%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV680-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 02:59:45 PM UTC 2026
% Result : Unsatisfiable 58.51s 9.11s
% Output : CNFRefutation 58.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of clauses : 70 ( 21 unt; 10 nHn; 27 RR)
% Number of literals : 128 ( 71 equ; 58 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 131 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_divide__inverse_0,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Ofield(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(cls_inverse__eq__divide_0,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
cnf(cls_power__one_0,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
cnf(clsrel_Ring__and__Field_Ofield_OrderedGroup_Omonoid__mult,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_OrderedGroup_Omonoid__mult) ).
cnf(cls_right__inverse__eq_1,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X2,X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
cnf(cls_conjecture_1,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_k,v_i,tc_nat),t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_j,t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_class__semiring_Opwr__mul_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
cnf(clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ocomm__semiring__1,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ocomm__semiring__1) ).
cnf(cls_class__semiring_Omul__c_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
cnf(cls_nat__mult__commute_0,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
cnf(cls_class__semiring_Opwr__pwr_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),X4,X1) = c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).
cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
cnf(cls_nonzero__power__divide_0,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).
cnf(cls_conjecture_0,negated_conjecture,
v_a != c_HOL_Ozero__class_Ozero(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_field__power__not__zero_0,axiom,
( c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
cnf(clsrel_Ring__and__Field_Ofield_Ring__and__Field_Oring__1__no__zero__divisors,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| class_Ring__and__Field_Oring__1__no__zero__divisors(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Oring__1__no__zero__divisors) ).
cnf(c_0_17,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X3,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_divide__inverse_0]) ).
cnf(c_0_18,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X3,X1),X1) ),
c_0_17 ).
cnf(c_0_19,negated_conjecture,
class_Ring__and__Field_Ofield(t_a),
tfree_tcs ).
cnf(c_0_20,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_inverse__eq__divide_0]) ).
cnf(c_0_21,plain,
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1) ),
inference(fof_simplification,[status(thm)],[cls_power__one_0]) ).
cnf(c_0_22,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| class_OrderedGroup_Omonoid__mult(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Ofield_OrderedGroup_Omonoid__mult]) ).
cnf(c_0_23,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X2,X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_right__inverse__eq_1]) ).
cnf(c_0_24,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_k,v_i,tc_nat),t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_j,t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a),
inference(fof_simplification,[status(thm)],[cls_conjecture_1]) ).
cnf(c_0_25,negated_conjecture,
c_HOL_Oinverse__class_Odivide(X1,X2,t_a) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,t_a),t_a),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1) ),
c_0_20 ).
cnf(c_0_27,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Opwr__mul_0]) ).
cnf(c_0_28,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ocomm__semiring__1]) ).
cnf(c_0_29,plain,
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1) ),
c_0_21 ).
cnf(c_0_30,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| class_OrderedGroup_Omonoid__mult(X1) ),
c_0_22 ).
cnf(c_0_31,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X2,X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
c_0_23 ).
cnf(c_0_32,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Omul__c_0]) ).
cnf(c_0_33,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_k,v_i,tc_nat),t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_j,t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a),
c_0_24 ).
cnf(c_0_34,negated_conjecture,
c_HOL_Oinverse__class_Odivide(X1,X2,t_a) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),X2,t_a),t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_19])]) ).
cnf(c_0_35,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
cls_nat__mult__commute_0 ).
cnf(c_0_36,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1) ),
c_0_27 ).
cnf(c_0_37,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X1) ),
c_0_28 ).
cnf(c_0_38,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),X4,X1) = c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1) ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Opwr__pwr_0]) ).
cnf(c_0_39,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_40,negated_conjecture,
( X1 = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oinverse__class_Odivide(X1,X1,t_a) = c_HOL_Oone__class_Oone(t_a) ),
inference(spm,[status(thm)],[c_0_31,c_0_19]) ).
cnf(c_0_41,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Osemiring__rules_I12_J_0]) ).
cnf(c_0_42,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1) ),
c_0_32 ).
cnf(c_0_43,negated_conjecture,
c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,v_j,t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),t_a),v_i,t_a) != c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_k,tc_nat),t_a),t_a),t_a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_34]),c_0_35]) ).
cnf(c_0_44,plain,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X4,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X2,X4,X3),X3) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),X4,X1) = c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1) ),
c_0_38 ).
cnf(c_0_46,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_nonzero__power__divide_0]) ).
cnf(c_0_47,negated_conjecture,
v_a != c_HOL_Ozero__class_Ozero(t_a),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_48,negated_conjecture,
( X1 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X1,t_a),X2,t_a) = c_HOL_Oinverse__class_Odivide(X1,X1,t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_19])]) ).
cnf(c_0_49,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2 ),
c_0_41 ).
cnf(c_0_50,plain,
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3) ),
inference(spm,[status(thm)],[c_0_42,c_0_37]) ).
cnf(c_0_51,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_j,t_a),v_i,t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a),t_a) != c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_k,tc_nat),t_a),t_a),t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_19])]) ).
cnf(c_0_52,plain,
( ~ class_Ring__and__Field_Ofield(X3)
| c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X3),X4,X3) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X3) ),
inference(spm,[status(thm)],[c_0_45,c_0_37]) ).
cnf(c_0_53,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1) ),
c_0_46 ).
cnf(c_0_54,negated_conjecture,
v_a != c_HOL_Ozero__class_Ozero(t_a),
c_0_47 ).
cnf(c_0_55,negated_conjecture,
( X2 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X1,t_a) = c_HOL_Oone__class_Oone(t_a) ),
inference(spm,[status(thm)],[c_0_48,c_0_40]) ).
cnf(c_0_56,plain,
( ~ class_Ring__and__Field_Ofield(X2)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X2),X2) = X1 ),
inference(spm,[status(thm)],[c_0_49,c_0_37]) ).
cnf(c_0_57,negated_conjecture,
c_HOL_Otimes__class_Otimes(X1,X2,t_a) = c_HOL_Otimes__class_Otimes(X2,X1,t_a),
inference(spm,[status(thm)],[c_0_50,c_0_19]) ).
cnf(c_0_58,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a),t_a) != c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_k,tc_nat),t_a),t_a),t_a),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_19])]),c_0_35]) ).
cnf(c_0_59,negated_conjecture,
( X2 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X2,t_a),X3,t_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X3,t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(X2,X3,t_a),t_a),t_a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_19]),c_0_34]) ).
cnf(c_0_60,negated_conjecture,
c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X1,t_a) = c_HOL_Oone__class_Oone(t_a),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_61,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(t_a),X1,t_a) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_19])]) ).
cnf(c_0_62,plain,
( c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_field__power__not__zero_0]) ).
cnf(c_0_63,negated_conjecture,
( c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_k,t_a),v_i,t_a),t_a),t_a) != c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_k,tc_nat),t_a),t_a),t_a)
| c_Power_Opower__class_Opower(v_a,v_k,t_a) = c_HOL_Ozero__class_Ozero(t_a) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_61]) ).
cnf(c_0_64,plain,
( c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
c_0_62 ).
cnf(c_0_65,negated_conjecture,
c_Power_Opower__class_Opower(v_a,v_k,t_a) = c_HOL_Ozero__class_Ozero(t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_52]),c_0_35]),c_0_19])]) ).
cnf(c_0_66,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| class_Ring__and__Field_Oring__1__no__zero__divisors(X1) ),
inference(fof_simplification,[status(thm)],[clsrel_Ring__and__Field_Ofield_Ring__and__Field_Oring__1__no__zero__divisors]) ).
cnf(c_0_67,negated_conjecture,
~ class_Ring__and__Field_Oring__1__no__zero__divisors(t_a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_54]) ).
cnf(c_0_68,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| class_Ring__and__Field_Oring__1__no__zero__divisors(X1) ),
c_0_66 ).
cnf(c_0_69,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV680-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 09:18:36 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.46 Running first-order theorem proving
% 0.16/0.46 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
% 58.51/9.11 % Version: 3.5.1
% 58.51/9.11 % Preprocessing class: FSLSSMSSSSSNFFN.
% 58.51/9.11 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 58.51/9.11 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 58.51/9.11 % Starting new_bool_3 with 300s (1) cores
% 58.51/9.11 % Starting new_bool_1 with 300s (1) cores
% 58.51/9.11 % Starting sh5l with 300s (1) cores
% 58.51/9.11 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 436156 completed with status 0
% 58.51/9.11 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 58.51/9.11 % Preprocessing class: FSLSSMSSSSSNFFN.
% 58.51/9.11 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 58.51/9.11 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 58.51/9.11 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 58.51/9.11 % No SInE strategy applied
% 58.51/9.11 % Search class: FGHSS-FSLM32-MFFFFFNN
% 58.51/9.11 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 58.51/9.11 % Starting SubtermCWHack with 136s (1) cores
% 58.51/9.11 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 58.51/9.11 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 58.51/9.11 % Starting new_bool_3 with 136s (1) cores
% 58.51/9.11 % Starting new_bool_1 with 136s (1) cores
% 58.51/9.11 % G-E--_208_B07_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 436165 completed with status 0
% 58.51/9.11 % Result found by G-E--_208_B07_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 58.51/9.11 % Preprocessing class: FSLSSMSSSSSNFFN.
% 58.51/9.11 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 58.51/9.11 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 58.51/9.11 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 58.51/9.11 % No SInE strategy applied
% 58.51/9.11 % Search class: FGHSS-FSLM32-MFFFFFNN
% 58.51/9.11 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 58.51/9.11 % Starting SubtermCWHack with 136s (1) cores
% 58.51/9.11 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 58.51/9.11 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 58.51/9.11 % Preprocessing time : 0.018 s
% 58.51/9.11 % Presaturation interreduction done
% 58.51/9.11
% 58.51/9.11 % Proof found!
% 58.51/9.11 % SZS status Unsatisfiable
% 58.51/9.11 % SZS output start CNFRefutation
% See solution above
% 58.51/9.11 % Parsed axioms : 731
% 58.51/9.11 % Removed by relevancy pruning/SinE : 0
% 58.51/9.11 % Initial clauses : 731
% 58.51/9.11 % Removed in clause preprocessing : 0
% 58.51/9.11 % Initial clauses in saturation : 731
% 58.51/9.11 % Processed clauses : 29301
% 58.51/9.11 % ...of these trivial : 241
% 58.51/9.11 % ...subsumed : 23240
% 58.51/9.11 % ...remaining for further processing : 5820
% 58.51/9.11 % Other redundant clauses eliminated : 2355
% 58.51/9.11 % Clauses deleted for lack of memory : 0
% 58.51/9.11 % Backward-subsumed : 859
% 58.51/9.11 % Backward-rewritten : 79
% 58.51/9.11 % Generated clauses : 158583
% 58.51/9.11 % ...of the previous two non-redundant : 143472
% 58.51/9.11 % ...aggressively subsumed : 0
% 58.51/9.11 % Contextual simplify-reflections : 84
% 58.51/9.11 % Paramodulations : 156167
% 58.51/9.11 % Factorizations : 16
% 58.51/9.11 % NegExts : 0
% 58.51/9.11 % Equation resolutions : 2400
% 58.51/9.11 % Disequality decompositions : 0
% 58.51/9.11 % Total rewrite steps : 89443
% 58.51/9.11 % ...of those cached : 86754
% 58.51/9.11 % Propositional unsat checks : 1
% 58.51/9.11 % Propositional check models : 0
% 58.51/9.11 % Propositional check unsatisfiable : 0
% 58.51/9.11 % Propositional clauses : 0
% 58.51/9.11 % Propositional clauses after purity: 0
% 58.51/9.11 % Propositional unsat core size : 0
% 58.51/9.11 % Propositional preprocessing time : 0.000
% 58.51/9.11 % Propositional encoding time : 0.171
% 58.51/9.11 % Propositional solver time : 0.115
% 58.51/9.11 % Success case prop preproc time : 0.000
% 58.51/9.11 % Success case prop encoding time : 0.000
% 58.51/9.11 % Success case prop solver time : 0.000
% 58.51/9.11 % Current number of processed clauses : 4327
% 58.51/9.11 % Positive orientable unit clauses : 221
% 58.51/9.11 % Positive unorientable unit clauses: 19
% 58.51/9.11 % Negative unit clauses : 312
% 58.51/9.11 % Non-unit-clauses : 3775
% 58.51/9.11 % Current number of unprocessed clauses: 111042
% 58.51/9.11 % ...number of literals in the above : 409544
% 58.51/9.11 % Current number of archived formulas : 0
% 58.51/9.11 % Current number of archived clauses : 1493
% 58.51/9.11 % Clause-clause subsumption calls (NU) : 2642178
% 58.51/9.11 % Rec. Clause-clause subsumption calls : 1154640
% 58.51/9.11 % Non-unit clause-clause subsumptions : 16811
% 58.51/9.11 % Unit Clause-clause subsumption calls : 91380
% 58.51/9.11 % Rewrite failures with RHS unbound : 0
% 58.51/9.11 % BW rewrite match attempts : 2531
% 58.51/9.11 % BW rewrite match successes : 341
% 58.51/9.11 % Condensation attempts : 0
% 58.51/9.11 % Condensation successes : 0
% 58.51/9.11 % Termbank termtop insertions : 3478850
% 58.51/9.11 % Search garbage collected termcells : 1854
% 58.51/9.11
% 58.51/9.11 % -------------------------------------------------
% 58.51/9.11 % User time : 8.140 s
% 58.51/9.11 % System time : 0.180 s
% 58.51/9.11 % Total time : 8.320 s
% 58.51/9.11 % Maximum resident set size: 4892 pages
% 58.51/9.11
% 58.51/9.11 % -------------------------------------------------
% 58.51/9.11 % User time : 40.442 s
% 58.51/9.11 % System time : 1.102 s
% 58.51/9.11 % Total time : 41.544 s
% 58.51/9.11 % Maximum resident set size: 5120 pages
% 58.51/9.11 % E exiting
%------------------------------------------------------------------------------