%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW257+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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:29:57 PM UTC 2026
% Result : Theorem 34.91s 5.88s
% Output : Refutation 36.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 37
% Syntax : Number of formulae : 188 ( 77 unt; 2 def)
% Number of atoms : 314 ( 163 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 225 ( 99 ~; 94 |; 4 &)
% ( 5 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 5 con; 0-3 aty)
% Number of variables : 356 ( 0 sgn 351 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_kas_I2_J) ).
fof(f10,axiom,
? [X0] : 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),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_Az_O_A1_A_L_Az_A_K_A_Ia_A_K_Az_A_094_A_Ik_A_N_A1_J_J_A_061_A0_096) ).
fof(f32,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(f33,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(f36,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(f39,axiom,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,X0) = c_Groups_Oplus__class_Oplus(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f40,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(f44,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(f50,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(f61,axiom,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
fof(f80,axiom,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(f89,axiom,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
fof(f107,axiom,
! [X0,X1,X2,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).
fof(f165,axiom,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
<=> ? [X1] : X0 = c_Nat_OSuc(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
fof(f424,axiom,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(f440,axiom,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
fof(f484,axiom,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> c_Polynomial_Omonom(X2,X1,c_Nat_OSuc(X0)) = c_Polynomial_OpCons(X2,c_Groups_Ozero__class_Ozero(X2),c_Polynomial_Omonom(X2,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__Suc) ).
fof(f485,axiom,
! [X0,X1] :
( class_Groups_Ozero(X1)
=> c_Polynomial_Omonom(X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__0) ).
fof(f486,axiom,
! [X0,X1,X2,X3,X4] :
( class_Rings_Ocomm__semiring__0(X4)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),c_Polynomial_Omonom(X4,X3,X2)),c_Polynomial_Omonom(X4,X1,X0)) = c_Polynomial_Omonom(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__monom) ).
fof(f528,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Polynomial_OpCons(X3,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(X3,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Polynomial_Opoly(X3,X1),X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pCons) ).
fof(f529,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Omonom(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__monom) ).
fof(f533,axiom,
! [X0] :
( class_Groups_Ozero(X0)
=> c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__0__0) ).
fof(f538,axiom,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( c_Polynomial_Omonom(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> X1 = c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__0__iff) ).
fof(f587,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__0(X1)
=> c_Polynomial_Osmult(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__right) ).
fof(f589,axiom,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__1__left) ).
fof(f633,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Osmult(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Polynomial_Opoly(X3,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__smult) ).
fof(f637,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> c_Polynomial_Osmult(X3,X2,c_Polynomial_Omonom(X3,X1,X0)) = c_Polynomial_Omonom(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__monom) ).
fof(f643,axiom,
! [X0,X1,X2,X3] :
( class_Rings_Ocomm__semiring__0(X3)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_OpCons(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X1,X2),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pCons__right) ).
fof(f1166,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f1178,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(f1179,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(f1196,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(f1229,axiom,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(f1256,axiom,
( ? [X0] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),v_k____)),v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1257,conjecture,
v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f1258,negated_conjecture,
~ v_thesis____,
inference(negated_conjecture,[status(cth)],[f1257]) ).
fof(f1259,plain,
~ v_thesis____,
inference(flattening,[],[f1258]) ).
fof(f1278,plain,
( v_thesis____
| ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),v_k____)),v_a____)) ),
inference(ennf_transformation,[],[f1256]) ).
fof(f1436,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f1474,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f440]) ).
fof(f1574,plain,
! [X0,X1,X2,X3] :
( c_Polynomial_Osmult(X3,X2,c_Polynomial_Omonom(X3,X1,X0)) = c_Polynomial_Omonom(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0)
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f637]) ).
fof(f1578,plain,
! [X0,X1,X2] :
( ( c_Polynomial_Omonom(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
<=> X1 = c_Groups_Ozero__class_Ozero(X2) )
| ~ class_Groups_Ozero(X2) ),
inference(ennf_transformation,[],[f538]) ).
fof(f1581,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Omonom(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f529]) ).
fof(f1582,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),c_Polynomial_Omonom(X4,X3,X2)),c_Polynomial_Omonom(X4,X1,X0)) = c_Polynomial_Omonom(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0))
| ~ class_Rings_Ocomm__semiring__0(X4) ),
inference(ennf_transformation,[],[f486]) ).
fof(f1583,plain,
! [X0,X1] :
( c_Polynomial_Omonom(X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Groups_Ozero(X1) ),
inference(ennf_transformation,[],[f485]) ).
fof(f1584,plain,
! [X0,X1,X2] :
( c_Polynomial_Omonom(X2,X1,c_Nat_OSuc(X0)) = c_Polynomial_OpCons(X2,c_Groups_Ozero__class_Ozero(X2),c_Polynomial_Omonom(X2,X1,X0))
| ~ class_Groups_Ozero(X2) ),
inference(ennf_transformation,[],[f484]) ).
fof(f1589,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_OpCons(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X1,X2),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0)))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(ennf_transformation,[],[f643]) ).
fof(f1600,plain,
! [X0] :
( c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ozero(X0) ),
inference(ennf_transformation,[],[f533]) ).
fof(f1602,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,[],[f528]) ).
fof(f1604,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,[],[f633]) ).
fof(f1616,plain,
! [X0,X1] :
( c_Polynomial_Osmult(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(ennf_transformation,[],[f587]) ).
fof(f1623,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1229]) ).
fof(f1648,plain,
! [X0,X1] :
( c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f589]) ).
fof(f1652,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,[],[f44]) ).
fof(f1655,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,[],[f40]) ).
fof(f1656,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,[],[f39]) ).
fof(f1659,plain,
! [X0,X1,X2,X3] :
( c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f36]) ).
fof(f1662,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,[],[f33]) ).
fof(f1663,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_Rings_Ocomm__semiring__1(X3) ),
inference(ennf_transformation,[],[f32]) ).
fof(f1815,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
| ~ class_RealVector_Oreal__normed__algebra(X3) ),
inference(ennf_transformation,[],[f107]) ).
fof(f1907,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),sK4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),sK4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4)],[f10]) ).
fof(f1991,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ! [X1] : c_Nat_OSuc(X1) != X0 )
& ( ? [X1] : X0 = c_Nat_OSuc(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
inference(nnf_transformation,[],[f165]) ).
fof(f1992,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ! [X1] : c_Nat_OSuc(X1) != X0 )
& ( ? [X2] : c_Nat_OSuc(X2) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
inference(rectify,[],[f1991]) ).
fof(f1993,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ! [X1] : c_Nat_OSuc(X1) != X0 )
& ( c_Nat_OSuc(sK9(X0)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X2,sK9(X0))],[f1992]) ).
fof(f1999,plain,
! [X0,X1,X2] :
( ( ( c_Polynomial_Omonom(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Groups_Ozero__class_Ozero(X2) != X1 )
& ( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Polynomial_Omonom(X2,X1,X0) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) ) )
| ~ class_Groups_Ozero(X2) ),
inference(nnf_transformation,[],[f1578]) ).
fof(f2063,plain,
! [X0] :
( v_thesis____
| c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),v_k____)),v_a____)) ),
inference(cnf_transformation,[],[f1278]) ).
fof(f2064,plain,
~ v_thesis____,
inference(cnf_transformation,[],[f1259]) ).
fof(f2102,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f80]) ).
fof(f2205,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),sK4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),sK4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
inference(cnf_transformation,[],[f1907]) ).
fof(f2207,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1179]) ).
fof(f2208,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1178]) ).
fof(f2234,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f61]) ).
fof(f2238,plain,
v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f3]) ).
fof(f2345,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f424]) ).
fof(f2353,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
inference(cnf_transformation,[],[f1436]) ).
fof(f2419,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1 ),
inference(cnf_transformation,[],[f1474]) ).
fof(f2465,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1) = X0,
inference(cnf_transformation,[],[f89]) ).
fof(f2584,plain,
! [X0] :
( c_Nat_OSuc(sK9(X0)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(cnf_transformation,[],[f1993]) ).
fof(f2604,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| c_Polynomial_Osmult(X3,X2,c_Polynomial_Omonom(X3,X1,X0)) = c_Polynomial_Omonom(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),X0) ),
inference(cnf_transformation,[],[f1574]) ).
fof(f2609,plain,
! [X2,X0,X1] :
( c_Polynomial_Omonom(X2,X1,X0) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Groups_Ozero__class_Ozero(X2) != X1
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f1999]) ).
fof(f2613,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(c_Polynomial_Opoly(X3,c_Polynomial_Omonom(X3,X2,X1)),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X3),X0),X1)) ),
inference(cnf_transformation,[],[f1581]) ).
fof(f2614,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Rings_Ocomm__semiring__0(X4)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4)),c_Polynomial_Omonom(X4,X3,X2)),c_Polynomial_Omonom(X4,X1,X0)) = c_Polynomial_Omonom(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)) ),
inference(cnf_transformation,[],[f1582]) ).
fof(f2615,plain,
! [X0,X1] :
( ~ class_Groups_Ozero(X1)
| c_Polynomial_Omonom(X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(cnf_transformation,[],[f1583]) ).
fof(f2616,plain,
! [X2,X0,X1] :
( c_Polynomial_Omonom(X2,X1,c_Nat_OSuc(X0)) = c_Polynomial_OpCons(X2,c_Groups_Ozero__class_Ozero(X2),c_Polynomial_Omonom(X2,X1,X0))
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f1584]) ).
fof(f2627,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),c_Polynomial_OpCons(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X1,X2),c_Polynomial_OpCons(X3,c_Groups_Ozero__class_Ozero(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X3)),X2),X0))) ),
inference(cnf_transformation,[],[f1589]) ).
fof(f2638,plain,
! [X0] :
( ~ class_Groups_Ozero(X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(X0,c_Groups_Ozero__class_Ozero(X0),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
inference(cnf_transformation,[],[f1600]) ).
fof(f2642,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,[],[f1602]) ).
fof(f2644,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,[],[f1604]) ).
fof(f2676,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X1,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ),
inference(cnf_transformation,[],[f1616]) ).
fof(f2683,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f1623]) ).
fof(f2700,plain,
! [X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X0) = X0 ),
inference(cnf_transformation,[],[f1648]) ).
fof(f2704,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,[],[f1652]) ).
fof(f2707,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,[],[f1655]) ).
fof(f2708,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,[],[f1656]) ).
fof(f2711,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X1,X0)) ),
inference(cnf_transformation,[],[f1659]) ).
fof(f2714,plain,
! [X2,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) ),
inference(cnf_transformation,[],[f1662]) ).
fof(f2715,plain,
! [X2,X3,X0,X1] :
( ~ class_Rings_Ocomm__semiring__1(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(cnf_transformation,[],[f1663]) ).
fof(f2882,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1196]) ).
fof(f2917,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1166]) ).
fof(f2930,plain,
! [X2,X3,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),c_Groups_Oplus__class_Oplus(X3,X1,X0)) = c_Groups_Oplus__class_Oplus(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)) ),
inference(cnf_transformation,[],[f1815]) ).
fof(f3070,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(X0)) = X0 ),
inference(definition_unfolding,[],[f2584,f2345]) ).
fof(f3082,plain,
! [X2,X0,X1] :
( ~ class_Groups_Ozero(X2)
| c_Polynomial_OpCons(X2,c_Groups_Ozero__class_Ozero(X2),c_Polynomial_Omonom(X2,X1,X0)) = c_Polynomial_Omonom(X2,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
inference(definition_unfolding,[],[f2616,f2345]) ).
fof(f3181,plain,
! [X2,X0] :
( ~ class_Groups_Ozero(X2)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_Omonom(X2,c_Groups_Ozero__class_Ozero(X2),X0) ),
inference(equality_resolution,[],[f2609]) ).
fof(f3277,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),v_k____)),v_a____)),
inference(forward_subsumption_resolution,[],[f2063,f2064]) ).
fof(f3294,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,[],[f2207,f2644]) ).
fof(f3295,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,[],[f2207,f2642]) ).
fof(f3296,plain,
! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X2,X1)),X0) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,X1)),X0)),
inference(superposition,[],[f3295,f3294]) ).
fof(f3297,plain,
! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X2),X1)),
inference(resolution,[],[f2208,f2613]) ).
fof(f3298,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,[],[f2708,f2208]) ).
fof(f3311,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,[],[f2714,f2208]) ).
fof(f3321,plain,
! [X0] : c_Groups_Ozero__class_Ozero(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),X0),v_k____))),
inference(superposition,[],[f3277,f3311]) ).
fof(f3322,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,v_k____)),X0)),
inference(forward_demodulation,[],[f3321,f3297]) ).
fof(f3325,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Omonom(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0),
inference(resolution,[],[f3181,f2882]) ).
fof(f3339,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X0) = X0,
inference(resolution,[],[f2704,f2208]) ).
fof(f3345,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X0,
inference(superposition,[],[f3298,f3339]) ).
fof(f3351,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = X0,
inference(resolution,[],[f2353,f2208]) ).
fof(f3354,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X0),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X2))),
inference(resolution,[],[f2627,f2207]) ).
fof(f3358,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,[],[f2707,f2208]) ).
fof(f3368,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(resolution,[],[f2676,f2207]) ).
fof(f3381,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(resolution,[],[f2638,f2882]) ).
fof(f3384,plain,
! [X2,X3,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)),c_Polynomial_Omonom(tc_Complex_Ocomplex,X2,X3)) = c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),
inference(resolution,[],[f2614,f2207]) ).
fof(f3385,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)),
inference(resolution,[],[f2930,f2917]) ).
fof(f3410,plain,
! [X0,X1] : c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)) = c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)),
inference(resolution,[],[f3082,f2882]) ).
fof(f3427,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2)),
inference(resolution,[],[f2715,f2208]) ).
fof(f3454,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X1)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1)),
inference(superposition,[],[f3385,f3351]) ).
fof(f3612,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),sK4),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),sK4),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
inference(superposition,[],[f2205,f3427]) ).
fof(f3622,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_a____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Omonom(tc_Complex_Ocomplex,sK4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),sK4))),
inference(forward_demodulation,[],[f3612,f3297]) ).
fof(f3635,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a____,c_Polynomial_Omonom(tc_Complex_Ocomplex,sK4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),sK4)),
inference(forward_demodulation,[],[f3622,f3294]) ).
fof(f3941,plain,
! [X0] : c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(resolution,[],[f2615,f2882]) ).
fof(f4158,plain,
! [X0] : c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X0) = X0,
inference(resolution,[],[f2700,f2208]) ).
fof(f4347,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),
inference(resolution,[],[f2711,f2208]) ).
fof(f4376,plain,
! [X2,X3,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),X3)),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,X3)),X2))),
inference(superposition,[],[f3296,f4347]) ).
fof(f4381,plain,
! [X2,X3,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,X1),X3)),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,X3)),X2)),
inference(forward_demodulation,[],[f4376,f3296]) ).
fof(f4577,plain,
! [X2,X0,X1] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_Omonom(tc_Complex_Ocomplex,X1,X2)) = c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1),X2),
inference(resolution,[],[f2604,f2207]) ).
fof(f4586,plain,
! [X2,X3,X0,X1] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2),X3)) = c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2)),X3),
inference(superposition,[],[f4577,f3427]) ).
fof(f4612,plain,
! [X2,X3,X0,X1] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2),X3)) = c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),X3)),
inference(forward_demodulation,[],[f4586,f4577]) ).
fof(f4617,plain,
! [X2,X3,X0,X1] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2),X3)) = c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,c_Polynomial_Omonom(tc_Complex_Ocomplex,X2,X3))),
inference(forward_demodulation,[],[f4612,f4577]) ).
fof(f4619,plain,
! [X2,X3,X0,X1] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,c_Polynomial_Omonom(tc_Complex_Ocomplex,X2,X3))) = c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_Omonom(tc_Complex_Ocomplex,X2,X3))),
inference(forward_demodulation,[],[f4617,f4577]) ).
fof(f5089,plain,
! [X2,X0,X1] : c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(superposition,[],[f3384,f3325]) ).
fof(f5100,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_Omonom(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
inference(forward_demodulation,[],[f5089,f4577]) ).
fof(f5108,definition,
( spl27_17
<=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
introduced(definition,[new_symbols(definition,[spl27_17])],[avatar_definition]) ).
fof(f5109,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ spl27_17 ),
inference(avatar_component_clause,[],[f5108]) ).
fof(f5110,plain,
( ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| spl27_17 ),
inference(avatar_component_clause,[],[f5108]) ).
fof(f5122,plain,
! [X0,X1] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(forward_demodulation,[],[f5100,f3325]) ).
fof(f5129,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(forward_demodulation,[],[f5122,f3368]) ).
fof(f5131,plain,
( ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
| spl27_17 ),
inference(resolution,[],[f5110,f2683]) ).
fof(f5132,plain,
( $false
| spl27_17 ),
inference(forward_subsumption_resolution,[],[f5131,f2208]) ).
fof(f5133,plain,
spl27_17,
inference(avatar_contradiction_clause,[],[f5132]) ).
fof(f5148,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0) = X0
| ~ spl27_17 ),
inference(resolution,[],[f5109,f2704]) ).
fof(f5152,plain,
( ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X0,X1) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X1,X0)
| ~ spl27_17 ),
inference(resolution,[],[f5109,f2708]) ).
fof(f8467,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)),c_Polynomial_OpCons(tc_Complex_Ocomplex,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
inference(superposition,[],[f3354,f5129]) ).
fof(f8472,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)),c_Polynomial_OpCons(tc_Complex_Ocomplex,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(forward_demodulation,[],[f8467,f3381]) ).
fof(f8475,plain,
( ! [X2,X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)),c_Polynomial_OpCons(tc_Complex_Ocomplex,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)))
| ~ spl27_17 ),
inference(forward_demodulation,[],[f8472,f5152]) ).
fof(f8477,plain,
( ! [X2,X0,X1] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)),c_Polynomial_OpCons(tc_Complex_Ocomplex,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))
| ~ spl27_17 ),
inference(forward_demodulation,[],[f8475,f5148]) ).
fof(f8479,plain,
( ! [X2,X0,X1] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)),c_Polynomial_Omonom(tc_Complex_Ocomplex,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ spl27_17 ),
inference(forward_demodulation,[],[f8477,f3941]) ).
fof(f8481,plain,
( ! [X2,X0,X1] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)) = c_Polynomial_Omonom(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ spl27_17 ),
inference(forward_demodulation,[],[f8479,f3384]) ).
fof(f8483,plain,
( ! [X2,X0,X1] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)) = c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_Omonom(tc_Complex_Ocomplex,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ spl27_17 ),
inference(forward_demodulation,[],[f8481,f4577]) ).
fof(f8484,plain,
( ! [X2,X0,X1] : c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X1)) = c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_Omonom(tc_Complex_Ocomplex,X2,X1))
| ~ spl27_17 ),
inference(forward_demodulation,[],[f8483,f2102]) ).
fof(f8517,plain,
( ! [X2,X3,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X3,c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,X2))),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_Omonom(tc_Complex_Ocomplex,X1,X2))),X1))
| ~ spl27_17 ),
inference(superposition,[],[f3296,f8484]) ).
fof(f9960,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a____,c_Polynomial_Omonom(tc_Complex_Ocomplex,sK4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),sK4))),
inference(superposition,[],[f3454,f3635]) ).
fof(f10114,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a____,c_Polynomial_Omonom(tc_Complex_Ocomplex,sK4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),sK4)),
inference(forward_demodulation,[],[f9960,f3294]) ).
fof(f10144,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a____,c_Polynomial_Omonom(tc_Complex_Ocomplex,sK4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),sK4)),
inference(forward_demodulation,[],[f10114,f3358]) ).
fof(f17760,definition,
( spl27_76
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_k____) ),
introduced(definition,[new_symbols(definition,[spl27_76])],[avatar_definition]) ).
fof(f17761,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_k____)
| ~ spl27_76 ),
inference(avatar_component_clause,[],[f17760]) ).
fof(f17762,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_k____)
| spl27_76 ),
inference(avatar_component_clause,[],[f17760]) ).
fof(f17824,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_k____))
| spl27_76 ),
inference(resolution,[],[f17762,f2419]) ).
fof(f17827,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| spl27_76 ),
inference(forward_demodulation,[],[f17824,f2234]) ).
fof(f17830,plain,
( v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| spl27_76 ),
inference(forward_demodulation,[],[f17827,f2102]) ).
fof(f17831,plain,
( $false
| spl27_76 ),
inference(forward_subsumption_resolution,[],[f17830,f2238]) ).
fof(f17832,plain,
spl27_76,
inference(avatar_contradiction_clause,[],[f17831]) ).
fof(f17833,plain,
( v_k____ = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK9(v_k____))
| ~ spl27_76 ),
inference(resolution,[],[f17761,f3070]) ).
fof(f17841,plain,
( ! [X0] : c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,v_k____) = c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,sK9(v_k____)))
| ~ spl27_76 ),
inference(superposition,[],[f3410,f17833]) ).
fof(f17848,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = sK9(v_k____)
| ~ spl27_76 ),
inference(superposition,[],[f2465,f17833]) ).
fof(f17880,plain,
( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,sK9(v_k____)))),X2) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,v_k____)),X2))
| ~ spl27_76 ),
inference(superposition,[],[f4381,f17841]) ).
fof(f17897,plain,
( ! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,v_k____)),X2)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,c_Polynomial_Omonom(tc_Complex_Ocomplex,X0,sK9(v_k____)))),X2)
| ~ spl27_76 ),
inference(forward_demodulation,[],[f17880,f3345]) ).
fof(f20682,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a____,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_Omonom(tc_Complex_Ocomplex,sK4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),sK4)),
inference(superposition,[],[f10144,f4619]) ).
fof(f20713,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X0,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a____,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,c_Polynomial_Omonom(tc_Complex_Ocomplex,sK4,sK9(v_k____))))),sK4))
| ~ spl27_76 ),
inference(forward_demodulation,[],[f20682,f17848]) ).
fof(f20771,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a____,c_Polynomial_Omonom(tc_Complex_Ocomplex,sK4,sK9(v_k____)))),sK4))
| ~ spl27_76 ),
inference(superposition,[],[f20713,f4158]) ).
fof(f20864,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,sK9(v_k____)))),sK4)
| ~ spl27_17
| ~ spl27_76 ),
inference(forward_demodulation,[],[f20771,f8517]) ).
fof(f20903,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,v_k____)),sK4))
| ~ spl27_17
| ~ spl27_76 ),
inference(forward_demodulation,[],[f20864,f17897]) ).
fof(f20936,plain,
( $false
| ~ spl27_17
| ~ spl27_76 ),
inference(forward_subsumption_resolution,[],[f20903,f3322]) ).
fof(f20937,plain,
( ~ spl27_17
| ~ spl27_76 ),
inference(avatar_contradiction_clause,[],[f20936]) ).
cnf(s14,plain,
spl27_17,
inference(sat_conversion,[],[f5133]) ).
cnf(s68,plain,
spl27_76,
inference(sat_conversion,[],[f17832]) ).
cnf(s96,plain,
( ~ spl27_17
| ~ spl27_76 ),
inference(sat_conversion,[],[f20937]) ).
cnf(s98,plain,
~ spl27_17,
inference(rat,[],[s96,s68]) ).
cnf(s107,plain,
$false,
inference(rat,[],[s14,s98]) ).
fof(f20964,plain,
$false,
inference(avatar_sat_refutation,[],[s107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW257+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.29 % Computer : n020.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8046.5625MB
% 0.12/0.29 % OS : Linux 6.8.0-71-generic
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Mon Sep 28 13:26:04 UTC 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.28/0.33 Running first-order theorem proving
% 0.28/0.34 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
% 13.61/2.85 % (158347)Detected formulas, will run a generic FOF schedule.
% 13.61/2.85 % (158354)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=2049977519:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 13.61/2.85 % (158352)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=4201536862:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 13.61/2.85 % (158355)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3231563558:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 13.61/2.85 % (158356)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=153604205:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 13.61/2.85 % (158353)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=4024753885:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 13.61/2.85 % (158358)dis-21_1_sil=8000:lcm=predicate:random_seed=2479564052: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)
% 13.61/2.85 % (158357)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=847703329:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 13.61/2.85 % (158355)Refutation not found, incomplete strategy
% 13.61/2.85 % (158355)------------------------------
% 13.61/2.85 % (158355)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.61/2.85 % (158355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.61/2.85 % (158355)CaDiCaL version: 2.1.3
% 13.61/2.85 % (158355)Termination reason: Refutation not found, incomplete strategy
% 13.61/2.85 % (158355)Time elapsed: 0.011 s
% 13.61/2.85 % (158355)Peak memory usage: 89 MB
% 13.61/2.85 % (158355)Instructions burned: 17 (million)
% 13.61/2.85 % (158358)Instruction limit reached!
% 13.61/2.85 % (158358)------------------------------
% 13.61/2.85 % (158358)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.61/2.85 % (158358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.61/2.85 % (158358)CaDiCaL version: 2.1.3
% 13.61/2.85 % (158358)Termination reason: Instruction limit
% 13.61/2.85 % (158358)Termination phase: Saturation
% 13.61/2.85 % (158358)Time elapsed: 0.067 s
% 13.61/2.85 % (158358)Peak memory usage: 91 MB
% 13.61/2.85 % (158358)Instructions burned: 130 (million)
% 13.61/2.85 % (158356)Instruction limit reached!
% 13.61/2.85 % (158356)------------------------------
% 13.61/2.85 % (158356)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.61/2.85 % (158356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.61/2.85 % (158356)CaDiCaL version: 2.1.3
% 13.61/2.85 % (158356)Termination reason: Instruction limit
% 13.61/2.85 % (158356)Termination phase: Saturation
% 13.61/2.85 % (158356)Time elapsed: 0.070 s
% 13.61/2.85 % (158356)Peak memory usage: 90 MB
% 13.61/2.85 % (158356)Instructions burned: 119 (million)
% 13.61/2.85 % (158357)Instruction limit reached!
% 13.61/2.85 % (158357)------------------------------
% 13.61/2.85 % (158357)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.61/2.85 % (158357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.61/2.85 % (158357)CaDiCaL version: 2.1.3
% 13.61/2.85 % (158357)Termination reason: Instruction limit
% 13.61/2.85 % (158357)Termination phase: Saturation
% 13.61/2.85 % (158357)Time elapsed: 0.073 s
% 13.61/2.85 % (158357)Peak memory usage: 91 MB
% 13.61/2.85 % (158357)Instructions burned: 140 (million)
% 13.61/2.85 % (158368)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3034683996:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 13.61/2.85 % (158367)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3878427363:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 13.61/2.85 % (158366)lrs+10_1_sil=8000:sp=occurrence:random_seed=1507460525:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 13.61/2.85 % (158367)Refutation not found, incomplete strategy
% 13.61/2.85 % (158367)------------------------------
% 13.61/2.85 % (158367)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.61/2.85 % (158367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.19/3.76 % (158367)CaDiCaL version: 2.1.3
% 20.19/3.76 % (158367)Termination reason: Refutation not found, incomplete strategy
% 20.19/3.76 % (158367)Time elapsed: 0.009 s
% 20.19/3.76 % (158367)Peak memory usage: 89 MB
% 20.19/3.76 % (158367)Instructions burned: 17 (million)
% 20.19/3.76 % (158355)------------------------------
% 20.19/3.76 % (158355)------------------------------
% 20.19/3.76 % (158372)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=731942473:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 20.19/3.76 % (158366)Instruction limit reached!
% 20.19/3.76 % (158366)------------------------------
% 20.19/3.76 % (158366)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.19/3.76 % (158366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.19/3.76 % (158366)CaDiCaL version: 2.1.3
% 20.19/3.76 % (158366)Termination reason: Instruction limit
% 20.19/3.76 % (158366)Termination phase: Saturation
% 20.19/3.76 % (158366)Time elapsed: 0.185 s
% 20.19/3.76 % (158366)Peak memory usage: 92 MB
% 20.19/3.76 % (158366)Instructions burned: 286 (million)
% 20.19/3.76 % (158368)Instruction limit reached!
% 20.19/3.76 % (158368)------------------------------
% 20.19/3.76 % (158368)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.19/3.76 % (158368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.19/3.76 % (158368)CaDiCaL version: 2.1.3
% 20.19/3.76 % (158368)Termination reason: Instruction limit
% 20.19/3.76 % (158368)Termination phase: Saturation
% 20.19/3.76 % (158368)Time elapsed: 0.197 s
% 20.19/3.76 % (158368)Peak memory usage: 91 MB
% 20.19/3.76 % (158368)Instructions burned: 325 (million)
% 20.19/3.76 % (158372)Instruction limit reached!
% 20.19/3.76 % (158372)------------------------------
% 20.19/3.76 % (158372)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.19/3.76 % (158372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.19/3.76 % (158372)CaDiCaL version: 2.1.3
% 20.19/3.76 % (158372)Termination reason: Instruction limit
% 20.19/3.76 % (158372)Termination phase: Saturation
% 20.19/3.76 % (158372)Time elapsed: 0.076 s
% 20.19/3.76 % (158372)Peak memory usage: 92 MB
% 20.19/3.76 % (158372)Instructions burned: 250 (million)
% 20.19/3.76 % (158367)------------------------------
% 20.19/3.76 % (158367)------------------------------
% 20.19/3.76 % (158374)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3082339883:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 20.19/3.76 % (158375)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=842394309:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 20.19/3.76 % (158376)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3425374172:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 20.19/3.76 % (158376)Instruction limit reached!
% 20.19/3.76 % (158376)------------------------------
% 20.19/3.76 % (158376)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.19/3.76 % (158376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.19/3.76 % (158376)CaDiCaL version: 2.1.3
% 20.19/3.76 % (158376)Termination reason: Instruction limit
% 20.19/3.76 % (158376)Termination phase: Saturation
% 20.19/3.76 % (158376)Time elapsed: 0.031 s
% 20.19/3.76 % (158376)Peak memory usage: 90 MB
% 20.19/3.76 % (158376)Instructions burned: 115 (million)
% 20.19/3.76 % (158377)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=4080234356:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 20.19/3.76 % (158377)Refutation not found, incomplete strategy
% 20.19/3.76 % (158377)------------------------------
% 20.19/3.76 % (158377)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.19/3.76 % (158377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.19/3.76 % (158377)CaDiCaL version: 2.1.3
% 20.19/3.76 % (158377)Termination reason: Refutation not found, incomplete strategy
% 20.19/3.76 % (158377)Time elapsed: 0.059 s
% 20.19/3.76 % (158377)Peak memory usage: 90 MB
% 20.19/3.76 % (158377)Instructions burned: 122 (million)
% 20.19/3.76 % (158374)Instruction limit reached!
% 20.19/3.76 % (158374)------------------------------
% 20.19/3.76 % (158374)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.19/3.76 % (158374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.19/3.76 % (158374)CaDiCaL version: 2.1.3
% 20.19/3.76 % (158374)Termination reason: Instruction limit
% 33.09/5.60 % (158374)Termination phase: Saturation
% 33.09/5.60 % (158374)Time elapsed: 0.166 s
% 33.09/5.60 % (158374)Peak memory usage: 92 MB
% 33.09/5.60 % (158374)Instructions burned: 295 (million)
% 33.09/5.60 % (158381)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2289545725:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 33.09/5.60 % (158381)Refutation not found, incomplete strategy
% 33.09/5.60 % (158381)------------------------------
% 33.09/5.60 % (158381)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.09/5.60 % (158381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.09/5.60 % (158381)CaDiCaL version: 2.1.3
% 33.09/5.60 % (158381)Termination reason: Refutation not found, incomplete strategy
% 33.09/5.60 % (158381)Time elapsed: 0.008 s
% 33.09/5.60 % (158381)Peak memory usage: 89 MB
% 33.09/5.60 % (158381)Instructions burned: 33 (million)
% 33.09/5.60 % (158383)lrs+10_1_sil=8000:sp=occurrence:random_seed=2623203087:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 33.09/5.60 % (158381)------------------------------
% 33.09/5.60 % (158381)------------------------------
% 33.09/5.60 % (158377)------------------------------
% 33.09/5.60 % (158377)------------------------------
% 33.09/5.60 % (158386)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2337305657:i=437:sd=1:aac=none:ss=included_2988 on theBenchmark for (2988ds/437Mi)
% 33.09/5.60 % (158387)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2694333316:i=5202:ss=axioms:sgt=16_2988 on theBenchmark for (2988ds/5202Mi)
% 33.09/5.60 % (158386)Instruction limit reached!
% 33.09/5.60 % (158386)------------------------------
% 33.09/5.60 % (158386)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.09/5.60 % (158386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.09/5.60 % (158386)CaDiCaL version: 2.1.3
% 33.09/5.60 % (158386)Termination reason: Instruction limit
% 33.09/5.60 % (158386)Termination phase: Saturation
% 33.09/5.60 % (158386)Time elapsed: 0.129 s
% 33.09/5.60 % (158386)Peak memory usage: 94 MB
% 33.09/5.60 % (158386)Instructions burned: 439 (million)
% 33.09/5.60 % (158390)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=4214279678:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2986 on theBenchmark for (2986ds/134Mi)
% 33.09/5.60 % (158390)Instruction limit reached!
% 33.09/5.60 % (158390)------------------------------
% 33.09/5.60 % (158390)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.09/5.60 % (158390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.09/5.60 % (158390)CaDiCaL version: 2.1.3
% 33.09/5.60 % (158390)Termination reason: Instruction limit
% 33.09/5.60 % (158390)Termination phase: Saturation
% 33.09/5.60 % (158390)Time elapsed: 0.071 s
% 33.09/5.60 % (158390)Peak memory usage: 92 MB
% 33.09/5.60 % (158390)Instructions burned: 135 (million)
% 33.09/5.60 % (158383)Instruction limit reached!
% 33.09/5.60 % (158383)------------------------------
% 33.09/5.60 % (158383)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.09/5.60 % (158383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.09/5.60 % (158383)CaDiCaL version: 2.1.3
% 33.09/5.60 % (158383)Termination reason: Instruction limit
% 33.09/5.60 % (158383)Termination phase: Saturation
% 33.09/5.60 % (158383)Time elapsed: 0.576 s
% 33.09/5.60 % (158383)Peak memory usage: 97 MB
% 33.09/5.60 % (158383)Instructions burned: 907 (million)
% 33.09/5.60 % (158392)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=1604953302:st=8:i=592:sd=3:ep=RST:ss=axioms_2983 on theBenchmark for (2983ds/592Mi)
% 33.09/5.60 % (158375)Instruction limit reached!
% 33.09/5.60 % (158375)------------------------------
% 33.09/5.60 % (158375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.09/5.60 % (158375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.09/5.60 % (158375)CaDiCaL version: 2.1.3
% 33.09/5.60 % (158375)Termination reason: Instruction limit
% 33.09/5.60 % (158375)Termination phase: Saturation
% 33.09/5.60 % (158375)Time elapsed: 1.064 s
% 33.09/5.60 % (158375)Peak memory usage: 145 MB
% 33.09/5.60 % (158375)Instructions burned: 2351 (million)
% 33.09/5.60 % (158393)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=2566836914:st=3:i=13193:sd=3:ss=axioms_2983 on theBenchmark for (2983ds/13193Mi)
% 33.09/5.60 % (158396)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=4231149108:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2981 on theBenchmark for (2981ds/125Mi)
% 34.91/5.88 % (158396)Instruction limit reached!
% 34.91/5.88 % (158396)------------------------------
% 34.91/5.88 % (158396)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 34.91/5.88 % (158396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.91/5.88 % (158396)CaDiCaL version: 2.1.3
% 34.91/5.88 % (158396)Termination reason: Instruction limit
% 34.91/5.88 % (158396)Termination phase: Saturation
% 34.91/5.88 % (158396)Time elapsed: 0.068 s
% 34.91/5.88 % (158396)Peak memory usage: 91 MB
% 34.91/5.88 % (158396)Instructions burned: 125 (million)
% 34.91/5.88 % (158392)Instruction limit reached!
% 34.91/5.88 % (158392)------------------------------
% 34.91/5.88 % (158392)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 34.91/5.88 % (158392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.91/5.88 % (158392)CaDiCaL version: 2.1.3
% 34.91/5.88 % (158392)Termination reason: Instruction limit
% 34.91/5.88 % (158392)Termination phase: Saturation
% 34.91/5.88 % (158392)Time elapsed: 0.338 s
% 34.91/5.88 % (158392)Peak memory usage: 97 MB
% 34.91/5.88 % (158392)Instructions burned: 593 (million)
% 34.91/5.88 % (158398)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=3675529836:i=134:gtgl=5:slsql=off:gtg=exists_sym_2978 on theBenchmark for (2978ds/134Mi)
% 34.91/5.88 % (158399)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=3683809817:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2978 on theBenchmark for (2978ds/141Mi)
% 34.91/5.88 % (158399)Refutation not found, incomplete strategy
% 34.91/5.88 % (158399)------------------------------
% 34.91/5.88 % (158399)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 34.91/5.88 % (158399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.91/5.88 % (158399)CaDiCaL version: 2.1.3
% 34.91/5.88 % (158399)Termination reason: Refutation not found, incomplete strategy
% 34.91/5.88 % (158399)Time elapsed: 0.007 s
% 34.91/5.88 % (158399)Peak memory usage: 89 MB
% 34.91/5.88 % (158399)Instructions burned: 11 (million)
% 34.91/5.88 % (158398)Instruction limit reached!
% 34.91/5.88 % (158398)------------------------------
% 34.91/5.88 % (158398)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 34.91/5.88 % (158398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.91/5.88 % (158398)CaDiCaL version: 2.1.3
% 34.91/5.88 % (158398)Termination reason: Instruction limit
% 34.91/5.88 % (158398)Termination phase: Saturation
% 34.91/5.88 % (158398)Time elapsed: 0.064 s
% 34.91/5.88 % (158398)Peak memory usage: 90 MB
% 34.91/5.88 % (158398)Instructions burned: 134 (million)
% 34.91/5.88 % (158402)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=1365125658:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2976 on theBenchmark for (2976ds/431Mi)
% 34.91/5.88 % (158399)------------------------------
% 34.91/5.88 % (158399)------------------------------
% 34.91/5.88 % (158404)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=3614637571:i=6060:aac=none:ins=25_2974 on theBenchmark for (2974ds/6060Mi)
% 34.91/5.88 % (158402)Instruction limit reached!
% 34.91/5.88 % (158402)------------------------------
% 34.91/5.88 % (158402)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 34.91/5.88 % (158402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.91/5.88 % (158402)CaDiCaL version: 2.1.3
% 34.91/5.88 % (158402)Termination reason: Instruction limit
% 34.91/5.88 % (158402)Termination phase: Saturation
% 34.91/5.88 % (158402)Time elapsed: 0.208 s
% 34.91/5.88 % (158402)Peak memory usage: 92 MB
% 34.91/5.88 % (158402)Instructions burned: 431 (million)
% 34.91/5.88 % (158406)lrs+10_16_anc=all:slsqr=32,1:sil=8000:avsql=on:sp=unary_frequency:lcm=predicate:urr=full:rp=on:br=off:slsqc=4:flr=on:sac=on:slsq=on:avsqc=1:random_seed=1086051096:avsq=on:s2a=on:i=150:kws=precedence:nicw=on:gsp=on:rawr=on_2972 on theBenchmark for (2972ds/150Mi)
% 34.91/5.88 % (158406)Instruction limit reached!
% 34.91/5.88 % (158406)------------------------------
% 34.91/5.88 % (158406)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 34.91/5.88 % (158406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.91/5.88 % (158406)CaDiCaL version: 2.1.3
% 34.91/5.88 % (158406)Termination reason: Instruction limit
% 34.91/5.88 % (158406)Termination phase: Saturation
% 34.91/5.88 % (158406)Time elapsed: 0.080 s
% 34.91/5.88 % (158406)Peak memory usage: 91 MB
% 34.91/5.88 % (158406)Instructions burned: 150 (million)
% 34.91/5.88 % (158408)lrs+1010_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=ground:npcc=on:sp=arity:urr=on:random_seed=1332281940:i=14155:bd=all_2970 on theBenchmark for (2970ds/14155Mi)
% 34.91/5.88 % (158387)Instruction limit reached!
% 34.91/5.88 % (158387)------------------------------
% 34.91/5.88 % (158387)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 34.91/5.88 % (158387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.91/5.88 % (158387)CaDiCaL version: 2.1.3
% 34.91/5.88 % (158387)Termination reason: Instruction limit
% 34.91/5.88 % (158387)Termination phase: Saturation
% 34.91/5.88 % (158387)Time elapsed: 1.957 s
% 34.91/5.88 % (158387)Peak memory usage: 166 MB
% 34.91/5.88 % (158387)Instructions burned: 5204 (million)
% 34.91/5.88 % (158410)lrs+10_1024_sil=16000:plsq=on:plsqr=32,1:sos=all:fs=off:gs=on:newcnf=on:random_seed=1825381684:i=667:av=off:fsr=off_2967 on theBenchmark for (2967ds/667Mi)
% 34.91/5.88 % (158410)Refutation not found, incomplete strategy
% 34.91/5.88 % (158410)------------------------------
% 34.91/5.88 % (158410)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 34.91/5.88 % (158410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.91/5.88 % (158410)CaDiCaL version: 2.1.3
% 34.91/5.88 % (158410)Termination reason: Refutation not found, incomplete strategy
% 34.91/5.88 % (158410)Time elapsed: 0.030 s
% 34.91/5.88 % (158410)Peak memory usage: 91 MB
% 34.91/5.88 % (158410)Instructions burned: 110 (million)
% 34.91/5.88 % (158410)------------------------------
% 34.91/5.88 % (158410)------------------------------
% 34.91/5.88 % (158412)ott-1011_3:1_anc=all_dependent:to=lpo:sil=8000:drc=ordering:sas=cadical:fdtod=off:sp=reverse_frequency:spb=goal_then_units:urr=full:lftc=20:newcnf=on:random_seed=4051741872:s2a=on:i=185:s2at=1.8:fdi=4_2963 on theBenchmark for (2963ds/185Mi)
% 34.91/5.88 % (158412)Instruction limit reached!
% 34.91/5.88 % (158412)------------------------------
% 34.91/5.88 % (158412)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 34.91/5.88 % (158412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.91/5.88 % (158412)CaDiCaL version: 2.1.3
% 34.91/5.88 % (158412)Termination reason: Instruction limit
% 34.91/5.88 % (158412)Termination phase: Saturation
% 34.91/5.88 % (158412)Time elapsed: 0.054 s
% 34.91/5.88 % (158412)Peak memory usage: 92 MB
% 34.91/5.88 % (158412)Instructions burned: 187 (million)
% 34.91/5.88 % (158414)dis+1010_14_anc=all:to=lpo:sil=8000:sp=arity:slsq=on:random_seed=2137145436:i=193:ins=10:fsr=off:ss=axioms:fsd=on_2962 on theBenchmark for (2962ds/193Mi)
% 34.91/5.88 % (158414)Instruction limit reached!
% 34.91/5.88 % (158414)------------------------------
% 34.91/5.88 % (158414)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 34.91/5.88 % (158414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.91/5.88 % (158414)CaDiCaL version: 2.1.3
% 34.91/5.88 % (158414)Termination reason: Instruction limit
% 34.91/5.88 % (158414)Termination phase: Saturation
% 34.91/5.88 % (158414)Time elapsed: 0.063 s
% 34.91/5.88 % (158414)Peak memory usage: 93 MB
% 34.91/5.88 % (158414)Instructions burned: 195 (million)
% 34.91/5.88 % (158416)dis+1011_7_sil=8000:sp=occurrence:sos=all:fd=off:random_seed=1608577041:st=5.3:i=4850:sd=4:av=off:sup=off:ss=included:sgt=16_2960 on theBenchmark for (2960ds/4850Mi)
% 34.91/5.88 % (158416)Refutation not found, incomplete strategy
% 34.91/5.88 % (158416)------------------------------
% 34.91/5.88 % (158416)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 34.91/5.88 % (158416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.91/5.88 % (158416)CaDiCaL version: 2.1.3
% 34.91/5.88 % (158416)Termination reason: Refutation not found, incomplete strategy
% 34.91/5.88 % (158416)Time elapsed: 0.025 s
% 34.91/5.88 % (158416)Peak memory usage: 91 MB
% 34.91/5.88 % (158416)Instructions burned: 94 (million)
% 34.91/5.88 % (158416)------------------------------
% 34.91/5.88 % (158416)------------------------------
% 34.91/5.88 % (158418)lrs+1011_1_ncem=casc2026/models/loop8.pt:sil=32000:tgt=ground:npcc=on:sp=const_frequency:acc=on:urr=on:random_seed=1441090370:i=12111:sd=1:ss=included_2957 on theBenchmark for (2957ds/12111Mi)
% 34.91/5.88 % (158393)First to succeed.
% 34.91/5.88 % (158393)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-158347"
% 34.91/5.88 % (158393)Refutation found. Thanks to Tanya!
% 34.91/5.88 % SZS status Theorem for theBenchmark
% 34.91/5.88 % SZS output start Proof for theBenchmark
% See solution above
% 36.36/6.08 % (158393)------------------------------
% 36.36/6.08 % (158393)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 36.36/6.08 % (158393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.36/6.08 % (158393)CaDiCaL version: 2.1.3
% 36.36/6.08 % (158393)Termination reason: Refutation
% 36.36/6.08 % (158393)Time elapsed: 2.929 s
% 36.36/6.08 % (158393)Peak memory usage: 166 MB
% 36.36/6.08 % (158393)Instructions burned: 4636 (million)
% 36.36/6.08 % (158393)------------------------------
% 36.36/6.08 % (158393)------------------------------
% 36.36/6.08 % (158347)Success in time 5.073 s
% 36.36/6.08 % Vampire exiting
%------------------------------------------------------------------------------