TSTP Solution File: SWW198+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SWW198+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n018.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 00:10:16 EDT 2022
% Result : Theorem 0.33s 1.52s
% Output : CNFRefutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 18
% Syntax : Number of formulae : 66 ( 60 unt; 0 def)
% Number of atoms : 74 ( 63 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 21 ( 13 ~; 6 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 77 ( 4 sgn 43 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
? [X23] : v_na____ = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',conj_0) ).
fof(fact_Bit0__def,axiom,
! [X8] : c_Int_OBit0(X8) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,X8),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Bit0__def) ).
fof(fact_Bit1__def,axiom,
! [X8] : c_Int_OBit1(X8) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X8),X8),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Bit1__def) ).
fof(fact_Suc__eq__plus1,axiom,
! [X13] : c_Nat_OSuc(X13) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(fact_nat__1__add__1,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_nat__1__add__1) ).
fof(fact_add__Pls__right,axiom,
! [X8] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,c_Int_OPls) = X8,
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_add__Pls__right) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Pls__def) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [X13] : c_Nat_OSuc(X13) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X13),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_mult__Suc,axiom,
! [X13,X10] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X10),X13) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,X13)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_mult__Suc) ).
fof(fact_odd__Suc__mult__two__ex,axiom,
! [X3] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
<=> ? [X23] : X3 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_odd__Suc__mult__two__ex) ).
fof(fact_semiring__norm_I115_J,axiom,
c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_semiring__norm_I115_J) ).
fof(fact_One__nat__def,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_One__nat__def) ).
fof(fact_nat__mult__1,axiom,
! [X13] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X13) = X13,
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_nat__mult__1) ).
fof(fact_add__mult__distrib,axiom,
! [X8,X13,X10] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X13),X8) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,X8),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X13,X8)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_add__mult__distrib) ).
fof(fact_nat__add__assoc,axiom,
! [X8,X13,X10] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X13),X8) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,X8)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_nat__add__commute,axiom,
! [X13,X10] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X13) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,X10),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_nat__add__left__commute,axiom,
! [X21,X17,X18] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X21)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X21)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_o,axiom,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_o) ).
fof(c_0_18,negated_conjecture,
~ ? [X23] : v_na____ = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23)),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_19,plain,
! [X9] : c_Int_OBit0(X9) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X9),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(c_0_20,plain,
! [X9] : c_Int_OBit1(X9) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X9),X9),
inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).
fof(c_0_21,negated_conjecture,
! [X24] : v_na____ != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X24)),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])]) ).
fof(c_0_22,plain,
! [X14] : c_Nat_OSuc(X14) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
cnf(c_0_23,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(split_conjunct,[status(thm)],[fact_nat__1__add__1]) ).
cnf(c_0_24,plain,
c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
c_Int_OBit1(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_26,plain,
! [X9] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,c_Int_OPls) = X9,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
cnf(c_0_27,negated_conjecture,
v_na____ != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,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_22]) ).
cnf(c_0_29,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_25]) ).
cnf(c_0_30,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_31,plain,
! [X14] : c_Nat_OSuc(X14) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X14),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).
fof(c_0_32,plain,
! [X14,X15] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X15),X14) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X15,X14)),
inference(variable_rename,[status(thm)],[fact_mult__Suc]) ).
fof(c_0_33,plain,
! [X24,X24,X26] :
( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X24)
| X24 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk6_1(X24))) )
& ( X24 != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X26))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X24) ) ),
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)],[inference(fof_simplification,[status(thm)],[fact_odd__Suc__mult__two__ex])])])])])])]) ).
cnf(c_0_34,plain,
c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(split_conjunct,[status(thm)],[fact_semiring__norm_I115_J]) ).
cnf(c_0_35,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_One__nat__def]) ).
cnf(c_0_37,negated_conjecture,
v_na____ != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_24]),c_0_28]),c_0_25]),c_0_25]) ).
cnf(c_0_38,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_30]),c_0_30]),c_0_30]) ).
cnf(c_0_39,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_31]) ).
cnf(c_0_40,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_41,plain,
! [X14] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X14) = X14,
inference(variable_rename,[status(thm)],[fact_nat__mult__1]) ).
cnf(c_0_42,plain,
( X1 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk6_1(X1)))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_43,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_24]),c_0_28]),c_0_28]),c_0_25]),c_0_25]) ).
cnf(c_0_44,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
inference(rw,[status(thm)],[c_0_35,c_0_30]) ).
cnf(c_0_45,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[c_0_36,c_0_28]) ).
fof(c_0_46,plain,
! [X14,X15,X16] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X15),X14) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X16,X14),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X15,X14)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib]) ).
fof(c_0_47,plain,
! [X14,X15,X16] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X15),X14) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X14)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
fof(c_0_48,plain,
! [X14,X15] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X14) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X15),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(c_0_49,plain,
! [X22,X23,X24] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X22)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X22)),
inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).
cnf(c_0_50,negated_conjecture,
v_na____ != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_38]) ).
cnf(c_0_51,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_39,c_0_28]) ).
cnf(c_0_52,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)),
inference(rw,[status(thm)],[c_0_40,c_0_28]) ).
cnf(c_0_53,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_54,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),esk6_1(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_24]),c_0_28]),c_0_25]),c_0_25]) ).
cnf(c_0_55,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
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)],[c_0_43,c_0_30]),c_0_44]),c_0_30]),c_0_44]),c_0_30]),c_0_44]),c_0_30]),c_0_44]),c_0_45]) ).
cnf(c_0_56,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_57,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_47]) ).
cnf(c_0_58,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_48]) ).
cnf(c_0_59,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_49]) ).
cnf(c_0_60,negated_conjecture,
v_na____ != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_53]) ).
cnf(c_0_61,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk6_1(X1),esk6_1(X1))) = X1
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
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(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_54,c_0_30]),c_0_44]),c_0_30]),c_0_44]),c_0_30]),c_0_44]),c_0_30]),c_0_44]),c_0_55]),c_0_56]),c_0_53]),c_0_53]),c_0_57]),c_0_58]),c_0_59]) ).
fof(c_0_62,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
inference(fof_simplification,[status(thm)],[fact_o]) ).
cnf(c_0_63,negated_conjecture,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| v_na____ != X1 ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_64,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_65,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_63]),c_0_64]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW198+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.12 % Command : run_ET %s %d
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 5 04:12:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.33/1.52 # Running protocol protocol_eprover_2d86bd69119e7e9cc4417c0ee581499eaf828bb2 for 23 seconds:
% 0.33/1.52 # SinE strategy is GSinE(CountFormulas,,1.1,,02,500,1.0)
% 0.33/1.52 # Preprocessing time : 0.072 s
% 0.33/1.52
% 0.33/1.52 # Proof found!
% 0.33/1.52 # SZS status Theorem
% 0.33/1.52 # SZS output start CNFRefutation
% See solution above
% 0.33/1.52 # Proof object total steps : 66
% 0.33/1.52 # Proof object clause steps : 33
% 0.33/1.52 # Proof object formula steps : 33
% 0.33/1.52 # Proof object conjectures : 9
% 0.33/1.52 # Proof object clause conjectures : 6
% 0.33/1.52 # Proof object formula conjectures : 3
% 0.33/1.52 # Proof object initial clauses used : 18
% 0.33/1.52 # Proof object initial formulas used : 18
% 0.33/1.52 # Proof object generating inferences : 2
% 0.33/1.52 # Proof object simplifying inferences : 57
% 0.33/1.52 # Training examples: 0 positive, 0 negative
% 0.33/1.52 # Parsed axioms : 1186
% 0.33/1.52 # Removed by relevancy pruning/SinE : 839
% 0.33/1.52 # Initial clauses : 564
% 0.33/1.52 # Removed in clause preprocessing : 24
% 0.33/1.52 # Initial clauses in saturation : 540
% 0.33/1.52 # Processed clauses : 755
% 0.33/1.52 # ...of these trivial : 45
% 0.33/1.52 # ...subsumed : 250
% 0.33/1.52 # ...remaining for further processing : 460
% 0.33/1.52 # Other redundant clauses eliminated : 21
% 0.33/1.52 # Clauses deleted for lack of memory : 0
% 0.33/1.52 # Backward-subsumed : 11
% 0.33/1.52 # Backward-rewritten : 38
% 0.33/1.52 # Generated clauses : 4029
% 0.33/1.52 # ...of the previous two non-trivial : 3431
% 0.33/1.52 # Contextual simplify-reflections : 7
% 0.33/1.52 # Paramodulations : 3958
% 0.33/1.52 # Factorizations : 10
% 0.33/1.52 # Equation resolutions : 61
% 0.33/1.52 # Current number of processed clauses : 396
% 0.33/1.52 # Positive orientable unit clauses : 66
% 0.33/1.52 # Positive unorientable unit clauses: 9
% 0.33/1.52 # Negative unit clauses : 39
% 0.33/1.52 # Non-unit-clauses : 282
% 0.33/1.52 # Current number of unprocessed clauses: 2621
% 0.33/1.52 # ...number of literals in the above : 6106
% 0.33/1.52 # Current number of archived formulas : 0
% 0.33/1.52 # Current number of archived clauses : 52
% 0.33/1.52 # Clause-clause subsumption calls (NU) : 10463
% 0.33/1.52 # Rec. Clause-clause subsumption calls : 8469
% 0.33/1.52 # Non-unit clause-clause subsumptions : 179
% 0.33/1.52 # Unit Clause-clause subsumption calls : 1079
% 0.33/1.52 # Rewrite failures with RHS unbound : 0
% 0.33/1.52 # BW rewrite match attempts : 785
% 0.33/1.52 # BW rewrite match successes : 112
% 0.33/1.52 # Condensation attempts : 0
% 0.33/1.52 # Condensation successes : 0
% 0.33/1.52 # Termbank termtop insertions : 123427
% 0.33/1.52
% 0.33/1.52 # -------------------------------------------------
% 0.33/1.52 # User time : 0.138 s
% 0.33/1.52 # System time : 0.006 s
% 0.33/1.52 # Total time : 0.144 s
% 0.33/1.52 # Maximum resident set size: 7848 pages
% 0.33/23.50 eprover: CPU time limit exceeded, terminating
% 0.33/23.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.52 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
% 0.33/23.53 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: CPU time limit exceeded, terminating
% 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.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.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.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.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.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.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.mepo_128.in
% 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.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
%------------------------------------------------------------------------------