%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW255+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 17.72s 3.72s
% Output : Refutation 21.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 32
% Syntax : Number of formulae : 133 ( 109 unt; 17 def)
% Number of atoms : 157 ( 128 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 44 ( 20 ~; 16 |; 0 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 37 ( 37 usr; 25 con; 0-3 aty)
% Number of variables : 136 ( 136 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_s0) ).
fof(f5,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r01) ).
fof(f13,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(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____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),v_w____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096poly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Aw_A_061poly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_L_Aw_A_094_Ak_A_K_Apoly_A_IpCons_Aa_As_J_Aw_096) ).
fof(f23,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/sandbox/benchmark/theBenchmark.p',fact_poly__smult) ).
fof(f55,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/sandbox/benchmark/theBenchmark.p',fact_poly__pCons) ).
fof(f102,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__0__left) ).
fof(f105,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Polynomial_Osmult(X3,X2,c_Polynomial_Osmult(X3,X1,X0)) = c_Polynomial_Osmult(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__smult) ).
fof(f124,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pqc0) ).
fof(f179,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/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(f187,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/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f197,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(f198,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(f1183,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(f1184,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(f1264,conjecture,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1265,negated_conjecture,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)))),
inference(negated_conjecture,[status(cth)],[f1264]) ).
fof(f1270,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)))),
inference(flattening,[],[f1265]) ).
fof(f1286,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,[],[f23]) ).
fof(f1318,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,[],[f55]) ).
fof(f1375,plain,
! [X0,X1] :
( c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(ennf_transformation,[],[f102]) ).
fof(f1379,plain,
! [X0,X1,X2,X3] :
( c_Polynomial_Osmult(X3,X2,c_Polynomial_Osmult(X3,X1,X0)) = c_Polynomial_Osmult(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f105]) ).
fof(f1487,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,[],[f179]) ).
fof(f1495,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,[],[f187]) ).
fof(f1506,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f197]) ).
fof(f1507,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f198]) ).
fof(f2792,plain,
v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cnf_transformation,[],[f2]) ).
fof(f2795,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f5]) ).
fof(f2803,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(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____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),v_w____))),
inference(cnf_transformation,[],[f13]) ).
fof(f2813,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,[],[f1286]) ).
fof(f2852,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,[],[f1318]) ).
fof(f2910,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(cnf_transformation,[],[f1375]) ).
fof(f2913,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X3,X2,c_Polynomial_Osmult(X3,X1,X0)) = c_Polynomial_Osmult(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0) ),
inference(cnf_transformation,[],[f1379]) ).
fof(f2941,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____),
inference(cnf_transformation,[],[f124]) ).
fof(f3017,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,[],[f1487]) ).
fof(f3025,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,[],[f1495]) ).
fof(f3035,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f1506]) ).
fof(f3036,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
inference(cnf_transformation,[],[f1507]) ).
fof(f4367,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1183]) ).
fof(f4368,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1184]) ).
fof(f4448,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),v_w____)) != c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)))),
inference(cnf_transformation,[],[f1270]) ).
fof(f4798,definition,
sF69 = c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),
introduced(definition,[new_symbols(definition,[sF69])],[function_definition]) ).
fof(f4799,plain,
c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____) = sF69,
inference(reorient_equations,[],[f4798]) ).
fof(f4800,definition,
sF70 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
introduced(definition,[new_symbols(definition,[sF70])],[function_definition]) ).
fof(f4801,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = sF70,
inference(reorient_equations,[],[f4800]) ).
fof(f4802,definition,
sF71 = hAPP(sF69,sF70),
introduced(definition,[new_symbols(definition,[sF71])],[function_definition]) ).
fof(f4803,plain,
hAPP(sF69,sF70) = sF71,
inference(reorient_equations,[],[f4802]) ).
fof(f4804,definition,
sF72 = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,sF71),
introduced(definition,[new_symbols(definition,[sF72])],[function_definition]) ).
fof(f4805,plain,
c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,sF71) = sF72,
inference(reorient_equations,[],[f4804]) ).
fof(f4806,definition,
sF73 = c_Polynomial_Osmult(tc_Complex_Ocomplex,sF72,v_q____),
introduced(definition,[new_symbols(definition,[sF73])],[function_definition]) ).
fof(f4807,plain,
c_Polynomial_Osmult(tc_Complex_Ocomplex,sF72,v_q____) = sF73,
inference(reorient_equations,[],[f4806]) ).
fof(f4808,definition,
sF74 = c_Polynomial_Opoly(tc_Complex_Ocomplex,sF73),
introduced(definition,[new_symbols(definition,[sF74])],[function_definition]) ).
fof(f4809,plain,
c_Polynomial_Opoly(tc_Complex_Ocomplex,sF73) = sF74,
inference(reorient_equations,[],[f4808]) ).
fof(f4810,definition,
sF75 = hAPP(sF74,v_w____),
introduced(definition,[new_symbols(definition,[sF75])],[function_definition]) ).
fof(f4811,plain,
hAPP(sF74,v_w____) = sF75,
inference(reorient_equations,[],[f4810]) ).
fof(f4812,definition,
sF76 = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF75),
introduced(definition,[new_symbols(definition,[sF76])],[function_definition]) ).
fof(f4813,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF75) = sF76,
inference(reorient_equations,[],[f4812]) ).
fof(f4814,definition,
sF77 = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
introduced(definition,[new_symbols(definition,[sF77])],[function_definition]) ).
fof(f4815,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = sF77,
inference(reorient_equations,[],[f4814]) ).
fof(f4816,definition,
sF78 = c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),
introduced(definition,[new_symbols(definition,[sF78])],[function_definition]) ).
fof(f4817,plain,
c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = sF78,
inference(reorient_equations,[],[f4816]) ).
fof(f4818,definition,
sF79 = hAPP(sF78,v_a____),
introduced(definition,[new_symbols(definition,[sF79])],[function_definition]) ).
fof(f4819,plain,
hAPP(sF78,v_a____) = sF79,
inference(reorient_equations,[],[f4818]) ).
fof(f4820,definition,
sF80 = c_Power_Opower__class_Opower(tc_Complex_Ocomplex),
introduced(definition,[new_symbols(definition,[sF80])],[function_definition]) ).
fof(f4821,plain,
c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = sF80,
inference(reorient_equations,[],[f4820]) ).
fof(f4822,definition,
sF81 = hAPP(sF80,v_w____),
introduced(definition,[new_symbols(definition,[sF81])],[function_definition]) ).
fof(f4823,plain,
hAPP(sF80,v_w____) = sF81,
inference(reorient_equations,[],[f4822]) ).
fof(f4824,definition,
sF82 = hAPP(sF81,v_k____),
introduced(definition,[new_symbols(definition,[sF82])],[function_definition]) ).
fof(f4825,plain,
hAPP(sF81,v_k____) = sF82,
inference(reorient_equations,[],[f4824]) ).
fof(f4826,definition,
sF83 = hAPP(sF79,sF82),
introduced(definition,[new_symbols(definition,[sF83])],[function_definition]) ).
fof(f4827,plain,
hAPP(sF79,sF82) = sF83,
inference(reorient_equations,[],[f4826]) ).
fof(f4828,definition,
sF84 = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,sF77,sF83),
introduced(definition,[new_symbols(definition,[sF84])],[function_definition]) ).
fof(f4829,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,sF77,sF83) = sF84,
inference(reorient_equations,[],[f4828]) ).
fof(f4830,definition,
sF85 = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF84),
introduced(definition,[new_symbols(definition,[sF85])],[function_definition]) ).
fof(f4831,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF84) = sF85,
inference(reorient_equations,[],[f4830]) ).
fof(f4832,plain,
sF76 != sF85,
inference(definition_folding,[],[f4448,f4831,f4829,f4827,f4825,f4823,f4821,f4819,f4817,f4815,f4813,f4811,f4809,f4807,f4805,f4803,f4801,f4799]) ).
fof(f4895,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),c_Groups_Ozero__class_Ozero(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____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),v_w____))),
inference(forward_demodulation,[],[f2803,f2941]) ).
fof(f4900,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(forward_demodulation,[],[f2795,f2941]) ).
fof(f4921,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(sF80,v_w____),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),v_w____))),
inference(forward_demodulation,[],[f4895,f4821]) ).
fof(f4925,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),sF70),
inference(forward_demodulation,[],[f4900,f4801]) ).
fof(f4938,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(sF81,v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),v_w____))),
inference(forward_demodulation,[],[f4921,f4823]) ).
fof(f4941,plain,
sF77 = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),sF70),
inference(forward_demodulation,[],[f4925,f4815]) ).
fof(f4945,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),sF82),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),v_w____))),
inference(forward_demodulation,[],[f4938,f4825]) ).
fof(f4949,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(sF78,sF82),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),v_w____))),
inference(forward_demodulation,[],[f4945,f4817]) ).
fof(f4950,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),sF70),hAPP(hAPP(sF78,sF82),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),v_w____))),
inference(forward_demodulation,[],[f4949,f4801]) ).
fof(f4951,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,sF77,hAPP(hAPP(sF78,sF82),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),v_w____))),
inference(forward_demodulation,[],[f4950,f4941]) ).
fof(f4957,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,[],[f4368,f2852]) ).
fof(f4958,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,[],[f4368,f2813]) ).
fof(f4959,plain,
! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,X1)),X2) = hAPP(hAPP(sF78,X0),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),X2)),
inference(forward_demodulation,[],[f4958,f4817]) ).
fof(f4960,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(sF78,X2),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),X2))),
inference(forward_demodulation,[],[f4957,f4817]) ).
fof(f4961,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,[],[f4960,f4959]) ).
fof(f4963,plain,
! [X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,v_q____)),X1) = hAPP(hAPP(sF78,X0),hAPP(sF69,X1)),
inference(superposition,[],[f4959,f4799]) ).
fof(f4970,plain,
! [X0] : hAPP(hAPP(sF78,sF72),hAPP(sF69,X0)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,sF73),X0),
inference(superposition,[],[f4963,f4807]) ).
fof(f4978,plain,
! [X0] : hAPP(hAPP(sF78,sF72),hAPP(sF69,X0)) = hAPP(sF74,X0),
inference(forward_demodulation,[],[f4970,f4809]) ).
fof(f5048,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,[],[f4367,f3017]) ).
fof(f5049,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,[],[f4367,f3025]) ).
fof(f5050,plain,
! [X0,X1] : hAPP(hAPP(sF78,X0),X1) = hAPP(hAPP(sF78,X1),X0),
inference(forward_demodulation,[],[f5048,f4817]) ).
fof(f5054,plain,
! [X0] : hAPP(hAPP(sF78,X0),v_a____) = hAPP(sF79,X0),
inference(superposition,[],[f5050,f4819]) ).
fof(f5059,plain,
! [X2,X0,X1] : hAPP(hAPP(sF78,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X1)),X2) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,X0)),X1),
inference(superposition,[],[f4959,f5050]) ).
fof(f5068,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,X1)),X0),X2) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X2,X1)),X0),
inference(superposition,[],[f4961,f5049]) ).
fof(f5125,plain,
! [X2,X0,X1] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X2)) = c_Polynomial_Osmult(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),
inference(resolution,[],[f2913,f4368]) ).
fof(f5126,plain,
! [X2,X0,X1] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X2)) = c_Polynomial_Osmult(tc_Complex_Ocomplex,hAPP(hAPP(sF78,X0),X1),X2),
inference(forward_demodulation,[],[f5125,f4817]) ).
fof(f5129,plain,
! [X2,X0,X1] : c_Polynomial_Osmult(tc_Complex_Ocomplex,hAPP(hAPP(sF78,X0),X1),X2) = c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,X2)),
inference(superposition,[],[f5126,f5050]) ).
fof(f5142,plain,
! [X2,X0,X1] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X2)) = c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,X2)),
inference(forward_demodulation,[],[f5129,f5126]) ).
fof(f5413,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),sF70),
inference(superposition,[],[f2941,f4801]) ).
fof(f5420,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = hAPP(sF69,sF70),
inference(forward_demodulation,[],[f5413,f4799]) ).
fof(f5425,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = sF71,
inference(forward_demodulation,[],[f5420,f4803]) ).
fof(f5720,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0),
inference(resolution,[],[f2910,f4368]) ).
fof(f5721,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osmult(tc_Complex_Ocomplex,sF70,X0),
inference(forward_demodulation,[],[f5720,f4801]) ).
fof(f5722,plain,
! [X0] : v_s____ = c_Polynomial_Osmult(tc_Complex_Ocomplex,sF70,X0),
inference(forward_demodulation,[],[f5721,f2792]) ).
fof(f5734,plain,
! [X0,X1] : v_s____ = c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_Osmult(tc_Complex_Ocomplex,sF70,X1)),
inference(superposition,[],[f5142,f5722]) ).
fof(f5741,plain,
! [X0] : v_s____ = c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,v_s____),
inference(forward_demodulation,[],[f5734,f5722]) ).
fof(f5762,plain,
! [X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,v_s____)),X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X0),X1),
inference(superposition,[],[f5068,f5741]) ).
fof(f6028,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(resolution,[],[f3035,f4367]) ).
fof(f6029,plain,
! [X0] : sF70 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),sF70),
inference(forward_demodulation,[],[f6028,f4801]) ).
fof(f6030,plain,
! [X0] : sF70 = hAPP(hAPP(sF78,X0),sF70),
inference(forward_demodulation,[],[f6029,f4817]) ).
fof(f6038,plain,
! [X0,X1] : sF70 = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,sF70,X0)),X1),
inference(superposition,[],[f5059,f6030]) ).
fof(f6039,plain,
! [X1] : sF70 = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),X1),
inference(forward_demodulation,[],[f6038,f5722]) ).
fof(f7429,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0) = X0,
inference(resolution,[],[f3036,f4367]) ).
fof(f7430,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,sF70,X0) = X0,
inference(forward_demodulation,[],[f7429,f4801]) ).
fof(f8734,plain,
! [X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,v_s____)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,sF70,X0),
inference(superposition,[],[f5762,f6039]) ).
fof(f8769,plain,
! [X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,v_s____)),X1) = X0,
inference(forward_demodulation,[],[f8734,f7430]) ).
fof(f8800,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,sF77,hAPP(hAPP(sF78,sF82),v_a____)),
inference(superposition,[],[f4951,f8769]) ).
fof(f8804,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,sF77,hAPP(sF79,sF82)),
inference(forward_demodulation,[],[f8800,f5054]) ).
fof(f8811,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,sF77,sF83) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),v_q____)),v_w____),
inference(forward_demodulation,[],[f8804,f4827]) ).
fof(f8813,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,sF77,sF83) = hAPP(hAPP(sF78,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____))),hAPP(sF69,v_w____)),
inference(forward_demodulation,[],[f8811,f4963]) ).
fof(f8815,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,sF77,sF83) = hAPP(hAPP(sF78,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,sF71)),hAPP(sF69,v_w____)),
inference(forward_demodulation,[],[f8813,f5425]) ).
fof(f8817,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,sF77,sF83) = hAPP(hAPP(sF78,sF72),hAPP(sF69,v_w____)),
inference(forward_demodulation,[],[f8815,f4805]) ).
fof(f8819,plain,
hAPP(sF74,v_w____) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,sF77,sF83),
inference(forward_demodulation,[],[f8817,f4978]) ).
fof(f8820,plain,
hAPP(sF74,v_w____) = sF84,
inference(forward_demodulation,[],[f8819,f4829]) ).
fof(f8821,plain,
sF75 = sF84,
inference(forward_demodulation,[],[f8820,f4811]) ).
fof(f8823,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sF75) = sF85,
inference(superposition,[],[f4831,f8821]) ).
fof(f8824,plain,
sF76 = sF85,
inference(forward_demodulation,[],[f8823,f4813]) ).
fof(f8825,plain,
$false,
inference(forward_subsumption_resolution,[],[f8824,f4832]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW255+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.17 % Computer : n006.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Mon Sep 28 13:24:55 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 Running first-order theorem proving
% 0.11/0.21 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.68/3.47 % (3963344)Detected formulas, will run a generic FOF schedule.
% 18.68/3.47 % (3963373)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=1195964978:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 18.68/3.47 % (3963372)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=2524635926:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 18.68/3.47 % (3963374)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=4206350652:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 18.68/3.47 % (3963377)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1075586874:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 18.68/3.47 % (3963376)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3235611728:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 18.68/3.47 % (3963378)dis-21_1_sil=8000:lcm=predicate:random_seed=4149588067: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)
% 18.68/3.47 % (3963375)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1177227622:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 18.68/3.47 % (3963375)Refutation not found, incomplete strategy
% 18.68/3.47 % (3963375)------------------------------
% 18.68/3.47 % (3963375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.68/3.47 % (3963375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.68/3.47 % (3963375)CaDiCaL version: 2.1.3
% 18.68/3.47 % (3963375)Termination reason: Refutation not found, incomplete strategy
% 18.68/3.47 % (3963375)Time elapsed: 0.022 s
% 18.68/3.47 % (3963375)Peak memory usage: 89 MB
% 18.68/3.47 % (3963375)Instructions burned: 21 (million)
% 18.68/3.47 % (3963378)Instruction limit reached!
% 18.68/3.47 % (3963378)------------------------------
% 18.68/3.47 % (3963378)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.68/3.47 % (3963378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.68/3.47 % (3963378)CaDiCaL version: 2.1.3
% 18.68/3.47 % (3963378)Termination reason: Instruction limit
% 18.68/3.47 % (3963378)Termination phase: Saturation
% 18.68/3.47 % (3963378)Time elapsed: 0.119 s
% 18.68/3.47 % (3963378)Peak memory usage: 91 MB
% 18.68/3.47 % (3963378)Instructions burned: 129 (million)
% 18.68/3.47 % (3963376)Instruction limit reached!
% 18.68/3.47 % (3963376)------------------------------
% 18.68/3.47 % (3963376)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.68/3.47 % (3963376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.68/3.47 % (3963376)CaDiCaL version: 2.1.3
% 18.68/3.47 % (3963376)Termination reason: Instruction limit
% 18.68/3.47 % (3963376)Termination phase: Saturation
% 18.68/3.47 % (3963376)Time elapsed: 0.120 s
% 18.68/3.47 % (3963376)Peak memory usage: 89 MB
% 18.68/3.47 % (3963376)Instructions burned: 119 (million)
% 18.68/3.47 % (3963377)Instruction limit reached!
% 18.68/3.47 % (3963377)------------------------------
% 18.68/3.47 % (3963377)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.68/3.47 % (3963377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.68/3.47 % (3963377)CaDiCaL version: 2.1.3
% 18.68/3.47 % (3963377)Termination reason: Instruction limit
% 18.68/3.47 % (3963377)Termination phase: Saturation
% 18.68/3.47 % (3963377)Time elapsed: 0.135 s
% 18.68/3.47 % (3963377)Peak memory usage: 91 MB
% 18.68/3.47 % (3963377)Instructions burned: 139 (million)
% 18.68/3.47 % (3963395)lrs+1011_1_sil=32000:sp=occurrence:random_seed=568549753:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 18.68/3.47 % (3963392)lrs+10_1_sil=8000:sp=occurrence:random_seed=1151585586:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 18.68/3.47 % (3963393)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1865252663:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 18.68/3.47 % (3963375)------------------------------
% 18.68/3.47 % (3963375)------------------------------
% 18.68/3.47 % (3963393)Instruction limit reached!
% 18.68/3.47 % (3963393)------------------------------
% 18.68/3.47 % (3963393)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.72/3.72 % (3963393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.72/3.72 % (3963393)CaDiCaL version: 2.1.3
% 17.72/3.72 % (3963393)Termination reason: Instruction limit
% 17.72/3.72 % (3963393)Termination phase: Saturation
% 17.72/3.72 % (3963393)Time elapsed: 0.145 s
% 17.72/3.72 % (3963393)Peak memory usage: 90 MB
% 17.72/3.72 % (3963393)Instructions burned: 157 (million)
% 17.72/3.72 % (3963403)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=2381724107:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 17.72/3.72 % (3963392)Instruction limit reached!
% 17.72/3.72 % (3963392)------------------------------
% 17.72/3.72 % (3963392)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.72/3.72 % (3963392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.72/3.72 % (3963392)CaDiCaL version: 2.1.3
% 17.72/3.72 % (3963392)Termination reason: Instruction limit
% 17.72/3.72 % (3963392)Termination phase: Saturation
% 17.72/3.72 % (3963392)Time elapsed: 0.220 s
% 17.72/3.72 % (3963392)Peak memory usage: 91 MB
% 17.72/3.72 % (3963392)Instructions burned: 286 (million)
% 17.72/3.72 % (3963395)Instruction limit reached!
% 17.72/3.72 % (3963395)------------------------------
% 17.72/3.72 % (3963395)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.72/3.72 % (3963395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.72/3.72 % (3963395)CaDiCaL version: 2.1.3
% 17.72/3.72 % (3963395)Termination reason: Instruction limit
% 17.72/3.72 % (3963395)Termination phase: Saturation
% 17.72/3.72 % (3963395)Time elapsed: 0.309 s
% 17.72/3.72 % (3963395)Peak memory usage: 92 MB
% 17.72/3.72 % (3963395)Instructions burned: 325 (million)
% 17.72/3.72 % (3963403)Instruction limit reached!
% 17.72/3.72 % (3963403)------------------------------
% 17.72/3.72 % (3963403)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.72/3.72 % (3963403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.72/3.72 % (3963403)CaDiCaL version: 2.1.3
% 17.72/3.72 % (3963403)Termination reason: Instruction limit
% 17.72/3.72 % (3963403)Termination phase: Saturation
% 17.72/3.72 % (3963403)Time elapsed: 0.114 s
% 17.72/3.72 % (3963403)Peak memory usage: 92 MB
% 17.72/3.72 % (3963403)Instructions burned: 249 (million)
% 17.72/3.72 % (3963408)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3853965845:i=2350_2991 on theBenchmark for (2991ds/2350Mi)
% 17.72/3.72 % (3963406)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2620971002:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2992 on theBenchmark for (2992ds/294Mi)
% 17.72/3.72 % (3963406)Refutation not found, incomplete strategy
% 17.72/3.72 % (3963406)------------------------------
% 17.72/3.72 % (3963406)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.72/3.72 % (3963406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.72/3.72 % (3963406)CaDiCaL version: 2.1.3
% 17.72/3.72 % (3963406)Termination reason: Refutation not found, incomplete strategy
% 17.72/3.72 % (3963406)Time elapsed: 0.075 s
% 17.72/3.72 % (3963406)Peak memory usage: 91 MB
% 17.72/3.72 % (3963406)Instructions burned: 76 (million)
% 17.72/3.72 % (3963412)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3939296137:i=127:av=off:fsr=off:sup=off_2990 on theBenchmark for (2990ds/127Mi)
% 17.72/3.72 % (3963410)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=913342610:cts=off:i=113:fsr=off:ss=included:sgt=4_2991 on theBenchmark for (2991ds/113Mi)
% 17.72/3.72 % (3963412)Refutation not found, incomplete strategy
% 17.72/3.72 % (3963412)------------------------------
% 17.72/3.72 % (3963412)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.72/3.72 % (3963412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.72/3.72 % (3963412)CaDiCaL version: 2.1.3
% 17.72/3.72 % (3963412)Termination reason: Refutation not found, incomplete strategy
% 17.72/3.72 % (3963412)Time elapsed: 0.055 s
% 17.72/3.72 % (3963412)Peak memory usage: 90 MB
% 17.72/3.72 % (3963412)Instructions burned: 118 (million)
% 17.72/3.72 % (3963410)Instruction limit reached!
% 17.72/3.72 % (3963410)------------------------------
% 17.72/3.72 % (3963410)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.72/3.72 % (3963410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.72/3.72 % (3963410)CaDiCaL version: 2.1.3
% 17.72/3.72 % (3963410)Termination reason: Instruction limit
% 17.72/3.72 % (3963410)Termination phase: Saturation
% 17.72/3.72 % (3963410)Time elapsed: 0.105 s
% 17.72/3.72 % (3963410)Peak memory usage: 90 MB
% 17.72/3.72 % (3963410)Instructions burned: 113 (million)
% 17.72/3.72 % (3963412)------------------------------
% 17.72/3.72 % (3963412)------------------------------
% 17.72/3.72 % (3963418)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3777574263:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2987 on theBenchmark for (2987ds/114Mi)
% 17.72/3.72 % (3963406)------------------------------
% 17.72/3.72 % (3963406)------------------------------
% 17.72/3.72 % (3963421)lrs+10_1_sil=8000:sp=occurrence:random_seed=2766626046:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2986 on theBenchmark for (2986ds/907Mi)
% 17.72/3.72 % (3963418)Instruction limit reached!
% 17.72/3.72 % (3963418)------------------------------
% 17.72/3.72 % (3963418)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.72/3.72 % (3963418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.72/3.72 % (3963418)CaDiCaL version: 2.1.3
% 17.72/3.72 % (3963418)Termination reason: Instruction limit
% 17.72/3.72 % (3963418)Termination phase: Saturation
% 17.72/3.72 % (3963418)Time elapsed: 0.104 s
% 17.72/3.72 % (3963418)Peak memory usage: 89 MB
% 17.72/3.72 % (3963418)Instructions burned: 115 (million)
% 17.72/3.72 % (3963423)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1061812819:i=437:sd=1:aac=none:ss=included_2985 on theBenchmark for (2985ds/437Mi)
% 17.72/3.72 % (3963425)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3901171056:i=5202:ss=axioms:sgt=16_2984 on theBenchmark for (2984ds/5202Mi)
% 17.72/3.72 % (3963423)Refutation not found, incomplete strategy
% 17.72/3.72 % (3963423)------------------------------
% 17.72/3.72 % (3963423)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.72/3.72 % (3963423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.72/3.72 % (3963423)CaDiCaL version: 2.1.3
% 17.72/3.72 % (3963423)Termination reason: Refutation not found, incomplete strategy
% 17.72/3.72 % (3963423)Time elapsed: 0.119 s
% 17.72/3.72 % (3963423)Peak memory usage: 91 MB
% 17.72/3.72 % (3963423)Instructions burned: 129 (million)
% 17.72/3.72 % (3963421)Instruction limit reached!
% 17.72/3.72 % (3963421)------------------------------
% 17.72/3.72 % (3963421)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.72/3.72 % (3963421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.72/3.72 % (3963421)CaDiCaL version: 2.1.3
% 17.72/3.72 % (3963421)Termination reason: Instruction limit
% 17.72/3.72 % (3963421)Termination phase: Saturation
% 17.72/3.72 % (3963421)Time elapsed: 0.489 s
% 17.72/3.72 % (3963421)Peak memory usage: 97 MB
% 17.72/3.72 % (3963421)Instructions burned: 908 (million)
% 17.72/3.72 % (3963433)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=803697941:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2980 on theBenchmark for (2980ds/134Mi)
% 17.72/3.72 % (3963423)------------------------------
% 17.72/3.72 % (3963423)------------------------------
% 17.72/3.72 % (3963433)Instruction limit reached!
% 17.72/3.72 % (3963433)------------------------------
% 17.72/3.72 % (3963433)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.72/3.72 % (3963433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.72/3.72 % (3963433)CaDiCaL version: 2.1.3
% 17.72/3.72 % (3963433)Termination reason: Instruction limit
% 17.72/3.72 % (3963433)Termination phase: Saturation
% 17.72/3.72 % (3963433)Time elapsed: 0.068 s
% 17.72/3.72 % (3963433)Peak memory usage: 91 MB
% 17.72/3.72 % (3963433)Instructions burned: 134 (million)
% 17.72/3.72 % (3963437)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=1622791043:st=8:i=592:sd=3:ep=RST:ss=axioms_2977 on theBenchmark for (2977ds/592Mi)
% 17.72/3.72 % (3963438)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=3207523532:st=3:i=13193:sd=3:ss=axioms_2977 on theBenchmark for (2977ds/13193Mi)
% 17.72/3.72 % (3963372)First to succeed.
% 17.72/3.72 % (3963372)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3963344"
% 17.72/3.72 % (3963437)Instruction limit reached!
% 17.72/3.72 % (3963437)------------------------------
% 17.72/3.72 % (3963437)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.72/3.72 % (3963437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.72/3.72 % (3963437)CaDiCaL version: 2.1.3
% 17.72/3.72 % (3963437)Termination reason: Instruction limit
% 17.72/3.72 % (3963437)Termination phase: Saturation
% 17.72/3.72 % (3963437)Time elapsed: 0.300 s
% 17.72/3.72 % (3963437)Peak memory usage: 96 MB
% 17.72/3.72 % (3963437)Instructions burned: 593 (million)
% 17.72/3.72 % (3963443)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=1160483022:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2972 on theBenchmark for (2972ds/125Mi)
% 17.72/3.72 % (3963443)Instruction limit reached!
% 17.72/3.72 % (3963443)------------------------------
% 17.72/3.72 % (3963443)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.72/3.72 % (3963443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.72/3.72 % (3963443)CaDiCaL version: 2.1.3
% 17.72/3.72 % (3963443)Termination reason: Instruction limit
% 17.72/3.72 % (3963443)Termination phase: Saturation
% 17.72/3.72 % (3963443)Time elapsed: 0.057 s
% 17.72/3.72 % (3963443)Peak memory usage: 90 MB
% 17.72/3.72 % (3963443)Instructions burned: 126 (million)
% 17.72/3.72 % (3963372)Refutation found. Thanks to Tanya!
% 17.72/3.72 % SZS status Theorem for theBenchmark
% 17.72/3.72 % SZS output start Proof for theBenchmark
% See solution above
% 21.18/3.92 % (3963372)------------------------------
% 21.18/3.92 % (3963372)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.18/3.92 % (3963372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.18/3.92 % (3963372)CaDiCaL version: 2.1.3
% 21.18/3.92 % (3963372)Termination reason: Refutation
% 21.18/3.92 % (3963372)Time elapsed: 2.320 s
% 21.18/3.92 % (3963372)Peak memory usage: 147 MB
% 21.18/3.92 % (3963372)Instructions burned: 2306 (million)
% 21.18/3.92 % (3963372)------------------------------
% 21.18/3.92 % (3963372)------------------------------
% 21.18/3.92 % (3963344)Success in time 2.971 s
% 21.18/3.92 % Vampire exiting
%------------------------------------------------------------------------------