%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWW245+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n014.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 : Fri Sep 25 03:29:19 PM UTC 2026
% Result : Theorem 30.92s 5.00s
% Output : CNFRefutation 30.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 98 ( 30 unt; 0 def)
% Number of atoms : 277 ( 245 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 307 ( 128 ~; 133 |; 34 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 10 con; 0-4 aty)
% Number of variables : 108 ( 0 sgn 83 !; 25 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
( class_Rings_Oidom(t_a)
=> ( v_c____ != c_Groups_Ozero__class_Ozero(t_a)
=> ? [X0,X1] :
( ? [X2] :
( ! [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_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))
=> 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) ) )
& X1 != c_Groups_Ozero__class_Ozero(t_a) ) ) ),
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] :
( ? [X2] :
( ! [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_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))
=> 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) ) )
& X1 != c_Groups_Ozero__class_Ozero(t_a) ) ) ),
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(f70,axiom,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(f71,axiom,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(f72,axiom,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(f96,axiom,
! [X0] : c_Nat_OSuc(X0) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
fof(f103,axiom,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X0) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).
fof(f189,axiom,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(f1160,conjecture,
? [X0,X1] :
( ? [X2] :
( ! [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_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))
=> 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) ) )
& X1 != c_Groups_Ozero__class_Ozero(t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1161,negated_conjecture,
~ ? [X0,X1] :
( ? [X2] :
( ! [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_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))
=> 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) ) )
& X1 != c_Groups_Ozero__class_Ozero(t_a) ),
inference(negated_conjecture,[status(cth)],[f1160]) ).
fof(f1162,axiom,
class_Rings_Oidom(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
fof(f1213,plain,
! [X0,X1] :
( ! [X2] :
( ? [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_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))
& 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_Groups_Ozero__class_Ozero(t_a) = X1 ),
inference(ennf_transformation,[],[f1161]) ).
fof(f1217,plain,
( ~ class_Rings_Oidom(t_a)
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| ? [X0,X1] :
( ? [X2] :
( ! [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_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))
| 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) ) )
& X1 != c_Groups_Ozero__class_Ozero(t_a) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f1218,plain,
( ~ class_Rings_Oidom(t_a)
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| ? [X0,X1] :
( ? [X2] :
( ! [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_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))
| 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) ) )
& X1 != c_Groups_Ozero__class_Ozero(t_a) ) ),
inference(flattening,[],[f1217]) ).
fof(f1219,plain,
( ~ class_Rings_Oidom(t_a)
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| ? [X0,X1] :
( ? [X2] :
( ! [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_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))
| 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) ) )
& X1 != c_Groups_Ozero__class_Ozero(t_a) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f1220,plain,
( ~ class_Rings_Oidom(t_a)
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| ? [X0,X1] :
( ? [X2] :
( ! [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_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))
| 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) ) )
& X1 != c_Groups_Ozero__class_Ozero(t_a) ) ),
inference(flattening,[],[f1219]) ).
fof(f1742,plain,
! [X0,X1] :
( ! [X2] :
( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK2(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK2(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK2(X0,X1,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_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))
& 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_Groups_Ozero__class_Ozero(t_a) = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f1213]) ).
fof(f1754,plain,
( ~ class_Rings_Oidom(t_a)
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| ( ! [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),sK7)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK8,sK9)),X3))
& ( 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(sK9,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,sK9))),sK7)) )
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| 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(sK9,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,sK9))),sK7)) )
& c_Groups_Ozero__class_Ozero(t_a) != sK8 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9)],[f1218]) ).
fof(f1755,plain,
( ~ class_Rings_Oidom(t_a)
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| ( ! [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),sK10)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK11,sK12)),X3))
& ( 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(sK12,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,sK12))),sK10)) )
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| 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(sK12,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,sK12))),sK10)) )
& c_Groups_Ozero__class_Ozero(t_a) != sK11 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12)],[f1220]) ).
fof(f1929,plain,
! [X2,X0,X1] :
( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK2(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK2(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK2(X0,X1,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_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))
| c_Groups_Ozero__class_Ozero(t_a) = X1 ),
inference(cnf_transformation,[],[f1742]) ).
fof(f1932,plain,
class_Rings_Oidom(t_a),
inference(cnf_transformation,[],[f1162]) ).
fof(f1954,plain,
! [X3] :
( ~ class_Rings_Oidom(t_a)
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| 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),sK7)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK8,sK9)),X3)) ),
inference(cnf_transformation,[],[f1754]) ).
fof(f1955,plain,
( ~ class_Rings_Oidom(t_a)
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| 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(sK9,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,sK9))),sK7)) ),
inference(cnf_transformation,[],[f1754]) ).
fof(f1956,plain,
( ~ class_Rings_Oidom(t_a)
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| 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(sK9,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,sK9))),sK7)) ),
inference(cnf_transformation,[],[f1754]) ).
fof(f1957,plain,
( ~ class_Rings_Oidom(t_a)
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| c_Groups_Ozero__class_Ozero(t_a) != sK8 ),
inference(cnf_transformation,[],[f1754]) ).
fof(f1958,plain,
! [X3] :
( ~ class_Rings_Oidom(t_a)
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| 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),sK10)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK11,sK12)),X3)) ),
inference(cnf_transformation,[],[f1755]) ).
fof(f1959,plain,
( ~ class_Rings_Oidom(t_a)
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| 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(sK12,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,sK12))),sK10)) ),
inference(cnf_transformation,[],[f1755]) ).
fof(f1960,plain,
( ~ class_Rings_Oidom(t_a)
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| 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(sK12,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,sK12))),sK10)) ),
inference(cnf_transformation,[],[f1755]) ).
fof(f1961,plain,
( ~ class_Rings_Oidom(t_a)
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| c_Groups_Ozero__class_Ozero(t_a) != sK11 ),
inference(cnf_transformation,[],[f1755]) ).
fof(f2051,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0),
inference(cnf_transformation,[],[f72]) ).
fof(f2052,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)),
inference(cnf_transformation,[],[f71]) ).
fof(f2053,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
inference(cnf_transformation,[],[f70]) ).
fof(f2130,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f189]) ).
fof(f2136,plain,
! [X0,X1] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X0),
inference(cnf_transformation,[],[f103]) ).
fof(f2141,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X0),
inference(cnf_transformation,[],[f96]) ).
fof(f2765,plain,
! [X2,X0,X1] :
( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK2(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK2(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK2(X0,X1,X2)))
| c_Groups_Oplus__class_Oplus(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_Polynomial_Odegree(t_a,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| 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) = X1 ),
inference(definition_unfolding,[],[f1929,f2130,f2130,f2130]) ).
fof(f2768,plain,
( ~ class_Rings_Oidom(t_a)
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != 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_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK9,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_Polynomial_Odegree(t_a,sK9),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK7),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(definition_unfolding,[],[f1956,f2130,f2130]) ).
fof(f2769,plain,
( ~ class_Rings_Oidom(t_a)
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| 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_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK9,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_Polynomial_Odegree(t_a,sK9),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK7),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(definition_unfolding,[],[f1955,f2130,f2130,f2130]) ).
fof(f2770,plain,
( ~ class_Rings_Oidom(t_a)
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != 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_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK12,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_Polynomial_Odegree(t_a,sK12),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK10),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(definition_unfolding,[],[f1960,f2130,f2130]) ).
fof(f2771,plain,
( ~ class_Rings_Oidom(t_a)
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| 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_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK12,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_Polynomial_Odegree(t_a,sK12),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK10),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(definition_unfolding,[],[f1959,f2130,f2130,f2130]) ).
fof(f2840,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
inference(definition_unfolding,[],[f2136,f2130,f2130]) ).
fof(f2845,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(definition_unfolding,[],[f2141,f2130]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( 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_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X0,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_Polynomial_Odegree(t_a,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK2(X1,X2,X0)),X1)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X2,X0)),sK2(X1,X2,X0))) != hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK2(X1,X2,X0)) ) ),
inference(cnf_transformation,[],[f2765]) ).
tcf(c_52,plain,
class_Rings_Oidom(t_a),
inference(cnf_transformation,[],[f1932]) ).
tcf(c_71,plain,
( ~ class_Rings_Oidom(t_a)
| ( c_Groups_Ozero__class_Ozero(t_a) != sK8 )
| ( c_Groups_Ozero__class_Ozero(t_a) != v_c____ ) ),
inference(cnf_transformation,[],[f1957]) ).
tcf(c_72,plain,
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK9,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_Polynomial_Odegree(t_a,sK9),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK7),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Rings_Oidom(t_a)
| ( c_Groups_Ozero__class_Ozero(t_a) != v_c____ )
| ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(cnf_transformation,[],[f2768]) ).
tcf(c_73,plain,
( ( 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_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK9,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_Polynomial_Odegree(t_a,sK9),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK7),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
| ~ class_Rings_Oidom(t_a)
| ( c_Groups_Ozero__class_Ozero(t_a) != v_c____ ) ),
inference(cnf_transformation,[],[f2769]) ).
tcf(c_74,plain,
! [X0: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X0),sK7)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK8,sK9)),X0)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X0) )
| ~ class_Rings_Oidom(t_a)
| ( c_Groups_Ozero__class_Ozero(t_a) != v_c____ ) ),
inference(cnf_transformation,[],[f1954]) ).
tcf(c_75,plain,
( ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
| ~ class_Rings_Oidom(t_a)
| ( c_Groups_Ozero__class_Ozero(t_a) != sK11 ) ),
inference(cnf_transformation,[],[f1961]) ).
tcf(c_76,plain,
( ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK12,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_Polynomial_Odegree(t_a,sK12),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK10),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ class_Rings_Oidom(t_a)
| ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(cnf_transformation,[],[f2770]) ).
tcf(c_77,plain,
( ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
| ( 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_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK12,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_Polynomial_Odegree(t_a,sK12),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK10),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
| ~ class_Rings_Oidom(t_a) ),
inference(cnf_transformation,[],[f2771]) ).
tcf(c_78,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X0),sK10)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK11,sK12)),X0)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X0) )
| ~ class_Rings_Oidom(t_a) ),
inference(cnf_transformation,[],[f1958]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(cnf_transformation,[],[f2051]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i,X2: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)),
inference(cnf_transformation,[],[f2052]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),
inference(cnf_transformation,[],[f2053]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f2840]) ).
tcf(c_253,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f2845]) ).
tcf(c_1346,plain,
( ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
| ( c_Groups_Ozero__class_Ozero(t_a) != sK11 ) ),
inference(global_subsumption_just,[status(thm)],[c_75,c_52,c_75]) ).
tcf(c_1348,plain,
( ( c_Groups_Ozero__class_Ozero(t_a) != v_c____ )
| ( c_Groups_Ozero__class_Ozero(t_a) != sK8 ) ),
inference(global_subsumption_just,[status(thm)],[c_71,c_52,c_71]) ).
tcf(c_1349,plain,
( ( c_Groups_Ozero__class_Ozero(t_a) != sK8 )
| ( c_Groups_Ozero__class_Ozero(t_a) != v_c____ ) ),
inference(renaming,[status(thm)],[c_1348]) ).
tcf(c_1380,plain,
( ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK12,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_Polynomial_Odegree(t_a,sK12),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK10),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = 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)) ) ),
inference(global_subsumption_just,[status(thm)],[c_76,c_52,c_76]) ).
tcf(c_1382,plain,
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK9,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_Polynomial_Odegree(t_a,sK9),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK7),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = 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_Groups_Ozero__class_Ozero(t_a) != v_c____ ) ),
inference(global_subsumption_just,[status(thm)],[c_72,c_52,c_72]) ).
tcf(c_1383,plain,
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK9,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_Polynomial_Odegree(t_a,sK9),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK7),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( c_Groups_Ozero__class_Ozero(t_a) != v_c____ )
| ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(renaming,[status(thm)],[c_1382]) ).
tcf(c_1387,plain,
( ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
| ( 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_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK12,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_Polynomial_Odegree(t_a,sK12),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK10),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(global_subsumption_just,[status(thm)],[c_77,c_52,c_77]) ).
tcf(c_1389,plain,
( ( 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_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK9,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_Polynomial_Odegree(t_a,sK9),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK7),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
| ( c_Groups_Ozero__class_Ozero(t_a) != v_c____ ) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).
tcf(c_3456,plain,
( ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
| ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1380,c_253]) ).
tcf(c_3457,plain,
( ( c_Groups_Ozero__class_Ozero(t_a) != v_c____ )
| ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1383,c_253]) ).
tcf(c_3460,plain,
c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(global_subsumption_just,[status(thm)],[c_3456,c_3457,c_3456]) ).
tcf(c_3480,plain,
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK9,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_Polynomial_Odegree(t_a,sK9),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK7),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
| ( c_Groups_Ozero__class_Ozero(t_a) != v_c____ ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1389,c_3460]) ).
tcf(c_3481,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(t_a) = X1 )
| ( c_Groups_Oplus__class_Oplus(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_Polynomial_Odegree(t_a,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK2(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK2(X0,X1,X2))) != hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK2(X0,X1,X2)) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_51,c_3460]) ).
tcf(c_3482,plain,
( ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK12,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_Polynomial_Odegree(t_a,sK12),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK10),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1387,c_3460]) ).
tcf(c_7222,plain,
! [X0: $i,X1: $i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(demodulation,[status(thm)],[c_248,c_164]) ).
tcf(c_8644,plain,
( ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_If(tc_Nat_Onat,c_fequal(sK12,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,sK12))))) = 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____))) ) ),
inference(demodulation,[status(thm)],[c_3482,c_164,c_165,c_166,c_7222]) ).
tcf(c_8651,plain,
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_If(tc_Nat_Onat,c_fequal(sK9,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,sK9))))) = 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_Ozero__class_Ozero(t_a) != v_c____ ) ),
inference(demodulation,[status(thm)],[c_3480,c_164,c_165,c_166,c_7222]) ).
tcf(c_8757,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Groups_Ozero__class_Ozero(t_a) = X1 )
| ( 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))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) != 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____))) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK2(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK2(X0,X1,X2))) != hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK2(X0,X1,X2)) ) ),
inference(demodulation,[status(thm)],[c_3481,c_164,c_166]) ).
tcf(c_19430,plain,
( ( c_Groups_Ozero__class_Ozero(t_a) != v_c____ )
| ( c_Groups_Ozero__class_Ozero(t_a) != sK8 ) ),
inference(prop_impl_just,[status(thm)],[c_1349]) ).
tcf(c_19431,plain,
( ( c_Groups_Ozero__class_Ozero(t_a) != sK8 )
| ( c_Groups_Ozero__class_Ozero(t_a) != v_c____ ) ),
inference(renaming,[status(thm)],[c_19430]) ).
tcf(c_19434,plain,
! [X0: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X0),sK7)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK8,sK9)),X0)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X0) )
| ( c_Groups_Ozero__class_Ozero(t_a) != v_c____ ) ),
inference(prop_impl_just,[status(thm)],[c_52,c_74]) ).
tcf(c_19436,plain,
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_If(tc_Nat_Onat,c_fequal(sK9,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,sK9))))) = 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_Ozero__class_Ozero(t_a) != v_c____ ) ),
inference(prop_impl_just,[status(thm)],[c_8651]) ).
tcf(c_19440,plain,
! [X0: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X0),sK10)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK11,sK12)),X0)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X0) )
| ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ ) ),
inference(prop_impl_just,[status(thm)],[c_52,c_78]) ).
tcf(c_19441,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X0),sK10)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK11,sK12)),X0)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X0) ) ),
inference(renaming,[status(thm)],[c_19440]) ).
tcf(c_19442,plain,
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_If(tc_Nat_Onat,c_fequal(sK12,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,sK12))))) = 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_Ozero__class_Ozero(t_a) = v_c____ ) ),
inference(prop_impl_just,[status(thm)],[c_8644]) ).
tcf(c_19443,plain,
( ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_If(tc_Nat_Onat,c_fequal(sK12,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,sK12))))) = 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____))) ) ),
inference(renaming,[status(thm)],[c_19442]) ).
tcf(c_38222,plain,
( ( c_Groups_Ozero__class_Ozero(t_a) = sK11 )
| ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK12,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,sK12))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK10,c_Groups_Oone__class_Oone(tc_Nat_Onat))) != 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____))) ) ),
inference(superposition,[status(thm)],[c_19441,c_8757]) ).
tcf(c_38300,plain,
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK12,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,sK12))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK10,c_Groups_Oone__class_Oone(tc_Nat_Onat))) != 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_Ozero__class_Ozero(t_a) = v_c____ ) ),
inference(global_subsumption_just,[status(thm)],[c_38222,c_1346,c_38222]) ).
tcf(c_38301,plain,
( ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK12,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,sK12))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK10,c_Groups_Oone__class_Oone(tc_Nat_Onat))) != 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____))) ) ),
inference(renaming,[status(thm)],[c_38300]) ).
tcf(c_38302,plain,
( ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_If(tc_Nat_Onat,c_fequal(sK12,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,sK12))))) != 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____))) ) ),
inference(demodulation,[status(thm)],[c_38301,c_165,c_7222]) ).
tcf(c_38351,plain,
c_Groups_Ozero__class_Ozero(t_a) = v_c____,
inference(forward_subsumption_resolution,[status(thm)],[c_19443,c_38302]) ).
tcf(c_38354,plain,
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_If(tc_Nat_Onat,c_fequal(sK9,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,sK9))))) = 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____))) )
| ( v_c____ != v_c____ ) ),
inference(demodulation,[status(thm)],[c_19436,c_38351]) ).
tcf(c_38357,plain,
! [X0: $i] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X0),sK7)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK8,sK9)),X0)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X0) )
| ( v_c____ != v_c____ ) ),
inference(demodulation,[status(thm)],[c_19434,c_38351]) ).
tcf(c_38360,plain,
( ( v_c____ != sK8 )
| ( v_c____ != v_c____ ) ),
inference(demodulation,[status(thm)],[c_19431,c_38351]) ).
tcf(c_38368,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = v_c____ )
| ( 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))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) != 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____))) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK2(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK2(X0,X1,X2))) != hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK2(X0,X1,X2)) ) ),
inference(demodulation,[status(thm)],[c_8757,c_38351]) ).
tcf(c_38369,plain,
v_c____ != sK8,
inference(equality_resolution_simp,[status(thm)],[c_38360]) ).
tcf(c_38376,plain,
! [X0: $i] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X0),sK7)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK8,sK9)),X0)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X0),
inference(equality_resolution_simp,[status(thm)],[c_38357]) ).
tcf(c_38377,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_If(tc_Nat_Onat,c_fequal(sK9,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,sK9))))) = 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____))),
inference(equality_resolution_simp,[status(thm)],[c_38354]) ).
tcf(c_39375,plain,
( ( v_c____ = sK8 )
| ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK9,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,sK9))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK7,c_Groups_Oone__class_Oone(tc_Nat_Onat))) != 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____))) ) ),
inference(superposition,[status(thm)],[c_38376,c_38368]) ).
tcf(c_39380,plain,
v_c____ = sK8,
inference(ground_joinability,[status(thm)],[c_39375,c_165,c_7222,c_38377]) ).
tcf(c_39381,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_39380,c_38369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWW245+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.41 % Computer : n014.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Thu Sep 24 21:50:49 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.47 Running first-order theorem proving
% 0.14/0.47 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.49
% 0.14/0.49 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.49
% 0.22/0.49 % Detected problem language: tptp
% 0.22/0.51 % Proving...
% 30.92/5.00 % SZS status Started for theBenchmark.p
% 30.92/5.00 ERROR - "ProverProcess:heur/409474:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 30.92/5.00 Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 30.92/5.00 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 3 --comb_mode clause_based --comb_res_mult 4 --comb_sup_deep_mult 2 --comb_sup_mult 0 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 500 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp false --inst_learning_factor 2 --inst_learning_loop_flag true --inst_learning_start 3000 --inst_lit_activity_flag true --inst_lit_sel "[+prop;+sign;+ground;-num_var;-num_symb]" --inst_lit_sel_side num_symb --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]" --inst_passive_queues_freq "[25;2]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 1. --inst_solver_per_active 1400 --inst_sos_flag false --inst_start_prop_sim_after_learn 3 --inst_subs_given false --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution false --res_forward_subs subset_subsumption --res_forward_subs_resolution true --res_lit_sel pos_max --res_lit_sel_side num_var --res_ordering kbo_pred --res_passive_queue_type priority_queues --res_passive_queues "[[-num_lits];[-conj_symb;-num_symb;+num_symb]]" --res_passive_queues_freq "[15;3]" --res_prop_simpl_given false --res_prop_simpl_new true --res_sim_input true --res_time_limit 202.80 --res_to_prop_solver passive --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[ACNormalisation]" --sup_immed_fw_main "[]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_bw "[]" --sup_input_fw "[ACNormalisation]" --sup_input_triv "[Unflattening]" --sup_iter_deepening 2 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[8;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 2 --sup_score sim_d_gen --sup_share_max_num_cl 500 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering invfreq --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 0.33" --time_out_real 1.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_esc6x8rz/udz33wy2 2>> /export/starexec/sandbox/tmp/iprover_out_esc6x8rz/udz33wy2_error
% 30.92/5.00 ERROR - "ProverProcess:heur/397442:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 30.92/5.00 Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 30.92/5.00 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 64 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 2 --comb_sup_mult 0 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 4 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp true --inst_learning_factor 8 --inst_learning_loop_flag true --inst_learning_start 2 --inst_lit_activity_flag false --inst_lit_sel "[-split]" --inst_lit_sel_side num_lit --inst_orphan_elimination false --inst_passive_queue_type priority_queues --inst_passive_queues "[[+conj_symb]]" --inst_passive_queues_freq "[50]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 0.8199321230744955 --inst_solver_per_active 4 --inst_sos_flag false --inst_start_prop_sim_after_learn 7 --inst_subs_given false --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[ACNormalisation]" --sup_immed_fw_main "[]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_bw "[]" --sup_input_fw "[ACNormalisation]" --sup_input_triv "[Unflattening]" --sup_iter_deepening 2 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[8;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 2 --sup_score sim_d_gen --sup_share_max_num_cl 500 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering invfreq --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 0.33" --time_out_real 1.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_esc6x8rz/148d73u8 2>> /export/starexec/sandbox/tmp/iprover_out_esc6x8rz/148d73u8_error
% 30.92/5.00 ERROR - "ProverProcess:heur/421498:1.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 30.92/5.00 Fatal error: exception Failure("Clausification error: res/vclausify_rel exits with an error status: 1")
% 30.92/5.00 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 8 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 2 --comb_sup_mult 0 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 512 --inst_dismatching true --inst_eager_unprocessed_to_passive false --inst_eq_res_simp true --inst_learning_factor 8 --inst_learning_loop_flag true --inst_learning_start 128 --inst_lit_activity_flag false --inst_lit_sel "[+sign;+prop]" --inst_lit_sel_side none --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[+num_symb;-age;-age];[+num_symb;+conj_non_prolific_symb]]" --inst_passive_queues_freq "[512;10]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew model --inst_solver_calls_frac 0.006221608720445637 --inst_solver_per_active 32768 --inst_sos_flag true --inst_sos_phase false --inst_sos_sth_lit_sel "[+non_prol_conj_symb;+sign;-depth;-prop]" --inst_start_prop_sim_after_learn 9 --inst_subs_given true --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[ACNormalisation]" --sup_immed_fw_main "[]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_bw "[]" --sup_input_fw "[ACNormalisation]" --sup_input_triv "[Unflattening]" --sup_iter_deepening 2 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[8;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 2 --sup_score sim_d_gen --sup_share_max_num_cl 500 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering invfreq --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 0.33" --time_out_real 1.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_esc6x8rz/pnabqn2b 2>> /export/starexec/sandbox/tmp/iprover_out_esc6x8rz/pnabqn2b_error
% 30.92/5.00 % SZS status Theorem for theBenchmark.p
% 30.92/5.00
% 30.92/5.00 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 30.92/5.00
% 30.92/5.00 % ------ iProver source info
% 30.92/5.00
% 30.92/5.00 % git: date: 2026-07-19 20:42:38 +0200
% 30.92/5.00 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 30.92/5.00 % git: non_committed_changes: false
% 30.92/5.00
% 30.92/5.00 % ------ Parsing...
% 30.92/5.00 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 30.92/5.00
% 30.92/5.00 % ------ Preprocessing... sup_sim: 89 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 29 sf_s rm: 2 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 30.92/5.00
% 30.92/5.00 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 30.92/5.00
% 30.92/5.00 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 30.92/5.00 % ------ Proving...
% 30.92/5.00 % ------ Problem Properties
% 30.92/5.00
% 30.92/5.00 %
% 30.92/5.00 % clauses 632
% 30.92/5.00 % conjectures 0
% 30.92/5.00 % EPR 28
% 30.92/5.00 % Horn 525
% 30.92/5.00 % unary 156
% 30.92/5.00 % binary 275
% 30.92/5.00 % lits 1347
% 30.92/5.00 % lits eq 566
% 30.92/5.00 % fd_pure 0
% 30.92/5.00 % fd_pseudo 0
% 30.92/5.00 % fd_cond 69
% 30.92/5.00 % fd_pseudo_cond 44
% 30.92/5.00 % AC symbols 0
% 30.92/5.00
% 30.92/5.00 % ------ Schedule dynamic 5 is on
% 30.92/5.00
% 30.92/5.00 % ------ no conjectures: strip conj schedule
% 30.92/5.00
% 30.92/5.00 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 30.92/5.00
% 30.92/5.00
% 30.92/5.00 % ------
% 30.92/5.00 % Current options:
% 30.92/5.00 % ------
% 30.92/5.00
% 30.92/5.00
% 30.92/5.00 %
% 30.92/5.00
% 30.92/5.00 % ------ Proving...
% 30.92/5.00 %
% 30.92/5.00
% 30.92/5.00 % SZS status Theorem for theBenchmark.p
% 30.92/5.00
% 30.92/5.00 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 30.92/5.00
% 30.92/5.00
%------------------------------------------------------------------------------