%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LAT291+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 01:02:34 PM UTC 2026
% Result : Theorem 0.12s 0.49s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 28
% Syntax : Number of formulae : 117 ( 28 unt; 18 def)
% Number of atoms : 328 ( 30 equ)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 335 ( 124 ~; 109 |; 76 &)
% ( 18 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 47 ( 45 usr; 19 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-4 aty)
% Number of variables : 29 ( 25 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A] :
( ( l3_lattices(A)
& ~ v3_realset2(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A)),k9_lopclset(A),k6_lattices(A)) = k7_lopclset(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A] :
( ( l3_lattices(A)
& ~ v3_realset2(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A)),k9_lopclset(A),k6_lattices(A)) = k7_lopclset(A) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f40,axiom,
! [A] :
( ( l1_lattices(A)
& ~ v3_struct_0(A) )
=> m1_subset_1(k5_lattices(A),u1_struct_0(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [A] :
( l3_lattices(A)
=> ( l2_lattices(A)
& l1_lattices(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f76,axiom,
? [A] :
( v1_finset_1(A)
& ~ v1_xboole_0(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f78,axiom,
? [A] :
( ~ v3_realset2(A)
& v17_lattices(A)
& v16_lattices(A)
& v15_lattices(A)
& v14_lattices(A)
& v13_lattices(A)
& v12_lattices(A)
& v11_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)
& l3_lattices(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f79,axiom,
? [A] :
( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A)
& ~ v1_xboole_0(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f90,axiom,
! [A] :
( ( l3_lattices(A)
& ~ v3_realset2(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k4_xboole_0(k7_lopclset(A),k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A)),k9_lopclset(A),B)) = k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A)),k9_lopclset(A),k7_lattices(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f93,axiom,
! [A] :
( ( l3_lattices(A)
& ~ v3_realset2(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A)),k9_lopclset(A),k5_lattices(A)) = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f94,axiom,
! [A] :
( ( l3_lattices(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> k7_lattices(A,k5_lattices(A)) = k6_lattices(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,axiom,
! [A] : k4_xboole_0(A,k1_xboole_0) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f103,plain,
? [A] :
( k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A)),k9_lopclset(A),k6_lattices(A)) != k7_lopclset(A)
& l3_lattices(A)
& ~ v3_realset2(A)
& v17_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f104,plain,
( k8_funct_2(u1_struct_0(sK0_skl),k1_zfmisc_1(k7_lopclset(sK0_skl)),k9_lopclset(sK0_skl),k6_lattices(sK0_skl)) != k7_lopclset(sK0_skl)
& l3_lattices(sK0_skl)
& ~ v3_realset2(sK0_skl)
& v17_lattices(sK0_skl)
& v10_lattices(sK0_skl)
& ~ v3_struct_0(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(A,sK0_skl)],[f103]) ).
fof(f105,plain,
~ v3_struct_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f106,plain,
v10_lattices(sK0_skl),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f107,plain,
v17_lattices(sK0_skl),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f108,plain,
~ v3_realset2(sK0_skl),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f109,plain,
l3_lattices(sK0_skl),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f110,plain,
k8_funct_2(u1_struct_0(sK0_skl),k1_zfmisc_1(k7_lopclset(sK0_skl)),k9_lopclset(sK0_skl),k6_lattices(sK0_skl)) != k7_lopclset(sK0_skl),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f232,plain,
! [A] :
( m1_subset_1(k5_lattices(A),u1_struct_0(A))
| ~ l1_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f233,plain,
! [X0] :
( m1_subset_1(k5_lattices(X0),u1_struct_0(X0))
| ~ l1_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f232]) ).
fof(f253,plain,
! [A] :
( ( l2_lattices(A)
& l1_lattices(A) )
| ~ l3_lattices(A) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f254,plain,
! [X0] :
( l1_lattices(X0)
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f331,plain,
( v1_finset_1(sK10_skl)
& ~ v1_xboole_0(sK10_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(A,sK10_skl)],[f76]) ).
fof(f332,plain,
~ v1_xboole_0(sK10_skl),
inference(cnf_transformation,[status(thm)],[f331]) ).
fof(f339,plain,
( ~ v3_realset2(sK12_skl)
& v17_lattices(sK12_skl)
& v16_lattices(sK12_skl)
& v15_lattices(sK12_skl)
& v14_lattices(sK12_skl)
& v13_lattices(sK12_skl)
& v12_lattices(sK12_skl)
& v11_lattices(sK12_skl)
& v10_lattices(sK12_skl)
& v9_lattices(sK12_skl)
& v8_lattices(sK12_skl)
& v7_lattices(sK12_skl)
& v6_lattices(sK12_skl)
& v5_lattices(sK12_skl)
& v4_lattices(sK12_skl)
& ~ v3_struct_0(sK12_skl)
& l3_lattices(sK12_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl]),skolemize(A,sK12_skl)],[f78]) ).
fof(f340,plain,
l3_lattices(sK12_skl),
inference(cnf_transformation,[status(thm)],[f339]) ).
fof(f341,plain,
~ v3_struct_0(sK12_skl),
inference(cnf_transformation,[status(thm)],[f339]) ).
fof(f348,plain,
v10_lattices(sK12_skl),
inference(cnf_transformation,[status(thm)],[f339]) ).
fof(f355,plain,
v17_lattices(sK12_skl),
inference(cnf_transformation,[status(thm)],[f339]) ).
fof(f356,plain,
~ v3_realset2(sK12_skl),
inference(cnf_transformation,[status(thm)],[f339]) ).
fof(f357,plain,
( v5_membered(sK13_skl)
& v4_membered(sK13_skl)
& v3_membered(sK13_skl)
& v2_membered(sK13_skl)
& v1_membered(sK13_skl)
& ~ v1_xboole_0(sK13_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(A,sK13_skl)],[f79]) ).
fof(f358,plain,
~ v1_xboole_0(sK13_skl),
inference(cnf_transformation,[status(thm)],[f357]) ).
fof(f397,plain,
! [A] :
( ! [B] :
( k4_xboole_0(k7_lopclset(A),k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A)),k9_lopclset(A),B)) = k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A)),k9_lopclset(A),k7_lattices(A,B))
| ~ m1_subset_1(B,u1_struct_0(A)) )
| ~ l3_lattices(A)
| v3_realset2(A)
| ~ v17_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f90]) ).
fof(f398,plain,
! [X0,X1] :
( k4_xboole_0(k7_lopclset(X0),k8_funct_2(u1_struct_0(X0),k1_zfmisc_1(k7_lopclset(X0)),k9_lopclset(X0),X1)) = k8_funct_2(u1_struct_0(X0),k1_zfmisc_1(k7_lopclset(X0)),k9_lopclset(X0),k7_lattices(X0,X1))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l3_lattices(X0)
| v3_realset2(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f397]) ).
fof(f406,plain,
! [A] :
( k8_funct_2(u1_struct_0(A),k1_zfmisc_1(k7_lopclset(A)),k9_lopclset(A),k5_lattices(A)) = k1_xboole_0
| ~ l3_lattices(A)
| v3_realset2(A)
| ~ v17_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f93]) ).
fof(f407,plain,
! [X0] :
( k8_funct_2(u1_struct_0(X0),k1_zfmisc_1(k7_lopclset(X0)),k9_lopclset(X0),k5_lattices(X0)) = k1_xboole_0
| ~ l3_lattices(X0)
| v3_realset2(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f406]) ).
fof(f408,plain,
! [A] :
( k7_lattices(A,k5_lattices(A)) = k6_lattices(A)
| ~ l3_lattices(A)
| ~ v17_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f94]) ).
fof(f409,plain,
! [X0] :
( k7_lattices(X0,k5_lattices(X0)) = k6_lattices(X0)
| ~ l3_lattices(X0)
| ~ v17_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f408]) ).
fof(f410,plain,
! [X0] : k4_xboole_0(X0,k1_xboole_0) = X0,
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f432,definition,
( sQ0_spl
<=> v3_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f433,plain,
( ~ sQ0_spl
| v3_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f432]) ).
fof(f435,definition,
( sQ1_spl
<=> v10_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f437,plain,
( sQ1_spl
| ~ v10_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f435]) ).
fof(f438,definition,
( sQ2_spl
<=> v17_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f440,plain,
( sQ2_spl
| ~ v17_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,definition,
( sQ3_spl
<=> l3_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( sQ3_spl
| ~ l3_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f448,plain,
( k7_lattices(sK0_skl,k5_lattices(sK0_skl)) = k6_lattices(sK0_skl)
| ~ l3_lattices(sK0_skl)
| ~ v17_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl) ),
inference(resolution,[status(thm)],[f409,f105]) ).
fof(f449,definition,
( sQ5_spl
<=> k7_lattices(sK0_skl,k5_lattices(sK0_skl)) = k6_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f450,plain,
( ~ sQ5_spl
| k7_lattices(sK0_skl,k5_lattices(sK0_skl)) = k6_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,plain,
( sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f448,f435,f438,f441,f449]) ).
fof(f453,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f443,f109]) ).
fof(f454,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f453]) ).
fof(f455,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f440,f107]) ).
fof(f456,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f455]) ).
fof(f457,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f437,f106]) ).
fof(f458,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f457]) ).
fof(f459,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f433,f105]) ).
fof(f460,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f459]) ).
fof(f492,definition,
( sQ9_spl
<=> m1_subset_1(k5_lattices(sK0_skl),u1_struct_0(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f494,plain,
( sQ9_spl
| ~ m1_subset_1(k5_lattices(sK0_skl),u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f503,definition,
( sQ11_spl
<=> v3_struct_0(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f504,plain,
( ~ sQ11_spl
| v3_struct_0(sK12_skl) ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f506,definition,
( sQ12_spl
<=> v10_lattices(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f508,plain,
( sQ12_spl
| ~ v10_lattices(sK12_skl) ),
inference(component_clause,[status(thm)],[f506]) ).
fof(f509,definition,
( sQ13_spl
<=> v17_lattices(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f511,plain,
( sQ13_spl
| ~ v17_lattices(sK12_skl) ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f512,definition,
( sQ14_spl
<=> l3_lattices(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f514,plain,
( sQ14_spl
| ~ l3_lattices(sK12_skl) ),
inference(component_clause,[status(thm)],[f512]) ).
fof(f531,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f514,f340]) ).
fof(f532,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f531]) ).
fof(f533,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f511,f355]) ).
fof(f534,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f533]) ).
fof(f535,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f508,f348]) ).
fof(f536,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f535]) ).
fof(f537,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f504,f341]) ).
fof(f538,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f537]) ).
fof(f543,definition,
( sQ19_spl
<=> v3_realset2(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f544,plain,
( ~ sQ19_spl
| v3_realset2(sK0_skl) ),
inference(component_clause,[status(thm)],[f543]) ).
fof(f550,plain,
( ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f544,f108]) ).
fof(f551,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f550]) ).
fof(f583,plain,
( k8_funct_2(u1_struct_0(sK0_skl),k1_zfmisc_1(k7_lopclset(sK0_skl)),k9_lopclset(sK0_skl),k5_lattices(sK0_skl)) = k1_xboole_0
| ~ l3_lattices(sK0_skl)
| ~ v17_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f407,f108]) ).
fof(f588,definition,
( sQ28_spl
<=> k8_funct_2(u1_struct_0(sK0_skl),k1_zfmisc_1(k7_lopclset(sK0_skl)),k9_lopclset(sK0_skl),k5_lattices(sK0_skl)) = k1_xboole_0 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f589,plain,
( ~ sQ28_spl
| k8_funct_2(u1_struct_0(sK0_skl),k1_zfmisc_1(k7_lopclset(sK0_skl)),k9_lopclset(sK0_skl),k5_lattices(sK0_skl)) = k1_xboole_0 ),
inference(component_clause,[status(thm)],[f588]) ).
fof(f591,plain,
( sQ28_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f583,f432,f435,f438,f441,f588]) ).
fof(f593,plain,
! [X0] :
( k4_xboole_0(k7_lopclset(sK0_skl),k8_funct_2(u1_struct_0(sK0_skl),k1_zfmisc_1(k7_lopclset(sK0_skl)),k9_lopclset(sK0_skl),X0)) = k8_funct_2(u1_struct_0(sK0_skl),k1_zfmisc_1(k7_lopclset(sK0_skl)),k9_lopclset(sK0_skl),k7_lattices(sK0_skl,X0))
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl))
| ~ l3_lattices(sK0_skl)
| ~ v17_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f398,f108]) ).
fof(f598,definition,
! [X0] :
( sQ30_spl
<=> ( k4_xboole_0(k7_lopclset(sK0_skl),k8_funct_2(u1_struct_0(sK0_skl),k1_zfmisc_1(k7_lopclset(sK0_skl)),k9_lopclset(sK0_skl),X0)) = k8_funct_2(u1_struct_0(sK0_skl),k1_zfmisc_1(k7_lopclset(sK0_skl)),k9_lopclset(sK0_skl),k7_lattices(sK0_skl,X0))
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f599,plain,
! [X0] :
( ~ sQ30_spl
| k4_xboole_0(k7_lopclset(sK0_skl),k8_funct_2(u1_struct_0(sK0_skl),k1_zfmisc_1(k7_lopclset(sK0_skl)),k9_lopclset(sK0_skl),X0)) = k8_funct_2(u1_struct_0(sK0_skl),k1_zfmisc_1(k7_lopclset(sK0_skl)),k9_lopclset(sK0_skl),k7_lattices(sK0_skl,X0))
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl)) ),
inference(component_clause,[status(thm)],[f598]) ).
fof(f601,plain,
( sQ30_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f593,f432,f435,f438,f441,f598]) ).
fof(f626,plain,
( ~ sQ28_spl
| ~ sQ30_spl
| k4_xboole_0(k7_lopclset(sK0_skl),k1_xboole_0) = k8_funct_2(u1_struct_0(sK0_skl),k1_zfmisc_1(k7_lopclset(sK0_skl)),k9_lopclset(sK0_skl),k7_lattices(sK0_skl,k5_lattices(sK0_skl)))
| ~ m1_subset_1(k5_lattices(sK0_skl),u1_struct_0(sK0_skl)) ),
inference(paramodulation,[status(thm)],[f589,f599]) ).
fof(f627,definition,
( sQ37_spl
<=> k4_xboole_0(k7_lopclset(sK0_skl),k1_xboole_0) = k8_funct_2(u1_struct_0(sK0_skl),k1_zfmisc_1(k7_lopclset(sK0_skl)),k9_lopclset(sK0_skl),k7_lattices(sK0_skl,k5_lattices(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f628,plain,
( ~ sQ37_spl
| k4_xboole_0(k7_lopclset(sK0_skl),k1_xboole_0) = k8_funct_2(u1_struct_0(sK0_skl),k1_zfmisc_1(k7_lopclset(sK0_skl)),k9_lopclset(sK0_skl),k7_lattices(sK0_skl,k5_lattices(sK0_skl))) ),
inference(component_clause,[status(thm)],[f627]) ).
fof(f630,plain,
( ~ sQ28_spl
| ~ sQ30_spl
| sQ37_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f626,f492,f627,f598,f588]) ).
fof(f631,plain,
( sQ9_spl
| ~ l1_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f494,f233]) ).
fof(f632,definition,
( sQ38_spl
<=> l1_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f634,plain,
( sQ38_spl
| ~ l1_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f632]) ).
fof(f635,plain,
( sQ9_spl
| ~ sQ38_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f631,f432,f632,f492]) ).
fof(f709,definition,
( sQ53_spl
<=> v3_realset2(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f710,plain,
( ~ sQ53_spl
| v3_realset2(sK12_skl) ),
inference(component_clause,[status(thm)],[f709]) ).
fof(f720,plain,
( ~ sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f710,f356]) ).
fof(f721,plain,
~ sQ53_spl,
inference(contradiction_clause,[status(thm)],[f720]) ).
fof(f945,definition,
( sQ95_spl
<=> v1_xboole_0(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f946,plain,
( ~ sQ95_spl
| v1_xboole_0(sK13_skl) ),
inference(component_clause,[status(thm)],[f945]) ).
fof(f950,plain,
( ~ sQ95_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f946,f358]) ).
fof(f951,plain,
~ sQ95_spl,
inference(contradiction_clause,[status(thm)],[f950]) ).
fof(f956,definition,
( sQ97_spl
<=> v1_xboole_0(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f957,plain,
( ~ sQ97_spl
| v1_xboole_0(sK10_skl) ),
inference(component_clause,[status(thm)],[f956]) ).
fof(f961,plain,
( ~ sQ97_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f957,f332]) ).
fof(f962,plain,
~ sQ97_spl,
inference(contradiction_clause,[status(thm)],[f961]) ).
fof(f1018,plain,
( sQ38_spl
| ~ l3_lattices(sK0_skl) ),
inference(resolution,[status(thm)],[f254,f634]) ).
fof(f1020,plain,
( sQ38_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1018,f441,f632]) ).
fof(f1021,plain,
( ~ sQ37_spl
| k7_lopclset(sK0_skl) = k8_funct_2(u1_struct_0(sK0_skl),k1_zfmisc_1(k7_lopclset(sK0_skl)),k9_lopclset(sK0_skl),k7_lattices(sK0_skl,k5_lattices(sK0_skl))) ),
inference(forward_demodulation,[status(thm)],[f410,f628]) ).
fof(f1022,plain,
( ~ sQ37_spl
| ~ sQ5_spl
| k7_lopclset(sK0_skl) = k8_funct_2(u1_struct_0(sK0_skl),k1_zfmisc_1(k7_lopclset(sK0_skl)),k9_lopclset(sK0_skl),k6_lattices(sK0_skl)) ),
inference(forward_demodulation,[status(thm)],[f450,f1021]) ).
fof(f1023,plain,
( ~ sQ37_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1022,f110]) ).
fof(f1024,plain,
( ~ sQ37_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f1023]) ).
fof(f1025,plain,
$false,
inference(sat_refutation,[status(thm)],[f452,f454,f456,f458,f460,f532,f534,f536,f538,f551,f591,f601,f630,f635,f721,f951,f962,f1020,f1024]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT291+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.42 % Computer : n020.cluster.edu
% 0.09/0.42 % Model : x86_64 x86_64
% 0.09/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.42 % Memory : 8046.5625MB
% 0.09/0.42 % OS : Linux 6.8.0-71-generic
% 0.09/0.42 % CPULimit : 300
% 0.09/0.42 % WCLimit : 300
% 0.09/0.42 % DateTime : Sun Sep 20 23:28:33 UTC 2026
% 0.09/0.43 % CPUTime :
% 0.09/0.44 % Drodi V4.1.1
% 0.12/0.49 % Refutation found
% 0.12/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.52 % Elapsed time: 0.078575 seconds
% 0.12/0.52 % CPU time: 0.307162 seconds
% 0.12/0.52 % Total memory used: 113.819 MB
% 0.12/0.52 % Net memory used: 113.611 MB
%------------------------------------------------------------------------------