%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW174+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:36:34 AM UTC 2025
% Result : Theorem 0.51s 0.69s
% Output : Proof 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 29
% Syntax : Number of formulae : 67 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 198 ( 113 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 206 ( 82 ~; 76 |; 0 &)
% ( 39 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 105 ( 93 !; 0 ?; 105 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: ( $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_Int_OPls_type,type,
c_Int_OPls: $i ).
tff(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(class_Int_Onumber__ring_type,type,
class_Int_Onumber__ring: $i > $o ).
tff(c_NthRoot_Osqrt_type,type,
c_NthRoot_Osqrt: $i > $i ).
tff(1,plain,
( class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
<=> class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
tff(3,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_x: $i,T_a: $i] :
refl(( ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [V_x: $i,T_a: $i] :
rewrite(( ( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_x: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_x: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = c_Power_Opower__class_Opower(T_a,V_x,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_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
tff(10,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( 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))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,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)))) ) )
<=> ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( 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))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,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(15,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( 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))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,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(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( 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))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,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)],[15,14]) ).
tff(17,plain,
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))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,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(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
( class_Int_Onumber__ring(tc_RealDef_Oreal)
<=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
tff(20,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,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_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(22,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)],[21]) ).
tff(23,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(24,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(25,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)],[24]) ).
tff(26,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(27,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)],[26,25]) ).
tff(28,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)],[27,23]) ).
tff(29,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(skolemize,[status(sab)],[28]) ).
tff(30,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)],[29,22]) ).
tff(31,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))) ) )
| ~ 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_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))) ) )
| ~ 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_Int_OPls))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,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))) ) )
| ~ 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_Int_OPls))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,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))) ) )
| ~ 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_Int_OPls))) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,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_Int_OPls))),
inference(unit_resolution,[status(thm)],[33,30,20]) ).
tff(35,plain,
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_Int_OPls)))) = 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))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
^ [V_w: $i,T_a: $i] :
refl(( ( ~ class_Int_Onumber__ring(T_a)
| ( 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)
| ( 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(37,plain,
( ! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( 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)
| ( 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)],[36]) ).
tff(38,plain,
( ! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( 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)
| ( 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(39,plain,
^ [V_w: $i,T_a: $i] :
rewrite(( ( class_Int_Onumber__ring(T_a)
=> ( 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)
| ( 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(40,plain,
( ! [V_w: $i,T_a: $i] :
( class_Int_Onumber__ring(T_a)
=> ( 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)
| ( 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)],[39]) ).
tff(41,axiom,
! [V_w: $i,T_a: $i] :
( class_Int_Onumber__ring(T_a)
=> ( 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(42,plain,
! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( 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)],[41,40]) ).
tff(43,plain,
! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( 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)],[42,38]) ).
tff(44,plain,
! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( 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)],[43]) ).
tff(45,plain,
! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( 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)],[44,37]) ).
tff(46,plain,
( ( ~ ! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( 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)
| ( 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_Int_OPls)))) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) )
<=> ( ~ ! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( 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)
| ( 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_Int_OPls)))) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( 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)
| ( 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_Int_OPls)))) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [V_w: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( 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)
| ( 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_Int_OPls)))) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
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_Int_OPls)))) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(unit_resolution,[status(thm)],[48,45,20]) ).
tff(50,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = 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_Int_OPls)))),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,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(transitivity,[status(thm)],[50,35,17]) ).
tff(52,plain,
^ [V_ya_2: $i,V_xa_2: $i] :
refl(( ( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2) )
<=> ( V_xa_2 = V_ya_2 ) )
<=> ( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2) )
<=> ( V_xa_2 = V_ya_2 ) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [V_ya_2: $i,V_xa_2: $i] :
( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2) )
<=> ( V_xa_2 = V_ya_2 ) )
<=> ! [V_ya_2: $i,V_xa_2: $i] :
( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2) )
<=> ( V_xa_2 = V_ya_2 ) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [V_ya_2: $i,V_xa_2: $i] :
( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2) )
<=> ( V_xa_2 = V_ya_2 ) )
<=> ! [V_ya_2: $i,V_xa_2: $i] :
( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2) )
<=> ( V_xa_2 = V_ya_2 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,axiom,
! [V_ya_2: $i,V_xa_2: $i] :
( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2) )
<=> ( V_xa_2 = V_ya_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__eq__iff) ).
tff(56,plain,
! [V_ya_2: $i,V_xa_2: $i] :
( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2) )
<=> ( V_xa_2 = V_ya_2 ) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [V_ya_2: $i,V_xa_2: $i] :
( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2) )
<=> ( V_xa_2 = V_ya_2 ) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [V_ya_2: $i,V_xa_2: $i] :
( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2) )
<=> ( V_xa_2 = V_ya_2 ) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
( ~ ! [V_ya_2: $i,V_xa_2: $i] :
( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2) )
<=> ( V_xa_2 = V_ya_2 ) )
| ( ( c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,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_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,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(quant_inst,[status(thm)],[]) ).
tff(60,plain,
( ( c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,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_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,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(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
( ( c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,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_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,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(62,axiom,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,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(63,plain,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,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)],[62,61]) ).
tff(64,plain,
( ~ ( ( c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,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_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,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_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,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_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(tc_RealDef_Oreal,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(tautology,[status(thm)],[]) ).
tff(65,plain,
( ~ ( ( c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,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_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,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_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(tc_RealDef_Oreal,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(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(tc_RealDef_Oreal,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(unit_resolution,[status(thm)],[65,60]) ).
tff(67,plain,
$false,
inference(unit_resolution,[status(thm)],[66,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW174+1 : TPTP v9.0.0. Released v5.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 11:14:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.51/0.69 % SZS status Theorem
% 0.51/0.69 % SZS output start Proof
% See solution above
% 0.57/0.75 % E exiting
%------------------------------------------------------------------------------