TSTP Solution File: ALG421-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG421-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 16:10:11 EDT 2022
% Result : Unsatisfiable 0.41s 0.61s
% Output : Proof 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 30
% Syntax : Number of formulae : 51 ( 17 unt; 12 typ; 0 def)
% Number of atoms : 97 ( 50 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 104 ( 48 ~; 44 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 7 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 104 ( 96 !; 0 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_Polynomial_Odegree_type,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(v_s_____type,type,
v_s____: $i ).
tff(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_r_____type,type,
v_r____: $i ).
tff(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(v_u_____type,type,
v_u____: $i ).
tff(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
tff(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring__0_type,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(1,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(2,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
tff(3,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_n: $i,V_x: $i,T_a: $i,V_p: $i] :
refl(
( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Opoly(c_Power_Opower__class_Opower(V_p,V_n,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(V_p,V_x,T_a),V_n,T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Opoly(c_Power_Opower__class_Opower(V_p,V_n,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(V_p,V_x,T_a),V_n,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_n: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Opoly(c_Power_Opower__class_Opower(V_p,V_n,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(V_p,V_x,T_a),V_n,T_a) ) )
<=> ! [V_n: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Opoly(c_Power_Opower__class_Opower(V_p,V_n,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(V_p,V_x,T_a),V_n,T_a) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_n: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Opoly(c_Power_Opower__class_Opower(V_p,V_n,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(V_p,V_x,T_a),V_n,T_a) ) )
<=> ! [V_n: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Opoly(c_Power_Opower__class_Opower(V_p,V_n,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(V_p,V_x,T_a),V_n,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [V_n: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Opoly(c_Power_Opower__class_Opower(V_p,V_n,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(V_p,V_x,T_a),V_n,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__power_0) ).
tff(8,plain,
! [V_n: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Opoly(c_Power_Opower__class_Opower(V_p,V_n,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(V_p,V_x,T_a),V_n,T_a) ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_n: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Opoly(c_Power_Opower__class_Opower(V_p,V_n,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(V_p,V_x,T_a),V_n,T_a) ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_n: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Opoly(c_Power_Opower__class_Opower(V_p,V_n,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(V_p,V_x,T_a),V_n,T_a) ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V_n: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Opoly(c_Power_Opower__class_Opower(V_p,V_n,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(V_p,V_x,T_a),V_n,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Power_Opower__class_Opower(v_r____,c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x,tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_n: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Opoly(c_Power_Opower__class_Opower(V_p,V_n,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(V_p,V_x,T_a),V_n,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Power_Opower__class_Opower(v_r____,c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x,tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [V_n: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Opoly(c_Power_Opower__class_Opower(V_p,V_n,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(V_p,V_x,T_a),V_n,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Power_Opower__class_Opower(v_r____,c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x,tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [V_n: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_Polynomial_Opoly(c_Power_Opower__class_Opower(V_p,V_n,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(V_p,V_x,T_a),V_n,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Power_Opower__class_Opower(v_r____,c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x,tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
c_Polynomial_Opoly(c_Power_Opower__class_Opower(v_r____,c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x,tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( ( c_Power_Opower__class_Opower(v_r____,c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(v_s____,v_u____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( c_Power_Opower__class_Opower(v_r____,c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(v_s____,v_u____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
c_Power_Opower__class_Opower(v_r____,c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(v_s____,v_u____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_u_0) ).
tff(17,plain,
c_Power_Opower__class_Opower(v_r____,c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(v_s____,v_u____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
c_Polynomial_Opoly(c_Power_Opower__class_Opower(v_r____,c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x,tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(v_s____,v_u____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x,tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(v_s____,v_u____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x,tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Power_Opower__class_Opower(v_r____,c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x,tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
tff(22,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
^ [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
refl(
( ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) )
<=> ! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) )
<=> ! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__mult_0) ).
tff(27,plain,
! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
( ( ~ ! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(v_s____,v_u____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(v_s____,v_u____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ~ ! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(v_s____,v_u____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
( ~ ! [V_q: $i,V_x: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(v_s____,v_u____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(v_s____,v_u____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[32,29,22]) ).
tff(34,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(v_s____,v_u____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x,tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[34,19,14]) ).
tff(36,plain,
( ( c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
<=> ( c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(38,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
$false,
inference(unit_resolution,[status(thm)],[38,35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG421-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 29 17:15:59 EDT 2022
% 0.13/0.34 % 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.
% 0.41/0.61 % SZS status Unsatisfiable
% 0.41/0.61 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------