%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG434-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 04:59:06 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.49s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 20
% Syntax : Number of formulae : 40 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 214 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 314 ( 149 ~; 145 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 97 ( 88 !; 0 ?; 97 :)
% Comments :
%------------------------------------------------------------------------------
tff(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_Ring__and__Field_Odvd__class_Odvd_type,type,
c_Ring__and__Field_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(c_Polynomial_Osmult_type,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(v_q_type,type,
v_q: $i ).
tff(v_a_type,type,
v_a: $i ).
tff(v_p_type,type,
v_p: $i ).
tff(1,plain,
^ [T_1: $i] :
refl(( ( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
<=> ( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
<=> ! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
<=> ! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).
tff(5,plain,
! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
tff(10,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) )
<=> ( ~ ! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [T_1: $i] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) )
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
<=> ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(17,plain,
~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_q,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
<=> c_Ring__and__Field_Odvd__class_Odvd(v_q,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
c_Ring__and__Field_Odvd__class_Odvd(v_q,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(20,plain,
c_Ring__and__Field_Odvd__class_Odvd(v_q,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
<=> c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pq_0) ).
tff(23,plain,
c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
trans(monotonicity(rewrite(( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) ) )),
( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) )),
rewrite(( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) ) )),
( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
tff(30,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) )
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_q,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) )
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_q,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_q,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_q,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_q,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) )
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_q,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_q,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) )
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_q,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(transitivity,[status(thm)],[36,34]) ).
tff(38,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_q,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a) )
| c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_q,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
$false,
inference(unit_resolution,[status(thm)],[39,33,23,20,17,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG434-1 : TPTP v9.0.0. Released v4.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Jun 19 11:14:08 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.20/0.49 % SZS status Unsatisfiable
% 0.20/0.49 % SZS output start Proof
% See solution above
% 0.20/0.51 % E exiting
%------------------------------------------------------------------------------