%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWW247+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 03:11:48 PM UTC 2026
% Result : Theorem 12.39s 2.15s
% Output : CNFRefutation 12.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 64 ( 16 unt; 0 def)
% Number of atoms : 122 ( 72 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 111 ( 53 ~; 47 |; 0 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 61 ( 10 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_x____) = hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_y____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_poly__pCons,axiom,
! [X14,X11,X12,X13] :
( class_Rings_Ocomm__semiring__0(X13)
=> hAPP(c_Polynomial_Opoly(X13,hAPP(hAPP(c_Polynomial_OpCons(X13),X12),X11)),X14) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X14),hAPP(c_Polynomial_Opoly(X13,X11),X14))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pCons) ).
fof(fact_C,axiom,
( class_Rings_Oidom(t_a)
=> ! [X4] :
( X4 != c_Groups_Ozero__class_Ozero(t_a)
=> hAPP(c_Polynomial_Opoly(t_a,v_cs____),X4) = c_Groups_Ozero__class_Ozero(t_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_C) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X12,X13] :
( class_Rings_Ocomm__semiring__1(X13)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X12),c_Groups_Ozero__class_Ozero(X13)) = c_Groups_Ozero__class_Ozero(X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(clrel_Rings_Oidom__Rings_Ocomm__semiring__1,axiom,
! [X91] :
( class_Rings_Oidom(X91)
=> class_Rings_Ocomm__semiring__1(X91) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ocomm__semiring__1) ).
fof(fact_add_Ocomm__neutral,axiom,
! [X12,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X12),c_Groups_Ozero__class_Ozero(X13)) = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(clrel_Rings_Oidom__Groups_Ocomm__monoid__add,axiom,
! [X91] :
( class_Rings_Oidom(X91)
=> class_Groups_Ocomm__monoid__add(X91) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Groups_Ocomm__monoid__add) ).
fof(tfree_0,hypothesis,
class_Rings_Oidom(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [X12,X13] :
( class_Rings_Ocomm__semiring__1(X13)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),c_Groups_Ozero__class_Ozero(X13)),X12) = c_Groups_Ozero__class_Ozero(X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(clrel_Rings_Oidom__Rings_Ocomm__semiring__0,axiom,
! [X91] :
( class_Rings_Oidom(X91)
=> class_Rings_Ocomm__semiring__0(X91) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ocomm__semiring__0) ).
fof(c_0_10,negated_conjecture,
hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_x____) != hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_y____),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_11,negated_conjecture,
hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_x____) != hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_y____),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_12,negated_conjecture,
hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_x____) != hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_y____),
inference(fof_nnf,[status(thm)],[c_0_11]) ).
fof(c_0_13,plain,
! [X138,X139,X140,X141] :
( hAPP(c_Polynomial_Opoly(X141,hAPP(hAPP(c_Polynomial_OpCons(X141),X140),X139)),X138) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X141),X140),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X141),X138),hAPP(c_Polynomial_Opoly(X141,X139),X138)))
| ~ class_Rings_Ocomm__semiring__0(X141) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__pCons])])]) ).
fof(c_0_14,plain,
( class_Rings_Oidom(t_a)
=> ! [X4] :
( X4 != c_Groups_Ozero__class_Ozero(t_a)
=> hAPP(c_Polynomial_Opoly(t_a,v_cs____),X4) = c_Groups_Ozero__class_Ozero(t_a) ) ),
inference(fof_simplification,[status(thm)],[fact_C]) ).
fof(c_0_15,plain,
! [X388,X389] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X389),X388),c_Groups_Ozero__class_Ozero(X389)) = c_Groups_Ozero__class_Ozero(X389)
| ~ class_Rings_Ocomm__semiring__1(X389) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])])]) ).
fof(c_0_16,plain,
! [X2919] :
( class_Rings_Ocomm__semiring__1(X2919)
| ~ class_Rings_Oidom(X2919) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Rings_Ocomm__semiring__1])])]) ).
fof(c_0_17,plain,
! [X431,X432] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X432),X431),c_Groups_Ozero__class_Ozero(X432)) = X431
| ~ class_Groups_Ocomm__monoid__add(X432) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])])]) ).
fof(c_0_18,plain,
! [X2918] :
( class_Groups_Ocomm__monoid__add(X2918)
| ~ class_Rings_Oidom(X2918) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Groups_Ocomm__monoid__add])])]) ).
cnf(c_0_19,negated_conjecture,
hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_x____) != hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_y____),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( ~ class_Rings_Ocomm__semiring__0(X1)
| hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Polynomial_OpCons(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(c_Polynomial_Opoly(X1,X3),X4))) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_21,plain,
! [X104] :
( hAPP(c_Polynomial_Opoly(t_a,v_cs____),X104) = c_Groups_Ozero__class_Ozero(t_a)
| X104 = c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Rings_Oidom(t_a) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
cnf(c_0_22,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( ~ class_Rings_Oidom(X1)
| class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( ~ class_Groups_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
( ~ class_Rings_Oidom(X1)
| class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
( ~ class_Rings_Ocomm__semiring__0(t_a)
| hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),v_y____) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_x____),hAPP(c_Polynomial_Opoly(t_a,v_cs____),v_x____))) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,plain,
( ~ class_Rings_Oidom(t_a)
| hAPP(c_Polynomial_Opoly(t_a,v_cs____),X1) = c_Groups_Ozero__class_Ozero(t_a)
| X1 = c_Groups_Ozero__class_Ozero(t_a) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,hypothesis,
class_Rings_Oidom(t_a),
inference(split_conjunct,[status(thm)],[tfree_0]) ).
cnf(c_0_29,plain,
( ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
( ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) = X2 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,negated_conjecture,
( ~ class_Rings_Ocomm__semiring__0(t_a)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_x____),hAPP(c_Polynomial_Opoly(t_a,v_cs____),v_x____))) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),hAPP(c_Polynomial_Opoly(t_a,v_cs____),v_y____))) ),
inference(spm,[status(thm)],[c_0_26,c_0_20]) ).
cnf(c_0_32,plain,
( X1 = c_Groups_Ozero__class_Ozero(t_a)
| hAPP(c_Polynomial_Opoly(t_a,v_cs____),X1) = c_Groups_Ozero__class_Ozero(t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
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(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_34,hypothesis,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),X1),c_Groups_Ozero__class_Ozero(t_a)) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_28]) ).
fof(c_0_35,plain,
! [X396,X397] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X397),c_Groups_Ozero__class_Ozero(X397)),X396) = c_Groups_Ozero__class_Ozero(X397)
| ~ class_Rings_Ocomm__semiring__1(X397) ),
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])])]) ).
cnf(c_0_36,negated_conjecture,
( ~ class_Rings_Ocomm__semiring__0(t_a)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),hAPP(c_Polynomial_Opoly(t_a,v_cs____),v_y____))) != v_c____
| c_Groups_Ozero__class_Ozero(t_a) = v_x____ ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34]) ).
fof(c_0_37,plain,
! [X2920] :
( class_Rings_Ocomm__semiring__0(X2920)
| ~ class_Rings_Oidom(X2920) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Rings_Ocomm__semiring__0])])]) ).
cnf(c_0_38,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( ~ class_Rings_Ocomm__semiring__0(t_a)
| c_Groups_Ozero__class_Ozero(t_a) = v_x____
| c_Groups_Ozero__class_Ozero(t_a) = v_y____ ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_32]),c_0_33]),c_0_34])]) ).
cnf(c_0_40,plain,
( ~ class_Rings_Oidom(X1)
| class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_41,plain,
( ~ class_Rings_Oidom(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_23]) ).
cnf(c_0_42,negated_conjecture,
( c_Groups_Ozero__class_Ozero(t_a) = v_y____
| c_Groups_Ozero__class_Ozero(t_a) = v_x____ ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_28])]) ).
cnf(c_0_43,hypothesis,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Ozero__class_Ozero(t_a)),X1) = c_Groups_Ozero__class_Ozero(t_a),
inference(spm,[status(thm)],[c_0_41,c_0_28]) ).
cnf(c_0_44,negated_conjecture,
( v_x____ != v_y____
| c_Groups_Ozero__class_Ozero(t_a) = v_y____ ),
inference(ef,[status(thm)],[c_0_42]) ).
cnf(c_0_45,hypothesis,
( v_x____ != v_y____
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),X1) = v_y____ ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_46,hypothesis,
( v_x____ != v_y____
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),X1),v_y____) = X1 ),
inference(spm,[status(thm)],[c_0_34,c_0_44]) ).
cnf(c_0_47,negated_conjecture,
( ~ class_Rings_Ocomm__semiring__0(t_a)
| v_x____ != v_y____
| c_Groups_Ozero__class_Ozero(t_a) = v_x____ ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_45]),c_0_46]) ).
cnf(c_0_48,negated_conjecture,
( v_x____ != v_y____
| c_Groups_Ozero__class_Ozero(t_a) = v_x____ ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_40]),c_0_28])]) ).
cnf(c_0_49,hypothesis,
( v_x____ != v_y____
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_x____),X1) = v_x____ ),
inference(spm,[status(thm)],[c_0_43,c_0_48]) ).
cnf(c_0_50,hypothesis,
( c_Groups_Ozero__class_Ozero(t_a) = v_y____
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_x____),X1) = v_x____ ),
inference(spm,[status(thm)],[c_0_43,c_0_42]) ).
cnf(c_0_51,negated_conjecture,
( ~ class_Rings_Ocomm__semiring__0(t_a)
| v_x____ != v_y____
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),hAPP(c_Polynomial_Opoly(t_a,v_cs____),v_y____))) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_x____) ),
inference(spm,[status(thm)],[c_0_31,c_0_49]) ).
cnf(c_0_52,negated_conjecture,
( ~ class_Rings_Ocomm__semiring__0(t_a)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),hAPP(c_Polynomial_Opoly(t_a,v_cs____),v_y____))) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_x____)
| c_Groups_Ozero__class_Ozero(t_a) = v_y____ ),
inference(spm,[status(thm)],[c_0_31,c_0_50]) ).
cnf(c_0_53,hypothesis,
( c_Groups_Ozero__class_Ozero(t_a) = v_y____
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),X1),v_x____) = X1 ),
inference(spm,[status(thm)],[c_0_34,c_0_42]) ).
cnf(c_0_54,hypothesis,
( ~ class_Rings_Ocomm__semiring__0(t_a)
| v_x____ != v_y____
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_x____) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_y____) ),
inference(spm,[status(thm)],[c_0_51,c_0_45]) ).
cnf(c_0_55,negated_conjecture,
( ~ class_Rings_Ocomm__semiring__0(t_a)
| c_Groups_Ozero__class_Ozero(t_a) = v_y____ ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_32]),c_0_33]),c_0_34]),c_0_53]) ).
cnf(c_0_56,hypothesis,
( v_x____ != v_y____
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_x____) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_c____),v_y____) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_40]),c_0_28])]) ).
cnf(c_0_57,hypothesis,
( v_x____ != v_y____
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),X1),v_x____) = X1 ),
inference(spm,[status(thm)],[c_0_34,c_0_48]) ).
cnf(c_0_58,negated_conjecture,
c_Groups_Ozero__class_Ozero(t_a) = v_y____,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_40]),c_0_28])]) ).
cnf(c_0_59,hypothesis,
v_x____ != v_y____,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_46]) ).
cnf(c_0_60,hypothesis,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),v_y____),X1) = v_y____,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_58]),c_0_58]) ).
cnf(c_0_61,hypothesis,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),X1),v_y____) = X1,
inference(rw,[status(thm)],[c_0_34,c_0_58]) ).
cnf(c_0_62,negated_conjecture,
~ class_Rings_Ocomm__semiring__0(t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_58]),c_0_59]),c_0_60]),c_0_61])]) ).
cnf(c_0_63,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_40]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW247+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 09:44:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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/benchmark/theBenchmark.p
% 12.39/2.15 % Version: 3.5.1
% 12.39/2.15 % Preprocessing class: FMLMSMSMSSSNFFN.
% 12.39/2.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.39/2.15 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 12.39/2.15 % Starting new_bool_3 with 300s (1) cores
% 12.39/2.15 % Starting new_bool_1 with 300s (1) cores
% 12.39/2.15 % Starting sh5l with 300s (1) cores
% 12.39/2.15 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2614329 completed with status 0
% 12.39/2.15 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 12.39/2.15 % Preprocessing class: FMLMSMSMSSSNFFN.
% 12.39/2.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.39/2.15 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 12.39/2.15 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 12.39/2.15 % No SInE strategy applied
% 12.39/2.15 % Search class: FGHSM-SSLM31-DFFFFFNN
% 12.39/2.15 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 12.39/2.15 % Starting SubtermCWHack with 136s (1) cores
% 12.39/2.15 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 12.39/2.15 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S2S with 136s (1) cores
% 12.39/2.15 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 136s (1) cores
% 12.39/2.15 % Starting G-E--_208_B07AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 12.39/2.15 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2614337 completed with status 0
% 12.39/2.15 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 12.39/2.15 % Preprocessing class: FMLMSMSMSSSNFFN.
% 12.39/2.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.39/2.15 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 12.39/2.15 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 12.39/2.15 % No SInE strategy applied
% 12.39/2.15 % Search class: FGHSM-SSLM31-DFFFFFNN
% 12.39/2.15 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 12.39/2.15 % Starting SubtermCWHack with 136s (1) cores
% 12.39/2.15 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 12.39/2.15 % Preprocessing time : 0.029 s
% 12.39/2.15 % Presaturation interreduction done
% 12.39/2.15
% 12.39/2.15 % Proof found!
% 12.39/2.15 % SZS status Theorem
% 12.39/2.15 % SZS output start CNFRefutation
% See solution above
% 12.39/2.15 % Parsed axioms : 1214
% 12.39/2.15 % Removed by relevancy pruning/SinE : 0
% 12.39/2.15 % Initial clauses : 1640
% 12.39/2.15 % Removed in clause preprocessing : 79
% 12.39/2.15 % Initial clauses in saturation : 1561
% 12.39/2.15 % Processed clauses : 4175
% 12.39/2.15 % ...of these trivial : 62
% 12.39/2.15 % ...subsumed : 1123
% 12.39/2.15 % ...remaining for further processing : 2990
% 12.39/2.15 % Other redundant clauses eliminated : 505
% 12.39/2.15 % Clauses deleted for lack of memory : 0
% 12.39/2.15 % Backward-subsumed : 108
% 12.39/2.15 % Backward-rewritten : 105
% 12.39/2.15 % Generated clauses : 53739
% 12.39/2.15 % ...of the previous two non-redundant : 48848
% 12.39/2.15 % ...aggressively subsumed : 0
% 12.39/2.15 % Contextual simplify-reflections : 13
% 12.39/2.15 % Paramodulations : 53217
% 12.39/2.15 % Factorizations : 11
% 12.39/2.15 % NegExts : 0
% 12.39/2.15 % Equation resolutions : 530
% 12.39/2.15 % Disequality decompositions : 0
% 12.39/2.15 % Total rewrite steps : 34632
% 12.39/2.15 % ...of those cached : 31804
% 12.39/2.15 % Propositional unsat checks : 0
% 12.39/2.15 % Propositional check models : 0
% 12.39/2.15 % Propositional check unsatisfiable : 0
% 12.39/2.15 % Propositional clauses : 0
% 12.39/2.15 % Propositional clauses after purity: 0
% 12.39/2.15 % Propositional unsat core size : 0
% 12.39/2.15 % Propositional preprocessing time : 0.000
% 12.39/2.15 % Propositional encoding time : 0.000
% 12.39/2.15 % Propositional solver time : 0.000
% 12.39/2.15 % Success case prop preproc time : 0.000
% 12.39/2.15 % Success case prop encoding time : 0.000
% 12.39/2.15 % Success case prop solver time : 0.000
% 12.39/2.15 % Current number of processed clauses : 1410
% 12.39/2.15 % Positive orientable unit clauses : 248
% 12.39/2.15 % Positive unorientable unit clauses: 7
% 12.39/2.15 % Negative unit clauses : 43
% 12.39/2.15 % Non-unit-clauses : 1112
% 12.39/2.15 % Current number of unprocessed clauses: 47044
% 12.39/2.15 % ...number of literals in the above : 147147
% 12.39/2.15 % Current number of archived formulas : 0
% 12.39/2.15 % Current number of archived clauses : 1430
% 12.39/2.15 % Clause-clause subsumption calls (NU) : 403698
% 12.39/2.15 % Rec. Clause-clause subsumption calls : 289713
% 12.39/2.15 % Non-unit clause-clause subsumptions : 687
% 12.39/2.15 % Unit Clause-clause subsumption calls : 5619
% 12.39/2.15 % Rewrite failures with RHS unbound : 0
% 12.39/2.15 % BW rewrite match attempts : 1232
% 12.39/2.15 % BW rewrite match successes : 143
% 12.39/2.15 % Condensation attempts : 0
% 12.39/2.15 % Condensation successes : 0
% 12.39/2.15 % Termbank termtop insertions : 1725228
% 12.39/2.15 % Search garbage collected termcells : 20525
% 12.39/2.15
% 12.39/2.15 % -------------------------------------------------
% 12.39/2.15 % User time : 1.560 s
% 12.39/2.15 % System time : 0.064 s
% 12.39/2.15 % Total time : 1.624 s
% 12.39/2.15 % Maximum resident set size: 10496 pages
% 12.39/2.15
% 12.39/2.15 % -------------------------------------------------
% 12.39/2.15 % User time : 6.997 s
% 12.39/2.15 % System time : 0.262 s
% 12.39/2.15 % Total time : 7.259 s
% 12.39/2.15 % Maximum resident set size: 6144 pages
% 12.39/2.15 % E exiting
%------------------------------------------------------------------------------