TSTP Solution File: SWW240+1 by E---3.2.0
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%------------------------------------------------------------------------------
% File : E---3.2.0
% Problem : SWW240+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n005.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 : Mon Jun 24 18:11:22 EDT 2024
% Result : Theorem 8.94s 1.82s
% Output : CNFRefutation 8.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 58 ( 21 unt; 0 def)
% Number of atoms : 101 ( 43 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 76 ( 33 ~; 29 |; 0 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 105 ( 4 sgn 63 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clrel_Rings_Ocomm__ring__1__Rings_Ocomm__semiring__1,axiom,
! [X86] :
( class_Rings_Ocomm__ring__1(X86)
=> class_Rings_Ocomm__semiring__1(X86) ),
file('/export/starexec/sandbox2/tmp/tmp.zWzrAAkXNT/E---3.1_19748.p',clrel_Rings_Ocomm__ring__1__Rings_Ocomm__semiring__1) ).
fof(fact_dvd__refl,axiom,
! [X6,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> c_Rings_Odvd__class_Odvd(X7,X6,X6) ),
file('/export/starexec/sandbox2/tmp/tmp.zWzrAAkXNT/E---3.1_19748.p',fact_dvd__refl) ).
fof(tfree_0,hypothesis,
class_Rings_Ocomm__ring__1(t_a),
file('/export/starexec/sandbox2/tmp/tmp.zWzrAAkXNT/E---3.1_19748.p',tfree_0) ).
fof(fact_dvd__mult__right,axiom,
! [X17,X10,X6,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> ( c_Rings_Odvd__class_Odvd(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),X10),X17)
=> c_Rings_Odvd__class_Odvd(X7,X10,X17) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zWzrAAkXNT/E---3.1_19748.p',fact_dvd__mult__right) ).
fof(fact_dvd__0__left,axiom,
! [X6,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> ( c_Rings_Odvd__class_Odvd(X7,c_Groups_Ozero__class_Ozero(X7),X6)
=> X6 = c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zWzrAAkXNT/E---3.1_19748.p',fact_dvd__0__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X6,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> c_Groups_Oplus__class_Oplus(X7,c_Groups_Ozero__class_Ozero(X7),X6) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.zWzrAAkXNT/E---3.1_19748.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X10,X6,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),X10) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X10),X6) ),
file('/export/starexec/sandbox2/tmp/tmp.zWzrAAkXNT/E---3.1_19748.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X6,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Ozero__class_Ozero(X7)) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.zWzrAAkXNT/E---3.1_19748.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [X6,X12,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> c_Groups_Oplus__class_Oplus(X7,X12,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Oone__class_Oone(X7))),X12) ),
file('/export/starexec/sandbox2/tmp/tmp.zWzrAAkXNT/E---3.1_19748.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.zWzrAAkXNT/E---3.1_19748.p',fact_ext) ).
fof(fact_nat__mult__1,axiom,
! [X5] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X5) = X5,
file('/export/starexec/sandbox2/tmp/tmp.zWzrAAkXNT/E---3.1_19748.p',fact_nat__mult__1) ).
fof(conj_0,conjecture,
hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_p)),v_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),
file('/export/starexec/sandbox2/tmp/tmp.zWzrAAkXNT/E---3.1_19748.p',conj_0) ).
fof(fact_poly__monom,axiom,
! [X4,X5,X6,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> hAPP(c_Polynomial_Opoly(X7,c_Polynomial_Omonom(X7,X6,X5)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X4),X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.zWzrAAkXNT/E---3.1_19748.p',fact_poly__monom) ).
fof(fact_poly__mult,axiom,
! [X4,X8,X9,X7] :
( class_Rings_Ocomm__semiring__0(X7)
=> hAPP(c_Polynomial_Opoly(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X9),X8)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Polynomial_Opoly(X7,X9),X4)),hAPP(c_Polynomial_Opoly(X7,X8),X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.zWzrAAkXNT/E---3.1_19748.p',fact_poly__mult) ).
fof(clrel_Rings_Ocomm__ring__1__Rings_Ocomm__semiring__0,axiom,
! [X86] :
( class_Rings_Ocomm__ring__1(X86)
=> class_Rings_Ocomm__semiring__0(X86) ),
file('/export/starexec/sandbox2/tmp/tmp.zWzrAAkXNT/E---3.1_19748.p',clrel_Rings_Ocomm__ring__1__Rings_Ocomm__semiring__0) ).
fof(c_0_15,plain,
! [X2977] :
( ~ class_Rings_Ocomm__ring__1(X2977)
| class_Rings_Ocomm__semiring__1(X2977) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Ocomm__ring__1__Rings_Ocomm__semiring__1])])]) ).
fof(c_0_16,plain,
! [X2010,X2011] :
( ~ class_Rings_Ocomm__semiring__1(X2011)
| c_Rings_Odvd__class_Odvd(X2011,X2010,X2010) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__refl])])]) ).
cnf(c_0_17,plain,
( class_Rings_Ocomm__semiring__1(X1)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,hypothesis,
class_Rings_Ocomm__ring__1(t_a),
inference(split_conjunct,[status(thm)],[tfree_0]) ).
fof(c_0_19,plain,
! [X1963,X1964,X1965,X1966] :
( ~ class_Rings_Ocomm__semiring__1(X1966)
| ~ c_Rings_Odvd__class_Odvd(X1966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1966),X1965),X1964),X1963)
| c_Rings_Odvd__class_Odvd(X1966,X1964,X1963) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__right])])]) ).
cnf(c_0_20,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,hypothesis,
class_Rings_Ocomm__semiring__1(t_a),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_22,plain,
! [X1961,X1962] :
( ~ class_Rings_Ocomm__semiring__1(X1962)
| ~ c_Rings_Odvd__class_Odvd(X1962,c_Groups_Ozero__class_Ozero(X1962),X1961)
| X1961 = c_Groups_Ozero__class_Ozero(X1962) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__0__left])])]) ).
cnf(c_0_23,plain,
( c_Rings_Odvd__class_Odvd(X1,X3,X4)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,hypothesis,
c_Rings_Odvd__class_Odvd(t_a,X1,X1),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_25,plain,
! [X235,X236] :
( ~ class_Rings_Ocomm__semiring__1(X236)
| c_Groups_Oplus__class_Oplus(X236,c_Groups_Ozero__class_Ozero(X236),X235) = X235 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])])]) ).
fof(c_0_26,plain,
! [X175,X176,X177] :
( ~ class_Rings_Ocomm__semiring__1(X177)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X177),X176),X175) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X177),X175),X176) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])])]) ).
cnf(c_0_27,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,hypothesis,
c_Rings_Odvd__class_Odvd(t_a,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_21])]) ).
fof(c_0_29,plain,
! [X253,X254] :
( ~ class_Rings_Ocomm__semiring__1(X254)
| c_Groups_Oplus__class_Oplus(X254,X253,c_Groups_Ozero__class_Ozero(X254)) = X253 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])])]) ).
fof(c_0_30,plain,
! [X497,X498,X499] :
( ~ class_Rings_Ocomm__semiring__1(X499)
| c_Groups_Oplus__class_Oplus(X499,X498,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X499),X497),X498)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X499),c_Groups_Oplus__class_Oplus(X499,X497,c_Groups_Oone__class_Oone(X499))),X498) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])])]) ).
cnf(c_0_31,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,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(spm,[status(thm)],[c_0_27,c_0_28]),c_0_21])]) ).
cnf(c_0_34,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_35,plain,
! [X90,X91] :
( hAPP(X91,esk1_2(X90,X91)) != hAPP(X90,esk1_2(X90,X91))
| X91 = X90 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])])]) ).
cnf(c_0_36,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,hypothesis,
c_Groups_Oplus__class_Oplus(t_a,c_Groups_Ozero__class_Ozero(t_a),X1) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_21]) ).
cnf(c_0_38,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_21])]) ).
cnf(c_0_39,hypothesis,
c_Groups_Oplus__class_Oplus(t_a,X1,c_Groups_Ozero__class_Ozero(t_a)) = X1,
inference(spm,[status(thm)],[c_0_34,c_0_21]) ).
cnf(c_0_40,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,hypothesis,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a)),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39]),c_0_21])]) ).
fof(c_0_42,plain,
! [X712] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X712) = X712,
inference(variable_rename,[status(thm)],[fact_nat__mult__1]) ).
fof(c_0_43,negated_conjecture,
hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_p)),v_x) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(c_0_44,plain,
! [X93,X94,X95,X96] :
( ~ class_Rings_Ocomm__semiring__1(X96)
| hAPP(c_Polynomial_Opoly(X96,c_Polynomial_Omonom(X96,X95,X94)),X93) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X96),X95),hAPP(hAPP(c_Power_Opower__class_Opower(X96),X93),X94)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__monom])])]) ).
cnf(c_0_45,hypothesis,
( X1 = hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a))
| hAPP(X1,esk1_2(hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a)),X1)) != esk1_2(hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a)),X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,plain,
hAPP(hAPP(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_42]) ).
fof(c_0_47,negated_conjecture,
hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_p)),v_x) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),
inference(fof_nnf,[status(thm)],[c_0_43]) ).
fof(c_0_48,plain,
! [X97,X98,X99,X100] :
( ~ class_Rings_Ocomm__semiring__0(X100)
| hAPP(c_Polynomial_Opoly(X100,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X100)),X99),X98)),X97) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X100),hAPP(c_Polynomial_Opoly(X100,X99),X97)),hAPP(c_Polynomial_Opoly(X100,X98),X97)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__mult])])]) ).
cnf(c_0_49,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Omonom(X1,X2,X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,hypothesis,
hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,negated_conjecture,
hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_p)),v_x) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_52,plain,
( hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Polynomial_Opoly(X1,X2),X4)),hAPP(c_Polynomial_Opoly(X1,X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_53,hypothesis,
hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),X1)),X2) = hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X2),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_46]),c_0_21])]) ).
fof(c_0_54,plain,
! [X2978] :
( ~ class_Rings_Ocomm__ring__1(X2978)
| class_Rings_Ocomm__semiring__0(X2978) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Ocomm__ring__1__Rings_Ocomm__semiring__0])])]) ).
cnf(c_0_55,negated_conjecture,
~ class_Rings_Ocomm__semiring__0(t_a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
cnf(c_0_56,plain,
( class_Rings_Ocomm__semiring__0(X1)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW240+1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jun 19 04:31:39 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.39/0.61 Running first-order theorem proving
% 0.39/0.61 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/tmp/tmp.zWzrAAkXNT/E---3.1_19748.p
% 8.94/1.82 # Version: 3.2.0
% 8.94/1.82 # Preprocessing class: FMLMSMSSSSSNFFN.
% 8.94/1.82 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.94/1.82 # Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 8.94/1.82 # Starting new_bool_3 with 300s (1) cores
% 8.94/1.82 # Starting new_bool_1 with 300s (1) cores
% 8.94/1.82 # Starting sh5l with 300s (1) cores
% 8.94/1.82 # G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with pid 19913 completed with status 0
% 8.94/1.82 # Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c
% 8.94/1.82 # Preprocessing class: FMLMSMSSSSSNFFN.
% 8.94/1.82 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.94/1.82 # Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 8.94/1.82 # No SInE strategy applied
% 8.94/1.82 # Search class: FGHSM-SMLM32-DFFFFFNN
% 8.94/1.82 # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 8.94/1.82 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 113s (1) cores
% 8.94/1.82 # Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 8.94/1.82 # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 8.94/1.82 # Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 8.94/1.82 # Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S5PRR_S00EN with 113s (1) cores
% 8.94/1.82 # G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 19966 completed with status 0
% 8.94/1.82 # Result found by G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 8.94/1.82 # Preprocessing class: FMLMSMSSSSSNFFN.
% 8.94/1.82 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.94/1.82 # Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 8.94/1.82 # No SInE strategy applied
% 8.94/1.82 # Search class: FGHSM-SMLM32-DFFFFFNN
% 8.94/1.82 # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 8.94/1.82 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 113s (1) cores
% 8.94/1.82 # Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 8.94/1.82 # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 8.94/1.82 # Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 8.94/1.82 # Preprocessing time : 0.025 s
% 8.94/1.82 # Presaturation interreduction done
% 8.94/1.82
% 8.94/1.82 # Proof found!
% 8.94/1.82 # SZS status Theorem
% 8.94/1.82 # SZS output start CNFRefutation
% See solution above
% 8.94/1.82 # Parsed axioms : 1197
% 8.94/1.82 # Removed by relevancy pruning/SinE : 0
% 8.94/1.82 # Initial clauses : 1712
% 8.94/1.82 # Removed in clause preprocessing : 70
% 8.94/1.82 # Initial clauses in saturation : 1642
% 8.94/1.82 # Processed clauses : 9468
% 8.94/1.82 # ...of these trivial : 315
% 8.94/1.82 # ...subsumed : 5431
% 8.94/1.82 # ...remaining for further processing : 3722
% 8.94/1.82 # Other redundant clauses eliminated : 693
% 8.94/1.82 # Clauses deleted for lack of memory : 0
% 8.94/1.82 # Backward-subsumed : 87
% 8.94/1.82 # Backward-rewritten : 88
% 8.94/1.82 # Generated clauses : 66754
% 8.94/1.82 # ...of the previous two non-redundant : 56882
% 8.94/1.82 # ...aggressively subsumed : 0
% 8.94/1.82 # Contextual simplify-reflections : 9
% 8.94/1.82 # Paramodulations : 66047
% 8.94/1.82 # Factorizations : 8
% 8.94/1.82 # NegExts : 0
% 8.94/1.82 # Equation resolutions : 713
% 8.94/1.82 # Disequality decompositions : 0
% 8.94/1.82 # Total rewrite steps : 45451
% 8.94/1.82 # ...of those cached : 42535
% 8.94/1.82 # Propositional unsat checks : 0
% 8.94/1.82 # Propositional check models : 0
% 8.94/1.82 # Propositional check unsatisfiable : 0
% 8.94/1.82 # Propositional clauses : 0
% 8.94/1.82 # Propositional clauses after purity: 0
% 8.94/1.82 # Propositional unsat core size : 0
% 8.94/1.82 # Propositional preprocessing time : 0.000
% 8.94/1.82 # Propositional encoding time : 0.000
% 8.94/1.82 # Propositional solver time : 0.000
% 8.94/1.82 # Success case prop preproc time : 0.000
% 8.94/1.82 # Success case prop encoding time : 0.000
% 8.94/1.82 # Success case prop solver time : 0.000
% 8.94/1.82 # Current number of processed clauses : 2078
% 8.94/1.82 # Positive orientable unit clauses : 295
% 8.94/1.82 # Positive unorientable unit clauses: 10
% 8.94/1.82 # Negative unit clauses : 74
% 8.94/1.82 # Non-unit-clauses : 1699
% 8.94/1.82 # Current number of unprocessed clauses: 50146
% 8.94/1.82 # ...number of literals in the above : 183143
% 8.94/1.82 # Current number of archived formulas : 0
% 8.94/1.82 # Current number of archived clauses : 1494
% 8.94/1.82 # Clause-clause subsumption calls (NU) : 523905
% 8.94/1.82 # Rec. Clause-clause subsumption calls : 272511
% 8.94/1.82 # Non-unit clause-clause subsumptions : 3401
% 8.94/1.82 # Unit Clause-clause subsumption calls : 4157
% 8.94/1.82 # Rewrite failures with RHS unbound : 0
% 8.94/1.82 # BW rewrite match attempts : 1735
% 8.94/1.82 # BW rewrite match successes : 284
% 8.94/1.82 # Condensation attempts : 0
% 8.94/1.82 # Condensation successes : 0
% 8.94/1.82 # Termbank termtop insertions : 1426997
% 8.94/1.82 # Search garbage collected termcells : 21706
% 8.94/1.82
% 8.94/1.82 # -------------------------------------------------
% 8.94/1.82 # User time : 1.099 s
% 8.94/1.82 # System time : 0.050 s
% 8.94/1.82 # Total time : 1.149 s
% 8.94/1.82 # Maximum resident set size: 8512 pages
% 8.94/1.82
% 8.94/1.82 # -------------------------------------------------
% 8.94/1.82 # User time : 5.131 s
% 8.94/1.82 # System time : 0.248 s
% 8.94/1.82 # Total time : 5.379 s
% 8.94/1.82 # Maximum resident set size: 3112 pages
% 8.94/1.82 % E---3.1 exiting
% 8.94/1.82 % E exiting
%------------------------------------------------------------------------------