%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW258+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:07:31 PM UTC 2026
% Result : Theorem 27.75s 4.19s
% Output : CNFRefutation 27.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 43
% Syntax : Number of formulae : 156 ( 44 unt; 21 def)
% Number of atoms : 390 ( 63 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 390 ( 156 ~; 166 |; 30 &)
% ( 30 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 33 ( 31 usr; 22 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 101 ( 101 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [V_b_2,V_aa_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))
<=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless__eq(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/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [V_aa_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f77,axiom,
! [V_x_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f108,axiom,
! [V_n_2,V_aa_2,T_a] :
( ( class_Rings_Ozero__neq__one(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Omult__zero(T_a)
& class_Power_Opower(T_a) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f202,axiom,
! [V_w,V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
=> V_z = V_w ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f205,axiom,
! [V_w,V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f206,axiom,
! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f235,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
<=> ( V_x_2 != V_y_2
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f928,axiom,
! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f942,axiom,
! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1111,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1125,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1133,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1139,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1148,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1157,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1168,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1181,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1272,conjecture,
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/sandbox2/benchmark/theBenchmark.p') ).
fof(f1273,negated_conjecture,
~ 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(negated_conjecture,[status(cth)],[f1272]) ).
fof(f1277,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f1278,plain,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f1397,plain,
! [V_b_2,V_aa_2,T_a] :
( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))
<=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f1398,plain,
! [V_b_2,V_aa_2,T_a] :
( ( ( ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) )
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a)) )
& ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(NNF_transformation,[status(thm)],[f1397]) ).
fof(f1399,plain,
! [T_a] :
( ( ! [V_b_2,V_aa_2] :
( ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) )
| c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a)) )
& ! [V_b_2,V_aa_2] :
( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(miniscoping,[status(thm)],[f1398]) ).
fof(f1402,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),X2),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Olinordered__ring__strict(X0) ),
inference(cnf_transformation,[status(thm)],[f1399]) ).
fof(f1425,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(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__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f1426,plain,
! [T_a] :
( ! [V_a] :
( ! [V_n] : c_Orderings_Oord__class_Oless__eq(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__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(miniscoping,[status(thm)],[f1425]) ).
fof(f1427,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2))
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(cnf_transformation,[status(thm)],[f1426]) ).
fof(f1431,plain,
! [V_aa_2,T_a] :
( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f1432,plain,
! [V_aa_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(NNF_transformation,[status(thm)],[f1431]) ).
fof(f1433,plain,
! [T_a] :
( ( ! [V_aa_2] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a)) )
& ! [V_aa_2] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(miniscoping,[status(thm)],[f1432]) ).
fof(f1434,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Rings_Oinverse__class_Oinverse(X0,X1),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Fields_Olinordered__field__inverse__zero(X0) ),
inference(cnf_transformation,[status(thm)],[f1433]) ).
fof(f1520,plain,
! [V_x_2,T_a] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f77]) ).
fof(f1521,plain,
! [V_x_2,T_a] :
( ( ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(NNF_transformation,[status(thm)],[f1520]) ).
fof(f1522,plain,
! [T_a] :
( ( ! [V_x_2] :
( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [V_x_2] :
( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(miniscoping,[status(thm)],[f1521]) ).
fof(f1523,plain,
! [X0,X1] :
( X1 = c_Groups_Ozero__class_Ozero(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(cnf_transformation,[status(thm)],[f1522]) ).
fof(f1624,plain,
! [V_n_2,V_aa_2,T_a] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Power_Opower(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f108]) ).
fof(f1625,plain,
! [V_n_2,V_aa_2,T_a] :
( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_aa_2 != c_Groups_Ozero__class_Ozero(T_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_n_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Power_Opower(T_a) ),
inference(NNF_transformation,[status(thm)],[f1624]) ).
fof(f1626,plain,
! [T_a] :
( ( ! [V_n_2,V_aa_2] :
( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_aa_2 != c_Groups_Ozero__class_Ozero(T_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) )
& ! [V_n_2,V_aa_2] :
( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_n_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Power_Opower(T_a) ),
inference(miniscoping,[status(thm)],[f1625]) ).
fof(f1627,plain,
! [X0,X1,X2] :
( X1 = c_Groups_Ozero__class_Ozero(X0)
| hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2) != c_Groups_Ozero__class_Ozero(X0)
| ~ class_Rings_Ozero__neq__one(X0)
| ~ class_Rings_Ono__zero__divisors(X0)
| ~ class_Rings_Omult__zero(X0)
| ~ class_Power_Opower(X0) ),
inference(cnf_transformation,[status(thm)],[f1626]) ).
fof(f1949,plain,
! [V_w,V_z] :
( V_z = V_w
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w) ),
inference(pre_NNF_transformation,[status(thm)],[f202]) ).
fof(f1950,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1949]) ).
fof(f1957,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f1958,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0),
inference(cnf_transformation,[status(thm)],[f206]) ).
fof(f2043,plain,
! [V_y_2,V_x_2] :
( ( V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) )
& ( ( V_x_2 != V_y_2
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
inference(NNF_transformation,[status(thm)],[f235]) ).
fof(f2044,plain,
( ! [V_y_2,V_x_2] :
( V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) )
& ! [V_y_2,V_x_2] :
( ( V_x_2 != V_y_2
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
inference(miniscoping,[status(thm)],[f2043]) ).
fof(f2045,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f2044]) ).
fof(f2046,plain,
! [X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f2044]) ).
fof(f2047,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f2044]) ).
fof(f4265,plain,
! [X0] : c_Nat_OSuc(X0) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[status(thm)],[f928]) ).
fof(f4286,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[status(thm)],[f942]) ).
fof(f4563,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f1111]) ).
fof(f4577,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f1125]) ).
fof(f4585,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f1133]) ).
fof(f4591,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f1139]) ).
fof(f4600,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f1148]) ).
fof(f4609,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f1157]) ).
fof(f4620,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f1168]) ).
fof(f4633,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f1181]) ).
fof(f4781,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(cnf_transformation,[status(thm)],[f1273]) ).
fof(f4821,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f2046]) ).
fof(f4969,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
inference(resolution,[status(thm)],[f2045,f1277]) ).
fof(f4974,definition,
( sQ5_spl
<=> class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f4976,plain,
( sQ5_spl
| ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f4974]) ).
fof(f5073,plain,
( v_m____ = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(resolution,[status(thm)],[f1950,f4969]) ).
fof(f5077,definition,
( sQ18_spl
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f5080,definition,
( sQ19_spl
<=> v_m____ = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f5081,plain,
( ~ sQ19_spl
| v_m____ = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f5080]) ).
fof(f5083,plain,
( sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f5073,f5077,f5080]) ).
fof(f5087,definition,
( sQ21_spl
<=> c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f5088,plain,
( ~ sQ21_spl
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f5087]) ).
fof(f5165,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| X0 = X1
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1) ),
inference(resolution,[status(thm)],[f2047,f1957]) ).
fof(f5176,plain,
( ~ sQ19_spl
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_m____,v_m____) ),
inference(backward_demodulation,[status(thm)],[f5081,f1277]) ).
fof(f5181,plain,
( ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5176,f4821]) ).
fof(f5182,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f5181]) ).
fof(f5231,definition,
( sQ42_spl
<=> class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f5233,plain,
( sQ42_spl
| ~ class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f5231]) ).
fof(f5804,plain,
( sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4563,f5233]) ).
fof(f5805,plain,
sQ42_spl,
inference(contradiction_clause,[status(thm)],[f5804]) ).
fof(f5866,definition,
( sQ119_spl
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f5868,plain,
( sQ119_spl
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(component_clause,[status(thm)],[f5866]) ).
fof(f5981,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4585,f4976]) ).
fof(f5982,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f5981]) ).
fof(f6317,plain,
( sQ119_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5868,f1958]) ).
fof(f6318,plain,
sQ119_spl,
inference(contradiction_clause,[status(thm)],[f6317]) ).
fof(f8035,definition,
( sQ389_spl
<=> class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ389_spl])],[split_symbol_definition]) ).
fof(f8037,plain,
( sQ389_spl
| ~ class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f8035]) ).
fof(f8088,plain,
( sQ389_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8037,f4577]) ).
fof(f8089,plain,
sQ389_spl,
inference(contradiction_clause,[status(thm)],[f8088]) ).
fof(f9812,plain,
( c_Orderings_Oord__class_Oless__eq(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_Groups_Ozero__class_Ozero(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(resolution,[status(thm)],[f4781,f5165]) ).
fof(f9813,definition,
( sQ522_spl
<=> 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____)) ),
introduced(definition,[new_symbols(definition,[sQ522_spl])],[split_symbol_definition]) ).
fof(f9814,plain,
( ~ sQ522_spl
| 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(component_clause,[status(thm)],[f9813]) ).
fof(f9816,definition,
( sQ523_spl
<=> c_Orderings_Oord__class_Oless__eq(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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(definition,[new_symbols(definition,[sQ523_spl])],[split_symbol_definition]) ).
fof(f9817,plain,
( ~ sQ523_spl
| c_Orderings_Oord__class_Oless__eq(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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(component_clause,[status(thm)],[f9816]) ).
fof(f9819,plain,
( sQ523_spl
| sQ522_spl ),
inference(split_clause,[status(thm)],[f9812,f9813,f9816]) ).
fof(f10277,plain,
( ~ sQ522_spl
| c_Orderings_Oord__class_Oless__eq(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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f9814,f1434]) ).
fof(f10287,definition,
( sQ575_spl
<=> c_Orderings_Oord__class_Oless__eq(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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(definition,[new_symbols(definition,[sQ575_spl])],[split_symbol_definition]) ).
fof(f10288,plain,
( ~ sQ575_spl
| c_Orderings_Oord__class_Oless__eq(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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(component_clause,[status(thm)],[f10287]) ).
fof(f10291,plain,
( ~ sQ522_spl
| sQ575_spl
| ~ sQ119_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f10277,f5231,f5866,f10287,f9813]) ).
fof(f10631,plain,
( ~ sQ523_spl
| c_Orderings_Oord__class_Oless__eq(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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f9817,f1434]) ).
fof(f10632,plain,
( ~ sQ523_spl
| sQ575_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f10631,f5231,f10287,f9816]) ).
fof(f10921,plain,
( ~ sQ575_spl
| c_Orderings_Oord__class_Oless__eq(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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f10288,f1402]) ).
fof(f10929,definition,
( sQ639_spl
<=> c_Orderings_Oord__class_Oless__eq(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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(definition,[new_symbols(definition,[sQ639_spl])],[split_symbol_definition]) ).
fof(f10930,plain,
( ~ sQ639_spl
| c_Orderings_Oord__class_Oless__eq(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_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(component_clause,[status(thm)],[f10929]) ).
fof(f10932,plain,
( ~ sQ575_spl
| sQ639_spl
| sQ18_spl
| ~ sQ389_spl ),
inference(split_clause,[status(thm)],[f10921,f8035,f5077,f10929,f10287]) ).
fof(f10933,definition,
( sQ640_spl
<=> c_Orderings_Oord__class_Oless__eq(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)))) ),
introduced(definition,[new_symbols(definition,[sQ640_spl])],[split_symbol_definition]) ).
fof(f10935,plain,
( sQ640_spl
| ~ c_Orderings_Oord__class_Oless__eq(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(component_clause,[status(thm)],[f10933]) ).
fof(f10938,plain,
( ~ sQ639_spl
| 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__eq(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(resolution,[status(thm)],[f10930,f1950]) ).
fof(f10939,definition,
( sQ641_spl
<=> 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))) ),
introduced(definition,[new_symbols(definition,[sQ641_spl])],[split_symbol_definition]) ).
fof(f10940,plain,
( ~ sQ641_spl
| 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(component_clause,[status(thm)],[f10939]) ).
fof(f10942,plain,
( ~ sQ639_spl
| sQ641_spl
| ~ sQ640_spl ),
inference(split_clause,[status(thm)],[f10938,f10933,f10939,f10929]) ).
fof(f10957,definition,
( sQ643_spl
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
introduced(definition,[new_symbols(definition,[sQ643_spl])],[split_symbol_definition]) ).
fof(f10959,plain,
( sQ643_spl
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(component_clause,[status(thm)],[f10957]) ).
fof(f10980,plain,
( sQ643_spl
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(resolution,[status(thm)],[f10959,f1957]) ).
fof(f11228,definition,
( sQ663_spl
<=> class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ663_spl])],[split_symbol_definition]) ).
fof(f11230,plain,
( sQ663_spl
| ~ class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f11228]) ).
fof(f11320,plain,
( sQ663_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f11230,f4600]) ).
fof(f11321,plain,
sQ663_spl,
inference(contradiction_clause,[status(thm)],[f11320]) ).
fof(f11855,plain,
( sQ640_spl
| ~ c_Orderings_Oord__class_Oless__eq(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(resolution,[status(thm)],[f10935,f1427]) ).
fof(f11856,plain,
( sQ640_spl
| ~ sQ643_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f11855,f4974,f10957,f10933]) ).
fof(f12487,definition,
( sQ805_spl
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
introduced(definition,[new_symbols(definition,[sQ805_spl])],[split_symbol_definition]) ).
fof(f12489,plain,
( sQ805_spl
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(component_clause,[status(thm)],[f12487]) ).
fof(f12498,plain,
( sQ805_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12489,f4633]) ).
fof(f12499,plain,
sQ805_spl,
inference(contradiction_clause,[status(thm)],[f12498]) ).
fof(f13855,plain,
( sQ643_spl
| v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[f10980,f1523]) ).
fof(f13858,definition,
( sQ961_spl
<=> v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
introduced(definition,[new_symbols(definition,[sQ961_spl])],[split_symbol_definition]) ).
fof(f13859,plain,
( ~ sQ961_spl
| v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(component_clause,[status(thm)],[f13858]) ).
fof(f13861,plain,
( sQ643_spl
| sQ961_spl
| ~ sQ805_spl ),
inference(split_clause,[status(thm)],[f13855,f12487,f13858,f10957]) ).
fof(f13864,plain,
( ~ sQ961_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13859,f1278]) ).
fof(f13865,plain,
~ sQ961_spl,
inference(contradiction_clause,[status(thm)],[f13864]) ).
fof(f14130,plain,
( ~ sQ21_spl
| v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(paramodulation,[status(thm)],[f5088,f1523]) ).
fof(f14133,plain,
( ~ sQ21_spl
| sQ961_spl
| ~ sQ119_spl
| ~ sQ805_spl ),
inference(split_clause,[status(thm)],[f14130,f12487,f5866,f13858,f5087]) ).
fof(f16593,plain,
( ~ sQ641_spl
| 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_Nat_OSuc(v_k____)) ),
inference(forward_demodulation,[status(thm)],[f4286,f10940]) ).
fof(f16859,definition,
( sQ1219_spl
<=> class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ1219_spl])],[split_symbol_definition]) ).
fof(f16861,plain,
( sQ1219_spl
| ~ class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f16859]) ).
fof(f16888,plain,
( sQ1219_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f16861,f4591]) ).
fof(f16889,plain,
sQ1219_spl,
inference(contradiction_clause,[status(thm)],[f16888]) ).
fof(f17739,definition,
( sQ1277_spl
<=> class_Rings_Omult__zero(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ1277_spl])],[split_symbol_definition]) ).
fof(f17741,plain,
( sQ1277_spl
| ~ class_Rings_Omult__zero(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f17739]) ).
fof(f17749,plain,
( sQ1277_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17741,f4609]) ).
fof(f17750,plain,
sQ1277_spl,
inference(contradiction_clause,[status(thm)],[f17749]) ).
fof(f19650,definition,
( sQ1394_spl
<=> class_Power_Opower(tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ1394_spl])],[split_symbol_definition]) ).
fof(f19652,plain,
( sQ1394_spl
| ~ class_Power_Opower(tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f19650]) ).
fof(f19716,plain,
( sQ1394_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f19652,f4620]) ).
fof(f19717,plain,
sQ1394_spl,
inference(contradiction_clause,[status(thm)],[f19716]) ).
fof(f19719,definition,
( sQ1407_spl
<=> c_Nat_OSuc(v_k____) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
introduced(definition,[new_symbols(definition,[sQ1407_spl])],[split_symbol_definition]) ).
fof(f19720,plain,
( ~ sQ1407_spl
| c_Nat_OSuc(v_k____) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(component_clause,[status(thm)],[f19719]) ).
fof(f19723,plain,
( ~ sQ1407_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f19720,f4265]) ).
fof(f19724,plain,
~ sQ1407_spl,
inference(contradiction_clause,[status(thm)],[f19723]) ).
fof(f19759,plain,
( ~ sQ641_spl
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_Rings_Ozero__neq__one(tc_RealDef_Oreal)
| ~ class_Rings_Ono__zero__divisors(tc_RealDef_Oreal)
| ~ class_Rings_Omult__zero(tc_RealDef_Oreal)
| ~ class_Power_Opower(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f16593,f1627]) ).
fof(f19774,plain,
( ~ sQ641_spl
| sQ21_spl
| ~ sQ663_spl
| ~ sQ1219_spl
| ~ sQ1277_spl
| ~ sQ1394_spl ),
inference(split_clause,[status(thm)],[f19759,f19650,f17739,f16859,f11228,f5087,f10939]) ).
fof(f19798,plain,
$false,
inference(sat_refutation,[status(thm)],[f5083,f5182,f5805,f5982,f6318,f8089,f9819,f10291,f10632,f10932,f10942,f11321,f11856,f12499,f13861,f13865,f14133,f16889,f17750,f19717,f19724,f19774]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW258+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n020.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 09:45:05 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.36/0.61 % Drodi V4.1.1
% 27.75/4.19 % Refutation found
% 27.75/4.19 % SZS status Theorem for theBenchmark: Theorem is valid
% 27.75/4.19 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 21.68/4.28 % Elapsed time: 3.816947 seconds
% 21.68/4.28 % CPU time: 28.722123 seconds
% 21.68/4.28 % Total memory used: 381.968 MB
% 21.68/4.28 % Net memory used: 369.621 MB
%------------------------------------------------------------------------------