TSTP Solution File: SWW290+1 by E-SAT---3.1.00
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%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : SWW290+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n002.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 06:45:13 EDT 2024
% Result : Theorem 5.45s 1.26s
% Output : CNFRefutation 5.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of formulae : 71 ( 33 unt; 0 def)
% Number of atoms : 141 ( 92 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 121 ( 51 ~; 48 |; 8 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 125 ( 14 sgn 73 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [X4,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ozero__class_Ozero(X7)),X4) = c_Groups_Ozero__class_Ozero(X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
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(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(fact_poly__pad__rule,axiom,
! [X18,X5] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X5),X18) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X5)),X18) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pad__rule) ).
fof(fact_mpoly__base__conv_I2_J,axiom,
! [X18,X6] : X6 = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mpoly__base__conv_I2_J) ).
fof(fact_mpoly__base__conv_I1_J,axiom,
! [X18] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mpoly__base__conv_I1_J) ).
fof(fact_poly__eq__iff,axiom,
! [X12,X9,X7] :
( ( class_Int_Oring__char__0(X7)
& class_Rings_Oidom(X7) )
=> ( c_Polynomial_Opoly(X7,X9) = c_Polynomial_Opoly(X7,X12)
<=> X9 = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__iff) ).
fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(fact_pCons__eq__0__iff,axiom,
! [X9,X10,X7] :
( class_Groups_Ozero(X7)
=> ( c_Polynomial_OpCons(X7,X10,X9) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))
<=> ( X10 = c_Groups_Ozero__class_Ozero(X7)
& X9 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).
fof(fact_pCons__eq__iff,axiom,
! [X12,X13,X9,X10,X7] :
( class_Groups_Ozero(X7)
=> ( c_Polynomial_OpCons(X7,X10,X9) = c_Polynomial_OpCons(X7,X13,X12)
<=> ( X10 = X13
& X9 = X12 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__iff) ).
fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(fact_smult__pCons,axiom,
! [X5,X8,X4,X7] :
( class_Rings_Ocomm__semiring__0(X7)
=> c_Polynomial_Osmult(X7,X4,c_Polynomial_OpCons(X7,X8,X5)) = c_Polynomial_OpCons(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X4),X8),c_Polynomial_Osmult(X7,X4,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__pCons) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(fact_smult__0__left,axiom,
! [X5,X7] :
( class_Rings_Ocomm__semiring__0(X7)
=> c_Polynomial_Osmult(X7,c_Groups_Ozero__class_Ozero(X7),X5) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__left) ).
fof(fact_mult__smult__right,axiom,
! [X11,X4,X5,X7] :
( class_Rings_Ocomm__semiring__0(X7)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X5),c_Polynomial_Osmult(X7,X4,X11)) = c_Polynomial_Osmult(X7,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X5),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__smult__right) ).
fof(fact_add__poly__code_I2_J,axiom,
! [X5,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X7),X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X7))) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).
fof(conj_0,conjecture,
c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_mult__pCons__right,axiom,
! [X11,X4,X5,X7] :
( class_Rings_Ocomm__semiring__0(X7)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X5),c_Polynomial_OpCons(X7,X4,X11)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X7),c_Polynomial_Osmult(X7,X4,X5),c_Polynomial_OpCons(X7,c_Groups_Ozero__class_Ozero(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X5),X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pCons__right) ).
fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
fof(c_0_20,plain,
! [X119,X120] :
( ~ class_Rings_Ocomm__semiring__1(X120)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X120),c_Groups_Ozero__class_Ozero(X120)),X119) = c_Groups_Ozero__class_Ozero(X120) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])])]) ).
fof(c_0_21,plain,
! [X89,X90] :
( hAPP(X90,esk1_2(X89,X90)) != hAPP(X89,esk1_2(X89,X90))
| X90 = X89 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])])]) ).
cnf(c_0_22,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__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
fof(c_0_24,plain,
! [X542,X543] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X543),X542) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X543)),X542) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__pad__rule])])]) ).
fof(c_0_25,plain,
! [X544,X545] : X545 = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X545,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),X544),
inference(variable_rename,[status(thm)],[fact_mpoly__base__conv_I2_J]) ).
cnf(c_0_26,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_28,plain,
! [X748] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X748),
inference(variable_rename,[status(thm)],[fact_mpoly__base__conv_I1_J]) ).
cnf(c_0_29,plain,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1)),X2) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),X2) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
X1 = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),X2),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_31,plain,
! [X1712,X1713,X1714] :
( ( c_Polynomial_Opoly(X1714,X1713) != c_Polynomial_Opoly(X1714,X1712)
| X1713 = X1712
| ~ class_Int_Oring__char__0(X1714)
| ~ class_Rings_Oidom(X1714) )
& ( X1713 != X1712
| c_Polynomial_Opoly(X1714,X1713) = c_Polynomial_Opoly(X1714,X1712)
| ~ class_Int_Oring__char__0(X1714)
| ~ class_Rings_Oidom(X1714) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__eq__iff])])])]) ).
cnf(c_0_32,plain,
( hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X1
| hAPP(X1,esk1_2(X1,hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_OpCons(tc_Complex_Ocomplex,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),X2) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X1 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( X2 = X3
| c_Polynomial_Opoly(X1,X2) != c_Polynomial_Opoly(X1,X3)
| ~ class_Int_Oring__char__0(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,plain,
c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Int_Oring__char__0]) ).
cnf(c_0_38,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oidom]) ).
cnf(c_0_39,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),X1) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(er,[status(thm)],[c_0_34]) ).
fof(c_0_40,plain,
! [X510,X511,X512] :
( ( X511 = c_Groups_Ozero__class_Ozero(X512)
| c_Polynomial_OpCons(X512,X511,X510) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X512))
| ~ class_Groups_Ozero(X512) )
& ( X510 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X512))
| c_Polynomial_OpCons(X512,X511,X510) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X512))
| ~ class_Groups_Ozero(X512) )
& ( X511 != c_Groups_Ozero__class_Ozero(X512)
| X510 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X512))
| c_Polynomial_OpCons(X512,X511,X510) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X512))
| ~ class_Groups_Ozero(X512) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__eq__0__iff])])])]) ).
cnf(c_0_41,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Opoly(tc_Complex_Ocomplex,X1) != hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38])]) ).
cnf(c_0_42,plain,
c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(spm,[status(thm)],[c_0_32,c_0_39]) ).
fof(c_0_43,plain,
! [X515,X516,X517,X518,X519] :
( ( X518 = X516
| c_Polynomial_OpCons(X519,X518,X517) != c_Polynomial_OpCons(X519,X516,X515)
| ~ class_Groups_Ozero(X519) )
& ( X517 = X515
| c_Polynomial_OpCons(X519,X518,X517) != c_Polynomial_OpCons(X519,X516,X515)
| ~ class_Groups_Ozero(X519) )
& ( X518 != X516
| X517 != X515
| c_Polynomial_OpCons(X519,X518,X517) = c_Polynomial_OpCons(X519,X516,X515)
| ~ class_Groups_Ozero(X519) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__eq__iff])])])]) ).
cnf(c_0_44,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_OpCons(X2,X3,X1) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_45,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]) ).
cnf(c_0_47,plain,
( X1 = X2
| c_Polynomial_OpCons(X3,X4,X1) != c_Polynomial_OpCons(X3,X5,X2)
| ~ class_Groups_Ozero(X3) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_48,plain,
c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]) ).
fof(c_0_49,plain,
! [X505,X506,X507,X508] :
( ~ class_Rings_Ocomm__semiring__0(X508)
| c_Polynomial_Osmult(X508,X507,c_Polynomial_OpCons(X508,X506,X505)) = c_Polynomial_OpCons(X508,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X508),X507),X506),c_Polynomial_Osmult(X508,X507,X505)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__pCons])])]) ).
cnf(c_0_50,plain,
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1
| c_Polynomial_OpCons(tc_Complex_Ocomplex,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_46])]) ).
cnf(c_0_51,plain,
( c_Polynomial_Osmult(X1,X2,c_Polynomial_OpCons(X1,X3,X4)) = c_Polynomial_OpCons(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Polynomial_Osmult(X1,X2,X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_52,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).
fof(c_0_53,plain,
! [X702,X703] :
( ~ class_Rings_Ocomm__semiring__0(X703)
| c_Polynomial_Osmult(X703,c_Groups_Ozero__class_Ozero(X703),X702) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X703)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__0__left])])]) ).
fof(c_0_54,plain,
! [X704,X705,X706,X707] :
( ~ class_Rings_Ocomm__semiring__0(X707)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X707)),X706),c_Polynomial_Osmult(X707,X705,X704)) = c_Polynomial_Osmult(X707,X705,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X707)),X706),X704)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__smult__right])])]) ).
cnf(c_0_55,plain,
( c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Polynomial_Osmult(tc_Complex_Ocomplex,X1,c_Polynomial_OpCons(tc_Complex_Ocomplex,X3,X2)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]) ).
cnf(c_0_56,plain,
( c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_57,plain,
! [X1679,X1680] :
( ~ class_Groups_Ocomm__monoid__add(X1680)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1680),X1679,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1680))) = X1679 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__poly__code_I2_J])])]) ).
fof(c_0_58,negated_conjecture,
c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(c_0_59,plain,
! [X520,X521,X522,X523] :
( ~ class_Rings_Ocomm__semiring__0(X523)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X523)),X522),c_Polynomial_OpCons(X523,X521,X520)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X523),c_Polynomial_Osmult(X523,X521,X522),c_Polynomial_OpCons(X523,c_Groups_Ozero__class_Ozero(X523),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X523)),X522),X520))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pCons__right])])]) ).
cnf(c_0_60,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),c_Polynomial_Osmult(X1,X3,X4)) = c_Polynomial_Osmult(X1,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_61,plain,
c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_52])]) ).
cnf(c_0_62,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_63,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__add]) ).
fof(c_0_64,negated_conjecture,
c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
inference(fof_nnf,[status(thm)],[c_0_58]) ).
cnf(c_0_65,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),c_Polynomial_OpCons(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X3,X2),c_Polynomial_OpCons(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X4)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_66,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_61]),c_0_52])]) ).
cnf(c_0_67,plain,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex),X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = X1,
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_68,negated_conjecture,
c_Polynomial_Osmult(tc_Complex_Ocomplex,v_a,v_q) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_q),c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_69,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1),c_Polynomial_OpCons(tc_Complex_Ocomplex,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Polynomial_Osmult(tc_Complex_Ocomplex,X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_48]),c_0_67]),c_0_52])]) ).
cnf(c_0_70,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SWW290+1 : TPTP v8.2.0. Released v5.2.0.
% 0.05/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n002.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sat May 18 20:52:37 EDT 2024
% 0.16/0.31 % CPUTime :
% 0.16/0.42 Running first-order model finding
% 0.16/0.42 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.45/1.26 # Version: 3.1.0
% 5.45/1.26 # Preprocessing class: FMLMSMSSSSSNFFN.
% 5.45/1.26 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.45/1.26 # Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 5.45/1.26 # Starting new_bool_3 with 300s (1) cores
% 5.45/1.26 # Starting new_bool_1 with 300s (1) cores
% 5.45/1.26 # Starting sh5l with 300s (1) cores
% 5.45/1.26 # G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with pid 16537 completed with status 0
% 5.45/1.26 # Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c
% 5.45/1.26 # Preprocessing class: FMLMSMSSSSSNFFN.
% 5.45/1.26 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.45/1.26 # Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 5.45/1.26 # SinE strategy is gf600_h_gu_R05_F100_L20000
% 5.45/1.26 # Search class: FGHSM-SSLM32-DFFFFFNN
% 5.45/1.26 # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 5.45/1.26 # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 113s (1) cores
% 5.45/1.26 # Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 5.45/1.26 # Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 5.45/1.26 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 5.45/1.26 # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 113s (1) cores
% 5.45/1.26 # G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with pid 16546 completed with status 0
% 5.45/1.26 # Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c
% 5.45/1.26 # Preprocessing class: FMLMSMSSSSSNFFN.
% 5.45/1.26 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.45/1.26 # Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 5.45/1.26 # SinE strategy is gf600_h_gu_R05_F100_L20000
% 5.45/1.26 # Search class: FGHSM-SSLM32-DFFFFFNN
% 5.45/1.26 # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 5.45/1.26 # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 113s (1) cores
% 5.45/1.26 # Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 5.45/1.26 # Preprocessing time : 0.017 s
% 5.45/1.26
% 5.45/1.26 # Proof found!
% 5.45/1.26 # SZS status Theorem
% 5.45/1.26 # SZS output start CNFRefutation
% See solution above
% 5.45/1.26 # Parsed axioms : 1205
% 5.45/1.26 # Removed by relevancy pruning/SinE : 114
% 5.45/1.26 # Initial clauses : 1477
% 5.45/1.26 # Removed in clause preprocessing : 70
% 5.45/1.26 # Initial clauses in saturation : 1407
% 5.45/1.26 # Processed clauses : 2305
% 5.45/1.26 # ...of these trivial : 150
% 5.45/1.26 # ...subsumed : 685
% 5.45/1.26 # ...remaining for further processing : 1470
% 5.45/1.26 # Other redundant clauses eliminated : 174
% 5.45/1.26 # Clauses deleted for lack of memory : 0
% 5.45/1.26 # Backward-subsumed : 12
% 5.45/1.26 # Backward-rewritten : 45
% 5.45/1.26 # Generated clauses : 37060
% 5.45/1.26 # ...of the previous two non-redundant : 32846
% 5.45/1.26 # ...aggressively subsumed : 0
% 5.45/1.26 # Contextual simplify-reflections : 3
% 5.45/1.26 # Paramodulations : 36720
% 5.45/1.26 # Factorizations : 14
% 5.45/1.26 # NegExts : 0
% 5.45/1.26 # Equation resolutions : 326
% 5.45/1.26 # Disequality decompositions : 0
% 5.45/1.26 # Total rewrite steps : 23541
% 5.45/1.26 # ...of those cached : 21308
% 5.45/1.26 # Propositional unsat checks : 0
% 5.45/1.26 # Propositional check models : 0
% 5.45/1.26 # Propositional check unsatisfiable : 0
% 5.45/1.26 # Propositional clauses : 0
% 5.45/1.26 # Propositional clauses after purity: 0
% 5.45/1.26 # Propositional unsat core size : 0
% 5.45/1.26 # Propositional preprocessing time : 0.000
% 5.45/1.26 # Propositional encoding time : 0.000
% 5.45/1.26 # Propositional solver time : 0.000
% 5.45/1.26 # Success case prop preproc time : 0.000
% 5.45/1.26 # Success case prop encoding time : 0.000
% 5.45/1.26 # Success case prop solver time : 0.000
% 5.45/1.26 # Current number of processed clauses : 1371
% 5.45/1.26 # Positive orientable unit clauses : 251
% 5.45/1.26 # Positive unorientable unit clauses: 9
% 5.45/1.26 # Negative unit clauses : 19
% 5.45/1.26 # Non-unit-clauses : 1092
% 5.45/1.26 # Current number of unprocessed clauses: 31915
% 5.45/1.26 # ...number of literals in the above : 97776
% 5.45/1.26 # Current number of archived formulas : 0
% 5.45/1.26 # Current number of archived clauses : 58
% 5.45/1.26 # Clause-clause subsumption calls (NU) : 98957
% 5.45/1.26 # Rec. Clause-clause subsumption calls : 63977
% 5.45/1.26 # Non-unit clause-clause subsumptions : 538
% 5.45/1.26 # Unit Clause-clause subsumption calls : 3071
% 5.45/1.26 # Rewrite failures with RHS unbound : 0
% 5.45/1.26 # BW rewrite match attempts : 719
% 5.45/1.26 # BW rewrite match successes : 99
% 5.45/1.26 # Condensation attempts : 0
% 5.45/1.26 # Condensation successes : 0
% 5.45/1.26 # Termbank termtop insertions : 906286
% 5.45/1.26 # Search garbage collected termcells : 20513
% 5.45/1.26
% 5.45/1.26 # -------------------------------------------------
% 5.45/1.26 # User time : 0.732 s
% 5.45/1.26 # System time : 0.032 s
% 5.45/1.26 # Total time : 0.764 s
% 5.45/1.26 # Maximum resident set size: 8436 pages
% 5.45/1.26
% 5.45/1.26 # -------------------------------------------------
% 5.45/1.26 # User time : 3.074 s
% 5.45/1.26 # System time : 0.120 s
% 5.45/1.26 # Total time : 3.194 s
% 5.45/1.26 # Maximum resident set size: 3108 pages
% 5.45/1.26 % E---3.1 exiting
%------------------------------------------------------------------------------