TSTP Solution File: SWW245+1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SWW245+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n023.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 : 300s
% DateTime : Tue May 21 06:41:59 EDT 2024
% Result : Theorem 9.36s 1.75s
% Output : CNFRefutation 9.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 21 unt; 0 def)
% Number of atoms : 165 ( 142 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 192 ( 77 ~; 68 |; 27 &)
% ( 0 <=>; 20 =>; 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 : 23 ( 23 usr; 10 con; 0-4 aty)
% Number of variables : 65 ( 1 sgn 26 !; 18 ?)
% 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/benchmark/theBenchmark.p',fact__096c_A_061_A_I0_058_058_Ha_J_061_061_062_AEX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_I_Iif_Aq_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_Aq_J_J_A_L_Ak_J_A_061_A_Iif_ApCons_Ac_Acs_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_A_IpCons_Ac_Acs_J_J_J_A_G_A_IALL_Az_O_Apoly_A_IpCons_Ac_Acs_J_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096) ).
fof(fact_Suc__not__Zero,axiom,
! [X22] : c_Nat_OSuc(X22) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
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/benchmark/theBenchmark.p',fact__096c_A_126_061_A_I0_058_058_Ha_J_061_061_062_AEX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_I_Iif_Aq_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_Aq_J_J_A_L_Ak_J_A_061_A_Iif_ApCons_Ac_Acs_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_A_IpCons_Ac_Acs_J_J_J_A_G_A_IALL_Az_O_Apoly_A_IpCons_Ac_Acs_J_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096) ).
fof(tfree_0,hypothesis,
class_Rings_Oidom(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
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/benchmark/theBenchmark.p',conj_0) ).
fof(fact_add__Suc__right,axiom,
! [X19,X22] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,c_Nat_OSuc(X19)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
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/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_add__Suc__shift,axiom,
! [X19,X22] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X22),X19) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,c_Nat_OSuc(X19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
fof(c_0_8,plain,
( 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)) ) ) ) ),
inference(fof_simplification,[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_9,plain,
! [X22] : c_Nat_OSuc(X22) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_simplification,[status(thm)],[fact_Suc__not__Zero]) ).
fof(c_0_10,plain,
( 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)) ) ) ) ),
inference(fof_simplification,[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]) ).
fof(c_0_11,plain,
! [X315] :
( ( esk11_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(esk12_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,esk12_0))),esk10_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(esk12_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,esk12_0))),esk10_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____)),X315) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X315),esk10_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk11_0,esk12_0)),X315))
| v_c____ != c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Rings_Oidom(t_a) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])])]) ).
fof(c_0_12,plain,
! [X331] : c_Nat_OSuc(X331) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_9])]) ).
fof(c_0_13,plain,
! [X311] :
( ( 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____)),X311) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X311),esk7_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk8_0,esk9_0)),X311))
| v_c____ = c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Rings_Oidom(t_a) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])])]) ).
cnf(c_0_14,plain,
( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk12_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,esk12_0))),esk10_0)) = 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))
| v_c____ != c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Rings_Oidom(t_a) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,hypothesis,
class_Rings_Oidom(t_a),
inference(split_conjunct,[status(thm)],[tfree_0]) ).
cnf(c_0_16,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
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(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_18,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)
| 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(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,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_14,c_0_15])]),c_0_16]) ).
fof(c_0_20,negated_conjecture,
! [X90,X91,X92] :
( ( 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____)),esk1_3(X90,X91,X92)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk1_3(X90,X91,X92)),X90)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X91,X92)),esk1_3(X90,X91,X92)))
| X91 = 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(X92,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,X92))),X90)) != 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____)),esk1_3(X90,X91,X92)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk1_3(X90,X91,X92)),X90)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X91,X92)),esk1_3(X90,X91,X92)))
| X91 = 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(X92,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,X92))),X90)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk1_3(X90,X91,X92)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk1_3(X90,X91,X92)),X90)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X91,X92)),esk1_3(X90,X91,X92)))
| X91 = 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(X92,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,X92))),X90)) != 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(X92,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,X92))),X90)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk1_3(X90,X91,X92)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk1_3(X90,X91,X92)),X90)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X91,X92)),esk1_3(X90,X91,X92)))
| X91 = c_Groups_Ozero__class_Ozero(t_a) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])])]) ).
fof(c_0_21,plain,
! [X337,X338] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X338,c_Nat_OSuc(X337)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X338,X337)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_22,plain,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,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_18,c_0_15])]),c_0_16]),c_0_19]) ).
fof(c_0_24,plain,
! [X477,X478] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X478,X477) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X477,X478),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
cnf(c_0_25,negated_conjecture,
( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| X3 = 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(X1,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,X1))),X2)) != c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
| hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk1_3(X2,X3,X1)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk1_3(X2,X3,X1)),X2)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X3,X1)),esk1_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,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))
| v_c____ = c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Rings_Oidom(t_a) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_28,plain,
! [X341,X342] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X342),X341) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X342,c_Nat_OSuc(X341)),
inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).
cnf(c_0_29,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_Groups_Ozero__class_Ozero(t_a) = v_c____ ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_15])]),c_0_23]) ).
cnf(c_0_30,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_24]) ).
cnf(c_0_31,plain,
( v_c____ = c_Groups_Ozero__class_Ozero(t_a)
| esk8_0 != c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Rings_Oidom(t_a) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_32,plain,
( 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(esk12_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,esk12_0))),esk10_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) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_33,negated_conjecture,
( X1 = c_Groups_Ozero__class_Ozero(t_a)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk1_3(X2,X1,X3)),X2)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X3)),esk1_3(X2,X1,X3))) != hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk1_3(X2,X1,X3))
| 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))),c_Nat_OSuc(X2)) != c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_23]) ).
cnf(c_0_34,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_27,c_0_15])]) ).
cnf(c_0_35,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk7_0,c_Nat_OSuc(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))))) = c_Nat_OSuc(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)],[c_0_29,c_0_30]),c_0_26]) ).
cnf(c_0_37,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_31,c_0_15])]) ).
cnf(c_0_38,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),esk10_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk11_0,esk12_0)),X1))
| v_c____ != c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Rings_Oidom(t_a) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_39,plain,
( esk11_0 != c_Groups_Ozero__class_Ozero(t_a)
| v_c____ != c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Rings_Oidom(t_a) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_40,plain,
( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk12_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,esk12_0))),esk10_0)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
| c_Groups_Ozero__class_Ozero(t_a) != v_c____ ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_15])]),c_0_23]) ).
cnf(c_0_41,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_33,c_0_34]),c_0_30]),c_0_35]),c_0_36]),c_0_37]) ).
cnf(c_0_42,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X1),esk10_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk11_0,esk12_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_38,c_0_15])]) ).
cnf(c_0_43,plain,
( c_Groups_Ozero__class_Ozero(t_a) != v_c____
| c_Groups_Ozero__class_Ozero(t_a) != esk11_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_15])]) ).
cnf(c_0_44,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk10_0,c_Nat_OSuc(c_If(tc_Nat_Onat,c_fequal(esk12_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,esk12_0))))) = c_Nat_OSuc(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)],[c_0_40,c_0_30]),c_0_26]) ).
cnf(c_0_45,negated_conjecture,
( X1 = v_c____
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk1_3(X2,X1,X3)),X2)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X3)),esk1_3(X2,X1,X3))) != hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk1_3(X2,X1,X3))
| 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))),c_Nat_OSuc(X2)) != c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) ),
inference(rw,[status(thm)],[c_0_33,c_0_41]) ).
cnf(c_0_46,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X1),esk10_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk11_0,esk12_0)),X1)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_41])]) ).
cnf(c_0_47,plain,
esk11_0 != v_c____,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_41]),c_0_41])]) ).
cnf(c_0_48,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk10_0,c_Nat_OSuc(c_If(tc_Nat_Onat,c_fequal(esk12_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,esk12_0))))) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_41])]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_30]),c_0_35]),c_0_48])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW245+1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat May 18 20:59:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.36/1.75 # Version: 3.1.0
% 9.36/1.75 # Preprocessing class: FMLMSMSMSSSNFFN.
% 9.36/1.75 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.36/1.75 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 9.36/1.75 # Starting new_bool_3 with 300s (1) cores
% 9.36/1.75 # Starting new_bool_1 with 300s (1) cores
% 9.36/1.75 # Starting sh5l with 300s (1) cores
% 9.36/1.75 # new_bool_1 with pid 32103 completed with status 0
% 9.36/1.75 # Result found by new_bool_1
% 9.36/1.75 # Preprocessing class: FMLMSMSMSSSNFFN.
% 9.36/1.75 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.36/1.75 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 9.36/1.75 # Starting new_bool_3 with 300s (1) cores
% 9.36/1.75 # Starting new_bool_1 with 300s (1) cores
% 9.36/1.75 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 9.36/1.75 # Search class: FGHSM-FSLM32-DFFFFFNN
% 9.36/1.75 # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 9.36/1.75 # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 23s (1) cores
% 9.36/1.75 # G-E--_301_C18_F1_URBAN_S5PRR_S0Y with pid 32106 completed with status 0
% 9.36/1.75 # Result found by G-E--_301_C18_F1_URBAN_S5PRR_S0Y
% 9.36/1.75 # Preprocessing class: FMLMSMSMSSSNFFN.
% 9.36/1.75 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.36/1.75 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 9.36/1.75 # Starting new_bool_3 with 300s (1) cores
% 9.36/1.75 # Starting new_bool_1 with 300s (1) cores
% 9.36/1.75 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 9.36/1.75 # Search class: FGHSM-FSLM32-DFFFFFNN
% 9.36/1.75 # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 9.36/1.75 # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 23s (1) cores
% 9.36/1.75 # Preprocessing time : 0.083 s
% 9.36/1.75
% 9.36/1.75 # Proof found!
% 9.36/1.75 # SZS status Theorem
% 9.36/1.75 # SZS output start CNFRefutation
% See solution above
% 9.36/1.75 # Parsed axioms : 1161
% 9.36/1.75 # Removed by relevancy pruning/SinE : 553
% 9.36/1.75 # Initial clauses : 864
% 9.36/1.75 # Removed in clause preprocessing : 55
% 9.36/1.75 # Initial clauses in saturation : 809
% 9.36/1.75 # Processed clauses : 3235
% 9.36/1.75 # ...of these trivial : 161
% 9.36/1.75 # ...subsumed : 1675
% 9.36/1.75 # ...remaining for further processing : 1398
% 9.36/1.75 # Other redundant clauses eliminated : 173
% 9.36/1.75 # Clauses deleted for lack of memory : 0
% 9.36/1.75 # Backward-subsumed : 53
% 9.36/1.75 # Backward-rewritten : 149
% 9.36/1.75 # Generated clauses : 45826
% 9.36/1.75 # ...of the previous two non-redundant : 41621
% 9.36/1.75 # ...aggressively subsumed : 0
% 9.36/1.75 # Contextual simplify-reflections : 25
% 9.36/1.75 # Paramodulations : 45582
% 9.36/1.75 # Factorizations : 9
% 9.36/1.75 # NegExts : 0
% 9.36/1.75 # Equation resolutions : 235
% 9.36/1.75 # Disequality decompositions : 0
% 9.36/1.75 # Total rewrite steps : 28073
% 9.36/1.75 # ...of those cached : 25346
% 9.36/1.75 # Propositional unsat checks : 0
% 9.36/1.75 # Propositional check models : 0
% 9.36/1.75 # Propositional check unsatisfiable : 0
% 9.36/1.75 # Propositional clauses : 0
% 9.36/1.75 # Propositional clauses after purity: 0
% 9.36/1.75 # Propositional unsat core size : 0
% 9.36/1.75 # Propositional preprocessing time : 0.000
% 9.36/1.75 # Propositional encoding time : 0.000
% 9.36/1.75 # Propositional solver time : 0.000
% 9.36/1.75 # Success case prop preproc time : 0.000
% 9.36/1.75 # Success case prop encoding time : 0.000
% 9.36/1.75 # Success case prop solver time : 0.000
% 9.36/1.75 # Current number of processed clauses : 1181
% 9.36/1.75 # Positive orientable unit clauses : 151
% 9.36/1.75 # Positive unorientable unit clauses: 12
% 9.36/1.75 # Negative unit clauses : 55
% 9.36/1.75 # Non-unit-clauses : 963
% 9.36/1.75 # Current number of unprocessed clauses: 39082
% 9.36/1.75 # ...number of literals in the above : 115529
% 9.36/1.75 # Current number of archived formulas : 0
% 9.36/1.75 # Current number of archived clauses : 202
% 9.36/1.75 # Clause-clause subsumption calls (NU) : 79522
% 9.36/1.75 # Rec. Clause-clause subsumption calls : 43695
% 9.36/1.75 # Non-unit clause-clause subsumptions : 958
% 9.36/1.75 # Unit Clause-clause subsumption calls : 4733
% 9.36/1.75 # Rewrite failures with RHS unbound : 0
% 9.36/1.75 # BW rewrite match attempts : 1524
% 9.36/1.75 # BW rewrite match successes : 95
% 9.36/1.75 # Condensation attempts : 0
% 9.36/1.75 # Condensation successes : 0
% 9.36/1.75 # Termbank termtop insertions : 892957
% 9.36/1.75 # Search garbage collected termcells : 14310
% 9.36/1.75
% 9.36/1.75 # -------------------------------------------------
% 9.36/1.75 # User time : 1.046 s
% 9.36/1.75 # System time : 0.061 s
% 9.36/1.75 # Total time : 1.108 s
% 9.36/1.75 # Maximum resident set size: 5616 pages
% 9.36/1.75
% 9.36/1.75 # -------------------------------------------------
% 9.36/1.75 # User time : 1.087 s
% 9.36/1.75 # System time : 0.064 s
% 9.36/1.75 # Total time : 1.150 s
% 9.36/1.75 # Maximum resident set size: 3096 pages
% 9.36/1.75 % E---3.1 exiting
% 9.36/1.75 % E exiting
%------------------------------------------------------------------------------