TSTP Solution File: SWW286+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SWW286+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 00:10:28 EDT 2022
% Result : Theorem 0.49s 25.66s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 38
% Syntax : Number of formulae : 168 ( 81 unt; 0 def)
% Number of atoms : 275 ( 170 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 189 ( 82 ~; 71 |; 4 &)
% ( 1 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 6 con; 0-3 aty)
% Number of variables : 328 ( 16 sgn 171 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_degree__mod__less,axiom,
! [X18,X17,X6] :
( class_Fields_Ofield(X6)
=> ( X17 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
=> ( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X6),X18,X17) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X6,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X6),X18,X17)),c_Polynomial_Odegree(X6,X17)) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_degree__mod__less) ).
fof(fact_less__zeroE,axiom,
! [X4] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_less__zeroE) ).
fof(fact_mod__smult__left,axiom,
! [X17,X18,X5,X6] :
( class_Fields_Ofield(X6)
=> c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X6),c_Polynomial_Osmult(X6,X5,X18),X17) = c_Polynomial_Osmult(X6,X5,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X6),X18,X17)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_mod__smult__left) ).
fof(fact_dp,axiom,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_dp) ).
fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
fof(fact_pe,axiom,
v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_pe) ).
fof(fact_poly__smult,axiom,
! [X18,X20,X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> hAPP(c_Polynomial_Opoly(X6,c_Polynomial_Osmult(X6,X5,X20)),X18) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),hAPP(c_Polynomial_Opoly(X6,X20),X18)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_poly__smult) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(fact_poly__0,axiom,
! [X18,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> hAPP(c_Polynomial_Opoly(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))),X18) = c_Groups_Ozero__class_Ozero(X6) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_poly__0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [X32,X34,X33,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X33),X34)),X32) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X33),X32)),X34) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(fact_smult__smult,axiom,
! [X20,X9,X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> c_Polynomial_Osmult(X6,X5,c_Polynomial_Osmult(X6,X9,X20)) = c_Polynomial_Osmult(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X9),X20) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_smult__smult) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [X12,X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X12),X12) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oplus__class_Oplus(X6,X5,c_Groups_Oone__class_Oone(X6))),X12) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(fact_smult__0__left,axiom,
! [X20,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> c_Polynomial_Osmult(X6,c_Groups_Ozero__class_Ozero(X6),X20) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_smult__0__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,c_Groups_Ozero__class_Ozero(X6),X5) = X5 ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_poly__pCons,axiom,
! [X18,X20,X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> hAPP(c_Polynomial_Opoly(X6,c_Polynomial_OpCons(X6,X5,X20)),X18) = c_Groups_Oplus__class_Oplus(X6,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X18),hAPP(c_Polynomial_Opoly(X6,X20),X18))) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_poly__pCons) ).
fof(fact_smult__add__left,axiom,
! [X20,X9,X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> c_Polynomial_Osmult(X6,c_Groups_Oplus__class_Oplus(X6,X5,X9),X20) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),c_Polynomial_Osmult(X6,X5,X20),c_Polynomial_Osmult(X6,X9,X20)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_smult__add__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [X5,X12,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,X12,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oplus__class_Oplus(X6,X5,c_Groups_Oone__class_Oone(X6))),X12) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oone__class_Oone(X6)),X5) = X5 ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X9,X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X9),X5) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [X19,X9,X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Groups_Oplus__class_Oplus(X6,X5,X9)),X19) = c_Groups_Oplus__class_Oplus(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X9),X19)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact__096_B_Bthesis_O_A_I_B_Bk_O_A_091_124_Ap_A_061_A_091_058k_058_093_059_Ak_A_126_061_A0_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [X26] :
( v_p = c_Polynomial_OpCons(tc_Complex_Ocomplex,X26,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
=> X26 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bk_O_A_091_124_Ap_A_061_A_091_058k_058_093_059_Ak_A_126_061_A0_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact_smult__1__left,axiom,
! [X20,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Polynomial_Osmult(X6,c_Groups_Oone__class_Oone(X6),X20) = X20 ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_smult__1__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oplus__class_Oplus(X6,X5,c_Groups_Ozero__class_Ozero(X6)) = X5 ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_mult__smult__right,axiom,
! [X21,X5,X20,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),X20),c_Polynomial_Osmult(X6,X5,X21)) = c_Polynomial_Osmult(X6,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),X20),X21)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_mult__smult__right) ).
fof(fact_smult__pCons,axiom,
! [X20,X9,X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> c_Polynomial_Osmult(X6,X5,c_Polynomial_OpCons(X6,X9,X20)) = c_Polynomial_OpCons(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X9),c_Polynomial_Osmult(X6,X5,X20)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_smult__pCons) ).
fof(fact_k_I1_J,axiom,
v_p = c_Polynomial_OpCons(tc_Complex_Ocomplex,v_k____,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_k_I1_J) ).
fof(fact_mult__pCons__right,axiom,
! [X21,X5,X20,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),X20),c_Polynomial_OpCons(X6,X5,X21)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),c_Polynomial_Osmult(X6,X5,X20),c_Polynomial_OpCons(X6,c_Groups_Ozero__class_Ozero(X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),X20),X21))) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_mult__pCons__right) ).
fof(fact_one__poly__def,axiom,
! [X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X6)) = c_Polynomial_OpCons(X6,c_Groups_Oone__class_Oone(X6),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_one__poly__def) ).
fof(fact_field__divide__inverse,axiom,
! [X9,X5,X6] :
( class_Fields_Ofield(X6)
=> c_Rings_Oinverse__class_Odivide(X6,X5,X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),c_Rings_Oinverse__class_Oinverse(X6,X9)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_field__divide__inverse) ).
fof(fact_mult__smult__left,axiom,
! [X21,X20,X5,X6] :
( class_Rings_Ocomm__semiring__0(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),c_Polynomial_Osmult(X6,X5,X20)),X21) = c_Polynomial_Osmult(X6,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X6)),X20),X21)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_mult__smult__left) ).
fof(fact_pCons__eq__iff,axiom,
! [X13,X10,X7,X8,X6] :
( class_Groups_Ozero(X6)
=> ( c_Polynomial_OpCons(X6,X8,X7) = c_Polynomial_OpCons(X6,X10,X13)
<=> ( X8 = X10
& X7 = X13 ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_pCons__eq__iff) ).
fof(conj_0,conjecture,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_k____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',conj_0) ).
fof(fact_field__inverse,axiom,
! [X5,X6] :
( class_Fields_Ofield(X6)
=> ( X5 != c_Groups_Ozero__class_Ozero(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),c_Rings_Oinverse__class_Oinverse(X6,X5)),X5) = c_Groups_Oone__class_Oone(X6) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_field__inverse) ).
fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(fact_field__class_Onormalizing__field__rules_I2_J,axiom,
! [X5,X6] :
( class_Fields_Ofield(X6)
=> c_Rings_Oinverse__class_Oinverse(X6,X5) = c_Rings_Oinverse__class_Odivide(X6,c_Groups_Oone__class_Oone(X6),X5) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_field__class_Onormalizing__field__rules_I2_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [X18,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X6),X18),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X6) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
! [X82] :
( class_Rings_Ocomm__semiring__1(X82)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X82)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(c_0_38,plain,
! [X19,X20,X21] :
( ~ class_Fields_Ofield(X21)
| X20 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X21))
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X21),X19,X20) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X21))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X21,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X21),X19,X20)),c_Polynomial_Odegree(X21,X20)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__mod__less])]) ).
fof(c_0_39,plain,
! [X5] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_less__zeroE])]) ).
fof(c_0_40,plain,
! [X19,X20,X21,X22] :
( ~ class_Fields_Ofield(X22)
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X22),c_Polynomial_Osmult(X22,X21,X20),X19) = c_Polynomial_Osmult(X22,X21,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X22),X20,X19)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__smult__left])]) ).
cnf(c_0_41,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X2,X3)),c_Polynomial_Odegree(X1,X3))
| c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X2,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_42,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_dp]) ).
cnf(c_0_43,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield]) ).
cnf(c_0_44,plain,
v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(split_conjunct,[status(thm)],[fact_pe]) ).
cnf(c_0_45,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_46,plain,
! [X21,X22,X23,X24] :
( ~ class_Rings_Ocomm__semiring__0(X24)
| hAPP(c_Polynomial_Opoly(X24,c_Polynomial_Osmult(X24,X23,X22)),X21) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24),X23),hAPP(c_Polynomial_Opoly(X24,X22),X21)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__smult])]) ).
cnf(c_0_47,plain,
( c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4) = c_Polynomial_Osmult(X1,X2,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(X1),X3,X4))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_48,plain,
c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X1,v_p) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]),c_0_44]),c_0_45]) ).
cnf(c_0_49,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Osmult(X1,X2,X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(c_Polynomial_Opoly(X1,X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_50,plain,
c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_48]),c_0_43])]) ).
cnf(c_0_51,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).
fof(c_0_52,plain,
! [X19,X20] :
( ~ class_Rings_Ocomm__semiring__0(X20)
| hAPP(c_Polynomial_Opoly(X20,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X20))),X19) = c_Groups_Ozero__class_Ozero(X20) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__0])]) ).
fof(c_0_53,plain,
! [X35,X36,X37,X38] :
( ~ class_Rings_Ocomm__semiring__1(X38)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),X37),X36)),X35) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X38),X37),X35)),X36) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J])]) ).
cnf(c_0_54,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X2)) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]) ).
cnf(c_0_55,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_56,plain,
! [X21,X22,X23,X24] :
( ~ class_Rings_Ocomm__semiring__0(X24)
| c_Polynomial_Osmult(X24,X23,c_Polynomial_Osmult(X24,X22,X21)) = c_Polynomial_Osmult(X24,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24),X23),X22),X21) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__smult])]) ).
fof(c_0_57,plain,
! [X13,X14,X15] :
( ~ class_Rings_Ocomm__semiring__1(X15)
| c_Groups_Oplus__class_Oplus(X15,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X14),X13),X13) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),c_Groups_Oplus__class_Oplus(X15,X14,c_Groups_Oone__class_Oone(X15))),X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])]) ).
cnf(c_0_58,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_59,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_51])]) ).
cnf(c_0_60,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
fof(c_0_61,plain,
! [X21,X22] :
( ~ class_Rings_Ocomm__semiring__0(X22)
| c_Polynomial_Osmult(X22,c_Groups_Ozero__class_Ozero(X22),X21) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X22)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__0__left])]) ).
cnf(c_0_62,plain,
( c_Polynomial_Osmult(X1,X2,c_Polynomial_Osmult(X1,X3,X4)) = c_Polynomial_Osmult(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_63,plain,
( c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1))),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_64,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_59]),c_0_60])]) ).
fof(c_0_65,plain,
! [X7,X8] :
( ~ class_Rings_Ocomm__semiring__1(X8)
| c_Groups_Oplus__class_Oplus(X8,c_Groups_Ozero__class_Ozero(X8),X7) = X7 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
fof(c_0_66,plain,
! [X21,X22,X23,X24] :
( ~ class_Rings_Ocomm__semiring__0(X24)
| hAPP(c_Polynomial_Opoly(X24,c_Polynomial_OpCons(X24,X23,X22)),X21) = c_Groups_Oplus__class_Oplus(X24,X23,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24),X21),hAPP(c_Polynomial_Opoly(X24,X22),X21))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__pCons])]) ).
fof(c_0_67,plain,
! [X21,X22,X23,X24] :
( ~ class_Rings_Ocomm__semiring__0(X24)
| c_Polynomial_Osmult(X24,c_Groups_Oplus__class_Oplus(X24,X23,X22),X21) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X24),c_Polynomial_Osmult(X24,X23,X21),c_Polynomial_Osmult(X24,X22,X21)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__add__left])]) ).
cnf(c_0_68,plain,
( c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_69,plain,
c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X2)) = c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_59]),c_0_51])]) ).
fof(c_0_70,plain,
! [X13,X14,X15] :
( ~ class_Rings_Ocomm__semiring__1(X15)
| c_Groups_Oplus__class_Oplus(X15,X14,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),X13),X14)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X15),c_Groups_Oplus__class_Oplus(X15,X13,c_Groups_Oone__class_Oone(X15))),X14) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])]) ).
fof(c_0_71,plain,
! [X7,X8] :
( ~ class_Rings_Ocomm__semiring__1(X8)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Groups_Oone__class_Oone(X8)),X7) = X7 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])]) ).
cnf(c_0_72,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_60])]) ).
cnf(c_0_73,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
fof(c_0_74,plain,
! [X10,X11,X12] :
( ~ class_Rings_Ocomm__semiring__1(X12)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12),X11),X10) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12),X10),X11) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).
fof(c_0_75,plain,
! [X20,X21,X22,X23] :
( ~ class_Rings_Ocomm__semiring__1(X23)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23),c_Groups_Oplus__class_Oplus(X23,X22,X21)),X20) = c_Groups_Oplus__class_Oplus(X23,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23),X22),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23),X21),X20)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])]) ).
cnf(c_0_76,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Polynomial_OpCons(X1,X2,X3)),X4) = c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
fof(c_0_77,plain,
( v_p = c_Polynomial_OpCons(tc_Complex_Ocomplex,esk2_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
& esk2_0 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_Bk_O_A_091_124_Ap_A_061_A_091_058k_058_093_059_Ak_A_126_061_A0_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096])])]) ).
cnf(c_0_78,plain,
( c_Polynomial_Osmult(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X4),c_Polynomial_Osmult(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_79,plain,
c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_51])]) ).
fof(c_0_80,plain,
! [X21,X22] :
( ~ class_Rings_Ocomm__semiring__1(X22)
| c_Polynomial_Osmult(X22,c_Groups_Oone__class_Oone(X22),X21) = X21 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__1__left])]) ).
cnf(c_0_81,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_82,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_83,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_60])]) ).
cnf(c_0_84,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
fof(c_0_85,plain,
! [X7,X8] :
( ~ class_Rings_Ocomm__semiring__1(X8)
| c_Groups_Oplus__class_Oplus(X8,X7,c_Groups_Ozero__class_Ozero(X8)) = X7 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).
cnf(c_0_86,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)),X4) = c_Groups_Oplus__class_Oplus(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_87,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_64]),c_0_51])]) ).
cnf(c_0_88,plain,
v_p = c_Polynomial_OpCons(tc_Complex_Ocomplex,esk2_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_89,plain,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_51])]) ).
cnf(c_0_90,plain,
( c_Polynomial_Osmult(X1,c_Groups_Oone__class_Oone(X1),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_91,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_64]),c_0_60])]),c_0_72]) ).
cnf(c_0_92,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_60])]) ).
fof(c_0_93,plain,
! [X22,X23,X24,X25] :
( ~ class_Rings_Ocomm__semiring__0(X25)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X25)),X24),c_Polynomial_Osmult(X25,X23,X22)) = c_Polynomial_Osmult(X25,X23,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X25)),X24),X22)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__smult__right])]) ).
fof(c_0_94,plain,
! [X21,X22,X23,X24] :
( ~ class_Rings_Ocomm__semiring__0(X24)
| c_Polynomial_Osmult(X24,X23,c_Polynomial_OpCons(X24,X22,X21)) = c_Polynomial_OpCons(X24,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24),X23),X22),c_Polynomial_Osmult(X24,X23,X21)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__pCons])]) ).
cnf(c_0_95,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_83]),c_0_60])]) ).
cnf(c_0_96,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_97,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_64]),c_0_60])]) ).
cnf(c_0_98,plain,
v_p = c_Polynomial_OpCons(tc_Complex_Ocomplex,v_k____,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(split_conjunct,[status(thm)],[fact_k_I1_J]) ).
cnf(c_0_99,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,esk2_0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_100,plain,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]),c_0_92]),c_0_60])]) ).
cnf(c_0_101,plain,
c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X2)) = c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_83]),c_0_51])]) ).
fof(c_0_102,plain,
! [X22,X23,X24,X25] :
( ~ class_Rings_Ocomm__semiring__0(X25)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X25)),X24),c_Polynomial_OpCons(X25,X23,X22)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X25),c_Polynomial_Osmult(X25,X23,X24),c_Polynomial_OpCons(X25,c_Groups_Ozero__class_Ozero(X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X25)),X24),X22))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pCons__right])]) ).
cnf(c_0_103,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),c_Polynomial_Osmult(X1,X3,X4)) = c_Polynomial_Osmult(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_104,plain,
( c_Polynomial_Osmult(X1,X2,c_Polynomial_OpCons(X1,X3,X4)) = c_Polynomial_OpCons(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Polynomial_Osmult(X1,X2,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_105,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = X1,
inference(rw,[status(thm)],[c_0_95,c_0_92]) ).
fof(c_0_106,plain,
! [X7] :
( ~ class_Rings_Ocomm__semiring__1(X7)
| c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X7)) = c_Polynomial_OpCons(X7,c_Groups_Oone__class_Oone(X7),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__poly__def])]) ).
fof(c_0_107,plain,
! [X10,X11,X12] :
( ~ class_Fields_Ofield(X12)
| c_Rings_Oinverse__class_Odivide(X12,X11,X10) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X12),X11),c_Rings_Oinverse__class_Oinverse(X12,X10)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__divide__inverse])]) ).
cnf(c_0_108,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_60])]) ).
cnf(c_0_109,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,esk2_0,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_k____,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_98]),c_0_99]) ).
fof(c_0_110,plain,
! [X22,X23,X24,X25] :
( ~ class_Rings_Ocomm__semiring__0(X25)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X25)),c_Polynomial_Osmult(X25,X24,X23)),X22) = c_Polynomial_Osmult(X25,X24,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X25)),X23),X22)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__smult__left])]) ).
cnf(c_0_111,plain,
c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),X2) = c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_100]),c_0_101]),c_0_92]) ).
cnf(c_0_112,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),c_Polynomial_OpCons(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X3,X2),c_Polynomial_OpCons(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X4)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_113,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_79]),c_0_79]),c_0_51])]) ).
cnf(c_0_114,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_79]),c_0_64]),c_0_79]),c_0_51])]) ).
cnf(c_0_115,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X2)) = c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_51])]) ).
cnf(c_0_116,plain,
( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X1)) = c_Polynomial_OpCons(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_117,plain,
( c_Rings_Oinverse__class_Odivide(X1,X2,X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Rings_Oinverse__class_Oinverse(X1,X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_118,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),esk2_0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_k____),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_108]) ).
fof(c_0_119,plain,
! [X14,X15,X16,X17,X18] :
( ( X17 = X15
| c_Polynomial_OpCons(X18,X17,X16) != c_Polynomial_OpCons(X18,X15,X14)
| ~ class_Groups_Ozero(X18) )
& ( X16 = X14
| c_Polynomial_OpCons(X18,X17,X16) != c_Polynomial_OpCons(X18,X15,X14)
| ~ class_Groups_Ozero(X18) )
& ( X17 != X15
| X16 != X14
| c_Polynomial_OpCons(X18,X17,X16) = c_Polynomial_OpCons(X18,X15,X14)
| ~ class_Groups_Ozero(X18) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__eq__iff])])]) ).
cnf(c_0_120,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),c_Polynomial_Osmult(X1,X2,X3)),X4) = c_Polynomial_Osmult(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_121,plain,
c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_111]),c_0_111]),c_0_51])]) ).
cnf(c_0_122,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),c_Polynomial_OpCons(tc_Complex_Ocomplex,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_51])]),c_0_114]),c_0_100]),c_0_101]),c_0_92]) ).
fof(c_0_123,negated_conjecture,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_k____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
inference(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_0_124,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_50]),c_0_60])]) ).
cnf(c_0_125,plain,
c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_108]),c_0_43])]) ).
fof(c_0_126,plain,
! [X7,X8] :
( ~ class_Fields_Ofield(X8)
| X7 = c_Groups_Ozero__class_Ozero(X8)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),c_Rings_Oinverse__class_Oinverse(X8,X7)),X7) = c_Groups_Oone__class_Oone(X8) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__inverse])]) ).
cnf(c_0_127,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_k____),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_118]),c_0_60])]) ).
cnf(c_0_128,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_108]),c_0_60])]) ).
cnf(c_0_129,plain,
( X2 = X4
| ~ class_Groups_Ozero(X1)
| c_Polynomial_OpCons(X1,X2,X3) != c_Polynomial_OpCons(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_130,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]) ).
cnf(c_0_131,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2),c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_51])]) ).
cnf(c_0_132,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_116]),c_0_60])]) ).
fof(c_0_133,negated_conjecture,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_k____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
inference(fof_simplification,[status(thm)],[c_0_123]) ).
cnf(c_0_134,plain,
c_Polynomial_Osmult(tc_Complex_Ocomplex,v_k____,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = v_p,
inference(rw,[status(thm)],[c_0_98,c_0_124]) ).
cnf(c_0_135,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,X2)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_96]),c_0_60])]) ).
cnf(c_0_136,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)),X2) = c_Groups_Oone__class_Oone(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_137,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),esk2_0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),v_k____),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_127]),c_0_60])]) ).
cnf(c_0_138,plain,
esk2_0 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_139,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_128]),c_0_128]),c_0_128]) ).
cnf(c_0_140,plain,
( X1 = v_k____
| c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,X2) != v_p ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_98]),c_0_130])]) ).
cnf(c_0_141,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,c_Polynomial_OpCons(tc_Complex_Ocomplex,X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Polynomial_Osmult(tc_Complex_Ocomplex,X3,c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,X1)),
inference(spm,[status(thm)],[c_0_131,c_0_122]) ).
cnf(c_0_142,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_101]),c_0_92]) ).
cnf(c_0_143,negated_conjecture,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_k____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
fof(c_0_144,plain,
! [X7,X8] :
( ~ class_Fields_Ofield(X8)
| c_Rings_Oinverse__class_Oinverse(X8,X7) = c_Rings_Oinverse__class_Odivide(X8,c_Groups_Oone__class_Oone(X8),X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__class_Onormalizing__field__rules_I2_J])]) ).
cnf(c_0_145,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),c_Polynomial_Osmult(tc_Complex_Ocomplex,v_k____,X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),X1),
inference(spm,[status(thm)],[c_0_131,c_0_134]) ).
cnf(c_0_146,plain,
c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,X2),X3)) = c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,X1,X2),X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_135]),c_0_51])]) ).
cnf(c_0_147,plain,
c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,v_k____,esk2_0) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_43])]),c_0_138]),c_0_139]),c_0_135]) ).
cnf(c_0_148,plain,
esk2_0 = v_k____,
inference(spm,[status(thm)],[c_0_140,c_0_88]) ).
cnf(c_0_149,plain,
c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X2)) = c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X2),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_116]),c_0_60])]),c_0_142]) ).
cnf(c_0_150,negated_conjecture,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),v_k____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rw,[status(thm)],[c_0_143,c_0_42]) ).
cnf(c_0_151,plain,
( c_Rings_Oinverse__class_Oinverse(X1,X2) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
cnf(c_0_152,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,v_k____,X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,X1),X2)),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_153,plain,
c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,v_k____,v_k____) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(rw,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_154,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_121]),c_0_60])]) ).
cnf(c_0_155,plain,
c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_90]),c_0_60])]) ).
cnf(c_0_156,negated_conjecture,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,v_k____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_43])]) ).
cnf(c_0_157,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_p),c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,v_k____),X1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_154]) ).
cnf(c_0_158,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = X1,
inference(rw,[status(thm)],[c_0_132,c_0_155]) ).
cnf(c_0_159,negated_conjecture,
c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,v_k____),v_p) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rw,[status(thm)],[c_0_156,c_0_122]) ).
cnf(c_0_160,plain,
c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,v_k____),v_p) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_157]),c_0_158]) ).
fof(c_0_161,plain,
! [X19,X20] :
( ~ class_Rings_Ocomm__semiring__1(X20)
| hAPP(hAPP(c_Power_Opower__class_Opower(X20),X19),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X20) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J])]) ).
cnf(c_0_162,negated_conjecture,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(rw,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_163,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_161]) ).
fof(c_0_164,plain,
! [X83] :
( ~ class_Rings_Ocomm__semiring__1(X83)
| class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X83)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__1])]) ).
cnf(c_0_165,negated_conjecture,
~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(spm,[status(thm)],[c_0_162,c_0_163]) ).
cnf(c_0_166,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_164]) ).
cnf(c_0_167,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_60])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW286+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.12 % Command : run_ET %s %d
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 5 05:49:07 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.47/23.50 eprover: CPU time limit exceeded, terminating
% 0.47/23.51 eprover: CPU time limit exceeded, terminating
% 0.47/23.51 eprover: CPU time limit exceeded, terminating
% 0.47/23.51 eprover: CPU time limit exceeded, terminating
% 0.49/25.66 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.49/25.66
% 0.49/25.66 # Failure: Resource limit exceeded (time)
% 0.49/25.66 # OLD status Res
% 0.49/25.66 # Preprocessing time : 0.130 s
% 0.49/25.66 # Running protocol protocol_eprover_f6eb5f7f05126ea361481ae651a4823314e3d740 for 23 seconds:
% 0.49/25.66 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,02,20000,1.0)
% 0.49/25.66 # Preprocessing time : 0.043 s
% 0.49/25.66
% 0.49/25.66 # Proof found!
% 0.49/25.66 # SZS status Theorem
% 0.49/25.66 # SZS output start CNFRefutation
% See solution above
% 0.49/25.66 # Proof object total steps : 168
% 0.49/25.66 # Proof object clause steps : 98
% 0.49/25.66 # Proof object formula steps : 70
% 0.49/25.66 # Proof object conjectures : 10
% 0.49/25.66 # Proof object clause conjectures : 7
% 0.49/25.66 # Proof object formula conjectures : 3
% 0.49/25.66 # Proof object initial clauses used : 39
% 0.49/25.66 # Proof object initial formulas used : 38
% 0.49/25.66 # Proof object generating inferences : 51
% 0.49/25.66 # Proof object simplifying inferences : 116
% 0.49/25.66 # Training examples: 0 positive, 0 negative
% 0.49/25.66 # Parsed axioms : 1170
% 0.49/25.66 # Removed by relevancy pruning/SinE : 634
% 0.49/25.66 # Initial clauses : 702
% 0.49/25.66 # Removed in clause preprocessing : 41
% 0.49/25.66 # Initial clauses in saturation : 661
% 0.49/25.66 # Processed clauses : 6588
% 0.49/25.66 # ...of these trivial : 591
% 0.49/25.66 # ...subsumed : 4722
% 0.49/25.66 # ...remaining for further processing : 1275
% 0.49/25.66 # Other redundant clauses eliminated : 60
% 0.49/25.66 # Clauses deleted for lack of memory : 0
% 0.49/25.66 # Backward-subsumed : 41
% 0.49/25.66 # Backward-rewritten : 323
% 0.49/25.66 # Generated clauses : 95976
% 0.49/25.66 # ...of the previous two non-trivial : 88759
% 0.49/25.66 # Contextual simplify-reflections : 91
% 0.49/25.66 # Paramodulations : 95875
% 0.49/25.66 # Factorizations : 4
% 0.49/25.66 # Equation resolutions : 85
% 0.49/25.66 # Current number of processed clauses : 896
% 0.49/25.66 # Positive orientable unit clauses : 321
% 0.49/25.66 # Positive unorientable unit clauses: 117
% 0.49/25.66 # Negative unit clauses : 23
% 0.49/25.66 # Non-unit-clauses : 435
% 0.49/25.66 # Current number of unprocessed clauses: 57793
% 0.49/25.66 # ...number of literals in the above : 122853
% 0.49/25.66 # Current number of archived formulas : 0
% 0.49/25.66 # Current number of archived clauses : 365
% 0.49/25.66 # Clause-clause subsumption calls (NU) : 16746
% 0.49/25.66 # Rec. Clause-clause subsumption calls : 12571
% 0.49/25.66 # Non-unit clause-clause subsumptions : 241
% 0.49/25.66 # Unit Clause-clause subsumption calls : 2671
% 0.49/25.66 # Rewrite failures with RHS unbound : 355
% 0.49/25.66 # BW rewrite match attempts : 11352
% 0.49/25.66 # BW rewrite match successes : 1267
% 0.49/25.66 # Condensation attempts : 0
% 0.49/25.66 # Condensation successes : 0
% 0.49/25.66 # Termbank termtop insertions : 2423641
% 0.49/25.66
% 0.49/25.66 # -------------------------------------------------
% 0.49/25.66 # User time : 1.225 s
% 0.49/25.66 # System time : 0.027 s
% 0.49/25.66 # Total time : 1.252 s
% 0.49/25.66 # Maximum resident set size: 55784 pages
% 0.49/46.52 eprover: CPU time limit exceeded, terminating
% 0.49/46.53 eprover: CPU time limit exceeded, terminating
% 0.49/46.54 eprover: CPU time limit exceeded, terminating
% 0.49/46.54 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.49/46.54 eprover: No such file or directory
% 0.49/46.54 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.49/46.54 eprover: No such file or directory
% 0.49/46.55 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.49/46.55 eprover: No such file or directory
% 0.49/46.55 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.49/46.55 eprover: No such file or directory
% 0.49/46.55 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.49/46.55 eprover: No such file or directory
% 0.49/46.55 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.49/46.55 eprover: No such file or directory
% 0.49/46.55 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.49/46.55 eprover: No such file or directory
% 0.49/46.56 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.49/46.56 eprover: No such file or directory
% 0.49/46.56 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.49/46.56 eprover: No such file or directory
% 0.49/46.56 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.49/46.56 eprover: No such file or directory
% 0.49/46.56 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.49/46.56 eprover: No such file or directory
% 0.49/46.56 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.49/46.56 eprover: No such file or directory
% 0.49/46.56 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.49/46.56 eprover: No such file or directory
% 0.49/46.56 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.49/46.56 eprover: No such file or directory
% 0.49/46.57 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.49/46.57 eprover: No such file or directory
% 0.49/46.57 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.49/46.57 eprover: No such file or directory
% 0.49/46.57 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.49/46.57 eprover: No such file or directory
% 0.49/46.57 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.49/46.57 eprover: No such file or directory
% 0.49/46.57 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.49/46.57 eprover: No such file or directory
% 0.49/46.57 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.49/46.57 eprover: No such file or directory
% 0.49/46.58 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.49/46.58 eprover: No such file or directory
% 0.49/46.58 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.49/46.58 eprover: No such file or directory
% 0.49/46.58 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.49/46.58 eprover: No such file or directory
% 0.49/46.58 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.49/46.58 eprover: No such file or directory
% 0.49/46.58 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.49/46.58 eprover: No such file or directory
% 0.49/46.58 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.49/46.58 eprover: No such file or directory
% 0.49/46.59 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.49/46.59 eprover: No such file or directory
% 0.49/46.59 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.49/46.59 eprover: No such file or directory
% 0.49/46.59 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.49/46.59 eprover: No such file or directory
% 0.49/46.59 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.49/46.59 eprover: No such file or directory
%------------------------------------------------------------------------------