%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG337-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 11:55:55 AM UTC 2026
% Result : Unsatisfiable 70.03s 10.92s
% Output : CNFRefutation 70.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 27
% Syntax : Number of clauses : 87 ( 53 unt; 0 nHn; 33 RR)
% Number of literals : 122 ( 74 equ; 43 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 131 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) != v_x____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_CHAINED_0_01,axiom,
c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
cnf(cls_Bit0__def_0,axiom,
c_Int_OBit0(X1) = c_HOL_Oplus__class_Oplus(X1,X1,tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Bit0__def_0) ).
cnf(cls_add__Bit1__Bit0_0,axiom,
c_HOL_Oplus__class_Oplus(c_Int_OBit1(X1),c_Int_OBit0(X2),tc_Int_Oint) = c_Int_OBit1(c_HOL_Oplus__class_Oplus(X1,X2,tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Bit1__Bit0_0) ).
cnf(cls_CHAINED_0,axiom,
c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_zadd__assoc_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_Int_Oint),X3,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_Int_Oint),tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zadd__assoc_0) ).
cnf(cls_add__Pls_0,axiom,
c_HOL_Oplus__class_Oplus(c_Int_OPls,X1,tc_Int_Oint) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Pls_0) ).
cnf(cls_diff__divide__distrib_0,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X2,X4,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).
cnf(cls_minus__diff__eq_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Ominus__class_Ominus(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
cnf(cls_class__semiring_Oadd__c_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
cnf(cls_comp__arith_I112_J_0,axiom,
( ~ class_Int_Onumber__ring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__arith_I112_J_0) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
cnf(cls_real__diff__def_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__diff__def_0) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
cnf(cls_class__semiring_Omul__0_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
cnf(cls_add__numeral__0_0,axiom,
( ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1),X2,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__numeral__0_0) ).
cnf(clsarity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
cnf(cls_equation__minus__iff_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
cnf(cls_class__semiring_Oadd__a_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
cnf(cls_diff__add__cancel_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X3,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
cnf(cls_real__average__minus__second_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__average__minus__second_0) ).
cnf(cls_right__minus_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).
cnf(cls_real__divide__def_0,axiom,
c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__divide__def_0) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
cnf(c_0_27,negated_conjecture,
c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) != v_x____,
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_28,axiom,
c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_CHAINED_0_01 ).
cnf(c_0_29,axiom,
c_Int_OBit0(X1) = c_HOL_Oplus__class_Oplus(X1,X1,tc_Int_Oint),
cls_Bit0__def_0 ).
cnf(c_0_30,axiom,
c_HOL_Oplus__class_Oplus(c_Int_OBit1(X1),c_Int_OBit0(X2),tc_Int_Oint) = c_Int_OBit1(c_HOL_Oplus__class_Oplus(X1,X2,tc_Int_Oint)),
cls_add__Bit1__Bit0_0 ).
cnf(c_0_31,axiom,
c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_CHAINED_0 ).
cnf(c_0_32,negated_conjecture,
c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) != v_x____,
c_0_27 ).
cnf(c_0_33,plain,
c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_29]),c_0_29]) ).
cnf(c_0_34,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_Int_Oint),X3,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,tc_Int_Oint),tc_Int_Oint),
cls_zadd__assoc_0 ).
cnf(c_0_35,plain,
c_HOL_Oplus__class_Oplus(c_Int_OBit1(X1),c_HOL_Oplus__class_Oplus(X2,X2,tc_Int_Oint),tc_Int_Oint) = c_Int_OBit1(c_HOL_Oplus__class_Oplus(X1,X2,tc_Int_Oint)),
inference(rw,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_36,axiom,
c_HOL_Oplus__class_Oplus(c_Int_OPls,X1,tc_Int_Oint) = X1,
cls_add__Pls_0 ).
cnf(c_0_37,plain,
c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_29]),c_0_29]),c_0_29]) ).
cnf(c_0_38,negated_conjecture,
c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) != v_x____,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_29]),c_0_29]),c_0_29]),c_0_29]) ).
cnf(c_0_39,plain,
c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_36]) ).
cnf(c_0_40,plain,
c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_34]),c_0_35]),c_0_36]) ).
cnf(c_0_41,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X2,X4,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_diff__divide__distrib_0]) ).
cnf(c_0_42,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Ominus__class_Ominus(X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_minus__diff__eq_0]) ).
cnf(c_0_43,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Oadd__c_0]) ).
cnf(c_0_44,plain,
( ~ class_Int_Onumber__ring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1) ),
inference(fof_simplification,[status(thm)],[cls_comp__arith_I112_J_0]) ).
cnf(c_0_45,negated_conjecture,
c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != v_x____,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_34]),c_0_35]),c_0_36]),c_0_39]),c_0_34]),c_0_35]),c_0_36]),c_0_40]) ).
cnf(c_0_46,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X2,X4,X1),c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1) ),
c_0_41 ).
cnf(c_0_47,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ofield ).
cnf(c_0_48,axiom,
c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_real__diff__def_0 ).
cnf(c_0_49,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Ominus__class_Ominus(X3,X2,X1) ),
c_0_42 ).
cnf(c_0_50,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add ).
cnf(c_0_51,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1) ),
c_0_43 ).
cnf(c_0_52,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_53,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Omul__0_0]) ).
cnf(c_0_54,plain,
( ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1),X2,X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_add__numeral__0_0]) ).
cnf(c_0_55,plain,
( ~ class_Int_Onumber__ring(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1) ),
c_0_44 ).
cnf(c_0_56,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Int_Onumber__ring ).
cnf(c_0_57,plain,
( ~ class_OrderedGroup_Ogroup__add(X1)
| X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_equation__minus__iff_1]) ).
cnf(c_0_58,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal) != v_x____,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]) ).
cnf(c_0_59,plain,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X3,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50])]) ).
cnf(c_0_60,plain,
c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X2,X1,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_61,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Oadd__a_0]) ).
cnf(c_0_62,plain,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X3,X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_diff__add__cancel_0]) ).
cnf(c_0_63,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_comm__monoid__add_Omult__commute_0]) ).
cnf(c_0_64,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_real__average__minus__second_0 ).
cnf(c_0_65,plain,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_right__minus_0]) ).
cnf(c_0_66,axiom,
c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_real__divide__def_0 ).
cnf(c_0_67,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
c_0_53 ).
cnf(c_0_68,plain,
( ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1),X2,X1) = X2 ),
c_0_54 ).
cnf(c_0_69,plain,
c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_70,plain,
( ~ class_OrderedGroup_Ogroup__add(X1)
| X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
c_0_57 ).
cnf(c_0_71,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add ).
cnf(c_0_72,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(v_x____,c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(v_x____,c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal) != v_x____,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59]),c_0_60]) ).
cnf(c_0_73,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) ),
c_0_61 ).
cnf(c_0_74,plain,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X3,X1) = X2 ),
c_0_62 ).
cnf(c_0_75,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1) ),
c_0_63 ).
cnf(c_0_76,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_29]),c_0_29]) ).
cnf(c_0_77,plain,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
c_0_65 ).
cnf(c_0_78,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_52])]) ).
cnf(c_0_79,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_68]),c_0_56])]),c_0_69]) ).
cnf(c_0_80,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = X1,
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_81,plain,
c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_70]),c_0_71])]) ).
cnf(c_0_82,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(v_x____,c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ominus__class_Ominus(v_x____,c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal) != v_x____,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_52])]) ).
cnf(c_0_83,plain,
( ~ class_OrderedGroup_Ogroup__add(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,X3),X3) = X2 ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_84,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X1,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_HOL_Oplus__class_Oplus(c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls),tc_Int_Oint),tc_RealDef_Oreal),tc_RealDef_Oreal) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_71])]),c_0_78]),c_0_79]),c_0_80]),c_0_81]) ).
cnf(c_0_85,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add ).
cnf(c_0_86,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]),c_0_85]),c_0_71])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG337-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 % Computer : n001.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Mon Sep 21 13:22:14 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.51 Running first-order theorem proving
% 0.17/0.51 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
% 70.03/10.92 % Version: 3.5.1
% 70.03/10.92 % Preprocessing class: FMLMSMSSSSSNFFN.
% 70.03/10.92 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 70.03/10.92 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 70.03/10.92 % Starting new_bool_3 with 300s (1) cores
% 70.03/10.92 % Starting new_bool_1 with 300s (1) cores
% 70.03/10.92 % Starting sh5l with 300s (1) cores
% 70.03/10.92 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with pid 3214289 completed with status 0
% 70.03/10.92 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c
% 70.03/10.92 % Preprocessing class: FMLMSMSSSSSNFFN.
% 70.03/10.92 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 70.03/10.92 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 70.03/10.92 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 70.03/10.92 % SinE strategy is gf600_h_gu_R05_F100_L20000
% 70.03/10.92 % Search class: FGHSM-SSLM31-DFFFFFNN
% 70.03/10.92 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 70.03/10.92 % Starting SubtermCWHack with 136s (1) cores
% 70.03/10.92 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 70.03/10.92 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S2S with 136s (1) cores
% 70.03/10.92 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 136s (1) cores
% 70.03/10.92 % Starting G-E--_208_B07AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 70.03/10.92 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with pid 3214294 completed with status 0
% 70.03/10.92 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c
% 70.03/10.92 % Preprocessing class: FMLMSMSSSSSNFFN.
% 70.03/10.92 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 70.03/10.92 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 70.03/10.92 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 70.03/10.92 % SinE strategy is gf600_h_gu_R05_F100_L20000
% 70.03/10.92 % Search class: FGHSM-SSLM31-DFFFFFNN
% 70.03/10.92 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 70.03/10.92 % Starting SubtermCWHack with 136s (1) cores
% 70.03/10.92 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 70.03/10.92 % Preprocessing time : 0.028 s
% 70.03/10.92
% 70.03/10.92 % Proof found!
% 70.03/10.92 % SZS status Unsatisfiable
% 70.03/10.92 % SZS output start CNFRefutation
% See solution above
% 70.03/10.92 % Parsed axioms : 1417
% 70.03/10.92 % Removed by relevancy pruning/SinE : 169
% 70.03/10.92 % Initial clauses : 1248
% 70.03/10.92 % Removed in clause preprocessing : 2
% 70.03/10.92 % Initial clauses in saturation : 1246
% 70.03/10.92 % Processed clauses : 32680
% 70.03/10.92 % ...of these trivial : 772
% 70.03/10.92 % ...subsumed : 26813
% 70.03/10.92 % ...remaining for further processing : 5095
% 70.03/10.92 % Other redundant clauses eliminated : 82
% 70.03/10.92 % Clauses deleted for lack of memory : 0
% 70.03/10.92 % Backward-subsumed : 254
% 70.03/10.92 % Backward-rewritten : 396
% 70.03/10.92 % Generated clauses : 251087
% 70.03/10.92 % ...of the previous two non-redundant : 233772
% 70.03/10.92 % ...aggressively subsumed : 0
% 70.03/10.92 % Contextual simplify-reflections : 4
% 70.03/10.92 % Paramodulations : 250896
% 70.03/10.92 % Factorizations : 8
% 70.03/10.92 % NegExts : 0
% 70.03/10.92 % Equation resolutions : 183
% 70.03/10.92 % Disequality decompositions : 0
% 70.03/10.92 % Total rewrite steps : 311920
% 70.03/10.92 % ...of those cached : 297684
% 70.03/10.92 % Propositional unsat checks : 0
% 70.03/10.92 % Propositional check models : 0
% 70.03/10.92 % Propositional check unsatisfiable : 0
% 70.03/10.92 % Propositional clauses : 0
% 70.03/10.92 % Propositional clauses after purity: 0
% 70.03/10.92 % Propositional unsat core size : 0
% 70.03/10.92 % Propositional preprocessing time : 0.000
% 70.03/10.92 % Propositional encoding time : 0.000
% 70.03/10.92 % Propositional solver time : 0.000
% 70.03/10.92 % Success case prop preproc time : 0.000
% 70.03/10.92 % Success case prop encoding time : 0.000
% 70.03/10.92 % Success case prop solver time : 0.000
% 70.03/10.92 % Current number of processed clauses : 4445
% 70.03/10.92 % Positive orientable unit clauses : 668
% 70.03/10.92 % Positive unorientable unit clauses: 39
% 70.03/10.92 % Negative unit clauses : 1625
% 70.03/10.92 % Non-unit-clauses : 2113
% 70.03/10.92 % Current number of unprocessed clauses: 201657
% 70.03/10.92 % ...number of literals in the above : 455696
% 70.03/10.92 % Current number of archived formulas : 0
% 70.03/10.92 % Current number of archived clauses : 652
% 70.03/10.92 % Clause-clause subsumption calls (NU) : 1610162
% 70.03/10.92 % Rec. Clause-clause subsumption calls : 563697
% 70.03/10.92 % Non-unit clause-clause subsumptions : 5384
% 70.03/10.92 % Unit Clause-clause subsumption calls : 177681
% 70.03/10.92 % Rewrite failures with RHS unbound : 0
% 70.03/10.92 % BW rewrite match attempts : 11679
% 70.03/10.92 % BW rewrite match successes : 1303
% 70.03/10.92 % Condensation attempts : 0
% 70.03/10.92 % Condensation successes : 0
% 70.03/10.92 % Termbank termtop insertions : 6065772
% 70.03/10.92 % Search garbage collected termcells : 3080
% 70.03/10.92
% 70.03/10.92 % -------------------------------------------------
% 70.03/10.92 % User time : 9.766 s
% 70.03/10.92 % System time : 0.301 s
% 70.03/10.92 % Total time : 10.067 s
% 70.03/10.92 % Maximum resident set size: 6444 pages
% 70.03/10.92
% 70.03/10.92 % -------------------------------------------------
% 70.03/10.92 % User time : 48.235 s
% 70.03/10.92 % System time : 1.458 s
% 70.03/10.92 % Total time : 49.694 s
% 70.03/10.92 % Maximum resident set size: 5888 pages
% 70.03/10.92 % E exiting
%------------------------------------------------------------------------------