%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP641+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 : n012.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 0.08s 0.33s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 24
% Syntax : Number of formulae : 111 ( 15 unt; 14 def)
% Number of atoms : 413 ( 30 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 499 ( 197 ~; 214 |; 56 &)
% ( 16 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 31 ( 29 usr; 15 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 78 ( 74 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,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)],[f1]) ).
fof(f9,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_1(B) )
=> ( B = k1_latsubgr(A)
<=> ! [C] :
( ( m1_group_2(C,A)
& v1_group_1(C) )
=> k1_funct_1(B,C) = u1_struct_0(C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ( m2_relset_1(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_2(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_1(k1_latsubgr(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A] :
( ( l1_group_1(A)
& ~ v3_struct_0(A) )
=> m1_subset_1(k2_group_1(A),u1_struct_0(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A] :
( l1_group_1(A)
=> l1_struct_0(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
( ( l1_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( l1_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ~ v1_xboole_0(u1_struct_0(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [A,B] :
? [C] :
( v1_funct_2(C,A,B)
& v1_funct_1(C)
& v1_relat_1(C)
& m1_relset_1(C,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( r2_hidden(A,B)
| v1_xboole_0(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> k2_group_1(B) = k2_group_1(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,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)],[f2]) ).
fof(f58,plain,
( ~ r2_hidden(k2_group_1(sK0_skl),k1_funct_1(k1_latsubgr(sK0_skl),sK1_skl))
& m1_group_2(sK1_skl,sK0_skl)
& v1_group_1(sK1_skl)
& l1_group_1(sK0_skl)
& v4_group_1(sK0_skl)
& v3_group_1(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)],[f57]) ).
fof(f59,plain,
~ v3_struct_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,plain,
v3_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f61,plain,
v4_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f62,plain,
l1_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f63,plain,
v1_group_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f64,plain,
m1_group_2(sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f65,plain,
~ r2_hidden(k2_group_1(sK0_skl),k1_funct_1(k1_latsubgr(sK0_skl),sK1_skl)),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f86,plain,
! [A] :
( ! [B] :
( ( B = k1_latsubgr(A)
<=> ! [C] :
( k1_funct_1(B,C) = u1_struct_0(C)
| ~ m1_group_2(C,A)
| ~ v1_group_1(C) ) )
| ~ m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ v1_funct_1(B) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f87,plain,
! [A] :
( ! [B] :
( ( ( ? [C] :
( k1_funct_1(B,C) != u1_struct_0(C)
& m1_group_2(C,A)
& v1_group_1(C) )
| B = k1_latsubgr(A) )
& ( ! [C] :
( k1_funct_1(B,C) = u1_struct_0(C)
| ~ m1_group_2(C,A)
| ~ v1_group_1(C) )
| B != k1_latsubgr(A) ) )
| ~ m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ v1_funct_1(B) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(NNF_transformation,[status(thm)],[f86]) ).
fof(f88,plain,
! [A] :
( ! [B] :
( ( ( ( k1_funct_1(B,sK2_skl(B,A)) != u1_struct_0(sK2_skl(B,A))
& m1_group_2(sK2_skl(B,A),A)
& v1_group_1(sK2_skl(B,A)) )
| B = k1_latsubgr(A) )
& ( ! [C] :
( k1_funct_1(B,C) = u1_struct_0(C)
| ~ m1_group_2(C,A)
| ~ v1_group_1(C) )
| B != k1_latsubgr(A) ) )
| ~ m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ v1_funct_1(B) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(C,sK2_skl(B,A))],[f87]) ).
fof(f89,plain,
! [X0,X1,X2] :
( k1_funct_1(X1,X2) = u1_struct_0(X2)
| ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| X1 != k1_latsubgr(X0)
| ~ m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_1(X1)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f96,plain,
! [A] :
( ( m2_relset_1(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_2(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_1(k1_latsubgr(A)) )
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f97,plain,
! [X0] :
( v1_funct_1(k1_latsubgr(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f98,plain,
! [X0] :
( v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f99,plain,
! [X0] :
( m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f100,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)],[f16]) ).
fof(f101,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)],[f100]) ).
fof(f102,plain,
! [A] :
( l1_struct_0(A)
| ~ l1_group_1(A) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f103,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
! [A] :
( ! [B] :
( ( l1_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
| ~ m1_group_2(B,A) )
| ~ l1_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f105,plain,
! [X0,X1] :
( ~ v3_struct_0(X1)
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f107,plain,
! [X0,X1] :
( l1_group_1(X1)
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f129,plain,
! [A] :
( ~ v1_xboole_0(u1_struct_0(A))
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f130,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f138,plain,
! [A,B] :
( v1_funct_2(sK9_skl(B,A),A,B)
& v1_funct_1(sK9_skl(B,A))
& v1_relat_1(sK9_skl(B,A))
& m1_relset_1(sK9_skl(B,A),A,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(C,sK9_skl(B,A))],[f38]) ).
fof(f141,plain,
! [X0,X1] : v1_funct_1(sK9_skl(X0,X1)),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f173,plain,
! [A,B] :
( r2_hidden(A,B)
| v1_xboole_0(B)
| ~ m1_subset_1(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f174,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f173]) ).
fof(f182,plain,
! [A] :
( ! [B] :
( k2_group_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)],[f52]) ).
fof(f183,plain,
! [X0,X1] :
( k2_group_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)],[f182]) ).
fof(f195,plain,
! [X0,X1] :
( k1_funct_1(k1_latsubgr(X0),X1) = u1_struct_0(X1)
| ~ m1_group_2(X1,X0)
| ~ v1_group_1(X1)
| ~ m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_1(k1_latsubgr(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f89]) ).
fof(f196,plain,
! [X0] :
( r2_hidden(k2_group_1(X0),u1_struct_0(X0))
| v1_xboole_0(u1_struct_0(X0))
| ~ l1_group_1(X0)
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f101,f174]) ).
fof(f204,definition,
( sQ0_spl
<=> l1_group_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( sQ0_spl
| ~ l1_group_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f211,plain,
! [X0] :
( sQ0_spl
| ~ m1_group_2(sK1_skl,X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f107,f206]) ).
fof(f212,plain,
( sQ0_spl
| ~ l1_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f211,f64]) ).
fof(f213,definition,
( sQ2_spl
<=> v3_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f214,plain,
( ~ sQ2_spl
| v3_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f216,definition,
( sQ3_spl
<=> v3_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f218,plain,
( sQ3_spl
| ~ v3_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f219,definition,
( sQ4_spl
<=> l1_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f221,plain,
( sQ4_spl
| ~ l1_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f212,f213,f216,f219,f204]) ).
fof(f223,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f221,f62]) ).
fof(f224,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f223]) ).
fof(f225,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f218,f60]) ).
fof(f226,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f225]) ).
fof(f227,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f214,f59]) ).
fof(f228,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f227]) ).
fof(f229,plain,
! [X0,X1] :
( k1_funct_1(k1_latsubgr(X0),X1) = u1_struct_0(X1)
| ~ m1_group_2(X1,X0)
| ~ v1_group_1(X1)
| ~ m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f195,f97]) ).
fof(f271,definition,
( sQ8_spl
<=> v4_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f273,plain,
( sQ8_spl
| ~ v4_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f271]) ).
fof(f324,plain,
! [X0] :
( k2_group_1(X0) = k2_group_1(sK0_skl)
| ~ m1_group_2(X0,sK0_skl)
| ~ l1_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f183,f61]) ).
fof(f325,definition,
! [X0] :
( sQ17_spl
<=> ( k2_group_1(X0) = k2_group_1(sK0_skl)
| ~ m1_group_2(X0,sK0_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f326,plain,
! [X0] :
( ~ sQ17_spl
| k2_group_1(X0) = k2_group_1(sK0_skl)
| ~ m1_group_2(X0,sK0_skl) ),
inference(component_clause,[status(thm)],[f325]) ).
fof(f328,plain,
( sQ17_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f324,f213,f216,f219,f325]) ).
fof(f360,plain,
( ~ sQ17_spl
| k2_group_1(sK1_skl) = k2_group_1(sK0_skl) ),
inference(resolution,[status(thm)],[f326,f64]) ).
fof(f365,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f273,f61]) ).
fof(f366,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f365]) ).
fof(f368,plain,
( ~ sQ17_spl
| ~ r2_hidden(k2_group_1(sK1_skl),k1_funct_1(k1_latsubgr(sK0_skl),sK1_skl)) ),
inference(backward_demodulation,[status(thm)],[f360,f65]) ).
fof(f400,plain,
! [X0,X1] :
( k1_funct_1(k1_latsubgr(X0),X1) = u1_struct_0(X1)
| ~ m1_group_2(X1,X0)
| ~ v1_group_1(X1)
| ~ m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f229,f98]) ).
fof(f401,plain,
! [X0] :
( k1_funct_1(k1_latsubgr(sK0_skl),X0) = u1_struct_0(X0)
| ~ m1_group_2(X0,sK0_skl)
| ~ v1_group_1(X0)
| ~ m2_relset_1(k1_latsubgr(sK0_skl),k1_group_3(sK0_skl),k1_zfmisc_1(u1_struct_0(sK0_skl)))
| ~ l1_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f400,f61]) ).
fof(f402,definition,
( sQ27_spl
<=> m2_relset_1(k1_latsubgr(sK0_skl),k1_group_3(sK0_skl),k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f404,plain,
( sQ27_spl
| ~ m2_relset_1(k1_latsubgr(sK0_skl),k1_group_3(sK0_skl),k1_zfmisc_1(u1_struct_0(sK0_skl))) ),
inference(component_clause,[status(thm)],[f402]) ).
fof(f405,definition,
! [X0] :
( sQ28_spl
<=> ( k1_funct_1(k1_latsubgr(sK0_skl),X0) = u1_struct_0(X0)
| ~ m1_group_2(X0,sK0_skl)
| ~ v1_group_1(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f406,plain,
! [X0] :
( ~ sQ28_spl
| k1_funct_1(k1_latsubgr(sK0_skl),X0) = u1_struct_0(X0)
| ~ m1_group_2(X0,sK0_skl)
| ~ v1_group_1(X0) ),
inference(component_clause,[status(thm)],[f405]) ).
fof(f408,plain,
( sQ28_spl
| ~ sQ27_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f401,f213,f216,f219,f402,f405]) ).
fof(f455,plain,
( sQ27_spl
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f404,f99]) ).
fof(f457,plain,
( sQ27_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f455,f213,f216,f271,f219,f402]) ).
fof(f461,plain,
( ~ sQ28_spl
| k1_funct_1(k1_latsubgr(sK0_skl),sK1_skl) = u1_struct_0(sK1_skl)
| ~ m1_group_2(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f406,f63]) ).
fof(f462,definition,
( sQ34_spl
<=> m1_group_2(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f464,plain,
( sQ34_spl
| ~ m1_group_2(sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,definition,
( sQ35_spl
<=> k1_funct_1(k1_latsubgr(sK0_skl),sK1_skl) = u1_struct_0(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( ~ sQ35_spl
| k1_funct_1(k1_latsubgr(sK0_skl),sK1_skl) = u1_struct_0(sK1_skl) ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f468,plain,
( ~ sQ28_spl
| sQ35_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f461,f462,f465,f405]) ).
fof(f469,plain,
( sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f464,f64]) ).
fof(f470,plain,
sQ34_spl,
inference(contradiction_clause,[status(thm)],[f469]) ).
fof(f477,definition,
( sQ37_spl
<=> v1_funct_1(sK9_skl(k1_zfmisc_1(u1_struct_0(sK0_skl)),k1_group_3(sK0_skl))) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f479,plain,
( sQ37_spl
| ~ v1_funct_1(sK9_skl(k1_zfmisc_1(u1_struct_0(sK0_skl)),k1_group_3(sK0_skl))) ),
inference(component_clause,[status(thm)],[f477]) ).
fof(f491,plain,
( sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f479,f141]) ).
fof(f492,plain,
sQ37_spl,
inference(contradiction_clause,[status(thm)],[f491]) ).
fof(f493,plain,
( ~ sQ17_spl
| ~ sQ35_spl
| ~ r2_hidden(k2_group_1(sK1_skl),u1_struct_0(sK1_skl)) ),
inference(backward_demodulation,[status(thm)],[f466,f368]) ).
fof(f494,plain,
( ~ sQ17_spl
| ~ sQ35_spl
| v1_xboole_0(u1_struct_0(sK1_skl))
| ~ l1_group_1(sK1_skl)
| v3_struct_0(sK1_skl) ),
inference(resolution,[status(thm)],[f493,f196]) ).
fof(f495,definition,
( sQ41_spl
<=> v3_struct_0(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f496,plain,
( ~ sQ41_spl
| v3_struct_0(sK1_skl) ),
inference(component_clause,[status(thm)],[f495]) ).
fof(f498,definition,
( sQ42_spl
<=> v1_xboole_0(u1_struct_0(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f499,plain,
( ~ sQ42_spl
| v1_xboole_0(u1_struct_0(sK1_skl)) ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f501,plain,
( ~ sQ17_spl
| ~ sQ35_spl
| sQ42_spl
| ~ sQ0_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f494,f495,f204,f498,f465,f325]) ).
fof(f502,plain,
! [X0] :
( ~ sQ41_spl
| ~ m1_group_2(sK1_skl,X0)
| ~ l1_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f496,f105]) ).
fof(f503,plain,
( ~ sQ42_spl
| ~ l1_struct_0(sK1_skl)
| v3_struct_0(sK1_skl) ),
inference(resolution,[status(thm)],[f499,f130]) ).
fof(f509,definition,
( sQ43_spl
<=> l1_struct_0(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f511,plain,
( sQ43_spl
| ~ l1_struct_0(sK1_skl) ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f512,plain,
( ~ sQ42_spl
| ~ sQ43_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f503,f495,f509,f498]) ).
fof(f520,plain,
( sQ43_spl
| ~ l1_group_1(sK1_skl) ),
inference(resolution,[status(thm)],[f511,f103]) ).
fof(f521,plain,
( sQ43_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f520,f204,f509]) ).
fof(f801,plain,
( ~ sQ41_spl
| ~ l1_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f502,f64]) ).
fof(f802,plain,
( ~ sQ41_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f801,f213,f216,f219,f495]) ).
fof(f803,plain,
$false,
inference(sat_refutation,[status(thm)],[f222,f224,f226,f228,f328,f366,f408,f457,f468,f470,f492,f501,f512,f521,f802]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP641+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.05/0.30 % Computer : n012.cluster.edu
% 0.05/0.30 % Model : x86_64 x86_64
% 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.30 % Memory : 8046.5625MB
% 0.05/0.30 % OS : Linux 6.8.0-71-generic
% 0.05/0.30 % CPULimit : 300
% 0.05/0.30 % WCLimit : 300
% 0.05/0.30 % DateTime : Sun Sep 20 20:24:38 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 % Drodi V4.1.1
% 0.08/0.33 % Refutation found
% 0.08/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.35 % Elapsed time: 0.037564 seconds
% 0.08/0.35 % CPU time: 0.122448 seconds
% 0.08/0.35 % Total memory used: 67.390 MB
% 0.08/0.35 % Net memory used: 67.277 MB
%------------------------------------------------------------------------------