%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW194+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 0.54s 0.70s
% Output : Proof 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 39
% Syntax : Number of formulae : 89 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 366 ( 56 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 448 ( 191 ~; 184 |; 0 &)
% ( 43 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 20 ( 20 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 169 ( 151 !; 0 ?; 169 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i > $i ).
tff(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
tff(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(c_Groups_Oabs__class_Oabs_type,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(v_x_____type,type,
v_x____: $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(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(class_Rings_Osemiring__1_type,type,
class_Rings_Osemiring__1: $i > $o ).
tff(class_Groups_Omonoid__mult_type,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(class_Groups_Oordered__ab__group__add__abs_type,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
tff(class_Rings_Olinordered__semidom_type,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(1,plain,
( class_Rings_Osemiring__1(tc_RealDef_Oreal)
<=> class_Rings_Osemiring__1(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
class_Rings_Osemiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__1) ).
tff(3,plain,
class_Rings_Osemiring__1(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [T_a: $i] :
refl(( ( ~ class_Rings_Osemiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) )
<=> ( ~ class_Rings_Osemiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [T_a: $i] :
( ~ class_Rings_Osemiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) )
<=> ! [T_a: $i] :
( ~ class_Rings_Osemiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [T_a: $i] :
( ~ class_Rings_Osemiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) )
<=> ! [T_a: $i] :
( ~ class_Rings_Osemiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [T_a: $i] :
rewrite(( ( class_Rings_Osemiring__1(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) )
<=> ( ~ class_Rings_Osemiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [T_a: $i] :
( class_Rings_Osemiring__1(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) )
<=> ! [T_a: $i] :
( ~ class_Rings_Osemiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [T_a: $i] :
( class_Rings_Osemiring__1(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__power2) ).
tff(10,plain,
! [T_a: $i] :
( ~ class_Rings_Osemiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [T_a: $i] :
( ~ class_Rings_Osemiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [T_a: $i] :
( ~ class_Rings_Osemiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [T_a: $i] :
( ~ class_Rings_Osemiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [T_a: $i] :
( ~ class_Rings_Osemiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Rings_Osemiring__1(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) )
<=> ( ~ ! [T_a: $i] :
( ~ class_Rings_Osemiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Rings_Osemiring__1(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [T_a: $i] :
( ~ class_Rings_Osemiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Rings_Osemiring__1(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [T_a: $i] :
( ~ class_Rings_Osemiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Rings_Osemiring__1(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(symmetry,[status(thm)],[17]) ).
tff(19,plain,
( class_Groups_Omonoid__mult(tc_RealDef_Oreal)
<=> class_Groups_Omonoid__mult(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
tff(21,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
^ [V_n: $i,T_a: $i] :
refl(( ( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) )
<=> ( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [V_n: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) )
<=> ! [V_n: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [V_n: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) )
<=> ! [V_n: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
^ [V_n: $i,T_a: $i] :
rewrite(( ( class_Groups_Omonoid__mult(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) )
<=> ( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [V_n: $i,T_a: $i] :
( class_Groups_Omonoid__mult(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) )
<=> ! [V_n: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,axiom,
! [V_n: $i,T_a: $i] :
( class_Groups_Omonoid__mult(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one) ).
tff(28,plain,
! [V_n: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [V_n: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
! [V_n: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [V_n: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[30,23]) ).
tff(32,plain,
( ( ~ ! [V_n: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Groups_Omonoid__mult(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_n: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Groups_Omonoid__mult(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [V_n: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Groups_Omonoid__mult(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [V_n: $i,T_a: $i] :
( ~ class_Groups_Omonoid__mult(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Groups_Omonoid__mult(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[34,31,21]) ).
tff(36,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(transitivity,[status(thm)],[35,18]) ).
tff(37,plain,
( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
<=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__2__eq__2) ).
tff(39,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(monotonicity,[status(thm)],[41,36]) ).
tff(43,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) ),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
<=> ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
<=> ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(47,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(modus_ponens,[status(thm)],[47,44]) ).
tff(49,plain,
( class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
<=> class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
tff(51,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) )
<=> ( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
^ [V_a: $i,T_a: $i] :
rewrite(( ( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) )
<=> ( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [V_a: $i,T_a: $i] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,axiom,
! [V_a: $i,T_a: $i] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__zero) ).
tff(58,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),
inference(unit_resolution,[status(thm)],[64,61,51]) ).
tff(66,plain,
( class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
<=> class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
tff(68,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
^ [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(( ( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
<=> ( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )),
inference(bind,[status(th)],[]) ).
tff(70,plain,
( ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
<=> ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
<=> ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,plain,
^ [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless__eq(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)) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| c_Orderings_Oord__class_Oless__eq(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)) ) )),
( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless__eq(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)) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| c_Orderings_Oord__class_Oless__eq(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)) ) ) )),
rewrite(( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| c_Orderings_Oord__class_Oless__eq(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)) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )),
( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless__eq(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)) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )),
( ( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless__eq(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_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) ) )),
rewrite(( ( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )),
( ( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless__eq(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)) ) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )),
inference(bind,[status(th)],[]) ).
tff(73,plain,
( ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless__eq(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] :
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,axiom,
! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless__eq(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/sandbox/benchmark/theBenchmark.p',fact_power__mono) ).
tff(75,plain,
! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ),
inference(modus_ponens,[status(thm)],[77,70]) ).
tff(79,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096abs_A_I2_A_K_Ax_J_A_060_061_A1_096) ).
tff(81,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
( ( ~ ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) )
<=> ( ~ ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))) )
<=> ( ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
( ( ~ ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))) )
<=> ( ~ ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) ) ),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
( ( ~ ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))) )
<=> ( ~ ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) ) ),
inference(transitivity,[status(thm)],[84,82]) ).
tff(86,plain,
( ~ ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
( ~ ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,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_Int_OPls)))),v_x____))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(unit_resolution,[status(thm)],[87,81,78,68,65]) ).
tff(89,plain,
$false,
inference(unit_resolution,[status(thm)],[88,48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW194+1 : TPTP v9.0.0. Released v5.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 11:14:25 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.54/0.70 % SZS status Theorem
% 0.54/0.70 % SZS output start Proof
% See solution above
% 0.59/0.76 % E exiting
%------------------------------------------------------------------------------