TSTP Solution File: SWW173+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW173+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 : Thu Sep 29 20:57:47 EDT 2022
% Result : Theorem 0.73s 0.78s
% Output : Proof 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 65
% Syntax : Number of formulae : 131 ( 48 unt; 20 typ; 0 def)
% Number of atoms : 366 ( 157 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 400 ( 169 ~; 144 |; 26 &)
% ( 49 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 15 >; 6 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 181 ( 156 !; 0 ?; 181 :)
% Comments :
%------------------------------------------------------------------------------
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i > $i ).
tff(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
tff(c_Rings_Oinverse__class_Odivide_type,type,
c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $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_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(tc_Int_Oint_type,type,
tc_Int_Oint: $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(v_x_type,type,
v_x: $i ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_Int_OPls_type,type,
c_Int_OPls: $i ).
tff(class_Fields_Ofield__inverse__zero_type,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
tff(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(class_Int_Onumber_type,type,
class_Int_Onumber: $i > $o ).
tff(class_Groups_Omonoid__mult_type,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(class_Int_Onumber__ring_type,type,
class_Int_Onumber__ring: $i > $o ).
tff(1,plain,
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) )
<=> ( c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) )
<=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) )
<=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__add__1) ).
tff(5,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),
inference(modus_ponens,[status(thm)],[5,2]) ).
tff(7,plain,
c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),
inference(modus_ponens,[status(thm)],[6,1]) ).
tff(8,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) = c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal)
<=> class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
tff(12,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_Fields_Ofield__inverse__zero(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) )
<=> ( ~ class_Fields_Ofield__inverse__zero(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Fields_Ofield__inverse__zero(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) )
<=> ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Fields_Ofield__inverse__zero(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Fields_Ofield__inverse__zero(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) )
<=> ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Fields_Ofield__inverse__zero(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
^ [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
rewrite(
( ( class_Fields_Ofield__inverse__zero(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) )
<=> ( ~ class_Fields_Ofield__inverse__zero(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) )
<=> ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Fields_Ofield__inverse__zero(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__divide) ).
tff(19,plain,
! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Fields_Ofield__inverse__zero(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Fields_Ofield__inverse__zero(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Fields_Ofield__inverse__zero(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Fields_Ofield__inverse__zero(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ( ~ ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Fields_Ofield__inverse__zero(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) )
| ~ class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) ) )
<=> ( ~ ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Fields_Ofield__inverse__zero(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) )
| ~ class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Fields_Ofield__inverse__zero(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) )
| ~ class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Fields_Ofield__inverse__zero(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) )
| ~ class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),
inference(unit_resolution,[status(thm)],[25,22,12]) ).
tff(27,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(monotonicity,[status(thm)],[8]) ).
tff(29,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
( class_Int_Onumber(tc_RealDef_Oreal)
<=> class_Int_Onumber(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
class_Int_Onumber(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber) ).
tff(32,plain,
class_Int_Onumber(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
( class_Groups_Omonoid__mult(tc_RealDef_Oreal)
<=> class_Groups_Omonoid__mult(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
tff(35,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
^ [V_w: $i,T_b: $i] :
refl(
( ( ~ class_Groups_Omonoid__mult(T_b)
| ~ class_Int_Onumber(T_b)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) )
<=> ( ~ class_Groups_Omonoid__mult(T_b)
| ~ class_Int_Onumber(T_b)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [V_w: $i,T_b: $i] :
( ~ class_Groups_Omonoid__mult(T_b)
| ~ class_Int_Onumber(T_b)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) )
<=> ! [V_w: $i,T_b: $i] :
( ~ class_Groups_Omonoid__mult(T_b)
| ~ class_Int_Onumber(T_b)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
^ [V_w: $i,T_b: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
<=> ~ ( ~ class_Groups_Omonoid__mult(T_b)
| ~ class_Int_Onumber(T_b) ) )),
( ~ ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
<=> ~ ~ ( ~ class_Groups_Omonoid__mult(T_b)
| ~ class_Int_Onumber(T_b) ) )),
rewrite(
( ~ ~ ( ~ class_Groups_Omonoid__mult(T_b)
| ~ class_Int_Onumber(T_b) )
<=> ( ~ class_Groups_Omonoid__mult(T_b)
| ~ class_Int_Onumber(T_b) ) )),
( ~ ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
<=> ( ~ class_Groups_Omonoid__mult(T_b)
| ~ class_Int_Onumber(T_b) ) )),
( ( ~ ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) )
<=> ( ~ class_Groups_Omonoid__mult(T_b)
| ~ class_Int_Onumber(T_b)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ) )),
rewrite(
( ( ~ class_Groups_Omonoid__mult(T_b)
| ~ class_Int_Onumber(T_b)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) )
<=> ( ~ class_Groups_Omonoid__mult(T_b)
| ~ class_Int_Onumber(T_b)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ) )),
( ( ~ ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) )
<=> ( ~ class_Groups_Omonoid__mult(T_b)
| ~ class_Int_Onumber(T_b)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [V_w: $i,T_b: $i] :
( ~ ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) )
<=> ! [V_w: $i,T_b: $i] :
( ~ class_Groups_Omonoid__mult(T_b)
| ~ class_Int_Onumber(T_b)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
^ [V_w: $i,T_b: $i] :
rewrite(
( ( ~ ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) )
<=> ( ~ ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [V_w: $i,T_b: $i] :
( ~ ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) )
<=> ! [V_w: $i,T_b: $i] :
( ~ ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
^ [V_w: $i,T_b: $i] :
rewrite(
( ( ~ ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) )
<=> ( ~ ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [V_w: $i,T_b: $i] :
( ~ ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) )
<=> ! [V_w: $i,T_b: $i] :
( ~ ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [V_w: $i,T_b: $i] :
( ~ ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) )
<=> ! [V_w: $i,T_b: $i] :
( ~ ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
^ [V_w: $i,T_b: $i] :
rewrite(
( ( ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) )
<=> ( ~ ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [V_w: $i,T_b: $i] :
( ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) )
<=> ! [V_w: $i,T_b: $i] :
( ~ ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,axiom,
! [V_w: $i,T_b: $i] :
( ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__square__number__of) ).
tff(48,plain,
! [V_w: $i,T_b: $i] :
( ~ ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [V_w: $i,T_b: $i] :
( ~ ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
! [V_w: $i,T_b: $i] :
( ~ ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ),
inference(modus_ponens,[status(thm)],[49,43]) ).
tff(51,plain,
! [V_w: $i,T_b: $i] :
( ~ ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ),
inference(modus_ponens,[status(thm)],[50,41]) ).
tff(52,plain,
! [V_w: $i,T_b: $i] :
( ~ ( class_Groups_Omonoid__mult(T_b)
& class_Int_Onumber(T_b) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [V_w: $i,T_b: $i] :
( ~ class_Groups_Omonoid__mult(T_b)
| ~ class_Int_Onumber(T_b)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ),
inference(modus_ponens,[status(thm)],[52,39]) ).
tff(54,plain,
! [V_w: $i,T_b: $i] :
( ~ class_Groups_Omonoid__mult(T_b)
| ~ class_Int_Onumber(T_b)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ),
inference(modus_ponens,[status(thm)],[53,37]) ).
tff(55,plain,
( ( ~ ! [V_w: $i,T_b: $i] :
( ~ class_Groups_Omonoid__mult(T_b)
| ~ class_Int_Onumber(T_b)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) )
| ~ class_Groups_Omonoid__mult(tc_RealDef_Oreal)
| ~ class_Int_Onumber(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) ) )
<=> ( ~ ! [V_w: $i,T_b: $i] :
( ~ class_Groups_Omonoid__mult(T_b)
| ~ class_Int_Onumber(T_b)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) )
| ~ class_Groups_Omonoid__mult(tc_RealDef_Oreal)
| ~ class_Int_Onumber(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
( ~ ! [V_w: $i,T_b: $i] :
( ~ class_Groups_Omonoid__mult(T_b)
| ~ class_Int_Onumber(T_b)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) )
| ~ class_Groups_Omonoid__mult(tc_RealDef_Oreal)
| ~ class_Int_Onumber(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
( ~ ! [V_w: $i,T_b: $i] :
( ~ class_Groups_Omonoid__mult(T_b)
| ~ class_Int_Onumber(T_b)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) )
| ~ class_Groups_Omonoid__mult(tc_RealDef_Oreal)
| ~ class_Int_Onumber(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) ) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),
inference(unit_resolution,[status(thm)],[57,54,35,32]) ).
tff(59,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
( class_Int_Onumber__ring(tc_RealDef_Oreal)
<=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(61,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
tff(62,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
^ [T_a: $i] :
refl(
( ( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) )
<=> ( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) )
<=> ! [T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
^ [T_a: $i] :
rewrite(
( ( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) )
<=> ( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) ) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) )
<=> ! [T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) )
<=> ! [T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
^ [T_a: $i] :
rewrite(
( ( class_Int_Onumber__ring(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) )
<=> ( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) ) )),
inference(bind,[status(th)],]) ).
tff(69,plain,
( ! [T_a: $i] :
( class_Int_Onumber__ring(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) )
<=> ! [T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,axiom,
! [T_a: $i] :
( class_Int_Onumber__ring(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__add__one__is__two) ).
tff(71,plain,
! [T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
! [T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) ),
inference(modus_ponens,[status(thm)],[72,66]) ).
tff(74,plain,
! [T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) ),
inference(modus_ponens,[status(thm)],[74,64]) ).
tff(76,plain,
( ( ~ ! [T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) )
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) )
<=> ( ~ ! [T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) )
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ~ ! [T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) )
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
( ~ ! [T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) )
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),
inference(unit_resolution,[status(thm)],[78,75,62]) ).
tff(80,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
^ [V_w: $i,T_a: $i] :
refl(
( ( ~ class_Int_Onumber__ring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ) )
<=> ( ~ class_Int_Onumber__ring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ) ) )),
inference(bind,[status(th)],]) ).
tff(83,plain,
( ! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ) )
<=> ! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ) )
<=> ! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
^ [V_w: $i,T_a: $i] :
rewrite(
( ( class_Int_Onumber__ring(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ) )
<=> ( ~ class_Int_Onumber__ring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [V_w: $i,T_a: $i] :
( class_Int_Onumber__ring(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ) )
<=> ! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,axiom,
! [V_w: $i,T_a: $i] :
( class_Int_Onumber__ring(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__number__of__Bit0) ).
tff(88,plain,
! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ) ),
inference(modus_ponens,[status(thm)],[90,83]) ).
tff(92,plain,
( ( ~ ! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ) )
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) ) )
<=> ( ~ ! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ) )
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ~ ! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ) )
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
( ~ ! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ) )
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) ) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),
inference(unit_resolution,[status(thm)],[94,91,62]) ).
tff(96,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),
inference(transitivity,[status(thm)],[96,81,59,29]) ).
tff(98,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(monotonicity,[status(thm)],[8]) ).
tff(99,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),
inference(monotonicity,[status(thm)],[99,97]) ).
tff(101,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(transitivity,[status(thm)],[100,27,9]) ).
tff(102,plain,
( ( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) )
<=> ( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
( ( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) )
<=> ( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
( ( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) )
<=> ( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) )
<=> ( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,axiom,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(107,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),
inference(modus_ponens,[status(thm)],[107,104]) ).
tff(109,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(modus_ponens,[status(thm)],[108,103]) ).
tff(110,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(modus_ponens,[status(thm)],[109,102]) ).
tff(111,plain,
$false,
inference(unit_resolution,[status(thm)],[110,101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW173+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 12:14:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.73/0.78 % SZS status Theorem
% 0.73/0.78 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------