%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG424-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 04:59:05 AM UTC 2025
% Result : Unsatisfiable 0.48s 0.66s
% Output : Proof 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 17
% Syntax : Number of formulae : 37 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 193 ( 132 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 279 ( 131 ~; 131 |; 0 &)
% ( 17 <=>; 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 : 0 ( 0 >; 0 *; 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_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_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)) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,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(6,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)),
inference(modus_ponens,[status(thm)],[5,4]) ).
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))
| ( 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(8,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(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) ) ),
inference(modus_ponens,[status(thm)],[8,7]) ).
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) ) ),
inference(modus_ponens,[status(thm)],[9,7]) ).
tff(11,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)],[10,7]) ).
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)],[11,7]) ).
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)],[12,7]) ).
tff(14,plain,
c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(unit_resolution,[status(thm)],[13,6]) ).
tff(15,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(16,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(17,plain,
c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,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(19,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)],[18]) ).
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(rewrite,[status(thm)],[]) ).
tff(21,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(22,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)],[21]) ).
tff(23,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(24,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)],[23,22]) ).
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)],[24,20]) ).
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(skolemize,[status(sab)],[25]) ).
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(modus_ponens,[status(thm)],[26,19]) ).
tff(28,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(29,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(30,plain,
v_pa____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,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(32,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(33,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)],[32]) ).
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(transitivity,[status(thm)],[33,31]) ).
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) ) ),
inference(quant_inst,[status(thm)],[]) ).
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) ) )
| ( 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)],[35,34]) ).
tff(37,plain,
$false,
inference(unit_resolution,[status(thm)],[36,30,27,17,14,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : ALG424-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 11:14:41 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.48/0.66 % SZS status Unsatisfiable
% 0.48/0.66 % SZS output start Proof
% See solution above
% 0.52/0.71 % E exiting
%------------------------------------------------------------------------------