TSTP Solution File: ALG424-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG424-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 16:10:12 EDT 2022
% Result : Unsatisfiable 0.56s 0.66s
% Output : Proof 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 31
% Syntax : Number of formulae : 51 ( 12 unt; 13 typ; 0 def)
% Number of atoms : 199 ( 138 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 281 ( 128 ~; 132 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 7 >; 8 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 63 ( 57 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
tff(class_Ring__and__Field_Oidom_type,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_Polynomial_Oorder_type,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(v_pa_____type,type,
v_pa____: $i ).
tff(v_a_____type,type,
v_a____: $i ).
tff(c_Ring__and__Field_Odvd__class_Odvd_type,type,
c_Ring__and__Field_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $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_qa_____type,type,
v_qa____: $i ).
tff(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).
tff(1,plain,
( class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
tff(3,plain,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) )
<=> ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ( $false
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
~ c_Ring__and__Field_Odvd__class_Odvd(v_pa____,c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(7,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_pa____,c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
<=> $false ),
inference(iff_false,[status(thm)],[6]) ).
tff(8,plain,
( ( c_Ring__and__Field_Odvd__class_Odvd(v_pa____,c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ( $false
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ) ) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
( ( c_Ring__and__Field_Odvd__class_Odvd(v_pa____,c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(transitivity,[status(thm)],[8,5]) ).
tff(10,plain,
( ( c_Ring__and__Field_Odvd__class_Odvd(v_pa____,c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ( c_Ring__and__Field_Odvd__class_Odvd(v_pa____,c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(v_pa____,c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_03) ).
tff(12,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_pa____,c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_pa____,c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(modus_ponens,[status(thm)],[12,10]) ).
tff(14,plain,
c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(modus_ponens,[status(thm)],[14,4]) ).
tff(16,plain,
( ( c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).
tff(18,plain,
c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
^ [V_a: $i,T_a: $i,V_p: $i] :
refl(
( ( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
^ [V_a: $i,T_a: $i,V_p: $i] :
trans(
monotonicity(
rewrite(
( ( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ) ) )),
( ( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ) )),
rewrite(
( ( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ) ) )),
( ( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) )
<=> ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
tff(25,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
( ( v_pa____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( v_pa____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
v_pa____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pne_0) ).
tff(31,plain,
v_pa____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
| ( v_pa____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
| ( v_pa____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ( ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( v_pa____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ( ( v_pa____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( v_pa____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
| ( v_pa____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ) ) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( v_pa____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
| ( v_pa____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ) ) ),
inference(transitivity,[status(thm)],[34,32]) ).
tff(36,plain,
( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( v_pa____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ( c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
( ~ ! [V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ( V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat) ) )
| ( v_pa____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
$false,
inference(unit_resolution,[status(thm)],[37,31,28,18,15,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ALG424-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n023.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 : Mon Aug 29 17:38:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.20/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.34 Usage: tptp [options] [-file:]file
% 0.20/0.34 -h, -? prints this message.
% 0.20/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.34 -m, -model generate model.
% 0.20/0.34 -p, -proof generate proof.
% 0.20/0.34 -c, -core generate unsat core of named formulas.
% 0.20/0.34 -st, -statistics display statistics.
% 0.20/0.34 -t:timeout set timeout (in second).
% 0.20/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.34 -<param>:<value> configuration parameter and value.
% 0.20/0.34 -o:<output-file> file to place output in.
% 0.56/0.66 % SZS status Unsatisfiable
% 0.56/0.66 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------