%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW198+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:36:36 AM UTC 2025
% Result : Theorem 0.91s 1.10s
% Output : Proof 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 39 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 176 ( 89 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 267 ( 148 ~; 81 |; 6 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 18 ( 18 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 77 ( 51 !; 20 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i > $i ).
tff(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(tptp_fun_B_m_0_type,type,
tptp_fun_B_m_0: $i > $i ).
tff(v_na_____type,type,
v_na____: $i ).
tff(c_Int_Onumber__class_Onumber__of_type,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(c_Int_OBit0_type,type,
c_Int_OBit0: $i > $i ).
tff(c_Int_OBit1_type,type,
c_Int_OBit1: $i > $i ).
tff(c_Int_OPls_type,type,
c_Int_OPls: $i ).
tff(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
tff(c_Parity_Oeven__odd__class_Oeven_type,type,
c_Parity_Oeven__odd__class_Oeven: ( $i * $i ) > $o ).
tff(1,plain,
^ [V_nb_2: $i] :
refl(( ~ ( ~ ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,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))),tptp_fun_B_m_0(V_nb_2))) ) )
| ~ ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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 = 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))),tptp_fun_B_m_0(V_nb_2))) ) )
| ~ ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_nb_2: $i] :
~ ( ~ ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,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))),tptp_fun_B_m_0(V_nb_2))) ) )
| ~ ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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)) ) ) )
<=> ! [V_nb_2: $i] :
~ ( ~ ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,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))),tptp_fun_B_m_0(V_nb_2))) ) )
| ~ ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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)) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [V_nb_2: $i] :
rewrite(( ~ ( ~ ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,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))),tptp_fun_B_m_0(V_nb_2))) ) )
| ~ ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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 = 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))),tptp_fun_B_m_0(V_nb_2))) ) )
| ~ ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [V_nb_2: $i] :
~ ( ~ ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,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))),tptp_fun_B_m_0(V_nb_2))) ) )
| ~ ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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)) ) ) )
<=> ! [V_nb_2: $i] :
~ ( ~ ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,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))),tptp_fun_B_m_0(V_nb_2))) ) )
| ~ ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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)) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [V_nb_2: $i] :
~ ( ~ ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,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))),tptp_fun_B_m_0(V_nb_2))) ) )
| ~ ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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)) ) ) )
<=> ! [V_nb_2: $i] :
~ ( ~ ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,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))),tptp_fun_B_m_0(V_nb_2))) ) )
| ~ ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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)) ) ) ) ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,plain,
^ [V_nb_2: $i] :
trans(monotonicity(rewrite(( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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: $i] : ( 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 = 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))),tptp_fun_B_m_0(V_nb_2))) ) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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 = 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))),tptp_fun_B_m_0(V_nb_2))) ) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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)) ) ) ) )),
rewrite(( ( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,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))),tptp_fun_B_m_0(V_nb_2))) ) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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 = 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))),tptp_fun_B_m_0(V_nb_2))) ) )
| ~ ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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 = 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))),tptp_fun_B_m_0(V_nb_2))) ) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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 = 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))),tptp_fun_B_m_0(V_nb_2))) ) )
| ~ ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [V_nb_2: $i] :
( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,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))),tptp_fun_B_m_0(V_nb_2))) ) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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)) ) ) )
<=> ! [V_nb_2: $i] :
~ ( ~ ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,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))),tptp_fun_B_m_0(V_nb_2))) ) )
| ~ ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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)) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [V_nb_2: $i] :
~ ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
<=> ? [B_m: $i] : ( 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)) ) )
<=> ! [V_nb_2: $i] :
~ ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
<=> ? [B_m: $i] : ( 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)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,plain,
^ [V_nb_2: $i] :
trans(rewrite(( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
<=> ? [B_m: $i] : ( 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: $i] : ( 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)) ) ) )),
rewrite(( ~ ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
<=> ? [B_m: $i] : ( 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: $i] : ( 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: $i] : ( 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: $i] : ( 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)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [V_nb_2: $i] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
<=> ? [B_m: $i] : ( 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)) ) )
<=> ! [V_nb_2: $i] :
~ ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
<=> ? [B_m: $i] : ( 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)) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,axiom,
! [V_nb_2: $i] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
<=> ? [B_m: $i] : ( 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',fact_odd__Suc__mult__two__ex) ).
tff(12,plain,
! [V_nb_2: $i] :
~ ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
<=> ? [B_m: $i] : ( 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)) ) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [V_nb_2: $i] :
~ ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
<=> ? [B_m: $i] : ( 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)) ) ),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
! [V_nb_2: $i] :
( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,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))),tptp_fun_B_m_0(V_nb_2))) ) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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)) ) ) ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [V_nb_2: $i] :
~ ( ~ ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,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))),tptp_fun_B_m_0(V_nb_2))) ) )
| ~ ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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)) ) ) ),
inference(modus_ponens,[status(thm)],[14,7]) ).
tff(16,plain,
! [V_nb_2: $i] :
~ ( ~ ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,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))),tptp_fun_B_m_0(V_nb_2))) ) )
| ~ ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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)) ) ) ),
inference(modus_ponens,[status(thm)],[15,5]) ).
tff(17,plain,
( ~ ! [V_nb_2: $i] :
~ ( ~ ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,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))),tptp_fun_B_m_0(V_nb_2))) ) )
| ~ ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
| ! [B_m: $i] : ( 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_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))),tptp_fun_B_m_0(v_na____))) ) )
| ~ ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____)
| ! [B_m: $i] : ( 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(quant_inst,[status(thm)],[]) ).
tff(18,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))),tptp_fun_B_m_0(v_na____))) ) )
| ~ ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____)
| ! [B_m: $i] : ( 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(unit_resolution,[status(thm)],[17,16]) ).
tff(19,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))),tptp_fun_B_m_0(v_na____))) ) )
| ~ ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____)
| ! [B_m: $i] : ( 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)) ) )
| 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))),tptp_fun_B_m_0(v_na____))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(20,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))),tptp_fun_B_m_0(v_na____))) ) ),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____)
<=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o) ).
tff(23,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,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))),tptp_fun_B_m_0(v_na____))) ) )
| 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))),tptp_fun_B_m_0(v_na____))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(25,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))),tptp_fun_B_m_0(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))),tptp_fun_B_m_0(v_na____))) ) ),
inference(unit_resolution,[status(thm)],[24,23]) ).
tff(26,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))),tptp_fun_B_m_0(v_na____))),
inference(unit_resolution,[status(thm)],[25,20]) ).
tff(27,plain,
^ [B_m: $i] :
refl(( ( 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)) )
<=> ( 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(bind,[status(th)],[]) ).
tff(28,plain,
( ! [B_m: $i] : ( 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)) )
<=> ! [B_m: $i] : ( 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(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ~ ? [B_m: $i] : ( 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)) )
<=> ~ ? [B_m: $i] : ( 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(rewrite,[status(thm)],[]) ).
tff(30,axiom,
~ ? [B_m: $i] : ( 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',conj_0) ).
tff(31,plain,
~ ? [B_m: $i] : ( 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(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
~ ? [B_m: $i] : ( 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(modus_ponens,[status(thm)],[31,29]) ).
tff(33,plain,
~ ? [B_m: $i] : ( 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(modus_ponens,[status(thm)],[32,29]) ).
tff(34,plain,
~ ? [B_m: $i] : ( 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(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
^ [B_m: $i] : refl($oeq(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)),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(bind,[status(th)],[]) ).
tff(36,plain,
! [B_m: $i] : ( 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(nnf-neg,[status(sab)],[34,35]) ).
tff(37,plain,
! [B_m: $i] : ( 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(modus_ponens,[status(thm)],[36,28]) ).
tff(38,plain,
( ~ ! [B_m: $i] : ( 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)) )
| ( 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))),tptp_fun_B_m_0(v_na____))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
$false,
inference(unit_resolution,[status(thm)],[38,37,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWW198+1 : TPTP v9.0.0. Released v5.2.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 11:14:40 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.91/1.10 % SZS status Theorem
% 0.91/1.10 % SZS output start Proof
% See solution above
% 0.91/1.17 % E exiting
%------------------------------------------------------------------------------