%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWW198+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 09:04:49 AM UTC 2026
% Result : Theorem 62.87s 63.19s
% Output : Proof 62.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 14 unt; 0 def)
% Number of atoms : 40 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 22 ~; 12 |; 5 &)
% ( 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 : 25 ( 1 sgn 17 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_o,axiom,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
file('theBenchmark.p',fact_o) ).
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(f_1_1,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
inference(fof_nnf,[status(thm)],[fact_o]) ).
fof(f_1_2,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
inference(definitional_conversion,[status(esa)],[f_1_1]) ).
cnf(f_1_3,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_49_1,plain,
! [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)) )
& ( ? [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(fof_nnf,[status(thm)],[fact_odd__Suc__mult__two__ex]) ).
fof(f_49_2,plain,
! [U_113] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,U_113)
| ! [U_112] : U_113 != 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))),U_112)) )
& ( ? [U_111] : U_113 = 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))),U_111))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,U_113) ) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
( ! [U_115] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,U_115)
| ! [U_112] : U_115 != 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))),U_112)) )
& ! [U_114] :
( ? [U_111] : U_114 = 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))),U_111))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,U_114) ) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
fof(f_49_4,plain,
( ! [U_115] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,U_115)
| ! [U_112] : U_115 != 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))),U_112)) )
& ! [U_114] :
( U_114 = 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))),sK1(U_114)))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,U_114) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_111,sK1(U_114))],[f_49_3]) ).
fof(f_49_5,plain,
( ! [U_112,U_115] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,U_115)
| U_115 != 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))),U_112)) )
& ! [U_114] :
( U_114 = 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))),sK1(U_114)))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,U_114) ) ),
inference(definitional_conversion,[status(esa)],[f_49_4]) ).
cnf(f_49_6,plain,
( U_114 = 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))),sK1(U_114)))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,U_114) ),
inference(clausify,[status(thm)],[f_49_5]) ).
fof(f_1186_1,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(negate,[status(cth)],[conj_0]) ).
fof(f_1186_2,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(fof_nnf,[status(thm)],[f_1186_1]) ).
fof(f_1186_3,negated_conjecture,
! [U_3015] : 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))),U_3015)),
inference(variable_rename,[status(thm)],[f_1186_2]) ).
fof(f_1186_4,negated_conjecture,
! [U_3015] : 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))),U_3015)),
inference(definitional_conversion,[status(esa)],[f_1186_3]) ).
cnf(f_1186_5,negated_conjecture,
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))),U_3015)),
inference(clausify,[status(thm)],[f_1186_4]) ).
cnf(t1,plain,
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))),sK1(v_na____))),
inference(start,[status(thm),parent(0:0)],[f_1186_5]) ).
cnf(t2,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____)
| 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))),sK1(v_na____))) ),
inference(extension,[status(thm),parent(t1:1)],[f_49_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
inference(extension,[status(thm),parent(t2:2)],[f_1_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW198+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 20 05:09:51 UTC 2026
% 0.11/0.39 % CPUTime :
% 62.87/63.19 % SZS status Theorem for theBenchmark
% 62.87/63.19 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------