%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW258+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:36:42 AM UTC 2025
% Result : Theorem 0.58s 0.72s
% Output : Proof 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 43
% Syntax : Number of formulae : 98 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 547 ( 47 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 715 ( 308 ~; 264 |; 0 &)
% ( 94 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 42 ( 42 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 7 con; 0-3 aty)
% Number of variables : 194 ( 174 !; 0 ?; 194 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize_type,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).
tff(c_Polynomial_OpCons_type,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(c_Polynomial_Omonom_type,type,
c_Polynomial_Omonom: ( $i * $i * $i ) > $i ).
tff(c_Groups_Ominus__class_Ominus_type,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
tff(v_k_____type,type,
v_k____: $i ).
tff(v_a_____type,type,
v_a____: $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_RealVector_Onorm__class_Onorm_type,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(v_w_____type,type,
v_w____: $i ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(v_m_____type,type,
v_m____: $i ).
tff(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(c_Rings_Oinverse__class_Oinverse_type,type,
c_Rings_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(class_Fields_Olinordered__field_type,type,
class_Fields_Olinordered__field: $i > $o ).
tff(class_Rings_Olinordered__semiring__strict_type,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(class_RealVector_Oreal__normed__vector_type,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(class_Rings_Olinordered__semidom_type,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(1,plain,
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) )
<=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_th02) ).
tff(3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))) ),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
<=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
<=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(11,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
( class_Fields_Olinordered__field(tc_RealDef_Oreal)
<=> class_Fields_Olinordered__field(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).
tff(14,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Fields_Olinordered__field(T_a) )
<=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Fields_Olinordered__field(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Fields_Olinordered__field(T_a) )
<=> ! [V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Fields_Olinordered__field(T_a) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Fields_Olinordered__field(T_a) )
<=> ! [V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Fields_Olinordered__field(T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
^ [V_a: $i,T_a: $i] :
trans(monotonicity(rewrite(( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) )),
( ( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) )
<=> ( class_Fields_Olinordered__field(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) )),
rewrite(( ( class_Fields_Olinordered__field(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) )
<=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Fields_Olinordered__field(T_a) ) )),
( ( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) )
<=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Fields_Olinordered__field(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V_a: $i,T_a: $i] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) )
<=> ! [V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Fields_Olinordered__field(T_a) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [V_a: $i,T_a: $i] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_positive__imp__inverse__positive) ).
tff(21,plain,
! [V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Fields_Olinordered__field(T_a) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))
| ~ class_Fields_Olinordered__field(tc_RealDef_Oreal) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Fields_Olinordered__field(T_a) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))
| ~ class_Fields_Olinordered__field(tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Fields_Olinordered__field(T_a) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))
| ~ class_Fields_Olinordered__field(tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Fields_Olinordered__field(T_a) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))
| ~ class_Fields_Olinordered__field(tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)),
inference(unit_resolution,[status(thm)],[27,24,14,11]) ).
tff(29,plain,
( class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal)
<=> class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
tff(31,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
<=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) )),
( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) )
<=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) )),
rewrite(( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) )
<=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) )),
( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) )
<=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) )),
( ( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) )
<=> ( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) )),
rewrite(( ( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) )
<=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) )),
( ( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) )
<=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
tff(38,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_m_I1_J) ).
tff(44,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) )
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ) ),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ) ),
inference(transitivity,[status(thm)],[47,45]) ).
tff(49,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(unit_resolution,[status(thm)],[50,44,41,31]) ).
tff(52,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(unit_resolution,[status(thm)],[51,28]) ).
tff(53,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))),
inference(modus_ponens,[status(thm)],[52,8]) ).
tff(54,plain,
( class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
tff(56,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
^ [V_x_2: $i,T_a: $i] :
refl(( ( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) )
<=> ( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(58,plain,
( ! [V_x_2: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) )
<=> ! [V_x_2: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [V_x_2: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) )
<=> ! [V_x_2: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
^ [V_x_2: $i,T_a: $i] :
trans(monotonicity(trans(rewrite(( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))
<=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
<=> ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) )),
rewrite(( ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) )
<=> ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) )),
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))
<=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
<=> ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) )),
( ( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))
<=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ( class_RealVector_Oreal__normed__vector(T_a)
=> ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) ) )),
rewrite(( ( class_RealVector_Oreal__normed__vector(T_a)
=> ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) )
<=> ( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) ) )),
( ( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))
<=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(61,plain,
( ! [V_x_2: $i,T_a: $i] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))
<=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) )
<=> ! [V_x_2: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,axiom,
! [V_x_2: $i,T_a: $i] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))
<=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).
tff(63,plain,
! [V_x_2: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [V_x_2: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
! [V_x_2: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [V_x_2: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) ),
inference(modus_ponens,[status(thm)],[65,58]) ).
tff(67,plain,
( ( ~ ! [V_x_2: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ ( ( v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ) )
<=> ( ~ ! [V_x_2: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ ( ( v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [V_x_2: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ ( ( v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [V_x_2: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ ( ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ ( ( v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
~ ( ( v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(unit_resolution,[status(thm)],[69,66,56]) ).
tff(71,plain,
( ( v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,axiom,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_w0) ).
tff(73,plain,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
( ( ( v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) )
| ( v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(tautology,[status(thm)],[]) ).
tff(75,plain,
( ( ( v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(unit_resolution,[status(thm)],[74,73]) ).
tff(76,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
inference(unit_resolution,[status(thm)],[75,70]) ).
tff(77,plain,
( class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
<=> class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
tff(79,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
^ [V_n: $i,V_a: $i,T_a: $i] :
refl(( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) )
<=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(81,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
^ [V_n: $i,V_a: $i,T_a: $i] :
trans(monotonicity(rewrite(( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) )),
( ( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) )
<=> ( class_Rings_Olinordered__semidom(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) )),
rewrite(( ( class_Rings_Olinordered__semidom(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) )
<=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ) )),
( ( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) )
<=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(84,plain,
( ! [V_n: $i,V_a: $i,T_a: $i] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) )
<=> ! [V_n: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,axiom,
! [V_n: $i,V_a: $i,T_a: $i] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power) ).
tff(86,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(modus_ponens,[status(thm)],[86,82]) ).
tff(88,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [V_n: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(modus_ponens,[status(thm)],[88,81]) ).
tff(90,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) )
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) )
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal) )
<=> ( ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) )
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ) ),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
( ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal) )
<=> ( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) )
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ) ),
inference(transitivity,[status(thm)],[92,90]) ).
tff(94,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
( ~ ! [V_n: $i,V_a: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) )
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(unit_resolution,[status(thm)],[95,89,79]) ).
tff(97,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))))),
inference(unit_resolution,[status(thm)],[96,76]) ).
tff(98,plain,
$false,
inference(unit_resolution,[status(thm)],[97,53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW258+1 : TPTP v9.0.0. Released v5.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.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 11:20:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.58/0.72 % SZS status Theorem
% 0.58/0.72 % SZS output start Proof
% See solution above
% 0.62/0.81 % E exiting
%------------------------------------------------------------------------------