TSTP Solution File: ALG374-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ALG374-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 16:07:31 EDT 2023
% Result : Unsatisfiable 1.02s 1.12s
% Output : CNFRefutation 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 86
% Syntax : Number of formulae : 102 ( 12 unt; 75 typ; 0 def)
% Number of atoms : 46 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 23 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 103 ( 68 >; 35 *; 0 +; 0 <<)
% Number of predicates : 46 ( 44 usr; 1 prp; 0-3 aty)
% Number of functors : 31 ( 31 usr; 7 con; 0-4 aty)
% Number of variables : 25 ( 2 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_23,type,
c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).
tff(decl_24,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(decl_25,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_26,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_27,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_29,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_30,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
tff(decl_31,type,
c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_32,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_33,type,
tc_nat: $i ).
tff(decl_34,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_35,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_36,type,
tc_RealDef_Oreal: $i ).
tff(decl_37,type,
c_RealDef_Oreal: ( $i * $i ) > $i ).
tff(decl_38,type,
c_Suc: $i > $i ).
tff(decl_39,type,
c_RComplete_Onatfloor: $i > $i ).
tff(decl_40,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_41,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_43,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(decl_44,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_45,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
tff(decl_46,type,
class_Ring__and__Field_Oabs__if: $i > $o ).
tff(decl_47,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(decl_48,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(decl_51,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_52,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_53,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_54,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(decl_55,type,
class_Power_Opower: $i > $o ).
tff(decl_56,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
tff(decl_57,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(decl_58,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1: ( $i * $i ) > $i ).
tff(decl_59,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_60,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_61,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_62,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_63,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_64,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_65,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_66,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_67,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_68,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(decl_69,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(decl_70,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
tff(decl_71,type,
v_r: $i ).
tff(decl_72,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(decl_73,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(decl_74,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_75,type,
tc_Complex_Ocomplex: $i ).
tff(decl_76,type,
v_p: $i ).
tff(decl_77,type,
v_sko__unknown__thm__rZ3__1: ( $i * $i ) > $i ).
tff(decl_78,type,
c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).
tff(decl_79,type,
v_sko__local__Xmth1__2: ( $i * $i ) > $i ).
tff(decl_80,type,
v_sko__local__Xmth1__1: ( $i * $i ) > $i ).
tff(decl_81,type,
v_sko__local__Xs__2: ( $i * $i * $i ) > $i ).
tff(decl_82,type,
v_sko__local__Xs__1: ( $i * $i * $i ) > $i ).
tff(decl_83,type,
v_s____: $i ).
tff(decl_84,type,
v_sko__local__Xmth2__1: ( $i * $i ) > $i ).
tff(decl_85,type,
v_sko__local__Xs1__1: ( $i * $i * $i ) > $i ).
tff(decl_86,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_87,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_88,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_89,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(decl_90,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_91,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(decl_92,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_93,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_94,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(decl_95,type,
v_n____: $i ).
tff(decl_96,type,
v_sko__CHAINED__1: ( $i * $i * $i * $i ) > $i ).
cnf(cls_equation__minus__iff_1,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
cnf(cls_conjecture_0,negated_conjecture,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_n____),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_CHAINED_2,axiom,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_n____,v_p,v_r,v_s____),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_n____),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_n____),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_2) ).
cnf(cls_CHAINED_1,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_sko__CHAINED__1(v_n____,v_p,v_r,v_s____),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_n____),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_1) ).
cnf(cls_real__0__less__add__iff_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__0__less__add__iff_0) ).
cnf(cls_minus__add__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
cnf(cls_zero__less__divide__1__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_1) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) ).
cnf(cls_real__of__nat__Suc__gt__zero_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(X1),tc_nat),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__of__nat__Suc__gt__zero_0) ).
cnf(c_0_11,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_equation__minus__iff_1 ).
cnf(c_0_12,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add ).
cnf(c_0_13,negated_conjecture,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_n____),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
cls_conjecture_0 ).
cnf(c_0_14,axiom,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_sko__CHAINED__1(v_n____,v_p,v_r,v_s____),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_n____),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_n____),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_CHAINED_2 ).
cnf(c_0_15,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_sko__CHAINED__1(v_n____,v_p,v_r,v_s____),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_n____),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_CHAINED_1 ).
cnf(c_0_16,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_real__0__less__add__iff_0 ).
cnf(c_0_17,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__add__cancel_0 ).
cnf(c_0_18,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_11,c_0_12]) ).
cnf(c_0_19,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_n____),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_20,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_12])]),c_0_18]) ).
cnf(c_0_21,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_n____),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__less__divide__1__iff_1 ).
cnf(c_0_23,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero ).
cnf(c_0_24,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field ).
cnf(c_0_25,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(X1),tc_nat),tc_RealDef_Oreal),
cls_real__of__nat__Suc__gt__zero_0 ).
cnf(c_0_26,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_21,c_0_22]),c_0_23]),c_0_24]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG374-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 05:17:46 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 1.02/1.12 % Version : CSE_E---1.5
% 1.02/1.12 % Problem : theBenchmark.p
% 1.02/1.12 % Proof found
% 1.02/1.12 % SZS status Theorem for theBenchmark.p
% 1.02/1.12 % SZS output start Proof
% See solution above
% 1.02/1.12 % Total time : 0.522000 s
% 1.02/1.12 % SZS output end Proof
% 1.02/1.12 % Total time : 0.540000 s
%------------------------------------------------------------------------------