TSTP Solution File: SWW245+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SWW245+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n028.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 00:10:23 EDT 2022
% Result : Theorem 0.33s 1.53s
% Output : CNFRefutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 60 ( 29 unt; 0 def)
% Number of atoms : 174 ( 149 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 195 ( 81 ~; 81 |; 21 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% 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 : 70 ( 2 sgn 31 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(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,axiom,
( class_Rings_Oidom(t_a)
=> ( v_c____ = c_Groups_Ozero__class_Ozero(t_a)
=> ? [X5,X6] :
( X6 != c_Groups_Ozero__class_Ozero(t_a)
& ? [X7] :
( ( 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(X7,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,X7))),X5)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X7,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,X7))),X5)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) )
& ! [X4] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X4),X5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X6,X7)),X4)) ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/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(fact_Suc__eq__plus1,axiom,
! [X19] : c_Nat_OSuc(X19) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(fact_Zero__not__Suc,axiom,
! [X22] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X22),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Zero__not__Suc) ).
fof(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,axiom,
( class_Rings_Oidom(t_a)
=> ( v_c____ != c_Groups_Ozero__class_Ozero(t_a)
=> ? [X5,X6] :
( X6 != c_Groups_Ozero__class_Ozero(t_a)
& ? [X7] :
( ( 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(X7,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,X7))),X5)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X7,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,X7))),X5)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) )
& ! [X4] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X4),X5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X6,X7)),X4)) ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/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(conj_0,conjecture,
? [X5,X6] :
( X6 != c_Groups_Ozero__class_Ozero(t_a)
& ? [X7] :
( ( 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(X7,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,X7))),X5)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X7,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,X7))),X5)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) )
& ! [X4] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X4),X5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X6,X7)),X4)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',conj_0) ).
fof(tfree_0,hypothesis,
class_Rings_Oidom(t_a),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',tfree_0) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [X19] : c_Nat_OSuc(X19) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X19),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_nat__add__commute,axiom,
! [X19,X22] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X19) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X22),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_nat__add__assoc,axiom,
! [X36,X19,X22] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X19),X36) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X36)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_nat__add__left__commute,axiom,
! [X35,X34,X11] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X35)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X35)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_nat__add__left__commute) ).
fof(c_0_10,plain,
! [X11] :
( ( esk8_0 != c_Groups_Ozero__class_Ozero(t_a)
| v_c____ != c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Rings_Oidom(t_a) )
& ( 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(esk9_0,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,esk9_0))),esk7_0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| v_c____ != c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Rings_Oidom(t_a) )
& ( 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(esk9_0,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,esk9_0))),esk7_0)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
| v_c____ != c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Rings_Oidom(t_a) )
& ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X11) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X11),esk7_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk8_0,esk9_0)),X11))
| v_c____ != c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Rings_Oidom(t_a) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[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(c_0_11,plain,
! [X20] : c_Nat_OSuc(X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(c_0_12,plain,
! [X23] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X23),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
fof(c_0_13,plain,
! [X11] :
( ( esk5_0 != c_Groups_Ozero__class_Ozero(t_a)
| v_c____ = c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Rings_Oidom(t_a) )
& ( 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(esk6_0,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,esk6_0))),esk4_0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| v_c____ = c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Rings_Oidom(t_a) )
& ( 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(esk6_0,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,esk6_0))),esk4_0)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
| v_c____ = c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Rings_Oidom(t_a) )
& ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X11) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X11),esk4_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk5_0,esk6_0)),X11))
| v_c____ = c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Rings_Oidom(t_a) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[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])])])])])])]) ).
cnf(c_0_14,plain,
( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk9_0,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,esk9_0))),esk7_0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Oidom(t_a)
| v_c____ != c_Groups_Ozero__class_Ozero(t_a)
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,negated_conjecture,
~ ? [X5,X6] :
( X6 != c_Groups_Ozero__class_Ozero(t_a)
& ? [X7] :
( ( 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(X7,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,X7))),X5)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X7,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,X7))),X5)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) )
& ! [X4] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X4),X5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X6,X7)),X4)) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_0_18,plain,
( v_c____ = c_Groups_Ozero__class_Ozero(t_a)
| c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk6_0,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,esk6_0))),esk4_0)) = 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(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk9_0,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,esk9_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),esk7_0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| v_c____ != c_Groups_Ozero__class_Ozero(t_a)
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ class_Rings_Oidom(t_a) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_15]) ).
cnf(c_0_20,hypothesis,
class_Rings_Oidom(t_a),
inference(split_conjunct,[status(thm)],[tfree_0]) ).
cnf(c_0_21,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[c_0_16,c_0_15]) ).
fof(c_0_22,negated_conjecture,
! [X8,X9,X10] :
( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk32_3(X8,X9,X10)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk32_3(X8,X9,X10)),X8)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X9,X10)),esk32_3(X8,X9,X10)))
| X9 = c_Groups_Ozero__class_Ozero(t_a) )
& ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X10,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,X10))),X8)) != c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk32_3(X8,X9,X10)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk32_3(X8,X9,X10)),X8)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X9,X10)),esk32_3(X8,X9,X10)))
| X9 = c_Groups_Ozero__class_Ozero(t_a) )
& ( 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(X10,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,X10))),X8)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk32_3(X8,X9,X10)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk32_3(X8,X9,X10)),X8)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X9,X10)),esk32_3(X8,X9,X10)))
| X9 = c_Groups_Ozero__class_Ozero(t_a) )
& ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X10,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,X10))),X8)) != 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(X10,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,X10))),X8)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk32_3(X8,X9,X10)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk32_3(X8,X9,X10)),X8)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X9,X10)),esk32_3(X8,X9,X10)))
| X9 = c_Groups_Ozero__class_Ozero(t_a) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])])])]) ).
fof(c_0_23,plain,
! [X20] : c_Nat_OSuc(X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X20),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).
cnf(c_0_24,plain,
( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk9_0,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,esk9_0))),esk7_0)) = 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))
| ~ class_Rings_Oidom(t_a)
| v_c____ != c_Groups_Ozero__class_Ozero(t_a) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_25,plain,
( v_c____ = c_Groups_Ozero__class_Ozero(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(esk6_0,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,esk6_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),esk4_0),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))
| ~ class_Rings_Oidom(t_a) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_15]),c_0_15]) ).
cnf(c_0_26,plain,
( 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(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]),c_0_21]) ).
cnf(c_0_27,negated_conjecture,
( X1 = c_Groups_Ozero__class_Ozero(t_a)
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk32_3(X2,X1,X3)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk32_3(X2,X1,X3)),X2)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X3)),esk32_3(X2,X1,X3)))
| c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X3,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,X3))),X2)) != c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_28,plain,
! [X23,X24] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X23) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X24),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(c_0_29,plain,
! [X37,X38,X39] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X38),X37) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X37)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
cnf(c_0_30,plain,
c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,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(esk9_0,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,esk9_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),esk7_0),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))
| v_c____ != c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Rings_Oidom(t_a) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_15]),c_0_15]),c_0_15]) ).
cnf(c_0_32,plain,
c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_20])]),c_0_21]),c_0_26]) ).
fof(c_0_33,plain,
! [X36,X37,X38] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X37,X36)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X37,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X36)),
inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).
cnf(c_0_34,plain,
( v_c____ = c_Groups_Ozero__class_Ozero(t_a)
| c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk6_0,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,esk6_0))),esk4_0)) = 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))
| ~ class_Rings_Oidom(t_a) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_35,negated_conjecture,
( X1 = c_Groups_Ozero__class_Ozero(t_a)
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk32_3(X2,X1,X3)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk32_3(X2,X1,X3)),X2)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X3)),esk32_3(X2,X1,X3)))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X3,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,X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2),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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_15]),c_0_15]),c_0_15]) ).
cnf(c_0_36,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),
inference(rw,[status(thm)],[c_0_30,c_0_15]) ).
cnf(c_0_39,plain,
( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X1),esk7_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk8_0,esk9_0)),X1))
| ~ class_Rings_Oidom(t_a)
| v_c____ != c_Groups_Ozero__class_Ozero(t_a) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_40,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk9_0,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,esk9_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),esk7_0),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(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_20])]),c_0_32]) ).
cnf(c_0_41,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_42,plain,
( ~ class_Rings_Oidom(t_a)
| v_c____ != c_Groups_Ozero__class_Ozero(t_a)
| esk8_0 != c_Groups_Ozero__class_Ozero(t_a) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_43,plain,
( v_c____ = c_Groups_Ozero__class_Ozero(t_a)
| 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(esk6_0,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,esk6_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),esk4_0),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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_15]),c_0_15]),c_0_15]) ).
cnf(c_0_44,plain,
( v_c____ = c_Groups_Ozero__class_Ozero(t_a)
| hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X1),esk4_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk5_0,esk6_0)),X1))
| ~ class_Rings_Oidom(t_a) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_45,negated_conjecture,
( X1 = c_Groups_Ozero__class_Ozero(t_a)
| 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,X3,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),esk32_3(X3,X1,X2)),X3)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),esk32_3(X3,X1,X2))) != hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk32_3(X3,X1,X2)) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38]),c_0_32]) ).
cnf(c_0_46,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X1),esk7_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk8_0,esk9_0)),X1)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X1)
| c_Groups_Ozero__class_Ozero(t_a) != v_c____ ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_20])]) ).
cnf(c_0_47,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk7_0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_If(tc_Nat_Onat,c_fequal(esk9_0,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,esk9_0))))) = 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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_38]),c_0_38]),c_0_38]),c_0_36]),c_0_41]) ).
cnf(c_0_48,plain,
( c_Groups_Ozero__class_Ozero(t_a) != v_c____
| c_Groups_Ozero__class_Ozero(t_a) != esk8_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_20])]) ).
cnf(c_0_49,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk6_0,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,esk6_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),esk4_0),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(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_20])]),c_0_32]) ).
cnf(c_0_50,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X1),esk4_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk5_0,esk6_0)),X1)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X1)
| c_Groups_Ozero__class_Ozero(t_a) = v_c____ ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_20])]) ).
cnf(c_0_51,negated_conjecture,
c_Groups_Ozero__class_Ozero(t_a) != v_c____,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_41]),c_0_36]),c_0_47]),c_0_48]) ).
cnf(c_0_52,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk4_0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_If(tc_Nat_Onat,c_fequal(esk6_0,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,esk6_0))))) = 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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_38]),c_0_38]),c_0_38]),c_0_36]),c_0_41]) ).
cnf(c_0_53,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X1),esk4_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk5_0,esk6_0)),X1)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X1),
inference(sr,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk4_0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_If(tc_Nat_Onat,c_fequal(esk6_0,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,esk6_0))))) = 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(sr,[status(thm)],[c_0_52,c_0_51]) ).
cnf(c_0_55,plain,
( v_c____ = c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Rings_Oidom(t_a)
| esk5_0 != c_Groups_Ozero__class_Ozero(t_a) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_56,negated_conjecture,
c_Groups_Ozero__class_Ozero(t_a) = esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_53]),c_0_41]),c_0_36]),c_0_54])]) ).
cnf(c_0_57,plain,
( c_Groups_Ozero__class_Ozero(t_a) = v_c____
| c_Groups_Ozero__class_Ozero(t_a) != esk5_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_20])]) ).
cnf(c_0_58,negated_conjecture,
esk5_0 != v_c____,
inference(rw,[status(thm)],[c_0_51,c_0_56]) ).
cnf(c_0_59,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_56]),c_0_56])]),c_0_58]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW245+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : run_ET %s %d
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 6 06:24:13 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.33/1.53 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.33/1.53 # Preprocessing time : 0.168 s
% 0.33/1.53
% 0.33/1.53 # Proof found!
% 0.33/1.53 # SZS status Theorem
% 0.33/1.53 # SZS output start CNFRefutation
% See solution above
% 0.33/1.53 # Proof object total steps : 60
% 0.33/1.53 # Proof object clause steps : 40
% 0.33/1.53 # Proof object formula steps : 20
% 0.33/1.53 # Proof object conjectures : 9
% 0.33/1.53 # Proof object clause conjectures : 6
% 0.33/1.53 # Proof object formula conjectures : 3
% 0.33/1.53 # Proof object initial clauses used : 16
% 0.33/1.53 # Proof object initial formulas used : 10
% 0.33/1.53 # Proof object generating inferences : 2
% 0.33/1.53 # Proof object simplifying inferences : 65
% 0.33/1.53 # Training examples: 0 positive, 0 negative
% 0.33/1.53 # Parsed axioms : 1161
% 0.33/1.53 # Removed by relevancy pruning/SinE : 0
% 0.33/1.53 # Initial clauses : 1591
% 0.33/1.53 # Removed in clause preprocessing : 77
% 0.33/1.53 # Initial clauses in saturation : 1514
% 0.33/1.53 # Processed clauses : 3084
% 0.33/1.53 # ...of these trivial : 97
% 0.33/1.53 # ...subsumed : 1237
% 0.33/1.53 # ...remaining for further processing : 1749
% 0.33/1.53 # Other redundant clauses eliminated : 211
% 0.33/1.53 # Clauses deleted for lack of memory : 0
% 0.33/1.53 # Backward-subsumed : 38
% 0.33/1.53 # Backward-rewritten : 96
% 0.33/1.53 # Generated clauses : 38235
% 0.33/1.53 # ...of the previous two non-trivial : 35426
% 0.33/1.53 # Contextual simplify-reflections : 214
% 0.33/1.53 # Paramodulations : 37963
% 0.33/1.53 # Factorizations : 4
% 0.33/1.53 # Equation resolutions : 266
% 0.33/1.53 # Current number of processed clauses : 1591
% 0.33/1.53 # Positive orientable unit clauses : 208
% 0.33/1.53 # Positive unorientable unit clauses: 11
% 0.33/1.53 # Negative unit clauses : 50
% 0.33/1.53 # Non-unit-clauses : 1322
% 0.33/1.53 # Current number of unprocessed clauses: 32314
% 0.33/1.53 # ...number of literals in the above : 107118
% 0.33/1.53 # Current number of archived formulas : 0
% 0.33/1.53 # Current number of archived clauses : 137
% 0.33/1.53 # Clause-clause subsumption calls (NU) : 336017
% 0.33/1.53 # Rec. Clause-clause subsumption calls : 162012
% 0.33/1.53 # Non-unit clause-clause subsumptions : 740
% 0.33/1.53 # Unit Clause-clause subsumption calls : 2774
% 0.33/1.53 # Rewrite failures with RHS unbound : 0
% 0.33/1.53 # BW rewrite match attempts : 861
% 0.33/1.53 # BW rewrite match successes : 125
% 0.33/1.53 # Condensation attempts : 0
% 0.33/1.53 # Condensation successes : 0
% 0.33/1.53 # Termbank termtop insertions : 956025
% 0.33/1.53
% 0.33/1.53 # -------------------------------------------------
% 0.33/1.53 # User time : 0.755 s
% 0.33/1.53 # System time : 0.021 s
% 0.33/1.53 # Total time : 0.776 s
% 0.33/1.53 # Maximum resident set size: 42884 pages
% 0.33/23.51 eprover: CPU time limit exceeded, terminating
% 0.33/23.52 eprover: CPU time limit exceeded, terminating
% 0.33/23.52 eprover: CPU time limit exceeded, terminating
% 0.33/23.53 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.53 eprover: No such file or directory
% 0.33/23.53 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.53 eprover: No such file or directory
% 0.33/23.54 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.54 eprover: No such file or directory
% 0.33/23.54 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.33/23.54 eprover: No such file or directory
% 0.33/23.54 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.54 eprover: No such file or directory
% 0.33/23.54 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.54 eprover: No such file or directory
% 0.33/23.54 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.33/23.54 eprover: No such file or directory
% 0.33/23.54 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.54 eprover: No such file or directory
% 0.33/23.54 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.54 eprover: No such file or directory
% 0.33/23.55 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.33/23.55 eprover: No such file or directory
% 0.33/23.55 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.55 eprover: No such file or directory
% 0.33/23.55 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.55 eprover: No such file or directory
% 0.33/23.55 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.33/23.55 eprover: No such file or directory
% 0.33/23.55 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.55 eprover: No such file or directory
% 0.33/23.55 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.55 eprover: No such file or directory
% 0.33/23.56 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.33/23.56 eprover: No such file or directory
% 0.33/23.56 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.56 eprover: No such file or directory
% 0.33/23.56 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.56 eprover: No such file or directory
% 0.33/23.56 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.33/23.56 eprover: No such file or directory
% 0.33/23.56 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.56 eprover: No such file or directory
% 0.33/23.57 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.57 eprover: No such file or directory
% 0.33/23.57 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.57 eprover: No such file or directory
% 0.33/23.57 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.33/23.57 eprover: No such file or directory
% 0.33/23.57 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.57 eprover: No such file or directory
% 0.33/23.57 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.57 eprover: No such file or directory
% 0.33/23.57 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.33/23.57 eprover: No such file or directory
% 0.33/23.58 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.58 eprover: No such file or directory
% 0.33/23.58 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.58 eprover: No such file or directory
% 0.33/23.58 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.33/23.58 eprover: No such file or directory
% 0.33/23.58 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.58 eprover: No such file or directory
% 0.33/23.58 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.33/23.58 eprover: No such file or directory
% 0.33/23.59 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.59 eprover: No such file or directory
% 0.33/23.59 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.33/23.59 eprover: No such file or directory
%------------------------------------------------------------------------------