(f421,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f420]) ).
fof(f441,plain,
( ~ sQ34_spl
| m2_lattice4(k19_filter_2(sK0_skl,sK1_skl),sK0_skl)
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f417,f93]) ).
fof(f442,plain,
( ~ sQ34_spl
| ~ v1_xboole_0(k19_filter_2(sK0_skl,sK1_skl))
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f417,f92]) ).
fof(f443,definition,
( sQ37_spl
<=> m2_lattice4(k19_filter_2(sK0_skl,sK1_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f446,plain,
( ~ sQ34_spl
| sQ37_spl
| ~ sQ19_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f441,f208,f211,f298,f443,f416]) ).
fof(f447,definition,
( sQ38_spl
<=> v1_xboole_0(k19_filter_2(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f450,plain,
( ~ sQ34_spl
| ~ sQ38_spl
| ~ sQ19_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f442,f208,f211,f298,f447,f416]) ).
fof(f468,plain,
! [X0,X1] :
( r1_tarski(X1,u1_struct_0(X0))
| ~ m2_lattice4(X1,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f95,f149]) ).
fof(f659,definition,
! [X1] :
( sQ54_spl
<=> ~ v1_xboole_0(X1) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f660,plain,
! [X0] :
( ~ sQ54_spl
| ~ v1_xboole_0(X0) ),
inference(component_clause,[status(thm)],[f659]) ).
fof(f686,plain,
! [X0,X1,X2] :
( ~ r1_tarski(X1,u1_struct_0(X0))
| r1_tarski(k19_filter_2(X0,X1),X2)
| ~ r1_tarski(X1,X2)
| ~ m2_filter_2(X2,X0)
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f396,f150]) ).
fof(f727,definition,
( sQ63_spl
<=> v1_xboole_0(k1_zfmisc_1(k1_xboole_0)) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f728,plain,
( ~ sQ63_spl
| v1_xboole_0(k1_zfmisc_1(k1_xboole_0)) ),
inference(component_clause,[status(thm)],[f727]) ).
fof(f740,definition,
( sQ65_spl
<=> r1_tarski(sK2_skl,u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f742,plain,
( sQ65_spl
| ~ r1_tarski(sK2_skl,u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f740]) ).
fof(f744,plain,
( sQ65_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f742,f189]) ).
fof(f745,plain,
sQ65_spl,
inference(contradiction_clause,[status(thm)],[f744]) ).
fof(f757,plain,
( r1_tarski(sK3_skl,k19_filter_2(sK0_skl,sK3_skl))
| v1_xboole_0(sK3_skl)
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f397,f56]) ).
fof(f769,definition,
( sQ68_spl
<=> r1_tarski(sK3_skl,k19_filter_2(sK0_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f770,plain,
( ~ sQ68_spl
| r1_tarski(sK3_skl,k19_filter_2(sK0_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f769]) ).
fof(f772,plain,
( sQ68_spl
| sQ22_spl
| ~ sQ19_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f757,f208,f211,f298,f352,f769]) ).
fof(f885,plain,
! [X0] :
( ~ sQ68_spl
| r1_tarski(X0,k19_filter_2(sK0_skl,sK3_skl))
| ~ r1_tarski(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f770,f144]) ).
fof(f928,plain,
( sQ1_spl
| ~ r1_tarski(k19_filter_2(sK0_skl,sK1_skl),u1_struct_0(sK0_skl))
| ~ r1_tarski(k19_filter_2(sK0_skl,sK1_skl),k19_filter_2(sK0_skl,sK1_skl))
| ~ m2_filter_2(k19_filter_2(sK0_skl,sK1_skl),sK0_skl)
| v1_xboole_0(k19_filter_2(sK0_skl,sK1_skl))
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f686,f170]) ).
fof(f933,definition,
( sQ83_spl
<=> r1_tarski(k19_filter_2(sK0_skl,sK1_skl),k19_filter_2(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f935,plain,
( sQ83_spl
| ~ r1_tarski(k19_filter_2(sK0_skl,sK1_skl),k19_filter_2(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f933]) ).
fof(f936,definition,
( sQ84_spl
<=> r1_tarski(k19_filter_2(sK0_skl,sK1_skl),u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f938,plain,
( sQ84_spl
| ~ r1_tarski(k19_filter_2(sK0_skl,sK1_skl),u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f936]) ).
fof(f939,plain,
( sQ1_spl
| ~ sQ84_spl
| ~ sQ83_spl
| ~ sQ34_spl
| sQ38_spl
| ~ sQ19_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f928,f208,f211,f298,f447,f416,f933,f936,f168]) ).
fof(f941,plain,
( sQ83_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f935,f139]) ).
fof(f942,plain,
sQ83_spl,
inference(contradiction_clause,[status(thm)],[f941]) ).
fof(f1150,plain,
( ~ sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f728,f114]) ).
fof(f1151,plain,
~ sQ63_spl,
inference(contradiction_clause,[status(thm)],[f1150]) ).
fof(f1171,plain,
( ~ sQ54_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f115,f660]) ).
fof(f1172,plain,
~ sQ54_spl,
inference(contradiction_clause,[status(thm)],[f1171]) ).
fof(f1980,plain,
( sQ84_spl
| ~ m2_lattice4(k19_filter_2(sK0_skl,sK1_skl),sK0_skl)
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f938,f468]) ).
fof(f1984,definition,
( sQ161_spl
<=> r1_tarski(sK1_skl,u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f1986,plain,
( sQ161_spl
| ~ r1_tarski(sK1_skl,u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f1984]) ).
fof(f1989,plain,
( sQ84_spl
| ~ sQ37_spl
| ~ sQ19_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f1980,f208,f211,f298,f443,f936]) ).
fof(f1994,plain,
( sQ2_spl
| ~ r1_tarski(sK2_skl,u1_struct_0(sK0_skl))
| ~ r1_tarski(sK2_skl,k19_filter_2(sK0_skl,sK3_skl))
| ~ m2_filter_2(k19_filter_2(sK0_skl,sK3_skl),sK0_skl)
| v1_xboole_0(sK2_skl)
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f174,f686]) ).
fof(f1995,definition,
( sQ162_spl
<=> r1_tarski(sK2_skl,k19_filter_2(sK0_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f1997,plain,
( sQ162_spl
| ~ r1_tarski(sK2_skl,k19_filter_2(sK0_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f1995]) ).
fof(f1999,plain,
( sQ2_spl
| ~ sQ65_spl
| ~ sQ162_spl
| ~ sQ32_spl
| sQ25_spl
| ~ sQ19_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f1994,f208,f211,f298,f362,f408,f1995,f740,f172]) ).
fof(f2017,definition,
( sQ163_spl
<=> v1_xboole_0(k1_zfmisc_1(sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f2018,plain,
( ~ sQ163_spl
| v1_xboole_0(k1_zfmisc_1(sK2_skl)) ),
inference(component_clause,[status(thm)],[f2017]) ).
fof(f2028,plain,
( ~ sQ163_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2018,f114]) ).
fof(f2029,plain,
~ sQ163_spl,
inference(contradiction_clause,[status(thm)],[f2028]) ).
fof(f2173,plain,
( sQ161_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1986,f190]) ).
fof(f2174,plain,
sQ161_spl,
inference(contradiction_clause,[status(thm)],[f2173]) ).
fof(f3440,definition,
( sQ289_spl
<=> l1_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ289_spl])],[split_symbol_definition]) ).
fof(f3442,plain,
( sQ289_spl
| ~ l1_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f3440]) ).
fof(f3452,plain,
( sQ289_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3442,f289]) ).
fof(f3453,plain,
sQ289_spl,
inference(contradiction_clause,[status(thm)],[f3452]) ).
fof(f3593,plain,
( sQ162_spl
| ~ sQ68_spl
| ~ r1_tarski(sK2_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f885,f1997]) ).
fof(f3613,plain,
( sQ162_spl
| ~ sQ68_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f3593,f165,f769,f1995]) ).
fof(f3645,plain,
$false,
inference(sat_refutation,[status(thm)],[f171,f175,f219,f221,f383,f385,f387,f411,f419,f421,f446,f450,f745,f772,f939,f942,f1151,f1172,f1989,f1999,f2029,f2174,f3453,f3613]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT310+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/5.45 % Computer : n026.cluster.edu
% 0.19/5.45 % Model : x86_64 x86_64
% 0.19/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.45 % Memory : 8046.5625MB
% 0.19/5.45 % OS : Linux 6.8.0-71-generic
% 0.19/5.45 % CPULimit : 300
% 0.19/5.45 % WCLimit : 300
% 0.19/5.45 % DateTime : Sun Sep 20 23:35:58 UTC 2026
% 0.19/5.45 % CPUTime :
% 0.19/5.47 % Drodi V4.1.1
% 0.23/5.89 % Refutation found
% 0.23/5.89 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/5.89 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/5.91 % Elapsed time: 0.437336 seconds
% 0.23/5.91 % CPU time: 3.218271 seconds
% 0.23/5.91 % Total memory used: 113.348 MB
% 0.23/5.91 % Net memory used: 110.142 MB
%------------------------------------------------------------------------------