%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP640+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 : n011.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 0.42s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 71 ( 17 unt; 7 def)
% Number of atoms : 394 ( 30 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 529 ( 206 ~; 222 |; 70 &)
% ( 9 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 8 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 92 ( 86 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( m1_group_2(C,A)
=> ! [D] :
( m1_group_2(D,A)
=> ! [E] :
( ( m2_relset_1(E,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(E) )
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
=> ( F = k2_xboole_0(u1_struct_0(C),u1_struct_0(D))
=> k2_funct_2(u1_struct_0(A),u1_struct_0(B),E,u1_struct_0(k8_group_4(A,C,D))) = k2_funct_2(u1_struct_0(A),u1_struct_0(B),E,u1_struct_0(k5_group_4(A,F))) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/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] :
( ( l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( m1_group_2(C,A)
=> ! [D] :
( m1_group_2(D,A)
=> ! [E] :
( ( m2_relset_1(E,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(E) )
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
=> ( F = k2_xboole_0(u1_struct_0(C),u1_struct_0(D))
=> k2_funct_2(u1_struct_0(A),u1_struct_0(B),E,u1_struct_0(k8_group_4(A,C,D))) = k2_funct_2(u1_struct_0(A),u1_struct_0(B),E,u1_struct_0(k5_group_4(A,F))) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f51,axiom,
! [A,B,C] :
( ( m1_group_2(C,A)
& v1_group_1(C)
& 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) )
=> ( r1_group_2(A,B,C)
<=> B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [A,B] :
( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ( m1_group_2(k5_group_4(A,B),A)
& v1_group_1(k5_group_4(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [A,B,C] :
( ( m1_group_2(C,A)
& m1_group_2(B,A)
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ( m1_group_2(k8_group_4(A,B,C),A)
& v1_group_1(k8_group_4(A,B,C)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ! [C] :
( m1_group_2(C,A)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( D = k2_xboole_0(u1_struct_0(B),u1_struct_0(C))
=> r1_group_2(A,k8_group_4(A,B,C),k5_group_4(A,D)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,plain,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ? [F] :
( k2_funct_2(u1_struct_0(A),u1_struct_0(B),E,u1_struct_0(k8_group_4(A,C,D))) != k2_funct_2(u1_struct_0(A),u1_struct_0(B),E,u1_struct_0(k5_group_4(A,F)))
& F = k2_xboole_0(u1_struct_0(C),u1_struct_0(D))
& m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) )
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B))
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(E) )
& m1_group_2(D,A) )
& m1_group_2(C,A) )
& l1_group_1(B)
& v4_group_1(B)
& v3_group_1(B)
& ~ v3_struct_0(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(f66,plain,
( k2_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl),sK4_skl,u1_struct_0(k8_group_4(sK0_skl,sK2_skl,sK3_skl))) != k2_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl),sK4_skl,u1_struct_0(k5_group_4(sK0_skl,sK5_skl)))
& sK5_skl = k2_xboole_0(u1_struct_0(sK2_skl),u1_struct_0(sK3_skl))
& m1_subset_1(sK5_skl,k1_zfmisc_1(u1_struct_0(sK0_skl)))
& m2_relset_1(sK4_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl))
& v1_funct_2(sK4_skl,u1_struct_0(sK0_skl),u1_struct_0(sK1_skl))
& v1_funct_1(sK4_skl)
& m1_group_2(sK3_skl,sK0_skl)
& m1_group_2(sK2_skl,sK0_skl)
& l1_group_1(sK1_skl)
& v4_group_1(sK1_skl)
& v3_group_1(sK1_skl)
& ~ v3_struct_0(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,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(C,sK2_skl),skolemize(D,sK3_skl),skolemize(E,sK4_skl),skolemize(F,sK5_skl)],[f65]) ).
fof(f67,plain,
~ v3_struct_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
v3_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f69,plain,
v4_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f70,plain,
l1_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f75,plain,
m1_group_2(sK2_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f76,plain,
m1_group_2(sK3_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f80,plain,
m1_subset_1(sK5_skl,k1_zfmisc_1(u1_struct_0(sK0_skl))),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f81,plain,
sK5_skl = k2_xboole_0(u1_struct_0(sK2_skl),u1_struct_0(sK3_skl)),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f82,plain,
k2_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl),sK4_skl,u1_struct_0(k8_group_4(sK0_skl,sK2_skl,sK3_skl))) != k2_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl),sK4_skl,u1_struct_0(k5_group_4(sK0_skl,sK5_skl))),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f200,plain,
! [A,B,C] :
( ( r1_group_2(A,B,C)
<=> B = C )
| ~ m1_group_2(C,A)
| ~ v1_group_1(C)
| ~ 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)],[f51]) ).
fof(f201,plain,
! [A,B,C] :
( ( ( B != C
| r1_group_2(A,B,C) )
& ( B = C
| ~ r1_group_2(A,B,C) ) )
| ~ m1_group_2(C,A)
| ~ v1_group_1(C)
| ~ 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)],[f200]) ).
fof(f202,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ r1_group_2(X0,X1,X2)
| ~ m1_group_2(X2,X0)
| ~ v1_group_1(X2)
| ~ 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)],[f201]) ).
fof(f207,plain,
! [A,B] :
( ( m1_group_2(k5_group_4(A,B),A)
& v1_group_1(k5_group_4(A,B)) )
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f55]) ).
fof(f208,plain,
! [X0,X1] :
( v1_group_1(k5_group_4(X0,X1))
| ~ m1_subset_1(X1,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)],[f207]) ).
fof(f209,plain,
! [X0,X1] :
( m1_group_2(k5_group_4(X0,X1),X0)
| ~ m1_subset_1(X1,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)],[f207]) ).
fof(f210,plain,
! [A,B,C] :
( ( m1_group_2(k8_group_4(A,B,C),A)
& v1_group_1(k8_group_4(A,B,C)) )
| ~ m1_group_2(C,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)],[f56]) ).
fof(f211,plain,
! [X0,X1,X2] :
( v1_group_1(k8_group_4(X0,X1,X2))
| ~ m1_group_2(X2,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)],[f210]) ).
fof(f212,plain,
! [X0,X1,X2] :
( m1_group_2(k8_group_4(X0,X1,X2),X0)
| ~ m1_group_2(X2,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)],[f210]) ).
fof(f226,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( r1_group_2(A,k8_group_4(A,B,C),k5_group_4(A,D))
| D != k2_xboole_0(u1_struct_0(B),u1_struct_0(C))
| ~ m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
| ~ m1_group_2(C,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)],[f64]) ).
fof(f227,plain,
! [X0,X1,X2,X3] :
( r1_group_2(X0,k8_group_4(X0,X1,X2),k5_group_4(X0,X3))
| X3 != k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2))
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_group_2(X2,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)],[f226]) ).
fof(f230,plain,
! [X0,X1,X2] :
( r1_group_2(X0,k8_group_4(X0,X1,X2),k5_group_4(X0,k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2))))
| ~ m1_subset_1(k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_group_2(X2,X0)
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f227]) ).
fof(f231,plain,
! [X0] :
( r1_group_2(X0,k8_group_4(X0,sK2_skl,sK3_skl),k5_group_4(X0,k2_xboole_0(u1_struct_0(sK2_skl),u1_struct_0(sK3_skl))))
| ~ m1_subset_1(sK5_skl,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_group_2(sK3_skl,X0)
| ~ m1_group_2(sK2_skl,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(paramodulation,[status(thm)],[f81,f230]) ).
fof(f232,plain,
! [X0] :
( r1_group_2(X0,k8_group_4(X0,sK2_skl,sK3_skl),k5_group_4(X0,sK5_skl))
| ~ m1_subset_1(sK5_skl,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_group_2(sK3_skl,X0)
| ~ m1_group_2(sK2_skl,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(forward_demodulation,[status(thm)],[f81,f231]) ).
fof(f240,plain,
! [X0,X1,X2,X3] :
( ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| v3_struct_0(X2)
| X1 = k5_group_4(X2,X3)
| ~ r1_group_2(X0,X1,k5_group_4(X2,X3))
| ~ m1_group_2(k5_group_4(X2,X3),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(resolution,[status(thm)],[f202,f208]) ).
fof(f254,definition,
( sQ4_spl
<=> v3_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( ~ sQ4_spl
| v3_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f257,definition,
( sQ5_spl
<=> v3_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( sQ5_spl
| ~ v3_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,definition,
( sQ6_spl
<=> l1_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f262,plain,
( sQ6_spl
| ~ l1_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f260]) ).
fof(f267,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f262,f70]) ).
fof(f268,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f267]) ).
fof(f269,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f259,f68]) ).
fof(f270,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f269]) ).
fof(f271,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f255,f67]) ).
fof(f272,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f271]) ).
fof(f276,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| X1 = k5_group_4(X0,X2)
| ~ r1_group_2(X0,X1,k5_group_4(X0,X2))
| ~ 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(resolution,[status(thm)],[f240,f209]) ).
fof(f277,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| X1 = k5_group_4(X0,X2)
| ~ r1_group_2(X0,X1,k5_group_4(X0,X2))
| ~ 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(duplicate_literals_removal,[status(thm)],[f276]) ).
fof(f284,plain,
! [X0,X1,X2,X3,X4] :
( ~ m1_group_2(X3,X1)
| ~ m1_group_2(X2,X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| ~ m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X0)))
| k8_group_4(X1,X2,X3) = k5_group_4(X0,X4)
| ~ r1_group_2(X0,k8_group_4(X1,X2,X3),k5_group_4(X0,X4))
| ~ m1_group_2(k8_group_4(X1,X2,X3),X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f277,f211]) ).
fof(f313,plain,
! [X0,X1,X2,X3] :
( ~ m1_group_2(X2,X0)
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(X2,X0)
| ~ m1_group_2(X1,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
| k8_group_4(X0,X1,X2) = k5_group_4(X0,X3)
| ~ r1_group_2(X0,k8_group_4(X0,X1,X2),k5_group_4(X0,X3))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f284,f212]) ).
fof(f314,plain,
! [X0,X1,X2,X3] :
( ~ m1_group_2(X2,X0)
| ~ m1_group_2(X1,X0)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X0)))
| k8_group_4(X0,X1,X2) = k5_group_4(X0,X3)
| ~ r1_group_2(X0,k8_group_4(X0,X1,X2),k5_group_4(X0,X3))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f313]) ).
fof(f321,plain,
! [X0] :
( ~ m1_subset_1(sK5_skl,k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_group_2(sK3_skl,X0)
| ~ m1_group_2(sK2_skl,X0)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0)
| ~ m1_group_2(sK3_skl,X0)
| ~ m1_group_2(sK2_skl,X0)
| ~ m1_subset_1(sK5_skl,k1_zfmisc_1(u1_struct_0(X0)))
| k8_group_4(X0,sK2_skl,sK3_skl) = k5_group_4(X0,sK5_skl)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(resolution,[status(thm)],[f314,f232]) ).
fof(f322,plain,
! [X0] :
( ~ m1_group_2(sK3_skl,X0)
| ~ m1_group_2(sK2_skl,X0)
| ~ m1_subset_1(sK5_skl,k1_zfmisc_1(u1_struct_0(X0)))
| k8_group_4(X0,sK2_skl,sK3_skl) = k5_group_4(X0,sK5_skl)
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| v3_struct_0(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f321]) ).
fof(f325,plain,
( ~ m1_group_2(sK3_skl,sK0_skl)
| ~ m1_group_2(sK2_skl,sK0_skl)
| k8_group_4(sK0_skl,sK2_skl,sK3_skl) = k5_group_4(sK0_skl,sK5_skl)
| ~ l1_group_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v3_group_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f322,f80]) ).
fof(f326,definition,
( sQ12_spl
<=> v4_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f328,plain,
( sQ12_spl
| ~ v4_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f326]) ).
fof(f329,definition,
( sQ13_spl
<=> k8_group_4(sK0_skl,sK2_skl,sK3_skl) = k5_group_4(sK0_skl,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f330,plain,
( ~ sQ13_spl
| k8_group_4(sK0_skl,sK2_skl,sK3_skl) = k5_group_4(sK0_skl,sK5_skl) ),
inference(component_clause,[status(thm)],[f329]) ).
fof(f332,definition,
( sQ14_spl
<=> m1_group_2(sK2_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f334,plain,
( sQ14_spl
| ~ m1_group_2(sK2_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f332]) ).
fof(f335,definition,
( sQ15_spl
<=> m1_group_2(sK3_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f337,plain,
( sQ15_spl
| ~ m1_group_2(sK3_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f335]) ).
fof(f338,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| sQ13_spl
| ~ sQ6_spl
| ~ sQ12_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f325,f254,f257,f326,f260,f329,f332,f335]) ).
fof(f339,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f337,f76]) ).
fof(f340,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f339]) ).
fof(f341,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f334,f75]) ).
fof(f342,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f341]) ).
fof(f343,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f328,f69]) ).
fof(f344,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f343]) ).
fof(f345,plain,
( ~ sQ13_spl
| k2_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl),sK4_skl,u1_struct_0(k5_group_4(sK0_skl,sK5_skl))) != k2_funct_2(u1_struct_0(sK0_skl),u1_struct_0(sK1_skl),sK4_skl,u1_struct_0(k5_group_4(sK0_skl,sK5_skl))) ),
inference(backward_demodulation,[status(thm)],[f330,f82]) ).
fof(f346,plain,
( ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f345]) ).
fof(f347,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f346]) ).
fof(f348,plain,
$false,
inference(sat_refutation,[status(thm)],[f268,f270,f272,f338,f340,f342,f344,f347]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP640+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 20:24:26 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.42 % Refutation found
% 0.08/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.45 % Elapsed time: 0.072305 seconds
% 0.08/0.45 % CPU time: 0.315389 seconds
% 0.08/0.45 % Total memory used: 110.234 MB
% 0.08/0.45 % Net memory used: 109.979 MB
%------------------------------------------------------------------------------