%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LAT346+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 : n014.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 01:02:51 PM UTC 2026
% Result : Theorem 0.12s 0.44s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 28
% Syntax : Number of formulae : 109 ( 7 unt; 17 def)
% Number of atoms : 395 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 439 ( 153 ~; 172 |; 81 &)
% ( 19 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 38 ( 37 usr; 18 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 51 ( 47 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A] :
( ( l2_conlat_1(A)
& ~ v3_conlat_1(A) )
=> r1_filter_1(k11_conlat_1(k7_conlat_2(A)),k1_lattice2(k11_conlat_1(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A] :
( ( l2_conlat_1(A)
& ~ v3_conlat_1(A) )
=> r1_filter_1(k11_conlat_1(k7_conlat_2(A)),k1_lattice2(k11_conlat_1(A))) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f14,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l3_lattices(B)
& v10_lattices(B)
& ~ v3_struct_0(B) )
=> ( r1_filter_1(A,B)
<=> ? [C] :
( v3_lattice4(C,A,B)
& m1_lattice4(C,A,B) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A] :
( ( l2_conlat_1(A)
& ~ v3_conlat_1(A) )
=> m1_lattice4(k10_conlat_2(A),k1_lattice2(k11_conlat_1(A)),k11_conlat_1(k7_conlat_2(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A] :
( ( l2_conlat_1(A)
& ~ v3_conlat_1(A) )
=> ( l3_lattices(k11_conlat_1(A))
& v3_lattices(k11_conlat_1(A))
& ~ v3_struct_0(k11_conlat_1(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
( l3_lattices(A)
=> ( l3_lattices(k1_lattice2(A))
& v3_lattices(k1_lattice2(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A] :
( ( l2_conlat_1(A)
& ~ v3_conlat_1(A) )
=> ( l2_conlat_1(k7_conlat_2(A))
& v4_conlat_1(k7_conlat_2(A))
& ~ v3_conlat_1(k7_conlat_2(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [A] :
( ( l2_conlat_1(A)
& ~ v3_conlat_1(A) )
=> ( v4_lattice3(k11_conlat_1(A))
& v15_lattices(k11_conlat_1(A))
& v14_lattices(k11_conlat_1(A))
& v13_lattices(k11_conlat_1(A))
& v10_lattices(k11_conlat_1(A))
& v9_lattices(k11_conlat_1(A))
& v8_lattices(k11_conlat_1(A))
& v7_lattices(k11_conlat_1(A))
& v6_lattices(k11_conlat_1(A))
& v5_lattices(k11_conlat_1(A))
& v4_lattices(k11_conlat_1(A))
& v3_lattices(k11_conlat_1(A))
& ~ v3_struct_0(k11_conlat_1(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [A] :
( ( l3_lattices(A)
& ~ v3_struct_0(A) )
=> ( v3_lattices(k1_lattice2(A))
& ~ v3_struct_0(k1_lattice2(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f69,axiom,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( v10_lattices(k1_lattice2(A))
& v9_lattices(k1_lattice2(A))
& v8_lattices(k1_lattice2(A))
& v7_lattices(k1_lattice2(A))
& v6_lattices(k1_lattice2(A))
& v5_lattices(k1_lattice2(A))
& v4_lattices(k1_lattice2(A))
& v3_lattices(k1_lattice2(A))
& ~ v3_struct_0(k1_lattice2(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f94,axiom,
! [A,B] :
( ( l3_lattices(B)
& v10_lattices(B)
& ~ v3_struct_0(B)
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ( r1_filter_1(A,B)
=> r1_filter_1(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,axiom,
! [A] :
( ( l2_conlat_1(A)
& ~ v3_conlat_1(A) )
=> v3_lattice4(k10_conlat_2(A),k1_lattice2(k11_conlat_1(A)),k11_conlat_1(k7_conlat_2(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f104,plain,
? [A] :
( ~ r1_filter_1(k11_conlat_1(k7_conlat_2(A)),k1_lattice2(k11_conlat_1(A)))
& l2_conlat_1(A)
& ~ v3_conlat_1(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f105,plain,
( ~ r1_filter_1(k11_conlat_1(k7_conlat_2(sK0_skl)),k1_lattice2(k11_conlat_1(sK0_skl)))
& l2_conlat_1(sK0_skl)
& ~ v3_conlat_1(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(A,sK0_skl)],[f104]) ).
fof(f106,plain,
~ v3_conlat_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f107,plain,
l2_conlat_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f108,plain,
~ r1_filter_1(k11_conlat_1(k7_conlat_2(sK0_skl)),k1_lattice2(k11_conlat_1(sK0_skl))),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f149,plain,
! [A] :
( ! [B] :
( ( r1_filter_1(A,B)
<=> ? [C] :
( v3_lattice4(C,A,B)
& m1_lattice4(C,A,B) ) )
| ~ l3_lattices(B)
| ~ v10_lattices(B)
| v3_struct_0(B) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f150,plain,
! [A] :
( ! [B] :
( ( ( ! [C] :
( ~ v3_lattice4(C,A,B)
| ~ m1_lattice4(C,A,B) )
| r1_filter_1(A,B) )
& ( ? [C] :
( v3_lattice4(C,A,B)
& m1_lattice4(C,A,B) )
| ~ r1_filter_1(A,B) ) )
| ~ l3_lattices(B)
| ~ v10_lattices(B)
| v3_struct_0(B) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(NNF_transformation,[status(thm)],[f149]) ).
fof(f151,plain,
! [A] :
( ! [B] :
( ( ( ! [C] :
( ~ v3_lattice4(C,A,B)
| ~ m1_lattice4(C,A,B) )
| r1_filter_1(A,B) )
& ( ( v3_lattice4(sK1_skl(B,A),A,B)
& m1_lattice4(sK1_skl(B,A),A,B) )
| ~ r1_filter_1(A,B) ) )
| ~ l3_lattices(B)
| ~ v10_lattices(B)
| v3_struct_0(B) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(C,sK1_skl(B,A))],[f150]) ).
fof(f154,plain,
! [X0,X1,X2] :
( ~ v3_lattice4(X2,X0,X1)
| ~ m1_lattice4(X2,X0,X1)
| r1_filter_1(X0,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f163,plain,
! [A] :
( m1_lattice4(k10_conlat_2(A),k1_lattice2(k11_conlat_1(A)),k11_conlat_1(k7_conlat_2(A)))
| ~ l2_conlat_1(A)
| v3_conlat_1(A) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f164,plain,
! [X0] :
( m1_lattice4(k10_conlat_2(X0),k1_lattice2(k11_conlat_1(X0)),k11_conlat_1(k7_conlat_2(X0)))
| ~ l2_conlat_1(X0)
| v3_conlat_1(X0) ),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f165,plain,
! [A] :
( ( l3_lattices(k11_conlat_1(A))
& v3_lattices(k11_conlat_1(A))
& ~ v3_struct_0(k11_conlat_1(A)) )
| ~ l2_conlat_1(A)
| v3_conlat_1(A) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f166,plain,
! [X0] :
( ~ v3_struct_0(k11_conlat_1(X0))
| ~ l2_conlat_1(X0)
| v3_conlat_1(X0) ),
inference(cnf_transformation,[status(thm)],[f165]) ).
fof(f168,plain,
! [X0] :
( l3_lattices(k11_conlat_1(X0))
| ~ l2_conlat_1(X0)
| v3_conlat_1(X0) ),
inference(cnf_transformation,[status(thm)],[f165]) ).
fof(f169,plain,
! [A] :
( ( l3_lattices(k1_lattice2(A))
& v3_lattices(k1_lattice2(A)) )
| ~ l3_lattices(A) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f171,plain,
! [X0] :
( l3_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0) ),
inference(cnf_transformation,[status(thm)],[f169]) ).
fof(f176,plain,
! [A] :
( ( l2_conlat_1(k7_conlat_2(A))
& v4_conlat_1(k7_conlat_2(A))
& ~ v3_conlat_1(k7_conlat_2(A)) )
| ~ l2_conlat_1(A)
| v3_conlat_1(A) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f177,plain,
! [X0] :
( ~ v3_conlat_1(k7_conlat_2(X0))
| ~ l2_conlat_1(X0)
| v3_conlat_1(X0) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f179,plain,
! [X0] :
( l2_conlat_1(k7_conlat_2(X0))
| ~ l2_conlat_1(X0)
| v3_conlat_1(X0) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f228,plain,
! [A] :
( ( v4_lattice3(k11_conlat_1(A))
& v15_lattices(k11_conlat_1(A))
& v14_lattices(k11_conlat_1(A))
& v13_lattices(k11_conlat_1(A))
& v10_lattices(k11_conlat_1(A))
& v9_lattices(k11_conlat_1(A))
& v8_lattices(k11_conlat_1(A))
& v7_lattices(k11_conlat_1(A))
& v6_lattices(k11_conlat_1(A))
& v5_lattices(k11_conlat_1(A))
& v4_lattices(k11_conlat_1(A))
& v3_lattices(k11_conlat_1(A))
& ~ v3_struct_0(k11_conlat_1(A)) )
| ~ l2_conlat_1(A)
| v3_conlat_1(A) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f237,plain,
! [X0] :
( v10_lattices(k11_conlat_1(X0))
| ~ l2_conlat_1(X0)
| v3_conlat_1(X0) ),
inference(cnf_transformation,[status(thm)],[f228]) ).
fof(f242,plain,
! [A] :
( ( v3_lattices(k1_lattice2(A))
& ~ v3_struct_0(k1_lattice2(A)) )
| ~ l3_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f55]) ).
fof(f243,plain,
! [X0] :
( ~ v3_struct_0(k1_lattice2(X0))
| ~ l3_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f242]) ).
fof(f312,plain,
! [A] :
( ( v10_lattices(k1_lattice2(A))
& v9_lattices(k1_lattice2(A))
& v8_lattices(k1_lattice2(A))
& v7_lattices(k1_lattice2(A))
& v6_lattices(k1_lattice2(A))
& v5_lattices(k1_lattice2(A))
& v4_lattices(k1_lattice2(A))
& v3_lattices(k1_lattice2(A))
& ~ v3_struct_0(k1_lattice2(A)) )
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f69]) ).
fof(f321,plain,
! [X0] :
( v10_lattices(k1_lattice2(X0))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f312]) ).
fof(f419,plain,
! [A,B] :
( r1_filter_1(B,A)
| ~ r1_filter_1(A,B)
| ~ l3_lattices(B)
| ~ v10_lattices(B)
| v3_struct_0(B)
| ~ l3_lattices(A)
| ~ v10_lattices(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f94]) ).
fof(f420,plain,
! [X0,X1] :
( r1_filter_1(X1,X0)
| ~ r1_filter_1(X0,X1)
| ~ l3_lattices(X1)
| ~ v10_lattices(X1)
| v3_struct_0(X1)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f423,plain,
! [A] :
( v3_lattice4(k10_conlat_2(A),k1_lattice2(k11_conlat_1(A)),k11_conlat_1(k7_conlat_2(A)))
| ~ l2_conlat_1(A)
| v3_conlat_1(A) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f424,plain,
! [X0] :
( v3_lattice4(k10_conlat_2(X0),k1_lattice2(k11_conlat_1(X0)),k11_conlat_1(k7_conlat_2(X0)))
| ~ l2_conlat_1(X0)
| v3_conlat_1(X0) ),
inference(cnf_transformation,[status(thm)],[f423]) ).
fof(f452,plain,
( l3_lattices(k11_conlat_1(sK0_skl))
| v3_conlat_1(sK0_skl) ),
inference(resolution,[status(thm)],[f168,f107]) ).
fof(f453,definition,
( sQ2_spl
<=> v3_conlat_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( ~ sQ2_spl
| v3_conlat_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,definition,
( sQ3_spl
<=> l3_lattices(k11_conlat_1(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( ~ sQ3_spl
| l3_lattices(k11_conlat_1(sK0_skl)) ),
inference(component_clause,[status(thm)],[f456]) ).
fof(f459,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f452,f453,f456]) ).
fof(f460,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f454,f106]) ).
fof(f461,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f460]) ).
fof(f462,plain,
( l2_conlat_1(k7_conlat_2(sK0_skl))
| v3_conlat_1(sK0_skl) ),
inference(resolution,[status(thm)],[f179,f107]) ).
fof(f463,definition,
( sQ4_spl
<=> l2_conlat_1(k7_conlat_2(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f464,plain,
( ~ sQ4_spl
| l2_conlat_1(k7_conlat_2(sK0_skl)) ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f466,plain,
( sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f462,f453,f463]) ).
fof(f467,plain,
( v10_lattices(k11_conlat_1(sK0_skl))
| v3_conlat_1(sK0_skl) ),
inference(resolution,[status(thm)],[f237,f107]) ).
fof(f468,definition,
( sQ5_spl
<=> v10_lattices(k11_conlat_1(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f469,plain,
( ~ sQ5_spl
| v10_lattices(k11_conlat_1(sK0_skl)) ),
inference(component_clause,[status(thm)],[f468]) ).
fof(f471,plain,
( sQ5_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f467,f453,f468]) ).
fof(f472,plain,
( ~ sQ3_spl
| l3_lattices(k1_lattice2(k11_conlat_1(sK0_skl))) ),
inference(resolution,[status(thm)],[f457,f171]) ).
fof(f473,plain,
( ~ sQ4_spl
| v10_lattices(k11_conlat_1(k7_conlat_2(sK0_skl)))
| v3_conlat_1(k7_conlat_2(sK0_skl)) ),
inference(resolution,[status(thm)],[f464,f237]) ).
fof(f475,plain,
( ~ sQ4_spl
| l3_lattices(k11_conlat_1(k7_conlat_2(sK0_skl)))
| v3_conlat_1(k7_conlat_2(sK0_skl)) ),
inference(resolution,[status(thm)],[f464,f168]) ).
fof(f476,definition,
( sQ6_spl
<=> v3_conlat_1(k7_conlat_2(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f477,plain,
( ~ sQ6_spl
| v3_conlat_1(k7_conlat_2(sK0_skl)) ),
inference(component_clause,[status(thm)],[f476]) ).
fof(f479,definition,
( sQ7_spl
<=> v10_lattices(k11_conlat_1(k7_conlat_2(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f482,plain,
( ~ sQ4_spl
| sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f473,f476,f479,f463]) ).
fof(f487,definition,
( sQ9_spl
<=> l3_lattices(k11_conlat_1(k7_conlat_2(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f490,plain,
( ~ sQ4_spl
| sQ9_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f475,f476,f487,f463]) ).
fof(f493,definition,
( sQ10_spl
<=> v3_struct_0(k11_conlat_1(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f494,plain,
( ~ sQ10_spl
| v3_struct_0(k11_conlat_1(sK0_skl)) ),
inference(component_clause,[status(thm)],[f493]) ).
fof(f504,plain,
( ~ sQ6_spl
| ~ l2_conlat_1(sK0_skl)
| v3_conlat_1(sK0_skl) ),
inference(resolution,[status(thm)],[f477,f177]) ).
fof(f505,definition,
( sQ13_spl
<=> l2_conlat_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f507,plain,
( sQ13_spl
| ~ l2_conlat_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f505]) ).
fof(f508,plain,
( ~ sQ6_spl
| ~ sQ13_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f504,f453,f505,f476]) ).
fof(f509,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f507,f107]) ).
fof(f510,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f509]) ).
fof(f511,plain,
( ~ sQ10_spl
| ~ l2_conlat_1(sK0_skl)
| v3_conlat_1(sK0_skl) ),
inference(resolution,[status(thm)],[f494,f166]) ).
fof(f512,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f511,f453,f505,f493]) ).
fof(f513,plain,
( ~ sQ5_spl
| v10_lattices(k1_lattice2(k11_conlat_1(sK0_skl)))
| ~ l3_lattices(k11_conlat_1(sK0_skl))
| v3_struct_0(k11_conlat_1(sK0_skl)) ),
inference(resolution,[status(thm)],[f321,f469]) ).
fof(f514,definition,
( sQ14_spl
<=> v10_lattices(k1_lattice2(k11_conlat_1(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f517,plain,
( ~ sQ5_spl
| sQ14_spl
| ~ sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f513,f493,f456,f514,f468]) ).
fof(f546,definition,
( sQ20_spl
<=> v3_struct_0(k11_conlat_1(k7_conlat_2(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f547,plain,
( ~ sQ20_spl
| v3_struct_0(k11_conlat_1(k7_conlat_2(sK0_skl))) ),
inference(component_clause,[status(thm)],[f546]) ).
fof(f583,plain,
( m1_lattice4(k10_conlat_2(sK0_skl),k1_lattice2(k11_conlat_1(sK0_skl)),k11_conlat_1(k7_conlat_2(sK0_skl)))
| v3_conlat_1(sK0_skl) ),
inference(resolution,[status(thm)],[f164,f107]) ).
fof(f592,definition,
( sQ28_spl
<=> m1_lattice4(k10_conlat_2(sK0_skl),k1_lattice2(k11_conlat_1(sK0_skl)),k11_conlat_1(k7_conlat_2(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f595,plain,
( sQ28_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f583,f453,f592]) ).
fof(f629,definition,
( sQ35_spl
<=> v3_struct_0(k1_lattice2(k11_conlat_1(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f630,plain,
( ~ sQ35_spl
| v3_struct_0(k1_lattice2(k11_conlat_1(sK0_skl))) ),
inference(component_clause,[status(thm)],[f629]) ).
fof(f632,definition,
( sQ36_spl
<=> l3_lattices(k1_lattice2(k11_conlat_1(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f634,plain,
( sQ36_spl
| ~ l3_lattices(k1_lattice2(k11_conlat_1(sK0_skl))) ),
inference(component_clause,[status(thm)],[f632]) ).
fof(f643,plain,
( sQ36_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f634,f472]) ).
fof(f644,plain,
( sQ36_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f643]) ).
fof(f715,plain,
( ~ sQ20_spl
| ~ l2_conlat_1(k7_conlat_2(sK0_skl))
| v3_conlat_1(k7_conlat_2(sK0_skl)) ),
inference(resolution,[status(thm)],[f547,f166]) ).
fof(f716,plain,
( ~ sQ20_spl
| ~ sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f715,f476,f463,f546]) ).
fof(f1642,plain,
( ~ sQ35_spl
| ~ l3_lattices(k11_conlat_1(sK0_skl))
| v3_struct_0(k11_conlat_1(sK0_skl)) ),
inference(resolution,[status(thm)],[f630,f243]) ).
fof(f1643,plain,
( ~ sQ35_spl
| ~ sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f1642,f493,f456,f629]) ).
fof(f2560,plain,
( v3_lattice4(k10_conlat_2(sK0_skl),k1_lattice2(k11_conlat_1(sK0_skl)),k11_conlat_1(k7_conlat_2(sK0_skl)))
| v3_conlat_1(sK0_skl) ),
inference(resolution,[status(thm)],[f424,f107]) ).
fof(f2585,definition,
( sQ366_spl
<=> v3_lattice4(k10_conlat_2(sK0_skl),k1_lattice2(k11_conlat_1(sK0_skl)),k11_conlat_1(k7_conlat_2(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ366_spl])],[split_symbol_definition]) ).
fof(f2586,plain,
( ~ sQ366_spl
| v3_lattice4(k10_conlat_2(sK0_skl),k1_lattice2(k11_conlat_1(sK0_skl)),k11_conlat_1(k7_conlat_2(sK0_skl))) ),
inference(component_clause,[status(thm)],[f2585]) ).
fof(f2588,plain,
( sQ366_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f2560,f453,f2585]) ).
fof(f3317,plain,
( ~ sQ366_spl
| ~ m1_lattice4(k10_conlat_2(sK0_skl),k1_lattice2(k11_conlat_1(sK0_skl)),k11_conlat_1(k7_conlat_2(sK0_skl)))
| r1_filter_1(k1_lattice2(k11_conlat_1(sK0_skl)),k11_conlat_1(k7_conlat_2(sK0_skl)))
| ~ l3_lattices(k11_conlat_1(k7_conlat_2(sK0_skl)))
| ~ v10_lattices(k11_conlat_1(k7_conlat_2(sK0_skl)))
| v3_struct_0(k11_conlat_1(k7_conlat_2(sK0_skl)))
| ~ l3_lattices(k1_lattice2(k11_conlat_1(sK0_skl)))
| ~ v10_lattices(k1_lattice2(k11_conlat_1(sK0_skl)))
| v3_struct_0(k1_lattice2(k11_conlat_1(sK0_skl))) ),
inference(resolution,[status(thm)],[f154,f2586]) ).
fof(f3322,definition,
( sQ490_spl
<=> r1_filter_1(k1_lattice2(k11_conlat_1(sK0_skl)),k11_conlat_1(k7_conlat_2(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ490_spl])],[split_symbol_definition]) ).
fof(f3323,plain,
( ~ sQ490_spl
| r1_filter_1(k1_lattice2(k11_conlat_1(sK0_skl)),k11_conlat_1(k7_conlat_2(sK0_skl))) ),
inference(component_clause,[status(thm)],[f3322]) ).
fof(f3325,plain,
( ~ sQ366_spl
| ~ sQ28_spl
| sQ490_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sQ20_spl
| ~ sQ36_spl
| ~ sQ14_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f3317,f629,f514,f632,f546,f479,f487,f3322,f592,f2585]) ).
fof(f3755,plain,
( ~ sQ490_spl
| r1_filter_1(k11_conlat_1(k7_conlat_2(sK0_skl)),k1_lattice2(k11_conlat_1(sK0_skl)))
| ~ l3_lattices(k11_conlat_1(k7_conlat_2(sK0_skl)))
| ~ v10_lattices(k11_conlat_1(k7_conlat_2(sK0_skl)))
| v3_struct_0(k11_conlat_1(k7_conlat_2(sK0_skl)))
| ~ l3_lattices(k1_lattice2(k11_conlat_1(sK0_skl)))
| ~ v10_lattices(k1_lattice2(k11_conlat_1(sK0_skl)))
| v3_struct_0(k1_lattice2(k11_conlat_1(sK0_skl))) ),
inference(resolution,[status(thm)],[f3323,f420]) ).
fof(f3764,definition,
( sQ556_spl
<=> r1_filter_1(k11_conlat_1(k7_conlat_2(sK0_skl)),k1_lattice2(k11_conlat_1(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ556_spl])],[split_symbol_definition]) ).
fof(f3765,plain,
( ~ sQ556_spl
| r1_filter_1(k11_conlat_1(k7_conlat_2(sK0_skl)),k1_lattice2(k11_conlat_1(sK0_skl))) ),
inference(component_clause,[status(thm)],[f3764]) ).
fof(f3767,plain,
( ~ sQ490_spl
| sQ556_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sQ20_spl
| ~ sQ36_spl
| ~ sQ14_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f3755,f629,f514,f632,f546,f479,f487,f3764,f3322]) ).
fof(f3768,plain,
( ~ sQ556_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3765,f108]) ).
fof(f3769,plain,
~ sQ556_spl,
inference(contradiction_clause,[status(thm)],[f3768]) ).
fof(f3770,plain,
$false,
inference(sat_refutation,[status(thm)],[f459,f461,f466,f471,f482,f490,f508,f510,f512,f517,f595,f644,f716,f1643,f2588,f3325,f3767,f3769]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT346+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 23:44:34 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.44 % Refutation found
% 0.12/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.47 % Elapsed time: 0.111090 seconds
% 0.12/0.47 % CPU time: 0.546670 seconds
% 0.12/0.47 % Total memory used: 105.249 MB
% 0.12/0.47 % Net memory used: 104.882 MB
%------------------------------------------------------------------------------