%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW198+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 03:07:25 PM UTC 2026
% Result : Theorem 0.23s 0.51s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 14 unt; 0 def)
% Number of atoms : 32 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 13 ~; 8 |; 3 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 19 ( 14 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [V_nb_2] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
<=> ? [B_m] : V_nb_2 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f735,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1186,conjecture,
? [B_m] : v_na____ = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1187,negated_conjecture,
~ ? [B_m] : v_na____ = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m)),
inference(negated_conjecture,[status(cth)],[f1186]) ).
fof(f1188,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f1280,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f1291,plain,
! [V_nb_2] :
( ( ! [B_m] : V_nb_2 != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2) )
& ( ? [B_m] : V_nb_2 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2) ) ),
inference(NNF_transformation,[status(thm)],[f49]) ).
fof(f1292,plain,
( ! [V_nb_2] :
( ! [B_m] : V_nb_2 != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2) )
& ! [V_nb_2] :
( ? [B_m] : V_nb_2 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2) ) ),
inference(miniscoping,[status(thm)],[f1291]) ).
fof(f1293,plain,
( ! [V_nb_2] :
( ! [B_m] : V_nb_2 != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2) )
& ! [V_nb_2] :
( V_nb_2 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sK0_skl(V_nb_2)))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B_m,sK0_skl(V_nb_2))],[f1292]) ).
fof(f1294,plain,
! [X0] :
( X0 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sK0_skl(X0)))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0) ),
inference(cnf_transformation,[status(thm)],[f1293]) ).
fof(f3460,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[status(thm)],[f735]) ).
fof(f4598,plain,
! [B_m] : v_na____ != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m)),
inference(pre_NNF_transformation,[status(thm)],[f1187]) ).
fof(f4599,plain,
! [X0] : v_na____ != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0)),
inference(cnf_transformation,[status(thm)],[f4598]) ).
fof(f5180,plain,
! [X0] : v_na____ != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)),
inference(backward_demodulation,[status(thm)],[f5181,f4599]) ).
fof(f5181,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[status(thm)],[f3460,f1280]) ).
fof(f5283,plain,
! [X0] :
( X0 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),sK0_skl(X0)))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0) ),
inference(forward_demodulation,[status(thm)],[f5181,f1294]) ).
fof(f5285,plain,
c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
inference(resolution,[status(thm)],[f5283,f5180]) ).
fof(f5302,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5285,f1188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW198+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 09:40:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.47 % Drodi V4.1.1
% 0.23/0.51 % Refutation found
% 0.23/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.56 % Elapsed time: 0.182230 seconds
% 0.23/0.56 % CPU time: 0.415859 seconds
% 0.23/0.56 % Total memory used: 209.200 MB
% 0.23/0.56 % Net memory used: 207.687 MB
%------------------------------------------------------------------------------