TSTP Solution File: ALG359-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG359-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 : Tue Sep 6 16:09:56 EDT 2022
% Result : Unsatisfiable 0.64s 0.76s
% Output : Proof 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 34
% Syntax : Number of formulae : 59 ( 21 unt; 13 typ; 0 def)
% Number of atoms : 155 ( 60 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 188 ( 88 ~; 82 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 8 >; 7 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 107 ( 96 !; 0 ?; 107 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_HOL_Oinverse__class_Odivide_type,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_RealVector_Oof__real_type,type,
c_RealVector_Oof__real: ( $i * $i ) > $i ).
tff(c_RealVector_Onorm__class_Onorm_type,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(v_b_type,type,
v_b: $i ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(v_na_____type,type,
v_na____: $i ).
tff(v_v_____type,type,
v_v____: $i ).
tff(c_NthRoot_Oroot_type,type,
c_NthRoot_Oroot: ( $i * $i ) > $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(class_RealVector_Oreal__algebra__1_type,type,
class_RealVector_Oreal__algebra__1: $i > $o ).
tff(class_Ring__and__Field_Ofield_type,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(class_Ring__and__Field_Odivision__by__zero_type,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(1,plain,
( ( c_Power_Opower__class_Opower(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),v_na____,tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) )
<=> ( c_Power_Opower__class_Opower(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),v_na____,tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
c_Power_Opower__class_Opower(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),v_na____,tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(3,plain,
c_Power_Opower__class_Opower(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),v_na____,tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
c_RealVector_Oof__real(c_Power_Opower__class_Opower(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),v_na____,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
( class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
<=> class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
tff(7,plain,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
^ [V_n: $i,V_x: $i,T_a: $i] :
refl(
( ( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Power_Opower__class_Opower(V_x,V_n,tc_RealDef_Oreal),T_a) = c_Power_Opower__class_Opower(c_RealVector_Oof__real(V_x,T_a),V_n,T_a) ) )
<=> ( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Power_Opower__class_Opower(V_x,V_n,tc_RealDef_Oreal),T_a) = c_Power_Opower__class_Opower(c_RealVector_Oof__real(V_x,T_a),V_n,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [V_n: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Power_Opower__class_Opower(V_x,V_n,tc_RealDef_Oreal),T_a) = c_Power_Opower__class_Opower(c_RealVector_Oof__real(V_x,T_a),V_n,T_a) ) )
<=> ! [V_n: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Power_Opower__class_Opower(V_x,V_n,tc_RealDef_Oreal),T_a) = c_Power_Opower__class_Opower(c_RealVector_Oof__real(V_x,T_a),V_n,T_a) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [V_n: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Power_Opower__class_Opower(V_x,V_n,tc_RealDef_Oreal),T_a) = c_Power_Opower__class_Opower(c_RealVector_Oof__real(V_x,T_a),V_n,T_a) ) )
<=> ! [V_n: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Power_Opower__class_Opower(V_x,V_n,tc_RealDef_Oreal),T_a) = c_Power_Opower__class_Opower(c_RealVector_Oof__real(V_x,T_a),V_n,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Power_Opower__class_Opower(V_x,V_n,tc_RealDef_Oreal),T_a) = c_Power_Opower__class_Opower(c_RealVector_Oof__real(V_x,T_a),V_n,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__power_0) ).
tff(12,plain,
! [V_n: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Power_Opower__class_Opower(V_x,V_n,tc_RealDef_Oreal),T_a) = c_Power_Opower__class_Opower(c_RealVector_Oof__real(V_x,T_a),V_n,T_a) ) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [V_n: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Power_Opower__class_Opower(V_x,V_n,tc_RealDef_Oreal),T_a) = c_Power_Opower__class_Opower(c_RealVector_Oof__real(V_x,T_a),V_n,T_a) ) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [V_n: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Power_Opower__class_Opower(V_x,V_n,tc_RealDef_Oreal),T_a) = c_Power_Opower__class_Opower(c_RealVector_Oof__real(V_x,T_a),V_n,T_a) ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( ( ~ ! [V_n: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Power_Opower__class_Opower(V_x,V_n,tc_RealDef_Oreal),T_a) = c_Power_Opower__class_Opower(c_RealVector_Oof__real(V_x,T_a),V_n,T_a) ) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_Power_Opower__class_Opower(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),v_na____,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_n: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Power_Opower__class_Opower(V_x,V_n,tc_RealDef_Oreal),T_a) = c_Power_Opower__class_Opower(c_RealVector_Oof__real(V_x,T_a),V_n,T_a) ) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_Power_Opower__class_Opower(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),v_na____,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
( ~ ! [V_n: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Power_Opower__class_Opower(V_x,V_n,tc_RealDef_Oreal),T_a) = c_Power_Opower__class_Opower(c_RealVector_Oof__real(V_x,T_a),V_n,T_a) ) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_Power_Opower__class_Opower(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),v_na____,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(17,plain,
( ~ ! [V_n: $i,V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Power_Opower__class_Opower(V_x,V_n,tc_RealDef_Oreal),T_a) = c_Power_Opower__class_Opower(c_RealVector_Oof__real(V_x,T_a),V_n,T_a) ) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_Power_Opower__class_Opower(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),v_na____,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
c_RealVector_Oof__real(c_Power_Opower__class_Opower(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),v_na____,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[17,14,7]) ).
tff(19,plain,
c_Power_Opower__class_Opower(c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_Power_Opower__class_Opower(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),v_na____,tc_RealDef_Oreal),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
c_Power_Opower__class_Opower(c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[19,4]) ).
tff(21,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
tff(24,plain,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
( class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
tff(27,plain,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
^ [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) )
<=> ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) )
<=> ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
^ [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
trans(
monotonicity(
rewrite(
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ) )),
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ) )),
rewrite(
( ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ) )),
( ( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) )
<=> ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,axiom,
! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__divide_0) ).
tff(34,plain,
! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[36,29]) ).
tff(38,plain,
( ( ~ ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) )
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____,c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) )
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____,c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ~ ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) )
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____,c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [V_n: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) )
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____,c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____,c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[40,37,27,24]) ).
tff(42,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____,c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[41,21]) ).
tff(43,plain,
( ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____,c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
<=> ( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____,c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,axiom,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____,c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(45,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____,c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
$false,
inference(unit_resolution,[status(thm)],[45,42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG359-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 29 15:54:00 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.64/0.76 % SZS status Unsatisfiable
% 0.64/0.76 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------