%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW230+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 : n004.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 01:29:54 PM UTC 2026
% Result : Theorem 7.00s 2.20s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 33
% Syntax : Number of formulae : 121 ( 108 unt; 22 def)
% Number of atoms : 134 ( 92 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 31 ( 18 ~; 12 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 47 ( 47 usr; 33 con; 0-3 aty)
% Number of variables : 57 ( 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096abs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_060_061_Aabs_A_Icmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_J_A_N_A_N_As_J_A_L_Acmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_A_N_Apoly_Ap_Az_J_096) ).
fof(f13,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sum__of__halves) ).
fof(f16,axiom,
! [X0,X1] :
( class_Int_Onumber__ring(X1)
=> c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0) = c_Groups_Oplus__class_Oplus(X1,X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__2) ).
fof(f25,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(f26,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls) ).
fof(f28,axiom,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(f111,axiom,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(f299,axiom,
! [X0] : c_Int_OBit1(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(f569,axiom,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(f1125,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
fof(f1171,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1172,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(negated_conjecture,[status(cth)],[f1171]) ).
fof(f1175,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(flattening,[],[f1172]) ).
fof(f1180,plain,
! [X0,X1] :
( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0) = c_Groups_Oplus__class_Oplus(X1,X0,X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f2582,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(cnf_transformation,[],[f3]) ).
fof(f2592,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X0,
inference(cnf_transformation,[],[f13]) ).
fof(f2596,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f1180]) ).
fof(f2609,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(cnf_transformation,[],[f25]) ).
fof(f2610,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
inference(cnf_transformation,[],[f26]) ).
fof(f2612,plain,
! [X0] : c_Int_OBit0(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f28]) ).
fof(f2715,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X0),
inference(cnf_transformation,[],[f111]) ).
fof(f3087,plain,
! [X0] : c_Int_OBit1(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0),X0),
inference(cnf_transformation,[],[f299]) ).
fof(f3496,plain,
! [X0] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[],[f569]) ).
fof(f4258,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1125]) ).
fof(f4304,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(cnf_transformation,[],[f1175]) ).
fof(f4310,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) = X0,
inference(definition_unfolding,[],[f2592,f2612,f3087,f2612,f3087]) ).
fof(f4314,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(definition_unfolding,[],[f2596,f2612,f3087]) ).
fof(f4586,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(definition_unfolding,[],[f4304,f2612,f3087,f2612,f3087]) ).
fof(f4768,definition,
sF47 = c_Groups_Oone__class_Oone(tc_Int_Oint),
introduced(definition,[new_symbols(definition,[sF47])],[function_definition]) ).
fof(f4769,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = sF47,
inference(reorient_equations,[],[f4768]) ).
fof(f4770,definition,
sF48 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF47,c_Int_OPls),
introduced(definition,[new_symbols(definition,[sF48])],[function_definition]) ).
fof(f4771,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF47,c_Int_OPls) = sF48,
inference(reorient_equations,[],[f4770]) ).
fof(f4772,definition,
sF49 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF48,c_Int_OPls),
introduced(definition,[new_symbols(definition,[sF49])],[function_definition]) ).
fof(f4773,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF48,c_Int_OPls) = sF49,
inference(reorient_equations,[],[f4772]) ).
fof(f4774,definition,
sF50 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF49,sF49),
introduced(definition,[new_symbols(definition,[sF50])],[function_definition]) ).
fof(f4775,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF49,sF49) = sF50,
inference(reorient_equations,[],[f4774]) ).
fof(f4776,definition,
sF51 = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF50),
introduced(definition,[new_symbols(definition,[sF51])],[function_definition]) ).
fof(f4777,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF50) = sF51,
inference(reorient_equations,[],[f4776]) ).
fof(f4778,definition,
sF52 = c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____),
introduced(definition,[new_symbols(definition,[sF52])],[function_definition]) ).
fof(f4779,plain,
c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____) = sF52,
inference(reorient_equations,[],[f4778]) ).
fof(f4780,definition,
sF53 = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF52),
introduced(definition,[new_symbols(definition,[sF53])],[function_definition]) ).
fof(f4781,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF52) = sF53,
inference(reorient_equations,[],[f4780]) ).
fof(f4782,definition,
sF54 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),
introduced(definition,[new_symbols(definition,[sF54])],[function_definition]) ).
fof(f4783,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____) = sF54,
inference(reorient_equations,[],[f4782]) ).
fof(f4784,definition,
sF55 = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,sF53,sF54),
introduced(definition,[new_symbols(definition,[sF55])],[function_definition]) ).
fof(f4785,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,sF53,sF54) = sF55,
inference(reorient_equations,[],[f4784]) ).
fof(f4786,definition,
sF56 = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,sF55),
introduced(definition,[new_symbols(definition,[sF56])],[function_definition]) ).
fof(f4787,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,sF55) = sF56,
inference(reorient_equations,[],[f4786]) ).
fof(f4788,definition,
sF57 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,sF56,sF51),
introduced(definition,[new_symbols(definition,[sF57])],[function_definition]) ).
fof(f4789,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,sF56,sF51) = sF57,
inference(reorient_equations,[],[f4788]) ).
fof(f4790,definition,
sF58 = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,sF51,sF57),
introduced(definition,[new_symbols(definition,[sF58])],[function_definition]) ).
fof(f4791,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,sF51,sF57) = sF58,
inference(reorient_equations,[],[f4790]) ).
fof(f4792,definition,
sF59 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),
introduced(definition,[new_symbols(definition,[sF59])],[function_definition]) ).
fof(f4793,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____) = sF59,
inference(reorient_equations,[],[f4792]) ).
fof(f4794,definition,
sF60 = hAPP(v_f____,sF59),
introduced(definition,[new_symbols(definition,[sF60])],[function_definition]) ).
fof(f4795,plain,
hAPP(v_f____,sF59) = sF60,
inference(reorient_equations,[],[f4794]) ).
fof(f4796,definition,
sF61 = v_g____(sF60),
introduced(definition,[new_symbols(definition,[sF61])],[function_definition]) ).
fof(f4797,plain,
v_g____(sF60) = sF61,
inference(reorient_equations,[],[f4796]) ).
fof(f4798,definition,
sF62 = c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,sF61),
introduced(definition,[new_symbols(definition,[sF62])],[function_definition]) ).
fof(f4799,plain,
c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,sF61) = sF62,
inference(reorient_equations,[],[f4798]) ).
fof(f4800,definition,
sF63 = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF62),
introduced(definition,[new_symbols(definition,[sF63])],[function_definition]) ).
fof(f4801,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF62) = sF63,
inference(reorient_equations,[],[f4800]) ).
fof(f4802,definition,
sF64 = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,sF63,sF54),
introduced(definition,[new_symbols(definition,[sF64])],[function_definition]) ).
fof(f4803,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,sF63,sF54) = sF64,
inference(reorient_equations,[],[f4802]) ).
fof(f4804,definition,
sF65 = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,sF64),
introduced(definition,[new_symbols(definition,[sF65])],[function_definition]) ).
fof(f4805,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,sF64) = sF65,
inference(reorient_equations,[],[f4804]) ).
fof(f4806,definition,
sF66 = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,sF62,sF52),
introduced(definition,[new_symbols(definition,[sF66])],[function_definition]) ).
fof(f4807,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,sF62,sF52) = sF66,
inference(reorient_equations,[],[f4806]) ).
fof(f4808,definition,
sF67 = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF66),
introduced(definition,[new_symbols(definition,[sF67])],[function_definition]) ).
fof(f4809,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF66) = sF67,
inference(reorient_equations,[],[f4808]) ).
fof(f4810,definition,
sF68 = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sF65,sF67),
introduced(definition,[new_symbols(definition,[sF68])],[function_definition]) ).
fof(f4811,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sF65,sF67) = sF68,
inference(reorient_equations,[],[f4810]) ).
fof(f4812,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sF58,sF68),
inference(definition_folding,[],[f4586,f4811,f4809,f4807,f4779,f4799,f4797,f4795,f4793,f4805,f4803,f4783,f4801,f4799,f4797,f4795,f4793,f4791,f4789,f4777,f4775,f4773,f4771,f4769,f4773,f4771,f4769,f4787,f4785,f4783,f4781,f4779,f4777,f4775,f4773,f4771,f4769,f4773,f4771,f4769]) ).
fof(f4933,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f4314,f2715]) ).
fof(f4937,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))) = X0,
inference(forward_demodulation,[],[f4310,f2715]) ).
fof(f4944,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),
inference(forward_demodulation,[],[f2582,f3496]) ).
fof(f4946,plain,
sF47 = sF48,
inference(forward_demodulation,[],[f4771,f2609]) ).
fof(f4947,plain,
sF48 = sF49,
inference(forward_demodulation,[],[f4773,f2609]) ).
fof(f4948,plain,
sF56 = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,sF55),
inference(forward_demodulation,[],[f4787,f3496]) ).
fof(f4949,plain,
sF65 = c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,sF64),
inference(forward_demodulation,[],[f4805,f3496]) ).
fof(f5008,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f4933,f2715]) ).
fof(f5012,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))))) = X0,
inference(forward_demodulation,[],[f4937,f2715]) ).
fof(f5019,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF52),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),sF52)))),
inference(forward_demodulation,[],[f4944,f4779]) ).
fof(f5021,plain,
sF47 = sF49,
inference(forward_demodulation,[],[f4947,f4946]) ).
fof(f5055,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5008,f2610]) ).
fof(f5059,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))) = X0,
inference(forward_demodulation,[],[f5012,f2610]) ).
fof(f5066,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF52),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,sF59)))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(hAPP(v_f____,sF59))),sF52)))),
inference(forward_demodulation,[],[f5019,f4793]) ).
fof(f5094,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5055,f2610]) ).
fof(f5098,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) = X0,
inference(forward_demodulation,[],[f5059,f2610]) ).
fof(f5105,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF52),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(sF60))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_g____(sF60)),sF52)))),
inference(forward_demodulation,[],[f5066,f4795]) ).
fof(f5127,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5094,f2609]) ).
fof(f5131,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls))))) = X0,
inference(forward_demodulation,[],[f5098,f2609]) ).
fof(f5138,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF52),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,sF61)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,sF61),sF52)))),
inference(forward_demodulation,[],[f5105,f4797]) ).
fof(f5156,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5127,f2609]) ).
fof(f5160,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = X0,
inference(forward_demodulation,[],[f5131,f2609]) ).
fof(f5167,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF52),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF62),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,sF62,sF52)))),
inference(forward_demodulation,[],[f5138,f4799]) ).
fof(f5181,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF47,sF47)),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5156,f4769]) ).
fof(f5185,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF47,sF47))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF47,sF47)))) = X0,
inference(forward_demodulation,[],[f5160,f4769]) ).
fof(f5192,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF52),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF62),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF66))),
inference(forward_demodulation,[],[f5167,f4807]) ).
fof(f5205,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF49,sF49)),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f5181,f5021]) ).
fof(f5209,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF49,sF49))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sF49,sF49)))) = X0,
inference(forward_demodulation,[],[f5185,f5021]) ).
fof(f5216,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF52),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF62),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),sF67)),
inference(forward_demodulation,[],[f5192,f4809]) ).
fof(f5229,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| c_Groups_Oplus__class_Oplus(X1,X0,X0) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,sF50),X0) ),
inference(forward_demodulation,[],[f5205,f4775]) ).
fof(f5233,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF50)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF50))) = X0,
inference(forward_demodulation,[],[f5209,f4775]) ).
fof(f5240,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF52),sF54)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF62),sF54)),sF67)),
inference(forward_demodulation,[],[f5216,f4783]) ).
fof(f5255,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,sF51),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X0,sF51)) = X0,
inference(forward_demodulation,[],[f5233,f4777]) ).
fof(f5262,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF52),sF54)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,sF63,sF54)),sF67)),
inference(forward_demodulation,[],[f5240,f4801]) ).
fof(f5277,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF52),sF54)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,sF64),sF67)),
inference(forward_demodulation,[],[f5262,f4803]) ).
fof(f5292,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF52),sF54)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sF65,sF67)),
inference(forward_demodulation,[],[f5277,f4949]) ).
fof(f5306,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF52),sF54)),sF68),
inference(forward_demodulation,[],[f5292,f4811]) ).
fof(f5320,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF52),sF54)),sF68),
inference(forward_demodulation,[],[f5306,f3496]) ).
fof(f5334,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,sF53,sF54)),sF68),
inference(forward_demodulation,[],[f5320,f4781]) ).
fof(f5348,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,sF55),sF68),
inference(forward_demodulation,[],[f5334,f4785]) ).
fof(f5359,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sF56,sF68),
inference(forward_demodulation,[],[f5348,f4948]) ).
fof(f5434,plain,
sF56 = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sF57,sF57),
inference(superposition,[],[f5255,f4789]) ).
fof(f6079,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,sF50),X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X0),
inference(resolution,[],[f4258,f5229]) ).
fof(f6082,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,sF51,X0) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X0,X0),
inference(forward_demodulation,[],[f6079,f4777]) ).
fof(f6093,plain,
sF58 = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,sF57,sF57),
inference(superposition,[],[f4791,f6082]) ).
fof(f6121,plain,
sF56 = sF58,
inference(forward_demodulation,[],[f6093,f5434]) ).
fof(f6189,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sF56,sF68),
inference(superposition,[],[f4812,f6121]) ).
fof(f6190,plain,
$false,
inference(forward_subsumption_resolution,[],[f6189,f5359]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW230+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n004.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 13:20:07 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running first-order theorem proving
% 0.07/0.23 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
% 7.00/2.20 % (353662)Detected formulas, will run a generic FOF schedule.
% 7.00/2.20 % (353671)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2455918687:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.00/2.20 % (353668)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=1318601222:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.00/2.20 % (353671)Instruction limit reached!
% 7.00/2.20 % (353671)------------------------------
% 7.00/2.20 % (353671)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/2.20 % (353671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/2.20 % (353671)CaDiCaL version: 2.1.3
% 7.00/2.20 % (353671)Termination reason: Instruction limit
% 7.00/2.20 % (353671)Termination phase: Saturation
% 7.00/2.20 % (353671)Time elapsed: 0.039 s
% 7.00/2.20 % (353671)Peak memory usage: 89 MB
% 7.00/2.20 % (353671)Instructions burned: 119 (million)
% 7.00/2.20 % (353670)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1083915867:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.00/2.20 % (353669)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=852895526:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.00/2.20 % (353667)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=4197790452:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.00/2.20 % (353672)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=856792031:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.00/2.20 % (353673)dis-21_1_sil=8000:lcm=predicate:random_seed=1392053915: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)
% 7.00/2.20 % (353670)Instruction limit reached!
% 7.00/2.20 % (353670)------------------------------
% 7.00/2.20 % (353670)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/2.20 % (353670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/2.20 % (353670)CaDiCaL version: 2.1.3
% 7.00/2.20 % (353670)Termination reason: Instruction limit
% 7.00/2.20 % (353670)Termination phase: Saturation
% 7.00/2.20 % (353670)Time elapsed: 0.059 s
% 7.00/2.20 % (353670)Peak memory usage: 90 MB
% 7.00/2.20 % (353670)Instructions burned: 111 (million)
% 7.00/2.20 % (353673)Instruction limit reached!
% 7.00/2.20 % (353673)------------------------------
% 7.00/2.20 % (353673)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/2.20 % (353673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/2.20 % (353673)CaDiCaL version: 2.1.3
% 7.00/2.20 % (353673)Termination reason: Instruction limit
% 7.00/2.20 % (353673)Termination phase: Saturation
% 7.00/2.20 % (353673)Time elapsed: 0.066 s
% 7.00/2.20 % (353673)Peak memory usage: 90 MB
% 7.00/2.20 % (353673)Instructions burned: 130 (million)
% 7.00/2.20 % (353679)lrs+10_1_sil=8000:sp=occurrence:random_seed=3269915078:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 7.00/2.20 % (353672)Instruction limit reached!
% 7.00/2.20 % (353672)------------------------------
% 7.00/2.20 % (353672)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/2.20 % (353672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/2.20 % (353672)CaDiCaL version: 2.1.3
% 7.00/2.20 % (353672)Termination reason: Instruction limit
% 7.00/2.20 % (353672)Termination phase: Saturation
% 7.00/2.20 % (353672)Time elapsed: 0.077 s
% 7.00/2.20 % (353672)Peak memory usage: 91 MB
% 7.00/2.20 % (353672)Instructions burned: 141 (million)
% 7.00/2.20 % (353679)Instruction limit reached!
% 7.00/2.20 % (353679)------------------------------
% 7.00/2.20 % (353679)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/2.20 % (353679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/2.20 % (353679)CaDiCaL version: 2.1.3
% 7.00/2.20 % (353679)Termination reason: Instruction limit
% 7.00/2.20 % (353679)Termination phase: Saturation
% 7.00/2.20 % (353679)Time elapsed: 0.097 s
% 7.00/2.20 % (353679)Peak memory usage: 92 MB
% 7.00/2.20 % (353679)Instructions burned: 285 (million)
% 7.00/2.20 % (353682)lrs+10_1_sil=32000:urr=on:br=off:random_seed=355570167:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 7.00/2.20 % (353683)lrs+1011_1_sil=32000:sp=occurrence:random_seed=619469618:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 7.00/2.20 % (353685)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=4280788284:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 7.00/2.20 % (353686)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2081270308:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 7.00/2.20 % (353682)Instruction limit reached!
% 7.00/2.20 % (353682)------------------------------
% 7.00/2.20 % (353682)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/2.20 % (353682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/2.20 % (353682)CaDiCaL version: 2.1.3
% 7.00/2.20 % (353682)Termination reason: Instruction limit
% 7.00/2.20 % (353682)Termination phase: Saturation
% 7.00/2.20 % (353682)Time elapsed: 0.090 s
% 7.00/2.20 % (353682)Peak memory usage: 91 MB
% 7.00/2.20 % (353682)Instructions burned: 157 (million)
% 7.00/2.20 % (353686)Instruction limit reached!
% 7.00/2.20 % (353686)------------------------------
% 7.00/2.20 % (353686)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/2.20 % (353686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/2.20 % (353686)CaDiCaL version: 2.1.3
% 7.00/2.20 % (353686)Termination reason: Instruction limit
% 7.00/2.20 % (353686)Termination phase: Saturation
% 7.00/2.20 % (353686)Time elapsed: 0.085 s
% 7.00/2.20 % (353686)Peak memory usage: 92 MB
% 7.00/2.20 % (353686)Instructions burned: 295 (million)
% 7.00/2.20 % (353685)Instruction limit reached!
% 7.00/2.20 % (353685)------------------------------
% 7.00/2.20 % (353685)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/2.20 % (353685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/2.20 % (353685)CaDiCaL version: 2.1.3
% 7.00/2.20 % (353685)Termination reason: Instruction limit
% 7.00/2.20 % (353685)Termination phase: Saturation
% 7.00/2.20 % (353685)Time elapsed: 0.142 s
% 7.00/2.20 % (353685)Peak memory usage: 92 MB
% 7.00/2.20 % (353685)Instructions burned: 249 (million)
% 7.00/2.20 % (353691)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3156872201:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 7.00/2.20 % (353683)Instruction limit reached!
% 7.00/2.20 % (353683)------------------------------
% 7.00/2.20 % (353683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/2.20 % (353683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/2.20 % (353683)CaDiCaL version: 2.1.3
% 7.00/2.20 % (353683)Termination reason: Instruction limit
% 7.00/2.20 % (353683)Termination phase: Saturation
% 7.00/2.20 % (353683)Time elapsed: 0.211 s
% 7.00/2.20 % (353683)Peak memory usage: 93 MB
% 7.00/2.20 % (353683)Instructions burned: 325 (million)
% 7.00/2.20 % (353692)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4240320345:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 7.00/2.20 % (353692)Instruction limit reached!
% 7.00/2.20 % (353692)------------------------------
% 7.00/2.20 % (353692)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/2.20 % (353692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/2.20 % (353692)CaDiCaL version: 2.1.3
% 7.00/2.20 % (353692)Termination reason: Instruction limit
% 7.00/2.20 % (353692)Termination phase: Saturation
% 7.00/2.20 % (353692)Time elapsed: 0.030 s
% 7.00/2.20 % (353692)Peak memory usage: 90 MB
% 7.00/2.20 % (353692)Instructions burned: 113 (million)
% 7.00/2.20 % (353693)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3164560452:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 7.00/2.20 % (353697)lrs+10_1_sil=8000:sp=occurrence:random_seed=2085002508:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2993 on theBenchmark for (2993ds/907Mi)
% 7.00/2.20 % (353693)Instruction limit reached!
% 7.00/2.20 % (353693)------------------------------
% 7.00/2.20 % (353693)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/2.20 % (353693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/2.20 % (353693)CaDiCaL version: 2.1.3
% 7.00/2.20 % (353693)Termination reason: Instruction limit
% 7.00/2.20 % (353693)Termination phase: Saturation
% 7.00/2.20 % (353693)Time elapsed: 0.061 s
% 7.00/2.20 % (353693)Peak memory usage: 90 MB
% 7.00/2.20 % (353693)Instructions burned: 127 (million)
% 7.00/2.20 % (353695)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3667479212:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 7.00/2.20 % (353695)Instruction limit reached!
% 7.00/2.20 % (353695)------------------------------
% 7.00/2.20 % (353695)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/2.20 % (353695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/2.20 % (353695)CaDiCaL version: 2.1.3
% 7.00/2.20 % (353695)Termination reason: Instruction limit
% 7.00/2.20 % (353695)Termination phase: Saturation
% 7.00/2.20 % (353695)Time elapsed: 0.056 s
% 7.00/2.20 % (353695)Peak memory usage: 90 MB
% 7.00/2.20 % (353695)Instructions burned: 115 (million)
% 7.00/2.20 % (353701)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2566443145:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 7.00/2.20 % (353702)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2845655260:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 7.00/2.20 % (353697)Instruction limit reached!
% 7.00/2.20 % (353697)------------------------------
% 7.00/2.20 % (353697)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/2.20 % (353697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/2.20 % (353697)CaDiCaL version: 2.1.3
% 7.00/2.20 % (353697)Termination reason: Instruction limit
% 7.00/2.20 % (353697)Termination phase: Saturation
% 7.00/2.20 % (353697)Time elapsed: 0.307 s
% 7.00/2.20 % (353697)Peak memory usage: 97 MB
% 7.00/2.20 % (353697)Instructions burned: 910 (million)
% 7.00/2.20 % (353701)Instruction limit reached!
% 7.00/2.20 % (353701)------------------------------
% 7.00/2.20 % (353701)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/2.20 % (353701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/2.20 % (353701)CaDiCaL version: 2.1.3
% 7.00/2.20 % (353701)Termination reason: Instruction limit
% 7.00/2.20 % (353701)Termination phase: Saturation
% 7.00/2.20 % (353701)Time elapsed: 0.235 s
% 7.00/2.20 % (353701)Peak memory usage: 94 MB
% 7.00/2.20 % (353701)Instructions burned: 438 (million)
% 7.00/2.20 % (353705)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3499779491:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2989 on theBenchmark for (2989ds/134Mi)
% 7.00/2.20 % (353705)Instruction limit reached!
% 7.00/2.20 % (353705)------------------------------
% 7.00/2.20 % (353705)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/2.20 % (353705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/2.20 % (353705)CaDiCaL version: 2.1.3
% 7.00/2.20 % (353705)Termination reason: Instruction limit
% 7.00/2.20 % (353705)Termination phase: Saturation
% 7.00/2.20 % (353705)Time elapsed: 0.039 s
% 7.00/2.20 % (353705)Peak memory usage: 91 MB
% 7.00/2.20 % (353705)Instructions burned: 135 (million)
% 7.00/2.20 % (353667)First to succeed.
% 7.00/2.20 % (353667)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-353662"
% 7.00/2.20 % (353708)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=1766862764:st=3:i=13193:sd=3:ss=axioms_2988 on theBenchmark for (2988ds/13193Mi)
% 7.00/2.20 % (353706)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3719754915:st=8:i=592:sd=3:ep=RST:ss=axioms_2988 on theBenchmark for (2988ds/592Mi)
% 7.00/2.20 % (353668)Also succeeded, but the first one will report.
% 7.00/2.20 % (353667)Refutation found. Thanks to Tanya!
% 7.00/2.20 % SZS status Theorem for theBenchmark
% 7.00/2.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/2.40 % (353667)------------------------------
% 0.21/2.40 % (353667)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/2.40 % (353667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/2.40 % (353667)CaDiCaL version: 2.1.3
% 0.21/2.40 % (353667)Termination reason: Refutation
% 0.21/2.40 % (353667)Time elapsed: 1.075 s
% 0.21/2.40 % (353667)Peak memory usage: 150 MB
% 0.21/2.40 % (353667)Instructions burned: 1729 (million)
% 0.21/2.40 % (353667)------------------------------
% 0.21/2.40 % (353667)------------------------------
% 0.21/2.40 % (353662)Success in time 1.531 s
% 0.21/2.40 % Vampire exiting
%------------------------------------------------------------------------------