%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LAT327+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 : n020.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 01:02:45 PM UTC 2026
% Result : Theorem 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 20
% Syntax : Number of formulae : 90 ( 14 unt; 16 def)
% Number of atoms : 352 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 440 ( 178 ~; 185 |; 43 &)
% ( 18 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 29 ( 28 usr; 17 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 63 ( 60 !; 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)
=> ( r2_hidden(C,k22_filter_2(A,B,C))
& r2_hidden(B,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)
=> ( r2_hidden(C,k22_filter_2(A,B,C))
& r2_hidden(B,k22_filter_2(A,B,C)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f33,axiom,
! [A,B,C] :
( ( m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(B,u1_struct_0(A))
& l3_lattices(A)
& v9_lattices(A)
& v8_lattices(A)
& v6_lattices(A)
& ~ v3_struct_0(A) )
=> r3_lattices(A,B,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [A] :
( l3_lattices(A)
=> ( ( v10_lattices(A)
& ~ v3_struct_0(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(f44,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))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r3_lattices(A,B,C)
=> ( r2_hidden(D,k22_filter_2(A,B,C))
<=> ( r3_lattices(A,D,C)
& r3_lattices(A,B,D) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,plain,
? [A] :
( ? [B] :
( ? [C] :
( ( ~ r2_hidden(C,k22_filter_2(A,B,C))
| ~ r2_hidden(B,k22_filter_2(A,B,C)) )
& r3_lattices(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)],[f2]) ).
fof(f46,plain,
( ( ~ r2_hidden(sK2_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl))
| ~ r2_hidden(sK1_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl)) )
& r3_lattices(sK0_skl,sK1_skl,sK2_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)],[f45]) ).
fof(f47,plain,
~ v3_struct_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
v10_lattices(sK0_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
l3_lattices(sK0_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f50,plain,
m1_subset_1(sK1_skl,u1_struct_0(sK0_skl)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f51,plain,
m1_subset_1(sK2_skl,u1_struct_0(sK0_skl)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f52,plain,
r3_lattices(sK0_skl,sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f53,plain,
( ~ r2_hidden(sK2_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl))
| ~ r2_hidden(sK1_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl)) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f121,plain,
! [A,B,C] :
( r3_lattices(A,B,B)
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l3_lattices(A)
| ~ v9_lattices(A)
| ~ v8_lattices(A)
| ~ v6_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f122,plain,
! [A,B] :
( r3_lattices(A,B,B)
| ! [C] : ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ l3_lattices(A)
| ~ v9_lattices(A)
| ~ v8_lattices(A)
| ~ v6_lattices(A)
| v3_struct_0(A) ),
inference(miniscoping,[status(thm)],[f121]) ).
fof(f123,plain,
! [X0,X1,X2] :
( r3_lattices(X0,X1,X1)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| ~ v9_lattices(X0)
| ~ v8_lattices(X0)
| ~ v6_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f138,plain,
! [A] :
( ( v9_lattices(A)
& v8_lattices(A)
& v7_lattices(A)
& v6_lattices(A)
& v5_lattices(A)
& v4_lattices(A)
& ~ v3_struct_0(A) )
| ~ v10_lattices(A)
| v3_struct_0(A)
| ~ l3_lattices(A) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f142,plain,
! [X0] :
( v6_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f144,plain,
! [X0] :
( v8_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f145,plain,
! [X0] :
( v9_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f151,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( ( r2_hidden(D,k22_filter_2(A,B,C))
<=> ( r3_lattices(A,D,C)
& r3_lattices(A,B,D) ) )
| ~ r3_lattices(A,B,C)
| ~ m1_subset_1(D,u1_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)],[f44]) ).
fof(f152,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( ( ( ~ r3_lattices(A,D,C)
| ~ r3_lattices(A,B,D)
| r2_hidden(D,k22_filter_2(A,B,C)) )
& ( ( r3_lattices(A,D,C)
& r3_lattices(A,B,D) )
| ~ r2_hidden(D,k22_filter_2(A,B,C)) ) )
| ~ r3_lattices(A,B,C)
| ~ m1_subset_1(D,u1_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(NNF_transformation,[status(thm)],[f151]) ).
fof(f155,plain,
! [X0,X1,X2,X3] :
( ~ r3_lattices(X0,X3,X2)
| ~ r3_lattices(X0,X1,X3)
| r2_hidden(X3,k22_filter_2(X0,X1,X2))
| ~ r3_lattices(X0,X1,X2)
| ~ m1_subset_1(X3,u1_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)],[f152]) ).
fof(f156,definition,
( sQ0_spl
<=> r2_hidden(sK1_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f159,definition,
( sQ1_spl
<=> r2_hidden(sK2_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f53,f156,f159]) ).
fof(f174,plain,
! [X0,X1,X2] :
( ~ r3_lattices(sK0_skl,X2,X1)
| ~ r3_lattices(sK0_skl,X0,X2)
| r2_hidden(X2,k22_filter_2(sK0_skl,X0,X1))
| ~ r3_lattices(sK0_skl,X0,X1)
| ~ m1_subset_1(X2,u1_struct_0(sK0_skl))
| ~ m1_subset_1(X1,u1_struct_0(sK0_skl))
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl))
| ~ l3_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f155,f48]) ).
fof(f175,definition,
( sQ2_spl
<=> v3_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( ~ sQ2_spl
| v3_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,definition,
( sQ3_spl
<=> l3_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( sQ3_spl
| ~ l3_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,definition,
! [X0,X1,X2] :
( sQ4_spl
<=> ( ~ r3_lattices(sK0_skl,X2,X1)
| ~ r3_lattices(sK0_skl,X0,X2)
| r2_hidden(X2,k22_filter_2(sK0_skl,X0,X1))
| ~ r3_lattices(sK0_skl,X0,X1)
| ~ m1_subset_1(X2,u1_struct_0(sK0_skl))
| ~ m1_subset_1(X1,u1_struct_0(sK0_skl))
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f182,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| ~ r3_lattices(sK0_skl,X2,X1)
| ~ r3_lattices(sK0_skl,X0,X2)
| r2_hidden(X2,k22_filter_2(sK0_skl,X0,X1))
| ~ r3_lattices(sK0_skl,X0,X1)
| ~ m1_subset_1(X2,u1_struct_0(sK0_skl))
| ~ m1_subset_1(X1,u1_struct_0(sK0_skl))
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,plain,
( sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f174,f175,f178,f181]) ).
fof(f203,plain,
! [X0] :
( ~ sQ4_spl
| ~ r3_lattices(sK0_skl,sK2_skl,X0)
| r2_hidden(sK2_skl,k22_filter_2(sK0_skl,sK1_skl,X0))
| ~ r3_lattices(sK0_skl,sK1_skl,X0)
| ~ m1_subset_1(sK2_skl,u1_struct_0(sK0_skl))
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl))
| ~ m1_subset_1(sK1_skl,u1_struct_0(sK0_skl)) ),
inference(resolution,[status(thm)],[f182,f52]) ).
fof(f204,plain,
! [X0] :
( ~ sQ4_spl
| ~ r3_lattices(sK0_skl,X0,sK1_skl)
| r2_hidden(sK1_skl,k22_filter_2(sK0_skl,X0,sK2_skl))
| ~ r3_lattices(sK0_skl,X0,sK2_skl)
| ~ m1_subset_1(sK1_skl,u1_struct_0(sK0_skl))
| ~ m1_subset_1(sK2_skl,u1_struct_0(sK0_skl))
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl)) ),
inference(resolution,[status(thm)],[f182,f52]) ).
fof(f205,definition,
( sQ5_spl
<=> m1_subset_1(sK1_skl,u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( sQ5_spl
| ~ m1_subset_1(sK1_skl,u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,definition,
! [X0] :
( sQ6_spl
<=> ( ~ r3_lattices(sK0_skl,sK2_skl,X0)
| r2_hidden(sK2_skl,k22_filter_2(sK0_skl,sK1_skl,X0))
| ~ r3_lattices(sK0_skl,sK1_skl,X0)
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f209,plain,
! [X0] :
( ~ sQ6_spl
| ~ r3_lattices(sK0_skl,sK2_skl,X0)
| r2_hidden(sK2_skl,k22_filter_2(sK0_skl,sK1_skl,X0))
| ~ r3_lattices(sK0_skl,sK1_skl,X0)
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,definition,
( sQ7_spl
<=> m1_subset_1(sK2_skl,u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( sQ7_spl
| ~ m1_subset_1(sK2_skl,u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f203,f205,f208,f211,f181]) ).
fof(f215,definition,
! [X0] :
( sQ8_spl
<=> ( ~ r3_lattices(sK0_skl,X0,sK1_skl)
| r2_hidden(sK1_skl,k22_filter_2(sK0_skl,X0,sK2_skl))
| ~ r3_lattices(sK0_skl,X0,sK2_skl)
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f216,plain,
! [X0] :
( ~ sQ8_spl
| ~ r3_lattices(sK0_skl,X0,sK1_skl)
| r2_hidden(sK1_skl,k22_filter_2(sK0_skl,X0,sK2_skl))
| ~ r3_lattices(sK0_skl,X0,sK2_skl)
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f204,f215,f211,f205,f181]) ).
fof(f219,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f207,f50]) ).
fof(f220,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f219]) ).
fof(f221,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f213,f51]) ).
fof(f222,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f221]) ).
fof(f223,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f180,f49]) ).
fof(f224,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f223]) ).
fof(f225,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f176,f47]) ).
fof(f226,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f225]) ).
fof(f377,definition,
( sQ20_spl
<=> v10_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f379,plain,
( sQ20_spl
| ~ v10_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f377]) ).
fof(f394,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f379,f48]) ).
fof(f395,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f394]) ).
fof(f601,plain,
( v9_lattices(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l3_lattices(sK0_skl) ),
inference(resolution,[status(thm)],[f145,f48]) ).
fof(f602,definition,
( sQ46_spl
<=> v9_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f603,plain,
( ~ sQ46_spl
| v9_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f602]) ).
fof(f605,plain,
( sQ46_spl
| sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f601,f178,f175,f602]) ).
fof(f607,plain,
! [X0,X1] :
( ~ sQ46_spl
| r3_lattices(sK0_skl,X0,X0)
| ~ m1_subset_1(X1,u1_struct_0(sK0_skl))
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl))
| ~ l3_lattices(sK0_skl)
| ~ v8_lattices(sK0_skl)
| ~ v6_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f603,f123]) ).
fof(f608,definition,
( sQ47_spl
<=> v6_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f610,plain,
( sQ47_spl
| ~ v6_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f608]) ).
fof(f611,definition,
( sQ48_spl
<=> v8_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f613,plain,
( sQ48_spl
| ~ v8_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f611]) ).
fof(f618,definition,
! [X0] :
( sQ50_spl
<=> ( r3_lattices(sK0_skl,X0,X0)
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f619,plain,
! [X0] :
( ~ sQ50_spl
| r3_lattices(sK0_skl,X0,X0)
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f618]) ).
fof(f621,definition,
! [X1] :
( sQ51_spl
<=> ~ m1_subset_1(X1,u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f622,plain,
! [X0] :
( ~ sQ51_spl
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f621]) ).
fof(f624,plain,
( ~ sQ46_spl
| sQ51_spl
| sQ50_spl
| ~ sQ3_spl
| ~ sQ48_spl
| ~ sQ47_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f607,f175,f608,f611,f178,f618,f621,f602]) ).
fof(f625,plain,
( sQ48_spl
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l3_lattices(sK0_skl) ),
inference(resolution,[status(thm)],[f613,f144]) ).
fof(f626,plain,
( sQ48_spl
| ~ sQ20_spl
| sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f625,f178,f175,f377,f611]) ).
fof(f627,plain,
( sQ47_spl
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl)
| ~ l3_lattices(sK0_skl) ),
inference(resolution,[status(thm)],[f610,f142]) ).
fof(f628,plain,
( sQ47_spl
| ~ sQ20_spl
| sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f627,f178,f175,f377,f608]) ).
fof(f648,plain,
( ~ sQ50_spl
| r3_lattices(sK0_skl,sK1_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f619,f50]) ).
fof(f649,plain,
( ~ sQ50_spl
| r3_lattices(sK0_skl,sK2_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f619,f51]) ).
fof(f651,plain,
( ~ sQ8_spl
| ~ sQ50_spl
| r2_hidden(sK1_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl))
| ~ r3_lattices(sK0_skl,sK1_skl,sK2_skl)
| ~ m1_subset_1(sK1_skl,u1_struct_0(sK0_skl)) ),
inference(resolution,[status(thm)],[f648,f216]) ).
fof(f656,definition,
( sQ53_spl
<=> r3_lattices(sK0_skl,sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f658,plain,
( sQ53_spl
| ~ r3_lattices(sK0_skl,sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f656]) ).
fof(f659,plain,
( ~ sQ8_spl
| ~ sQ50_spl
| sQ0_spl
| ~ sQ53_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f651,f205,f656,f156,f618,f215]) ).
fof(f678,plain,
( sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f658,f52]) ).
fof(f679,plain,
sQ53_spl,
inference(contradiction_clause,[status(thm)],[f678]) ).
fof(f682,plain,
( ~ sQ6_spl
| ~ sQ50_spl
| r2_hidden(sK2_skl,k22_filter_2(sK0_skl,sK1_skl,sK2_skl))
| ~ r3_lattices(sK0_skl,sK1_skl,sK2_skl)
| ~ m1_subset_1(sK2_skl,u1_struct_0(sK0_skl)) ),
inference(resolution,[status(thm)],[f649,f209]) ).
fof(f687,plain,
( ~ sQ6_spl
| ~ sQ50_spl
| sQ1_spl
| ~ sQ53_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f682,f211,f656,f159,f618,f208]) ).
fof(f704,plain,
( ~ sQ51_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f50,f622]) ).
fof(f707,plain,
~ sQ51_spl,
inference(contradiction_clause,[status(thm)],[f704]) ).
fof(f708,plain,
$false,
inference(sat_refutation,[status(thm)],[f162,f184,f214,f218,f220,f222,f224,f226,f395,f605,f624,f626,f628,f659,f679,f687,f707]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT327+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n020.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 20 23:39:17 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.14/0.38 % Refutation found
% 0.14/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.40 % Elapsed time: 0.055851 seconds
% 0.14/0.40 % CPU time: 0.171088 seconds
% 0.14/0.40 % Total memory used: 83.555 MB
% 0.14/0.40 % Net memory used: 83.426 MB
%------------------------------------------------------------------------------