%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW240+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:10:08 PM UTC 2026
% Result : Theorem 14.32s 2.38s
% Output : CNFRefutation 14.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 59 ( 22 unt; 0 def)
% Number of atoms : 102 ( 44 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 77 ( 34 ~; 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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',fact_dvd__refl) ).
fof(tfree_0,hypothesis,
class_Rings_Ocomm__ring__1(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',fact_ext) ).
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/sandbox/benchmark/theBenchmark.p',conj_0) ).
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/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).
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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',clrel_Rings_Ocomm__ring__1__Rings_Ocomm__semiring__0) ).
fof(c_0_15,plain,
! [X2977] :
( class_Rings_Ocomm__semiring__1(X2977)
| ~ class_Rings_Ocomm__ring__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] :
( c_Rings_Odvd__class_Odvd(X2011,X2010,X2010)
| ~ class_Rings_Ocomm__semiring__1(X2011) ),
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__ring__1(X1)
| class_Rings_Ocomm__semiring__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] :
( c_Rings_Odvd__class_Odvd(X1966,X1964,X1963)
| ~ c_Rings_Odvd__class_Odvd(X1966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1966),X1965),X1964),X1963)
| ~ class_Rings_Ocomm__semiring__1(X1966) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__right])])]) ).
cnf(c_0_20,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X2) ),
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] :
( X1961 = c_Groups_Ozero__class_Ozero(X1962)
| ~ c_Rings_Odvd__class_Odvd(X1962,c_Groups_Ozero__class_Ozero(X1962),X1961)
| ~ class_Rings_Ocomm__semiring__1(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)
| ~ class_Rings_Ocomm__semiring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,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] :
( c_Groups_Oplus__class_Oplus(X236,c_Groups_Ozero__class_Ozero(X236),X235) = X235
| ~ class_Rings_Ocomm__semiring__1(X236) ),
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] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X177),X176),X175) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X177),X175),X176)
| ~ class_Rings_Ocomm__semiring__1(X177) ),
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,
( ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Ocomm__semiring__1(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1) ),
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] :
( c_Groups_Oplus__class_Oplus(X254,X253,c_Groups_Ozero__class_Ozero(X254)) = X253
| ~ class_Rings_Ocomm__semiring__1(X254) ),
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] :
( 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)
| ~ class_Rings_Ocomm__semiring__1(X499) ),
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,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) ),
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,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_35,plain,
! [X90,X91] :
( X91 = X90
| hAPP(X91,esk1_2(X90,X91)) != hAPP(X90,esk1_2(X90,X91)) ),
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,
( ~ class_Rings_Ocomm__semiring__1(X1)
| 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) ),
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]) ).
fof(c_0_40,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(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_0_41,plain,
( hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,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_43,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_44,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)],[c_0_40]) ).
fof(c_0_45,plain,
! [X93,X94,X95,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))
| ~ class_Rings_Ocomm__semiring__1(X96) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__monom])])]) ).
cnf(c_0_46,hypothesis,
( hAPP(X1,esk1_2(X1,hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a)))) != esk1_2(X1,hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a)))
| hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a)) = X1 ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,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_43]) ).
fof(c_0_48,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_44]) ).
fof(c_0_49,plain,
! [X97,X98,X99,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))
| ~ class_Rings_Ocomm__semiring__0(X100) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__mult])])]) ).
cnf(c_0_50,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| 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)) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_51,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_46,c_0_47]) ).
cnf(c_0_52,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_48]) ).
cnf(c_0_53,plain,
( ~ class_Rings_Ocomm__semiring__0(X1)
| 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)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_54,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_50,c_0_51]),c_0_47]),c_0_21])]) ).
fof(c_0_55,plain,
! [X2978] :
( class_Rings_Ocomm__semiring__0(X2978)
| ~ class_Rings_Ocomm__ring__1(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_56,negated_conjecture,
~ class_Rings_Ocomm__semiring__0(t_a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
cnf(c_0_57,plain,
( ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_58,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW240+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 09:41:05 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 14.32/2.38 % Version: 3.5.1
% 14.32/2.38 % Preprocessing class: FMLMSMSSSSSNFFN.
% 14.32/2.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.32/2.38 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 14.32/2.38 % Starting new_bool_3 with 300s (1) cores
% 14.32/2.38 % Starting new_bool_1 with 300s (1) cores
% 14.32/2.38 % Starting sh5l with 300s (1) cores
% 14.32/2.38 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with pid 769571 completed with status 0
% 14.32/2.38 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c
% 14.32/2.38 % Preprocessing class: FMLMSMSSSSSNFFN.
% 14.32/2.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.32/2.38 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 14.32/2.38 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.32/2.38 % No SInE strategy applied
% 14.32/2.38 % Search class: FGHSM-SMLM32-DFFFFFNN
% 14.32/2.38 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 14.32/2.38 % Starting SubtermCWHack with 136s (1) cores
% 14.32/2.38 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 14.32/2.38 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 14.32/2.38 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 14.32/2.38 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 14.32/2.38 % G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 769582 completed with status 0
% 14.32/2.38 % Result found by G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 14.32/2.38 % Preprocessing class: FMLMSMSSSSSNFFN.
% 14.32/2.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.32/2.38 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 14.32/2.38 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.32/2.38 % No SInE strategy applied
% 14.32/2.38 % Search class: FGHSM-SMLM32-DFFFFFNN
% 14.32/2.38 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 14.32/2.38 % Starting SubtermCWHack with 136s (1) cores
% 14.32/2.38 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 14.32/2.38 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 14.32/2.38 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 14.32/2.38 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 14.32/2.38 % Preprocessing time : 0.027 s
% 14.32/2.38 % Presaturation interreduction done
% 14.32/2.38
% 14.32/2.38 % Proof found!
% 14.32/2.38 % SZS status Theorem
% 14.32/2.38 % SZS output start CNFRefutation
% See solution above
% 14.32/2.38 % Parsed axioms : 1197
% 14.32/2.38 % Removed by relevancy pruning/SinE : 0
% 14.32/2.38 % Initial clauses : 1712
% 14.32/2.38 % Removed in clause preprocessing : 70
% 14.32/2.38 % Initial clauses in saturation : 1642
% 14.32/2.38 % Processed clauses : 9468
% 14.32/2.38 % ...of these trivial : 315
% 14.32/2.38 % ...subsumed : 5430
% 14.32/2.38 % ...remaining for further processing : 3723
% 14.32/2.38 % Other redundant clauses eliminated : 693
% 14.32/2.38 % Clauses deleted for lack of memory : 0
% 14.32/2.38 % Backward-subsumed : 87
% 14.32/2.38 % Backward-rewritten : 88
% 14.32/2.38 % Generated clauses : 66868
% 14.32/2.38 % ...of the previous two non-redundant : 56973
% 14.32/2.38 % ...aggressively subsumed : 0
% 14.32/2.38 % Contextual simplify-reflections : 9
% 14.32/2.38 % Paramodulations : 66161
% 14.32/2.38 % Factorizations : 8
% 14.32/2.38 % NegExts : 0
% 14.32/2.38 % Equation resolutions : 713
% 14.32/2.38 % Disequality decompositions : 0
% 14.32/2.38 % Total rewrite steps : 45459
% 14.32/2.38 % ...of those cached : 42543
% 14.32/2.38 % Propositional unsat checks : 0
% 14.32/2.38 % Propositional check models : 0
% 14.32/2.38 % Propositional check unsatisfiable : 0
% 14.32/2.38 % Propositional clauses : 0
% 14.32/2.38 % Propositional clauses after purity: 0
% 14.32/2.38 % Propositional unsat core size : 0
% 14.32/2.38 % Propositional preprocessing time : 0.000
% 14.32/2.38 % Propositional encoding time : 0.000
% 14.32/2.38 % Propositional solver time : 0.000
% 14.32/2.38 % Success case prop preproc time : 0.000
% 14.32/2.38 % Success case prop encoding time : 0.000
% 14.32/2.38 % Success case prop solver time : 0.000
% 14.32/2.38 % Current number of processed clauses : 2079
% 14.32/2.38 % Positive orientable unit clauses : 295
% 14.32/2.38 % Positive unorientable unit clauses: 10
% 14.32/2.38 % Negative unit clauses : 74
% 14.32/2.38 % Non-unit-clauses : 1700
% 14.32/2.38 % Current number of unprocessed clauses: 50237
% 14.32/2.38 % ...number of literals in the above : 183869
% 14.32/2.38 % Current number of archived formulas : 0
% 14.32/2.38 % Current number of archived clauses : 1494
% 14.32/2.38 % Clause-clause subsumption calls (NU) : 412479
% 14.32/2.38 % Rec. Clause-clause subsumption calls : 217033
% 14.32/2.38 % Non-unit clause-clause subsumptions : 3400
% 14.32/2.38 % Unit Clause-clause subsumption calls : 4293
% 14.32/2.38 % Rewrite failures with RHS unbound : 0
% 14.32/2.38 % BW rewrite match attempts : 1735
% 14.32/2.38 % BW rewrite match successes : 284
% 14.32/2.38 % Condensation attempts : 0
% 14.32/2.38 % Condensation successes : 0
% 14.32/2.38 % Termbank termtop insertions : 1438263
% 14.32/2.38 % Search garbage collected termcells : 21704
% 14.32/2.38
% 14.32/2.38 % -------------------------------------------------
% 14.32/2.38 % User time : 1.793 s
% 14.32/2.38 % System time : 0.066 s
% 14.32/2.38 % Total time : 1.860 s
% 14.32/2.38 % Maximum resident set size: 10164 pages
% 14.32/2.38
% 14.32/2.38 % -------------------------------------------------
% 14.32/2.38 % User time : 8.532 s
% 14.32/2.38 % System time : 0.367 s
% 14.32/2.38 % Total time : 8.900 s
% 14.32/2.38 % Maximum resident set size: 6144 pages
% 14.32/2.38 % E exiting
%------------------------------------------------------------------------------