%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP642+3 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 12:34:56 PM UTC 2026
% Result : Theorem 2.03s 2.96s
% Output : CNFRefutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 10 unt; 0 def)
% Number of atoms : 102 ( 13 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 127 ( 53 ~; 40 |; 27 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 23 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f29,axiom,
! [A] :
( A = k1_xboole_0
<=> ! [B] : ~ r2_hidden(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13983,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) )
=> r2_hidden(k2_group_1(A),k1_funct_1(k1_latsubgr(A),B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13984,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) )
=> k1_funct_1(k1_latsubgr(A),B) != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13985,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) )
=> k1_funct_1(k1_latsubgr(A),B) != k1_xboole_0 ) ),
inference(negated_conjecture,[status(cth)],[f13984]) ).
fof(f14075,plain,
! [A] :
( ( ? [B] : r2_hidden(B,A)
| A = k1_xboole_0 )
& ( ! [B] : ~ r2_hidden(B,A)
| A != k1_xboole_0 ) ),
inference(NNF_transformation,[status(thm)],[f29]) ).
fof(f14076,plain,
( ! [A] :
( ? [B] : r2_hidden(B,A)
| A = k1_xboole_0 )
& ! [A] :
( ! [B] : ~ r2_hidden(B,A)
| A != k1_xboole_0 ) ),
inference(miniscoping,[status(thm)],[f14075]) ).
fof(f14077,plain,
( ! [A] :
( r2_hidden(sK22_skl(A),A)
| A = k1_xboole_0 )
& ! [A] :
( ! [B] : ~ r2_hidden(B,A)
| A != k1_xboole_0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22_skl]),skolemize(B,sK22_skl(A))],[f14076]) ).
fof(f14078,plain,
! [X0,X1] :
( ~ r2_hidden(X1,X0)
| X0 != k1_xboole_0 ),
inference(cnf_transformation,[status(thm)],[f14077]) ).
fof(f59577,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)],[f13983]) ).
fof(f59578,plain,
! [X0,X1] :
( r2_hidden(k2_group_1(X0),k1_funct_1(k1_latsubgr(X0),X1))
| ~ 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)],[f59577]) ).
fof(f59579,plain,
? [A] :
( ? [B] :
( k1_funct_1(k1_latsubgr(A),B) = k1_xboole_0
& 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)],[f13985]) ).
fof(f59580,plain,
( k1_funct_1(k1_latsubgr(sK4179_skl),sK4180_skl) = k1_xboole_0
& 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)],[f59579]) ).
fof(f59581,plain,
~ v3_struct_0(sK4179_skl),
inference(cnf_transformation,[status(thm)],[f59580]) ).
fof(f59582,plain,
v3_group_1(sK4179_skl),
inference(cnf_transformation,[status(thm)],[f59580]) ).
fof(f59583,plain,
v4_group_1(sK4179_skl),
inference(cnf_transformation,[status(thm)],[f59580]) ).
fof(f59584,plain,
l1_group_1(sK4179_skl),
inference(cnf_transformation,[status(thm)],[f59580]) ).
fof(f59585,plain,
v1_group_1(sK4180_skl),
inference(cnf_transformation,[status(thm)],[f59580]) ).
fof(f59586,plain,
m1_group_2(sK4180_skl,sK4179_skl),
inference(cnf_transformation,[status(thm)],[f59580]) ).
fof(f59587,plain,
k1_funct_1(k1_latsubgr(sK4179_skl),sK4180_skl) = k1_xboole_0,
inference(cnf_transformation,[status(thm)],[f59580]) ).
fof(f62888,plain,
! [X0] : ~ r2_hidden(X0,k1_xboole_0),
inference(destructive_equality_resolution,[status(thm)],[f14078]) ).
fof(f66491,plain,
( r2_hidden(k2_group_1(sK4179_skl),k1_xboole_0)
| ~ 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(paramodulation,[status(thm)],[f59587,f59578]) ).
fof(f66493,plain,
( r2_hidden(k2_group_1(sK4179_skl),k1_xboole_0)
| ~ 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) ),
inference(forward_subsumption_resolution,[status(thm)],[f66491,f59581]) ).
fof(f66498,plain,
( r2_hidden(k2_group_1(sK4179_skl),k1_xboole_0)
| ~ m1_group_2(sK4180_skl,sK4179_skl)
| ~ v1_group_1(sK4180_skl)
| ~ l1_group_1(sK4179_skl)
| ~ v4_group_1(sK4179_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f66493,f59582]) ).
fof(f66499,plain,
( ~ m1_group_2(sK4180_skl,sK4179_skl)
| ~ v1_group_1(sK4180_skl)
| ~ l1_group_1(sK4179_skl)
| ~ v4_group_1(sK4179_skl) ),
inference(resolution,[status(thm)],[f66498,f62888]) ).
fof(f66501,plain,
( ~ m1_group_2(sK4180_skl,sK4179_skl)
| ~ v1_group_1(sK4180_skl)
| ~ l1_group_1(sK4179_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f66499,f59583]) ).
fof(f66503,plain,
( ~ m1_group_2(sK4180_skl,sK4179_skl)
| ~ v1_group_1(sK4180_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f66501,f59584]) ).
fof(f66504,plain,
~ v1_group_1(sK4180_skl),
inference(resolution,[status(thm)],[f66503,f59586]) ).
fof(f66506,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f66504,f59585]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP642+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.55 % Computer : n004.cluster.edu
% 0.09/0.55 % Model : x86_64 x86_64
% 0.09/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.55 % Memory : 8046.5625MB
% 0.09/0.55 % OS : Linux 6.8.0-71-generic
% 0.09/0.55 % CPULimit : 300
% 0.09/0.55 % WCLimit : 300
% 0.09/0.55 % DateTime : Sun Sep 20 20:25:26 UTC 2026
% 0.09/0.55 % CPUTime :
% 1.86/2.30 % Drodi V4.1.1
% 2.03/2.96 % Refutation found
% 2.03/2.96 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.03/2.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.06/3.27 % Elapsed time: 2.670287 seconds
% 2.06/3.27 % CPU time: 7.251393 seconds
% 2.06/3.27 % Total memory used: 3.911 GB
% 2.06/3.27 % Net memory used: 3.890 GB
%------------------------------------------------------------------------------