%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LAT300+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 : n003.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 01:02:37 PM UTC 2026
% Result : Theorem 0.15s 0.46s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 75 ( 19 unt; 7 def)
% Number of atoms : 200 ( 6 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 215 ( 90 ~; 86 |; 21 &)
% ( 7 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 8 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-1 aty)
% Number of variables : 63 ( 57 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A] :
( ( l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_filter_2(B,A)
=> ? [C] :
( r2_hidden(C,B)
& m1_subset_1(C,u1_struct_0(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)
=> ? [C] :
( r2_hidden(C,B)
& m1_subset_1(C,u1_struct_0(A)) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f15,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(f16,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(f23,axiom,
! [A] :
? [B] : m1_subset_1(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
? [A] : v1_xboole_0(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( r2_hidden(A,B)
| v1_xboole_0(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) )
=> m1_subset_1(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,plain,
? [A] :
( ? [B] :
( ! [C] :
( ~ r2_hidden(C,B)
| ~ m1_subset_1(C,u1_struct_0(A)) )
& m2_filter_2(B,A) )
& l3_lattices(A)
& v10_lattices(A)
& ~ v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f47,plain,
( ! [C] :
( ~ r2_hidden(C,sK1_skl)
| ~ m1_subset_1(C,u1_struct_0(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)],[f46]) ).
fof(f48,plain,
~ v3_struct_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
v10_lattices(sK0_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
l3_lattices(sK0_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,plain,
m2_filter_2(sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f52,plain,
! [X0] :
( ~ r2_hidden(X0,sK1_skl)
| ~ m1_subset_1(X0,u1_struct_0(sK0_skl)) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f77,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)],[f15]) ).
fof(f78,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)],[f77]) ).
fof(f79,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)],[f77]) ).
fof(f80,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)],[f16]) ).
fof(f81,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)],[f80]) ).
fof(f93,plain,
! [A] : m1_subset_1(sK7_skl(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(B,sK7_skl(A))],[f23]) ).
fof(f94,plain,
! [X0] : m1_subset_1(sK7_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f103,plain,
! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f113,plain,
v1_xboole_0(sK12_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl]),skolemize(A,sK12_skl)],[f31]) ).
fof(f114,plain,
v1_xboole_0(sK12_skl),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f136,plain,
! [A,B] :
( r2_hidden(A,B)
| v1_xboole_0(B)
| ~ m1_subset_1(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f137,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f142,plain,
! [A,B,C] :
( m1_subset_1(A,C)
| ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f143,plain,
! [A,C] :
( m1_subset_1(A,C)
| ! [B] :
( ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ) ),
inference(miniscoping,[status(thm)],[f142]) ).
fof(f144,plain,
! [X0,X1,X2] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f148,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f149,plain,
! [X0] :
( X0 = k1_xboole_0
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f158,plain,
! [X0] :
( ~ m2_filter_2(sK12_skl,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f114,f78]) ).
fof(f164,plain,
! [X0] :
( r2_hidden(sK7_skl(X0),X0)
| v1_xboole_0(X0) ),
inference(resolution,[status(thm)],[f94,f137]) ).
fof(f166,plain,
sK12_skl = k1_xboole_0,
inference(resolution,[status(thm)],[f149,f114]) ).
fof(f168,plain,
! [X0] :
( X0 = sK12_skl
| ~ v1_xboole_0(X0) ),
inference(backward_demodulation,[status(thm)],[f166,f149]) ).
fof(f181,definition,
( sQ0_spl
<=> v1_xboole_0(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f182,plain,
( ~ sQ0_spl
| v1_xboole_0(sK1_skl) ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f188,plain,
( ~ sQ0_spl
| sK1_skl = sK12_skl ),
inference(resolution,[status(thm)],[f182,f168]) ).
fof(f194,plain,
! [X0] :
( ~ sQ0_spl
| ~ m2_filter_2(sK1_skl,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(backward_demodulation,[status(thm)],[f188,f158]) ).
fof(f201,plain,
( ~ sQ0_spl
| ~ l3_lattices(sK0_skl)
| ~ v10_lattices(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f194,f51]) ).
fof(f202,definition,
( sQ2_spl
<=> v3_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f203,plain,
( ~ sQ2_spl
| v3_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,definition,
( sQ3_spl
<=> v10_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( sQ3_spl
| ~ v10_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,definition,
( sQ4_spl
<=> l3_lattices(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f210,plain,
( sQ4_spl
| ~ l3_lattices(sK0_skl) ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f201,f202,f205,f208,f181]) ).
fof(f212,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f210,f50]) ).
fof(f213,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f212]) ).
fof(f214,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f207,f49]) ).
fof(f215,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f214]) ).
fof(f216,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f203,f48]) ).
fof(f217,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f216]) ).
fof(f235,plain,
! [X0,X1] :
( ~ m2_filter_2(X1,X0)
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0)
| m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f81,f79]) ).
fof(f236,plain,
! [X0,X1] :
( ~ m2_filter_2(X1,X0)
| m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l3_lattices(X0)
| ~ v10_lattices(X0)
| v3_struct_0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f235]) ).
fof(f252,definition,
( sQ7_spl
<=> v1_xboole_0(k1_zfmisc_1(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f253,plain,
( ~ sQ7_spl
| v1_xboole_0(k1_zfmisc_1(sK12_skl)) ),
inference(component_clause,[status(thm)],[f252]) ).
fof(f263,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f253,f103]) ).
fof(f264,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f263]) ).
fof(f278,plain,
( 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)],[f236,f51]) ).
fof(f279,definition,
( sQ12_spl
<=> m1_subset_1(sK1_skl,k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( ~ sQ12_spl
| m1_subset_1(sK1_skl,k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f282,plain,
( sQ12_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f278,f202,f205,f208,f279]) ).
fof(f283,plain,
! [X0] :
( ~ sQ12_spl
| m1_subset_1(X0,u1_struct_0(sK0_skl))
| ~ r2_hidden(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f280,f144]) ).
fof(f286,plain,
! [X0] :
( ~ sQ12_spl
| ~ r2_hidden(X0,sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f283,f52]) ).
fof(f294,definition,
( sQ15_spl
<=> v1_xboole_0(k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f295,plain,
( ~ sQ15_spl
| v1_xboole_0(k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
inference(component_clause,[status(thm)],[f294]) ).
fof(f301,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f295,f103]) ).
fof(f302,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f301]) ).
fof(f303,plain,
( ~ sQ12_spl
| v1_xboole_0(sK1_skl) ),
inference(resolution,[status(thm)],[f286,f164]) ).
fof(f304,plain,
( ~ sQ12_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f303,f181,f279]) ).
fof(f305,plain,
$false,
inference(sat_refutation,[status(thm)],[f211,f213,f215,f217,f264,f282,f302,f304]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT300+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n003.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sun Sep 20 23:32:01 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.44 % Drodi V4.1.1
% 0.15/0.46 % Refutation found
% 0.15/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.49 % Elapsed time: 0.053079 seconds
% 0.15/0.49 % CPU time: 0.140700 seconds
% 0.15/0.49 % Total memory used: 31.219 MB
% 0.15/0.49 % Net memory used: 31.190 MB
%------------------------------------------------------------------------------