%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW198+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 : Sun Sep 27 09:13:55 AM UTC 2026
% Result : Theorem 5.69s 1.43s
% Output : CNFRefutation 5.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 7 unt; 0 def)
% Number of atoms : 23 ( 12 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 11 ~; 7 |; 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 : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 14 ( 1 sgn 8 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_odd__Suc__mult__two__ex,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('theBenchmark.p',fact_odd__Suc__mult__two__ex) ).
fof(conj_0,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('theBenchmark.p',conj_0) ).
fof(conj_0_neg,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(assume_negation,[status(cth)],[conj_0]) ).
fof(fact_o,axiom,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
file('theBenchmark.p',fact_o) ).
cnf(c_1582,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
inference(clausify,[status(thm)],[fact_o]) ).
fof(nnf_38,plain,
! [V_nb_2] :
( ( ! [B_m] : 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)) != V_nb_2
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2) )
& ( ? [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))),X0)) = V_nb_2
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2) ) ),
inference(fof_nnf,[status(thm)],[fact_odd__Suc__mult__two__ex]) ).
fof(sk_fact_odd__Suc__mult__two__ex_sk,plain,
! [V_nb_2] :
( ( ! [B_m] : 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)) != V_nb_2
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,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(V_nb_2))) = V_nb_2
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0(V_nb_2))],[nnf_38]) ).
fof(sk_fact_odd__Suc__mult__two__ex,plain,
( ! [VAR_0,VAR_1] :
( 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))),VAR_1)) != VAR_0
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,VAR_0) )
& ! [VAR_0] :
( 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(VAR_0))) = VAR_0
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_fact_odd__Suc__mult__two__ex_sk]) ).
cnf(c_1637,plain,
( 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(A))) = A
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,A) ),
inference(split_conjunct,[status(thm)],[sk_fact_odd__Suc__mult__two__ex]) ).
cnf(c_2638,negated_conjecture,
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))),A)) != v_na____,
inference(clausify,[status(thm)],[conj_0_neg]) ).
cnf(c_6071,plain,
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(v_na____))) = v_na____,
inference(resolve,[status(thm)],[c_1637,c_1582]) ).
cnf(c_6070,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2638,c_6071]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW198+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 15:25:32 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1554079 was started by sandbox on n006,
% 0.08/0.36 % Sat Sep 26 15:25:32 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.31/0.59
% 0.31/0.59 % From the command line: assign(max_seconds, 300).
% 0.31/0.59
% 0.31/0.59 % SInE: 715 to sos, 470 to usable, of 1185 axioms (tolerance 2.00, depth 0 fixpoint).
% 5.69/1.43
% 5.69/1.43 % SZS status Theorem for theBenchmark
% 5.69/1.43
% 5.69/1.43 % Proof 1 at 0.65 (+ 0.10) seconds.
% 5.69/1.43 % Length of proof is 6.
% 5.69/1.43 % Level of proof is 2.
% 5.69/1.43 % Maximum clause weight is 145.000.
% 5.69/1.43 % Given clauses 159.
% 5.69/1.43
% 5.69/1.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------