%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW260+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 : Tue Sep 29 01:29:57 PM UTC 2026
% Result : Theorem 12.44s 2.60s
% Output : Refutation 15.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 25
% Syntax : Number of formulae : 145 ( 100 unt; 0 def)
% Number of atoms : 190 ( 134 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 92 ( 47 ~; 30 |; 0 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 7 con; 0-3 aty)
% Number of variables : 302 ( 302 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,X1)),X0) = c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__of__real__power) ).
fof(f7,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wm1) ).
fof(f9,axiom,
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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_w) ).
fof(f11,axiom,
! [X0,X1,X2] :
( class_RealVector_Oreal__algebra__1(X2)
=> c_RealVector_Oof__real(X2,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,c_RealVector_Oof__real(X2,X1),c_RealVector_Oof__real(X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__diff) ).
fof(f14,axiom,
! [X0] :
( class_RealVector_Oreal__algebra__1(X0)
=> c_RealVector_Oof__real(X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__1) ).
fof(f108,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(f109,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(f110,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(f121,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(f122,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f146,axiom,
! [X0,X1,X2,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ominus__class_Ominus(X3,X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__left) ).
fof(f148,axiom,
! [X0,X1,X2,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Ominus__class_Ominus(X3,X1,X0)) = c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__right) ).
fof(f149,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
fof(f150,axiom,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
fof(f169,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oone__class_Oone(X2))),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(f225,axiom,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__diff__def) ).
fof(f639,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__smult) ).
fof(f650,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pCons) ).
fof(f651,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Omonom(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__monom) ).
fof(f1180,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f1187,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
fof(f1194,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(f1195,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(f1204,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(f1276,conjecture,
c_Groups_Oplus__class_Oplus(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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1277,negated_conjecture,
c_Groups_Oplus__class_Oplus(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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),
inference(negated_conjecture,[status(cth)],[f1276]) ).
fof(f1280,plain,
c_Groups_Oplus__class_Oplus(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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),
inference(flattening,[],[f1277]) ).
fof(f1284,plain,
! [X0,X1,X2] :
( c_RealVector_Oof__real(X2,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,c_RealVector_Oof__real(X2,X1),c_RealVector_Oof__real(X2,X0))
| ~ class_RealVector_Oreal__algebra__1(X2) ),
inference(ennf_transformation,[],[f11]) ).
fof(f1288,plain,
! [X0] :
( c_RealVector_Oof__real(X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(X0)
| ~ class_RealVector_Oreal__algebra__1(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f1397,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0)
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f108]) ).
fof(f1398,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f109]) ).
fof(f1399,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f110]) ).
fof(f1413,plain,
! [X0,X1,X2,X3] :
( c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f121]) ).
fof(f1414,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f122]) ).
fof(f1439,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ominus__class_Ominus(X3,X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0))
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(ennf_transformation,[],[f146]) ).
fof(f1441,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Ominus__class_Ominus(X3,X1,X0)) = c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(ennf_transformation,[],[f148]) ).
fof(f1442,plain,
! [X0,X1,X2] :
( c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f149]) ).
fof(f1443,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f150]) ).
fof(f1464,plain,
! [X0,X1,X2] :
( c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oone__class_Oone(X2))),X0)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f169]) ).
fof(f1965,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Opoly(X3,X1),X0))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f639]) ).
fof(f1977,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f650]) ).
fof(f1978,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Omonom(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f651]) ).
fof(f2806,plain,
! [X0,X1] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,X1)),X0) = c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f2808,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(cnf_transformation,[],[f7]) ).
fof(f2810,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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f9]) ).
fof(f2812,plain,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__algebra__1(X2)
| c_RealVector_Oof__real(X2,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X0)) = c_Groups_Ominus__class_Ominus(X2,c_RealVector_Oof__real(X2,X1),c_RealVector_Oof__real(X2,X0)) ),
inference(cnf_transformation,[],[f1284]) ).
fof(f2815,plain,
! [X0] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_RealVector_Oof__real(X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(X0) ),
inference(cnf_transformation,[],[f1288]) ).
fof(f2939,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(cnf_transformation,[],[f1397]) ).
fof(f2940,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(cnf_transformation,[],[f1398]) ).
fof(f2941,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1) ),
inference(cnf_transformation,[],[f1399]) ).
fof(f2954,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,X1,c_Groups_Oplus__class_Oplus(X3,X2,X0)) ),
inference(cnf_transformation,[],[f1413]) ).
fof(f2955,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1) ),
inference(cnf_transformation,[],[f1414]) ).
fof(f2989,plain,
! [X2,X3,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),c_Groups_Ominus__class_Ominus(X3,X2,X1)),X0) = c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) ),
inference(cnf_transformation,[],[f1439]) ).
fof(f2991,plain,
! [X2,X3,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Ominus__class_Ominus(X3,X1,X0)) = c_Groups_Ominus__class_Ominus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(cnf_transformation,[],[f1441]) ).
fof(f2992,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Ominus__class_Ominus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X0),X0) = X1 ),
inference(cnf_transformation,[],[f1442]) ).
fof(f2993,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ogroup__add(X2)
| c_Groups_Oplus__class_Oplus(X2,c_Groups_Ominus__class_Ominus(X2,X1,X0),X0) = X1 ),
inference(cnf_transformation,[],[f1443]) ).
fof(f3012,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| c_Groups_Oplus__class_Oplus(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oone__class_Oone(X2))),X0) ),
inference(cnf_transformation,[],[f1464]) ).
fof(f3094,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),
inference(cnf_transformation,[],[f225]) ).
fof(f3680,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
inference(cnf_transformation,[],[f1965]) ).
fof(f3692,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(c_Polynomial_Opoly(X3,c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0))) ),
inference(cnf_transformation,[],[f1977]) ).
fof(f3693,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Omonom(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)) ),
inference(cnf_transformation,[],[f1978]) ).
fof(f4373,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1180]) ).
fof(f4380,plain,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1187]) ).
fof(f4387,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1194]) ).
fof(f4388,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1195]) ).
fof(f4397,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1204]) ).
fof(f4469,plain,
c_Groups_Oplus__class_Oplus(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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),
inference(cnf_transformation,[],[f1280]) ).
fof(f4703,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),
inference(resolution,[],[f4387,f2955]) ).
fof(f4707,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0),X1),
inference(superposition,[],[f3094,f4703]) ).
fof(f4708,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X0),
inference(resolution,[],[f2941,f4387]) ).
fof(f4754,plain,
! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),X2)),
inference(resolution,[],[f3680,f4388]) ).
fof(f4765,plain,
! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X2),X1)),
inference(resolution,[],[f3693,f4387]) ).
fof(f4773,plain,
! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X2),X1)),X0),
inference(superposition,[],[f4708,f4765]) ).
fof(f4819,plain,
! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1)),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),X2))),
inference(resolution,[],[f3692,f4388]) ).
fof(f4820,plain,
! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1)),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,X1)),X2)),
inference(forward_demodulation,[],[f4819,f4754]) ).
fof(f4825,plain,
! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1)),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,X1)),X2),X0),
inference(superposition,[],[f4703,f4820]) ).
fof(f4827,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X2)),
inference(resolution,[],[f2954,f4387]) ).
fof(f4838,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,X0)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1)),
inference(superposition,[],[f4827,f4703]) ).
fof(f4849,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X2),X1),
inference(superposition,[],[f4703,f4827]) ).
fof(f4870,plain,
! [X2,X3,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1)),X2)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,X1)),X2),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3,X0)),
inference(superposition,[],[f4838,f4820]) ).
fof(f4875,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,X0)),
inference(superposition,[],[f4838,f3094]) ).
fof(f4883,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,X1)),
inference(superposition,[],[f4827,f4838]) ).
fof(f4894,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,X0),X1),
inference(forward_demodulation,[],[f4875,f4707]) ).
fof(f4899,plain,
! [X2,X3,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,X1)),X2)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3,X0),X1)),X2),
inference(forward_demodulation,[],[f4870,f4825]) ).
fof(f4963,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),
inference(superposition,[],[f2810,f2808]) ).
fof(f4976,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(forward_demodulation,[],[f4963,f3094]) ).
fof(f4984,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),X1) = X0,
inference(resolution,[],[f4397,f2992]) ).
fof(f4986,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1),X1) = X0,
inference(resolution,[],[f4397,f2993]) ).
fof(f4987,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)) = X0,
inference(forward_demodulation,[],[f4986,f4703]) ).
fof(f4989,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X1)) = X0,
inference(forward_demodulation,[],[f4984,f4894]) ).
fof(f4992,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(superposition,[],[f4987,f4976]) ).
fof(f5003,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(forward_demodulation,[],[f4992,f4703]) ).
fof(f5007,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X0,
inference(superposition,[],[f4989,f4976]) ).
fof(f5036,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0) = X0,
inference(superposition,[],[f4703,f5007]) ).
fof(f5063,plain,
! [X0] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0),
inference(superposition,[],[f3094,f5036]) ).
fof(f5067,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X0),
inference(superposition,[],[f4989,f5036]) ).
fof(f5646,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(resolution,[],[f2815,f4380]) ).
fof(f5997,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)),
inference(resolution,[],[f2991,f4373]) ).
fof(f6013,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X1)),
inference(superposition,[],[f5067,f5997]) ).
fof(f6032,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(forward_demodulation,[],[f6013,f5067]) ).
fof(f6046,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),X0),
inference(superposition,[],[f4708,f6032]) ).
fof(f6051,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),
inference(superposition,[],[f5997,f6032]) ).
fof(f6056,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),
inference(forward_demodulation,[],[f6051,f5063]) ).
fof(f6062,plain,
! [X0,X1] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)),
inference(forward_demodulation,[],[f6056,f5063]) ).
fof(f6551,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),X1),
inference(resolution,[],[f3012,f4387]) ).
fof(f6552,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),
inference(forward_demodulation,[],[f6551,f4703]) ).
fof(f6567,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),X0),
inference(superposition,[],[f6552,f6046]) ).
fof(f6576,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),
inference(superposition,[],[f4708,f6552]) ).
fof(f6606,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X0),
inference(forward_demodulation,[],[f6567,f5003]) ).
fof(f6616,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X0) = X0,
inference(forward_demodulation,[],[f6606,f5007]) ).
fof(f7390,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X0,X1)),X2) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),
inference(resolution,[],[f2989,f4373]) ).
fof(f7399,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0)),X1),
inference(superposition,[],[f7390,f6046]) ).
fof(f7452,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),X1),
inference(forward_demodulation,[],[f7399,f5063]) ).
fof(f7469,plain,
! [X0,X1] : c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),X1),
inference(forward_demodulation,[],[f7452,f5063]) ).
fof(f7479,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),X1),
inference(forward_demodulation,[],[f7469,f6062]) ).
fof(f7843,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)),
inference(resolution,[],[f2940,f4387]) ).
fof(f7868,plain,
! [X2,X3,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X2),X1))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)),X2)),
inference(superposition,[],[f7843,f4765]) ).
fof(f7910,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)),X1),
inference(superposition,[],[f4708,f7843]) ).
fof(f7946,plain,
! [X2,X3,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X2),X1))) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X3,c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1))),X2),
inference(forward_demodulation,[],[f7868,f4754]) ).
fof(f7966,plain,
! [X2,X3,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X3,c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1))),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Omonom(tc_Complex_Ocomplex,X3,X1)),X2)),
inference(forward_demodulation,[],[f7946,f4765]) ).
fof(f7976,plain,
! [X2,X3,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X3,c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1))),X2) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_Omonom(tc_Complex_Ocomplex,X3,X1))),X2),
inference(forward_demodulation,[],[f7966,f4754]) ).
fof(f8845,plain,
! [X0,X1] : c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,X1)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X0),c_RealVector_Oof__real(tc_Complex_Ocomplex,X1)),
inference(resolution,[],[f2812,f4380]) ).
fof(f8847,plain,
! [X0] : c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,X0)),
inference(superposition,[],[f8845,f5646]) ).
fof(f8978,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),
inference(resolution,[],[f2939,f4387]) ).
fof(f9029,plain,
! [X2,X3,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X2),X3))) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X3)),X2),
inference(superposition,[],[f4765,f8978]) ).
fof(f9041,plain,
! [X2,X3,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X3)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Omonom(tc_Complex_Ocomplex,X1,X3)),X2)),
inference(forward_demodulation,[],[f9029,f4765]) ).
fof(f9072,plain,
! [X2,X3,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X3)),X2) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_Omonom(tc_Complex_Ocomplex,X1,X3))),X2),
inference(forward_demodulation,[],[f9041,f4754]) ).
fof(f10240,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0)),
inference(superposition,[],[f6576,f4703]) ).
fof(f10424,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X0)),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0)),
inference(superposition,[],[f10240,f3094]) ).
fof(f10500,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X1))),
inference(forward_demodulation,[],[f10424,f7479]) ).
fof(f13011,plain,
c_Groups_Oplus__class_Oplus(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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),
inference(superposition,[],[f4469,f7910]) ).
fof(f13039,plain,
c_Groups_Oplus__class_Oplus(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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),
inference(forward_demodulation,[],[f13011,f4773]) ).
fof(f13083,plain,
c_Groups_Oplus__class_Oplus(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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),
inference(forward_demodulation,[],[f13039,f9072]) ).
fof(f13107,plain,
c_Groups_Oplus__class_Oplus(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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),
inference(forward_demodulation,[],[f13083,f7976]) ).
fof(f13121,plain,
c_Groups_Oplus__class_Oplus(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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),
inference(forward_demodulation,[],[f13107,f4820]) ).
fof(f13127,plain,
c_Groups_Oplus__class_Oplus(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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)))) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),
inference(forward_demodulation,[],[f13121,f4708]) ).
fof(f13131,plain,
c_Groups_Oplus__class_Oplus(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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)))) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),
inference(forward_demodulation,[],[f13127,f8847]) ).
fof(f13135,plain,
c_Groups_Oplus__class_Oplus(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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)))) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),
inference(forward_demodulation,[],[f13131,f2806]) ).
fof(f13138,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))))),
inference(forward_demodulation,[],[f13135,f4849]) ).
fof(f13140,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))))),
inference(forward_demodulation,[],[f13138,f4883]) ).
fof(f13142,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)))),
inference(forward_demodulation,[],[f13140,f4820]) ).
fof(f13144,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),
inference(forward_demodulation,[],[f13142,f4899]) ).
fof(f13146,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____))),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),
inference(forward_demodulation,[],[f13144,f10500]) ).
fof(f13148,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_w____),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____))),
inference(forward_demodulation,[],[f13146,f6616]) ).
fof(f13149,plain,
$false,
inference(trivial_inequality_removal,[],[f13148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW260+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n015.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 13:28:47 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.57/2.30 % (2625207)Detected formulas, will run a generic FOF schedule.
% 12.57/2.30 % (2625217)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1882882505:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 12.57/2.30 % (2625216)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2468466429:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 12.57/2.30 % (2625218)dis-21_1_sil=8000:lcm=predicate:random_seed=2087467109:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 12.57/2.30 % (2625212)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3450848044:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 12.57/2.30 % (2625215)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3423745689:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 12.57/2.30 % (2625213)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1092284986:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 12.57/2.30 % (2625214)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=715862980:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 12.57/2.30 % (2625215)Refutation not found, incomplete strategy
% 12.57/2.30 % (2625215)------------------------------
% 12.57/2.30 % (2625215)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.57/2.30 % (2625215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.57/2.30 % (2625215)CaDiCaL version: 2.1.3
% 12.57/2.30 % (2625215)Termination reason: Refutation not found, incomplete strategy
% 12.57/2.30 % (2625215)Time elapsed: 0.018 s
% 12.57/2.30 % (2625215)Peak memory usage: 90 MB
% 12.57/2.30 % (2625215)Instructions burned: 32 (million)
% 12.57/2.30 % (2625217)Instruction limit reached!
% 12.57/2.30 % (2625217)------------------------------
% 12.57/2.30 % (2625217)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.57/2.30 % (2625217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.57/2.30 % (2625217)CaDiCaL version: 2.1.3
% 12.57/2.30 % (2625217)Termination reason: Instruction limit
% 12.57/2.30 % (2625217)Termination phase: Saturation
% 12.57/2.30 % (2625217)Time elapsed: 0.041 s
% 12.57/2.30 % (2625217)Peak memory usage: 91 MB
% 12.57/2.30 % (2625217)Instructions burned: 140 (million)
% 12.57/2.30 % (2625216)Instruction limit reached!
% 12.57/2.30 % (2625216)------------------------------
% 12.57/2.30 % (2625216)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.57/2.30 % (2625216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.57/2.30 % (2625216)CaDiCaL version: 2.1.3
% 12.57/2.30 % (2625216)Termination reason: Instruction limit
% 12.57/2.30 % (2625216)Termination phase: Saturation
% 12.57/2.30 % (2625216)Time elapsed: 0.068 s
% 12.57/2.30 % (2625216)Peak memory usage: 90 MB
% 12.57/2.30 % (2625216)Instructions burned: 119 (million)
% 12.57/2.30 % (2625218)Instruction limit reached!
% 12.57/2.30 % (2625218)------------------------------
% 12.57/2.30 % (2625218)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.57/2.30 % (2625218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.57/2.30 % (2625218)CaDiCaL version: 2.1.3
% 12.57/2.30 % (2625218)Termination reason: Instruction limit
% 12.57/2.30 % (2625218)Termination phase: Saturation
% 12.57/2.30 % (2625218)Time elapsed: 0.068 s
% 12.57/2.30 % (2625218)Peak memory usage: 91 MB
% 12.57/2.30 % (2625218)Instructions burned: 129 (million)
% 12.57/2.30 % (2625226)lrs+10_1_sil=8000:sp=occurrence:random_seed=2152646061:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 12.57/2.30 % (2625227)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3710354719:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 12.57/2.30 % (2625228)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2793372329:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 12.57/2.30 % (2625226)Instruction limit reached!
% 12.57/2.30 % (2625226)------------------------------
% 12.57/2.30 % (2625226)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.57/2.30 % (2625226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.44/2.60 % (2625226)CaDiCaL version: 2.1.3
% 12.44/2.60 % (2625226)Termination reason: Instruction limit
% 12.44/2.60 % (2625226)Termination phase: Saturation
% 12.44/2.60 % (2625226)Time elapsed: 0.101 s
% 12.44/2.60 % (2625226)Peak memory usage: 92 MB
% 12.44/2.60 % (2625226)Instructions burned: 287 (million)
% 12.44/2.60 % (2625215)------------------------------
% 12.44/2.60 % (2625215)------------------------------
% 12.44/2.60 % (2625227)Instruction limit reached!
% 12.44/2.60 % (2625227)------------------------------
% 12.44/2.60 % (2625227)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.44/2.60 % (2625227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.44/2.60 % (2625227)CaDiCaL version: 2.1.3
% 12.44/2.60 % (2625227)Termination reason: Instruction limit
% 12.44/2.60 % (2625227)Termination phase: Saturation
% 12.44/2.60 % (2625227)Time elapsed: 0.094 s
% 12.44/2.60 % (2625227)Peak memory usage: 91 MB
% 12.44/2.60 % (2625227)Instructions burned: 158 (million)
% 12.44/2.60 % (2625232)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=493714238:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 12.44/2.60 % (2625233)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1039165917:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 12.44/2.60 % (2625228)Instruction limit reached!
% 12.44/2.60 % (2625228)------------------------------
% 12.44/2.60 % (2625228)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.44/2.60 % (2625228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.44/2.60 % (2625228)CaDiCaL version: 2.1.3
% 12.44/2.60 % (2625228)Termination reason: Instruction limit
% 12.44/2.60 % (2625228)Termination phase: Saturation
% 12.44/2.60 % (2625228)Time elapsed: 0.206 s
% 12.44/2.60 % (2625228)Peak memory usage: 92 MB
% 12.44/2.60 % (2625228)Instructions burned: 326 (million)
% 12.44/2.60 % (2625232)Instruction limit reached!
% 12.44/2.60 % (2625232)------------------------------
% 12.44/2.60 % (2625232)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.44/2.60 % (2625232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.44/2.60 % (2625232)CaDiCaL version: 2.1.3
% 12.44/2.60 % (2625232)Termination reason: Instruction limit
% 12.44/2.60 % (2625232)Termination phase: Saturation
% 12.44/2.60 % (2625232)Time elapsed: 0.075 s
% 12.44/2.60 % (2625232)Peak memory usage: 92 MB
% 12.44/2.60 % (2625232)Instructions burned: 250 (million)
% 12.44/2.60 % (2625234)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1287944396:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 12.44/2.60 % (2625237)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2833787858:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 12.44/2.60 % (2625233)Instruction limit reached!
% 12.44/2.60 % (2625233)------------------------------
% 12.44/2.60 % (2625233)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.44/2.60 % (2625233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.44/2.60 % (2625233)CaDiCaL version: 2.1.3
% 12.44/2.60 % (2625233)Termination reason: Instruction limit
% 12.44/2.60 % (2625233)Termination phase: Saturation
% 12.44/2.60 % (2625233)Time elapsed: 0.156 s
% 12.44/2.60 % (2625233)Peak memory usage: 91 MB
% 12.44/2.60 % (2625233)Instructions burned: 296 (million)
% 12.44/2.60 % (2625237)Instruction limit reached!
% 12.44/2.60 % (2625237)------------------------------
% 12.44/2.60 % (2625237)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.44/2.60 % (2625237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.44/2.60 % (2625237)CaDiCaL version: 2.1.3
% 12.44/2.60 % (2625237)Termination reason: Instruction limit
% 12.44/2.60 % (2625237)Termination phase: Saturation
% 12.44/2.60 % (2625237)Time elapsed: 0.034 s
% 12.44/2.60 % (2625237)Peak memory usage: 91 MB
% 12.44/2.60 % (2625237)Instructions burned: 114 (million)
% 12.44/2.60 % (2625238)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=986909418:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 12.44/2.60 % (2625238)Refutation not found, incomplete strategy
% 12.44/2.60 % (2625238)------------------------------
% 12.44/2.60 % (2625238)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.44/2.60 % (2625238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.44/2.60 % (2625238)CaDiCaL version: 2.1.3
% 12.44/2.60 % (2625238)Termination reason: Refutation not found, incomplete strategy
% 12.44/2.60 % (2625238)Time elapsed: 0.050 s
% 12.44/2.60 % (2625238)Peak memory usage: 90 MB
% 12.44/2.60 % (2625238)Instructions burned: 93 (million)
% 12.44/2.60 % (2625242)lrs+10_1_sil=8000:sp=occurrence:random_seed=3538923933:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 12.44/2.60 % (2625241)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=311048260:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 12.44/2.60 % (2625241)Instruction limit reached!
% 12.44/2.60 % (2625241)------------------------------
% 12.44/2.60 % (2625241)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.44/2.60 % (2625241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.44/2.60 % (2625241)CaDiCaL version: 2.1.3
% 12.44/2.60 % (2625241)Termination reason: Instruction limit
% 12.44/2.60 % (2625241)Termination phase: Saturation
% 12.44/2.60 % (2625241)Time elapsed: 0.058 s
% 12.44/2.60 % (2625241)Peak memory usage: 90 MB
% 12.44/2.60 % (2625241)Instructions burned: 115 (million)
% 12.44/2.60 % (2625238)------------------------------
% 12.44/2.60 % (2625238)------------------------------
% 12.44/2.60 % (2625246)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=211800861:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 12.44/2.60 % (2625242)Instruction limit reached!
% 12.44/2.60 % (2625242)------------------------------
% 12.44/2.60 % (2625242)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.44/2.60 % (2625242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.44/2.60 % (2625242)CaDiCaL version: 2.1.3
% 12.44/2.60 % (2625242)Termination reason: Instruction limit
% 12.44/2.60 % (2625242)Termination phase: Saturation
% 12.44/2.60 % (2625242)Time elapsed: 0.313 s
% 12.44/2.60 % (2625242)Peak memory usage: 98 MB
% 12.44/2.60 % (2625242)Instructions burned: 909 (million)
% 12.44/2.60 % (2625247)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=4006698500:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 12.44/2.60 % (2625249)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3058027938:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2987 on theBenchmark for (2987ds/134Mi)
% 12.44/2.60 % (2625246)Instruction limit reached!
% 12.44/2.60 % (2625246)------------------------------
% 12.44/2.60 % (2625246)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.44/2.60 % (2625246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.44/2.60 % (2625246)CaDiCaL version: 2.1.3
% 12.44/2.60 % (2625246)Termination reason: Instruction limit
% 12.44/2.60 % (2625246)Termination phase: Saturation
% 12.44/2.60 % (2625246)Time elapsed: 0.217 s
% 12.44/2.60 % (2625246)Peak memory usage: 93 MB
% 12.44/2.60 % (2625246)Instructions burned: 438 (million)
% 12.44/2.60 % (2625249)Instruction limit reached!
% 12.44/2.60 % (2625249)------------------------------
% 12.44/2.60 % (2625249)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.44/2.60 % (2625249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.44/2.60 % (2625249)CaDiCaL version: 2.1.3
% 12.44/2.60 % (2625249)Termination reason: Instruction limit
% 12.44/2.60 % (2625249)Termination phase: Saturation
% 12.44/2.60 % (2625249)Time elapsed: 0.040 s
% 12.44/2.60 % (2625249)Peak memory usage: 92 MB
% 12.44/2.60 % (2625249)Instructions burned: 137 (million)
% 12.44/2.60 % (2625253)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=3929923721:st=3:i=13193:sd=3:ss=axioms_2986 on theBenchmark for (2986ds/13193Mi)
% 12.44/2.60 % (2625252)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=1765234800:st=8:i=592:sd=3:ep=RST:ss=axioms_2986 on theBenchmark for (2986ds/592Mi)
% 12.44/2.60 % (2625252)Instruction limit reached!
% 12.44/2.60 % (2625252)------------------------------
% 12.44/2.60 % (2625252)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.44/2.60 % (2625252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.44/2.60 % (2625252)CaDiCaL version: 2.1.3
% 12.44/2.60 % (2625252)Termination reason: Instruction limit
% 12.44/2.60 % (2625252)Termination phase: Saturation
% 12.44/2.60 % (2625252)Time elapsed: 0.292 s
% 12.44/2.60 % (2625252)Peak memory usage: 98 MB
% 12.44/2.60 % (2625252)Instructions burned: 592 (million)
% 12.44/2.60 % (2625213)First to succeed.
% 12.44/2.60 % (2625213)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2625207"
% 12.44/2.60 % (2625256)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=187588932:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2982 on theBenchmark for (2982ds/125Mi)
% 12.44/2.60 % (2625256)Instruction limit reached!
% 12.44/2.60 % (2625256)------------------------------
% 12.44/2.60 % (2625256)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.44/2.60 % (2625256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.44/2.60 % (2625256)CaDiCaL version: 2.1.3
% 12.44/2.60 % (2625256)Termination reason: Instruction limit
% 12.44/2.60 % (2625256)Termination phase: Saturation
% 12.44/2.60 % (2625256)Time elapsed: 0.063 s
% 12.44/2.60 % (2625256)Peak memory usage: 91 MB
% 12.44/2.60 % (2625256)Instructions burned: 127 (million)
% 12.44/2.60 % (2625234)Instruction limit reached!
% 12.44/2.60 % (2625234)------------------------------
% 12.44/2.60 % (2625234)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.44/2.60 % (2625234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.44/2.60 % (2625234)CaDiCaL version: 2.1.3
% 12.44/2.60 % (2625234)Termination reason: Instruction limit
% 12.44/2.60 % (2625234)Termination phase: Saturation
% 12.44/2.60 % (2625234)Time elapsed: 1.424 s
% 12.44/2.60 % (2625234)Peak memory usage: 148 MB
% 12.44/2.60 % (2625234)Instructions burned: 2350 (million)
% 12.44/2.60 % (2625213)Refutation found. Thanks to Tanya!
% 12.44/2.60 % SZS status Theorem for theBenchmark
% 12.44/2.60 % SZS output start Proof for theBenchmark
% See solution above
% 15.53/2.79 % (2625213)------------------------------
% 15.53/2.79 % (2625213)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.53/2.79 % (2625213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.53/2.79 % (2625213)CaDiCaL version: 2.1.3
% 15.53/2.79 % (2625213)Termination reason: Refutation
% 15.53/2.79 % (2625213)Time elapsed: 1.693 s
% 15.53/2.79 % (2625213)Peak memory usage: 149 MB
% 15.53/2.79 % (2625213)Instructions burned: 2799 (million)
% 15.53/2.79 % (2625213)------------------------------
% 15.53/2.79 % (2625213)------------------------------
% 15.53/2.79 % (2625207)Success in time 2.163 s
% 15.53/2.79 % Vampire exiting
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