TSTP Solution File: SWV627-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV627-1 : 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 : n023.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 : Thu Aug 31 21:47:34 EDT 2023
% Result : Unsatisfiable 0.47s 0.65s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 87
% Syntax : Number of formulae : 107 ( 22 unt; 73 typ; 0 def)
% Number of atoms : 48 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 17 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 87 ( 68 >; 19 *; 0 +; 0 <<)
% Number of predicates : 57 ( 55 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 31 ( 8 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
tff(decl_23,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_24,type,
c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_25,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(decl_26,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_27,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_28,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_29,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
tff(decl_30,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(decl_31,type,
class_Int_Onumber: $i > $o ).
tff(decl_32,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_33,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(decl_34,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_35,type,
c_Ring__and__Field_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(decl_36,type,
class_Ring__and__Field_Odvd: $i > $o ).
tff(decl_37,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_38,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_39,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_40,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_41,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
tff(decl_43,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(decl_44,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_45,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_46,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_47,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(decl_48,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_49,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(decl_50,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_51,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
tc_nat: $i ).
tff(decl_53,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(decl_54,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
tff(decl_55,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(decl_56,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
tff(decl_57,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_58,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
tff(decl_59,type,
class_Ring__and__Field_Oabs__if: $i > $o ).
tff(decl_60,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_61,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_62,type,
class_Ring__and__Field_Opordered__ring__abs: $i > $o ).
tff(decl_63,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_64,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
tff(decl_65,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
tff(decl_66,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(decl_67,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
tff(decl_68,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(decl_69,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_70,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_71,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_72,type,
class_SEQ_Obanach: $i > $o ).
tff(decl_73,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_74,type,
c_Transcendental_Oexp: ( $i * $i ) > $i ).
tff(decl_75,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(decl_76,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(decl_77,type,
v_k: $i ).
tff(decl_78,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_79,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(decl_80,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
tff(decl_81,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_82,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(decl_83,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(decl_84,type,
class_Ring__and__Field_Oring__1: $i > $o ).
tff(decl_85,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_86,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(decl_87,type,
class_Power_Opower: $i > $o ).
tff(decl_88,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_89,type,
v_n: $i ).
tff(decl_90,type,
tc_Complex_Ocomplex: $i ).
tff(decl_91,type,
c_Complex_Oexpi: $i > $i ).
tff(decl_92,type,
c_FFT__Mirabelle_Oroot: $i > $i ).
tff(decl_93,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_94,type,
tc_Int_Oint: $i ).
cnf(cls_conjecture_0,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_inverse__eq__divide_0,axiom,
( c_HOL_Oinverse__class_Oinverse(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
cnf(cls_inverse__1_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__1_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
cnf(cls_power__one_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
cnf(cls_right__minus__eq_1,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
cnf(cls_divide_Ozero_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
cnf(cls_nonzero__power__inverse_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X2,X1),X3,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).
cnf(cls_root__unity_0,axiom,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),X1,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__unity_0) ).
cnf(cls_root__nonzero_0,axiom,
c_FFT__Mirabelle_Oroot(X1) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__nonzero_0) ).
cnf(c_0_14,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
cls_conjecture_0 ).
cnf(c_0_15,axiom,
( c_HOL_Oinverse__class_Oinverse(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_inverse__eq__divide_0 ).
cnf(c_0_16,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ofield ).
cnf(c_0_17,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
cls_inverse__1_0 ).
cnf(c_0_18,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring ).
cnf(c_0_19,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_power__one_0 ).
cnf(c_0_20,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult ).
cnf(c_0_21,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_right__minus__eq_1 ).
cnf(c_0_22,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add ).
cnf(c_0_23,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
cls_divide_Ozero_0 ).
cnf(c_0_24,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field ).
cnf(c_0_25,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_26,axiom,
( c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X2,X1),X3,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
cls_nonzero__power__inverse_0 ).
cnf(c_0_27,axiom,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),X1,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
cls_root__unity_0 ).
cnf(c_0_28,plain,
c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_29,plain,
c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_30,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_31,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_32,axiom,
c_FFT__Mirabelle_Oroot(X1) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
cls_root__nonzero_0 ).
cnf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[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(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_18])]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWV627-1 : TPTP v8.1.2. Released v4.1.0.
% 0.03/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.31 % Computer : n023.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue Aug 29 08:01:25 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.15/0.52 start to proof: theBenchmark
% 0.47/0.65 % Version : CSE_E---1.5
% 0.47/0.65 % Problem : theBenchmark.p
% 0.47/0.65 % Proof found
% 0.47/0.65 % SZS status Theorem for theBenchmark.p
% 0.47/0.65 % SZS output start Proof
% See solution above
% 0.47/0.65 % Total time : 0.102000 s
% 0.47/0.65 % SZS output end Proof
% 0.47/0.65 % Total time : 0.121000 s
%------------------------------------------------------------------------------