%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW186+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.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 5 05:29:28 PM UTC 2026
% Result : Theorem 7.48s 5.07s
% Output : CNFRefutation 7.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 75 ( 19 unt; 0 def)
% Number of atoms : 134 ( 75 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 104 ( 45 ~; 41 |; 2 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 109 ( 13 sgn 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_offset__poly__eq__0__lemma,axiom,
! [X6,X7,X8,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),c_Polynomial_Osmult(X5,X8,X7),c_Polynomial_OpCons(X5,X6,X7)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
=> X7 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__eq__0__lemma) ).
fof(conj_0,hypothesis,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(conj_1,hypothesis,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(tfree_0,hypothesis,
class_Rings_Ocomm__semiring__0(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
fof(fact_add__0,axiom,
! [X6,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Ozero__class_Ozero(X5),X6) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).
fof(clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add,axiom,
! [X87] :
( class_Rings_Ocomm__semiring__0(X87)
=> class_Groups_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add) ).
fof(fact_coeff__0,axiom,
! [X48,X5] :
( class_Groups_Ozero(X5)
=> hAPP(c_Polynomial_Ocoeff(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X48) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_coeff__0) ).
fof(fact_smult__0__right,axiom,
! [X6,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Polynomial_Osmult(X5,X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__right) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
! [X88] :
( class_Rings_Ocomm__semiring__0(X88)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
fof(fact_poly__0,axiom,
! [X27,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> hAPP(c_Polynomial_Opoly(X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))),X27) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__0) ).
fof(clrel_Rings_Ocomm__semiring__0__Groups_Ozero,axiom,
! [X87] :
( class_Rings_Ocomm__semiring__0(X87)
=> class_Groups_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Ocomm__semiring__0__Groups_Ozero) ).
fof(fact_mult__zero__left,axiom,
! [X6,X5] :
( class_Rings_Omult__zero(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X6) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).
fof(clrel_Rings_Ocomm__semiring__0__Rings_Omult__zero,axiom,
! [X87] :
( class_Rings_Ocomm__semiring__0(X87)
=> class_Rings_Omult__zero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Ocomm__semiring__0__Rings_Omult__zero) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
fof(fact_add_Ocomm__neutral,axiom,
! [X6,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> c_Groups_Oplus__class_Oplus(X5,X6,c_Groups_Ozero__class_Ozero(X5)) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(conj_2,conjecture,
( v_a = c_Groups_Ozero__class_Ozero(t_a)
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
fof(fact_poly__smult,axiom,
! [X27,X7,X6,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> hAPP(c_Polynomial_Opoly(X5,c_Polynomial_Osmult(X5,X6,X7)),X27) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X6),hAPP(c_Polynomial_Opoly(X5,X7),X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__smult) ).
fof(fact_poly__pCons,axiom,
! [X27,X7,X6,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> hAPP(c_Polynomial_Opoly(X5,c_Polynomial_OpCons(X5,X6,X7)),X27) = c_Groups_Oplus__class_Oplus(X5,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X27),hAPP(c_Polynomial_Opoly(X5,X7),X27))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pCons) ).
fof(c_0_18,plain,
! [X3075,X3076,X3077,X3078] :
( ~ class_Rings_Ocomm__semiring__0(X3078)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3078),c_Polynomial_Osmult(X3078,X3077,X3076),c_Polynomial_OpCons(X3078,X3075,X3076)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3078))
| X3076 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3078)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__eq__0__lemma])]) ).
fof(c_0_19,hypothesis,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(fof_nnf,[status(thm)],[conj_0]) ).
cnf(c_0_20,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),c_Polynomial_OpCons(X1,X4,X3)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,hypothesis,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(split_conjunct,[status(thm)],[conj_1]) ).
cnf(c_0_22,hypothesis,
class_Rings_Ocomm__semiring__0(t_a),
inference(split_conjunct,[status(thm)],[tfree_0]) ).
fof(c_0_23,plain,
! [X3150,X3151] :
( ~ class_Groups_Ocomm__monoid__add(X3151)
| c_Groups_Oplus__class_Oplus(X3151,c_Groups_Ozero__class_Ozero(X3151),X3150) = X3150 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).
fof(c_0_24,plain,
! [X5976] :
( ~ class_Rings_Ocomm__semiring__0(X5976)
| class_Groups_Ocomm__monoid__add(X5976) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add])]) ).
fof(c_0_25,plain,
! [X4723,X4724] :
( ~ class_Groups_Ozero(X4724)
| hAPP(c_Polynomial_Ocoeff(X4724,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4724))),X4723) = c_Groups_Ozero__class_Ozero(X4724) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_coeff__0])]) ).
cnf(c_0_26,hypothesis,
( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,hypothesis,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
fof(c_0_28,plain,
! [X3109,X3110] :
( ~ class_Rings_Ocomm__semiring__0(X3110)
| c_Polynomial_Osmult(X3110,X3109,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3110))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3110)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__0__right])]) ).
cnf(c_0_29,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( class_Groups_Ocomm__monoid__add(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_31,plain,
! [X6026] :
( ~ class_Rings_Ocomm__semiring__0(X6026)
| class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X6026)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__0])]) ).
fof(c_0_32,plain,
! [X3812,X3813] :
( ~ class_Rings_Ocomm__semiring__0(X3813)
| hAPP(c_Polynomial_Opoly(X3813,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3813))),X3812) = c_Groups_Ozero__class_Ozero(X3813) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__0])]) ).
cnf(c_0_33,plain,
( hAPP(c_Polynomial_Ocoeff(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,hypothesis,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = v_p,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).
fof(c_0_35,plain,
! [X5982] :
( ~ class_Rings_Ocomm__semiring__0(X5982)
| class_Groups_Ozero(X5982) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Ocomm__semiring__0__Groups_Ozero])]) ).
fof(c_0_36,plain,
! [X3335,X3336] :
( ~ class_Rings_Omult__zero(X3336)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3336),c_Groups_Ozero__class_Ozero(X3336)),X3335) = c_Groups_Ozero__class_Ozero(X3336) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__left])]) ).
fof(c_0_37,plain,
! [X5980] :
( ~ class_Rings_Ocomm__semiring__0(X5980)
| class_Rings_Omult__zero(X5980) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Ocomm__semiring__0__Rings_Omult__zero])]) ).
cnf(c_0_38,plain,
( c_Polynomial_Osmult(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_39,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_40,plain,
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_41,plain,
! [X3063,X3064] :
( hAPP(X3064,esk1_2(X3063,X3064)) != hAPP(X3063,esk1_2(X3063,X3064))
| X3064 = X3063 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
cnf(c_0_42,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_32]) ).
cnf(c_0_43,hypothesis,
( hAPP(c_Polynomial_Ocoeff(t_a,v_p),X1) = c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Groups_Ozero(t_a) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_44,plain,
( class_Groups_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Omult__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,plain,
( class_Rings_Omult__zero(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_47,plain,
! [X3144,X3145] :
( ~ class_Groups_Ocomm__monoid__add(X3145)
| c_Groups_Oplus__class_Oplus(X3145,X3144,c_Groups_Ozero__class_Ozero(X3145)) = X3144 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).
fof(c_0_48,negated_conjecture,
~ ( v_a = c_Groups_Ozero__class_Ozero(t_a)
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(assume_negation,[status(cth)],[conj_2]) ).
cnf(c_0_49,hypothesis,
c_Polynomial_Osmult(t_a,X1,v_p) = v_p,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_34]),c_0_22])]) ).
cnf(c_0_50,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = X2
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_51,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_52,hypothesis,
hAPP(c_Polynomial_Opoly(t_a,v_p),X1) = c_Groups_Ozero__class_Ozero(t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_34]),c_0_22])]) ).
cnf(c_0_53,hypothesis,
hAPP(c_Polynomial_Ocoeff(t_a,v_p),X1) = c_Groups_Ozero__class_Ozero(t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_22])]) ).
cnf(c_0_54,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
fof(c_0_55,plain,
! [X3814,X3815,X3816,X3817] :
( ~ class_Rings_Ocomm__semiring__0(X3817)
| hAPP(c_Polynomial_Opoly(X3817,c_Polynomial_Osmult(X3817,X3816,X3815)),X3814) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3817),X3816),hAPP(c_Polynomial_Opoly(X3817,X3815),X3814)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__smult])]) ).
cnf(c_0_56,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_57,negated_conjecture,
( v_a != c_Groups_Ozero__class_Ozero(t_a)
| v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(fof_nnf,[status(thm)],[c_0_48]) ).
fof(c_0_58,plain,
! [X3358,X3359,X3360,X3361] :
( ~ class_Rings_Ocomm__semiring__0(X3361)
| hAPP(c_Polynomial_Opoly(X3361,c_Polynomial_OpCons(X3361,X3360,X3359)),X3358) = c_Groups_Oplus__class_Oplus(X3361,X3360,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3361),X3358),hAPP(c_Polynomial_Opoly(X3361,X3359),X3358))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__pCons])]) ).
cnf(c_0_59,hypothesis,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),v_p,c_Polynomial_OpCons(t_a,v_a,v_p)) = v_p,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_27]),c_0_27]),c_0_34]),c_0_49]),c_0_34]),c_0_34]) ).
cnf(c_0_60,hypothesis,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),v_p,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_34]),c_0_22])]) ).
cnf(c_0_61,hypothesis,
( c_Polynomial_Opoly(t_a,v_p) = X1
| hAPP(X1,esk1_2(X1,c_Polynomial_Opoly(t_a,v_p))) != c_Groups_Ozero__class_Ozero(t_a) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_62,hypothesis,
( X1 = c_Polynomial_Ocoeff(t_a,v_p)
| hAPP(X1,esk1_2(c_Polynomial_Ocoeff(t_a,v_p),X1)) != c_Groups_Ozero__class_Ozero(t_a) ),
inference(spm,[status(thm)],[c_0_51,c_0_53]) ).
cnf(c_0_63,hypothesis,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Ozero__class_Ozero(t_a)),X1) = c_Groups_Ozero__class_Ozero(t_a),
inference(spm,[status(thm)],[c_0_54,c_0_22]) ).
cnf(c_0_64,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_55]) ).
cnf(c_0_65,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_30]) ).
cnf(c_0_66,negated_conjecture,
( v_a != c_Groups_Ozero__class_Ozero(t_a)
| v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_67,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_58]) ).
cnf(c_0_68,hypothesis,
c_Polynomial_OpCons(t_a,v_a,v_p) = v_p,
inference(rw,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_69,hypothesis,
c_Polynomial_Opoly(t_a,v_p) = c_Polynomial_Ocoeff(t_a,v_p),
inference(spm,[status(thm)],[c_0_61,c_0_53]) ).
cnf(c_0_70,hypothesis,
c_Polynomial_Ocoeff(t_a,v_p) = hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Ozero__class_Ozero(t_a)),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_71,hypothesis,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),X1),c_Groups_Ozero__class_Ozero(t_a)) = c_Groups_Ozero__class_Ozero(t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_49]),c_0_52]),c_0_52]),c_0_22])]) ).
cnf(c_0_72,hypothesis,
c_Groups_Oplus__class_Oplus(t_a,X1,c_Groups_Ozero__class_Ozero(t_a)) = X1,
inference(spm,[status(thm)],[c_0_65,c_0_22]) ).
cnf(c_0_73,negated_conjecture,
c_Groups_Ozero__class_Ozero(t_a) != v_a,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_34])]) ).
cnf(c_0_74,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_70]),c_0_63]),c_0_69]),c_0_70]),c_0_63]),c_0_71]),c_0_72]),c_0_22])]),c_0_73]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW186+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n027.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 06:23:35 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 7.48/5.07 % Version : CSE_E---1.7
% 7.48/5.07 % Problem : theBenchmark.p
% 7.48/5.07 % SZS status Theorem for theBenchmark.p
% 7.48/5.07 % SZS output start CNFRefutation
% See solution above
% 7.48/5.10 % Total time : 3.543s
%------------------------------------------------------------------------------