%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LAT313+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 : n002.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 01:02:41 PM UTC 2026
% Result : Theorem 0.16s 5.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 34
% Syntax : Number of formulae : 140 ( 19 unt; 19 def)
% Number of atoms : 452 ( 30 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 516 ( 204 ~; 222 |; 46 &)
% ( 22 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 32 ( 30 usr; 20 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 98 ( 96 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_filter_2(B,A)
=> ( ( r2_hidden(k6_lattices(A),B)
& v14_lattices(A) )
=> ( B = u1_struct_0(A)
& r1_filter_2(u1_struct_0(A),B,k17_filter_2(A)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_filter_2(B,A)
=> ( ( r2_hidden(k6_lattices(A),B)
& v14_lattices(A) )
=> ( B = u1_struct_0(A)
& r1_filter_2(u1_struct_0(A),B,k17_filter_2(A)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f7,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> k17_filter_2(A) = u1_struct_0(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> m2_filter_2(k17_filter_2(A),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,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(f19,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(f29,axiom,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [A,B,C] :
( ( m1_subset_1(C,k1_zfmisc_1(A))
& m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(A) )
=> ( r1_filter_2(A,B,C)
<=> B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [A,B] : r1_tarski(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [A,B,C] :
( ( m1_subset_1(C,k1_zfmisc_1(A))
& m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(A) )
=> ( r1_filter_2(A,B,C)
=> r1_filter_2(A,C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( r2_hidden(A,B)
| v1_xboole_0(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_filter_2(B,A)
=> r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,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) )
=> ( ( r2_hidden(k6_lattices(A),B)
& v14_lattices(A) )
=> ( k19_filter_2(A,B) = u1_struct_0(A)
& r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),k17_filter_2(A)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& r2_hidden(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,plain,
? [A] :
( ? [B] :
( ( B != u1_struct_0(A)
| ~ r1_filter_2(u1_struct_0(A),B,k17_filter_2(A)) )
& r2_hidden(k6_lattices(A),B)
& v14_lattices(A)
& m2_filter_2(B,A) )
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f53,plain,
( ( sK1_skl != u1_struct_0(sK0_skl)
| ~ r1_filter_2(u1_struct_0(sK0_skl),sK1_skl,k17_filter_2(sK0_skl)) )
& r2_hidden(k6_lattices(sK0_skl),sK1_skl)
& v14_lattices(sK0_skl)
& m2_filter_2(sK1_skl,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]),skolemize(A,sK0_skl),skolemize(B,sK1_skl)],[f52]) ).
fof(f54,plain,
~ v3_struct_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
v10_lattices(sK0_skl),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f56,plain,
l3_lattices(sK0_skl),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f57,plain,
m2_filter_2(sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f58,plain,
v14_lattices(sK0_skl),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f59,plain,
r2_hidden(k6_lattices(sK0_skl),sK1_skl),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f60,plain,
( sK1_skl != u1_struct_0(sK0_skl)
| ~ r1_filter_2(u1_struct_0(sK0_skl),sK1_skl,k17_filter_2(sK0_skl)) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f76,plain,
! [A] :
( k17_filter_2(A) = u1_struct_0(A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f77,plain,
! [X0] :
( k17_filter_2(X0) = u1_struct_0(X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
! [A] :
( m2_filter_2(k17_filter_2(A),A)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f79,plain,
! [X0] :
( m2_filter_2(k17_filter_2(X0),X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
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)],[f18]) ).
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)],[f19]) ).
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)],[f29]) ).
fof(f138,plain,
! [A,B,C] :
( ( r1_filter_2(A,B,C)
<=> B = C )
| ~ m1_subset_1(C,k1_zfmisc_1(A))
| ~ m1_subset_1(B,k1_zfmisc_1(A))
| v1_xboole_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f139,plain,
! [A,B,C] :
( ( ( B != C
| r1_filter_2(A,B,C) )
& ( B = C
| ~ r1_filter_2(A,B,C) ) )
| ~ m1_subset_1(C,k1_zfmisc_1(A))
| ~ m1_subset_1(B,k1_zfmisc_1(A))
| v1_xboole_0(A) ),
inference(NNF_transformation,[status(thm)],[f138]) ).
fof(f140,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ r1_filter_2(X0,X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f145,plain,
! [A] : r1_tarski(A,A),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f146,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f147,plain,
! [A,B,C] :
( r1_filter_2(A,C,B)
| ~ r1_filter_2(A,B,C)
| ~ m1_subset_1(C,k1_zfmisc_1(A))
| ~ m1_subset_1(B,k1_zfmisc_1(A))
| v1_xboole_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f148,plain,
! [X0,X1,X2] :
( r1_filter_2(X0,X2,X1)
| ~ r1_filter_2(X0,X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f149,plain,
! [A,B] :
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f150,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f151,plain,
! [A,B] :
( r2_hidden(A,B)
| v1_xboole_0(B)
| ~ m1_subset_1(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f152,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f153,plain,
! [A] :
( ! [B] :
( r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),B)
| ~ m2_filter_2(B,A) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f154,plain,
! [X0,X1] :
( r1_filter_2(u1_struct_0(X0),k19_filter_2(X0,X1),X1)
| ~ m2_filter_2(X1,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f155,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)],[f45]) ).
fof(f156,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)],[f155]) ).
fof(f158,plain,
! [X0,X1] :
( ~ r1_tarski(X0,X1)
| m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f159,plain,
! [A] :
( ! [B] :
( ( k19_filter_2(A,B) = u1_struct_0(A)
& r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),k17_filter_2(A)) )
| ~ r2_hidden(k6_lattices(A),B)
| ~ v14_lattices(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)],[f46]) ).
fof(f161,plain,
! [X0,X1] :
( k19_filter_2(X0,X1) = u1_struct_0(X0)
| ~ r2_hidden(k6_lattices(X0),X1)
| ~ v14_lattices(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)],[f159]) ).
fof(f170,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f171,plain,
! [B] :
( ~ v1_xboole_0(B)
| ! [A] : ~ r2_hidden(A,B) ),
inference(miniscoping,[status(thm)],[f170]) ).
fof(f172,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f176,definition,
( sQ0_spl
<=> r1_filter_2(u1_struct_0(sK0_skl),sK1_skl,k17_filter_2(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f178,plain,
( sQ0_spl
| ~ r1_filter_2(u1_struct_0(sK0_skl),sK1_skl,k17_filter_2(sK0_skl)) ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f179,definition,
( sQ1_spl
<=> sK1_skl = u1_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( sQ1_spl
| sK1_skl != u1_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f60,f176,f179]) ).
fof(f185,plain,
! [X0,X1] :
( k19_filter_2(X0,X1) = u1_struct_0(X0)
| ~ r2_hidden(k6_lattices(X0),X1)
| ~ v14_lattices(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f161,f172]) ).
fof(f188,plain,
( k17_filter_2(sK0_skl) = u1_struct_0(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f77,f56]) ).
fof(f189,definition,
( sQ2_spl
<=> v3_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( ~ sQ2_spl
| v3_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,definition,
( sQ3_spl
<=> v10_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( sQ3_spl
| ~ v10_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,definition,
( sQ4_spl
<=> k17_filter_2(sK0_skl) = u1_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( ~ sQ4_spl
| k17_filter_2(sK0_skl) = u1_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f195]) ).
fof(f198,plain,
( sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f188,f189,f192,f195]) ).
fof(f199,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ r1_filter_2(u1_struct_0(sK0_skl),sK1_skl,u1_struct_0(sK0_skl)) ),
inference(backward_demodulation,[status(thm)],[f196,f178]) ).
fof(f200,plain,
( m2_filter_2(k17_filter_2(sK0_skl),sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f79,f56]) ).
fof(f201,definition,
( sQ5_spl
<=> m2_filter_2(k17_filter_2(sK0_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f202,plain,
( ~ sQ5_spl
| m2_filter_2(k17_filter_2(sK0_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f204,plain,
( sQ5_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f200,f189,f192,f201]) ).
fof(f205,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f194,f55]) ).
fof(f206,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f205]) ).
fof(f207,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f190,f54]) ).
fof(f208,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f207]) ).
fof(f210,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| m2_filter_2(u1_struct_0(sK0_skl),sK0_skl) ),
inference(forward_demodulation,[status(thm)],[f196,f202]) ).
fof(f244,plain,
( ~ v1_xboole_0(sK1_skl)
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f92,f57]) ).
fof(f245,definition,
( sQ13_spl
<=> l3_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f247,plain,
( sQ13_spl
| ~ l3_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f248,definition,
( sQ14_spl
<=> v1_xboole_0(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f251,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f244,f189,f192,f245,f248]) ).
fof(f252,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f247,f56]) ).
fof(f253,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f252]) ).
fof(f311,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ v1_xboole_0(u1_struct_0(sK0_skl))
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f210,f92]) ).
fof(f312,definition,
( sQ26_spl
<=> v1_xboole_0(u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f315,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ26_spl
| ~ sQ13_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f311,f189,f192,f245,f312,f195,f201]) ).
fof(f316,plain,
m1_subset_1(k6_lattices(sK0_skl),sK1_skl),
inference(resolution,[status(thm)],[f150,f59]) ).
fof(f321,plain,
( m2_lattice4(sK1_skl,sK0_skl)
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f93,f57]) ).
fof(f326,definition,
( sQ28_spl
<=> m2_lattice4(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f327,plain,
( ~ sQ28_spl
| m2_lattice4(sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f326]) ).
fof(f329,plain,
( sQ28_spl
| ~ sQ13_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f321,f189,f192,f245,f326]) ).
fof(f384,plain,
( r2_hidden(k6_lattices(sK0_skl),sK1_skl)
| v1_xboole_0(sK1_skl) ),
inference(resolution,[status(thm)],[f316,f152]) ).
fof(f385,definition,
( sQ36_spl
<=> r2_hidden(k6_lattices(sK0_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f388,plain,
( sQ36_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f384,f248,f385]) ).
fof(f389,plain,
( ~ sQ28_spl
| m1_subset_1(sK1_skl,k1_zfmisc_1(u1_struct_0(sK0_skl)))
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f327,f95]) ).
fof(f390,definition,
( sQ37_spl
<=> m1_subset_1(sK1_skl,k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f391,plain,
( ~ sQ37_spl
| m1_subset_1(sK1_skl,k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
inference(component_clause,[status(thm)],[f390]) ).
fof(f393,plain,
( ~ sQ28_spl
| sQ37_spl
| ~ sQ13_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f389,f189,f192,f245,f390,f326]) ).
fof(f467,plain,
( r1_filter_2(u1_struct_0(sK0_skl),k19_filter_2(sK0_skl,sK1_skl),sK1_skl)
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f154,f57]) ).
fof(f476,definition,
( sQ52_spl
<=> r1_filter_2(u1_struct_0(sK0_skl),k19_filter_2(sK0_skl,sK1_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f477,plain,
( ~ sQ52_spl
| r1_filter_2(u1_struct_0(sK0_skl),k19_filter_2(sK0_skl,sK1_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f476]) ).
fof(f479,plain,
( sQ52_spl
| ~ sQ13_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f467,f189,f192,f245,f476]) ).
fof(f505,plain,
! [X0] : m1_subset_1(X0,k1_zfmisc_1(X0)),
inference(resolution,[status(thm)],[f158,f146]) ).
fof(f572,plain,
( ~ sQ52_spl
| r1_filter_2(u1_struct_0(sK0_skl),sK1_skl,k19_filter_2(sK0_skl,sK1_skl))
| ~ m1_subset_1(sK1_skl,k1_zfmisc_1(u1_struct_0(sK0_skl)))
| ~ m1_subset_1(k19_filter_2(sK0_skl,sK1_skl),k1_zfmisc_1(u1_struct_0(sK0_skl)))
| v1_xboole_0(u1_struct_0(sK0_skl)) ),
inference(resolution,[status(thm)],[f477,f148]) ).
fof(f573,plain,
( ~ sQ52_spl
| k19_filter_2(sK0_skl,sK1_skl) = sK1_skl
| ~ m1_subset_1(sK1_skl,k1_zfmisc_1(u1_struct_0(sK0_skl)))
| ~ m1_subset_1(k19_filter_2(sK0_skl,sK1_skl),k1_zfmisc_1(u1_struct_0(sK0_skl)))
| v1_xboole_0(u1_struct_0(sK0_skl)) ),
inference(resolution,[status(thm)],[f477,f140]) ).
fof(f574,definition,
( sQ66_spl
<=> m1_subset_1(k19_filter_2(sK0_skl,sK1_skl),k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f576,plain,
( sQ66_spl
| ~ m1_subset_1(k19_filter_2(sK0_skl,sK1_skl),k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
inference(component_clause,[status(thm)],[f574]) ).
fof(f577,definition,
( sQ67_spl
<=> r1_filter_2(u1_struct_0(sK0_skl),sK1_skl,k19_filter_2(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f578,plain,
( ~ sQ67_spl
| r1_filter_2(u1_struct_0(sK0_skl),sK1_skl,k19_filter_2(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f577]) ).
fof(f580,plain,
( ~ sQ52_spl
| sQ67_spl
| ~ sQ37_spl
| ~ sQ66_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f572,f312,f574,f390,f577,f476]) ).
fof(f581,definition,
( sQ68_spl
<=> k19_filter_2(sK0_skl,sK1_skl) = sK1_skl ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f582,plain,
( ~ sQ68_spl
| k19_filter_2(sK0_skl,sK1_skl) = sK1_skl ),
inference(component_clause,[status(thm)],[f581]) ).
fof(f584,plain,
( ~ sQ52_spl
| sQ68_spl
| ~ sQ37_spl
| ~ sQ66_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f573,f312,f574,f390,f581,f476]) ).
fof(f588,plain,
( ~ sQ37_spl
| k19_filter_2(sK0_skl,sK1_skl) = u1_struct_0(sK0_skl)
| ~ r2_hidden(k6_lattices(sK0_skl),sK1_skl)
| ~ v14_lattices(sK0_skl)
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f391,f185]) ).
fof(f593,definition,
( sQ69_spl
<=> v14_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f595,plain,
( sQ69_spl
| ~ v14_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f593]) ).
fof(f600,definition,
( sQ71_spl
<=> k19_filter_2(sK0_skl,sK1_skl) = u1_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f601,plain,
( ~ sQ71_spl
| k19_filter_2(sK0_skl,sK1_skl) = u1_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f600]) ).
fof(f603,plain,
( ~ sQ37_spl
| sQ71_spl
| ~ sQ36_spl
| ~ sQ69_spl
| ~ sQ13_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f588,f189,f192,f245,f593,f385,f600,f390]) ).
fof(f612,definition,
( sQ74_spl
<=> v1_xboole_0(k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f613,plain,
( ~ sQ74_spl
| v1_xboole_0(k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
inference(component_clause,[status(thm)],[f612]) ).
fof(f619,plain,
( sQ69_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f595,f58]) ).
fof(f620,plain,
sQ69_spl,
inference(contradiction_clause,[status(thm)],[f619]) ).
fof(f621,plain,
( ~ sQ74_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f613,f114]) ).
fof(f622,plain,
~ sQ74_spl,
inference(contradiction_clause,[status(thm)],[f621]) ).
fof(f627,plain,
( sQ66_spl
| ~ sQ71_spl
| ~ m1_subset_1(u1_struct_0(sK0_skl),k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
inference(backward_demodulation,[status(thm)],[f601,f576]) ).
fof(f628,plain,
( sQ66_spl
| ~ sQ71_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f627,f505]) ).
fof(f629,plain,
( sQ66_spl
| ~ sQ71_spl ),
inference(contradiction_clause,[status(thm)],[f628]) ).
fof(f630,plain,
( ~ sQ67_spl
| ~ sQ71_spl
| r1_filter_2(u1_struct_0(sK0_skl),sK1_skl,u1_struct_0(sK0_skl)) ),
inference(forward_demodulation,[status(thm)],[f601,f578]) ).
fof(f631,plain,
( ~ sQ67_spl
| ~ sQ71_spl
| sQ0_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f630,f199]) ).
fof(f632,plain,
( ~ sQ67_spl
| ~ sQ71_spl
| sQ0_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f631]) ).
fof(f654,plain,
( ~ sQ68_spl
| ~ sQ71_spl
| u1_struct_0(sK0_skl) = sK1_skl ),
inference(forward_demodulation,[status(thm)],[f601,f582]) ).
fof(f658,plain,
( sQ1_spl
| ~ sQ68_spl
| ~ sQ71_spl
| sK1_skl != sK1_skl ),
inference(forward_demodulation,[status(thm)],[f654,f181]) ).
fof(f659,plain,
( sQ1_spl
| ~ sQ68_spl
| ~ sQ71_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f658]) ).
fof(f660,plain,
( sQ1_spl
| ~ sQ68_spl
| ~ sQ71_spl ),
inference(contradiction_clause,[status(thm)],[f659]) ).
fof(f661,plain,
$false,
inference(sat_refutation,[status(thm)],[f182,f198,f204,f206,f208,f251,f253,f315,f329,f388,f393,f479,f580,f584,f603,f620,f622,f629,f632,f660]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT313+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.42 % Computer : n002.cluster.edu
% 0.16/5.42 % Model : x86_64 x86_64
% 0.16/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.42 % Memory : 8046.5625MB
% 0.16/5.42 % OS : Linux 6.8.0-71-generic
% 0.16/5.42 % CPULimit : 300
% 0.16/5.42 % WCLimit : 300
% 0.16/5.42 % DateTime : Sun Sep 20 23:36:38 UTC 2026
% 0.16/5.43 % CPUTime :
% 0.16/5.44 % Drodi V4.1.1
% 0.16/5.49 % Refutation found
% 0.16/5.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/5.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/5.52 % Elapsed time: 0.077227 seconds
% 0.19/5.52 % CPU time: 0.310732 seconds
% 0.19/5.52 % Total memory used: 75.375 MB
% 0.19/5.52 % Net memory used: 75.223 MB
%------------------------------------------------------------------------------