%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP641+3 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:34:55 PM UTC 2026
% Result : Theorem 12.56s 3.60s
% Output : CNFRefutation 14.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 14 unt; 8 def)
% Number of atoms : 177 ( 0 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 194 ( 71 ~; 74 |; 29 &)
% ( 10 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 17 usr; 9 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 25 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7470,axiom,
! [A] :
( ( l1_group_1(A)
& ~ v3_struct_0(A) )
=> m1_subset_1(k2_group_1(A),u1_struct_0(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8757,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> r1_rlvect_1(B,k2_group_1(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13982,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m1_group_2(B,A)
& v1_group_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k1_funct_1(k1_latsubgr(A),B))
<=> r1_rlvect_1(B,C) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13983,conjecture,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m1_group_2(B,A)
& v1_group_1(B) )
=> r2_hidden(k2_group_1(A),k1_funct_1(k1_latsubgr(A),B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13984,negated_conjecture,
~ ! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m1_group_2(B,A)
& v1_group_1(B) )
=> r2_hidden(k2_group_1(A),k1_funct_1(k1_latsubgr(A),B)) ) ),
inference(negated_conjecture,[status(cth)],[f13983]) ).
fof(f36616,plain,
! [A] :
( m1_subset_1(k2_group_1(A),u1_struct_0(A))
| ~ l1_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f7470]) ).
fof(f36617,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f36616]) ).
fof(f40343,plain,
! [A] :
( ! [B] :
( r1_rlvect_1(B,k2_group_1(A))
| ~ m1_group_2(B,A) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f8757]) ).
fof(f40344,plain,
! [X0,X1] :
( r1_rlvect_1(X1,k2_group_1(X0))
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f40343]) ).
fof(f59572,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( r2_hidden(C,k1_funct_1(k1_latsubgr(A),B))
<=> r1_rlvect_1(B,C) )
| ~ m1_subset_1(C,u1_struct_0(A)) )
| ~ m1_group_2(B,A)
| ~ v1_group_1(B) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f13982]) ).
fof(f59573,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ~ r1_rlvect_1(B,C)
| r2_hidden(C,k1_funct_1(k1_latsubgr(A),B)) )
& ( r1_rlvect_1(B,C)
| ~ r2_hidden(C,k1_funct_1(k1_latsubgr(A),B)) ) )
| ~ m1_subset_1(C,u1_struct_0(A)) )
| ~ m1_group_2(B,A)
| ~ v1_group_1(B) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(NNF_transformation,[status(thm)],[f59572]) ).
fof(f59575,plain,
! [X0,X1,X2] :
( ~ r1_rlvect_1(X1,X2)
| r2_hidden(X2,k1_funct_1(k1_latsubgr(X0),X1))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_group_2(X1,X0)
| ~ v1_group_1(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f59573]) ).
fof(f59576,plain,
? [A] :
( ? [B] :
( ~ r2_hidden(k2_group_1(A),k1_funct_1(k1_latsubgr(A),B))
& m1_group_2(B,A)
& v1_group_1(B) )
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f13984]) ).
fof(f59577,plain,
( ~ r2_hidden(k2_group_1(sK4179_skl),k1_funct_1(k1_latsubgr(sK4179_skl),sK4180_skl))
& m1_group_2(sK4180_skl,sK4179_skl)
& v1_group_1(sK4180_skl)
& l1_group_1(sK4179_skl)
& v4_group_1(sK4179_skl)
& v3_group_1(sK4179_skl)
& ~ v3_struct_0(sK4179_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4179_skl,sK4180_skl]),skolemize(A,sK4179_skl),skolemize(B,sK4180_skl)],[f59576]) ).
fof(f59578,plain,
~ v3_struct_0(sK4179_skl),
inference(cnf_transformation,[status(thm)],[f59577]) ).
fof(f59579,plain,
v3_group_1(sK4179_skl),
inference(cnf_transformation,[status(thm)],[f59577]) ).
fof(f59580,plain,
v4_group_1(sK4179_skl),
inference(cnf_transformation,[status(thm)],[f59577]) ).
fof(f59581,plain,
l1_group_1(sK4179_skl),
inference(cnf_transformation,[status(thm)],[f59577]) ).
fof(f59582,plain,
v1_group_1(sK4180_skl),
inference(cnf_transformation,[status(thm)],[f59577]) ).
fof(f59583,plain,
m1_group_2(sK4180_skl,sK4179_skl),
inference(cnf_transformation,[status(thm)],[f59577]) ).
fof(f59584,plain,
~ r2_hidden(k2_group_1(sK4179_skl),k1_funct_1(k1_latsubgr(sK4179_skl),sK4180_skl)),
inference(cnf_transformation,[status(thm)],[f59577]) ).
fof(f70832,plain,
( m1_subset_1(k2_group_1(sK4179_skl),u1_struct_0(sK4179_skl))
| v3_struct_0(sK4179_skl) ),
inference(resolution,[status(thm)],[f36617,f59581]) ).
fof(f70833,definition,
( sQ1246_spl
<=> v3_struct_0(sK4179_skl) ),
introduced(definition,[new_symbols(definition,[sQ1246_spl])],[split_symbol_definition]) ).
fof(f70834,plain,
( ~ sQ1246_spl
| v3_struct_0(sK4179_skl) ),
inference(component_clause,[status(thm)],[f70833]) ).
fof(f70836,definition,
( sQ1247_spl
<=> m1_subset_1(k2_group_1(sK4179_skl),u1_struct_0(sK4179_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1247_spl])],[split_symbol_definition]) ).
fof(f70839,plain,
( sQ1247_spl
| sQ1246_spl ),
inference(split_clause,[status(thm)],[f70832,f70833,f70836]) ).
fof(f70840,plain,
( ~ sQ1246_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f70834,f59578]) ).
fof(f70841,plain,
~ sQ1246_spl,
inference(contradiction_clause,[status(thm)],[f70840]) ).
fof(f70843,definition,
( sQ1248_spl
<=> v3_group_1(sK4179_skl) ),
introduced(definition,[new_symbols(definition,[sQ1248_spl])],[split_symbol_definition]) ).
fof(f70845,plain,
( sQ1248_spl
| ~ v3_group_1(sK4179_skl) ),
inference(component_clause,[status(thm)],[f70843]) ).
fof(f70846,definition,
( sQ1249_spl
<=> l1_group_1(sK4179_skl) ),
introduced(definition,[new_symbols(definition,[sQ1249_spl])],[split_symbol_definition]) ).
fof(f70848,plain,
( sQ1249_spl
| ~ l1_group_1(sK4179_skl) ),
inference(component_clause,[status(thm)],[f70846]) ).
fof(f70853,plain,
( sQ1249_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f70848,f59581]) ).
fof(f70854,plain,
sQ1249_spl,
inference(contradiction_clause,[status(thm)],[f70853]) ).
fof(f70855,plain,
( sQ1248_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f70845,f59579]) ).
fof(f70856,plain,
sQ1248_spl,
inference(contradiction_clause,[status(thm)],[f70855]) ).
fof(f72189,plain,
( r1_rlvect_1(sK4180_skl,k2_group_1(sK4179_skl))
| ~ l1_group_1(sK4179_skl)
| ~ v4_group_1(sK4179_skl)
| ~ v3_group_1(sK4179_skl)
| v3_struct_0(sK4179_skl) ),
inference(resolution,[status(thm)],[f59583,f40344]) ).
fof(f72200,definition,
( sQ1256_spl
<=> v4_group_1(sK4179_skl) ),
introduced(definition,[new_symbols(definition,[sQ1256_spl])],[split_symbol_definition]) ).
fof(f72202,plain,
( sQ1256_spl
| ~ v4_group_1(sK4179_skl) ),
inference(component_clause,[status(thm)],[f72200]) ).
fof(f72203,definition,
( sQ1257_spl
<=> v1_group_1(sK4180_skl) ),
introduced(definition,[new_symbols(definition,[sQ1257_spl])],[split_symbol_definition]) ).
fof(f72205,plain,
( sQ1257_spl
| ~ v1_group_1(sK4180_skl) ),
inference(component_clause,[status(thm)],[f72203]) ).
fof(f72281,definition,
( sQ1278_spl
<=> r1_rlvect_1(sK4180_skl,k2_group_1(sK4179_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1278_spl])],[split_symbol_definition]) ).
fof(f72284,plain,
( sQ1278_spl
| ~ sQ1249_spl
| ~ sQ1256_spl
| ~ sQ1248_spl
| sQ1246_spl ),
inference(split_clause,[status(thm)],[f72189,f70833,f70843,f72200,f70846,f72281]) ).
fof(f72310,plain,
( sQ1256_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f72202,f59580]) ).
fof(f72311,plain,
sQ1256_spl,
inference(contradiction_clause,[status(thm)],[f72310]) ).
fof(f72312,plain,
( sQ1257_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f72205,f59582]) ).
fof(f72313,plain,
sQ1257_spl,
inference(contradiction_clause,[status(thm)],[f72312]) ).
fof(f72314,plain,
( ~ r1_rlvect_1(sK4180_skl,k2_group_1(sK4179_skl))
| ~ m1_subset_1(k2_group_1(sK4179_skl),u1_struct_0(sK4179_skl))
| ~ m1_group_2(sK4180_skl,sK4179_skl)
| ~ v1_group_1(sK4180_skl)
| ~ l1_group_1(sK4179_skl)
| ~ v4_group_1(sK4179_skl)
| ~ v3_group_1(sK4179_skl)
| v3_struct_0(sK4179_skl) ),
inference(resolution,[status(thm)],[f59584,f59575]) ).
fof(f72315,definition,
( sQ1284_spl
<=> m1_group_2(sK4180_skl,sK4179_skl) ),
introduced(definition,[new_symbols(definition,[sQ1284_spl])],[split_symbol_definition]) ).
fof(f72317,plain,
( sQ1284_spl
| ~ m1_group_2(sK4180_skl,sK4179_skl) ),
inference(component_clause,[status(thm)],[f72315]) ).
fof(f72318,plain,
( ~ sQ1278_spl
| ~ sQ1247_spl
| ~ sQ1284_spl
| ~ sQ1257_spl
| ~ sQ1249_spl
| ~ sQ1256_spl
| ~ sQ1248_spl
| sQ1246_spl ),
inference(split_clause,[status(thm)],[f72314,f70833,f70843,f72200,f70846,f72203,f72315,f70836,f72281]) ).
fof(f72319,plain,
( sQ1284_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f72317,f59583]) ).
fof(f72320,plain,
sQ1284_spl,
inference(contradiction_clause,[status(thm)],[f72319]) ).
fof(f72321,plain,
$false,
inference(sat_refutation,[status(thm)],[f70839,f70841,f70854,f70856,f72284,f72311,f72313,f72318,f72320]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP641+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.48 % Computer : n019.cluster.edu
% 0.19/0.48 % Model : x86_64 x86_64
% 0.19/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.48 % Memory : 8046.5625MB
% 0.19/0.48 % OS : Linux 6.8.0-71-generic
% 0.19/0.48 % CPULimit : 300
% 0.19/0.48 % WCLimit : 300
% 0.19/0.48 % DateTime : Sun Sep 20 20:24:52 UTC 2026
% 0.19/0.48 % CPUTime :
% 1.66/2.11 % Drodi V4.1.1
% 12.56/3.60 % Refutation found
% 12.56/3.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 12.56/3.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.04/4.02 % Elapsed time: 3.490628 seconds
% 2.04/4.02 % CPU time: 13.720694 seconds
% 2.04/4.02 % Total memory used: 3.928 GB
% 2.04/4.02 % Net memory used: 3.901 GB
%------------------------------------------------------------------------------