%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW285+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:36:46 AM UTC 2025
% Result : Theorem 0.48s 0.71s
% Output : Proof 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 46
% Syntax : Number of formulae : 115 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 331 ( 119 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 373 ( 169 ~; 145 |; 0 &)
% ( 41 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 12 ( 12 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 136 ( 120 !; 0 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
tff(v_q_type,type,
v_q: $i ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(class_Power_Opower_type,type,
class_Power_Opower: $i > $o ).
tff(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(c_Polynomial_Odegree_type,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(v_p_type,type,
v_p: $i ).
tff(class_Groups_Ozero_type,type,
class_Groups_Ozero: $i > $o ).
tff(v_r_____type,type,
v_r____: $i ).
tff(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(class_Rings_Ocomm__semiring__0_type,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(class_Rings_Ozero__neq__one_type,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(1,plain,
^ [T_1: $i] :
refl(( ( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
<=> ( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
<=> ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
<=> ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [T_1: $i] :
rewrite(( ( class_Rings_Ocomm__semiring__1(T_1)
=> class_Power_Opower(tc_Polynomial_Opoly(T_1)) )
<=> ( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Power_Opower(tc_Polynomial_Opoly(T_1)) )
<=> ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Power_Opower(tc_Polynomial_Opoly(T_1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).
tff(7,plain,
! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
<=> class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
tff(13,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) )
<=> ( ~ ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [T_1: $i] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( ~ class_Power_Opower(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) )
<=> ( ~ class_Power_Opower(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
^ [V_a: $i,T_a: $i] :
rewrite(( ( class_Power_Opower(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) )
<=> ( ~ class_Power_Opower(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [V_a: $i,T_a: $i] :
( class_Power_Opower(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [V_a: $i,T_a: $i] :
( class_Power_Opower(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0) ).
tff(24,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Power_Opower(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
( ~ class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(unit_resolution,[status(thm)],[30,27]) ).
tff(32,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[31,17]) ).
tff(33,plain,
( ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pe) ).
tff(35,plain,
v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
( class_Groups_Ozero(tc_Complex_Ocomplex)
<=> class_Groups_Ozero(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
tff(40,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
^ [T_a: $i] :
refl(( ( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
<=> ( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
<=> ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
<=> ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
^ [T_a: $i] :
rewrite(( ( class_Groups_Ozero(T_a)
=> ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
<=> ( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [T_a: $i] :
( class_Groups_Ozero(T_a)
=> ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
<=> ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
! [T_a: $i] :
( class_Groups_Ozero(T_a)
=> ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__0) ).
tff(47,plain,
! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
( ( ~ ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Groups_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
<=> ( ~ ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Groups_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Groups_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [T_a: $i] :
( ~ class_Groups_Ozero(T_a)
| ( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Groups_Ozero(tc_Complex_Ocomplex)
| ( c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(unit_resolution,[status(thm)],[53,50,40]) ).
tff(55,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),
inference(transitivity,[status(thm)],[55,37]) ).
tff(57,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),v_r____) )
<=> ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),v_r____) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,axiom,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),v_r____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r) ).
tff(61,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),v_r____),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),v_r____) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p,
inference(symmetry,[status(thm)],[35]) ).
tff(64,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p) = hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),v_r____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_r____),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_r____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),v_r____),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
( class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
<=> class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
tff(70,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
^ [V_q: $i,T_a: $i] :
refl(( ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
^ [V_q: $i,T_a: $i] :
rewrite(( ( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [V_q: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,axiom,
! [V_q: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__poly__0__left) ).
tff(77,plain,
! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[79,72]) ).
tff(81,plain,
( ( ~ ! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_r____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
<=> ( ~ ! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_r____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,plain,
( ~ ! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_r____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
( ~ ! [V_q: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_r____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_r____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[83,80,70]) ).
tff(85,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),v_r____),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(transitivity,[status(thm)],[85,67,62,58,32]) ).
tff(87,plain,
^ [T_1: $i] :
refl(( ( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
<=> ( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) )),
inference(bind,[status(th)],[]) ).
tff(88,plain,
( ! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
<=> ! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
( ! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
<=> ! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,plain,
^ [T_1: $i] :
rewrite(( ( class_Rings_Ocomm__semiring__1(T_1)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) )
<=> ( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) )),
inference(bind,[status(th)],[]) ).
tff(91,plain,
( ! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) )
<=> ! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,axiom,
! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
tff(93,plain,
! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[93,89]) ).
tff(95,plain,
! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(skolemize,[status(sab)],[94]) ).
tff(96,plain,
! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(modus_ponens,[status(thm)],[95,88]) ).
tff(97,plain,
( ( ~ ! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) )
<=> ( ~ ! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,plain,
( ~ ! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [T_1: $i] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[99,13,96]) ).
tff(101,plain,
^ [T_a: $i] :
refl(( ( ~ class_Rings_Ozero__neq__one(T_a)
| ( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) )
<=> ( ~ class_Rings_Ozero__neq__one(T_a)
| ( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(102,plain,
( ! [T_a: $i] :
( ~ class_Rings_Ozero__neq__one(T_a)
| ( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) )
<=> ! [T_a: $i] :
( ~ class_Rings_Ozero__neq__one(T_a)
| ( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,plain,
( ! [T_a: $i] :
( ~ class_Rings_Ozero__neq__one(T_a)
| ( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) )
<=> ! [T_a: $i] :
( ~ class_Rings_Ozero__neq__one(T_a)
| ( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
^ [T_a: $i] :
rewrite(( ( class_Rings_Ozero__neq__one(T_a)
=> ( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) )
<=> ( ~ class_Rings_Ozero__neq__one(T_a)
| ( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(105,plain,
( ! [T_a: $i] :
( class_Rings_Ozero__neq__one(T_a)
=> ( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) )
<=> ! [T_a: $i] :
( ~ class_Rings_Ozero__neq__one(T_a)
| ( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,axiom,
! [T_a: $i] :
( class_Rings_Ozero__neq__one(T_a)
=> ( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__neq__one) ).
tff(107,plain,
! [T_a: $i] :
( ~ class_Rings_Ozero__neq__one(T_a)
| ( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
! [T_a: $i] :
( ~ class_Rings_Ozero__neq__one(T_a)
| ( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[107,103]) ).
tff(109,plain,
! [T_a: $i] :
( ~ class_Rings_Ozero__neq__one(T_a)
| ( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ),
inference(skolemize,[status(sab)],[108]) ).
tff(110,plain,
! [T_a: $i] :
( ~ class_Rings_Ozero__neq__one(T_a)
| ( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ),
inference(modus_ponens,[status(thm)],[109,102]) ).
tff(111,plain,
( ( ~ ! [T_a: $i] :
( ~ class_Rings_Ozero__neq__one(T_a)
| ( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
<=> ( ~ ! [T_a: $i] :
( ~ class_Rings_Ozero__neq__one(T_a)
| ( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(112,plain,
( ~ ! [T_a: $i] :
( ~ class_Rings_Ozero__neq__one(T_a)
| ( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(113,plain,
( ~ ! [T_a: $i] :
( ~ class_Rings_Ozero__neq__one(T_a)
| ( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[113,110,100]) ).
tff(115,plain,
$false,
inference(unit_resolution,[status(thm)],[114,86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWW285+1 : TPTP v9.0.0. Released v5.2.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 11:23:26 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.48/0.71 % SZS status Theorem
% 0.48/0.71 % SZS output start Proof
% See solution above
% 0.57/0.78 % E exiting
%------------------------------------------------------------------------------