TSTP Solution File: ALG350-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ALG350-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n029.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 : Tue Aug 22 10:32:35 EDT 2023

% Result   : Unsatisfiable 7.89s 2.84s
% Output   : CNFRefutation 8.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   61
% Syntax   : Number of formulae    :   68 (   7 unt;  57 typ;   0 def)
%            Number of atoms       :   15 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   11 (   7   ~;   4   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   72 (  50   >;  22   *;   0   +;   0  <<)
%            Number of predicates  :   35 (  34 usr;   1 prp; 0-3 aty)
%            Number of functors    :   23 (  23 usr;   7 con; 0-3 aty)
%            Number of variables   :    6 (;   6   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_lessequals > c_HOL_Oord__class_Oless > hBOOL > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Oidom > class_Ring__and__Field_Ocomm__semiring__1 > class_RealVector_Oreal__normed__vector > class_Orderings_Otop > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_Orderings_Obot > class_OrderedGroup_Opordered__cancel__ab__semigroup__add > class_OrderedGroup_Opordered__ab__semigroup__add__imp__le > class_OrderedGroup_Opordered__ab__semigroup__add > class_OrderedGroup_Opordered__ab__group__add__abs > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Olordered__ab__group__add__meet > class_OrderedGroup_Olordered__ab__group__add__join > class_OrderedGroup_Olordered__ab__group__add__abs > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ogroup__add > class_OrderedGroup_Ocomm__monoid__add > class_OrderedGroup_Ocancel__semigroup__add > class_OrderedGroup_Ocancel__ab__semigroup__add > class_OrderedGroup_Oab__semigroup__add > class_OrderedGroup_Oab__group__add > class_Lattices_Oupper__semilattice > class_Lattices_Olower__semilattice > class_Lattices_Olattice > class_Lattices_Odistrib__lattice > class_Lattices_Obounded__lattice > class_Lattices_Oboolean__algebra > class_Int_Onumber__ring > c_Orderings_Oord__class_Omin > c_Orderings_Oord__class_Omax > c_Lattices_Oupper__semilattice__class_Osup > c_Lattices_Olower__semilattice__class_Oinf > c_HOL_Oplus__class_Oplus > c_HOL_Ominus__class_Ominus > hAPP > c_Transcendental_Oexp > c_RealVector_Onorm__class_Onorm > c_HOL_Ouminus__class_Ouminus > c_HOL_Oabs__class_Oabs > c_COMBI > #nlpp > c_Transcendental_Oarctan > c_Orderings_Otop__class_Otop > c_Orderings_Obot__class_Obot > c_NthRoot_Osqrt > v_xa > v_x____ > v_Y____ > v_P > v_L____ > tc_RealDef_Oreal > t_a

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(v_L____,type,
    v_L____: $i ).

tff(class_Orderings_Olinorder,type,
    class_Orderings_Olinorder: $i > $o ).

tff(class_OrderedGroup_Opordered__ab__semigroup__add,type,
    class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).

tff(class_Int_Onumber__ring,type,
    class_Int_Onumber__ring: $i > $o ).

tff(c_HOL_Oord__class_Oless,type,
    c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).

tff(c_Orderings_Otop__class_Otop,type,
    c_Orderings_Otop__class_Otop: $i > $i ).

tff(v_Y____,type,
    v_Y____: $i ).

tff(class_OrderedGroup_Ocancel__ab__semigroup__add,type,
    class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).

tff(v_xa,type,
    v_xa: $i ).

tff(v_P,type,
    v_P: $i ).

tff(v_x____,type,
    v_x____: $i ).

tff(class_Lattices_Obounded__lattice,type,
    class_Lattices_Obounded__lattice: $i > $o ).

tff(class_OrderedGroup_Opordered__ab__group__add__abs,type,
    class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).

tff(class_Lattices_Olattice,type,
    class_Lattices_Olattice: $i > $o ).

tff(class_OrderedGroup_Oab__semigroup__add,type,
    class_OrderedGroup_Oab__semigroup__add: $i > $o ).

tff(t_a,type,
    t_a: $i ).

tff(class_OrderedGroup_Olordered__ab__group__add__meet,type,
    class_OrderedGroup_Olordered__ab__group__add__meet: $i > $o ).

tff(class_OrderedGroup_Olordered__ab__group__add,type,
    class_OrderedGroup_Olordered__ab__group__add: $i > $o ).

tff(class_Orderings_Oorder,type,
    class_Orderings_Oorder: $i > $o ).

tff(class_Orderings_Opreorder,type,
    class_Orderings_Opreorder: $i > $o ).

tff(class_OrderedGroup_Olordered__ab__group__add__join,type,
    class_OrderedGroup_Olordered__ab__group__add__join: $i > $o ).

tff(tc_RealDef_Oreal,type,
    tc_RealDef_Oreal: $i ).

tff(c_Orderings_Obot__class_Obot,type,
    c_Orderings_Obot__class_Obot: $i > $i ).

tff(c_Lattices_Oupper__semilattice__class_Osup,type,
    c_Lattices_Oupper__semilattice__class_Osup: ( $i * $i * $i ) > $i ).

tff(class_Lattices_Oboolean__algebra,type,
    class_Lattices_Oboolean__algebra: $i > $o ).

tff(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).

tff(class_Orderings_Otop,type,
    class_Orderings_Otop: $i > $o ).

tff(c_Orderings_Oord__class_Omin,type,
    c_Orderings_Oord__class_Omin: ( $i * $i * $i ) > $i ).

tff(class_Ring__and__Field_Oordered__idom,type,
    class_Ring__and__Field_Oordered__idom: $i > $o ).

tff(class_OrderedGroup_Ocancel__semigroup__add,type,
    class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).

tff(c_lessequals,type,
    c_lessequals: ( $i * $i * $i ) > $o ).

tff(class_OrderedGroup_Opordered__cancel__ab__semigroup__add,type,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).

tff(class_OrderedGroup_Ocomm__monoid__add,type,
    class_OrderedGroup_Ocomm__monoid__add: $i > $o ).

tff(c_COMBI,type,
    c_COMBI: ( $i * $i ) > $i ).

tff(c_Orderings_Oord__class_Omax,type,
    c_Orderings_Oord__class_Omax: ( $i * $i * $i ) > $i ).

tff(c_NthRoot_Osqrt,type,
    c_NthRoot_Osqrt: $i > $i ).

tff(class_Ring__and__Field_Oidom,type,
    class_Ring__and__Field_Oidom: $i > $o ).

tff(class_RealVector_Oreal__normed__vector,type,
    class_RealVector_Oreal__normed__vector: $i > $o ).

tff(c_HOL_Oplus__class_Oplus,type,
    c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).

tff(class_Lattices_Oupper__semilattice,type,
    class_Lattices_Oupper__semilattice: $i > $o ).

tff(c_Transcendental_Oexp,type,
    c_Transcendental_Oexp: ( $i * $i ) > $i ).

tff(class_OrderedGroup_Oab__group__add,type,
    class_OrderedGroup_Oab__group__add: $i > $o ).

tff(c_RealVector_Onorm__class_Onorm,type,
    c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).

tff(hAPP,type,
    hAPP: ( $i * $i ) > $i ).

tff(class_OrderedGroup_Olordered__ab__group__add__abs,type,
    class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).

tff(class_Lattices_Odistrib__lattice,type,
    class_Lattices_Odistrib__lattice: $i > $o ).

tff(c_HOL_Ouminus__class_Ouminus,type,
    c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).

tff(class_OrderedGroup_Ogroup__add,type,
    class_OrderedGroup_Ogroup__add: $i > $o ).

tff(hBOOL,type,
    hBOOL: $i > $o ).

tff(c_HOL_Oabs__class_Oabs,type,
    c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).

tff(class_Lattices_Olower__semilattice,type,
    class_Lattices_Olower__semilattice: $i > $o ).

tff(class_Ring__and__Field_Ocomm__semiring__1,type,
    class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).

tff(c_HOL_Ominus__class_Ominus,type,
    c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).

tff(class_Orderings_Obot,type,
    class_Orderings_Obot: $i > $o ).

tff(class_OrderedGroup_Opordered__ab__group__add,type,
    class_OrderedGroup_Opordered__ab__group__add: $i > $o ).

tff(c_Transcendental_Oarctan,type,
    c_Transcendental_Oarctan: $i > $i ).

tff(c_Lattices_Olower__semilattice__class_Oinf,type,
    c_Lattices_Olower__semilattice__class_Oinf: ( $i * $i * $i ) > $i ).

tff(f_2444,axiom,
    hBOOL(hAPP(v_P,v_xa)),
    file(unknown,unknown) ).

tff(f_2443,axiom,
    ! [V_x] :
      ( c_HOL_Oord__class_Oless(V_x,v_Y____,tc_RealDef_Oreal)
      | ~ hBOOL(hAPP(v_P,V_x)) ),
    file(unknown,unknown) ).

tff(f_2289,axiom,
    ! [V_x,V_y] :
      ( c_lessequals(V_x,V_y,tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ),
    file(unknown,unknown) ).

tff(f_2446,axiom,
    ~ c_lessequals(v_xa,v_Y____,tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(c_704,plain,
    hBOOL(hAPP(v_P,v_xa)),
    inference(cnfTransformation,[status(thm)],[f_2444]) ).

tff(c_933,plain,
    ! [V_x_1182] :
      ( ~ hBOOL(hAPP(v_P,V_x_1182))
      | c_HOL_Oord__class_Oless(V_x_1182,v_Y____,tc_RealDef_Oreal) ),
    inference(cnfTransformation,[status(thm)],[f_2443]) ).

tff(c_942,plain,
    c_HOL_Oord__class_Oless(v_xa,v_Y____,tc_RealDef_Oreal),
    inference(resolution,[status(thm)],[c_704,c_933]) ).

tff(c_1058,plain,
    ! [V_x_1194,V_y_1195] :
      ( ~ c_HOL_Oord__class_Oless(V_x_1194,V_y_1195,tc_RealDef_Oreal)
      | c_lessequals(V_x_1194,V_y_1195,tc_RealDef_Oreal) ),
    inference(cnfTransformation,[status(thm)],[f_2289]) ).

tff(c_706,plain,
    ~ c_lessequals(v_xa,v_Y____,tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_2446]) ).

tff(c_1061,plain,
    ~ c_HOL_Oord__class_Oless(v_xa,v_Y____,tc_RealDef_Oreal),
    inference(resolution,[status(thm)],[c_1058,c_706]) ).

tff(c_1065,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_942,c_1061]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ALG350-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35  % Computer : n029.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 20:41:37 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 7.89/2.84  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.89/2.84  
% 7.89/2.84  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.12/2.87  
% 8.12/2.87  Inference rules
% 8.12/2.87  ----------------------
% 8.12/2.87  #Ref     : 1
% 8.12/2.87  #Sup     : 60
% 8.12/2.87  #Fact    : 2
% 8.12/2.87  #Define  : 0
% 8.12/2.87  #Split   : 0
% 8.12/2.87  #Chain   : 0
% 8.12/2.87  #Close   : 0
% 8.12/2.87  
% 8.12/2.87  Ordering : KBO
% 8.12/2.87  
% 8.12/2.87  Simplification rules
% 8.12/2.87  ----------------------
% 8.12/2.87  #Subsume      : 57
% 8.12/2.87  #Demod        : 8
% 8.12/2.87  #Tautology    : 53
% 8.12/2.87  #SimpNegUnit  : 0
% 8.12/2.87  #BackRed      : 0
% 8.12/2.87  
% 8.12/2.87  #Partial instantiations: 0
% 8.12/2.87  #Strategies tried      : 1
% 8.12/2.87  
% 8.12/2.87  Timing (in seconds)
% 8.12/2.87  ----------------------
% 8.12/2.87  Preprocessing        : 1.20
% 8.12/2.87  Parsing              : 0.66
% 8.12/2.87  CNF conversion       : 0.11
% 8.12/2.87  Main loop            : 0.63
% 8.12/2.87  Inferencing          : 0.13
% 8.12/2.87  Reduction            : 0.24
% 8.12/2.87  Demodulation         : 0.15
% 8.12/2.87  BG Simplification    : 0.11
% 8.12/2.87  Subsumption          : 0.16
% 8.12/2.87  Abstraction          : 0.02
% 8.12/2.87  MUC search           : 0.00
% 8.12/2.87  Cooper               : 0.00
% 8.12/2.87  Total                : 1.87
% 8.12/2.87  Index Insertion      : 0.00
% 8.12/2.87  Index Deletion       : 0.00
% 8.12/2.87  Index Matching       : 0.00
% 8.12/2.87  BG Taut test         : 0.00
%------------------------------------------------------------------------------