%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW275+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:36:45 AM UTC 2025
% Result : Theorem 0.49s 0.71s
% Output : Proof 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 24
% Syntax : Number of formulae : 58 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 169 ( 59 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 183 ( 78 ~; 74 |; 1 &)
% ( 21 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-3 aty)
% Number of variables : 119 ( 105 !; 0 ?; 119 :)
% Comments :
%------------------------------------------------------------------------------
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Groups_Ominus__class_Ominus_type,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $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(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(v_na_____type,type,
v_na____: $i ).
tff(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
tff(c_Polynomial_OpCons_type,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
tff(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(c_Groups_Ouminus__class_Ouminus_type,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(v_r_____type,type,
v_r____: $i ).
tff(1,plain,
^ [T_1: $i] :
refl(( ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
<=> ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
<=> ! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(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_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
<=> ! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(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_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) )
<=> ( class_Rings_Ocomm__semiring__1(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_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) )
<=> ! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(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_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
tff(7,plain,
! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(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_Rings_Ocomm__semiring__1(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_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(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_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) )
<=> ( ~ ! [T_1: $i] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Rings_Ocomm__semiring__1(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_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Rings_Ocomm__semiring__1(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_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) )
| class_Rings_Ocomm__semiring__1(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_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
refl(( ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) )
<=> ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) )
<=> ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
^ [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
rewrite(( ( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) )
<=> ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
tff(24,plain,
! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) ) )
<=> ( ~ ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
( ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) ) ),
inference(unit_resolution,[status(thm)],[30,27]) ).
tff(32,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),
inference(unit_resolution,[status(thm)],[31,17]) ).
tff(33,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
^ [V_m: $i,V_n: $i] :
refl(( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [V_m: $i,V_n: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) )
<=> ! [V_m: $i,V_n: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [V_m: $i,V_n: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) )
<=> ! [V_m: $i,V_n: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
^ [V_m: $i,V_n: $i] :
rewrite(( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [V_m: $i,V_n: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) )
<=> ! [V_m: $i,V_n: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,axiom,
! [V_m: $i,V_n: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
tff(40,plain,
! [V_m: $i,V_n: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [V_m: $i,V_n: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
! [V_m: $i,V_n: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [V_m: $i,V_n: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ),
inference(modus_ponens,[status(thm)],[42,35]) ).
tff(44,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),v_na____)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),v_na____) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),v_na____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096order_Aa_Ap_A_060_061_An_096) ).
tff(46,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),v_na____),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
( ( ~ ! [V_m: $i,V_n: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),v_na____)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))) = v_na____ ) )
<=> ( ~ ! [V_m: $i,V_n: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),v_na____)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))) = v_na____ ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [V_m: $i,V_n: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),v_na____)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))) = v_na____ ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [V_m: $i,V_n: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),v_na____)
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))) = v_na____ ) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))) = v_na____,
inference(unit_resolution,[status(thm)],[49,46,43]) ).
tff(51,plain,
v_na____ = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),
inference(transitivity,[status(thm)],[52,33]) ).
tff(54,plain,
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) )
<=> ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,axiom,
~ ( ( ( v_r____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_na____) )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(56,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),
inference(or_elim,[status(thm)],[55]) ).
tff(57,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_na____) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_na____,c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),
inference(modus_ponens,[status(thm)],[56,54]) ).
tff(58,plain,
$false,
inference(unit_resolution,[status(thm)],[57,53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW275+1 : TPTP v9.0.0. Released v5.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 11:22:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.49/0.71 % SZS status Theorem
% 0.49/0.71 % SZS output start Proof
% See solution above
% 0.60/0.80 % E exiting
%------------------------------------------------------------------------------