%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW245+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 : n003.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 01:29:56 PM UTC 2026
% Result : Theorem 3.47s 1.16s
% Output : Refutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 20
% Syntax : Number of formulae : 121 ( 14 unt; 15 def)
% Number of atoms : 397 ( 131 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 469 ( 193 ~; 215 |; 34 &)
% ( 15 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 18 ( 16 usr; 15 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 10 con; 0-4 aty)
% Number of variables : 85 ( 0 sgn 60 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
( class_Rings_Oidom(t_a)
=> ( v_c____ != c_Groups_Ozero__class_Ozero(t_a)
=> ? [X0,X1] :
( X1 != c_Groups_Ozero__class_Ozero(t_a)
& ? [X2] :
( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) )
& ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096c_A_126_061_A_I0_058_058_Ha_J_061_061_062_AEX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_I_Iif_Aq_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_Aq_J_J_A_L_Ak_J_A_061_A_Iif_ApCons_Ac_Acs_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_A_IpCons_Ac_Acs_J_J_J_A_G_A_IALL_Az_O_Apoly_A_IpCons_Ac_Acs_J_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096) ).
fof(f5,axiom,
( class_Rings_Oidom(t_a)
=> ( v_c____ = c_Groups_Ozero__class_Ozero(t_a)
=> ? [X0,X1] :
( X1 != c_Groups_Ozero__class_Ozero(t_a)
& ? [X2] :
( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) )
& ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096c_A_061_A_I0_058_058_Ha_J_061_061_062_AEX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_I_Iif_Aq_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_Aq_J_J_A_L_Ak_J_A_061_A_Iif_ApCons_Ac_Acs_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_A_IpCons_Ac_Acs_J_J_J_A_G_A_IALL_Az_O_Apoly_A_IpCons_Ac_Acs_J_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096) ).
fof(f188,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/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(f1160,conjecture,
? [X0,X1] :
( X1 != c_Groups_Ozero__class_Ozero(t_a)
& ? [X2] :
( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) )
& ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1161,negated_conjecture,
~ ? [X0,X1] :
( X1 != c_Groups_Ozero__class_Ozero(t_a)
& ? [X2] :
( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) )
& ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3)) ) ),
inference(negated_conjecture,[status(cth)],[f1160]) ).
fof(f1162,axiom,
class_Rings_Oidom(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
fof(f1353,plain,
( ? [X0,X1] :
( X1 != c_Groups_Ozero__class_Ozero(t_a)
& ? [X2] :
( ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3)) ) )
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(ennf_transformation,[],[f4]) ).
fof(f1354,plain,
( ? [X0,X1] :
( X1 != c_Groups_Ozero__class_Ozero(t_a)
& ? [X2] :
( ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3)) ) )
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(flattening,[],[f1353]) ).
fof(f1355,plain,
( ? [X0,X1] :
( X1 != c_Groups_Ozero__class_Ozero(t_a)
& ? [X2] :
( ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3)) ) )
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(ennf_transformation,[],[f5]) ).
fof(f1356,plain,
( ? [X0,X1] :
( X1 != c_Groups_Ozero__class_Ozero(t_a)
& ? [X2] :
( ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3)) ) )
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(flattening,[],[f1355]) ).
fof(f2264,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(t_a) = X1
| ! [X2] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))
& c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) != c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
& c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ? [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3)) ) ),
inference(ennf_transformation,[],[f1161]) ).
fof(f2272,plain,
( ( c_Groups_Ozero__class_Ozero(t_a) != sK6
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK7))),sK5))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK7))),sK5))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK6,sK7)),X3)) )
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f1354]) ).
fof(f2273,plain,
( ( c_Groups_Ozero__class_Ozero(t_a) != sK9
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK10))),sK8))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK10))),sK8))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK8)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK9,sK10)),X3)) )
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10)],[f1356]) ).
fof(f2528,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(t_a) = X1
| ! [X2] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))
& c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) != c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
& c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK32(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK32(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK32(X0,X1,X2))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(X3,sK32(X0,X1,X2))],[f2264]) ).
fof(f2534,plain,
! [X3] :
( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK6,sK7)),X3))
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(cnf_transformation,[],[f2272]) ).
fof(f2535,plain,
( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK7))),sK5))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(cnf_transformation,[],[f2272]) ).
fof(f2536,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK7))),sK5))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(cnf_transformation,[],[f2272]) ).
fof(f2537,plain,
( c_Groups_Ozero__class_Ozero(t_a) != sK6
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(cnf_transformation,[],[f2272]) ).
fof(f2538,plain,
! [X3] :
( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK8)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK9,sK10)),X3))
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(cnf_transformation,[],[f2273]) ).
fof(f2539,plain,
( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK10))),sK8))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(cnf_transformation,[],[f2273]) ).
fof(f2540,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK10))),sK8))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(cnf_transformation,[],[f2273]) ).
fof(f2541,plain,
( c_Groups_Ozero__class_Ozero(t_a) != sK9
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(cnf_transformation,[],[f2273]) ).
fof(f2783,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,[],[f188]) ).
fof(f3831,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(t_a) = X1
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) != c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
| hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK32(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK32(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK32(X0,X1,X2))) ),
inference(cnf_transformation,[],[f2528]) ).
fof(f3832,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(t_a) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK32(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK32(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK32(X0,X1,X2))) ),
inference(cnf_transformation,[],[f2528]) ).
fof(f3834,plain,
class_Rings_Oidom(t_a),
inference(cnf_transformation,[],[f1162]) ).
fof(f3835,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK7))),sK5))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(definition_unfolding,[],[f2536,f2783,f2783]) ).
fof(f3836,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK7))),sK5)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(definition_unfolding,[],[f2535,f2783,f2783,f2783]) ).
fof(f3837,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK10))),sK8))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(definition_unfolding,[],[f2540,f2783,f2783]) ).
fof(f3838,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK10))),sK8))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(definition_unfolding,[],[f2539,f2783,f2783,f2783]) ).
fof(f3965,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(t_a) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,X2))),X0))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK32(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK32(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK32(X0,X1,X2))) ),
inference(definition_unfolding,[],[f3832,f2783,f2783]) ).
fof(f3966,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(t_a) = X1
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,X2))),X0))
| hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK32(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK32(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK32(X0,X1,X2))) ),
inference(definition_unfolding,[],[f3831,f2783,f2783,f2783]) ).
fof(f4141,definition,
! [X0,X1] :
( sQ33_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ33_eqProxy])],[equality_proxy_definition]) ).
fof(f4147,plain,
( ~ sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),sK6)
| sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),v_c____)
| ~ class_Rings_Oidom(t_a) ),
inference(equality_proxy_replacement,[],[f2537,f4141,f4141]) ).
fof(f4148,plain,
( sQ33_eqProxy(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK7))),sK5)))
| ~ sQ33_eqProxy(c_Polynomial_OpCons(t_a,v_c____,v_cs____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
| sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),v_c____)
| ~ class_Rings_Oidom(t_a) ),
inference(equality_proxy_replacement,[],[f3835,f4141,f4141,f4141]) ).
fof(f4149,plain,
( sQ33_eqProxy(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK7))),sK5)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))))
| sQ33_eqProxy(c_Polynomial_OpCons(t_a,v_c____,v_cs____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
| sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),v_c____)
| ~ class_Rings_Oidom(t_a) ),
inference(equality_proxy_replacement,[],[f3836,f4141,f4141,f4141]) ).
fof(f4150,plain,
! [X3] :
( sQ33_eqProxy(hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK6,sK7)),X3)))
| sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),v_c____)
| ~ class_Rings_Oidom(t_a) ),
inference(equality_proxy_replacement,[],[f2534,f4141,f4141]) ).
fof(f4151,plain,
( ~ sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),sK9)
| ~ sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),v_c____)
| ~ class_Rings_Oidom(t_a) ),
inference(equality_proxy_replacement,[],[f2541,f4141,f4141]) ).
fof(f4152,plain,
( sQ33_eqProxy(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK10))),sK8)))
| ~ sQ33_eqProxy(c_Polynomial_OpCons(t_a,v_c____,v_cs____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
| ~ sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),v_c____)
| ~ class_Rings_Oidom(t_a) ),
inference(equality_proxy_replacement,[],[f3837,f4141,f4141,f4141]) ).
fof(f4153,plain,
( sQ33_eqProxy(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK10))),sK8)))
| sQ33_eqProxy(c_Polynomial_OpCons(t_a,v_c____,v_cs____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
| ~ sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),v_c____)
| ~ class_Rings_Oidom(t_a) ),
inference(equality_proxy_replacement,[],[f3838,f4141,f4141,f4141]) ).
fof(f4154,plain,
! [X3] :
( sQ33_eqProxy(hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK8)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK9,sK10)),X3)))
| ~ sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),v_c____)
| ~ class_Rings_Oidom(t_a) ),
inference(equality_proxy_replacement,[],[f2538,f4141,f4141]) ).
fof(f4897,plain,
! [X2,X0,X1] :
( sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),X1)
| ~ sQ33_eqProxy(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,X2))),X0)))
| ~ sQ33_eqProxy(c_Polynomial_OpCons(t_a,v_c____,v_cs____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
| ~ sQ33_eqProxy(hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK32(X0,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK32(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK32(X0,X1,X2)))) ),
inference(equality_proxy_replacement,[],[f3965,f4141,f4141,f4141,f4141]) ).
fof(f4898,plain,
! [X2,X0,X1] :
( sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),X1)
| sQ33_eqProxy(c_Polynomial_OpCons(t_a,v_c____,v_cs____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
| ~ sQ33_eqProxy(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,X2))),X0)))
| ~ sQ33_eqProxy(hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK32(X0,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK32(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK32(X0,X1,X2)))) ),
inference(equality_proxy_replacement,[],[f3966,f4141,f4141,f4141,f4141]) ).
fof(f4901,plain,
! [X0,X1] :
( sQ33_eqProxy(X1,X0)
| ~ sQ33_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f4141]) ).
fof(f4907,definition,
( spl34_1
<=> sQ33_eqProxy(c_Polynomial_OpCons(t_a,v_c____,v_cs____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) ),
introduced(definition,[new_symbols(definition,[spl34_1])],[avatar_definition]) ).
fof(f4910,definition,
( spl34_2
<=> ! [X2,X0,X1] :
( sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),X1)
| ~ sQ33_eqProxy(hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK32(X0,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK32(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK32(X0,X1,X2))))
| ~ sQ33_eqProxy(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,X2))),X0))) ) ),
introduced(definition,[new_symbols(definition,[spl34_2])],[avatar_definition]) ).
fof(f4911,plain,
( ! [X2,X0,X1] :
( ~ sQ33_eqProxy(hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK32(X0,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK32(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK32(X0,X1,X2))))
| sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),X1)
| ~ sQ33_eqProxy(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,X2))),X0))) )
| ~ spl34_2 ),
inference(avatar_component_clause,[],[f4910]) ).
fof(f4912,plain,
( spl34_1
| spl34_2 ),
inference(avatar_split_clause,[],[f4898,f4910,f4907]) ).
fof(f4915,definition,
( spl34_3
<=> ! [X2,X0,X1] :
( sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),X1)
| ~ sQ33_eqProxy(hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK32(X0,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK32(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK32(X0,X1,X2))))
| ~ sQ33_eqProxy(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,X2))),X0))) ) ),
introduced(definition,[new_symbols(definition,[spl34_3])],[avatar_definition]) ).
fof(f4916,plain,
( ! [X2,X0,X1] :
( ~ sQ33_eqProxy(hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK32(X0,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK32(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK32(X0,X1,X2))))
| sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),X1)
| ~ sQ33_eqProxy(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,X2))),X0))) )
| ~ spl34_3 ),
inference(avatar_component_clause,[],[f4915]) ).
fof(f4917,plain,
( ~ spl34_1
| spl34_3 ),
inference(avatar_split_clause,[],[f4897,f4915,f4907]) ).
fof(f4937,definition,
( spl34_9
<=> class_Rings_Oidom(t_a) ),
introduced(definition,[new_symbols(definition,[spl34_9])],[avatar_definition]) ).
fof(f4938,plain,
( ~ class_Rings_Oidom(t_a)
| spl34_9 ),
inference(avatar_component_clause,[],[f4937]) ).
fof(f4963,definition,
( spl34_16
<=> sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),v_c____) ),
introduced(definition,[new_symbols(definition,[spl34_16])],[avatar_definition]) ).
fof(f4966,definition,
( spl34_17
<=> ! [X3] : sQ33_eqProxy(hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK8)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK9,sK10)),X3))) ),
introduced(definition,[new_symbols(definition,[spl34_17])],[avatar_definition]) ).
fof(f4967,plain,
( ! [X3] : sQ33_eqProxy(hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK8)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK9,sK10)),X3)))
| ~ spl34_17 ),
inference(avatar_component_clause,[],[f4966]) ).
fof(f4968,plain,
( ~ spl34_9
| ~ spl34_16
| spl34_17 ),
inference(avatar_split_clause,[],[f4154,f4966,f4963,f4937]) ).
fof(f4970,definition,
( spl34_18
<=> sQ33_eqProxy(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK10))),sK8))) ),
introduced(definition,[new_symbols(definition,[spl34_18])],[avatar_definition]) ).
fof(f4972,plain,
( ~ spl34_9
| ~ spl34_16
| spl34_1
| spl34_18 ),
inference(avatar_split_clause,[],[f4153,f4970,f4907,f4963,f4937]) ).
fof(f4974,definition,
( spl34_19
<=> sQ33_eqProxy(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK10))),sK8))) ),
introduced(definition,[new_symbols(definition,[spl34_19])],[avatar_definition]) ).
fof(f4976,plain,
( ~ spl34_9
| ~ spl34_16
| ~ spl34_1
| spl34_19 ),
inference(avatar_split_clause,[],[f4152,f4974,f4907,f4963,f4937]) ).
fof(f4978,definition,
( spl34_20
<=> sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),sK9) ),
introduced(definition,[new_symbols(definition,[spl34_20])],[avatar_definition]) ).
fof(f4980,plain,
( ~ spl34_9
| ~ spl34_16
| ~ spl34_20 ),
inference(avatar_split_clause,[],[f4151,f4978,f4963,f4937]) ).
fof(f4983,definition,
( spl34_21
<=> ! [X3] : sQ33_eqProxy(hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK6,sK7)),X3))) ),
introduced(definition,[new_symbols(definition,[spl34_21])],[avatar_definition]) ).
fof(f4984,plain,
( ! [X3] : sQ33_eqProxy(hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK6,sK7)),X3)))
| ~ spl34_21 ),
inference(avatar_component_clause,[],[f4983]) ).
fof(f4985,plain,
( ~ spl34_9
| spl34_16
| spl34_21 ),
inference(avatar_split_clause,[],[f4150,f4983,f4963,f4937]) ).
fof(f4987,definition,
( spl34_22
<=> sQ33_eqProxy(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK7))),sK5)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))) ),
introduced(definition,[new_symbols(definition,[spl34_22])],[avatar_definition]) ).
fof(f4988,plain,
( sQ33_eqProxy(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK7))),sK5)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))))
| ~ spl34_22 ),
inference(avatar_component_clause,[],[f4987]) ).
fof(f4989,plain,
( ~ spl34_9
| spl34_16
| spl34_1
| spl34_22 ),
inference(avatar_split_clause,[],[f4149,f4987,f4907,f4963,f4937]) ).
fof(f4991,definition,
( spl34_23
<=> sQ33_eqProxy(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK7))),sK5))) ),
introduced(definition,[new_symbols(definition,[spl34_23])],[avatar_definition]) ).
fof(f4993,plain,
( ~ spl34_9
| spl34_16
| ~ spl34_1
| spl34_23 ),
inference(avatar_split_clause,[],[f4148,f4991,f4907,f4963,f4937]) ).
fof(f4995,definition,
( spl34_24
<=> sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),sK6) ),
introduced(definition,[new_symbols(definition,[spl34_24])],[avatar_definition]) ).
fof(f4997,plain,
( ~ spl34_9
| spl34_16
| ~ spl34_24 ),
inference(avatar_split_clause,[],[f4147,f4995,f4963,f4937]) ).
fof(f5014,plain,
( $false
| spl34_9 ),
inference(resolution,[],[f4938,f3834]) ).
fof(f5015,plain,
spl34_9,
inference(avatar_contradiction_clause,[],[f5014]) ).
fof(f5016,plain,
( sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),sK9)
| ~ sQ33_eqProxy(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK10))),sK8)))
| ~ spl34_2
| ~ spl34_17 ),
inference(resolution,[],[f4967,f4911]) ).
fof(f5019,plain,
( ~ spl34_18
| spl34_20
| ~ spl34_2
| ~ spl34_17 ),
inference(avatar_split_clause,[],[f5016,f4966,f4910,f4978,f4970]) ).
fof(f5020,plain,
( sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),sK6)
| ~ sQ33_eqProxy(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK7))),sK5)))
| ~ spl34_2
| ~ spl34_21 ),
inference(resolution,[],[f4984,f4911]) ).
fof(f5022,definition,
( spl34_29
<=> sQ33_eqProxy(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK7))),sK5))) ),
introduced(definition,[new_symbols(definition,[spl34_29])],[avatar_definition]) ).
fof(f5023,plain,
( ~ sQ33_eqProxy(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK7))),sK5)))
| spl34_29 ),
inference(avatar_component_clause,[],[f5022]) ).
fof(f5025,plain,
( ~ spl34_29
| spl34_24
| ~ spl34_2
| ~ spl34_21 ),
inference(avatar_split_clause,[],[f5020,f4983,f4910,f4995,f5022]) ).
fof(f5047,plain,
( ~ sQ33_eqProxy(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK7))),sK5)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))))
| spl34_29 ),
inference(resolution,[],[f4901,f5023]) ).
fof(f5050,plain,
( $false
| ~ spl34_22
| spl34_29 ),
inference(resolution,[],[f5047,f4988]) ).
fof(f5052,plain,
( ~ spl34_22
| spl34_29 ),
inference(avatar_contradiction_clause,[],[f5050]) ).
fof(f5055,plain,
( sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),sK9)
| ~ sQ33_eqProxy(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK10))),sK8)))
| ~ spl34_3
| ~ spl34_17 ),
inference(resolution,[],[f4916,f4967]) ).
fof(f5056,plain,
( sQ33_eqProxy(c_Groups_Ozero__class_Ozero(t_a),sK6)
| ~ sQ33_eqProxy(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK7))),sK5)))
| ~ spl34_3
| ~ spl34_21 ),
inference(resolution,[],[f4916,f4984]) ).
fof(f5059,plain,
( ~ spl34_23
| spl34_24
| ~ spl34_3
| ~ spl34_21 ),
inference(avatar_split_clause,[],[f5056,f4983,f4915,f4995,f4991]) ).
fof(f5061,plain,
( ~ spl34_19
| spl34_20
| ~ spl34_3
| ~ spl34_17 ),
inference(avatar_split_clause,[],[f5055,f4966,f4915,f4978,f4974]) ).
cnf(s1,plain,
( spl34_1
| spl34_2 ),
inference(sat_conversion,[],[f4912]) ).
cnf(s2,plain,
( ~ spl34_1
| spl34_3 ),
inference(sat_conversion,[],[f4917]) ).
cnf(s10,plain,
( ~ spl34_9
| ~ spl34_16
| spl34_17 ),
inference(sat_conversion,[],[f4968]) ).
cnf(s11,plain,
( spl34_1
| ~ spl34_9
| ~ spl34_16
| spl34_18 ),
inference(sat_conversion,[],[f4972]) ).
cnf(s12,plain,
( ~ spl34_1
| ~ spl34_9
| ~ spl34_16
| spl34_19 ),
inference(sat_conversion,[],[f4976]) ).
cnf(s13,plain,
( ~ spl34_9
| ~ spl34_16
| ~ spl34_20 ),
inference(sat_conversion,[],[f4980]) ).
cnf(s14,plain,
( ~ spl34_9
| spl34_16
| spl34_21 ),
inference(sat_conversion,[],[f4985]) ).
cnf(s15,plain,
( spl34_1
| ~ spl34_9
| spl34_16
| spl34_22 ),
inference(sat_conversion,[],[f4989]) ).
cnf(s16,plain,
( ~ spl34_1
| ~ spl34_9
| spl34_16
| spl34_23 ),
inference(sat_conversion,[],[f4993]) ).
cnf(s17,plain,
( ~ spl34_9
| spl34_16
| ~ spl34_24 ),
inference(sat_conversion,[],[f4997]) ).
cnf(s22,plain,
spl34_9,
inference(sat_conversion,[],[f5015]) ).
cnf(s23,plain,
( ~ spl34_2
| ~ spl34_17
| ~ spl34_18
| spl34_20 ),
inference(sat_conversion,[],[f5019]) ).
cnf(s24,plain,
( ~ spl34_2
| ~ spl34_21
| spl34_24
| ~ spl34_29 ),
inference(sat_conversion,[],[f5025]) ).
cnf(s26,plain,
( ~ spl34_22
| spl34_29 ),
inference(sat_conversion,[],[f5052]) ).
cnf(s27,plain,
( ~ spl34_3
| ~ spl34_21
| ~ spl34_23
| spl34_24 ),
inference(sat_conversion,[],[f5059]) ).
cnf(s28,plain,
( ~ spl34_3
| ~ spl34_17
| ~ spl34_19
| spl34_20 ),
inference(sat_conversion,[],[f5061]) ).
cnf(s33,plain,
( spl34_16
| ~ spl34_24 ),
inference(rat,[],[s17,s22]) ).
cnf(s34,plain,
( ~ spl34_1
| spl34_16
| spl34_23 ),
inference(rat,[],[s16,s22]) ).
cnf(s35,plain,
( spl34_1
| spl34_16
| spl34_22 ),
inference(rat,[],[s15,s22]) ).
cnf(s36,plain,
( spl34_16
| spl34_21 ),
inference(rat,[],[s14,s22]) ).
cnf(s37,plain,
( ~ spl34_16
| ~ spl34_20 ),
inference(rat,[],[s13,s22]) ).
cnf(s38,plain,
( ~ spl34_1
| ~ spl34_16
| spl34_19 ),
inference(rat,[],[s12,s22]) ).
cnf(s39,plain,
( spl34_1
| ~ spl34_16
| spl34_18 ),
inference(rat,[],[s11,s22]) ).
cnf(s40,plain,
( ~ spl34_16
| spl34_17 ),
inference(rat,[],[s10,s22]) ).
cnf(s46,plain,
( spl34_16
| spl34_1 ),
inference(rat,[],[s26,s24,s35,s36,s33,s1]) ).
cnf(s47,plain,
spl34_1,
inference(rat,[],[s23,s39,s40,s37,s46,s1]) ).
cnf(s48,plain,
spl34_3,
inference(rat,[],[s2,s47]) ).
cnf(s49,plain,
spl34_16,
inference(rat,[],[s27,s34,s36,s33,s48,s47]) ).
cnf(s50,plain,
~ spl34_20,
inference(rat,[],[s37,s49]) ).
cnf(s51,plain,
spl34_17,
inference(rat,[],[s40,s49]) ).
cnf(s52,plain,
spl34_19,
inference(rat,[],[s38,s47,s49]) ).
cnf(s53,plain,
$false,
inference(rat,[],[s28,s50,s48,s51,s52]) ).
fof(f5062,plain,
$false,
inference(avatar_sat_refutation,[],[s53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW245+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n003.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 13:25:43 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 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
% 3.47/1.16 % (1579164)Detected formulas, will run a generic FOF schedule.
% 3.47/1.16 % (1579172)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1750000811:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.47/1.16 % (1579172)Instruction limit reached!
% 3.47/1.16 % (1579172)------------------------------
% 3.47/1.16 % (1579172)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.16 % (1579172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.16 % (1579172)CaDiCaL version: 2.1.3
% 3.47/1.16 % (1579172)Termination reason: Instruction limit
% 3.47/1.16 % (1579172)Termination phase: Saturation
% 3.47/1.16 % (1579172)Time elapsed: 0.036 s
% 3.47/1.16 % (1579172)Peak memory usage: 90 MB
% 3.47/1.16 % (1579172)Instructions burned: 111 (million)
% 3.47/1.16 % (1579173)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2356891353:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.47/1.16 % (1579174)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4070217772:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.47/1.16 % (1579175)dis-21_1_sil=8000:lcm=predicate:random_seed=2424864587: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)
% 3.47/1.16 % (1579169)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=2816031544:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.47/1.16 % (1579171)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=1141771740:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.47/1.16 % (1579170)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=3894450949:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.47/1.16 % (1579175)First to succeed.
% 3.47/1.16 % (1579175)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1579164"
% 3.47/1.16 % (1579173)Instruction limit reached!
% 3.47/1.16 % (1579173)------------------------------
% 3.47/1.16 % (1579173)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.16 % (1579173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.16 % (1579173)CaDiCaL version: 2.1.3
% 3.47/1.16 % (1579173)Termination reason: Instruction limit
% 3.47/1.16 % (1579173)Termination phase: Saturation
% 3.47/1.16 % (1579173)Time elapsed: 0.070 s
% 3.47/1.16 % (1579173)Peak memory usage: 90 MB
% 3.47/1.16 % (1579173)Instructions burned: 119 (million)
% 3.47/1.16 % (1579174)Instruction limit reached!
% 3.47/1.16 % (1579174)------------------------------
% 3.47/1.16 % (1579174)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.16 % (1579174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.16 % (1579174)CaDiCaL version: 2.1.3
% 3.47/1.16 % (1579174)Termination reason: Instruction limit
% 3.47/1.16 % (1579174)Termination phase: Saturation
% 3.47/1.16 % (1579174)Time elapsed: 0.080 s
% 3.47/1.16 % (1579174)Peak memory usage: 90 MB
% 3.47/1.16 % (1579174)Instructions burned: 140 (million)
% 3.47/1.16 % (1579183)lrs+10_1_sil=8000:sp=occurrence:random_seed=350683910:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.47/1.16 % (1579183)Instruction limit reached!
% 3.47/1.16 % (1579183)------------------------------
% 3.47/1.16 % (1579183)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.16 % (1579183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.16 % (1579183)CaDiCaL version: 2.1.3
% 3.47/1.16 % (1579183)Termination reason: Instruction limit
% 3.47/1.16 % (1579183)Termination phase: Saturation
% 3.47/1.16 % (1579183)Time elapsed: 0.100 s
% 3.47/1.16 % (1579183)Peak memory usage: 92 MB
% 3.47/1.16 % (1579183)Instructions burned: 285 (million)
% 3.47/1.16 % (1579184)lrs+10_1_sil=32000:urr=on:br=off:random_seed=194177456:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.47/1.16 % (1579185)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1692566082:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.47/1.16 % (1579187)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=191065372:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 3.47/1.16 % (1579184)Instruction limit reached!
% 3.47/1.16 % (1579184)------------------------------
% 3.47/1.16 % (1579184)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.16 % (1579184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.16 % (1579184)CaDiCaL version: 2.1.3
% 3.47/1.16 % (1579184)Termination reason: Instruction limit
% 3.47/1.16 % (1579184)Termination phase: Saturation
% 3.47/1.16 % (1579184)Time elapsed: 0.090 s
% 3.47/1.16 % (1579184)Peak memory usage: 91 MB
% 3.47/1.16 % (1579184)Instructions burned: 158 (million)
% 3.47/1.16 % (1579175)Refutation found. Thanks to Tanya!
% 3.47/1.16 % SZS status Theorem for theBenchmark
% 3.47/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 3.91/1.35 % (1579175)------------------------------
% 3.91/1.35 % (1579175)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.35 % (1579175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.35 % (1579175)CaDiCaL version: 2.1.3
% 3.91/1.35 % (1579175)Termination reason: Refutation
% 3.91/1.35 % (1579175)Time elapsed: 0.047 s
% 3.91/1.35 % (1579175)Peak memory usage: 91 MB
% 3.91/1.35 % (1579175)Instructions burned: 94 (million)
% 3.91/1.35 % (1579175)------------------------------
% 3.91/1.35 % (1579175)------------------------------
% 3.91/1.35 % (1579164)Success in time 0.507 s
% 3.91/1.35 % Vampire exiting
%------------------------------------------------------------------------------