TSTP Solution File: ALG379-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG379-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 16:10:01 EDT 2022
% Result : Unsatisfiable 0.60s 0.68s
% Output : Proof 0.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 38
% Syntax : Number of formulae : 63 ( 16 unt; 14 typ; 0 def)
% Number of atoms : 301 ( 155 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 456 ( 220 ~; 207 |; 0 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 9 >; 7 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 105 ( 95 !; 0 ?; 105 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(c_HOL_Ouminus__class_Ouminus_type,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(v_s_____type,type,
v_s____: $i ).
tff(c_RealVector_Onorm__class_Onorm_type,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).
tff(v_z_____type,type,
v_z____: $i ).
tff(v_p_type,type,
v_p: $i ).
tff(class_Int_Onumber__ring_type,type,
class_Int_Onumber__ring: $i > $o ).
tff(class_Ring__and__Field_Oidom_type,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__group__add__abs_type,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
tff(c_HOL_Oabs__class_Oabs_type,type,
c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(1,plain,
( class_Int_Onumber__ring(tc_RealDef_Oreal)
<=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
tff(3,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
<=> class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
tff(6,plain,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) )
<=> ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(9,plain,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(
( ( ( V_x = V_y )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_x = V_y )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a) )
<=> ( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a) ) )),
( ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
rewrite(
( ( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
( ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
( ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_x = V_y ) )
<=> ( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_x = V_y ) ) )),
rewrite(
( ( ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_x = V_y ) )
<=> ( ( V_x = V_y )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
( ( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_x = V_y ) )
<=> ( ( V_x = V_y )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_x = V_y ) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
tff(16,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) )
| ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) )
| ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ( ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) )
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
<=> ( ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) )
| ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) )
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) )
| ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) )
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) )
| ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) )
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Ring__and__Field_Oidom(T_a)
| ( c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal) )
| ~ class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[25,19,9,6,3]) ).
tff(27,plain,
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
<=> class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).
tff(29,plain,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
( ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(32,plain,
c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
^ [V_a: $i,T_a: $i] :
rewrite(
( ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
tff(39,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ( ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
<=> ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
inference(transitivity,[status(thm)],[45,43]) ).
tff(47,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_HOL_Ozero__class_Ozero(T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ( c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
$false,
inference(unit_resolution,[status(thm)],[48,42,32,29,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ALG379-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 29 16:26:35 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.60/0.68 % SZS status Unsatisfiable
% 0.60/0.68 % SZS output start Proof
% See solution above
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