%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LAT337+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 01:02:48 PM UTC 2026
% Result : Theorem 0.17s 0.52s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 30
% Syntax : Number of formulae : 130 ( 15 unt; 20 def)
% Number of atoms : 633 ( 0 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 802 ( 299 ~; 330 |; 127 &)
% ( 20 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 43 ( 42 usr; 21 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 78 ( 75 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( r3_lattices(A,B,C)
& l3_lattices(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( l3_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& v17_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& v10_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& ~ v3_struct_0(k23_filter_2(A,k22_filter_2(A,B,C))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( r3_lattices(A,B,C)
& l3_lattices(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( l3_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& v17_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& v10_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& ~ v3_struct_0(k23_filter_2(A,k22_filter_2(A,B,C))) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f12,axiom,
! [A] :
( l3_lattices(A)
=> ( ( v17_lattices(A)
& ~ v3_struct_0(A) )
=> ( v16_lattices(A)
& v15_lattices(A)
& v14_lattices(A)
& v13_lattices(A)
& v11_lattices(A)
& ~ v3_struct_0(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] :
( l3_lattices(A)
=> ( ( v16_lattices(A)
& v15_lattices(A)
& v11_lattices(A)
& ~ v3_struct_0(A) )
=> ( v17_lattices(A)
& ~ v3_struct_0(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] :
( l3_lattices(A)
=> ( ( v11_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( v12_lattices(A)
& v10_lattices(A)
& v9_lattices(A)
& v8_lattices(A)
& v7_lattices(A)
& v6_lattices(A)
& v5_lattices(A)
& v4_lattices(A)
& ~ v3_struct_0(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B,C] :
( ( m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(B,u1_struct_0(A))
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( m2_lattice4(k22_filter_2(A,B,C),A)
& ~ v1_xboole_0(k22_filter_2(A,B,C)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A,B] :
( ( m2_lattice4(B,A)
& ~ v1_xboole_0(B)
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> m2_nat_lat(k23_filter_2(A,B),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_nat_lat(B,A)
=> ( l3_lattices(B)
& v10_lattices(B)
& ~ v3_struct_0(B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [A,B] :
( ( m2_lattice4(B,A)
& ~ v1_xboole_0(B)
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( v10_lattices(k23_filter_2(A,B))
& v9_lattices(k23_filter_2(A,B))
& v8_lattices(k23_filter_2(A,B))
& v7_lattices(k23_filter_2(A,B))
& v6_lattices(k23_filter_2(A,B))
& v5_lattices(k23_filter_2(A,B))
& v4_lattices(k23_filter_2(A,B))
& v3_lattices(k23_filter_2(A,B))
& ~ v3_struct_0(k23_filter_2(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f81,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m2_lattice4(B,A)
& ~ v1_xboole_0(B) )
=> ( v11_lattices(A)
=> v11_lattices(k23_filter_2(A,B)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( r3_lattices(A,B,C)
& v12_lattices(A)
& l3_lattices(A)
& v16_lattices(A)
& v15_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( l3_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& v16_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& v15_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& v10_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& ~ v3_struct_0(k23_filter_2(A,k22_filter_2(A,B,C))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f85,plain,
? [A] :
( ? [B] :
( ? [C] :
( ( ~ l3_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
| ~ v17_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
| ~ v10_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
| v3_struct_0(k23_filter_2(A,k22_filter_2(A,B,C))) )
& r3_lattices(A,B,C)
& l3_lattices(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A)
& m1_subset_1(C,u1_struct_0(A)) )
& m1_subset_1(B,u1_struct_0(A)) )
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f86,plain,
( ( ~ l3_lattices(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl)))
| ~ v17_lattices(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl)))
| ~ v10_lattices(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl)))
| v3_struct_0(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl))) )
& r3_lattices(sK0_skl,sK1_skl,sK2_skl)
& l3_lattices(sK0_skl)
& v17_lattices(sK0_skl)
& v10_lattices(sK0_skl)
& ~ v3_struct_0(sK0_skl)
& m1_subset_1(sK2_skl,u1_struct_0(sK0_skl))
& m1_subset_1(sK1_skl,u1_struct_0(sK0_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]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(C,sK2_skl)],[f85]) ).
fof(f87,plain,
~ v3_struct_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f88,plain,
v10_lattices(sK0_skl),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f89,plain,
l3_lattices(sK0_skl),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f90,plain,
m1_subset_1(sK1_skl,u1_struct_0(sK0_skl)),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f91,plain,
m1_subset_1(sK2_skl,u1_struct_0(sK0_skl)),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f94,plain,
v17_lattices(sK0_skl),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f96,plain,
r3_lattices(sK0_skl,sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f97,plain,
( ~ l3_lattices(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl)))
| ~ v17_lattices(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl)))
| ~ v10_lattices(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl)))
| v3_struct_0(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl))) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f129,plain,
! [A] :
( ( v16_lattices(A)
& v15_lattices(A)
& v14_lattices(A)
& v13_lattices(A)
& v11_lattices(A)
& ~ v3_struct_0(A) )
| ~ v17_lattices(A)
| v3_struct_0(A)
| ~ l3_lattices(A) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f131,plain,
! [X0] :
( v11_lattices(X0)
| ~ v17_lattices(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f134,plain,
! [X0] :
( v15_lattices(X0)
| ~ v17_lattices(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f135,plain,
! [X0] :
( v16_lattices(X0)
| ~ v17_lattices(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f136,plain,
! [A] :
( ( v17_lattices(A)
& ~ v3_struct_0(A) )
| ~ v16_lattices(A)
| ~ v15_lattices(A)
| ~ v11_lattices(A)
| v3_struct_0(A)
| ~ l3_lattices(A) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f138,plain,
! [X0] :
( v17_lattices(X0)
| ~ v16_lattices(X0)
| ~ v15_lattices(X0)
| ~ v11_lattices(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f139,plain,
! [A] :
( ( v12_lattices(A)
& v10_lattices(A)
& v9_lattices(A)
& v8_lattices(A)
& v7_lattices(A)
& v6_lattices(A)
& v5_lattices(A)
& v4_lattices(A)
& ~ v3_struct_0(A) )
| ~ v11_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A)
| ~ l3_lattices(A) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f148,plain,
! [X0] :
( v12_lattices(X0)
| ~ v11_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f152,plain,
! [A,B,C] :
( ( m2_lattice4(k22_filter_2(A,B,C),A)
& ~ v1_xboole_0(k22_filter_2(A,B,C)) )
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f153,plain,
! [X0,X1,X2] :
( ~ v1_xboole_0(k22_filter_2(X0,X1,X2))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f154,plain,
! [X0,X1,X2] :
( m2_lattice4(k22_filter_2(X0,X1,X2),X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f155,plain,
! [A,B] :
( m2_nat_lat(k23_filter_2(A,B),A)
| ~ m2_lattice4(B,A)
| v1_xboole_0(B)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f156,plain,
! [X0,X1] :
( m2_nat_lat(k23_filter_2(X0,X1),X0)
| ~ m2_lattice4(X1,X0)
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f166,plain,
! [A] :
( ! [B] :
( ( l3_lattices(B)
& v10_lattices(B)
& ~ v3_struct_0(B) )
| ~ m2_nat_lat(B,A) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f167,plain,
! [X0,X1] :
( ~ v3_struct_0(X1)
| ~ m2_nat_lat(X1,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f169,plain,
! [X0,X1] :
( l3_lattices(X1)
| ~ m2_nat_lat(X1,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f227,plain,
! [A,B] :
( ( v10_lattices(k23_filter_2(A,B))
& v9_lattices(k23_filter_2(A,B))
& v8_lattices(k23_filter_2(A,B))
& v7_lattices(k23_filter_2(A,B))
& v6_lattices(k23_filter_2(A,B))
& v5_lattices(k23_filter_2(A,B))
& v4_lattices(k23_filter_2(A,B))
& v3_lattices(k23_filter_2(A,B))
& ~ v3_struct_0(k23_filter_2(A,B)) )
| ~ m2_lattice4(B,A)
| v1_xboole_0(B)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f236,plain,
! [X0,X1] :
( v10_lattices(k23_filter_2(X0,X1))
| ~ m2_lattice4(X1,X0)
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f227]) ).
fof(f400,plain,
! [A] :
( ! [B] :
( v11_lattices(k23_filter_2(A,B))
| ~ v11_lattices(A)
| ~ m2_lattice4(B,A)
| v1_xboole_0(B) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f81]) ).
fof(f401,plain,
! [X0,X1] :
( v11_lattices(k23_filter_2(X0,X1))
| ~ v11_lattices(X0)
| ~ m2_lattice4(X1,X0)
| v1_xboole_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f400]) ).
fof(f405,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( l3_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& v16_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& v15_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& v10_lattices(k23_filter_2(A,k22_filter_2(A,B,C)))
& ~ v3_struct_0(k23_filter_2(A,k22_filter_2(A,B,C))) )
| ~ r3_lattices(A,B,C)
| ~ v12_lattices(A)
| ~ l3_lattices(A)
| ~ v16_lattices(A)
| ~ v15_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A)
| ~ m1_subset_1(C,u1_struct_0(A)) )
| ~ m1_subset_1(B,u1_struct_0(A)) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f83]) ).
fof(f408,plain,
! [X0,X1,X2] :
( v15_lattices(k23_filter_2(X0,k22_filter_2(X0,X1,X2)))
| ~ r3_lattices(X0,X1,X2)
| ~ v12_lattices(X0)
| ~ l3_lattices(X0)
| ~ v16_lattices(X0)
| ~ v15_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f405]) ).
fof(f409,plain,
! [X0,X1,X2] :
( v16_lattices(k23_filter_2(X0,k22_filter_2(X0,X1,X2)))
| ~ r3_lattices(X0,X1,X2)
| ~ v12_lattices(X0)
| ~ l3_lattices(X0)
| ~ v16_lattices(X0)
| ~ v15_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f405]) ).
fof(f414,definition,
( sQ0_spl
<=> v3_struct_0(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f415,plain,
( ~ sQ0_spl
| v3_struct_0(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl))) ),
inference(component_clause,[status(thm)],[f414]) ).
fof(f417,definition,
( sQ1_spl
<=> v10_lattices(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f419,plain,
( sQ1_spl
| ~ v10_lattices(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl))) ),
inference(component_clause,[status(thm)],[f417]) ).
fof(f420,definition,
( sQ2_spl
<=> v17_lattices(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f422,plain,
( sQ2_spl
| ~ v17_lattices(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl))) ),
inference(component_clause,[status(thm)],[f420]) ).
fof(f423,definition,
( sQ3_spl
<=> l3_lattices(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f425,plain,
( sQ3_spl
| ~ l3_lattices(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl))) ),
inference(component_clause,[status(thm)],[f423]) ).
fof(f426,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f97,f414,f417,f420,f423]) ).
fof(f429,plain,
! [X0,X1,X2] :
( v15_lattices(k23_filter_2(X0,k22_filter_2(X0,X1,X2)))
| ~ r3_lattices(X0,X1,X2)
| ~ v12_lattices(X0)
| ~ v16_lattices(X0)
| ~ v15_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f408]) ).
fof(f430,plain,
! [X0,X1,X2] :
( v16_lattices(k23_filter_2(X0,k22_filter_2(X0,X1,X2)))
| ~ r3_lattices(X0,X1,X2)
| ~ v12_lattices(X0)
| ~ v16_lattices(X0)
| ~ v15_lattices(X0)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f409]) ).
fof(f434,definition,
( sQ4_spl
<=> l3_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f436,plain,
( sQ4_spl
| ~ l3_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,definition,
( sQ5_spl
<=> v3_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f438,plain,
( ~ sQ5_spl
| v3_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f446,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f438,f87]) ).
fof(f447,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f446]) ).
fof(f448,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f436,f89]) ).
fof(f449,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f448]) ).
fof(f476,definition,
( sQ11_spl
<=> v10_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f478,plain,
( sQ11_spl
| ~ v10_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f476]) ).
fof(f480,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f478,f88]) ).
fof(f481,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f480]) ).
fof(f556,plain,
! [X0] :
( sQ3_spl
| ~ m2_nat_lat(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl)),X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f169,f425]) ).
fof(f559,plain,
( sQ3_spl
| ~ m2_lattice4(k22_filter_2(sK0_skl,sK1_skl,sK2_skl),sK0_skl)
| v1_xboole_0(k22_filter_2(sK0_skl,sK1_skl,sK2_skl))
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f556,f156]) ).
fof(f560,definition,
( sQ25_spl
<=> v1_xboole_0(k22_filter_2(sK0_skl,sK1_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f561,plain,
( ~ sQ25_spl
| v1_xboole_0(k22_filter_2(sK0_skl,sK1_skl,sK2_skl)) ),
inference(component_clause,[status(thm)],[f560]) ).
fof(f563,definition,
( sQ26_spl
<=> m2_lattice4(k22_filter_2(sK0_skl,sK1_skl,sK2_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f565,plain,
( sQ26_spl
| ~ m2_lattice4(k22_filter_2(sK0_skl,sK1_skl,sK2_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f563]) ).
fof(f566,plain,
( sQ3_spl
| ~ sQ26_spl
| sQ25_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f559,f437,f476,f434,f560,f563,f423]) ).
fof(f567,plain,
( sQ2_spl
| ~ v16_lattices(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl)))
| ~ v15_lattices(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl)))
| ~ v11_lattices(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl)))
| v3_struct_0(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl)))
| ~ l3_lattices(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl))) ),
inference(resolution,[status(thm)],[f422,f138]) ).
fof(f568,definition,
( sQ27_spl
<=> v11_lattices(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl))) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f570,plain,
( sQ27_spl
| ~ v11_lattices(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl))) ),
inference(component_clause,[status(thm)],[f568]) ).
fof(f571,definition,
( sQ28_spl
<=> v15_lattices(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl))) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f573,plain,
( sQ28_spl
| ~ v15_lattices(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl))) ),
inference(component_clause,[status(thm)],[f571]) ).
fof(f574,definition,
( sQ29_spl
<=> v16_lattices(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl))) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f576,plain,
( sQ29_spl
| ~ v16_lattices(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl))) ),
inference(component_clause,[status(thm)],[f574]) ).
fof(f577,plain,
( sQ2_spl
| ~ sQ29_spl
| ~ sQ28_spl
| ~ sQ27_spl
| sQ0_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f567,f423,f414,f568,f571,f574,f420]) ).
fof(f578,plain,
! [X0] :
( ~ sQ0_spl
| ~ m2_nat_lat(k23_filter_2(sK0_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl)),X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f415,f167]) ).
fof(f579,plain,
( sQ26_spl
| ~ m1_subset_1(sK2_skl,u1_struct_0(sK0_skl))
| ~ m1_subset_1(sK1_skl,u1_struct_0(sK0_skl))
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f565,f154]) ).
fof(f580,definition,
( sQ30_spl
<=> m1_subset_1(sK1_skl,u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f582,plain,
( sQ30_spl
| ~ m1_subset_1(sK1_skl,u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f580]) ).
fof(f583,definition,
( sQ31_spl
<=> m1_subset_1(sK2_skl,u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f585,plain,
( sQ31_spl
| ~ m1_subset_1(sK2_skl,u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f583]) ).
fof(f586,plain,
( sQ26_spl
| ~ sQ31_spl
| ~ sQ30_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f579,f437,f476,f434,f580,f583,f563]) ).
fof(f587,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f585,f91]) ).
fof(f588,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f587]) ).
fof(f589,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f582,f90]) ).
fof(f590,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f589]) ).
fof(f591,plain,
( ~ sQ25_spl
| ~ m1_subset_1(sK2_skl,u1_struct_0(sK0_skl))
| ~ m1_subset_1(sK1_skl,u1_struct_0(sK0_skl))
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f561,f153]) ).
fof(f592,plain,
( ~ sQ25_spl
| ~ sQ31_spl
| ~ sQ30_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f591,f437,f476,f434,f580,f583,f560]) ).
fof(f593,plain,
( ~ sQ0_spl
| ~ m2_lattice4(k22_filter_2(sK0_skl,sK1_skl,sK2_skl),sK0_skl)
| v1_xboole_0(k22_filter_2(sK0_skl,sK1_skl,sK2_skl))
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f578,f156]) ).
fof(f594,plain,
( ~ sQ0_spl
| ~ sQ26_spl
| sQ25_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f593,f437,f476,f434,f560,f563,f414]) ).
fof(f703,plain,
( sQ1_spl
| ~ m2_lattice4(k22_filter_2(sK0_skl,sK1_skl,sK2_skl),sK0_skl)
| v1_xboole_0(k22_filter_2(sK0_skl,sK1_skl,sK2_skl))
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f236,f419]) ).
fof(f706,plain,
( sQ1_spl
| ~ sQ26_spl
| sQ25_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f703,f437,f476,f434,f560,f563,f417]) ).
fof(f969,plain,
( sQ28_spl
| ~ r3_lattices(sK0_skl,sK1_skl,sK2_skl)
| ~ v12_lattices(sK0_skl)
| ~ v16_lattices(sK0_skl)
| ~ v15_lattices(sK0_skl)
| ~ m1_subset_1(sK2_skl,u1_struct_0(sK0_skl))
| ~ m1_subset_1(sK1_skl,u1_struct_0(sK0_skl))
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f429,f573]) ).
fof(f970,definition,
( sQ91_spl
<=> v15_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f972,plain,
( sQ91_spl
| ~ v15_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f970]) ).
fof(f973,definition,
( sQ92_spl
<=> v16_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f975,plain,
( sQ92_spl
| ~ v16_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f973]) ).
fof(f976,definition,
( sQ93_spl
<=> v12_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f978,plain,
( sQ93_spl
| ~ v12_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f976]) ).
fof(f979,definition,
( sQ94_spl
<=> r3_lattices(sK0_skl,sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f981,plain,
( sQ94_spl
| ~ r3_lattices(sK0_skl,sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f979]) ).
fof(f982,plain,
( sQ28_spl
| ~ sQ94_spl
| ~ sQ93_spl
| ~ sQ92_spl
| ~ sQ91_spl
| ~ sQ31_spl
| ~ sQ30_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f969,f437,f476,f434,f580,f583,f970,f973,f976,f979,f571]) ).
fof(f983,plain,
( sQ94_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f981,f96]) ).
fof(f984,plain,
sQ94_spl,
inference(contradiction_clause,[status(thm)],[f983]) ).
fof(f989,plain,
( sQ93_spl
| ~ v11_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l3_lattices(sK0_skl) ),
inference(resolution,[status(thm)],[f978,f148]) ).
fof(f990,definition,
( sQ95_spl
<=> v11_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f992,plain,
( sQ95_spl
| ~ v11_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f990]) ).
fof(f993,plain,
( sQ93_spl
| ~ sQ95_spl
| ~ sQ11_spl
| sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f989,f434,f437,f476,f990,f976]) ).
fof(f994,plain,
( sQ27_spl
| ~ v11_lattices(sK0_skl)
| ~ m2_lattice4(k22_filter_2(sK0_skl,sK1_skl,sK2_skl),sK0_skl)
| v1_xboole_0(k22_filter_2(sK0_skl,sK1_skl,sK2_skl))
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f570,f401]) ).
fof(f996,plain,
( sQ27_spl
| ~ sQ95_spl
| ~ sQ26_spl
| sQ25_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f994,f437,f476,f434,f560,f563,f990,f568]) ).
fof(f998,plain,
( sQ92_spl
| ~ v17_lattices(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l3_lattices(sK0_skl) ),
inference(resolution,[status(thm)],[f975,f135]) ).
fof(f999,definition,
( sQ96_spl
<=> v17_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f1001,plain,
( sQ96_spl
| ~ v17_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f999]) ).
fof(f1002,plain,
( sQ92_spl
| ~ sQ96_spl
| sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f998,f434,f437,f999,f973]) ).
fof(f1003,plain,
( sQ96_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1001,f94]) ).
fof(f1004,plain,
sQ96_spl,
inference(contradiction_clause,[status(thm)],[f1003]) ).
fof(f1005,plain,
( sQ91_spl
| ~ v17_lattices(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l3_lattices(sK0_skl) ),
inference(resolution,[status(thm)],[f972,f134]) ).
fof(f1006,plain,
( sQ91_spl
| ~ sQ96_spl
| sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1005,f434,f437,f999,f970]) ).
fof(f1041,plain,
( sQ95_spl
| ~ v17_lattices(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l3_lattices(sK0_skl) ),
inference(resolution,[status(thm)],[f992,f131]) ).
fof(f1042,plain,
( sQ95_spl
| ~ sQ96_spl
| sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1041,f434,f437,f999,f990]) ).
fof(f1043,plain,
( sQ29_spl
| ~ r3_lattices(sK0_skl,sK1_skl,sK2_skl)
| ~ v12_lattices(sK0_skl)
| ~ v16_lattices(sK0_skl)
| ~ v15_lattices(sK0_skl)
| ~ m1_subset_1(sK2_skl,u1_struct_0(sK0_skl))
| ~ m1_subset_1(sK1_skl,u1_struct_0(sK0_skl))
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f576,f430]) ).
fof(f1045,plain,
( sQ29_spl
| ~ sQ94_spl
| ~ sQ93_spl
| ~ sQ92_spl
| ~ sQ91_spl
| ~ sQ31_spl
| ~ sQ30_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f1043,f437,f476,f434,f580,f583,f970,f973,f976,f979,f574]) ).
fof(f1047,plain,
$false,
inference(sat_refutation,[status(thm)],[f426,f447,f449,f481,f566,f577,f586,f588,f590,f592,f594,f706,f982,f984,f993,f996,f1002,f1004,f1006,f1042,f1045]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT337+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n005.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sun Sep 20 23:41:33 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.52 % Refutation found
% 0.17/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.55 % Elapsed time: 0.102874 seconds
% 0.17/0.55 % CPU time: 0.500021 seconds
% 0.17/0.55 % Total memory used: 95.593 MB
% 0.17/0.55 % Net memory used: 95.382 MB
%------------------------------------------------------------------------------