TSTP Solution File: SWW197+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW197+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 : Thu Sep 29 20:57:52 EDT 2022
% Result : Theorem 0.79s 0.82s
% Output : Proof 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 55
% Syntax : Number of formulae : 101 ( 40 unt; 24 typ; 0 def)
% Number of atoms : 292 ( 111 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 341 ( 145 ~; 137 |; 0 &)
% ( 35 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of FOOLs : 19 ( 19 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 15 >; 7 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 9 con; 0-3 aty)
% Number of variables : 170 ( 151 !; 0 ?; 170 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_RealVector_Onorm__class_Onorm_type,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_m_____type,type,
v_m____: $i ).
tff(c_Int_Onumber__class_Onumber__of_type,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(c_Int_OBit0_type,type,
c_Int_OBit0: $i > $i ).
tff(c_Int_OBit1_type,type,
c_Int_OBit1: $i > $i ).
tff(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(tc_Int_Oint_type,type,
tc_Int_Oint: $i ).
tff(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
tff(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt_type,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt: $i > $i ).
tff(v_z_____type,type,
v_z____: $i ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(v_b_type,type,
v_b: $i ).
tff(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(c_Int_Osucc_type,type,
c_Int_Osucc: $i > $i ).
tff(c_Int_OPls_type,type,
c_Int_OPls: $i ).
tff(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(v_na_____type,type,
v_na____: $i ).
tff(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
tff(1,plain,
( class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
<=> class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
tff(3,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
refl(
( ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
rewrite(
( ( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
tff(10,plain,
! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),v_m____) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____)) ) )
<=> ( ~ ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),v_m____) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),v_m____) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [V_q: $i,V_p: $i,V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),v_m____) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____)) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),v_m____) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____)),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
( ( c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) )
<=> ( c_Int_Osucc(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ( c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) )
<=> ( c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,axiom,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__Pls) ).
tff(21,plain,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
c_Int_Osucc(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(modus_ponens,[status(thm)],[21,18]) ).
tff(23,plain,
c_Int_OBit0(c_Int_Osucc(c_Groups_Ozero__class_Ozero(tc_Int_Oint))) = c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_Osucc(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_Osucc(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
^ [V_z: $i] :
refl(
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_Osucc(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = V_z )
<=> ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_Osucc(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = V_z ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [V_z: $i] : ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_Osucc(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = V_z )
<=> ! [V_z: $i] : ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_Osucc(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = V_z ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
^ [V_z: $i] :
rewrite(
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = V_z )
<=> ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_Osucc(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = V_z ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [V_z: $i] : ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = V_z )
<=> ! [V_z: $i] : ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_Osucc(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = V_z ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
^ [V_z: $i] :
rewrite(
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_z )
<=> ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = V_z ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [V_z: $i] : ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_z )
<=> ! [V_z: $i] : ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = V_z ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [V_z: $i] : ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_z )
<=> ! [V_z: $i] : ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_z ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
! [V_z: $i] : ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_csqrt) ).
tff(34,plain,
! [V_z: $i] : ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_z ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [V_z: $i] : ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = V_z ),
inference(modus_ponens,[status(thm)],[34,31]) ).
tff(36,plain,
! [V_z: $i] : ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_Osucc(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = V_z ),
inference(modus_ponens,[status(thm)],[35,29]) ).
tff(37,plain,
! [V_z: $i] : ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_Osucc(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = V_z ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [V_z: $i] : ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_Osucc(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = V_z ),
inference(modus_ponens,[status(thm)],[37,27]) ).
tff(39,plain,
( ~ ! [V_z: $i] : ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_Osucc(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = V_z )
| ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_Osucc(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = v_z____ ) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_Osucc(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) = v_z____,
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
v_z____ = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_Osucc(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
v_z____ = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),
inference(transitivity,[status(thm)],[41,25]) ).
tff(43,plain,
hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____) = hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))),v_m____),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____)),
inference(transitivity,[status(thm)],[44,17]) ).
tff(46,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____)))),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),v_na____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
<=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),v_na____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
<=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),v_na____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(rewrite,[status(thm)],]) ).
tff(51,axiom,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),v_na____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(52,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),v_na____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(modus_ponens,[status(thm)],[52,49]) ).
tff(54,plain,
( class_Orderings_Oorder(tc_RealDef_Oreal)
<=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(55,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
tff(56,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
^ [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
refl(
( ( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) ) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) )
<=> ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) )
<=> ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
^ [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( V_b = V_c )
=> c_Orderings_Oord__class_Oless(T_a,V_c,V_a) )
<=> ( ( V_b != V_c )
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) )),
( ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ( ( V_b = V_c )
=> c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) )
<=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ( ( V_b != V_c )
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) )),
rewrite(
( ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ( ( V_b != V_c )
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ( V_b != V_c ) ) )),
( ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ( ( V_b = V_c )
=> c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ( V_b != V_c ) ) )),
( ( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ( ( V_b = V_c )
=> c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) )
<=> ( class_Orderings_Oorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ( V_b != V_c ) ) ) )),
rewrite(
( ( class_Orderings_Oorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ( V_b != V_c ) ) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) ) )),
( ( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ( ( V_b = V_c )
=> c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) ) )),
inference(bind,[status(th)],]) ).
tff(61,plain,
( ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ( ( V_b = V_c )
=> c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) )
<=> ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,axiom,
! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ( ( V_b = V_c )
=> c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I2_J) ).
tff(63,plain,
! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) ),
inference(modus_ponens,[status(thm)],[65,58]) ).
tff(67,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(rewrite,[status(thm)],]) ).
tff(68,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_z) ).
tff(69,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
( ( ~ ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))) ) )
<=> ( ~ ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))) ) )
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ( ~ ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))) ) )
<=> ( ~ ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))) ) ) ),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( ( ~ ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))) ) )
<=> ( ~ ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))) ) ) ),
inference(transitivity,[status(thm)],[72,70]) ).
tff(74,plain,
( ~ ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
( ~ ! [V_c: $i,V_a: $i,V_b: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ class_Orderings_Oorder(T_a)
| ( V_b != V_c ) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))) ) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_z____),v_m____)))) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(v_z____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),v_m____))))),
inference(unit_resolution,[status(thm)],[75,69,66,56,53]) ).
tff(77,plain,
$false,
inference(unit_resolution,[status(thm)],[76,48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW197+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 12:32:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.79/0.82 % SZS status Theorem
% 0.79/0.82 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------