TSTP Solution File: SWW469+5 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWW469+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n001.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 11:07:19 EDT 2023

% Result   : Theorem 4.70s 2.20s
% Output   : CNFRefutation 5.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   40
% Syntax   : Number of formulae    :   44 (   5 unt;  37 typ;   0 def)
%            Number of atoms       :    9 (   4 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    7 (   5   ~;   1   |;   0   &)
%                                         (   1 <=>;   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  :   67 (  28   >;  39   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   34 (  34 usr;   9 con; 0-7 aty)
%            Number of variables   :    5 (;   3   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ hBOOL > enum > cl_HOL_Oequal > hAPP > type_definition > ti > sum_sum > node > fun > #nlpp > undefined > member > induct_equal > hoare_509422987triple > hoare_244953527triple > hoare_2037801986triple > hoare_1580379338ep_set > fequal > equal_equal > collect > state > induct_true > induct_false > hoare_1883395792gleton > com > bool > #skF_6 > #skF_9 > #skF_10 > #skF_5 > #skF_2 > #skF_8 > #skF_1 > #skF_11 > #skF_7 > #skF_3 > #skF_12 > #skF_4

%Foreground sorts:

%Background operators:

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

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

tff(hoare_1580379338ep_set,type,
    hoare_1580379338ep_set: $i > $i ).

tff('#skF_6',type,
    '#skF_6': ( $i * $i ) > $i ).

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

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

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

tff('#skF_9',type,
    '#skF_9': ( $i * $i * $i * $i * $i * $i * $i ) > $i ).

tff(hoare_1883395792gleton,type,
    hoare_1883395792gleton: $i ).

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

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

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

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

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

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

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

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

tff('#skF_10',type,
    '#skF_10': ( $i * $i * $i * $i * $i * $i * $i ) > $i ).

tff('#skF_5',type,
    '#skF_5': ( $i * $i * $i ) > $i ).

tff('#skF_2',type,
    '#skF_2': $i ).

tff('#skF_8',type,
    '#skF_8': ( $i * $i * $i * $i * $i * $i ) > $i ).

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

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

tff('#skF_1',type,
    '#skF_1': $i ).

tff('#skF_11',type,
    '#skF_11': ( $i * $i * $i * $i ) > $i ).

tff('#skF_7',type,
    '#skF_7': ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(hoare_2037801986triple,type,
    hoare_2037801986triple: $i > $i ).

tff(hoare_244953527triple,type,
    hoare_244953527triple: $i > $i ).

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

tff('#skF_3',type,
    '#skF_3': ( $i * $i * $i ) > $i ).

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

tff(hoare_509422987triple,type,
    hoare_509422987triple: $i > $i ).

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

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

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

tff('#skF_12',type,
    '#skF_12': $i ).

tff('#skF_4',type,
    '#skF_4': ( $i * $i ) > $i ).

tff(f_270,hypothesis,
    hBOOL(hoare_1883395792gleton),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

tff(f_275,negated_conjecture,
    ~ ! [T] :
        ~ ! [S] : ( ti(state,S) = ti(state,T) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

tff(f_69,axiom,
    ( hBOOL(hoare_1883395792gleton)
  <=> ? [S,T] : ( ti(state,S) != ti(state,T) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_state__not__singleton__def) ).

tff(c_154,plain,
    hBOOL(hoare_1883395792gleton),
    inference(cnfTransformation,[status(thm)],[f_270]) ).

tff(c_156,plain,
    ! [S_160] : ( ti(state,S_160) = ti(state,'#skF_12') ),
    inference(cnfTransformation,[status(thm)],[f_275]) ).

tff(c_40,plain,
    ( ( ti(state,'#skF_2') != ti(state,'#skF_1') )
    | ~ hBOOL(hoare_1883395792gleton) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_167,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_154,c_156,c_156,c_40]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SWW469+5 : TPTP v8.1.2. Released v5.3.0.
% 0.12/0.13  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35  % Computer : n001.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 19:50:25 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 4.70/2.20  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.70/2.21  
% 4.70/2.21  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.01/2.23  
% 5.01/2.23  Inference rules
% 5.01/2.23  ----------------------
% 5.01/2.23  #Ref     : 0
% 5.01/2.23  #Sup     : 0
% 5.01/2.23  #Fact    : 0
% 5.01/2.23  #Define  : 0
% 5.01/2.23  #Split   : 0
% 5.01/2.23  #Chain   : 0
% 5.01/2.23  #Close   : 0
% 5.01/2.23  
% 5.01/2.23  Ordering : KBO
% 5.01/2.23  
% 5.01/2.23  Simplification rules
% 5.01/2.23  ----------------------
% 5.01/2.23  #Subsume      : 73
% 5.01/2.23  #Demod        : 13
% 5.01/2.23  #Tautology    : 3
% 5.01/2.23  #SimpNegUnit  : 0
% 5.01/2.23  #BackRed      : 0
% 5.01/2.23  
% 5.01/2.23  #Partial instantiations: 0
% 5.01/2.23  #Strategies tried      : 1
% 5.01/2.23  
% 5.01/2.23  Timing (in seconds)
% 5.01/2.23  ----------------------
% 5.01/2.24  Preprocessing        : 0.97
% 5.01/2.24  Parsing              : 0.49
% 5.01/2.24  CNF conversion       : 0.05
% 5.01/2.24  Main loop            : 0.18
% 5.01/2.24  Inferencing          : 0.00
% 5.01/2.24  Reduction            : 0.11
% 5.01/2.24  Demodulation         : 0.09
% 5.01/2.24  BG Simplification    : 0.04
% 5.01/2.24  Subsumption          : 0.05
% 5.01/2.24  Abstraction          : 0.02
% 5.01/2.24  MUC search           : 0.00
% 5.01/2.24  Cooper               : 0.00
% 5.01/2.24  Total                : 1.21
% 5.01/2.24  Index Insertion      : 0.00
% 5.01/2.24  Index Deletion       : 0.00
% 5.01/2.24  Index Matching       : 0.00
% 5.01/2.24  BG Taut test         : 0.00
%------------------------------------------------------------------------------